Abstract

Existing for almost four decades, liquid crystal on Silicon (LCOS) technology is rapidly growing into photonic applications. We review the basics of the technology, from the wafer to the driving solutions, the progress over the last decade and the future outlook. Furthermore we review the most exciting industrial and scientific applications of the LCOS technology.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The basis of the LCOS technology was created in the 1970s by engineers of Hughes Aircraft corporation and further developed in cooperation with JVC [1–4]. In the late 1990s and early 2000s the development of LCOS technology was driven purely by the success of LCOS in cinema projectors and rear projection TVs. The market-related attention to other very different applications of LCOS technology began to rise later.

Number of LCOS-related technology reviews arised in last two decades. The review articles and books on display and microdisplay technology, might often have a chapter on LCOS technology. The “Introduction to microdisplays” [5] describes many relevant topics. The large and comprehensive Handbook of visual display technology [6] comprises a chapter on micro display technologies, including LCOS (Vol.4, Section X). Zhang et al. [7] provides a thorough technological insight specifically on the phase-only LCOS devices. Lazarev et al. [8] reviews both the LCOS technology and the broad spectrum of applications. The chapter 18, written by Frisken et al. in the Vol. VIA of the monumental compendium on optical fiber communication [9] is providing the technology basics, including analysis of the parameters of the phase-only LCOS devices, specific for the telecommunication applications and a survey of the telecommunication-related applications of those devices.

There is also a number of reviews for specific application fields. So Maurer et al. [10] is giving an extensive review of microscopic applications of LCOS. Marom et al. [11] is providing a detailed survey and analysis of ROADM architectures, largely based on phase-only LCOS devices. Huang et al. [12] is giving an LCOS technology overview with the focus on fringing field (cross talk) effects and applications in AR/VR. Hasegawa and Hayasaki published a review about LCOS-based femtosecond laser material processing [13]. More references are given in section 3.

In this work we aim to provide an extended overview of the LCOS phase-only technology and selected key non-display application topics. The AR/VR and/or holographic display topics although very exciting are left out of the scope of this review.

2. LCOS technology

The LCOS technology comprises generally the LCOS panel (“imager” or “microdisplay” in classical display applications terminology) and the way to address or to drive the panel, implemented on the control unit. The LCOS panel is effectively the LCOS cell, packaged onto the substrate with an appropriate electrical connection interface.

The LCOS cell is a sandwich-like structure, built largely on three basis components: LCOS backplane, liquid crystal mixture (LC) and cover glass. Both the LCOS backplane and the cover glass have number of additional layers, which will be described further. The simplified structure is depicted at Fig. 1.

 figure: Fig. 1

Fig. 1 LCOS cell and its structure: main components.

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We will go through these components and analyze them in more details below. We will begin with the basis of any LCOS device, the backplane. The LCOS backplane is a term describing the CMOS circuit with reflective pixel electrodes. The circuit is providing pixel logic and addressing of the array. Thus it is performing both the electrical and the optical functions.

2.1. Electrical function of the pixel and the wafer

Every pixel on the array should provide the electrical potential in the way, that the electrical field will be applied onto liquid crystal molecules between the pixel electrode and the transparent (common-, also called counter-) electrode on the inner side of the cover glass. Ideally this should be an analog voltage, whereas one applies the individual desired voltage to each pixel of the pixel array simultaneously.

2.1.1. Pixel architectures

The simplest pixel architecture is based on the DRAM-type (dynamic random access memory) cell, containing only one transistor (switch) and the capacitor (storage). Figure 2 is showing this case (bold lines), additionally it is illustrating parasitic capacitances, existing by this layout [14]. The storage capacitance can be implemented as MIM (metal-insulator-metal) structure. The capacitance of the LC cell itself also acts as an analog storage, especially by larger pixel sizes, however this capacitance is a function of the applied voltage with associated unwanted effects [15]. Thanks to the very simple structure and the small number of elements, such pixel can be implemented in very small sizes. This however would decrease the storage capability. With the time the leakage current causes the storage to discharge continuously. This results in the drop of the voltage on the pixel between the writing (refreshing) cycles. So finally the phase-modulation and the diffraction efficiency will experience low-frequency periodic fluctuations (flickering) over time. Over the history of the LCOS development number of improved DRAM schemes with e.g. larger number of transistors were proposed [16–19]

 figure: Fig. 2

Fig. 2 Simplified analog pixel, image courtesy [14].

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Another weakness of the simple DRAM layout is related to the implementation of the field inversion (also known as the DC balancing), which is necessary to avoid the unidirectional flow of the ions in the cell, where the constant charge might be built at the surface and consequently cause both the electrolytic degradation of the liquid crystal mixture and affect the modulating properties of the device.

The principle of the DC balancing is illustrated by Fig. 3. Here the LC cell is driven consequently with e.g. 4V and 2V voltage, which is periodically inverted in order to eliminate the DC component (so called field inversion). The nematic LC reacts only on the absolute value of the voltage and apart from the balancing the charge, the response of the LC is not dependent on the polarity.

 figure: Fig. 3

Fig. 3 Voltage applied to LC cell.

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The voltage applied to the LC cell is the difference between the voltage of the counter electrode VITO and the pixel voltage Vpix:

VLC=VpixVITO

To implement the field inversion, one can keep the VITO constant and flip the pixel voltage around (Fig. 4a). This approach was used extensively in analog DRAM-type LCOS. However it requires the pixel (transistor) voltage to be obviously at least twice higher, as the voltage swing in the display (in the real circuit the factor is considerably exceeding 2). Furthermore should the VITO doesn’t meet exactly the middle value regarding the Vpix, also due to the effects mentioned above, the DC balancing doesn’t work properly anymore and the LC layer sees the modulated voltage, which causes again the flickering effect. In fact this is barely avoidable, because of fundamental reasons [14, 20].

Different solutions were proposed to mitigate the complexity of the DC balancing problem. The inversion can be done frame-based, row-based, column-based or with a specific pattern. Finally the only suitable solution to avoid the modulation of pixel voltages (and hence to halve the required pixel voltage) is to implement the field inversion with a modulated counter electrode, Fig. 4(b). This technique is usual in many digitally driven LCOS implementations (will be discussed below), but in DRAM-pixels it requires additional buffer memory behind every pixel in order to provide “global shutter” functionality instead of “progressive scan”. This is needed to eliminate the conflict between the modulated (common) counter electrode and the not-yet-updated individual pixel voltages in the array. Number of improved DRAM-based pixel circuits with buffer memory and associated DC balancing features were proposed [17, 21–23].

 figure: Fig. 4

Fig. 4 Field inversion: (a) by constant ITO voltage, (b) by modulated ITO voltage.

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The difficulties with DRAM-type pixels caused researchers to come up with the SRAM-type (static random access memory) pixel circuits. The SRAM type of storage is pure digital, built by flip-flop logic gates. Classical SRAM-type pixels are based on 6 transistors architecture: four for flip-flop and two switches, it may optionally contain also X-OR block for e.g. frame inversion, Fig. 5.

The SRAM-architecture was natural to use with bistable ferro-electric liquid crystals [24]. This was later adapted to nematic liquid crystals, where the effect of the analog voltage was emulated by the time-averaged electro-optical response to the RMS of the binary voltage (to be discussed below in 2.1.2).

 figure: Fig. 5

Fig. 5 SRAM pixel schematic from [25].

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To our knowledge the only attempt to represent analog-like response for the limited set of quantized voltage levels was reported by Lee et al. [26, 27]. It used SRAM architecture with 3 bit memory behind every pixel to represent 8 values of the pixel voltage (that would mean 8 phase values). However this architecture was too complex to implement a larger number of phase levels (like 8 bit). A similar idea was described earlier by McKnight in [25], whereas a MEMS-based phase modulator with 3 bit SRAM pixels was presented recently [28].

So the SRAM-type pixel needs larger number of transistors and hence larger space. To mitigate this, VLSI developers are successfully moving to smaller technology nodes, e.g. from 250 nm to 180, 130 or even 90 nm. This challenges silicon foundry processes, because of the LCOS requirement for relatively high voltage swing (3 to 5V) on the pixel. The severity can be partially eased by using lower voltages for memory transistors (e.g. 1.8V), but higher voltage is still desired for the pixel electrodes. The layout optimization is playing an important role as well, the pixel circuit size and the position don’t have to be exactly equal with the corresponding pixel electrode and one can pack the pixels more dense [29, 30], so that the pixel sizes of 3 micron and below were reported [31, 32].

For the implementation of larger arrays (ultra high-definition 4k resolutions and higher) following should be considered. Larger resolution requires larger chip size (die size), so less dies can be placed onto the wafer and the cost grows rapidly. The field size of CMOS steppers and scanners, used at silicon fabs is usually 33x26 mm or less [33]. The backplane should reserve 1-2 mm on each side for the gasket, which makes the maximum possible pixel array size even smaller. From this reason, the die sizes usually do not exceed 0.7"-0.8". Larger size require stitching between multiple exposures, which is difficult to perform seamless and costly in production. Sony was doing LCOS chips up to the size of 1.55" with 4k resolution for professional cinema projectors [34]. JVC presented 8k prototype with 1.75" die size [35]. The largest LCOS die, implemented without the stitching, seems to be 1.2" with 4k resolution announced recently by Jasper display [36]. Another challenge is the amount of data, which should be generated and transferred to the chip in order to provide a feasible frame rate.

2.1.2. Modulation approaches: digital or analog pixel

While the analog pixel is supposed to deliver a certain precise individual voltage value within each frame, the digital options can be more diverse. Developed initially for visual display applications, the digital modulation was supposed to provide an average intensity perceived by the integrating detector, i.e., human eye. For this purpose the pulse-width modulation (PWM) was implemented in a number of devices. Grey levels were achieved by changing the duration of the single pulse, applied to the pixel. Different artefacts in the image caused by strongly uneven distribution of the “on” and “off” times within the frame, but rather relative complexity and cost of the pixel circuit, forced industry to introduce advances into the simple PWM scheme, particularly to increase the number of modulated pulses (e.g. two pulses withing the frame, each pulse with changing duration). Unfortunately PWM is not suitable for phase modulation, because the phase would have very strong variation between the begin and the end of the frame.

In projection applications, pulse-code modulation (PCM) also called binary pulse-width modulation became quickly very popular. It can provide a large number of binary pulses, following with high frequency, so one could rather achieve more even distribution within the frame. Each addressed “analog” value is decomposed into the sequence of bits (spatial representation of bit/pulse is called bitplane), as shown in Fig. 6. The duration of each bitplane is fixed for all pixels of the array, however the bitplanes possess different weights (duration) and bits in the bitplane can be turned on and off individually, depending on the addressed value, which is defined by the look-up table (LUT).

These scheme in abstract sense is very complicated. One has a large number of bitplanes available within each frame (e.g. 50 or 100) and should represent e.g., 8bit or 10bit intensity values. Furthermore the dynamic electro-optical response of the liquid crystal, averaged for intensity, will be less smooth (or even non-monotonic), than for classical PWM. The number of combinations for a sequence of 50 independent bits is immense. So certain rules were developed, how to distribute the weight and the order of the bitplanes to satisfy the requirements of display applications and minimize possible image artefacts.

When first applied for the phase modulation, the result was confusing, because of the strong temporal variation of the phase within the frame. This effect is usually called flicker or super modulation [37]. Still, with improvements in addressing schemes [38], frequency, sequence design (number, order and duration of individual bitplanes) [39, 40] and LCOS cell design, this approach has shown the ability for the phase modulation applications [41], which we will follow in 2.7.

 figure: Fig. 6

Fig. 6 Pulse-code (sequence) modulation: (a) pixel values in the frame are represented by the time sequence of binary values, (b) each “grey” value frame is decomposed into the sequence of bitplanes, from [25].

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2.2. Optical function of the pixel and the wafer

The top metal layer on the backplane is usually made of Aluminium. The top metal layer is patterned with pixel electrodes, which need to be electrically isolated from each other. The pixel electrodes possess typically the interpixel gaps of 200 nm to 500 nm, whereas the pixel sizes are usually between 2 and 10 microns. When the electrical potential is applied to the pixel electrodes and to the transparent electrode, the spatial electrical field causes the LC molecules to change their orientation and thus change the optical properties of the LCOS cell (electrical and optical anisotropy). The light incident onto the LCOS cell, propagates through the cover glass and the LC layer and is finally reflected by the top metal layer. The top metal layer is thus used in this case as the reflection layer as well. Figure 7 is showing such pixelated structure from the top.

 figure: Fig. 7

Fig. 7 LCOS backplane under REM [42]

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2.2.1. Reflectivity of the backplane

The quality of the top metal layer is very important for the performance of the LCOS device. This comprises first of all the reflectivity, but also the laser-induced damage threshold (LIDT), parasite diffraction orders and stray light.

The reflectivity of the Aluminium is limited by approx. 90%. For the pixelated area, this drops however to 60-80% depending on the pixel size, the interpixel gap, the wavelength and the fabrication processes at the silicon fab.

In earlier days the quality of the metal mirror, produced by silicon fabs was not sufficient, the Aluminium reflectivity was degraded by the high temperature processes, applied to the backplane, so additional post-processing was required, where the surface were prepared and extra metal layer was deposited [43].

Oliver and Enlian [44] propose to replace Aluminium top metal layer with Silver, that improves the reflectivity, especially in the near infrared range (700-900 nm), where Aluminium suffers from the increased absorption. This is however difficult, due to the oxidation properties of the Silver and the usual incompatibility with the standard semiconductor processes.

Another problem is imposed by the light leakage through interpixel gaps into the underlying CMOS structure. The light, penetrating into the p-n junctions of MOS transistors causes the generation of the photocurrent and hence affects the voltage, applied to the pixel. From this reason, the light blocking layers from the metal or absorbing material are applied, in order to isolate the CMOS circuitry from the incident light [45, 46].

Figure 8 is showing a focused ion beam (FIB) section of a pixelated structure of a typical LCOS backplane. One observes the pixel electrodes with passivation dielectrics on the top. The pixel electrodes are connected with the pixel vias (two of them per pixel). The light blocking elements are placed below the interpixel gaps (which are around 200 nm wide). One sees further wiring structures on the lower part of the image.

 figure: Fig. 8

Fig. 8 LCOS backplane under FIB section.

