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An all-dielectric, subwavelength grated based metal-oxide nano-hair structure for optical vortex beam generation has been presented in the paper. The nano-hair structure fabricated with alternating layers of alumina/hafnia on a fused silica substrate has a high diffraction efficiency of ~90% around the design wavelength, λo = 1.55 μm and is insensitive to the polarization of the incident optical beam. The phase in transmission of these devices are controlled by azimuthally varying the fill fraction of the subwavelength grating. Realization of phase optical elements in an all-dielectric platform, based on subwavelength gratings offering full 0-2π phase modulation, is important for miniaturization and integration of conventional refractive optical elements.
© 2015 Optical Society of America
1. Introduction
Diffraction gratings continue to play an important role in modern optics with applications ranging from polarizers, beam splitters, mode converters, holography, beam deflection, interferometry, to name a few [1]. Diffraction grating based elements or artificial dielectric elements have been shown to mimic the optical functionalities of conventional diffractive optical elements (DOEs) [2–5]. In order to control the propagation of light like a DOE with artificial dielectric elements, it is imperative to design devices that provide for both amplitude and phase modulation (between 0 and 2π) simultaneously. In addition to realizing the optical functionalities, artificial dielectric elements have been shown to have other interesting properties, such as being able to manipulate polarization [6], achromaticity [5], anti-reflective properties [7, 8], hydrophobicity [7], etc.
One of the DOEs that has attracted significant attention in the recent years for its unique properties is for generation of beams that carry orbital angular momentum (OAM), often referred to as optical vortices [9, 10]. The electric field distribution of an optical vortex function is mathematically represented as E ~exp (j · m · φ), where φ is the azimuthal angle distribution around the center of beam propagation axis and, m is the topological charge of the optical vortex [9, 10]. Since an optical vortex beam carries an angular momentum of (m ) per photon, it has been proposed that these beams are capable of providing another multiplexing dimension to increasing the data capacity of existing optical communication systems [11, 12]. OAM carrying beams have been developed for other applications including micromanipulation [13], optical trapping [14], and quantum entanglement [15].
Optical vortex beams can be generated using many techniques, such as by using spatial light modulators [16], and spiral phase plates [17]. More recently, grating based approaches have been used to generate OAM carrying beams [18–22]. Metasurfaces for OAM generation have gained a lot of interest because of their ability to achieve planar, compact elements with a single lithographic step (without a need for complex and precise alignment between the different layers), that will enable integration of these optical elements using micro-fabrication techniques. Many implementations of planar OAM generators have been realized, but suffer from the issue of poor efficiency when fabricated. Plasmonic metasurfaces suffer from limited efficiencies because of high intrinsic absorption present near the plasmonic resonances in the metal [18, 19], thus making them impractical for applications requiring high efficiencies in transmission. Dielectric metasurfaces have an advantage by offering a solution to the issue of losses encountered in plasmonics. High contrast grating based OAM generators were investigated in [20, 21]. Much of the efforts so far have been by using either plasmonic resonances in the metal or Mie resonances in dielectric materials. Designs based on non-resonant structures for OAM generation have not been explored in great detail due to the high aspect ratio requirements of these elements.
In this paper, subwavelength grating based multi-material, all-dielectric nano-hair structures will be introduced for successful OAM generation at λo = 1.55 μm with a high diffraction efficiency. Nano-hair geometry based optical element for cylindrical beam array generation in transmission was proposed in [23]. For the fabrication of these vortex elements, conformal deposition and etching has been utilized and an elegant way to achieve high aspect ratio gratings in fused silica has been described. The phase of the transmitted beam is manipulated by the nano-hair structures based on their width and spatial density. The phase is modulated by these structures in two different regions (above and below the substrate), thereby providing an additional degree of freedom in realizing DOEs [23, 24]. In addition, a graded index system has been created within each of the submicron sized nano-hairs that helps relax the aspect ratio requirement of the device and simultaneously provides a high efficiency in transmission.
