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We designed, fabricated, and tested, polarization selective, graded-reflectivity resonant filters; based on a radial-gradient spatially-distributed, guided-mode resonance device architecture. The demonstrated filters have polarized spectral-resonance responses, distributed across their aperture extent, in the range between 1535nm and 1540nm wavelengths. Spectral sensitivity was observed on device tests, for wavelength changes as low as 0.2nm. Using multiple lithographic exposures and biasing exposure methods, the devices were engineered to have a sub-aperture region, with no hard boundaries or diffraction anomalies.
©2010 Optical Society of America
1. Introduction
Optical filters with spatially varying spectral responses can be divided into two major categories: Graded Reflectivity Mirrors (GRM) and Graded Transmittance Filters (GTF). GRM are used in stable and unstable laser cavities for mode control and output beam shaping [1–3]. Their function is to provide spatially distributed reflectivity conditions across their aperture profile, in order to control the transverse extent of the output beam or, increase the laser cavity volume feedback conditions. One of the main fabrication issues for GRM is the use of patterned or shaped multilayered thin film coatings, which can be difficult to achieve for high spectral discrimination. A variety of coating and film growth techniques have been developed, with different degrees of difficulty in implementation [4,5].
Guided-mode resonance filters (GMRF) have been demonstrated for many wavelength bands, and with various optical material combinations [6–9]. The principle of GMRF function is resonant coupling of evanescent modes into a leaky waveguide, and their subsequent re-emergence in the side of the incident radiation region. The basic GMRF design consists of a patterned sub-wavelength grating and a waveguide layer, supported by a passive substrate. The advantage of this structure, over a multilayered thin film reflective stack, is that the fabrication issues are relegated to the planar grating layer patterning, which can be addressed by many methods such as e-beam, DUV or conventional photolithography. In general, one-dimensional line grating profiles have polarization sensitivity, whereas hexagonal gratings are polarization insensitive [10]. The challenges in photolithography come from the implementation of sub-wavelength scale feature dimensions, which can be achieved using direct writing techniques at the expense of the final component size or, lithographic interference direct patterning methods that relinquish the control of modern micro-fabrication device integration processes. Uniform duty-cycle linear grating-based GMRF devices are polarization sensitive, with the incident polarizations resonating at different wavelengths, usually separated by tens of nanometers. Designs that have cascading layers of separate linear grating GMRF have been reported as well [11].
A GMRF with spatial-gradient-profile grating features, results in guided-mode resonance filters with space-variant functionality, that can provide frequency dependent spatially distributed reflection and transmission [12]. In the last reference, such a GMRF was designed, fabricated, and tested using a GMRF basis design with a spectral linewidth between 5 and 9nm, and a spatial resonance distribution aperture diameter of 160µm. Optical tests confirmed wavelength-dependent device performance, and its capabilities to apodize and shape the transverse profile of an incident Gaussian beam. Other designs have been presented in the literature, including single layer GMRF spatial-gradient-profile gratings, where the sub-wavelength grating is also acting as the leaky waveguide, with high index contrast compared to the substrate [13,14].
An added feature of GMRF is their ability to encode polarization specific responses through geometrical facets of the unit cell. Moreover, by encoding polarization sensitive spectral responses into a specific design, polarization specific resonance GRM can be placed within a typical gain spectrum of a solid state media. Using the concept of a space-variant GMRF grating, a polarization sensitive device was designed and fabricated. The aperture diameter of the device presented in this report is 1.7mm, an order of magnitude larger than previously reported, with sub-nanometer spatial and spectral polarization selectivity. Conventional photolithographic techniques were used to fabricate the sub-wavelength period grating. A centrally located soft sub-aperture, with smooth boundary transitions in the patterned grating layer was realized, to allow for transverse-profile beam control. Strong polarization discrimination was measured between spectrally-selected transmission regions of the component, enabling polarization selective graded-transmittance. The optical performance of such devices is attractive for laser out-coupling applications and polarized spectral filtering, where polarization and spectral selectivity can be used to isolate optical mixed cavity states.