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The idea to separate the electrical and optical functions, where the light will be reflected by a dielectric stack, deposited on top of the pixelated electrodes was proposed e.g. in [47–50]. The idea was further developed for the wafer-scale fabrication of the broadband high-reflective high-resolution devices [51–53]. Figure 9 shows the performance of the reflectivity-enhanced LCOS in the visible waveband (measured sample is Holoeye Pluto C-56), Fig. 10 is showing the reflectivity of the same type of backplane, with the dielectric stack optimized for the near infrared (NIR) band. One observes the values in average higher as 98% over the approximately 300 nm band. Also versions for 950-1200 nm, shortwave infrared (SWIR) and UV bands were implemented [51–53].Alternative to the dielectric stack, one can use a high-reflective subwavelength grating structure [54].

 figure: Fig. 9

Fig. 9 Reflectivity-enhanced LCOS backplane for visible band [55].

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 figure: Fig. 10

Fig. 10 Reflectivity-enhanced LCOS backplane for NIR band [52].

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2.2.2. Advanced functionalities

The improvement of the optical performance on the wafer is not limited to the increase of reflectivity values. Another interesting option is to achieve the polarization-independent phase-only modulation with the LCOS device. The effect can be easily demonstrated by inserting a transmissive quarter wave retarder (QWP) into the reflective homogenous (or homeotropic) LC cell [56–58]. The light propagating through the birefringent medium (LC layer in our case) is represented by two orthogonal components p and s (extraordinary and ordinary wave respectively). Extraordinary wave sees the electrically controlled refractive index neff, whereas the ordinary wave experiences the constant no. If one places the QWP as suggested above (Fig. 11), with its optic axis oriented at 45° relative to the LC alignment, the light will propagate twice through the retarder and thus experience the half-wave retardance, which will turn the polarization by double angle, i.e., 90°. This effectively flips the original extraordinary and ordinary waves (or p and s respectively), so that by travelling back the former extraordinary wave (now ordinary) sees only no, whereas the former ordinary wave experiences the phase modulation with neff. So for any input polarization there will be a phase modulation performed, which value corresponds to the half of the phase modulation without the QWP component.

 figure: Fig. 11

Fig. 11 Polarisation-independent configuration with QWP, with permission from [58].

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One can use polymerized LC mixtures, also known as reactive mesogenes as QWP films [59]. The main drawback of the method is, that the thickness of the layer is relatively high and it further grows with the wavelength. This layer affects strongly the electrical properties of the LCOS cell, acting as a voltage divider, so that the effective voltage, applied to the LC layer, drops. Apart of that, the distance between the electrodes on the backplane and the counter electrode grows as well, which causes the crosstalk to increase (crosstalk discussion is in 2.7.2). This makes it challenging, to apply this technique at longer wavelengths, where the layer can be several microns thick.

An alternative implementation can involve an effective medium approach. One can implement a polarization retarder, using the “wire grid” gratings, either dielectric or metal, where the period of these gratings is smaller than the wavelength of light used. Because of the small period of such grating, only the zero diffraction order of the grating can propagate and the medium acts as birefringent film with certain optic axis orientation and the indices ne and no. Such gratings can be typically thinner as LC polymer layers for the same retardance value. Here however the manufacturing of high aspect ratio gratings on the LCOS backplane seems to be a challenging issue. Metal gratings (wire grid) are suggested in [60, 61], dielectric gratings proposed in [62].

2.3. LCOS cell with its components

2.3.1. Liquid crystal and alignment modes

The phase of the liquid crystal and its orientation in the LCOS cell defines largely the properties of the LCOS spatial light modulator (SLM). Most of phase-only LCOS devices are using nematic liquid crystals (nematic phase, NLCs). Other part is mostly using ferro-electric liquid crystals (FLC, smectic phase).

The devices based on FLCs are showing binary phase-only modulation, featuring high switching speed in multiple kHz range [63]. The ability to reproduce only two phase levels is unfortunately limiting so far the application scope of these devices. Nevertheless in the LC research the continuous phase modulation with vertically aligned deformed-helix FLCs was already demonstrated [64], also planar aligned helix-free FLCs could show continuous modulation [65], which makes it potentially suitable for use within the LCOS technology.

As optically anisotropic medium the liquid crystal has an optic axis (some LCs can be biaxial however), which defines its optical orientation in space. The averaged spatial distribution of the “preferred” direction of the LC molecules and hence of their optic axes can be characterized by a unit vector, called director.

Without external electrical field the director orientation n of the nematic LC is governed by the minimization of the Franks free energy density:

F=12K11(n)2+12K22(n×n)2+12K33|n××n|2 
where K11,K22,K33 are elastic constants for splay, twist and bend respectively. Depending on the alignment (boundary) conditions, one can implement a homeotropic (also known as vertical alignment, VAN), homogenous (also known as planar alignment, PAN) or twisted (TN) mode. Other modes are also possible, e.g hybrid [66] and pi-cell (OCB) [67]. TN mode is not well suited for the phase modulation. The pi-cell was not yet used in LCOS to our knowledge, however the fast phase retarder was reported [68]. In modern practice, LCOS is using homeotropic and homogenous modes, see Fig. 12.

 figure: Fig. 12

Fig. 12 Homogenous and homeotropic modes.

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When the electric field is applied between the top and the bottom substrates, the free energy from Eq. (2) is further contributed by the electrostatic free energy

u=12D2ϵΔϵsin2(θ)
where θ is the azimuthal angle of LC-director, Δϵ=ϵϵ is dielectric anisotropy, ϵ, are components of the dielectric tensor, D is electric displacement. The director orientation θ changes in order to minimize the total free energy.

In the homogeneous mode, the LCs with positive dielectric anisotropy are used, Δϵ>0, the electrical field forces the molecules to align along with the field, thus the angle between the director and the substrate increases (θ decreases) and, with the increasing voltage, the orientation of the molecules approaches the homeotropic mode (see Eq. (3)).

In the homeotropic mode the LCs with Δϵ<0 are used, so the molecules are rotating into opposite direction, i.e., perpendicular to the field and the orientation by applied voltage is approaching the homogeneous mode.

For an arbitrary polarized light, in the birefringent medium two orthogonally polarized waves will propagate (ordinary and extraordinary). When the incident light wave is linear polarized and the polarization is in the same plane with the optic axis of the LC, only the extraordinary wave will exist. After the double path through the LC cell, this extraordinary wave will experience the retardance l, defined by the layer thickness d and effective refractive index neff:

neff=ne2no2ne2cos2(θ)+no2sin2(θ)
so that the retardance l=20dneff(θ(z))dz.

2.3.2. Alignment methods

The industrially used alignment methods for LCOS comprise the so called organic alignment (polyimide is spin-coated onto the wafer, backed and rubbed with a velvet cloth or brush in the alignment direction) and the inorganic alignment with silicon oxide, deposited onto the surface under an oblique angle. The polyimide (PI or organic) alignment is usually used for planar (homogenous) mode with small pretilt angles, however it can be used also for homeotropic modes within various range of pretilt angles [69]. The inorganic alignment is implying an evaporated silicon oxide (or more generally SiOx), which is usually used for homeotropic alignment, but was reported also to provide smaller pretilt angles, suitable for planar or hybrid alignment [70, 71].

The advantage of the inorganic alignment is its robustness against UV radiation and altering, which makes it good choice for use in higher-intensity applications in visible spectral band. Polyimide is known to increase absorption under UV illumination [69], which alters alignment properties (such as pretilt angle) and thus is not the best choice for higher intensities at shorter wavelengths.

Other methods including photoalignment [72, 73] could be used in principle.

2.3.3. Major properties of common nematic LC mixtures

The properties of the LC mixtures are important in defining the performance of LCOS device. The most important parameters are: birefringence Δn, dielectric anisotropy Δϵ, elastic constants Kii, rotational viscosity γ1, temperature range, where nematic phase exists, absorption. The parameters of NLC are all functions of temperature. The optical parameters (Δn and absorption) are wavelength dependent.

The birefringence Δn is usually desired to be as high as possible in order to enable thinner cell gaps (especially at longer wavelengths and/or by smaller pixel sizes). Commercially available LC mixtures show Δn<0.3 at D-line (589.3nm) by room temperature. With increasing temperature and wavelength, the birefringence drops. Research-grade LC mixtures can show birefringence exceeding 0.4 [74].

High dielectric anisotropy allows to drive the LCOS cell with lower voltages, which is useful when smaller pixels are often limited in available voltage swing.

The rotational viscosity is critical in determining the dynamic behaviour of the device, particular its temporal behaviour (switching time), but also temporal noise level (see 2.7.1). Rotational viscosity quickly drops with increasing temperature.

Temperature range is important in real application with its storage and operational temperature requirements. LCs turn to solid phase when the temperature is crossing the crystallization (melting) temperature, this can be -40°C, but for some LC mixtures can happen also at way higher value, which even prevents the outdoor usage and storage. The clearing temperature (might be between e.g. 80°C and 120°C) is defining the transition into isotropic phase, where Δn is becoming equal zero.

LCs usually show increasing absorption at shorter wavelengths below approximately 400 nm. Some mixtures, especially high-birefringent ones, can begin to absorb significantly even by longer wavelength, e.g. 500 nm. The absorption bands exist also in long wavelengths spectrum close to 2000nm and further absorption in MWIR range can occur [75]. Thus the lifetime under UV illumination can be reduced considerably and depending on particular LC properties the device can be destroyed quickly if higher intensities on shorter wavelengths (e.g. in UV) are used.

2.3.4. Common electrode

The transparent conductive electrode on the inner side of the cover glass is usually based on indium tin oxide (ITO), which shows low sheet resistance and high transmittance. The LCD (liquid crystal display) industry was looking for a replacement of ITO with other transparent conductive oxides (TCOs) like AZO and GZO [76], or getting rid of the counter electrode by using the inplane-switching (IPS) or fringe-field switching (FFS). This is caused largely by cost issue. Since LCOS has relatively small surface, both the cost of the material and the sheet resistance are usually don’t impose any difficulties.

Still by applications with higher power and/or in the spectral range below approximately 400 nm, where ITO is suffering from the increasing absorption as well, the absorption in the ITO and LC material can become a bottleneck for the performance and for the damage threshold.

For the minimization of multiple interference effects from the different layers in LCOS cell, which can be very annoying in phase-modulation applications, the index-match layer can be deposited between the ITO and the glass, in order to match the refractive indices of the glass, ITO and LC with each other within a given spectral range. The index tuning of the ITO itself is possible as well. The front side of the cover glass can contain AR coatings for the similar purpose.

2.4. Cell fabrication

The fabrication of LCOS cell can be done in two different ways. For very small quantities single cell (die level) assembly is used. The LCOS wafer is singulated and the cell is built individually on the die, it comprises rather manual work.

For the industrial production the single cell assembly is not suitable. Wafer-scale manufacturing is used. The LCOS wafer and the glass wafer are receiving alignment layers (as mentioned above, polyimide is usually spin-coated, baked and rubbed, whereas SiOx can be evaporated). Then the gasket glue rings are formed on the LCOS wafer at each die. The rings foresee a side opening for the later LC filling. Different spacer architectures were used in the past [5, 46], whereas today for the moderate to small die sizes the spacers are usually distributed within the gasket glue ring. The sandwich is formed by the aligned glass wafer and the LCOS wafer and the structure is baked and cured afterwards. At this point the wafer-level process ends. The sandwich structure is singulated into individual cells using sawing and/or scribe-and-break processes. The cells are placed in the vacuum chamber, where the pressure gradient causes LC to fill the cells after vacuum is released. The filling openings are sealed and cured afterwards.

2.5. IC packaging of LCOS cell

The LCOS cell contains the CMOS circuitry and the LC, however it needs mechanical and electrical interfaces to be used in practice. The electrical connection is usually provided by the flexible printed circuit (FPC) type of cable. The FPC can be connected to the LCOS cell permanently with wire bonding, which is used in most commercial implementations, as shown in Fig. 13. However one could use other interconnect technologies as well, e.g. anisotropic conductive film (ACF) or even through-silicon-vias with flip-chip. The main limitation is imposed by the relative fragility of the LCOS cell, which can’t survive too high temperatures and pressure.

LCOS cell is brought to the substrate (die attachment). The substrates from metal, ceramic or PCB (FR4) were used, whereas the influence of material’s thermal coefficient of expansion (TCE), the thermal conductivity and the long-time environmental stability should be considered. Typically glue, epoxy, paste, film or tape are used as die attach adhesives. The use of high-performance bonding technologies like soldering or sintering is still very challenging due to the fragility of the LCOS cell.

 figure: Fig. 13

Fig. 13 LCOS packaging: (a) LCOS cell on the package, (b) bond pads to FPC connection.

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If the metal or ceramic substrate is used, the FPC is usually framing the LCOS cell and the parts are assembled in the specific process steps [77]. This includes the connection of the counter electrode (ITO layer). Typically the counter electrode is connected separately to the FPC (or other type of electrical interface, including the on-chip ITO pads). On Fig. 13a, one can recognize the ITO connection to FPC at the top center, behind the laser-inscribed number. To simplify this process, special substrates/cavities were proposed where the preformed pillar is used for the connection, the ITO and pads in the cavity are connected to the pads on the LCOS backplane using e.g., simple ACF interconnection [78, 79].

The environmental requirements in some applications, e.g., telecommunications or automotive industry, follow respective standards. It might require a hermetically sealed packaging, which can be implemented in different ways, the most straightforward of it is to build a cavity with a glass window [80], others propose a cavity, where the cell is embedded in kind of resin [81].

The substrate should comply with mounting requirements, at the same time the LCOS cell should be freed from the mechanical stress, which could degrade the cell form. As an alternative, the direct mounting of a cavity with LCOS chip on the adjacent optical elements, like beam splitter cube is sometimes used [82], i.e., combined mechanical and optical bonding is implemented on the same surface.

2.6. Drivers and signal interfaces

To drive the digital high-resolution LCOS backplane high performance electronics is needed. In consumer electronics applications in earlier days, this task was accomplished by a dedicated chip - ASIC, which is economically feasible by very large quantities in mass production. In industrial applications, the quantities are often not achieving enough high volume, whereas the variety of applications still requires application-specific approach. Powerful FPGAs are the usual choice today, which offer additional functionalities (e.g. built-in ARM processor), allowing to build a system on chip with on-board image generation around the LCOS SLM [83].

