Open Access
Add to BibSonomy
Abstract
Photon sieves, a collection of randomly positioned apertures, focus electromagnetic radiation diffractively and find applications in x-ray optics to astronomy to bio-medical imaging. Femtosecond laser direct writing is an emerging rapid, reliable, and versatile technique for creating diffraction-limited features in dielectrics and metals. Using this technique, we produce localized spots with a modified refractive index within bulk glass and thus fabricate phase photon sieves for optical wavelengths. The distribution of spots was based on numerical simulations. A comparison of the performance of the phase photon sieves and zone-plates created showed a superior performance of the former in terms of tighter focusing and reduction of secondary maxima, thus offering better spatial resolution and imaging capabilities.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Photon sieves - novel diffractive patterns, first proposed in 2001 [1] - have emerged as versatile components that are becoming of increasing utility in optical systems in astronomy [2,3], soft X-ray microscopy [1,4,5], biomedical devices [6], and in imaging in general [7–9]. They are essentially collections of random spots (apertures) that satisfy specific statistical conditions to focus electromagnetic radiation diffractively rather than refractively. These planar diffractive optical elements offer the distinct advantages of being lightweight, compact and flexible, and possess the ability to overcome focusing limitations of the conventional diffractive optical element, the zone plate [1,10]. However, their design is still evolving and undergoing application-specific improvements [11,12]. From the design of kinoform lenses [13,14] with diffractive-refractive behaviors, modifications to the sieve have been proposed over the years that have involved altering pinhole distributions [15–17] or focusing in alternate orientations [18,19].
Micron scale tailoring of materials remains a challenge that has been sought to be addressed by numerous approaches like machining, photo-lithography, electron-beam lithography, molding and other chemical and light-assisted techniques. Femtosecond laser based material modification and micro-structure writing is now an emerging field in photonics. Femtosecond laser systems have been used for direct laser writing of micron-sized features by ablating materials from the surface to create relief patterns. In this manner, zone-plates and photon sieves have been made on metal-coated substrates [20–22], and dielectrics [23–26]. The multi-step technique of femtosecond laser induced two-photon polymerization, followed by selective washing has also been used to create diffractive elements in resins [27,28].
The micro- and nano-Joule energy regimes associated with ultrafast lasers are also known to induce permanent refractive index changes in a material by thermal and non-thermal melting [29], resulting is diverse micro-nano structured modifications. It brings with it the advantages of high precision, reduced thermal damage and three-dimensional writing capabilities. The multiphoton absorption process gives a handle for light-matter interaction to overcome the diffraction limit of the femtosecond laser focusing optics, thereby allowing structure formation with smaller features [30]. Since these variations are ideal for optical engineering, we have explored the application of this technique to create diffractive optics where light bends about comparably-sized obstacles such that the output can be tailored into desired patterns and intensities.
The photon sieve is a diffractive optical element which focuses uniform incident light to a spot due to an arrangement of appropriately positioned pinholes or apertures in an otherwise opaque material. Here, we present a “phase photon sieve” where, instead of apertures, localized regions of modified refractive index are created which introduce a phase difference between light passing through the unmodified and modified regions, resulting in diffraction. Phase photon-sieves reported thus far have been formed by engraving out material from the surface to obtain optical elements of patterned thickness, offering a spatially varying path-difference to the incident optical wave front [25,26], or used a combination of selective coating and selective etching to achieve the same effect [31]. We report here the first realization of a phase photon sieve that is based on refractive index changes in the material. Such sieves were fabricated using two femtosecond laser systems - an oscillator with repetition rate of 5.1 MHz and an amplified system with repetition rate of 1 kHz, and the fabrication parameters optimized. The design of the photon sieves was optimized by systematic numerical modeling based on the Fresnel-Kirchhoff theory. The performance of these diffractive elements was compared with that of a zone plate, and superior focusing capability is demonstrated, both in terms of smaller focal spot size and suppression of secondary maxima. This paves the way for rapid, large-scale mass production of photon sieves in a single-step, mask-less process that may be readily computerized.
2. Fabrication technique
We describe in the following the technique that we have used to fabricate our phase photon sieves.
2.1 Experimental arrangement
Figure 1 shows a schematic of our set-up. Light from a femtosecond laser is directed through a microscope objective and is focused onto the sample. A combination of a half wave-plate (HWP) and a thin film polarizer (P) is inserted in the path in order to adjust the energy reaching the sample (substrate) to its absorption threshold. The sample is mounted on a computerized three-dimensional XYZ translation stage (Sigma-Koki, step size 1 μm). A CCD camera is utilized to monitor the writing on the target in real time. A photodetector (PD, Thorlabs) monitors the pulse repetition rate, an autocorrelator (AC) the pulse duration and a fiber-optic spectrometer (SP, Ocean Optics) the spectrum of the light emerging from the laser.