2. Device design and analysis
The schematic of the proposed device is shown in Fig. 1. The metal-oxide nano-hair optical vortex is based on a simple, all-dielectric structure that can be fabricated with a relaxed process space; and the precision alignment, depths associated with the fabrication of a conventional DOEs are not required.
Fig. 1 Schematic of the proposed subwavelength grating based, metal-oxide OAM generating nano-hair structure. (a) Unit cell of the device showing the alternate material layers. (b) Overall morphology of the device showing the gradually changing fill fraction about the azimuth.
The necessary phase in transmission to mimic an optical vortex structure was obtained by modulating the fill fraction of subwavelength gratings azimuthally about the center of the device [Fig. 1(b)]. This is possible provided the periodicity of the grating is such that only the 0th order propagates in transmission at the design wavelength λo and all the other higher orders are evanescent. When this condition is satisfied, the effective refractive index of the grating structure can be obtained by effective medium theory [25]; which states that a subwavelength grating can be approximated as a homogenous layer having an effective refractive index. At λo = 1.55 μm, for a grating to be fully subwavelength when the substrate is fused silica (nFS = 1.4438) and the superstrate is air (nAir = 1.0), the grating period should be, Λ < (λo/nFS) or Λ < 1.073 μm. A grating period of Λ = 1.00 μm was chosen for the device implementation. To obtain a polarization insensitive response at normal incidence, a hexagonal grating geometry was chosen with the same grating periodicity. There are no closed form approximations available for estimating the accurate effective refractive index of 2D subwavelength gratings. Numerical methods based on rigorous electromagnetic routines are often employed to obtain the effective refractive index [26].
The optical performance of the device was analyzed using Rigorous Coupled Wave Analysis (RCWA) [27] before device fabrication. The device geometry for one of the fill fractions in shown in [Fig. 1(a)]. The lateral grating period is Λ = 1.00 μm, design wavelength λo = 1.55 μm, the height of the nano-hairs above the substrate, ha = 4.50 μm, the height of the nano-hairs below the substrate, hb = 0.50 μm, and the incident polarization vector is along the y- direction. The nano-hair posts were created with a multi-material geometry. The posts were formed in a fused silica substrate and consist of alternate cylinders of alumina and hafnia. Mixed material optical films have been used for optical interference coatings [28], high reflectance coatings for the UV [29], bandpass filters and antireflection coatings [30], among many other applications. In this paper, a similar approach has been employed and mixed metal-oxide coatings have been used for the device design. In order to have a high transmission at the design wavelength while simultaneously achieving the desired phase modulation over the device, the thickness of the first layer of alumina was chosen to be 60 nm, the second layer consists of 100 nm of hafnia, the third layer consists of 60 nm of alumina, and the fourth layer consists of 250 nm of hafnia. The thickness of all the materials combined is less than 0.50 μm. This is much less than the overall height of the device (5.00 μm); thereby relieving the stresses in the optical films.
The amplitude and phase response of the different fill fractions (varied between 45% and 80%) at the design wavelength in transmission is shown in [Fig. 2(a)]. It can be seen that the transmitted amplitude, at normal incidence, through these structures is greater than 95% for all the fill fractions considered. Phase modulation between 0 and 2π can also be obtained for these multi-material structures. The overall effective refractive index variation of the nano-hair with fill fraction modulation is shown in [Fig. 2(b)]. The effective refractive index of the multi-material nano-hair structure changes from 1.20 to 1.56 as the fill fraction increases from 45% to 80%. The multi-material metal-oxide nano-hairs help reduce the aspect ratio requirements of the device and has a high efficiency in transmission since the incident wave is optically impedance matched better with the device geometry, reducing the refractive index discontinuities at the interfaces. In contrast to this, a pure alumina based nano-hair structure would demand a much higher aspect ratio to achieve the full 2π phase modulation since the effective refractive index of such a device varies from 1.16 to 1.39 for the same fill fraction variation [Fig. 2(b)]. The propagation of a Gaussian beam through the nano-hair structure based OAM generator proposed in [Fig. 1(b)] has been depicted in [Fig. 3(a)]. It can be seen that a planar wavefront incident on the device (lying on the x-y plane) travels in a helical pattern along the axis of propagation (z-axis) after passing through the device. The far-field intensity and phase profiles of a Gaussian beam incident on the vortex nano-hair structure of [Fig. 1(b)] were simulated using beam propagation method using the computed effective index of the individual wedges of the device. A 2D projection of the simulated far-field optical vortex intensity pattern looks like a ring or a “donut” [Fig. 3(b)] with the size of the dark center increasing with the topological charge m of the vortex. The simulated far-field phase generated by the device is shown in [Fig. 3(c)].