The LCD or pixel clock in the digital display can be in the range of 140-300 MHz or even higher. This is required to address large pixel arrays, as e.g. 4160x2464 pixels [42]. The databus on the LCOS chip can handle up to 128 bit [84] in order to provide enough high bandwidth for ultra-high resolution.

Such frequencies challenge both the driver boards and the electrical interfaces, so that the design of the connector and the FPC of feasible length is becoming critical task.

Attractive way to reduce the amount of transferred data, power consumption and cost in the digitally driven LCOS device is to integrate the driver and the memory buffer into the single LCOS chip, the panel is then addressed by e.g., 4 channels MIPI interface [85].

The requirements on resolution and frame rate can go sometimes beyond the usual requirements of the video-industry. This creates a problem of finding the right interface on the input side of the driving electronics. The use of a dedicated PCIe card for the PC is not always the user-friendly choice, neither it is desired in most of the industrial applications. The adaptation of newer high performance video interfaces is still possible. So HDMI 2.0 was used to transmit the video stream of 1920x1080 pixels with 8bit intensity (or phase) levels at 720 Hz frame rate for 3D sensor application [83], alternatively an on-board parametric pattern generator was used. However for higher frame rates and/or resolutions, the HDMI 2.0 interface could become the bottleneck. Higher bandwidth is offered by e.g. Display Port 1.4 or Thunderbolt 3 hardware interfaces.

2.7. Design and performance parameters

2.7.1. Temporal performance

As it was discussed in section 2.1.2, all LCOS devices show a temporal noise, which has periodic character. In the SRAM (digital) scheme, the LC is driven with a complicated binary waveform of weighted pulses (bitplanes), which follow with the frequency of several kHz. The devices on Figs. 14 and 15 were using 3 to 7kHz, whereas 15.5kHz was reported in [83]. The resulting phase modulated signal is built on temporal response of the LCOS cell, which has inherent switching times defined by the elastic and viscous parameters of the LC by the given temperature, driving voltage and the cell gap. Fastest of the LCOS devices, built on nematic LCs for amplitude modulation, are in the range of 1ms at 55°C [83], but the phase modulators, which require at least double thickness, compared to usual displays, can be in the 5 to 100 ms range, depending on the design wavelength and, of course, temperature. So obviously higher addressing frequency is less resolved in the temporal response of the LCOS cell and the rest noise is lower.

Figure 14(a) is showing the temporal phase response for an addressed phase value, measured interferometrically with high resolution on time scale (the track length is around 20 ms). For each addressed phase value, there is an own combination of bits, so the phase noise of different addressed phase values is not the same. Figure 14(b) is summarizing this, showing for each addressed value (“grey level”) the maximum, minimum and mean value of the measured temporal response. The standard deviation over all addressed values is 0.4% in respect to the total modulation range of 2pi.

Figure 15 is showing a low-noise LCOS SLM (Holoeye Pluto2 C-73) with an advanced driving bit pattern. The non-calibrated electro-optical (EO) response curve (left side of the figure) shows a non-monotonic behaviour, however the phase noise is rather low. The linearized phase response on the right shows a good linearity and a pretty low standard deviation of 0.16% (total modulation range close to 2.5pi, measured at 1550 nm wavelength). The switching time of this low-noise device is around 100ms at room temperature.

Depending on the application, the phase noise usually shows up as the periodic fluctuation of the diffraction efficiency (the diffracted orders experience periodic fluctuation of intensity in the same frequency range). Since the noise has perfectly periodic systematic character and the limited frequency band, solutions on system level can help to eliminate its influence (e.g. synchronized light sources and detectors, band-pass or band-stop filters etc.).

 figure: Fig. 14

Fig. 14 Phase response and phase noise: (a) Periodic phase fluctuation for certain addressed phase value, (b) Statistical representation for 8 bit addressed phase values.

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 figure: Fig. 15

Fig. 15 Low-noise phase-modulating LCOS SLM, original EO response (left) and linearized phase curve (right) [53].

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2.7.2. Spatial performance

Static performance: cell form

Ideally the LCOS device is perfectly flat with the even cell gap, without any spatial variation. In the reality both the cell form and the cell gap can show warpage and deviations. Figure 16 (right) shows an interferogram of the panel withhighly curved shape (multiple fringes hint to several microns sag of the reflected wavefront from the plane surface). However the form is largely spherical, which is easier to correct. At the left of Fig. 16, another sample is shown, the number of fringes is much lower, so the deviation counts around one micrometer for the reflected wavefront, however the form is almost exclusively cylindrical.

Figure 17 is showing the wavefront measurement of another LCOS sample, the maximum deviation within the active area is 0.84μ m. The deviation within the central part (8 mm diameter) is 0.52μm.

The thickness distribution of the LC layer (cell gap) is another important parameter. The spacers are usually set only on the perimeter of the cell, outside the active area. During the assembly, the sandwich of LCOS wafer and coverglass undergoes a temperature treatment, which builds a stress in the structure due to TCE mismatch. When the sandwich is singulated, the stress in the structure and its components (particularly LCOS wafer) is partially released and the cells are changing the shape. If the shape of the LCOS backplane and the cover glass are not the same, obviously there will be spatial variation in the cell gap, which leads to the spatial variation of the phase shift [86].

Further important factor is the packaging of the cell, which was discussed above in section 2.5. The packaging adds materials, connections, uses a mechanical and thermal treatment, which again influences the shape of the assembled device.

 figure: Fig. 16

Fig. 16 Flatness issues: astigmatism (left) and strong sphere (right).

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 figure: Fig. 17

Fig. 17 Cell shape of LCOS sample measured with wavefront sensor.

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Since the cell form has a strong influence on the optical performance, the researchers have tried different techniques to characterize and calibrate the commercially available LCOS SLMs [87–92]. The analysis of the spatial non-uniformity or the spatial phase distribution can be done using different methods, such as phase-shifting interferometry [87], Twyman-Green interferometry[88], Ronchi grating method [89, 91] and phase retrieval method [90, 92]. The retrieved information about the spatial response can be then used for the compensation of the non-perfect cell shape and cell gap.

Particularly several methods have been proposed to correct the spatial variation, e.g. the scaling method [87, 89] or polynomial fitting method [93]. The scaling method is either based on the correction of global LUT or multiple local LUTs for static phase nonuniformity. The recorded spatial phase nonuniformity would serve as a reference. With the consideration from the reference phase distribution, the desired “grey” level can be estimated by multiplying the LUT with a correction factor to provide the linear response. The polynomial representation can work with different sampling grid and allows to save memory and resources by a higher correction accuracy, representing the calibration data with just few polynomial coefficients.

Spatial modulation properties: crosstalk

Ideally the modulation characteristic on individual pixel is not dependent on the values for adjacent pixels. In the real situation, however, it is not valid. In old analog progressive scan displays, where the analog signal was going from the board through the video interface into the microdisplay, the higher frequencies in the signal suffered from the low-pass filtering on the non-perfect electrical wires and components and the high spatial frequencies in the content were somewhat suppressed. This kind of electrical cross-talk doesn’t come up in modern LCOS devices.

Another type of the electrical crosstalk is the influence of the electrical field in neighbouring pixels on each other. This is the task of VLSI designer to minimize this influence and typically the level of such crosstalk is order of magnitude lower than the pixel crosstalk in the assembled LCOS cell.

 figure: Fig. 18

Fig. 18 Fragment of Fresnel lens structure, addressed on phase SLM.

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We will consider only the pixel crosstalk in the cell, which is the most important type of the crosstalk. Figure 18 is showing a fragment of LCOS SLM with an addressed Fresnel-lens structure (it is showing a differential interference contrast microscopic image, which visualizes the phase information). The 2pi wraps (“flyback” regions) along the vertical axis look sharp, signifying a low level of crosstalk. The flybacks along the horizontal axis are extended about half of the pixel, so in this direction the crosstalk is somewhat higher, but is still quite moderate.

Figure 19 shows the simulated LC director distribution in the same LCOS cell with the same driving voltages, when two different binary linear gratings are addressed: period 2 pixels (highest spatial frequency, one pixel on, one pixel off) and period 8 pixels (4 pixels on, 4 pixels off). It is easy to observe on the retardance curve, that the square form of the 8 pixel binary grating is preserved rather well, the transition zone is less than one pixel wide and the retardance is close to 450 nm (because of the double path, the real retardance is actually twice of this value). The 2 pixel binary grating is far from the square form and resembles a distorted sine function. The retardance achieves less than 230 nm, which is roughly 50% of the value by the 8 pixel grating. As the result, the diffraction efficiency from these two gratings will be noticeably different, both for the first and for the zero diffraction order. Using higher voltage swing, one can increase the retardance by 2 pixel grating, however the retardance of 8 pixel grating will also grow, so that the resulting diffraction efficiencies will not be equal again.

 figure: Fig. 19

Fig. 19 Linear binary grating: LC director and retardance, (a) period 2 pixel, (b) period 8 pixel.

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Next effect to observe on Fig. 19(a) is that the retardance curve is not symmetrical (whereas the pixel voltage is). The asymmetry is caused by the non-zero pretilt angle, which is required to provide the preferred direction of the rotation for the LC molecules and eliminate reverse tilt and disclination effects. However this also means, that one direction of the rotation is “easy” direction and another direction is not. By increased crosstalk this difference becomes very pronounced and results in an asymmetrical distribution of intensity in the diffraction orders from such grating. Furthermore, this means, that e.g. blaze gratings for beam steering (which is typical application in telecom, see section 3.2) will show different efficiency, dependent on the steering direction.

The electrical potential lines between the small pixel and the common electrode (ITO) are not the vertical straight lines, but are running broader with increasing cell gap. In fact there is a lateral field between the adjacent pixels, because of the different potential, applied to them. This results in the observed crosstalk.

 figure: Fig. 20

Fig. 20 Linear binary grating, lateral field is perpendicular to the alignment.

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The problem becomes more complicated, if one considers a 3D case. In Fig. 19 the grating vector runs parallel to the alignment of the LC director (grating lines are perpendicular to the alignment). Let us consider the case, when the grating is rotated by 90° relative to the alignment direction (Fig. 20). In this case, the lateral field between pixels is perpendicular to the alignment direction. The LC molecules experience out of plane torque and the director distribution in the cell gets three dimensional character. On the figure, the electrical field is visualized with red arrows. Over the middle of the pixel electrode, the electrical field is aligned as expected vertically, the LC director tilts in the alignment plane (perpendicular to the plane of the figure). But the area between the pixels has a clearly pronounced lateral field. The LC-director forms a twist structure by strong out of plane rotation. The blue curve on the figure is showing the intensity after the polarizer, parallel to the alignment direction (no diffraction is considered). One can observe the modulation of the intensity having minima between the pixels, caused by the rotation of the LC director.

It is obvious, that the polarization of the incident light will not be maintained anymore. The phase grating becomes kind of polarization grating and the diffracted orders will show an elliptical polarization with parameters dependent on the diffraction order and the crosstalk severity in the cell [94].

It is noteworthy to mention, that the retardance distribution is perfectly symmetric in this case. The pretilt angle is in the perpendicular plane and the LC molecules react to the square of the field, which is then symmetric as well.

Different methods were proposed to overcome the crosstalk problem, elaborated discussion on it can be found in [12].

2.8. Optical modeling of LCOS SLM

To design the LCOS SLM with the desired optical performance, two parts have to be considered. The first part is the suitable electro-opto-mechanical simulation method, where the usual software for LCD simulation can provide satisfactory results. The other part would be finding the suitable optical modeling method, which is essential for the evaluation of the optical performance of certain design, such as reflectance, polarization state and diffraction efficiency. Here, we will divide the discussion of optical modeling into two categories. One is based on the wave optics modeling which uses scalar field to describe polarization and diffraction, the other is based on electromagnetic optics, which involves directly solving Maxwell’s equations with certain boundary conditions.

The optical modeling methods in wave optics that are commonly used for birefringent materials are the Jones matrix method, extended Jones matrix method and Mueller matrix method. The theoretical details can be found in a textbook, e.g. [95].

For basic reflectance analysis, Jones matrix method, which is extensively used for LCOS microdisplay [96–98] can also be applied to the analysis of phase-only LCOS SLM [99]. The basic assumption of Jones matrix method is an ideally coherent beam with normal incidence and forward propagation only, which means multiple reflection between the layers were not taken into the consideration. So along the propagation direction, LC layer is viewed as the combination of consecutive wave plates with different direction of fast axis and described by set of Jones matrices. The pixelated backplane of LCOS is assumed to be a prefect mirror, light leakage between the pixels and diffraction were neglected. As for the reflected light from the LCOS backplane, that is presented by arranging reversely the series of Jones matrices of wave plates. In [99], the authors have used Jones matrix method to find suitable configuration of LC alignment for phase applications, where the amplitude modulation over the different grey levels is small.

The extended Jones matrix method, which can be used to model incident angle other than normal incidence, is also used by researchers. For example, in [98], it is applied to predict the optical influence due to the fringing field (crosstalk) effect. The flyback region is separated into smaller domains, where in each domain, the Jones matrix can be calculated separately so the influence can be roughly estimated.

For polarization prediction and analysis, especially in the presence of the depolarization and diattenuation, Mueller matrix method and Stokes parameters were used for LCOS microdisplays [100] as well as for phase-modulating LCOS SLM [101–108]. The Mueller matrix method can handle not only the polarized light, but also partially polarized light and unpolarized light as input beam. Another difference between the Jones matrix method and the Mueller matrix method is that the latter deals with the intensity rather than amplitude of the propagated light. By measuring the Mueller matrix of LCOS SLM, the model-based analysis of phase-mostly modulation for TN type LCOS microdisplay was applied in [101–106], while similar model was used for prediction of the flicker influence from homogeneously aligned LCOS device in [108, 109].