2. Device concept, design, and simulation results
For a linearly polarized optical beam incident normally on a polarization insensitive optical component, the polarization state of the transmitted beam can be determined using a linear polarizer as an analyzer. If the optical device under test is polarization sensitive, it will transmit the optical beam according to the rotational alignment with its polarization axis to the original incident field direction. A following analyzer will measure the degree of polarization with respect to the device polarization axis, as the orientation of maximum transmittance. In general, the spectral sensitivity of such an optical device depends on material properties. An optical component that has polarization properties that are narrow-band frequency-dependent, acts as a linear polarizer in a certain transverse orientation direction σ, for a small wavelength range; whereas, for an adjacent wavelength band, it responds as a linear polarizer in a different orientation π (Fig. 1 ). Using an analyzer in this case will result in a polarized wavelength-dependent measured response. Both the polarization direction and the spectral transmittance can be measured independently, the first by rotating the polarizer at a fixed wavelength, and the latter by changing incident wavelengths and keeping the polarizer at a fixed orientation.
Fig. 1 Schematic illustration to test the functionality of a polarization sensitive GMRF filter, based on a two-dimensional grating diffractive structure. The incident field has an arbitrary linear polarization orientation α, and it is incident normally on the GMRF. The linear polarization axes of the GMRF are indicated as σ and π. The transmitted fields can be analyzed by rotating the linear polarizer (analyzer) through angles γ.
Linear uniform-grating-based GMRF have this property, but only for wavebands that are separated by spectral widths of the order of tens of nanometers that could exceed a typical gain spectrum. In order to circumvent this limitation, a two-dimensional grating device can be engineered to have a transverse gradient structured profile, whose optical response will be a smooth transition from wavelength band to band, resulting in a location-dependent polarized spectral sensitivity across its aperture. For such an optical device, the transmission response past the analyzer can be summarized in the conceptual schematic of Fig. 2 . The device response, to a certain spatial beam profile and incident wavelength (λ2), allows linearly polarized light to go through, which is then analyzed by a final linear polarizer. With the analyzer at position φ, only the central portion of the beam is selected, whereas when the analyzer is in position φ-π/4 the mixed linear polarization states φ and φ ± π/2 both have transmitted components. As the incident light wavelength changes, with the analyzer orientation fixed at φ, the central portion of the device transmits more (or less) light, indicating that the φ polarization is now passing through the device un-attenuated (or more attenuated), and therefore the central portion of the device aperture is completely blocking (or passing) the orthogonal linear polarization φ ± π/2. This implies that the polarized transmittance of the device’s central and annular regions can be inverted using wavelength control, as detected by the analyzer oriented at φ. An optical device with such a spatially-distributed polarized spectral response has been designed and fabricated, with polarized spectral sensitivity to within less than a nanometer. A GMRF filter was used as the basis of the design, due to its very narrow-resonance spectral response. The devices perform as Polarization selective Graded-Reflectivity Resonant Filters, and will be referred to hereafter as P-GRRF.
Fig. 2 Schematic diagram of the transverse intensity profiles passing through the proposed graded-transmittance filter, with wavelength dependent polarization selectivity. The wavelengths shown (λ1, λ2, λ3) are in increasing order, and the analyzer orientation (φ) is arbitrary. The analyzer position φ-π/4 allows mixed linear polarization states to pass through, where the orientation φ allows only pure states. The wavelength response is location dependent across the filter aperture by design.
A polarization insensitive GMRF can be implemented using a grating layer patterned with a hexagonal two-dimensional basis lattice [10]. The hexagonal-periodicity basis-cell hole diameter sizes and depths determine the resonant properties of the device, such as the spectral location of the resonance, the linewidth and the resonance peak value. Fabrication tolerances affect the performance of the device, however, with selective process control, some of the deviation effects can be minimized [15]. The dependence of the GMRF resonance as a function of the hexagonal basis-cell hole diameter, has been simulated using rigorous coupled-wave analysis (RCWA). The results are shown in Fig. 3(a) . The simulated device lattice constant Λ is 1150nm, the guiding layer has a thickness of 360nm and an index of refraction of 1.948, the grating layer has a thickness of 170nm, and it is formed in a 245nm top layer, with index of 1.457. The substrate, with index 1.444, was taken to be of infinite extent below the structure. The wavelength region of interest was chosen from 1530nm to 1550nm, which renders the grating as sub-wavelength in period. Therefore, only the zeroth-diffraction order propagates outside the grating regions, with all other orders becoming evanescent. The choice of this architecture results in resonances that are sub-nanometer in linewidth (FWHM). The resonant response shown if Fig. 3(a), can be interpreted as spectral reflectance or transmittance, with the color scale inverted. The device material absorption and surface scatter are negligible for simulations purposes.