Fig. 1. (a) Schematic depiction of the experimental set-up. AC is the autocorrelator, PD is the photodetector, and SP is the fiber coupled spectrometer, XYZ is the micro-position translation stage, MO is the microscope objective, CCD is the camera and S is the sample irradiated. (b) Magnified section of the dotted circle in (a) representing the fabrication process.
2.2 Laser system
Two different femtosecond lasers systems – an oscillator system (Femtosource XL200) and an oscillator-amplifier system (Odin) - were used to write the microstructures and their performance was compared. While the former delivered pulses of temporal width ∼60 fs, the latter gave pulses of ∼40 fs. The wavelengths of both lasers were centered at 800 nm. While the oscillator system had a repetition rate of 5.1 MHz, and maximum pulse energy of 200 nJ, the amplifier system produced pulses at 1 kHz, and yielded maximum pulse energy of ∼4 mJ. Using these parameters we established the role of pulse repetition rate and pulse energy on the structures that were laser written, and to ascertain the best parameters for material modification for phase-diffractive optics.
2.3 Sample preparation
The transparent samples chosen for this study were soda-lime and BK7 glass, materials that ensure that laser-written devices can be cost-effectively prepared and with optimal performance. The glass was thoroughly cleaned [32] prior to femtosecond direct writing to remove dirt, oils, and organic residues from the manufacture-packaging process.
2.4 Speed and depth
Microscope objectives used for the experiment were Nikon 10×, 0.10 NA and Nikon 40×, 0.75 NA. The higher numerical aperture (NA 0.75) objective was used with the MHz system, while the low NA objective was used with the 1 kHz system to achieve threshold intensity for index modification. There is a slight dissimilarity in the fabrication thresholds observed in the two glasses due to differences in their absorption edge. Soda-lime glass is found to be ‘softer’ in nature than BK7, with a lower incident threshold requirement for modification. However, no significant differences were observed in the morphologies of structures formed in either type of glass.
The tightly focused femtosecond laser pulses that are incident on the dielectric sample in our experiments are capable of inducing highly localized refractive index modifications in it, with minimal damage to the vicinity. We could produce permanent refractive index changes in borosilicate glass of ∼3×10−3 [33] using the oscillator system (MHz pulse repetition rate) and ∼10−4 [34] using the amplifier system (1 kHz repetition rate). Features as small as ∼1 μm could easily be written. When written in the bulk, even though the laser penetrates the material, the energy is so adjusted that material modification occurs only within the focal region. Microstructures were written by manipulating the sample position, and exposing different regions to the desired extent. These laser-written structures were systematically optimized for translation speed and depth of focused laser irradiation to observe an assortment of textures. Some of the textures obtained in soda-lime glass using the oscillator system are shown in Fig. 2. We found that finer features are obtained when the laser is focused at or close to the surface due to minimal aberrations of the focused light. As seen from Fig. 2(b), lower translation speeds resulted in wider modified regions. When Fresnel zone plates were written at these speeds, unwanted overlap occurred between adjacent traces within the same zone. High repetition rate (MHz) pulses were found to cause structural changes through an accumulation of pulses resulting in symmetric profiles. With the amplifier system delivering pulses at a low repetition rate (kHz), the accumulation of energy from subsequent pulses is essentially absent. Some micro-fabricated elements like gratings require continuous modified regions, with no gaps. The photon sieves, on the other hand, require discrete modified regions to form the ‘apertures’ for diffraction, and hence achieving well-separated dot pattern morphologies in glasses [35,36] of particular interest in our study. The separation of the dots is dependent on the energy dose delivered. The parameters that we found best for obtaining the desired microstructures were an incident energy 0.09 μJ at a translational speed of 5 mm/s for the oscillator system (MHz repetition rate), and an incident energy of 1.2 µJ at a translational speed of 1 cm/s for the oscillator-amplifier system (1 kHz repetition rate). Photon sieves were successfully fabricated using both the oscillator and amplifier femtosecond laser systems, enabling comparison of performance of the diffractive elements.
Fig. 2. The different traces obtained in soda lime glass upon varying the translational parameters for direct femtosecond laser writing using the oscillator system (MHz repetition rate) (a) Variation in modification, as the femtosecond laser focus is moved deeper into the sample, starting from 0 (surface), to a depth of 80 μm, in steps of 5 μm and translation speed of 5 mm/s (b) Variation with speed. All lines, in this case, were drawn on the surface, and in the same direction.
An important observation with the oscillator system is that the Gaussian intensity profile of the incident femtosecond laser beam results in a gradient index variation within discrete modified spots. In contrast, previously reported photon sieves [e.g., 10,11,37,38] of the amplitude type consist of appropriately positioned apertures and, hence, possess a uniform variation in each spot due to the complete absence of material. The same is the case with binary photon sieves [22–26], which consist of step variations in material thickness.
