Polarization-independent tunable optical
filters using bilayer polarization gratings
Elena Nicolescu and Michael J. Escuti*
Department of Electrical and Computer Engineering, North Carolina State University,
2410 Campus Shore Drive, Raleigh, North Carolina 27606, USA
*Corresponding author: email@example.com
Received 28 January 2010; revised 9 June 2010; accepted 11 June 2010;
posted 15 June 2010 (Doc. ID 123511); published 6 July 2010
We demonstrate a polarization-independent tunable optical filter based on switchable polarization
gratings (PGs) formed using reactive and nonreactive liquid crystals (LCs). PGs are anisotropic diffrac-
tion gratings that exhibit unique properties, including a zero-order transmittance that is independent of
incident polarization and that can vary from ∼0% to ∼100%, depending on wavelength and applied
voltage. A stack of several PGs of varying thicknesses combined with an elemental angle filter yields
polarization-independent bandpass tuning with minimal loss. We introduce a novel hybrid PG consisting
of both reactiveand nonreactive LC layers, whichallows very thick gratings to be created with thin active
LC layers. We demonstrate a tunable optical filter with a peak transmittance of 84% of unpolarized light,
a minimum full width at half-maximum of 64nm, and a maximum tuning range of 140nm.
Optical Society of America
120.2440, 230.3720, 230.0250.
Tunable optical filters have a wide range of applica-
tions, including spectroscopy, optical communication
networks, remote sensing, and biomedical imaging
and diagnostics [1–3]. In recent years, research ef-
forts have focused on miniaturizing tunable optical
filters into physically small packages for compact
portable spectroscopy and hyperspectral imaging ap-
plications, such as real-time medical diagnostics and
defense applications . Competing filter implemen-
tations, including dispersive elements matched with
aperture stops (Czerny–Turner) [5,6], mechanically
tuned etalons (Fabry–Perot) [7,8], liquid crystal (LC)
tunable reflection filters [9,10], and assemblies of
stacked birefringent wave plates and polarizers
(Lyot, Solc, and Evans), [11,12] are not completely
ideal for these applications due to the high cost of im-
plementation, high insertion losses, strong polariza-
tion sensitivity, or difficulty in miniaturization.
Here we introduce an alternative tunable filter ap-
proach that is based on polarization gratings (PGs)
[13–16], with the key advantage of having higher
throughput and no polarizers. Also called anisotropic
or vectorial gratings, PGs are a class of thin film dif-
fractive elements, which are described as spatially
varying, periodic profiles of optical anisotropy. They
operate by periodically modulating the polarization
state of the wavefront passing through them (as
opposed to modulating phase or amplitude alone).
These gratings can be created in two varieties:
switchable [17,18] (tunable by applied voltage) and
nonswitchable  (polymer). Both types of gratings
exhibit the unique diffraction properties shown in
For the purposes of this discussion, we will mainly
be concerned with the zeroth diffracted order, which
corresponds to the light that is directly transmitted
through the grating having a diffraction angle θm¼
0. The zeroth-order diffraction efficiency (η0) spec-
trum for light normally incident (within ?20°Þ is
η0ðλÞ ¼ cos2ðΓ=2Þ;
where Γ ¼ 2πΔnd=λ is the retardation, Δn is the LC
birefringence, d is the LC thickness, and λ is the
© 2010 Optical Society of America
3900APPLIED OPTICS / Vol. 49, No. 20 / 10 July 2010
vacuum wavelength of incident light. Note that dif-
fraction efficiency is a normalized term that de-
scribes the inherent diffraction behavior of a single
PG, ignoring all absorption/reflection losses in the
substrates or at the interfaces. Light that does not
go into the zero order can diffract into only the
? first orders (m ¼ ?1) with the diffraction angle
(θm) governed by the grating equation, sinθm¼
mλ=Λ þ sinθin.