Fig. 2 Simulations of the spectral and optical performance of the device at the design wavelength, λo = 1.55 μm. (a) Intensity and phase variations in transmission through different fill fractions. (b) Effective refractive index of the multi-material (HfO2 + Al2O3) and single material (Al2O3 only) nano-hair structures, as the fill fraction is modulated.
Fig. 3 (a) Propagation of a Gaussian beam through the subwavelength grating based nano-hair vortex creating a vortex beam of topological charge m = + 1; the Poynting vector of the generated beam wraps around the axis of propagation creating a spiral wave with a null at the center due to the phase singularity present in the device. Simulated far field (b) “donut” shaped intensity profile, and (c) phase profile, generated by the multi-material nano-hair vortex structure.
Numerical simulations were performed in RCWA to understand the electric field intensity distribution inside a unit cell of the multi-material nano-hair structure. For the field computations in Fig. 4, a plane wave of unity intensity was assumed to be normally incident on a unit cell of the device (45% fill fraction) from the top and the fused silica substrate was present below the posts. Two different polarization scenarios were considered; for the cases when the electric field vector is along the x- and y- directions. It can be seen that the fields present in the unit cell of the nano-hair structure are not highly confined to the posts; but exist in a more homogeneous environment (effective index structure) leading to a standing-wave interference pattern within the unit cell. There is interaction between the adjacent posts at the design wavelength for both the polarization conditions and the nano-hair structures cannot be considered as low quality resonators at λo.
Fig. 4 Field intensity distributions in a unit cell of the multi-material nano-hair structure for a specific fill fraction of 45% for two different polarization conditions – electric field vector along the x- and y- directions. Plane wave with unity intensity is incident from the top of the device with the fused silica substrate present below the nano-hair posts.
3. Device fabrication
The devices were fabricated using a standard photolithographic process as illustrated in Fig. 5. The fabrication of the multi-material, metal-oxide nano-hair devices were carried out on a 4” fused silica substrate. The fabrication process developed in this publication is capable of producing multiple devices on a single substrate as opposed to other techniques like e-beam lithography where each one of the devices have to be written individually. The chrome layer was deposited on the substrate to a thickness of 300 nm [Fig. 5(a)]. Before spin coating the photoresist, a spin-on anti-reflection layer was coated on the chrome layer to suppress any backside reflections. AZ MiR 701 photoresist was then coated on the substrate.
Fig. 5 Illustration of the fabrication sequence. (a) Chrome coated fused silica substrate. (b) Gratings patterned on a thin photoresist layer; transferred into the spin-on antireflection coating layer. (c) Photoresist layer used as a mask to transfer the grating patterns into the chrome layer via a dry chrome etch process. (d) Chrome grating patterns on the fused silica substrate. (e) Coat a thick layer of positive photoresist over the chrome grating patterns. (f) Expose the substrate from the backside to transfer the gratings into the thick photoresist layer. (g) Deep etch the fused silica substrate using the chrome/thick photoresist mask. (h) High aspect ratio holes etched into the fused silica substrate. (i) Alternate layers of alumina and hafnia deposited using a conformal deposition process. (j) Etch the planar layer on the top exposing the filled cylindrical holes. (k) Etch the fused silica substrate around the filled holes to expose the multi-material, metal-oxide nano-hair grating patterns.