Fourier transformation is used for diffraction prediction and analysis in phase applications. Basically, the phase (retardance) profile can be obtained from the spatially simulated LC director distribution. Afterwards the far field diffraction pattern can be obtained with fast Fourier transformation (FFT). Otherwise, the phase profile can also be obtained experimentally with either measuring the Jones matrix at sub pixel level to incorporate the influence of the crosstalk (fringing field) effect [110] or using polarization or interference microscopy to retrieve the phase profile from the measured light intensity [111].

Later on, the measured phase profile can be used to simulate the far field diffraction pattern. But for more complex phase profiles such as diffractive beam splitter with multiple beams or other CGH, the feedback loop optical system with different algorithms is needed for optimization of the optical performance [112], because the scalar model is not accurate enough.

The modeling tools based on wave optics have two major problems with advanced LCOS simulation. One is the assumption of the stratified medium, which contradicts to the fact that LC director can have an arbitrary three dimensional distribution. This has also been emphasized since the fringing field (crosstalk) effect becomes severe with the development of LCOS SLM towards smaller pixels, higher resolution and applications for longer wavelength. The other is that the diffraction effects from the pixelated metal electrodes become prominent as pixel sizes and interpixel gaps shrink down to be comparable or even smaller than the wavelength of the incident beam. An illustrative image is provided in Fig. 21, which shows the diffraction effect from the LCOS backplane pixels (calculated with RCWA method). The perturbations in the reflected wave, caused by the interpixel gaps are clearly seen.

As the result, several optical simulation models based on numerically solving the Maxwell’s equations for vectorial fields, which were used for modeling of general LC devices [113–118], have also been applied to LCOS investigation. For example, beam propagation method (BPM) [119–123], finite difference time domain method (FDTD) [124, 125], rigorous coupled wave analysis (RCWA) [126, 127], and also other hybrid methods that combine different simulation models [128] were used on predicting optical performance of LCOS.

 figure: Fig. 21

Fig. 21 Electromagnetic field diffracted from the pixelated LCOS backplane, modelled with RCWA [52].

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BPM is a forward propagation only solution to Maxwell’s equations in the frequency domain, used with slowly varying envelope approximation (SVEA) [113], which means the variation for the amplitude of the field along the propagation direction, i.e., z direction, is assumed to be small. Another assumption is that the refractive index has small variation along the propagation direction. Thus, an effective refractive index (neff) can be estimated along the propagation direction. Together with SVEA the propagation field can be thus simplified i.e., E(x,y,z)exp (jkneffz) and H(x,y,z)exp (jkneffz), which reduces the calculation.

Moreover, the forward propagation only solution implies that multiple reflections inside the simulation device were assumed to be negligible. Therefore, for the reflection from the pixelated metal structure, either ideal metal is assumed [128]or reflectance of the metal is estimated and multiplied on the field that propagates all the way down to LC-backplane interface [119, 120], then mirror image of the LCOS structure is used for forward propagating the field back to the top of glass substrate.

Under these assumptions, the basic calculation procedure involves slicing the simulation domain into multiple slabs along z direction, then with the known input field at the plane z=z0, the propagation field for slabs with thickness δz at z=z0 can be calculated, then the outcome will serve as the input for the next slab at z=z0+δz. So after iteratively calculating the field through the slabs, the field distribution of the entire simulation domain can be obtained.

Two major methods were developed to employ full vectorial field calculation, which were based on constructing simulation geometries and spatial permittivity distributions either with finite difference method (FDM) or with finite element method (FEM). For FDM-BPM [113–115, 119, 120], the derivative operator in Maxwell’s equations was discretized with Crank-Nicolson scheme to achieve unconditional numerical stability. This also means the simulation geometry is discretized with rectangular grid. The simulation results of reflectance on LC device have shown that FDM-BPM based simulation method is comparable to that of FDTD results [114] (more details on FDTD will be explained later on).

When comparing to the experiment results on LCOS [119], FDM-BPM can provide qualitative prediction on how different the incident polarized light can minimize the loss of light due to the crosstalk effect.

In FEM-BPM, the simulation geometry is typically discretized with triangular elements, where the basis functions were employed on the mesh nodes of the simulation domain, by finding the proper weight of the basis function on each nodes, approximated solution to Maxwell’s equations can be obtained to represent the electromagnetic field of the simulation domain. This method has been used to predict the fringing field effect and diffraction effects on the pixels in LCOS device [121–123]. One advantage of FEM-BPM is that it can better handle complex geometries such as curved surface, and also there’s no need to use Padé approximation for the adaption of the usage on wide angle beam.

In FDTD method, there are no typical BPM assumptions for solving Maxwell’s equations in time domain. The derivative operator in Maxwell’s equation is discretized with central difference scheme to achieve 2nd order accuracy in the approximation. The so called Yee lattice is the core of the FDTD, where the electric and magnetic field are stored at staggered grid [129]. Then, the calculation of field is completed by leapfrog scheme within the time marching iterations.

This method also leads to divergence-free nature, which will not create fictitious free charge and cause instability in the simulation. Typically, perfectly matched layer is used around the boundary of simulation domain to prevent spurious reflections from the boundary and provide the analogy for field propagation from or toward infinity.

Researchers used FDTD method on 2D LCOS SLM simulation in the early development of optical phased array [124, 125], periodic boundary conditions were applied on the sides of simulation domain. After retrieving near field information of LCOS SLM, Helmholtz-Kirchoff integral was used to obtain the far field diffraction efficiency. Comparing the theoretical results for the ideal blazed grating and experiment results, 2D FDTD provides good prediction for 1st order diffraction efficiency.

In the semi-analytical RCWA method, Maxwell’s equations are solved in spatial frequency and frequency domain for the periodic structure [130]. Typically, the simulation geometry was divided into layers along the propagation axis, i.e., along z axis. Within each layer, the material properties along the propagation direction are required to be homogeneous, while in the other two directions the material properties can vary with respect to x,y direction, i.e., ϵ(x,y). By using plane wave expansion method, we can first compute the eigenmodes of incident light. Then by using continuous tangential field boundary conditions, we can compute the eigenmodes and calculate the scattering matrix of each layer.

Then, one iteratively updates the overall scattering matrix by computing eigenmodes and scattering matrix through all layers. Finally, the overall scattering matrix of whole simulation structure can be obtained, where reflection and transmission coefficients are calculated. So the reflected and transmitted fields can be computed based on the known coefficients. The researchers have applied RCWA to investigate how the alignment of LC and pixel area influences the far field diffraction pattern of blazed grating displayed on LCOS and analyze the phase transition between the two adjacent pixels for the holographic application [126, 127]. This method has been shown to provide good physical insights for the investigation.

Finally, hybrid methods can be proposed to the analysis of the reflectance of LCOS. FDTD or FDM-BPM methods were combined with extended Jones matrix method to predict the optical performance [128]. The simulation was divided in two parts. First, the stratified medium, air, polarizer, and glass, were simulated with the extend Jones Matrix method. Then, the LC layer and perfectly conducting layer were simulated with FDTD or FDM-BPM method. Above LC layer, an infinite thick glass layer was simulated with perfectly matched layer boundary conditions on top. The periodic boundary conditions were applied on each side of the FDTD simulation domain. The calculation procedure used first the extend Jones matrix method to calculate the output field when light propagated from air to glass. Then, the output field serves as input field for FDTD or BPM method. After the light propagated through glass, LC layer, and perfect metal layer, the reflected light that travels back to the top of glass layer were decomposed to eigen propagation modes by plane-wave expansion methods. Then, these modes serve as the input for the extended Jones matrix to propagate back to the top air layer again.

From the simulation results, both methods have shown better reflectance prediction for the present fringing field effect compared to simulation results with only extended Jones matrix method. Even at the wide incident angle case, the hybrid simulation method with FDTD or BPM have nearly identical results on reflectance. But the advantage of BPM method is that it is computationally less expensive compared to FDTD method.

Still some topics remain challenging for optical modeling in LCOS design, since the research works cited above have used simplified structures and materials properties representation for simulation of LCOS SLM. To design and model high efficiency LCOS SLM, the knowledge about material properties (wavelength and temperature dependent) is required. The pixelated metal electrodes and ITO layer have to be taken into account properly. Finally, the multiple reflections inside the structure are also not negligible [131], which limits the application of BPM as well. The multiple reflections have significant influence in the phase-modulation applications of LCOS SLM.

As for the rigorous methods such as FDTD, RCWA or FEM, the simulation domain, that involves pixelated metal structure with correct material parameters is important for adequate optical modeling. Smaller grid size or more mesh elements are needed, which suggests high computational cost for the whole LCOS simulation domain.

A further optical study has been carried out by using 2D FEM to simulate the whole LCOS structure with binary gratings [53], the results with 8 pixels per period binary grating are shown in Fig. 22. Here the horizontal grating means that grating lines are parallel to the alignment direction of LC (and the grating vector is perpendicular respectively) while vertical grating means the opposite. In simulation, the thickness of the glass layer was assumed to be infinite by using PML on top of the glass layer.

The asymmetry of the results for the vertical and horizontal gratings in LCOS phase modulators is inherent to the alignment properties of the nematic LCs and were extensively reported in the past (see e.g. [132]).

The FEM simulation results have shown good qualitative predictions for diffraction efficiency from 5th to +5th diffraction orders. However, there is still space to improve the quantitative prediction since the reflection and multiple reflections at the air-glass interface should also be considered.

Nevertheless, it’s difficult to directly simulate the whole LCOS structure using only FEM methods, or other rigorous methods as well, especially in 3D, since this is a multi-scale optical modeling problem, ranging from the millimeter scale for the glass layer to the nanometer scale for the interpixel gap. Thus, hybrid approaches combining different optical modeling methods are required for advanced LCOS SLM design.

 figure: Fig. 22

Fig. 22 (left) Horizontal and (right) vertical binary grating simulation (red squares) and experiment results (blue rhombs) [53].

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2.9. Summary and outlook on LCOS technology

Most LCOS backplane designs tend to shrink the pixel sizes in order to save the cost and fit higher resolutions into the feasible die size. Smaller pixel designs are dominated by digital schemes. The postprocessing of the CMOS wafers can allow better light efficiency. Small pixels, low voltage, digital drive schemes, infrared spectal band and specific application needs are creating a set of new, sometimes challenging requirements on the LC mixtures, packaging processes and driving solutions for use in phase modulating LCOS devices. Below we discuss the selected application topics of LCOS technology, which will drive the industrial phase-only LCOS development, both commercially and technologically, in the next years.

3. Photonic applications of phase-only LCOS devices

3.1. Structured light in time and space

One of the most promising applications of LCOS SLM technology is in so-called Structured Light [133]. Structured light refers to the ability to customized optical fields both spatially and temporally, the former referring to control in amplitude (intensity), phase (wavefront) and polarization, while the latter referring to time and frequency spectrum control. Originally such laser beam shaping was performed with hard-coded computer generated holograms (CGHs) by exploiting the dynamic phase change, Δθ(x,y)=kn(x,y)d(x,y), when an optical field passes through a medium. Here the wavenumber (k), refractive index (n) and thickness (d) determine the phase change (Δθ) experienced by the field. This was traditionally implemented with diffractive micro-optical elements and restricted almost entirely to scalar modes in the spatial domain [134–136]. The dynamic phase in this case exploited a spatially varying depth, d(x,y), and by interference produced the desired intensity and/or phase, usually in the far-field. By the 1990s the ability to compute such CGHs was well-known but the time, cost and complexity of implementation hindered, and in some cases restricted, their application. The advent of LCOS SLMs allowed the depth to remain fixed, varying the local refractive index of each pixel instead, thus achieving a dynamic phase change through the factor n(x,y). As explained in earlier sections, this is a rewritable process and consequently the erstwhile CGH techniques have been further refined for both static and dynamic control of light [137]. The result has seen the rapid growth in structured light by SLMs [138], spurning a myriad of applications in communications [139–142], quantum optics [143, 144], imaging [145], microscopy [10], optical trapping and tweezing [146, 147], lasers [148–150] and even education [151–153]. Some examples of the holograms and the respective structured light fields are shown in Fig. 23. While most techniques and applications have considered scalar structured light fields, complex vectorial fields [154, 155] and time-frequency control [156] have likewise gain prominence.

In this section we will briefly cover the salient history and seminal advances in the use of SLMs for structured light, referring the reader to the aforementioned reviews for more comprehensive literature on the subject.

 figure: Fig. 23

Fig. 23 Structuring or tailoring light means the conversion of one optical field into another. The conversion may be in amplitude, phase, polarization and/or frequency/time spectrum. Here some example holograms with the resulting structured light fields are shown. Adapted from [138] with permission from the OSA.

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Initially the use of SLM technology for structured light considered only scalar optical fields. Using design procedures adapted for pixellated phase-only devices [157–159], recently optimised for real applications [160, 161], SLMs were used to create a myriad of beam types, including well-known solutions to the wave equation in free-space such as Hermite-Gaussian [162], Laguerre-Gaussian [163, 164], Ince-Gaussian [165] and Bessel-Gaussian beams [166, 167], as well as other exotic beam types including Airy, flat-top and general non-diffracting fields [168–170]. Following this, many approaches have been developed to extend the applications of the technology, for example, to structure light more efficiently [171, 172], faster [173] and across a broad wavelength range for white-light beam control [174]. Today it is possible to create any structured light field as a single beam or as a multiplexed array of many beams, demonstrated up to 200 from a single device [162].

A particularly topical subject has been the creation of structured light that carries orbital angular momentum [175], first created on an SLM more than two decades ago [176]. Such beams require an azimuthally varying phase pattern of the form exp (ilϕ) with a twisting parameter (topological charge) l determining the number of phase spirals about the azimuth (ϕ). This type of beam has become topical both for fundamental and applied studies, but in the context of SLMs they are popular because only a phase hologram is required. When the spiral hologram is combined with a linear grating to separate the desired beam away from the zero diffraction order, a fork-like pattern is observed. Although it is easy to create an OAM beam by such a hologram, the result is not an eigenmode of free-space because the incoming beam is not modulated in amplitude to account for the radial dependence of the Laguerre-Gaussian beams. Instead, such helical beams are now understood to be hypergeometric modes with significant power distributed across many radial modes [177, 178]. By employing phase and amplitude modulation following the design approaches now available for phase-only devices [137], pure free-space eigenmodes that carry OAM can be created. These days it is also possible to create such OAM beams by geometric phase rather that dynamic phase (as used by SLMs). This is achieved, for example, by using liquid crystals where the optical axis is orientated in a spatially dependent matter; for OAM beams this would require an azimuthal dependence on the axis orientation with position [179, 180]. Nevertheless, SLMs have become the standard laboratory tool for the generation of such beams.