Our filter concept comprises a stack of multiple
PGs, as shown in Fig. 1, where the individual stages
in the filter stack are PGs of increasing thickness. As
light passes through the first grating, it diffracts
such that the zero order contains a wide passband
centered on the design wavelength, and all other
wavelengths are coupled into the first orders. Light
from the zero order then enters the second grating,
and it diffracts again, resulting in a narrower pass-
band coupled into the zero order [Fig. 1(a)]. Each ad-
ditional grating is thicker than the previous and
diffracts more wavelengths off axis, thereby achiev-
ing increasingly narrower passbands [Fig. 1(b)]. All
but the zero order is then blocked using an angle fil-
ter. Note that in order to achieve proper separation of
the orders, we stack the PGs such that the grating
vector of each is rotated with respect to the previous.
This results in the first orders being separated spa-
tially, such that at the plane of the angle filter, the
first-order diffracted beams are arranged in a circle
around the zero order.
The transmittance of the system is a multiplica-
tion of each PG zero-order diffraction efficiency and
the losses due to absorption/reflection from sub-
strates and interfaces:
TðλÞ ¼ KNY
η0;nðλÞ ¼ KNY
where N is the total number of stages, K is the trans-
mittance of the substrates used in each individual
PG element (essentially including any reflection and
absorption of the electrodes), η0;nðλÞ is the zeroth or-
der diffraction efficiency of stage n, and dnis the LC
layer thickness of grating n. Note that the transmit-
tance in Eq. (2) is a real-world measure of through-
put, defined as the output intensity of the zero order
(Iout) divided by the input intensity to the system
(Iin). Figure 1(c) shows the representative transmit-
tance spectra for ideal filters with three and five
stages centered at 600nm with birefringence Δn ¼
0:2 ignoring absorption and reflection losses.
The filter is tuned across the visible range by re-
ducing its effective birefringence [ΔnðVÞ] through
applied voltage. By individually controlling each PG
with an applied voltage, we lower the effective bire-
fringence, shifting the passband toward lower wave-
lengths, according to Eq. (1). Depending on small
fabrication variations, some of the PGs may be initi-
ally biased, so that the operational peak occurs at the
We identify three design possibilities or filter pro-
gressions involving the choice of dnand N. Within
each design, trade-offs between minimum possible
full width at half-maximum (FWHM), minimum
number of gratings, and maximum required grating
thickness must be considered. The three progres-
sions are exponential (d ¼ d02n−1), linear (d ¼ d0n),
and compound (first three gratings follow the linear
progression, then the third grating is repeated). Fig-
ure 2 shows simulation results for the three config-
urations, where Δn ¼ 0:2, the thickness of the first
grating is d0¼ 3μm, and the design wavelength is
λ0¼ 600nm . The simulation shows that the ex-
ponential progression is the optimum configuration
for minimizing both FWHM and the number of grat-
ings required. Minimizing the number of gratings is
important because the minimal absorption of light by
the indium tin oxide (ITO) and glass surfaces can
become appreciable when multiplied through many
interfaces. For example, a filter with target FWHM
of 30nm requires four, six, and thirteen gratings
for the exponential, linear, and compound construc-
The trade-off is that the exponential progression
requires cells with a much thicker LC layer. For the
same case as above, the exponential, linear, and com-
pound progressions require a maximum LC layer
thickness of 25μm, 15μm, and 9μm, respectively.
As with all LC devices, large thicknesses (e.g.,
d > 50μm) are not desirable because they tend to
(a) Diffraction behavior oftwo stackedPGs. (b) Generalfilter struc-
ture with PG stack and angle filter. (c) Representative transmit-
tance spectra for filters with three and five stages, where each
stage has twice the retardation of the previous, the peak wave-
length is 600nm, and the birefringence Δn ¼ 0:2.
(Color online) Stacked PG tunable optical filter concept.
10 July 2010 / Vol. 49, No. 20 / APPLIED OPTICS 3901
have slow response times and are prone to defects.