For certain range of femtosecond pulse energies, we found a marked difference in the shapes of the modified area created by the oscillator system and the amplifier system (Fig. 3). These shapes arise due to the meeting of heat fronts of successive spots, and are different for the two laser systems due to their different energy content and pulse repetition rates. Let us consider the situation when the sample is being moved from right to left, as is the case for Fig. 3(a). This is equivalent to the situation where the sample is stationary, and the laser beam is being translated from left to right. Light pulses from the oscillator system arrive on the sample every ∼195 ns. Localized heating of the exposed spot gives rise to an expanding heat front, which ideally should expand equally in all directions. However, towards the left it encounters the still-expanding front due to the previous spot, which had originated 195 ns before. Therefore, the heat front expands asymmetrically, preferentially to the right, as is seen in the Fig. 3(a). Consider next the case of femtosecond pulses from the amplifier system. In this case, the pulses contain more energy, but arrive on the sample at a slower rate (1 ms interval between pulses). The expansion of the heat front is more symmetric - outward, away from the trace of successive incident pulses (Fig. 3(b)).
Fig. 3. Gradient index variation within spots created by femtosecond laser direct writing using (a) oscillator system and (b) amplifier system.
3. From a zone-plate to a photon sieve
Fresnel zone plates are usually used when compact, lightweight lenses are required. However, they have a number of drawbacks that have been addressed by several researchers [1,2,37]. These include unwanted contributions from the various diffraction orders, uncompensated edge-effects arising from the finite-sized zone plate, and the limitation to the spatial resolution imposed by the width of the outermost zone. The first two contributions lead to the formation of secondary maxima. The contribution of higher-order and edge diffractive effects also leads to additional foci along the longitudinal axis. The secondary maxima rings around the principal focus cause blurring of images. The photon sieve helps overcome most of these drawbacks.
A photon sieve is described [1] as a diffractive micro-pattern comprising apertures such that the optical path length of rays from the source via the center of the apertures to the image plane travels an integral number of wavelengths. With the famously known Fresnel zone plate as its archetype, a photon sieve is made by discretizing the zones into a collection of apertures dispersed in annular rings. It is typically an opaque material with a pattern of holes or apertures, and hence the name “photon sieve”. It is, thus, an amplitude diffractive element, where the diffraction occurs due to an absence of material (aperture). A photon sieve may also be made by creating reliefs in a material, so that the varying thickness of the material and the consequent path differences give rise to phase diffraction [22,25]. Here, we present a new form of the phase photon sieve, where the refractive index of the sieve material is modified in localized spots within the bulk of the medium such that a phase difference is introduced in the transmitted light, leading to diffraction.
The underlying design is that of a standard phase zone plate that consists of concentric rings (or zones), with alternating but uniform refractive indices, n1 and n2. Successive zones of increasing diameter but equal areas contribute light constructively or destructively to a sharp focus (Fig. 4(a)). For the photon sieve, we begin with a material where all “zones” have a refractive index n1, and position in alternate ones, discrete spots of refractive index n2. The size-distribution of the spots yields different types of photon sieves, as depicted in Figs 4(b–d). In a regular photon-sieve (Fig. 4(b)), the spots are arranged in concentric circles such that the spot sizes match the width of the underlying zone. In the case of an amplitude photon sieve, the different zones do not necessarily transmit an equal amount of light; it is proportional to the total area of the apertures in a zone. In the case of the phase photon sieve, on the other hand, the throughput is higher and equal for all zones. In both cases (amplitude and phase sieves) all spots do not deviate light by the same amount; this depends on the size of the spot. This could lead to a loss in focusing power. It is understood that in diffractive optics, the boundaries play an important role, as diffraction effects arise from here. By increasing such edge effects through increased aperture density and by altering the size [1] the amount of light transferred into the focal point can be controlled. This may be achieved by photon sieves of the types shown in Fig. 4(c) where all apertures have the same size, and in Fig. 4(d), where the sizes are randomly distributed, but follow a statistical rule.
Fig. 4. (a) The zone plate; (b) the photon sieve with discrete spots of size similar to the zone width; (c) photon sieve with discrete spots having size smaller than the zone width; and (d) photon sieve with randomized discrete spot sizes within the zones.
With the discretization of the zones in the photon sieve, the major drawback of zone plates, namely the existence of secondary maxima around the focus, can be largely eliminated. Each ring in a zone plate covers an equal expanse of area which, when uniformly illuminated, contributes an equal amplitude to the focus. This contribution drops abruptly to zero beyond the outermost ring that leads to strong intensity oscillations in the diffraction pattern. These secondary maxima are easily minimized by adjusting the number density or size of discrete spots in a photon sieve to yield a smooth transition at the edges. This is borne out both by our simulations and measurements using the photon sieves that we have fabricated.