Fig. 3 RCWA simulated resonant-response of (a) a polarization insensitive, and (b) a polarization sensitive GMRF, as a function of the hexagonal basis-cell hole diameter d. In (b) the orthogonal axes σ and π are shown with respect to the “defect” in the hexagonal unit cell. The incident polarization state of the simulated field is direction α (along the bisector of the σ-π angle). The curves represent resonant reflectance with the dark red color as 100% and the navy blue as 0%, or resonant transmittance with the color scheme reversed.
As the diameter of the holes in the grating layer increases, the spectral reflection peak shifts to lower wavelengths, due to the decrease of the effective index in the grating-waveguide coupling condition. The device transmits all incident wavelengths except the one that satisfies the coupling condition, which is reflected at >99%. The simulation results show that the resonant wavelength peak location is nearly a linear function for hole diameter values from 500nm to 750nm.
The introduction of a “defect” in the hexagonal basis lattice results in the resonant behavior shown in Fig. 3(b). The defect is an extra hole in the hex-cell, with a diameter 75% the value of the original basis-cell hole diameters. The simulations indicate that the device resonance is now polarization dependent. This is due to the reduction of the hexagonal symmetry of the original cell, to two mirror-symmetry axes, along the σ-direction and π-direction shown in the insert of Fig. 3(b). For an incident polarization state along the bi-sector orientation (α), there are now two resonant peaks. The polarization response of the P-GRRF device, with respect to different incident polarized light, is shown in Fig. 4 .
Fig. 4 RCWA simulated resonance response of the polarization sensitive GMRF with constant grating basis-cell hole diameters. The device simulated has a hexagonal basis cell, with a 560nm hole “defect” inserted as shown in the graphic. All the other structural values are the same as in Fig. 3, with hexagonal basis-cell hole diameters of 750nm. The resonance is not constant as a function of the incident field polarization. The resonance spectral line crossections for the π- (30°, blue points) and σ-polarization (120°, red points) incident field states are shown to the right. The π-peak maximum is located at 1535.4nm, and the σ-peak maximum at 1536.7nm. The resonance FWHM are 0.6nm and 0.7nm respectively. The incident polarized field orientations are measured clock-wise from the horizontal direction shown in the insert as the dashed axis.
For different incident polarization states the resonance forms two separable peaks, the stronger one (~95%) for light polarized along the σ-axis, and a weaker (~60%) aligned to the orthogonal π-axis. The results in Fig. 3(b) were obtained for an incident polarization along the α-axis, which is the bisector of the σ-π orthogonal directions. The latter orientation of the reflected field contains a mixture of the two resonances.
Analytically, we can express the polarized spectral response function of the P-GRRF in terms of the σ-π unit orthogonal directions as:
Where the functions gσ,π(λ) are the Lorentzian lineshapes in Fig. 4. For an incident field polarized along an arbitrary β direction, the result can be expressed as:The quantities in the brackets are the dot products of β with the unit vector directions σ and π. The relative phases between the incident and reflected polarization states are ζ and ξ.A polarizer (analyzer) can separate the mixed state result in Eq. (2), to obtain either pure state or mixed state projections. This allows the computation of the weights and FWHM separately.
The polarized spectral response, gσ,π(λ), is an implicit function of the basis-cell hole diameters d. Using the simulation data from Fig. 3(b) and Fig. 4, the functionality can be made explicit. The response of the spectral FWHM and the spatial distribution of the resonances, were used to further design the P-GRRF. The FWHM response shows a region of small relative changes in diameters, between 700nm and 800nm. Above and below that region the FWHM changes rapidly, which will have an impact in the resonant discrimination of the device. For a slow-gradient change of the basis-cell diameters, the resonances of different regions will partially overlap, thus creating a smooth spatial intensity transition across a device. This effect is equivalent to dispersion, with an artificially engineered “material” device. In principle, modulating the basis-cell hole diameters of the P-GRRF, one can in continuously vary the spatial location of the resonant resonance and FWHM overlap.
Allowing the spatial “breath” of wavelength resonances to overlap in specific regions requires the controlled placement of variable GMRF basis-cell features across the device aperture. Such a design allows for spatial, spectral and polarization control of the incident optical radiation.
3. Polarization selective graded-reflectivity resonant filter device fabrication
The P-GRRF thin film structure was fabricated using Plasma-Enhanced Chemical Vapor Deposition (PECVD). First a 360nm thick silicon nitride (SixNy) film was deposited on a UV-grade fused silica substrate. This was then over-coated with a 245nm silicon oxide film (SiOx), to form respectively the guiding and grating layers. The stratified structure was coated with photoresist to pattern the grating layer.