Furthermore, a larger thickness imposes a larger
grating period (typically Λ ≥ 1:5d) . While this
is achievable using holographic techniques, a large
Λ leads to a small angle separating the zero and first
orders and restricts the angular aperture of the tun-
We overcome these limitations by introducing a no-
vel bilayer PG (BPG) consisting of both reactive and
nonreactive LC layers that allows very thick gratings
to be created with thin active LC layers. The BPG is
a combination of a switchable PG and a polymer
PG with the basic structure shown in Figs. 3(a)
and 3(b), where the polymer layer determines the
nominal thickness of the grating and we add only a
thin layer (one full-wave retardation) of nematic LC
to achieve tuning by the applied voltage. This struc-
ture demonstrates two complex anchoring conditions
with high quality: (i) a polymer PG aligning a switch-
able LC and (ii) a degenerate-planar anchoring sur-
face with low pretilt enabling uniform orientation,
without defects, of the switchable LC. The BPG exhi-
bits the same favorable characteristics as a normal
PG and can be directly integrated with the filter
design described above.
The basic fabrication process of a BPG consists of a
combination of the switchable and polymer PG fab-
rication steps [13,18]. First, a polarization hologram
is created by superimposing two coherent orthogo-
nally polarized beams from an ultraviolet laser with
a small angle between them. Next, one ITO-coated
glass substrate is coated with a photoalignment ma-
terial, in this case, ROP103-2CP (Rolic Technologies,
Limited). The substrate is then exposed to the polar-
ization hologram, capturing the pattern in the photo-
alignment layer. The polymer LC RMS03-001C
(Merck) is then spin coated onto the substrate in thin
layers. After each layer is applied, it must be photo-
polymerized by exposure to UV light. This process is
repeated until a polymer layer of the desired thick-
ness is achieved. A second ITO glass substrate is
then coated to achieve a degenerate-planar anchor-
ing condition [22,23], which improves switchable LC
alignment to the polymer surface. The two ITO sub-
strates are then laminated together, such that a
uniform thickness (usually a few μm) is achieved.
Finally, a nematic LC (in this case MDA06-177,
Merck) is injected into the cell gap and fills by capil-
lary action. The surfaces direct the LC orientation to
create the appropriate structure.
The diffraction from the BPG follows the same pat-
tern as that of a traditional PG. Accounting for the
individual retardation of each layer, the total retar-
dation (Γ) is written as
Γ ¼ 2πðΔnpdpþ ΔnLCdLCÞ=λ;
where dPand ΔnPrefer to the properties of the
polymer layer and dLCand ΔnLCrefer to the proper-
ties of the switchable layer. The BPG has zero-order
diffraction efficiency peaks occurring at wavelengths
the total number of PGs in the filter stack and the minimum
FWHM achieved for the three filter configurations, where the peak
wavelength is 600nm, Δn ¼ 0:2, and d0¼ 3μm.
(Color online) Theoretical plot of the relationship between
results of the BPG tunable optical filter. (a) BPG with no applied
voltage, (b) BPG with applied voltage (V ≫ Vth), (c) experimental
spectra of three individual BPGs of exponentially increasing thick-
ness, and (d) tuning characteristic of the entire three-stage BPG
(Color online) Structure of the BPG and experimental
3902APPLIED OPTICS / Vol. 49, No. 20 / 10 July 2010
λM¼ Δnpdp=M þ ΔnLCdLC=M;
where M corresponds to the spectral fringe. The
minimum value of the desired tuning range is set
by the birefringence and thickness of the polymer
layer, and the maximum limit of the tuning range is
determined by the birefringence and thickness of the
For experimental demonstration of our design, we
built an exponential progression filter with three
stages and a peak wavelength of 685nm. The three
gratings exhibited one, two, and four full waves of re-
tardation at the center wavelength. The first grating
had no polymer layer, and its LC layer was 4:8μm
thick. The second and third gratings had polymer
layers of 4.6 and 9:1μm, respectively, in addition to
the 4:8μm LC layer. The thicknesses were calculated
based on transmission spectra of the samples and
material birefringence . The three gratings were
laminated together using the optical adhesive
NOA65 (Norland Products).