The exposures of the gradient fill fraction hexagonal grating patterns were carried out on a 5X-reduction stepper using a four-step process. The substrate is not removed during the four-step process; so there is no need for complex alignment to fabricate the structures. The first exposure exposes the base hexagonal grating with a period of 1.00 μm with a fill fraction of 40% at an energy Eo mJ/cm2. The subsequent three exposures with binary masks over the base grating modulates the fill fraction of the hexagonal grating in the different sections [31]. For instance, the first wedge does not have an additional bias exposure, so the exposure energy of the gratings in that wedge is simply Eo mJ/cm2. The second wedge has an additional bias exposure, thereby making the exposure energy of the gratings in that wedge equal to (Eo + 1·Eb) mJ/cm2. Proceeding in a similar manner, the last wedge has an exposure energy equal to (Eo + 7·Eb) mJ/cm2. For obtaining 8 wedges with different fill fractions, 3 binary masks are used over the base hexagonal grating pattern. This process resulted in producing the modulated vortex fill fraction pattern over a 5 mm by 5 mm die size. The modulated grating patterns thus produced were etched into the anti-reflection layer [Fig. 5(b)] using an oxygen plasma etch process with 30 sccm (standard cubic centimeters per minute) of O2, 1000 W of ICP power and 50 W of RF power at a pressure of 5mTorr, 15 °C.
The patterned and developed photoresist layer was used as a mask to transfer the vortex grating patterns into the chrome layer using a dry etch process [Fig. 5(c)]. The reactive ion etch (RIE) process used 50 sccm of Cl2, 15 sccm of O2, RF power of 45 W, pressure of 95 mTorr at 30 °C to etch through the chrome layer. The remaining photoresist and anti-reflection layer were cleaned from the substrate leaving behind the chrome grating patterns alone [Fig. 5(d)]. SPR 220 photoresist was coated over the chrome grating patterns to completely fill the grating holes as shown in [Fig. 5(e)]. The photoresist was exposed from the backside (through the fused silica substrate), and the chrome grating patterns are transferred into the thick photoresist layer as seen in [Fig. 5(f)]. The well preserved modulated vortex grating patterns in the chrome and photoresist layer allows both the materials to act as an etch mask for the subsequent deep fused silica etch process.
An ICP etch process is used to deep etch the fused silica substrate using a CHF3/O2 gas chemistry. The etch process calls for 70 sccm of CHF3, 2 sccm of O2, ICP power of 800 W, RF power of 80 W at a pressure of 10 mTorr, 15 °C. The presence of the two etch masks helps in achieving an etch depth ~5.00 μm for submicron sized hexagonally placed holes without much of an etch bias between the different fill fraction wedges while simultaneously having a good anisotropy. The chrome layer is not etched all the way through to avoid mask erosion [Fig. 5(g)]. The residual organic matter after the fused silica etch was removed by using an oxygen plasma clean. The remaining chrome layer on the wafer was cleared by using a wet chrome etchant [Fig. 5(h)].