It is well known that when a diffractive element is used as a lens, the width of the smallest aperture determines its spatial resolution [1]. The smaller the aperture, the larger the diffraction angle, and hence the better its resolution, or its ability to separate two closely placed point sources located at the focal plane. In the case of a zone plate, the smallest aperture size is the width (ΔrN) of the outermost zone, and the resolution is given by 1.22ΔrN [39]. In the case of the photon sieve, the resolution can be improved over that of the underlying zone plate. The spatial resolution (Δx) of the photon sieve with d as the discrete spot diameter and w the width of the underlying zone, is given by [1] :
This improved spatial resolution is, in fact, the main advantage of the photon sieve over the zone plate.4. Numerical simulations
We now draw attention to the effect that aperture size and number distributions have on the focusing capabilities. Our femtosecond direct laser writing experiments and our numerical simulations had as a blueprint, a surface-tailored zone plate designed for a 25 mm focal length for light at 632.8 nm wavelength. Beginning with amplitude zones plates [21] we extended our studies towards the photon sieve. Numerical simulations were carried out for zones ranging from 1 to 10 zones. The programs, written in Mathematica, utilize Huygens’s principle where every transparent point on the diffractive element acts as a source of secondary spherical wavefronts. The intensity pattern at any desired plane was calculated by summing the amplitudes of the electric vectors of the different spherical waves reaching that plane, and squaring the resultant. In this manner, we calculated the intensity pattern expected from the zone plates and from the photon sieves.
In order to estimate the resolution of the diffractive elements that we simulate (and also fabricated), we have measured the size of the focal spot, that is, the width of the first intensity maximum. As the transmission of light is reversible, the size of the focal spot and the spatial resolution are equivalent [40].
In Fig. 5 we compare the results of the numerical simulation for the zone plates comprising 2, 4, 6, 8, and 10 zones to their corresponding optimized sieves. Here, the successive outer zones of the sieves were taken to have more spots in order to match throughput. Special emphasis was laid on the size of the focal spot and the intensities of the secondary maxima, and parameters that could reduce both these quantities were investigated. It was seen that for the zone plate, as the number of zones increased, though the size of the focal spot reduced, the number of secondary maxima, and the intensities in these, increased. In contrast to this, in the case of the photon sieve on increasing the number of zones, the size of the focal spot reduced, and also the unwanted secondary maxima decreased in intensity – that is, focusing performance was significantly enhanced. The changes in spot size are summarized in Table 1. In all the cases we found that the photon-sieve yields better focussing (as quantified by the size of the focal spot) compared to what we observed using a zone plate. This effect is more prominent when the number of zones are small; this is understandable, as the resolution of a zone plate is determined by the width of the outermost zone. As the number of zones increases, their radii increase and their widths decrease. Conversely, when the number of zones is reduced, the width of the outermost zone increases. On the other hand, for the photon sieve, the resolution is determined by the size of the smallest size of the spot (or aperture), which could be in any zone. Thus, the percentage difference in spatial resolution is larger when the number of zones is reduced.
Fig. 5. Comparison of the focusing properties of the zone plate and the photon sieves. The top row depicts computer generated zone plates with 2, 4, 6, 8, and 10 zones. The next row gives the corresponding intensity pattern in the focal plane. The third row depicts the computer generated photon sieves with 2, 4, 6, 8, and 10 zones with randomised apertures. The last row gives the corresponding intensity pattern in the focal plane.
Table 1. Comparison of size of focal spot obtained from numerical simulations for the zone plate and photon sieves of 2, 4, 6, 8, and 10 zones.
The transmission windows utilized in experiments reported in the literature suggest the pinhole density in the sieve be typically reduced as we move from center to the periphery. However, the overall number of apertures in all the diffractive elements shown in Fig. 5 was maintained in the same range. The size of the focal spot decreased as expected with the increase in zone number. For the case of the diffractive elements in row 3, successive outer zones contain more apertures than the preceding inner ones. In terms of the irradiance, due to the fewer apertures in the inner zones, significant contributions to the pattern in the image plane is due to light coming from the outermost zone. Such a distribution was adopted because during the course of optimizing the design by the numerical simulations, a particular distribution of spots in the photon sieve enabled a significant reduction in the focal spot size. Figures 6(a), (b), (c) show, respectively, a zone plate, a “random-single” photon-sieve, and a “random-double” photon sieve. Shown underneath each figure are the corresponding simulated intensity profiles in their focal planes. The zone plate has alternate zones that are opaque or transparent. The random-single is a discretized version of the zone plate, having 360 apertures, randomly located in each bright zone. The random-double is also a discretized version of the zone plate, with zones 1–13 having 180 randomly located apertures, and zones 14–26 having 360 randomly located apertures. While the focal spot size is nearly the same for zone plates shown in Figs. 6(a) and 6(b), it is significantly lower for the zone plate shown in Fig. 6(c). Further simulations confirmed that fewer apertures in the inner zone compared to the outer ones yielded better focusing.