We designed the PGs to have a grating period
Λ ¼ 16μm, which leads to a diffraction angle θm¼
2:3°. We chose the grating period based on elastic-
continuum theory , which suggests that the mini-
mum grating period likely to support a defect-free
structure for this design is ≥12μm.
In order to achieve proper angular filtering of the
zero and first orders, we implemented a simple spa-
tial filter [lens/stop/lens in Fig. 1(b)]. For this setup,
we define two constraints on the divergence (Ω) of the
Ω ≤ arcsinðλmin=2ΛÞ;
Ω ≤ π=N;
where Ω is the half-angle of the cone of the input
beam, λminis the minimum wavelength in the spec-
trum that is within the tuning range of the filter, Λ is
the grating period, and N is the number of stages in
the filter. The first constraint ensures that there is no
overlap between the zero order and the first orders.
This equation comes from a direction cosine space
analysis of PGs . The second constraint ensures
that there is no overlap between the first orders
(achieved by rotating each grating vector), which
could cause coupling of light back into the zero order.
For any N, the maximum value of Ω is the smaller of
the two values found in Eq. (5). In this experiment we
used a collimated input and angular aperture of≤2:3°
for data collection.
Figure 3(c) shows the zero-voltage spectra of the
three BPGs with M ¼ 1, 2, and 4. Figure 3(d) shows
the experimental spectrum of the filter as well as its
tuning characteristics. The behavior of the filter is
similar to the theoretical prediction, with a FWHM
of ∼64nm and a peak transmittance of ∼84%.
Although the theoretical diffraction efficiency of each
BPG is ∼100%, in the experimental result we see the
effects of absorption and reflections within the sub-
strates and at interfaces as well as defects caused by
nonideal fabrication techniques.
The filter shows low leakage in the stop bands.
We also note the secondary spectral peak occurs at
∼420nm. This peak is used to measure the free spec-
tral range (FSR), which refers to the distance be-
tween adjacent bandpass peaks. In this case, the
FSR is ∼260nm—leading to a finesse of approxi-
The tuning range is approximately 140nm, which
is achieved by applying voltage across each of the
BPGs, such that the grating is erased in the switch-
able LC portion of each cell, as in Fig. 3(b). The
tuning range can be increased by increasing the
thickness of the switchable LC layer. Table 1 shows
how the transmittance, peak wavelength, and
FWHM of the filter change with applied voltage.
We notice a reduction in the peak transmittance with
applied voltage, which we suspect is caused by a spa-
tially nonuniform tilt profile of the LC director as a
voltage is applied. If so, then this is not a fundamen-
tal limitation and could be improved by more careful
fabrication. We believe that photoalignment materi-
als and processing techniques that enable stronger
anchoring strength will reduce this effect. We also
notice a reduction in the FWHM of the filter with
applied voltage, which we attribute to dispersion
In summary, we have experimentally demon-
strated a polarization-independent tunable optical
filter with a maximum peak transmittance of 84%
of unpolarized light, minimum FWHM ¼ 64nm, a
maximum tuning range of 140nm, FSR ¼ 260nm,
finesse ¼ 4, and an initial peak wavelength of
685nm. We also introduced a novel BPG with high
quality that integrates both switchable and polymer
varieties. We demonstrated a polarizer-free approach
using materials and construction with strong poten-
tial for low cost and small size implementations. We
also described the theoretical operation and dis-
cussed the design trade-offs. We have shown experi-
mentally that the exponential progression is most
favorable as long as the switchable layer remains
thin (i.e., by implementing the BPG). In order to
further improve on current results, we suggest the
addition of more stages to the filter in the exponen-
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