The high aspect ratio holes formed in fused silica were coated with alumina and hafnia using an atomic layer deposition (ALD) process. The ALD process is self-limiting, conformal in nature and very important for forming the optical nano-hair structures – deposits materials equally on all faces (top, bottom, and sides), even for high aspect ratio structures. Plasma processes involving O2 and the corresponding precursors for alumina (TriMethyl Aluminum, TMA) and hafnia (TetrakisEthylMethylAmino Hafnium, TEMAH) were used for the deposition. TMA has high vapor pressure and is directly drawn into the chamber without any bubbling during the ALD cycle. The precursor attaches itself to the surface of the substrate by chemisorption and this is followed by an Ar gas purge. At this stage, oxygen plasma is used to form a well controlled, atomic layer of alumina. A short post plasma purge completes one ALD cycle which takes ~5 seconds to complete and the deposition rate of alumina formed this way was found to be 0.122 nm/cycle. TEMAH has a very low vapor pressure and has to be bubbled into the chamber using Ar gas during the ALD cycle. The rest of the steps to form a monolayer of hafnia are similar to the TMA deposition processes. The deposition rate of hafnia is ~0.103 nm/cycle and each cycle takes ~15 seconds. These depositions were used to form the alternate alumina and hafnia layers for the vortex nano-hair structure. The first layer is formed with 60 nm of alumina, the second layer is formed with 100 nm of hafnia, the third layer is formed with 60 nm alumina and the last layer is formed with 250 nm of hafnia [Fig. 5(i)]. The overall deposition thickness is much less than the height of the grating structure (5.00 μm). The conformal nature of the ALD deposition is crucial for forming the structures since any other deposition method will call for much higher deposition thicknesses, thereby increasing the stresses in the films. There are no air voids that are formed within the cylindrical holes and the deposition fully submerges the grating layer below a planar layer of alumina/hafnia. This is not limited to the two alumina/hafnia layer pairs and can be extended to multiple layer pair depositions within the high aspect ratio cylinders.
The next step in the fabrication sequence was to etch the planar layer of alumina/hafnia formed over the grating region. A BCl3 and Ar based etch process was used to etch the metal-oxide layers. The etch process uses 20 sccm of BCl3, 5 sccm of Ar, 1250 W of ICP power and 100 W of RF power at a pressure of 2 mTorr, 25 °C. This process exposes the alternating layers of alumina and hafnia in the cylindrical holes [Fig. 5(j)]. A similar fabrication process has been used to form encapsulated resonant filter structures [32]. In the last step of the fabrication process, the fused silica substrate around the filled high aspect ratio cylinders is etched down to 4.50 μm forming the optical nano-hair structures [Fig. 5(k)]; using the fused silica etch process described above using CHF3 and O2. The etch chemistry used to remove the fused silica does not react with the alumina and hafnia in the cylinders, thus acting as a natural etch stop. The final result is a hexagonal array of modulated fill fraction gratings having concentric layers of alumina and hafnia 4.50 μm tall above the substrate surrounded by air and 0.50 μm below the fused silica substrate. The outlined fabrication sequence is used to make all-dielectric, low-index material system based multi-material, metal-oxide nano-hair optical vortex structure.
SEM micrographs of the fabricated subwavelength grating based multi-material, metal-oxide nano-hair optical vortex are shown in Fig. 6. The fill fraction modulations in the different wedges of the nano-hair vortex were measured and found to vary between 45% and 80% [Fig. 6(a)]. It can be seen that the last wedge of the device does not have the nano-hair structures. This is because of the chrome etch process which tends to be partially isotropic – the diameter of the grating holes expand upon etching, causing the holes to merge if they are too close to each other. This is the reason that the fill fractions of the holes in the different wedges are higher than what was originally exposed and developed. Due to the absence of the nano-hair structures in the last wedge, the effective refractive index of that wedge tends to be closer to 1. Incompletely closed holes on each of the nano-hairs arise due to insufficient deposition of ALD materials to completely planarize on top of the grating structures; the holes can be completely filled by depositing a thicker coating of the last hafnia layer or by adding a layer of alumina. The depth of the holes in the center of each of the nano-hairs were found to be shallow, and the presence of these holes did not affect the optical performance of the device. Figures 6(b) and 6(c) depict the intersection of two different wedges clearly showing the fill fraction modulation present in the device. The profiles of the nano-hair structures can be seen in [Fig. 6(d)]. The image was taken at a defect area on a different location of the substrate to understand the morphology of the fabricated nano-hair structures.
Fig. 6 SEM micrographs of the fabricated subwavelength grating based multi-material, metal-oxide nano-hair optical vortex. (a) Top-down micrograph showing the fill fraction variation in the different wedges. (b) Intersection of two wedges showing different fill fractions. (c) Intersection of two different wedges showing multiple fill fractions. (d) Structure of the nano-hairs imaged at a defect area on a different section of the substrate.