Fig. 6. Simulation of (a) Regular zone plate; (b) Random-single zones; and (c) Random-double zones (see text), each having 26 zones. Given below each is the calculated intensity pattern at its focal plane.
Thus we conclude that randomizing the pinholes and maximizing the contributions from the outermost zone resulted in reducing the intensities in the secondary maxima, as may be seen from the intensity patterns of sieves with larger number of zones (Figs. 5 and 6).
5. Femtosecond laser direct written phase photon sieves: observations and discussion
We present in the following our results on the fabrication of the photon sieve using two different femtosecond laser systems. With refractive index changes of ∼3×10−3, and refractive index modified regions of ∼10 μm, the phase change introduced to light of wavelength 632 nm is expected to be ∼π/10 radians. In the optical micrographs in Fig. 7 we show some of the diffractive elements created by femtosecond laser writing. All the displayed elements have 49 zones (25 dark and 24 bright). Exposing the sample to femtosecond irradiation while it is located at one position gives rise to a modified spot. Translating the sample over a circular path, while simultaneously exposing it to femtosecond irradiation gives rise to a thin ring of modified material. Creating several such rings, concentric to each other and separated by ∼2 μm, gives rise to a zone. Close-up views of the elements reveal that while continuous or overlapping spots are obtained at low sample translational speed using either the oscillator or the amplifier system, distinct, well-separated spots are obtained at faster speeds (1 cm/s or higher) in those cases where the amplifier system is used. In the case of the oscillator system, much higher translational speeds (50 cm/s or higher), with concomitant reduction in pulse energy, was required to create well-separated spots. Due to the high speeds, the modified regions were not circular.
Fig. 7. (a) A typical femtosecond written zone plate of 49 zones that we fabricated. Close-up of written diffractive element with N = 49 zones by an (b) oscillator, 1.5 mm/s translation speed; (c) amplifier, 5 mm/s translation speed; (d) amplifier, 1 cm/s translation speed. The sizes of the modified spots are ∼3 ± 0.3 μm.
In Fig. 8, we show typical experimental results for phase zone plates and phase photon sieves that were laser written using the oscillator and the amplifier systems. As illustrative examples, diffractive elements with 49 zones and 15 are discussed. These have diameters of 1.7 mm and 1 mm, respectively. While zone plates in Fig. 8(a) and (c) have the same number of zones, and are expected to show the same focusing properties, we find that the zone plate fabricated with the oscillator system has a finer focus. On the other hand, that made with the amplifier system has a cleaner focus – the unwanted secondary maxima are much reduced. The same is the case with zone plates shown in Figs. 8(b) and 8(d). We attribute these to the fact that the oscillator and amplifier systems alter the refractive index of the material by different amounts. Also, as shown in Fig. 3, the refractive index gradients within each modified spot are different. We have fabricated phase photon sieves using the amplifier system, and representative cases, which are discretized versions of the 49- and 15-zone zone plates, are shown in Figs. 8(e, f). These have a gap of ∼5 μm between spots in adjacent circles within a zone, while those shown in Fig. 8(g) have larger gaps (∼10 μm). On comparing Figs. 8(e) and 8(f), it is seen that, as predicted from theory [1], the greater the number of zones, the better the focusing. On comparing Figs. 8(f) and 8(g), we find, in addition, that not only the size of the spots, but the mean spacing between them also affects the focusing.
Fig. 8. Zone plates of (a) 49 zones and (b) 15 zones made with the oscillator system, zone plates of (c) 49 zones and (d) 15 zones made using the amplifier system, photon sieves of (e) 49 and (f, g) 15 zones made with the amplifier system. See text for more details. The discrete spots for the photon sieves are randomized in position and size (type shown in Fig. 4(d)). The parameter Δx is the focal spot size. Data analyzed and reported is from an aggregate of a minimum of four sieves each. The focal spot measurements have an error bar of ± 0.3μm.
We see thus, that a number of parameters have to optimized, first individually and then, iteratively. In the numerical modeling, these include the number density of spots, size distribution, and location pattern. In actual fabrication, these include pulse energy, focusing depth of the objective lens, and translational speed of the sample. This systematic and iterative investigation led us to two important findings, one on the distribution of spots in the various zones, as illustrated in Fig. 6, and the other on the depth at which femtosecond laser induced material modification is carried out, which we discuss below.