The technique used to implement the spatial basis-cell hole-gradient profile consists of first exposing a bias into the resist, followed by the exposure of the two-dimensional planar grating profile at a lower than the desired dose-to-size value, in order to modulate the feature diameters (holes) across the device surface area [16,17]. A GCA g-line stepper was used for both exposure processes. The bias exposure was realized using a phase-only mask, projecting a quadratic intensity distribution across a 1.7mm diameter soft aperture. The required hexagonal basis-cell lattice constant for the planar grating was 1150nm, and the modulated hole-diameter targets ranged between 500nm and 900nm. To overcome the stepper’s imaging limitation of the device periodicity, a multiple exposure and alignment scheme was employed [15]. The device amplitude mask, used for the grating, had a lattice constant of 2300nm with unit-cell hole diameters of 800nm. This mask was used to overlay four consecutive and locally aligned exposures to pattern the P-GRRF diffractive cell, essentially achieving patterning via spatial frequency doubling. Each die had a P-GRRF footprint of 1.7mm in diameter, inside a 5.0x5.0 mm2 die frame. The final hole diameter gradient-profile consisted of smaller diameter holes in the center of the die, with smoothly increasing sizes towards the edge of the device. An SEM micrograph of the footprint of the device is shown in Fig. 5 .
Fig. 5 (a) Schematic illustrating the radial gradient duty-cycle variation of the P-GRRF hexagonal basis-cell hole diameters, for two separate zones in the device. The SEM images shown in the inserts to the right are from the etched final devices, after the exposures of the cells and the circular bias profile. (b) Low magnification SEM micrograph of the etched biased-grating layer. The circular exposure-bias footprint contrasts against the uniform unbiased device around it. This boundary defines the device soft aperture.
Once the resist was fully patterned, it was used as a soft etch mask to transfer the topography 170nm into the top oxide layer of the devices, with a Unaxis Versaline Inductively-Coupled Plasma (ICP) oxide etcher. The etched holes were measured using an SEM, to quantify the basis-cell hole diameter radial variation. The grating basis-cell hole diameter dilation (δd, in nm), varied with the device polar coordinate position (ρ, in mm), as:
For the data shown in Fig. 5(b), the smallest hole diameter is 680nm, at the center of the optic, and it enlarges to 850nm at the perimeter. The quadratic dependence of the gradient results in a 0.5mm diameter region at the center of the die, where the grating hole diameter varies very slowly, from 680nm to 705nm. Whereas in the larger zone from 0.5mm to 1.7mm diameter, the grating hole diameter varies considerably faster, from 705nm to 850nm. This change in the modulation gradient defines a central sub-aperture. The sub-aperture doesn’t have a hard defined boundary, which is undesirable due to possible diffraction effects or the introduction of spectral anomalies.RCWA simulations were performed to predict the spatial and spectral responses of the fabricated dice, using the measured dependence of the P-GRRF hole diameter dilation as a function of the device radial polar coordinate Eq. (3). The simulation model mapped a grating basis-cell hole diameter variation as a function of the radial coordinate ρ. The compromise was that each simulation iteration assumed a constant value of d across the entire device, and once the resonance result was obtained, the device was re-evaluated with d + δd, increased as per the function in Eq. (3), not a linear incremental value. The results are shown in Fig. 6 .Fig. 6 RCWA simulation of the resonant normalized reflected intensity (a), and phase in radians (b), of the P-GRRF, as a function of the device radial polar coordinate ρ. The incident field has a polarization direction β as shown in the insert. (c) and (d) are horizontal data sections from (a) and (b) for the fixed wavelengths given in µm in the legend. The normalized reflected intensity and phase are shown as a function of the radial polar coordinate ρ. (e) and (f) are the corresponding normalized transmitted intensity and phase results, for the same incident wavelengths across the aperture of the optic. The functional dependence of the P-GRRF hexagonal basis-cell diameter to the radial coordinate is given in the text by Eq. (3). The shaded regions indicate the location of a bright (dark) ring in reflection (transmission) at a wavelength of 1537nm. The reflected phase in the central region of the device has a π/2 phase shift to the outer region.