The additional benefit of a geometric phase approach for controlling light is the ability to create vector beams [181]. Combinations of geometric phase elements and SLMs have been deployed for custom vector beams (see for example [182]) but it is possible to create vector states of light directly with LCOS phase-only SLMs. Unlike a scalar field that is characterized by a homogeneous polarization distribution, say U(x,y)=uh(x,y)H^, where the entire beam is horizontally polarized, in a vector beam the spatial mode associated with each polarization component may differ, e.g., U(x,y)=uh(x,y)H^+uv(x,y)V^ where uhuv. In terms of spatially structured light the vectorial field is clearly the general case, reducing to the scalar beam when the two fields, uh and uv, differ only by a complex number (fixed amplitude and phase ratio). The standard method to create such vector beams is by interferometric approaches [183–185]: each polarization component is modulated independently and then combined. In early work the polarization components were first separated, each passed onto a different region of the SLM, appropriately modulated, and then recombined. Because SLMs by design modulated only one polarization component, a waveplate would typically be used in one arm. For example, if the SLM only modulated the horizontal component of the incoming field then the path with the vertical component would be passed through a half-wave-plate to convert it to a horizontally polarized state prior to the SLM, and then back to vertical after the SLM. Combination of the two components can then easily be achieved with a polarizing beam-splitter. An alternative is to first modulate the desired beam into an array of multiplexed scalar fields travelling along two directions and then alter the polarization of one, finally combining to form the vector beam [186, 187]. In another approach the SLM is deliberately made inefficient so that a large zeroth diffraction order exists. By not using a blazed grating, the modulated beam from the SLM follows the same path as the unmodulated component. This fact can be exploited to create specific types of vector beams [188, 189]. For example, if a diagonally polarized beam is incident on the SLM but only the horizontal component is modulated then the outgoing beam will be transformed as UinD^=UinH^+UinV^Uinexp (iΔθSLM)H^+UinV^. This approach has been used to create propagation invariant vector flat-top beams by using an incoming Gaussian mode modulated with a spiral hologram [190]. Using two SLMs allows full polarization, phase and amplitude control for the creation of exotic structured light patterns [191–193].

 figure: Fig. 24

Fig. 24 SLMs have found use in frequence and time control of light pulses. Here the authors of Ref. [194] overcome SLM artifacts such as pixellation by judicious choice of phase mask. Adapted from [194] with permission from theOSA.

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All the aforementioned examples concerned the spatial structuring of light, yet SLMs have been proven equally versatile in the temporal structuring of light [195, 196]. A typical configuration would see the incoming beam dispersed by a grating and then Fourier transformed by a lens to spatially distribute the wavelengths (Fig. 24). This means that the frequency spectrum is now spatially distributed and can be modulated in phase and amplitude. If a reflective SLM is used then the beam is returned and recombined by the reciprocal nature of the propagation, albeit now with a modified frequency spectrum which manifests as a structured temporal pulse. Further, simple 1D devices may be used without any adverse spectral aberrations due to pixellation [194]. This type of temporal structuring of pulsed light fields has found many applications in ultra-fast imaging [197], ultra-fast spectroscopy [198], coherent control [199] and many more. An exciting development is the combination of both spatial and temporal control with SLMs [200, 201], opening a path towards enhanced imaging, microscopy, communication and material fabrication with 4D structured light.

A unique feature of light is the principle of reciprocity. In the case of structured light this suggests that if a particular hologram converts beam A into beam B, then in reverse this hologram will convert B into A. If A is something that is easily detected, for example a Gaussian mode coupled into a single mode fibre, then the combination of the hologram and the fibre represents a structured light detector [138]. This idea has been exploited for qualitative analysis of structured light beams. Other optical transformations using SLMs have exploited various conformal mapping approaches to design mode sorters for structured light, with a notable example the mapping of OAM to angle, which together with a lens (which maps angle to position) allows for a simple OAM detector [202]. It is routine today to use SLMs for such mode transformations in order to detect spatial modes, a crucial step in MDM (mode division multiplexing). For a quantitative analysis of some unknown structured light the entire field can be modally decomposed into some orthogonal basis, and modal decomposition used to extract the necessary modal amplitudes and phases. This has been successfully demonstrated using SLMs [203, 204] and used to extract all the physical parameters of the field, including OAM density, wavefront, Poynting vector and beam quality factor [205–208]. The dynamic nature of the LCOS SLM means that these approaches can be executed at very fast rates, demonstrated for example by the real-time analysis of vector beams [209, 210].

The detection of structured light modes is a crucial element for exploiting modes of light as a basis in quantum studies. This is because in most quantum experiments with single photon spatial modes it is the final detection that determines what is studied, so-called post-selection. This was first done with physical holograms for OAM modes; the use of SLMs quickly followed [211–214] and have been shown to be extremely versatile in both fundamental and applied quantum experiments, particularly those exploiting OAM as the basis (see [143, 144] for recent reviews). Notably, all the holographic techniques to create and detect classical structured light could be directly applied to the quantum world. Using SLMs, quantum entanglement has been extended to high OAM values [215], tested with a range of spatial modes [216, 217], used to test uncertainty relations [218], quantum interference [219, 220], violations of Bell inequalities [221, 222] (see Fig. 25) and more recently to control the state of multi-dimensional, multi-photon experiments [223–226]. In summary, the application of phase-only LCOS devices has already gained traction in the domain of structured light. As such devices improve in performance and drop in price one can expect to see these exciting laboratory demonstrations translate into new technologies for commercial exploitation.

 figure: Fig. 25

Fig. 25 The top panel shows the first experiment to perform a Bell-like violation using LCOS SLMs [221], with a typical result shown below for entangled Bessel beams [216]. Adapted with permission from the OSA.

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3.2. Telecommunication applications

In commercial telecommunication system the primary application of LCOS is inside wavelength selective switches (WSS) that enable reconfiguration and routing within optical networks. Modern longhaul telecommunication systems operate in the C+L wavelength bands (1520-1620 nm) and typically carry approximately 100-200 wavelength channels all around the world through terrestrial networks or through undersea cables. These systems can obtain trans-Atlantic or trans-Pacific capacities on the order of 50 TB/s per fiber. The spans in terrestrial networks are much shorter, 50-1000km, but there are many more of them and they are highly interconnected due to the density of populations. Reconfigurable optical add drop multiplexers (ROADMs) are used to direct traffic between the nodes [227–229]. Within a ROADM node there can be as many as 20 WSSes each with its own LCOS device!

LCOS devices are the spatial switching element that enable flexible grid functionality of wavelength selective switches (WSS). They have replaced MEMs switches because the software defined programmability of the display allows the “mirrors” to be defined arbitrarily [230]. Pixels can be grouped together to produce arbitrarily shaped beam steering components to adapt to the shape of the beams that often have complex shapes such as a crescent, they can be shifted around fractions of a wavelength to adapt to changes caused by temperature, and can be spaced nonuniformly to compensate for non uniform dispersion from a diffraction grating. Additionally, there are virtually no gaps between the pixels which minimizes the dead space between channels and enable flexible grid operation [231]. State of the art WSS can obtain 50-GHz spaced passbands with 0.5-dB 40-GHz bandwidths. Some aberrations of the optical system inside a WSS can be corrected by the LCOS including wavefront curvatures (see discussion in section 2.7.2).

Many WSSes are placed inside ROADM switching nodes. They typically are specified by degree, which means the number of different input/output fiber pairs the node is connected to. A typical ROADM will contain 1 pair of WSSes for each degree along with additional WSSes or other switching elements to drop and add traffic to the node. For a good background into the past, present, and future of optical switching, please refer to [11, 232–234].

This section will provide a basic tutorial on wavelength switching using LCOS devices in addition to providing a few state-of-the art examples and speculations on future directions of WSS.

3.2.1. Basic wavelength selective switching

The function of a 1×N WSS is to direct any wavelength from one input/common fiber to any of the N output fibers. Modern ROADMs typical employ twin 1×20 WSS modules that contain two independent WSSes that share a single LCOS and the same optics.

A WSS is basically an array of 1×N spatial switches with 1 switch per wavelength. Fig. 26(a) shows a basic beam steering switch which typically uses one spatial dimension for beam steering which leaves the other orthogonal spatial dimension for wavelengths. It comprises a fiber array with collimation lenses and an LCOS steering element which is represented as a tilted mirror. They are each placed 1 focal length away from a Fourier lens that focus the spatially separated ports to a single spatial position on the LCOS. In this configuration, light enters through the common port, and depending on the linear phase imparted by the LCOS, the beam is directed towards any of the N output ports.

The number of pixels in the LCOS sets the upper limit of the number of supported ports in any 1×N switch. However, to obtain the upper limit, the beams must fill the LCOS and each port must be as close as possible in angle space. The collimator lens array increases the fill factor of the beams in the spatial dimension which places the ports closer together in angle space at the LCOS. To give some typical numbers, a fiber collimator array has 127 μm pitch/spacing using fibers with mode field diameters (MFD) around 10 μm. After the collimator array, the MFD can be increased to 70 μm and still have 127 μm pitch. The Fourier lens focal length is then adjusted such that the beam size is maximized on the LCOS.

The upper limit of the number of ports is ultimately dictated by the additional diffractive loss from the blazed sawtooth beam steering gratings approximating a perfect linear phase. Figure 26(b) shows an approximation of a linear phase ramp with a hologram with period somewhere between 3 and 4 pixels. Losses and crosstalk occur because the ideal linear phase can only be approximated (see crosstalk discussion above, 2.7.2.2). There are three types of errors in this approximation: digitization errors (limited number of phase levels), pixelization errors (wraps occur every 3 or 4 periods) and modulo 2π errors or flybacks. The flybacks are the dominant source of additional non-theoretical loss and crosstalk at steep angles. During a flyback, the phase is slowly changes from phase 2π to 0 which rounds off the ideal instantaneous transition that introduces significant error into the ideal phase. The number of flybacks increase with angle (grating period decreases), which increases the loss and crosstalk significantly for ports at steep angles. Applying pre-emphasis to the hologram can partially correct the flybacks at the expense of requiring a larger phase-stroke from the panel [235].

Digitization and pixelization errors are closely related. Digitization errors based on the number of available phase levels (typically 256) do not cause any noticable loss. However, at steep angles such as in the example hologram with only 3 or 4 levels per wrap the hologram is effectively digitized to have 3 or 4 levels. Theoretical losses of a blazed grating with 3 or 4 levels is around 2-dB. Additional errors from pixelization are from non-uniform wrap patterns. In this example, the wraps occur mostly every 4 pixels but sometimes 3 pixels. This implies that this hologram will produce additional tones at seemingly random spatial frequencies introducing crosstalk into other ports that is hard to control. Under these constraints, 2-dB loss can be obtained if holograms have periods greater than 5 pixels. Additionally, the WSS must perform attenuation to enable wavelength equalization. Beam steering holograms only can redistribute the energy and therefore require dummy ports to throw attenuated light. With attenuation, more than 5 pixels per period is advisable to allow for more degrees of freedom in the attenuation hologram design. Therefore, LCOS with many more pixels are highly desirable to reduce pixelization artifacts.

 figure: Fig. 26

Fig. 26 Principles of WSS with LCOS device: (a) Beam steering spatial switch, (b) Mirror phase vs. approximation of linear phase by LCOS, (c) WSS with astigmatic optics for independent optimization of steering dimension and wavelength dimension including polarization optics, and spectrometer section.

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The WSS is constructed by adding wavelengths to the spatial switch and sending each wavelength to a different spatial section of the LCOS that is orthogonal to the ports. Another complication in WSS is to maximize the transmission for both polarizations. Since the LCOS and diffraction grating typically only pass one polarization, polarization diversity schemes that spatially separate the two polarizations into effectively additional ports are required to pass the orthogonal polarization (see the discussion on polarization independence above, section 2.2.2).

Figure 26(c) depicts a simplified WSS that has polarization diversity and uses cylindrical optics to separately optimize the steering and the wavelength splitting functionality. Although there are many ways to build a WSS, they all need to steer beams and focus light. Therefore, almost all WSSes comprise: 1) a spectrometer section that disperses wavelength across the wavelength axis of a LCOS, and the 2) front optics that prepare the beams for the spectrometer section and often includes polarization diversity optics toeliminate polarization dependent effects. Tweaking the front optics can resize the beams through the system and help to optimize for a particular number of ports, and spectral resolution. Looking at the sideview (port direction) the parallel beams from the fiber array are polarization split and directed towards the spectrometer. In this axis, the beams pass through the grating almost unaffected. A cylindrical steering lens (i.e., Fourier lens) which can be constructed as a single lens or a lens pair focuses the beams onto the LCOS panel. The two polarization paths through the switch swap paths in the forward and backwards directions which minimizes polarization dependent loss. In the wavelength direction (topview), a collimation lens collimates the beam to illuminate enough lines on the grating to obtain a desired spectral resolution. A lens between the spectrometer and grating focuses each wavelength to a different spatial location on the LCoS.

Figure 27 shows a research prototype of a packaged WSS to illustrate the optics and size of a typical WSS [236].

 figure: Fig. 27

Fig. 27 Packaged WSS with a Holoeye Pluto-2 controller running an embedded Linux system with Ethernet interface.

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3.2.2. Challenges of LCOS for wavelength selective switching

WSSs push the LCOS capability towards its limits. The WSS application requires the LCOS to switch upwards of 200 wavelength channels to as many as 100 separate output ports with attenuation up to 20-dB without producing crosstalk (i.e., no uncontrolled stray light). This requires full control of every pixel on the display and huge set of holograms. From a telecommunication system level, it is desirable to keep crosstalk levels below -35dB to prevent degradation to the communications signal. Telecom grade WSSes must also operate over a large temperature range which possibly requires additional holograms and/or driving configurations for every temperature, largely because of the temperature dependency of the LC properties (especially birefringence and switching speed). Alternatively (and preferably) the module should be temperature-controlled.