In the course of viewing the fabrication process in real-time on the CCD camera whilst optimizing parameters, we observed an unanticipated occurrence. When the modifications were formed at a depth of 45–50 μm from the surface of the sample, we observed very vigorous alterations inside the material, similar to rapid formation of globules, possibly due to highly localized melting. These appeared as dark spots while viewed in transillumination. A plausible explanation is that at these depths, energy accumulates within the sample and is unable to dissipate out easily. This depth appears to be optimal; a deeper focusing would lead to less input energy reaching the spot, while shallower focusing would result in faster dissipation of accumulated energy. Thus, for soda-lime glass, for input pulse energy of 100 nJ within ∼60 fs pulses at a repetition rate of 5.1 MHz focused with a 40× microscope objective, very intense local accumulation of energy occurs when the light energy is delivered at a depth of 45–50 μm. This results in strong material modification. We tested this behavior for repeatability by laser writing straight lines in the positive and negative directions of one axis of the incident plane. As long as the material composition was uniform, the rapid globule formation was consistently observed. A mild heat affected zone was observed in such cases, due to the high amount of energy being dumped into a localized spot; the heat-flow direction was indicative of the translation direction of the sample. By adjusting the sample translation, the same pattern could also be obtained for circular translation of the sample. When programmed for zone plate design, adjacent circle traces produced these globules at non-overlapping locations. However, there is a definite heat affected zone present that propagates into the non-modified zones. These effects are illustrated in Fig. 9(a).
Fig. 9. (a) Photomicrograph of a modified region at a depth of ∼45 μm. Each circular region is an index-modified spot fabricated by irradiation by the femtosecond pulses from the oscillator. (b) A photon sieve fabricated at a depth of ∼45 μm. The discrete spots for the photon sieve are randomized in position and size (type shown in Fig. 4d).
A complete photon sieve was fabricated in this manner, at a depth of ∼45 μm (Fig. 9(b)). The modified spots, formed in alternate zones only, were uniform in diameter and were measured to have an average size of 2.15 ± 0.15 μm. The random dark streaks observed in the figure are not cracks. They are sideways extrusions of the material as a consequence of an overlap of heat affected zones between adjacent circle traces. These could be avoided by introducing gaps between the modified regions so as to allow for heat dissipation and better separation of traces. The photon sieve shown in Fig. 9(b) has 26 zones (13 dark and 13 bright). Despite the formation of the unintended streaks, the sieve was tested for its focusing characteristics. Surprisingly, the optics displayed a perfectly clean focus, with no sign of contributions to secondary maxima. For the fabricated sieve, this spot size is expected to be about 10.4 μm. On measurement with a 632 nm laser beam we found this spot size to be 9 μm (Fig. 10). The outermost zone width in this case (26th zone) is 12 μm; the expected resolution of the conventional refractive lens counterpart would be 25 μm and its zone plate counterpart would be 14.6 µm.
Thus the phase photon sieve, fabricated at the optimum depth of 45–50 μm, shows very good focusing capability and, hence, superior resolution. Several such photon sieves fabricated with optimized parameters were made with the amplifier system also. These were then characterized by sending a collimated He-Ne laser beam through them, and examining the focusing properties. The fabrication parameters were optimized for smallest focal spot size (and, hence, best spatial resolution). The performance results in Table 2 show that the photon sieve produces a smaller focal spot than that expected for a zone plate.
Table 2. Focusing parameters for photon sieve of designed focal length 25 mm, fabricated by femtosecond oscillator (5.1 MHz) or amplifier (1 kHz) system.
6. Summary
We have utilized the technique of femtosecond laser writing to fabricate photon sieves. Specifically, we have demonstrated the feasibility of fabricating phase photon sieves where, instead of conventional use of apertures, laser writing is used to create localized alterations of refractive index in a material. Such index changes introduce a phase difference between light passing through modified and unmodified regions of a sample and give rise to diffraction. The laser writing parameters have been optimized using two different femtosecond laser systems: a 5.1 MHz repetition rate oscillator system and an amplified system with 1 kHz repetition rate. We have evaluated the performance of our laser written diffractive elements and found that photon sieves to give smaller focal spot size and better suppression of secondary maxima, implying superior spatial resolution and improved imaging capabilities compared to zone plates.
Carrying out systematic numerical modeling based on the Fresnel-Kirchhoff theory helped to further optimize the design of our photon sieve; we discovered that fewer apertures in the inner zones, and more in the outer ones, yielded smaller focal spots and, hence, better resolution. Measurements were made that confirmed that our optimized phase photon sieves yielded smaller focal spots than corresponding zone plates, with an observed elimination of secondary maxima in the image plane.
From an applications viewpoint, a major advantage of our fabrication technique is the attainment of higher throughput of light. As the laser writing can be such that refractive index alterations occur entirely within bulk material, the photon sieves can be made to have an absolutely planar geometry, and can be impervious to dust and surface contamination on the surface of the material. Moreover, laser writing paves the way for rapid, large-scale mass production of photon sieves in a single-step, mask-less and chemical-free process that may be readily computerized. It is clear that phase photon sieves with distributed pinholes hold promise in diverse areas of bio-imaging and data storage applications.