For an incident field with a polarization state aligned 15° off the π-axis (shown as β), we observe that near the center of the device (0< ρ <0.2mm) the reflectance is high for a wavelength of 1537.8nm. As the wavelength values decrease below 1537.0nm, the reflectance has a central null that expands towards the perimeter of the device. This defines a centrally-located radially-symmetric region that acts as a band-stop, with polarization and spectral discrimination properties. For the case where the incident polarization is 15° off the σ-axis, the spatial resonance extent is the same in width, with peaks at higher values (~0.9). The resonances in the latter case are red-shifted by a nanometer, having the band-stop/pass center of the device have a high reflectance at 1538.8nm, and an expanding null for λ<1538.0nm. The conceptual schematics in Fig. 2 are for a transmission filter, and the simulation results are shown in Fig. 6(e) and 6(f). The results show sub-nanometer sensitivity between the central reflection maximum (transmission minimum) and null. The phase response requires more analysis and discussion. For the spatially broad, centrally located sub-aperture resonances (λ>1538.0nm), the transmitted phase (Fig. 6(f)) is smoothly varying with a phase shift located within the resonance region of the device. For resonances below 1538.0nm, the narrow region of the annulus boundary undergoes a phase inversion of less than π/4 radians, which coincides in space with the transmission minimum at the specific incident wavelength. Outside the resonance annulus the transmitted phase is unchanged. The reflected phase (Fig. 6(d)) changes more drastically. For longer wavelengths (λ>1538.0nm), the reflected phase-difference between the center of the device and the edges is 0<δφ<π/2 radians. For shorter wavelengths (λ<1538.0nm), the annulus region separates the central phase and the peripheral phase by π/2<δφ<π radians. These results indicate that, in reflection, the P-GRRF can have wavelength dependent dichroic and/or focusing properties. These properties have been suggested and analyzed in recent reports by others, for high-index contrast devices [18,19].
4. Optical test results and discussion
The fabricated P-GRRF dice were tested using a tunable laser (Agilent 81640A), to selectively scan through illuminating wavelengths from 1530nm to 1545nm. The experimental layout is shown in Fig. 7 . The beam is carried by a single mode fiber to a 3mm beam-expander and collimator (OMS102-4-APC). Light exiting the collimator illuminates the P-GRRF device at normal incidence, and the transmitted beam is profiled on a CCD array detector (COHU-7512), without use of external imaging optics. The 3mm collimated beam overfills the 1.7mm diameter P-GRRF active soft aperture on the plane of the device. A 3mm hard-aperture linear polarizer was used as an analyzer between the P-GRRF and the CCD array, in order to determine the polarization state of the beam transmitted through the P-GRRF. When the incident wavelengths are out-of-band, there is no resonant reflection from the P-GRRF device; and all the light is transmitted through to the analyzer. Due to the 3mm hard-aperture of the linear analyzer, edge diffraction effects were observed in the CCD images collected. Those were identified without the P-GRRF in place. Since the analyzer is located after the P-GRRF, the hard-aperture diffraction effects do not interfere with the P-GRRF performance. The detector was placed against the polarizer holder, minimizing the beam propagation distance. Images from the CCD detector were recorded with a frame-grabber and stored. Passive alignment of the optical system was used to ensure on-axis normal incidence.
Fig. 7 Schematic diagram of the optical test setup. Light from the tunable laser source is expanded to a 3mm diameter collimated beam, through a single mode fiber-optic cable. The output is linearly polarized. The beam is incident along the normal direction on the 1.7mm diameter P-GRRF device, and then it passes through a 3mm hard-aperture linear polarizer. The polarizer is rotated through 360° to act as an analyzer of the P-GRRF transmitted signal. A COHU 7512 CCD camera is used to directly image the beam profile, without any collimation or focusing optics.
A set of the measured data, for various illuminating wavelengths and analyzer positions, is shown in Fig. 8 , as relative intensity graphs. In order to investigate the polarization and wavelength discrimination of the P-GRRF performance, the incident polarization state was fixed to a direction 15° off the π-axis, to enhance the relatively weaker contribution to the resonance and still allow some of the σ-polarization to filter through. The choice of this value for the incident polarization is justified below. A set of wavelength scans were collected with the analyzer at 60° and 105°. These choices were made because the former is not aligned to any of the relevant axes or the incident polarization, and the latter because it is orthogonal to the incident field polarization.