The settling time of commercial WSS modules is typically specified as few hundreds of milliseconds, which doesn’t impose any difficulties for LCOS device. The switching speed of LCOS can be optimized towards tens of milliseconds or below that, which however would cause the unwanted temporal noise to increase (see section 2.1.2).

Future directions of WSS include increasing the spectral range covered to unlock more fiber capacity, reducing the losses to reduce unnecessary amplification, and to increase the number of ports. More pixels is the obvious solution. For instance, a 4k panel can support twice as many wavelength channels and twice as many ports as standard 2k panel. Reducing the loss will require optimization of the backplane and the LCOS cell - both the increase of reflectivity and the effective resolution (i.e. elimination of the pixel crosstalk, to get the sharp phase transitions in the flybacks).

In the literature there are many types of wavelength selective switching devices with new functionality. There are some reports of WSS operating beyond the C+L bands that use special optical amplifiers to match the spectral bandwidth of the WSS to expand fiber capacity [236]. WSS with ports of 100 have been proposed using LCOS panels with more pixels and a 2D arrangement of ports [237]. Wavelength selective cross connects that can arbitrary switch any wavelength from any of the M input ports to any of the N output ports [238–242] potentially have the ability to greatly simplify the number of devices in a ROADM node. Planar light wave circuits have been added to the front optics to add complex functionality [239, 243, 244]. Multiplane light conversion devices have been added inside the front optics to produce beams that are rectangular on the LCOS to optimize switching capacity of the LCOS [245] potentially doubling the number of ports a WSS can support.

Further telecommunication applications with LCOS SLMs comprise space- and mode-division multiplexing [246], quantum key distribution for secure communication [247, 248], turbulence compensation by free-space communications [249].

3.3. Laser material processing

LCOS-Technology is applied in laser material processing as a tool for holographic light shaping, which is industrial application of the structured light approach, discussed above. In this large field of material processing applications, the LCOS SLM is used to aim for various benefits. Mainly it is used to increase the productivity of a process and the quality of the resulting product.

 figure: Fig. 28

Fig. 28 The first row shows the intensity distribution shaped by an LCOS SLM which is used in structuring the surface of metal depicted in the second row [250]. The presence of speckle is clearly visible in the rectangular and triangular shapes. Since the powerful ultrashort pulsed laser sources are available [251] and are ready for the market, the performance bottleneck is currently the distribution of the energy on the material to be processed. Two basic approaches can be found to use more of the available power without running into bad process results e.g. heat accumulation and incubation [252]. First solution is to spread the laser power even faster using new scanning technology, e.g. polygon scanners and piezo scanners, while the standard tools like galvanometer scanners are by far too slow. The other way pursued by researchers and engineers is to split up into multiple beamlets or distribute the power homogeneously over a large area. To distribute the intensity dynamically, several technologies are investigated, e.g. deformable mirrors [253], acousto-optic beam shaping [254] and most frequently LCOS SLM [255]. These new technologies are combined with established systems.

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Here we consider only the LCOS-based processing with holographic light shaping. When employing an LCOS SLM for material processing these tools have to guarantee successful operation at some tens or even hundreds Watt of laser power at infrared wavelength of 1μm. Here an increase of the laser induced damage threshold (LIDT) of these devices over the last few years can be seen. While a safe operation at maximum 2W/cm2 was guaranteed by LCOS microdisplay vendors for projection applications in the past, now water cooled products can handle from 50W to more than 200W/cm2 [52, 256]. Having solved this, the LCOS SLM can be applied to use higher laser power and also to investigate how to improve the quality of the modified material by a more homogeneous ablation, morphology adjustment and damage size. This is achieved by idle intensity distributions, adaption of the local polarization and aberration correction. All three aspects will be discussed in the following.

 figure: Fig. 29

Fig. 29 (a) Multi-spot structuring to avoid speckle [257] (b) quality of the generated structure dependent on the amount of alternative holograms [254] (c,d) well and surface morphology adjustment by polarisation shaping [13, 258]. Adapted with permission from OSA.

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In 2007 Sanner et al. presented the first-time holographic laser beam shaping using an LCOS SLM in material processing [250]. In their publication they demonstrated spatial ablation of basic geometric shapes on metal shown in Fig. 28. Here one of the major problems using holographic laser beam shaping can be seen easily at the rectangle or triangle. Strong speckle effect occurs, because only the amplitude in the focal plane is taken care of and the phase has a random character. To guarantee a smooth structure, the effect of speckles must be avoided. A quite simple way is to generate the desired shape by multi-spot ablation. In [257] the authors suggest a stitching of the aimed shape by several consecutive multi-spot distributions, where each spot is spatially separated in order not to interfere with a nearby spot. When all holograms are imaged at the LCOS SLM the superimposed intensity and hence the result is the desired shape, compare Fig. 29(a).

Another way is presented by Glueckstad, who introduced the so-called generalized phase contrast (GPC) method [259]. Here the desired intensity distribution is displayed at the LCOS SLM. This results in a phase modification of the coherent laser beam. To convert this into an intensity distribution, the modified beam is interfered with a reference beam. By interference of both beams the phase information is transferred into an intensity distribution. The elegance of GPC is the simplicity of this method. The reference wave is generated using the non-modified part of the beam (mostly the zero-order) which is shifted by a phase plate (similar as in usual phase contrast method, well-known from microscopy). Another advantage is that the SLM plane and the pattern plane are optically conjugated (in contrast to usual Fourier relation), so the dispersion effects are not so strong even when using light sources with broader spectrum. Unfortunately, the phase plate itself is exposed by a high intensity when doing material processing. This makes the design and the choice of the material for the phase plate very challenging, which limits the applicability of GPC in material processing.

Chang et al. demonstrated a holographic laser beam shaping and preventing the effect of speckle to generate a homogeneous intensity distribution by amplitude and phase control [260]. Here the intensity contrast in the focal plane will be reduced and a higher noise is accepted. That allows for a homogeneous distribution with constant amplitude and phase, but also results in a lower efficient processing [261].

Currently the most promising approach is to use alternating holograms which all lead to the same desired shape of the intensity distribution but with different speckle distribution. This is possible due to the large space of solutions of the hologram calculation with an identical intensity distribution [254]. Recently Haefner et al. showed, that less than 100 alternating holograms are necessary to generate homogeneous structures on stainless steel Fig. 29(b). Other approach suggests to shift the same hologram spatially, which allows to reduce hologram calculations [262]. These methods allow for holographic laser beam shaping in material processing with high efficiency, but due to the low switching rate of the available LCOS SLMs the holograms can not be changed for each laser pulse. It means the processing time is set by the cycle of all alternating holograms being displayed. That makes faster LCOS devices necessary. Neverthless the commercial applications for laser marking based on phase-modulating LCOS were reported [263, 264].

The second aspect where LCOS SLMs are applied is the adaption of the local polarisation of the processing focus. It was found in 1965 that periodic surface structures were organized by the polarisation of the incident laser light [265] when structuring the surface of some material. The latest investigations and applications of these laser induced periodic surface structures (LIPSS) are reviewed in the article by Mueller et al. [266]. They report of adjusting the reflectivity, the wettability and the friction and thus the wear of the structured material in tribological systems (surface functionalization). While the polarisation and therefore the orientation of the LIPSS is static in these investigations, Jin et al. and Hasegawa et al. use LCOS SLM technology to create dynamic and arbitrary polarisation [13, 258]. This adds another degree of freedom in the appearance of LIPSS and is used to better mimic the surface functionality of the nature, compare Fig. 29(c) and (d).

 figure: Fig. 30

Fig. 30 Structuring of diamond is successful when the spherical aberration (SA) is corrected [267]. Adapted with permission from OSA.

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The third aspect which is investigated by the use of LCOS SLM in material processing is in-volume structuring. Here Booth and Jesacher presented in 2010 the importance of aberration correction when structuring in the volume of transparent material [267]. They demonstrated successfully structuring of diamond which is challenging due to its high refractive index resulting in strong aberrations. Figure 30 shows their results: structuring of a 3D helix without aberration correction is unsuccessful, even a higher pulse energy does not result in the desired structure. When the aberrations are compensated in advance using an LCOS SLM, the helical structure is generated over the entire depth with a constant damage size. This finding is used to mark diamonds with a small defined structure or to write optical waveguides into transparent material to generate optical logic circuits [268, 269].

3.4. Summary and outlook on LCOS applications

The whole variety of applications of phase-modulating LCOS technology far exceeds the scope and the volume of this work. Since almost in every LCOS application the light is structured, we provided a general review on this topic. This was followed by two selected industrial application fields, indeed both of them are using structured light. While the applications, which are currently used commercially (e.g. WSS-ROADM or laser marking) are implying scalar structuring, the emerging applications are tending to use vectorial fields.

4. Concluding remarks

LCOS technology is experiencing these days a revival, in form of phase-modulating SLMs. This is driven by industrial and scientific topics, where LCOS is able to create significantly higher value as phase modulator, also in commercial sense. These applications impose challenging requirements, particularly on resolution, laser induced damage threshold and temporal performance, however they provide also great opportunities for further technological development of LCOS technology.

Funding

H2020 Marie Skłodowska-Curie Actions, Marie Curie Fellowship (675745 [NOLOSS]). German Research Foundation (DFG) grant SCHM 2115/67-1.

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2019 (3)

T. Bartlett, B. McDonald, and J. Hall, “Adapting Texas Instruments DLP technology to demonstrate a phase spatial light modulator,” Proc. SPIE 10932, 109320S (2019).

J. Pupeikis, N. Bigler, S. Hrisafov, C. R. Phillips, and U. Keller, “Programmable pulse shaping for time-gated amplifiers,” Opt. Express 27, 175–184 (2019).
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P.-J. Chen, P. Engel, G. Lazarev, A. Mazur, and P. Urbach, “Design, implementation, and study of the high-resolution high-efficiency liquid crystal on silicon spatial light modulator for the telecommunication application in the short-wave infraredspectral band,” Proc.SPIE 10941, 109410E (2019).

2018 (20)

Y. Huang, E. Liao, R. Chen, and S.-T. Wu, “Liquid-crystal-on-silicon for augmented reality displays,” Appl. Sci. 8, 2366 (2018).
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D. Y. Alsaka, Ç. Arpali, and S. A. Arpali, “A comparison of iterative Fourier transform algorithms for image quality estimation,” Opt. Rev. 25, 625–637 (2018).
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M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photons: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17111–17146 (2018).
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N. Bhebhe, P. A. Williams, C. Rosales-Guzmán, V. Rodriguez-Fajardo, and A. Forbes, “A vector holographic optical trap,” Sci. Reports 8, 17387 (2018).
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B. Ndagano, I. Nape, M. A. Cox, C. Rosales-Guzmán, and A. Forbes, “Creation and detection of vector vortex modes for classical and quantum communication,” J. Light. Technol. 36, 292–301 (2018).
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J. Chen, C. Wan, and Q. Zhan, “Vectorial optical fields: recent advances and future prospects,” Sci. Bull. 63, 54–74 (2018).
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X.-L. Wang, Y.-H. Luo, H.-L. Huang, M.-C. Chen, Z.-E. Su, C. Liu, C. Chen, W. Li, Y.-Q. Fang, X. Jiang, J. Zhang, L. Li, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “18-qubit entanglement with six photons' three degrees of freedom,” Phys. Rev. Lett. 120, 260502 (2018).
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D. Mikhaylov, T. Kiedrowski, and A. F. Lasagni, “Heat accumulation effects during ultrashort pulse laser ablation with spatially shaped beams,” J. Laser Micro Nanoeng. 13, 95–99 (2018).

C. Rosales-Guzmán, B. Ndagano, and A. Forbes, “A review of complex vector light fields and their applications,” J. Opt. 20, 123001 (2018).
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T. Haefner, J. Strauss, C. Roider, J. Heberle, and M. Schmidt, “Tailored laser beam shaping for efficient and accurate microstructuring,” Appl. Phys. A 124, 111 (2018).
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S. Yan, Y. Liu, R. Wang, H. Zhang, and Z. Liu, “P-9.10: Design and fabrication of micro-lens array based on micro-LED projector,” SID Symp. Dig. Tech. Pap. 49, 688–691 (2018).
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X. Wang, Z. Nie, Y. Liang, J. Wang, T. Li, and B. Jia, “Recent advances on optical vortex generation,” Nanophotonics 7, 1533–1556 (2018).
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P. J. Winzer, D. T. Neilson, and A. R. Chraplyvy, “Fiber-optic transmission and networking: the previous 20 and the next 20 years,” Opt. Express 26, 24190–24239 (2018).
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B. Sun, P. S. Salter, C. Roider, A. Jesacher, J. Strauss, J. Heberle, M. Schmidt, and M. J. Booth, “Four-dimensional light shaping: manipulating ultrafast spatiotemporal foci in space and time,” Light Sci. Appl. 7, 17117 (2018).
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M. Erhard, M. Malik, M. Krenn, and A. Zeilinger, “Experimental Greenberger–Horne–Zeilinger entanglement beyond qubits,” Nat. Photon. 12, 759–764 (2018).
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H.-M. P. Chen, J.-P. Yang, H.-T. Yen, Z.-N. Hsu, Y. Huang, and S.-T. Wu, “Pursuing high quality phase-only liquid crystal on silicon (LCoS) devices,” Appl. Sci. 8, 2323 (2018).
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N. Bhebhe, C. Rosales-Guzmán, and A. Forbes, “Classical and quantum analysis of propagation invariant vector flat-top beams,” Appl. Opt. 57, 5451–5458 (2018).
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R. Hashimoto, S. Yamaoka, Y. Mori, H. Hasegawa, K.-I. Sato, K. Yamaguchi, K. Seno, and K. Suzuki, “First demonstration of subsystem-modular optical cross-connect using single-module 6× 6 wavelength-selective switch,” J. Light. Technol. 36, 1435–1442 (2018).
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P.-A. Moreau, E. Toninelli, T. Gregory, and M. J. Padgett, “Ghost imaging using optical correlations,” Laser Photonics Rev. 12, 1700143 (2018).
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A. K. Abeeluck, A. Iverson, H. Goetz, and E. Passon, “58–2: Invited paper: High-performance displays for wearable and HUD applications,” SID Symp. Dig. Tech. Pap. 49, 768–771 (2018).
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2017 (18)

A. Forbes, “Controlling light’s helicity at the source: orbital angular momentum states from lasers,” Philos. Transactions Royal Soc. A 375, 20150436 (2017).
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Z. Qu and I. B. Djordjevic, “High-speed free-space optical continuous-variable quantum key distribution enabled by three-dimensional multiplexing,” Opt. Express 25, 7919–7928 (2017).
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G. Lazarev, F. Kerbstadt, and J. Luberek, “High-resolution high-reflective LCOS spatial light modulator for beam manipulation beyond visible spectrum,” Proc. SPIE 10090, 100900T (2017).
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Y. Zhang, M. Agnew, T. Roger, F. S. Roux, T. Konrad, D. Faccio, J. Leach, and A. Forbes, “Simultaneous entanglement swapping of multiple orbital angular momentum states of light,” Nat. Commun. 8, 632 (2017).
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J. Wang, “Data information transfer using complex optical fields: a review and perspective,” Chin. Opt. Lett. 15, 030005 (2017).
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M. J. Padgett, “Orbital angular momentum 25 years on,” Opt. Express 25, 11265–11274 (2017).
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C. Rosales-Guzmán, N. Bhebhe, N. Mahonisi, and A. Forbes, “Multiplexing 200 spatial modes with a single hologram,” J. Opt. 19, 113501 (2017).
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S. McDermott, P. Li, G. Williams, and A. Maiden, “Characterizing a spatial light modulator using ptychography,” Opt. Lett. 42, 371–374 (2017).
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M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero Caballero, “LCoS SLM study and its application in wavelength selective switch,” Photonics 4, 22 (2017).
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P. J. Winzer and D. T. Neilson, “From scaling disparities to integrated parallelism: A decathlon for a decade,” J. Light. Technol. 35, 1099–1115 (2017).
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G. Lazarev, S. Bonifer, P. Engel, D. Hoehne, and G. Notni, “High-resolution LCOS microdisplay with sub-kHz frame rate for high performance, high precision 3D sensor,” Proc.vSPIE 10335, 103351B (2017).