4. Device testing
The fabricated subwavelength-grating based nano-hair vortex devices were tested at 1.55 μm. Based on RCWA simulations covered in Section 2, the phase in transmission of the fabricated devices were estimated to be ~2.30π; the estimated phase is greater than 2π since one of the wedges of the device does not have the nano-hair structures, as explained in the previous section. This causes the effective refractive index of light propagating through that wedge to be equal to 1.
The far field intensity patterns generated by the fabricated device was investigated experimentally at λo = 1.55 μm using a tunable laser source with an output power of 0.50 mW as shown in Fig. 7. The polarized laser output was coupled into a fiber collimator that produces a beam with 1/e2 diameter of 1.364 mm. The nano-hair optical vortex device was placed in the beam path and was directed to be normally incident on the device. An imaging camera placed at the far field plane with respect to the device captured the transmitted intensity pattern through the nano-hair vortex device. Simulated far-field vortex intensity pattern is shown in [Fig. 7(a)]. The far field transmitted beam profiles were recorded both away from the device and over the center of it. Away from the device, only the transmitted Gaussian beam pattern was observed, whereas it can be seen in [Fig. 7(b)] that the device produces a “donut” shaped intensity pattern consistent with the operation of an optical vortex which possesses OAM; due to the fact that the phase in undefined at the center of the beam. Linear interference between a Gaussian beam and the intensity pattern generated by the nano-hair vortex structure used to study the phase modulation showed a single fork shaped pattern [Fig. 7(c)] confirming that the far-field beam profile indeed represents an optical vortex structure (m = + 1). The pinching observed in the intensity pattern is because the phase imparted to the incident beam is not exactly 2π, but ~2.30π. Normalized to the incident power, ~90% of power was measured to be transmitted through the device plane. This value is consistent with the diffraction efficiency estimated through numerical simulations, while accounting for the Fresnel losses that arise when an optical beam passes through a substrate. This measurement confirms that all the incident power is transmitted through the device in the 0th diffraction order only and there is no power coupled into the higher orders. The far-field intensity profile and the measured diffraction efficiency were fairly constant across a wide spectral bandwidth from 1.51 μm to 1.56 μm and such non-resonant device designs can be used for designing broadband achromatic structures.
Fig. 7 Schematic of the experimental setup to characterize the subwavelength-grating based nano-hair vortex structures at λo = 1.55 μm. (a) Simulated far-field profile of an optical vortex beam. (b) Beam intensity profile observed on the far-field image plane when the center of the device is illuminated; confirming the operation of the optical vortex by producing a “donut” shaped intensity profile. (c) Interference pattern of a Gaussian beam with the vortex beam generated by the nano-hair structure indicating the presence of a single fork-pattern (m = + 1 device).
5. Conclusion
In summary, an all-dielectric, polarization insensitive, subwavelength grating based metal-oxide nano-hair structure was introduced for OAM generation at λo = 1.55 μm. The implementation of the device is fully based on effective medium theory. In addition, the nano-hair structures were formed with alternate layers of alumina/hafnia on a fused silica substrate, thereby providing high diffraction efficiency in transmission. Presence of multiple materials also relaxes the aspect ratio requirements of the DOE. Device design, simulation, fabrication, and experimental testing of the optical vortex nano-structure have been presented. The measured diffraction efficiency of the device at the design wavelength was ~90%. Realization of the nano-hair based structure is possible due to the exploitation of the conformal coating property of the ALD, even for high aspect ratio structures. The full control of amplitude and phase of the transmitted beam is crucial for miniaturization and integration of the conventional refractive optical elements like lenses and blazed gratings, and the proposed structures have the capability to achieve that based on the experimental results presented.
Acknowledgments
This work was supported by HEL-JTO/AFOSR MRI – “3D Meta-Optics for High Energy Lasers” FA9550-10-1-0543.
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