Funding
Joint Manipal Academy of Higher Education and FIST Program of the Department of Science and Technology, Government of India (SR/FT/PSI-174/2012); Science and Engineering Research Board (SERB) of the Department of Science & Technology, Government of India (J. C. Bose National Fellowship (SR/S2/JCB-29/2006)).
References
1. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001). [CrossRef]
2. G. Andersen and D. Tullson, “Photon sieve telescope,” in Astronomical Telescopes and Instrumentation, International Society for Optics and Photonics, (2006).
3. G. Andersen and D. Tullson, “Broadband antihole photon sieve telescope,” Appl. Opt. 46(18), 3706–3708 (2007). [CrossRef]
4. Y. Cheng, J. Zhu, Y. He, Y. Tang, S. Hu, and L. Zhao, “Quadratic grating apodized photon sieves for simultaneous multiplane microscopy,” Opt. Lasers Eng. 97, 78–85 (2017). [CrossRef]
5. G. Cheng, C. Hu, P. Xu, and T. Xing, “Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy,” Opt. Lett. 35(21), 3610–3612 (2010). [CrossRef]
6. W. Jiang, S. Hu, Y. He, and Y. Bu, “An artificial compound eye of photon Sieves,” Opt. Laser Technol. 74, 93–96 (2015). [CrossRef]
7. K. Huang, H. Liu, F. J. Garcia-Vidal, M. Hong, B. Luk’yanchuk, J. Teng, and C.-W. Qiu, “Ultrahigh-capacity non-periodic photon sieves operating in visible light,” Nat. Commun. 6(1), 7059 (2015). [CrossRef]
8. F. S. Oktem, J. M. Dovila, and F. Kamalabadi, “Image formation model for photon sieves,” in Image Processing (ICIP), 20th IEEE International Conference on. IEEE (2013).
9. X. Zhao, J. Hu, Y. Lin, F. Xu, X. Zhu, D. Pu, L. Chen, and C. Wang, “Ultra-broadband achromatic imaging with diffractive photon sieves,” Sci. Rep. 6(1), 28319–28329 (2016). [CrossRef]
10. G. Andersen, “Large optical photon sieve,” Opt. Lett. 30(22), 2976–2978 (2005). [CrossRef]
11. G. Cheng, T. Xing, Z. Liao, Y. Yang, and J. Ma “Resolution enhancement of photon sieve based on apodization. in Holography and Diffractive Optics III,” International Society for Optics and Photonics (2008).
12. C. Rubio, J. M Fuster, S. Castiñeira-Ibáñez, A. Uris, F. Belmar, and P. Candelas, “Pinhole Zone Plate Lens for Ultrasound Focusing,” Sensors 17(7), 1690 (2017). [CrossRef]
13. T. R. M. Sales and G. M. Morris, “Diffractive–refractive behavior of kinoform lenses,” Appl. Opt. 36(1), 253–257 (1997). [CrossRef]
14. J. Jordan, P. M. Hirsch, L. B. Lesem, and D. L. Van Rooy, “Kinoform lenses,” Appl. Opt. 9(8), 1883–1887 (1970). [CrossRef]
15. A. Sabatyan and S. Mirzaie, “Efficiency-enhanced photon sieve using Gaussian/overlapping distribution of pinholes,” Appl. Opt. 50(11), 1517–1522 (2011). [CrossRef]
16. Z. Chen, C. Wang, D. Pu, J. Hu, and L. Chen, “Ultra-large multi-region photon sieves,” Opt. Express 18(15), 16279–16288 (2010). [CrossRef]
17. Q. Cao and J. Jahns, “Nonparaxial model for the focusing of high-numerical-aperture photon sieves,” J. Opt. Soc. Am. A 20(6), 1005–1012 (2003). [CrossRef]
18. M. Kalläne, J. Buck, S. Harm, R. Seemann, K. Rossnagel, and L. Kipp, “Focusing light with a reflection photon sieve,” Opt. lett. 36(13), 2405–2407 (2011). [CrossRef]
19. W. Sun, Y. Hu, D. G. MacDonnell, H. J. Kim, C. Weimer, and R. R. Baize, “Fully reflective photon sieve,” J. Quant. Spectrosc. Radiat. Transfer 206, 101–104 (2018). [CrossRef]
20. F. J. Salgado-Remacha, L. M. Sanchez-Brea, F. J. Alvarez-Rios, and E. Bernabeu, “Rough Fresnel zone plates over metallic surfaces,” Appl. Opt. 49(10), 1750–1756 (2010). [CrossRef]
21. V. R. Rodrigues, J. Thomas, S. Chidangil, H. Ramachandran, and D. Mathur, “Microfabrication of Fresnel zone plates by laser induced solid ablation,” J. Opt. 18(7), 075403 (2016). [CrossRef]
22. M. N. Julian, D. G. MacDonnell, and M. C. Gupta, “Fabrication of photon sieves by laser ablation and optical properties,” Opt. Express 25(25), 31528–31538 (2017). [CrossRef]
23. J. K. Kim, J. Kim, K. Oh, I.-B. Sohn, W. Shin, H. Y. Choi, and B. Lee, “Fabrication of micro Fresnel zone plate lens on a mode-expanded hybrid optical fiber using a femtosecond laser ablation system,” IEEE Photon. Technol. Lett. 21(1), 21–23 (2009). [CrossRef]
24. R. M. Vázquez, S. M. Eaton, R. Ramponi, G. Cerullo, and R. Osellame, “Fabrication of binary Fresnel lenses in PMMA by femtosecond laser surface ablation,” Opt. Express 19(2), 11597–11604 (2011). [CrossRef]
25. M. N. Julian, D. G. MacDonnell, and M. C. Gupta, “Binary phase photon sieves on flexible polyimide substrates by laser ablation,” Opt. Lett. 43(10), 2368–2371 (2018). [CrossRef]
26. M. N. Julian, D. G. MacDonnell, and M. C. Gupta, “High Efficiency Photon Sieves by Laser Direct Writing,” in Frontiers in Optics / Laser Science, OSA Technical Digest (Optical Society of America, 2018), paper JW3A.10].