T. Haefner, J. Heberle, D. Holder, and M. Schmidt, “Speckle reduction techniques in holographic beam shaping for accurate and efficient picosecond laser structuring,” J. Laser Appl. 29, 022205 (2017).
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N. Radwell, R. F. Offer, A. Selyem, and S. Franke-Arnold, “Optimisation of arbitrary light beam generation with spatial light modulators,” J. Opt. 19, 095605 (2017).
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C. Rosales-Guzmán, N. Bhebhe, and A. Forbes, “Simultaneous generation of multiple vector beams on a single SLM,” Opt. Express 25, 25697–25706 (2017).
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C. Alpmann, C. Schlickriede, E. Otte, and C. Denz, “Dynamic modulation of Poincaré beams,” Sci. Reports 7, 8076 (2017).
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D. M. Marom, P. D. Colbourne, A. Derrico, N. K. Fontaine, Y. Ikuma, R. Proietti, L. Zong, J. M. Rivas-Moscoso, and I. Tomkos, “Survey of photonic switching architectures and technologies in support of spatially and spectrally flexible optical networking,” IEEE/OSA J. Opt. Commun. Netw. 9, 1–26 (2017).
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M. Krenn, M. Malik, M. Erhard, and A. Zeilinger, “Orbital angular momentum of photons and the entanglement of Laguerre–Gaussian modes,” Philos. Transactions Royal Soc. A 375, 20150442 (2017).
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G. Lazarev, F. Gaedeke, and J. Luberek, “Ultrahigh-resolution phase-only LCOS spatial light modulator,” Proc.vSPIE 10125, 101250M (2017).

2016 (18)

G. Lazarev, “Optimization of the liquid crystal on silicon technology for laser microprocessing applications,” Phys. Procedia 83, 1153 – 1159 (2016).
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D. Gossman, B. Perez-Garcia, R. I. Hernandez-Aranda, and A. Forbes, “Optical interference with digital holograms,” Am. J. Phys. 84, 508–516 (2016).
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B. Ndagano, H. Sroor, M. McLaren, C. Rosales-Guzmán, and A. Forbes, “Beam quality measure for vector beams,” Opt. Lett. 41, 3407–3410 (2016).
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B. Sephton, A. Dudley, and A. Forbes, “Revealing the radial modes in vortex beams,” Appl. Opt. 55, 7830–7835 (2016).
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Y. Zhang, S. Prabhakar, C. Rosales-Guzmán, F. S. Roux, E. Karimi, and A. Forbes, “Hong-Ou-Mandel interference of entangled Hermite-Gauss modes,” Phys. Rev. A 94, 033855 (2016).
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M. Malik, M. Erhard, M. Huber, M. Krenn, R. Fickler, and A. Zeilinger, “Multi-photon entanglement in high dimensions,” Nat. Photon. 10, 248–252 (2016).
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A. Forbes, A. Dudley, and M. McLaren, “Creation and detection of optical modes with spatial light modulators,” Adv. Opt. Photonics 8, 200–227 (2016).
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J. Wang, “Advances in communications using optical vortices,” Photonics Res. 4, B14–B28 (2016).
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V. Lopez, A. Gonzalez-Vega, A. Aguilar, J. Landgrave, and J. Garcia-Marquez, “Non-uniform spatial response of the LCoS spatial light modulator,” Opt. Commun. 366, 419 – 424 (2016).
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H. Rubinsztein-Dunlop, A. Forbes, M. V. Berry, M. R. Dennis, D. L. Andrews, M. Mansuripur, C. Denz, C. Alpmann, P. Banzer, T. Bauer, E. Karimi, L. Marrucci, M. Padgett, M. Ritsch-Marte, N. M. Litchinitser, N. P. Bigelow, C. Rosales-Guzmán, A. Belmonte, J. P. Torres, T. W. Neely, M. Baker, R. Gordon, A. B. Stilgoe, J. Romero, A. G. White, R. Fickler, A. E. Willner, G. Xie, B. McMorran, and A. M. Weiner, “Roadmap on structured light,” J. Opt. 19, 013001 (2016).
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H. Yang, B. Robertson, P. Wilkinson, and D. Chu, “Small phase pattern 2d beam steering and a single LCOS design of 40 1× 12 stacked wavelength selective switches,” Opt. Express 24, 12240–12253 (2016).
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T. W. Clark, R. F. Offer, S. Franke-Arnold, A. S. Arnold, and N. Radwell, “Comparison of beam generation techniques using a phase only spatial light modulator,” Opt. Express 24, 6249–6264 (2016).
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E. Otte, C. Alpmann, and C. Denz, “Higher-order polarization singularitites in tailored vector beams,” J. Opt. 18, 074012 (2016).
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Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach, and A. Forbes, “Engineering two-photon high-dimensional states through quantum interference,” Sci. Adv. 2, e1501165 (2016).
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X. Sun, I. B. Djordjevic, and M. A. Neifeld, “Multiple spatial modes based QKD over marine free-space optical channels in the presence of atmospheric turbulence,” Opt. Express 24, 27663–27673 (2016).
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F. A. Mueller, C. Kunz, and S. Graef, “Bio-inspired functional surfaces based on laser-induced periodic surface structures,” Materials 9, 476 (2016).
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M. J. Escuti, J. Kim, and M. W. Kudenov, “Controlling light with geometric-phase holograms,” Opt. Photonics News 27, 22–29 (2016).
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S. Hasegawa and Y. Hayasaki, “Holographic femtosecond laser manipulation for advanced material processing,” Adv. Opt. Technol. 5, 39–54 (2016).

2015 (10)

H. Molsen, “3D optical metrology and super-resolution microscopy with structured illumination based on QXGA (2048x1536) resolution,” Proc.SPIE 9525, 952506 (2015).

I. Moreno, J. A. Davis, M. M. Sánchez-López, K. Badham, and D. M. Cottrell, “Nondiffracting Bessel beams with polarization state that varies with propagation distance,” Opt. Lett. 40, 5451–5454 (2015).
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A. E. Willner, H. Huang, Y. Yan, Y. Ren, N. Ahmed, G. Xie, C. Bao, L. Li, Y. Cao, Z. Zhao, J. Wang, M. P. J. Lavery, M. Tur, S. Ramachandran, A. F. Molisch, N. Ashrafi, and S. Ashrafi, “Optical communications using orbital angular momentum beams,”Adv. Opt. Photonics 7, 66–106 (2015).
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C. Chang, J. Xia, L. Yang, W. Lei, Z. Yang, and J. Chen, “Speckle-suppressed phase-only holographic three-dimensional display based on double-constraint Gerchberg–Saxton algorithm,” Appl. Opt. 54, 6994–7001 (2015).
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A. Marquez, F. Martinez, S. Gallego, M. Ortuno, J. Frances, A. Belendez, and I. Pascual, “Static and dynamic effects of flicker in phase multilevel elements on LCoS devices,” Proc. SPIE 9598, 95980C (2015).

A. Andreev, T. Andreeva, I. Kompanets, R. Starikov, and N. Zalyapin, “Novel FLC- materials open new possibilities for FLCoS based microdisplays and video projectors,” Phys. Procedia 73, 87 – 94 (2015).
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D. Spangenberg, P. Neethling, E. Rohwer, M. H. Brügmann, and T. Feurer, “Time-domain ptychography,” Phys. Rev. A 91, 021803 (2015).
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T. Lu, M. Pivnenko, B. Robertson, and D. Chu, “Pixel-level fringing-effect model to describe the phase profile and diffraction efficiency of a liquid crystal on silicon device,” Appl. Opt. 54, 5903–5910 (2015).
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F. J. Martínez, A. Márquez, S. Gallego, M. Ortuno, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54, 1379–1386 (2015).
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L. Zong, H. Zhao, Z. Feng, and Y. Yan, “8 × 8 flexible wavelength cross-connect for CDC ROADM application,” IEEE Photonics Technol. Lett. 27, 2603–2606 (2015).
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2014 (7)

D. Spangenberg, A. Dudley, P. H. Neethling, E. G. Rohwer, and A. Forbes, “White light wavefront control with a spatial light modulator,” Opt. Express 22, 13870–13879 (2014).
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F. J. Martínez, A. Márquez, S. Gallego, M. Ortuno, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22, 15064–15074 (2014).
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Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light. Sci. Appl. 3, e213 (2014).
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J. L. Martínez, I. Moreno, M. del Mar Sánchez-López, A. Vargas, and P. García-Martínez, “Analysis of multiple internal reflections in a parallel aligned liquid crystal on silicon SLM,” Opt. Express 22, 25866–25879 (2014).
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A. Dudley, G. Milione, R. R. Alfano, and A. Forbes, “All-digital wavefront sensing for structured light beams,” Opt. Express 22, 14031–14040 (2014).
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F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39, 1011–1014 (2014).
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B. Neuenschwander, B. Jaeggi, M. Schmid, and G. Hennig, “Surface structuring with ultra-short laser pulses: Basics, limitations and needs for high throughput,” Phys. Procedia 56, 1047 – 1058 (2014).
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2013 (15)

J. Pavlin, N. Vaupotič, and M. Čepič, “Liquid crystals: a new topic in physics for undergraduates,” Eur. J. Phys. 34, 745–761 (2013).
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S. Ngcobo, I. Litvin, L. Burger, and A. Forbes, “A digital laser for on-demand laser modes,” Nat. Commun. 4, 2289 (2013).
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M. Krenn, R. Fickler, M. Huber, R. Lapkiewicz, W. Plick, S. Ramelow, and A. Zeilinger, “Entangled singularity patterns of photons in Ince-Gauss modes,” Phys. Rev. A 87, 012326 (2013).
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G. Thalhammer, R. W. Bowman, G. D. Love, M. J. Padgett, and M. Ritsch-Marte, “Speeding up liquid crystal SLMs using overdrive with phase change reduction,” Opt. Express 21, 1779–1797 (2013).
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C. Schulze, A. Dudley, D. Flamm, M. Duparré, and A. Forbes, “Measurement of the orbital angular momentum density of light by modal decomposition,” New J. Phys. 15, 073025 (2013).
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Y. Jin, O. J. Allegre, W. Perrie, K. Abrams, J. Ouyang, E. Fearon, S. P. Edwardson, and G. Dearden, “Dynamic modulation of spatially structured polarization fields for real-time control of ultrafast laser-material interactions,” Opt. Express 21, 25333–25343 (2013).
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W. Cheng, W. Han, and Q. Zhan, “Compact flattop laser beam shaper using vectorial vortex,” Appl. Opt. 52, 4608–4612 (2013).
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W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21, 20692–20706 (2013).
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D. Flamm, C. Schulze, D. Naidoo, S. Schroter, A. Forbes, and M. Duparre, “All-digital holographic tool for mode excitation and analysis in optical fibers,” J. Light. Technol. 31, 1023–1032 (2013).
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D. Engström, M. Persson, J. Bengtsson, and M. Goksör, “Calibration of spatial light modulators suffering from spatially varying phase response,” Opt. Express 21, 16086–16103 (2013).
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J.-P. Negel, A. Voss, M. Abdou Ahmed, D. Bauer, D. Sutter, A. Killi, and T. Graf, “1.1 kW average output power from a thin-disk multipass amplifier for ultrashort laser pulses,” Opt. Lett. 38, 5442–5445 (2013).
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H. H. Cheng, A. K. Bhowmik, and P. J. Bos, “Fast-response liquid crystal variable optical retarder and multilevel attenuator,” Opt. Eng. 52, 107105 (2013).
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S. Reichelt, “Spatially resolved phase-response calibration of liquid-crystal-based spatial light modulators,” Appl. Opt. 52, 2610–2618 (2013).
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A. Dudley, Y. Li, T. Mhlanga, M. Escuti, and A. Forbes, “Generating and measuring nondiffracting vector Bessel beams,” Opt. Lett. 38, 3429–3432 (2013).
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E. Pozhidaev, A. Kiselev, A. Srivastava, V. Chigrinov, H. Kwok, and M. Minchenko, “Orientational Kerr effect and phase modulation of light in deformed-helix ferroelectric liquid crystals with subwavelength pitch,” Phys. Rev. E 87, 052502 (2013).
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2012 (12)

