15. M. K. Poutous, Z. Roth, K. Buhl, A. Pung, R. C. Rumpf, and E. G. Johnson, “Correlation of fabrication
tolerances with the performance of guided-mode-resonance micro-optical components,” Proc. SPIE 7205,
72050Y (2009).
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27764
16. P. Srinivasan, Z. A. Roth, M. K. Poutous, and E. G. Johnson, “Novel method for the fabrication of spatially
variant structures,” J. Micro/Nanolith. MEMS- MOEMS 8, 013010 (2009).
17. J. Sung, H. Hockel, and E. G. Johnson, “Analog micro-optics fabrication by use of a two-dimensional binary
phase-grating mask,” Opt. Lett. 30(2), 150–152 (2005).
18. F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical aperture
low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18(12),
12606–12614 (2010).
19. D. Pietroy, A. V. Tishchenko, M. Flury, and O. Parriaux, “Bridging pole and coupled wave formalisms for
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.
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27765
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.
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.
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27766
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.
An
alyze
r T
ransm
issi
on
Incident wavelength
An
alyze
r T
ransm
issi
on
Incident wavelength
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-
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27767
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.
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:
0
0
gG
g
(1)
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:
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27768
ˆ ˆ( ) ( ) sin ( ) cosi i
incG E g e g e
(2)
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 δ 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.
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.
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.
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27769
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.
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:
2( ) 227 0.2 85d (3)
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.
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27770
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.
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.
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].
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27771
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.
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27772
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.
Tunable Laser
Agilent 81640ACCD
camera
P-GRRF
Linear analyzer
Fiber output
beam collimator
Single mode
fiber
Tunable Laser
Agilent 81640ACCD
camera
P-GRRF
Linear analyzer
Fiber output
beam collimator
Single mode
fiber
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.
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
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27773
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.
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27774
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.
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27775
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.
#138136 - $15.00 USD Received 12 Nov 2010; revised 10 Dec 2010; accepted 11 Dec 2010; published 16 Dec 2010(C) 2010 OSA 20 December 2010 / Vol. 18, No. 26 / OPTICS EXPRESS 27776