27. Y. Li, Y. Yu, L. Guo, S. Wu, C. Chen, L. Niu, A. Li, and H. Yang, “High efficiency multilevel phase-type Fresnel zone plates produced by two-photon polymerization of SU-8,” J. Opt. 12(3), 035203 (2010). [CrossRef]
28. D. Wu, L.-G. Niu, Q.-D. Chen, R. Wang, and H. B. Sun, “High efficiency multilevel phase type fractal zone plates,” Opt. Lett. 33(24), 2913–2915 (2008). [CrossRef]
29. B. Rethfeld, K. Sokolowski-Tinten, D. Von Der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys. A 79(4–6), 767–769 (2004). [CrossRef]
30. A. P. Joglekar, H. Liu, E. Meyhöfer, G. Mourou, and A. J. Hunt, “Optics at critical intensity: Applications to nanomorphing,” Proc. Natl. Acad. Sci. USA 101(16), 5856–5861 (2004). [CrossRef]
31. C. Hou, “Novel diffractive optical element: binary photon sieve,” Opt. Eng. 50(6), 068001 (2011). [CrossRef]
32. The pre-fabrication cleaning process consists of an acid-wash to leach out ions, first by soaking in 5% HNO3 in deionised water for 2 hours followed by rinsing in de-ionised water and drying. Next, a base-wash is carried out by soaking in NaOH, followed by rinsing and drying. The glass is thereafter cleaned by acetone and methanol, and given a final washing with de-ionised water and blow dried. After fabrication, the element is cleaned with methanol and ultrasonicated to remove surface contaminants due to handling.
33. K. Mittholiya, P. K. Anshad, A. K. Mallik, S. Bhardwaj, A. Hegde, A. Bhatnagar, R. Bernard, J. A. Dharmadhikari, D. Mathur, and A. K. Dharmadhikari, “Inscription of waveguides and power splitters in borosilicate glass using ultrashort laser pulses,” J. Opt. 46(3), 304–310 (2017). [CrossRef]
34. J. A. Dharmadhikari, K. Pradyna, A. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, “Effect of chirp on the index contrast of waveguides written in BK7 glass with ultrashort laser pulses,” Opt. Commun. 287(2), 122–127 (2013). [CrossRef]
35. J. Thomas, S. Chidangil, A. Bhatnagar, R. Bernard, J. A. Dharmadhikari, A. K. Dharmdhikari, and D. Mathur, “Femtosecond Laser-Induced Dot-pattern Formation in BK7 Glasses,” in International Conference on Fibre Optics and Photonics, Optical Society of America (2012).
36. J. Thomas, R. Bernard, K. Alti, A. K. Dharmadhikari, J. A. Dharmadhikari, A. Bhatnagar, S. Chidangil, and D. Mathur, “Pattern formation in transparent media using ultrashort laser pulses,” Opt. Commun. 304(1), 29–38 (2013). [CrossRef]
37. R. Menon, D. Gil, G. Barbastathis, and H. I. Smith, “Photon-sieve lithography,” J. Opt. Soc. Am. A 22(2), 342–345 (2005). [CrossRef]
38. S. D. Eder, X. Guo, T. Kaltenbacher, M. M. Greve, M. Kallane, L. Kipp, and B. Holst, “Focusing of a neutral helium beam with a photon-sieve structure,” Phys. Rev. A 91(4), 043608 (2015). [CrossRef]
39. J. Kirz and D. Attwood, “X-ray Data Booklet,” Section 4.4 : Zone Plates, https://xdb.lbl.gov/Section4/Sec_4-4.html
40. D. Attwood, “Zone Plate Microscopy,” Lecture 22, http://www.coe.berkeley.edu/AST/srms.