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photon. 6, 283 (2012).
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R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338, 640–643 (2012).
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I. A. Litvin, A. Dudley, F. S. Roux, and A. Forbes, “Azimuthal decomposition with digital holograms,” Opt. Express 20, 10996–11004 (2012).
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M. Salsi, C. Koebele, D. Sperti, P. Tran, H. Mardoyan, P. Brindel, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, and L. Provost, “Mode-division multiplexing of 2 ×100 Gb/s channels using an LCOS-based spatial modulator,” J. Light. Technol. 30, 618–623 (2012).
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D. Huang, H. Timmers, A. Roberts, N. Shivaram, and A. S. Sandhu, “A low-cost spatial light modulator for use in undergraduate and graduate optics labs,” Am. J. Phys. 80, 211–215 (2012).
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A. Stadler, “Transparent conducting oxides - an up-to-date overview,” Materials 5, 661–683 (2012).
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C. Lingel, T. Haist, and W. Osten, “Examination and optimizing of a liquid crystal display used as spatial light modulator concerning the fringing field effect,” Proc. SPIE 8490, 84900H (2012).
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C. Schulze, D. Naidoo, D. Flamm, O. A. Schmidt, A. Forbes, and M. Duparré, “Wavefront reconstruction by modal decomposition,” Opt. Express 20, 19714–19725 (2012).
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D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré, “Mode analysis with a spatial light modulator as a correlation filter,” Opt. Lett. 37, 2478–2480 (2012).
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O. Gerstel, M. Jinno, A. Lord, and S. B. Yoo, “Elastic optical networking: A new dawn for the optical layer?” IEEE Commun. Mag. 50, s12–s20 (2012).
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M. McLaren, M. Agnew, J. Leach, F. S. Roux, M. J. Padgett, R. W. Boyd, and A. Forbes, “Entangled Bessel-Gaussian beams,” Opt. Express 20, 23589–23597 (2012).
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I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20, 364–376 (2012).
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2011 (9)

A. M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” Opt. Commun. 284, 3669–3692 (2011).
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O. Parri, G. Smith, R. Harding, H.-J. Yoon, I. Gardiner, J. Sargent, and K. Skjonnemand, “Patterned retarder films using reactive mesogen technology,” Proc. SPIE 7956, 79560W (2011).
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J. P Parry, R. J Beck, J. D Shephard, and D. Hand, “Application of a liquid crystal spatial light modulator to laser marking,” Appl. Opt. 50, 1779–1785 (2011).
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A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, “Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities,” Nat. Phys. 7, 677–680 (2011).
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C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5, 81–101 (2011).
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P. J. M. Vanbrabant, J. Beeckman, K. Neyts, R. James, and F. A. Fernandez, “Optical analysis of small pixel liquid crystal microdisplays,” J. Disp. Technol. 7, 156–161 (2011).
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I. A. Litvin, A. Dudley, and A. Forbes, “Poynting vector and orbital angular momentum density of superpositions of Bessel beams,” Opt. Express 19, 16760–16771 (2011).
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L. Lobato, A. Lizana, A. Márquez, I. Moreno, C. Iemmi, J. Campos, and M. Yzuel, “Characterization of the anamorphic and frequency dependent phenomenon in liquid crystal on silicon displays,” J. Europ. Opt. Soc. Rap. Public. 6, 11012s (2011).
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M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photon. 5, 343–348 (2011).
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2010 (10)

J. Leach, B. Jack, J. Romero, A. K. Jha, A. M. Yao, S. Franke-Arnold, D. G. Ireland, R. W. Boyd, S. M. Barnett, and M. J. Padgett, “Quantum correlations in optical angle–orbital angular momentum variables,” Science 329, 662–665 (2010).
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R. Verma, M. Swami, S. Manhas, and P. Gupta, “Mueller matrix-based optimization of reflective type twisted nematic liquid crystal SLM at oblique incidences,” Opt. Commun. 283, 2580 – 2587 (2010).
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P. J. M. Vanbrabant, J. Beeckman, K. Neyts, E. Willman, and F. A. Fernandez, “Diffraction and fringing field effects in small pixel liquid crystal devices with homeotropic alignment,” J. Appl. Phys. 108, 083104 (2010).
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C. López-Mariscal and K. Helmerson, “Shaped nondiffracting beams,” Opt. Lett. 35, 1215–1217 (2010).
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G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
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H. Ma, Z. Liu, P. Zhou, X. Wang, Y. Ma, and X. Xu, “Generation of flat-top beam with phase-only liquid crystal spatial light modulators,” J. Opt. 12, 045704 (2010).
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T. A. Strasser and J. L. Wagener, “Wavelength-selective switches for ROADM applications,” IEEE J. selected topics Quantum Electron. 16, 1150–1157 (2010).
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C. Brif, R. Chakrabarti, and H. Rabitz, “Control of quantum phenomena: past, present and future,” New J. Phys. 12, 075008 (2010).
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A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Experss 18, 21090–21099 (2010).
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2009 (10)

R. Vasilyeu, A. Dudley, N. Khilo, and A. Forbes, “Generating superpositions of higher-order Bessel beams,” Opt. Express 17, 23389–23395 (2009).
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J. Beeckman, R. James, F. Fernández, W. D. Cort, P. J. M. Vanbrabant, and K. Neyts, “Calculation of fully anisotropic liquid crystal waveguide modes,” J. Light. Technol. 27, 3812–3819 (2009).
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G. Lima, A. Vargas, L. Neves, R. Guzmán, and C. Saavedra, “Manipulating spatial qudit states with programmable optical devices,” Opt. Express 17, 10688–10696 (2009).
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G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17, 12546–12554 (2009).
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C. Kohler, F. Zhang, and W. Osten, “Characterization of a spatial light modulator and its application in phase retrieval,” Appl. Opt. 48, 4003–4008 (2009).
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P. J. M. Vanbrabant, J. Beeckman, K. Neyts, R. James, and F. A. Fernandez, “A finite element beam propagation method for simulation of liquid crystal devices,” Opt. Express 17, 10895–10909 (2009).
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J. Leach, B. Jack, J. Romero, M. Ritsch-Marte, R. W. Boyd, A. K. Jha, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces,” Opt. Express 17, 8287–8293 (2009).
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T. Ando, Y. Ohtake, N. Matsumoto, T. Inoue, and N. Fukuchi, “Mode purities of Laguerre–Gaussian beams generated via complex-amplitude modulation using phase-only spatial light modulators,” Opt. Lett. 34, 34–36 (2009).
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B. Jack, J. Leach, H. Ritsch, S. M. Barnett, M. J. Padgett, and S. Franke-Arnold, “Precise quantum tomography of photon pairs with entangled orbital angular momentum,” New J. Phys. 11, 103024 (2009).
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2008 (10)

M. Gruneisen, W. Miller, R. Dymale, and A. Sweiti, “Holographic generation of complex fields with spatial light modulators: Application to quantum key distribution,” Appl. Opt. 47, A32 (2008).
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J. Homa and K. Bala, “ROADM architectures and their enabling wss technology,” IEEE Commun. Mag. 46, 150–154 (2008).
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I. Moreno, A. Lizana, J. Campos, A. Márquez, C. Iemmi, and M. J. Yzuel, “Combined Mueller and Jones matrix method for the evaluation of the complex modulation in a liquid-crystal-on-silicon display,” Opt. Lett. 33, 627–629 (2008).
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A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Near-perfect hologram reconstruction with a spatial light modulator,” Opt. Express 16, 2597–2603 (2008).
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Z. Kuang, W. Perrie, J. Leach, M. Sharp, S. P. Edwardson, M. Padgett, G. Dearden, and K. G. Watkins, “High throughput diffractive multi-beam femtosecond laser processing using a spatial light modulator,” Appl. Surf. Sci. 255, 2284 – 2289 (2008).
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A. Lizana, I. Moreno, C. Iemmi, A. Márquez, J. Campos, and M. J. Yzuel, “Time-resolved Mueller matrix analysis of a liquid crystal on silicon display,” Appl. Opt. 47, 4267–4274 (2008).
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A. Jesacher, C. Maurer, A. Schwaighofer, S. Bernet, and M. Ritsch-Marte, “Full phase and amplitude control of holographic optical tweezers with high efficiency,” Opt. Express 16, 4479–4486 (2008).
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A. Márquez, I. Moreno, C. Iemmi, A. Lizana, J. Campos, and M. J. Yzuel, “Mueller-Stokes characterization and optimization of a liquid crystal on silicon display showing depolarization,” Opt. Express 16, 1669–1685(2008).
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P. Clemente, V. Durán, L. Martínez-León, V. Climent, E. Tajahuerce, and J. Lancis, “Use of polar decomposition of mueller matrices for optimizing the phase response of a liquid-crystal-on-silicon display,” Opt. Express 16, 1965–1974 (2008).
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A. Lizana, A. Marquez, I. Moreno, C. Iemmi, J. Campos, and M. Yzuel, “Wavelength dependence of polarimetric and phase-shift characterization of a liquid crystal on silicon display,” J. The Eur. Opt. Soc. Publ. 3, 08012 (2008).
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2007 (11)

V. Arrizon, U. Ruiz, R. Carrada, and L. a. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A 24, 3500–3507 (2007).
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E. Karimi, G. Zito, B. Piccirillo, L. Marrucci, and E. Santamato, “Hypergeometric-gaussian modes,” Opt. Lett. 32, 3053–3055 (2007).
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C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9, 78 (2007).
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Y. Ohtake, T. Ando, N. Fukuchi, N. Matsumoto, H. Ito, and T. Hara, “Universal generation of higher-order multiringed Laguerre-Gaussian beams by using a spatial light modulator,” Opt. Lett. 32, 1411–1413 (2007).
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E. Frumker and Y. Silberberg, “Phase and amplitude pulse shaping with two-dimensional phase-only spatial light modulators,” J. Opt. Soc. Am. B 24, 2940–2947 (2007).
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H. Zhang, J. Zhang, and L. Wu, “Evaluation of phase-only liquid crystal spatial light modulator for phase modulation performance using a Twyman–Green interferometer,” Meas. Sci. Technol. 18, 1724–1728 (2007).
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J. Otón, P. Ambs, M. S. Millán, and E. Pérez-Cabré, “Multipoint phase calibration for improved compensation of inherent wavefront distortion in parallel aligned liquid crystal on silicon displays,” Appl. Opt. 46, 5667–5679 (2007).
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J. B. Bentley, J. A. Davis, M. A. Bandres, and J. C. Gutiérrez-Vega, “Generation of helical Ince-Gaussian beams with a liquid-crystal display,” Opt. Lett. 31, 649–651 (2006).
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J. E. Wolfe and R. A. Chipman, “Polarimetric characterization of liquid-crystal-on-silicon panels,” Appl. Opt. 45, 1688–1703 (2006).
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E. Yao, S. Franke-Arnold, J. Courtial, M. J. Padgett, and S. M. Barnett, “Observation of quantum entanglement using spatial light modulators,” Opt. Express 14, 13089–13094 (2006).
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Y. Song and Z. Ling, “A new driving method for LCoS with frame buffer pixels,” Proc. SPIE 6030, 60300H (2006).
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J. L. Sanford and H. V. Goetz, “Late-news paper: Small digital 1080p LCOS for TriMa technology,” SID Symp. Dig. Tech. Pap. 37, 1665–1668 (2006).
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R. James, M. C. Gardner, F. A. Fernández, and S. E. Day, “3d modelling of high resolution devices,” Mol. Cryst. Liq. Cryst. 450, 105–118 (2006).
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2005 (3)

K.-H. F. Chiang, S.-H. Chen, and S.-T. Wu, “Diffraction effect on high-resolution liquid-crystal-on-silicon devices,” Jpn. J. Appl. Phys. 44, 3068–3072 (2005).
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B. Zhang, H.-S. Kwok, and H.-C. Huang, “Three-dimensional optical modeling and optimizations of color filter liquid-crystal-on-silicon microdisplays,” J. Appl. Phys. 98, 123103 (2005).
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K.-H. F. Chiang, S.-H. Chen, and S.-T. Wu, “Fringing-field effects on high-resolution liquid crystal microdisplays,” J. Disp. Technol. 1, 304–313 (2005).
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2004 (9)

X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43, 6400–6406 (2004).
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X. Wang, B. Wang, J. J. Pouch, F. A. Miranda, J. E. Anderson, and P. J. Bos, “Performance evaluation of a liquid-crystal-on-silicon spatial light modulator,” Opt. Eng. 43, 2769–2774 (2004).
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S. Lee, J. Morizio, and K. M. Johnson, “Novel frame buffer pixel circuits for liquid-crystal-on-silicon microdisplays,” IEEE J. Solid-State Circuits 39, 132–139 (2004).
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H. D. Smet, J. V. den Steen, and D. Cuypers, “Electrical model of a liquid crystal pixel with dynamic, voltage history-dependent capacitance value,” Liq. Cryst. 31, 705–711 (2004).
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H. Dai, K. X. Y. Liu, X. Wang, and J. Liu, “Characteristics of LCoS phase-only spatial light modulator and its applications,” Opt. Commun. 238, 269 – 276 (2004).
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M. Lu, “Liquid crystal orientation induced by Van der Waals interaction,” Jpn. J. Appl. Phys. 43, 8156–8160 (2004).
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G. F. Barrick, P. J. Bos, C. M. Titus, and B. K. Winker, “Computing the liquid crystal director field in optical phased arrays,” Opt. Eng. 43, 924–932 (2004).
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B. Apter, U. Efron, and E. Bahat-Treidel, “On the fringing-field effect in liquid-crystal beam-steering devices,” Appl. Opt. 43, 11–19 (2004).
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2002 (7)

H. D. Smet, D. Cuypers, A. V. Calster, J. V. den Steen, and G. V. Doorselaer, “Design, fabrication and evaluation of a high-performance xga van-lcos microdisplay,” Displays 23, 89 – 98 (2002).
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2000 (3)

H.-C. Huang, D.-D. Huang, and J. Chen, “Two-dimensional optical analysis of small pixels in reflective silicon microdisplay,” Jpn. J. Appl. Phys. 39, 485–489 (2000).
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