Fig. 8 3D view of the measured beam-profile intensity transmitted through the analyzer, using the test setup in Fig. 7. The laser source wavelength and polarization (β), and the orientation of the analyzer (γ) are shown for each case at the bottom of the figures. The “rim” around the beam profile is due to diffraction from the analyzer’s hard-aperture. The diametrically opposite missing segments in the circular aperture, indicated by the arrows, are due to the analyzer holder contact points. The measurements to the left are along a “mixed” P-GRRF axis condition, whereas the ones to the right are close to the pure σ orientation, and orthogonal to the input polarization β. The profiles change drastically for wavelength differences of less than a nanometer. The intensity scales are relative within the frames, but not absolute from frame to frame.
The measurements presented in Fig. 8 indicate that the devices have a polarization and spectral sensitivity, radially distributed across their aperture. As the incident wavelengths increase in value, the P-GRRF center sub-aperture (0.5mm) acts first as a band-pass filter, thus reflecting an annulus around the center; and then as a band-stop filter, transmitting an annulus. This is observed for both analyzer settings of 60° and 105°. This observation also confirms the polarization sensitivity of the devices tested. Since the analyzer position at 105° is orthogonal to the incident polarization orientation, if the device was polarization insensitive, the output would be a null across the entire aperture, independent of wavelength. If the P-GRRF acts as an intermediate linear polarizer, a transmitted intensity is observed through the analyzer at these settings. Further, the definition of the central sub-aperture is of very high quality, which confirms the high spatial and spectral discrimination of the device. This spectral selectivity is evident for changes in wavelength of the order of a nanometer. The entire cycle of spectral activity of the fabricated device is within 2.5nm, from 1536.0 to 1538.5nm, in good agreement with the simplified model simulation results (Fig. 6).
At fixed incident wavelengths the P-GRRF performance is polarization dependent. For the analyzer orientation at 105° (i.e. orthogonal to the incident polarization state) the presence of the high transmittance peak within the central sub-aperture is a clear indication that the P-GRRF has changed the incident linear polarization state orientation. The contrast between the central sub-aperture and the surrounding annulus is lowered as the orientation of the polarizer is changed to smaller value angles, i.e. aligning with the π-axis. This indicates that more light “leaks” through the surrounding annulus, and it is therefore present past the P-GRRF. For analyzer angles below 40°, the transmitted profile contrast is not enough to distinguish between the central sub-aperture and the annulus. Therefore, the surrounding annulus has a strong polarization transmission dependence, which at 1536.8nm wavelength is composed of both σ and π polarizations, but due to the incident polarization orientation, π is stronger. The reason that the central region transmission peak is not converted to a transmission null is because the central region grating basis-cell hole diameters are 680nm and thus are not resonating with the 1536.8nm wavelength, as light passes through the device. As the analyzer angle is oriented closer to 105°, the σ-polarization passes through and the π is blocked. In reflectivity terms, the behavior is reversed. The central sub-aperture is not reflecting at all, for 1536.8nm, whereas the annulus is weakly reflecting for both P-GRRF axes. There is no doubt that phase is part of the overall transmittance through the optic; however, the present measurements were restricted to intensities only. The phase distortion imposed on the transmitted beam, for the various polarization states, is slowly varying and does not appear to significantly distort the images; however, this can be exploited in some cases for resonator and/or spatial filtering.
5. Conclusions
Polarization sensitive, graded-reflectivity resonant filters (P-GRRF), based on guided-mode resonance filters with radial-gradient spatially distributed features were designed, fabricated, and tested. The demonstrated devices have a sub-nanometer spectral resonance response between 1535 and 1540nm, and high polarization sensitivity for linearly polarized incident light. The results from the simulations agreed very well with the experimental measurements.
Using multiple lithographic exposures and biasing methods, the P-GRRF was engineered to have a central sub-aperture, with no hard boundaries or diffraction anomalies. Such devices can be used as laser cavity mirrors, to minimize the effects of hard-apertures, and in unstable laser cavities, as graded-reflectivity output couplers. The fabrication and design methods outlined in this work can be further used to control polarization sensitive dispersion. The P-GRRF performs as a resonant polarizer in transmission, and can therefore de-couple light beams with different polarized wavelength content. Although most of the data presented was for transmission through the devices, it is expected that phase, amplitude, and polarization can be encoded into the elements for reflection and/or desired transmission properties. This approach can be extended to include multiple responses if desired and should open the possibility of novel optics for a variety of applications.
Acknowledgements
This work was funded in part through the National Science Foundation (NSF) CAREER Grant: ECS0348280, and through the ASAS and Air Force Research Laboratory (AFRL) Grant: FA9550-10-1-0543.
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