Angle-insensitive and narrow band grating filter
with a gradient-index layer
Gaige Zheng,
1,
* Jiawei Cong,
2
Linhua Xu,
1
and Wei Su
3
1
School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China
2
School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China
3
Department of Electrical and Computer Engineering, University of Victoria, Victoria, B.C. V8W 3P6, Canada
*Corresponding author: jsnanophotonics@yahoo.com
Received August 27, 2014; accepted September 13, 2014;
posted September 18, 2014 (Doc. ID 221737); published October 10, 2014
We demonstrate the design of an efficient angle-insensitive guided mode resonance filter (GMRF), with narrow
bandwidth and low sideband reflection, for TE-polarized waves. The reflection properties of the multilayer struc-
ture have been studied, and the results verify that the thin film design of the gradient-index layer is important for the
realization of an angle-insensitive filter. Various gradient coefficients of the thin film have distinct effects on
the reflection spectrum. For an increasing incident angle, although the line-shape symmetry becomes less perfect,
the positions of the resonant peak remain the same. The GMRF proposed here has many desirable attributes that
lends itself to being an excellent platform, for devices such as lasers, detectors, filters, and sensors. © 2014 Optical
Society of America
OCIS codes: (230.7408) Wavelength filtering devices; (050.1950) Diffraction gratings; (310.4165) Multilayer design;
(310.2790) Guided waves.
http://dx.doi.org/10.1364/OL.39.005929
A resonant grating filter, also known as guided-mode
resonance filter (GMRF), has attracted considerable in-
terest, by virtue of the simple structure and nearly
100% diffraction efficiency at the resonant wavelength
[
1–4], which is promising in the applications of many
fields, such as laser devices, dense-wavelength-division
multiplexing systems in optical communication, high-
sensitivity sensors, and so on. When the evanescent
waves diffracted by the grating layer are coupled into
the waveguide layer, energy from an incident wave will
be coupled into a leaky mode, and then back into one or
more radiation modes. The guided mode resonance
(GMR) effect will occur and r esult in an efficient energy
exchange, between the reflected wave and the transmit-
ted wave [
5–9].
To make GMRFs for practical applications, the reso-
nance spectral response such as symmetry, sideband
suppression, spectral width, and line shape should be
controlled through precise design. A method has been
presented in [
10] for reducing the spectral width of
GMR, to enhance the Q factor. The introduced dielectric
film to the bottom of the membrane was shown to be
capable of effectively reducing the coupling, and enhanc-
ing the resonant Q factor. The proposed method provided
an effective means of adjusting the resonance property
without varying the original GMR structure [
10]. A nar-
row GMRF with a high-index substrate has been reported
in [
11], as well as an added layer on the substrate. The
refractive index and thickness of the added layer were
the critical parameters for the GMR effect [
11]. Recently,
a design has been presented of a conformal graded-
index-layer (GRIN) sinusoidal-profile GMR grating, and
a conformal step-index multilayer sinusoidal-profile
GMR grating [
12]. To the best of our knowledge, most
research to date has focused on configurations in which
the refractive index of the thin film layer is constant;
much less attention has been paid to GMR devices with
a GRIN layer. In this Letter, an efficient GMRF with a
GRIN layer is presented, and its main properties are
investigated; t he results show that the introduction of
a GRIN material into a GMR structure is a good way
to balance the needs of high performance of spectral re-
sponse, and large angular tolerance.
The selected angle-insensitive GMRF is a triple-layer
stack comprising the grating layer, the planar waveguide
layer, the GRIN layer, and the substrate layer from top to
bottom. The parameters of the device as well as the in-
cident plane wave are shown in Fig.
1. The filter structure
critically affects the coupling of incident light. The band-
width and peak position of the reflected beam spectra
can be tuned with the structural parameters, including
the refractive indices (n), layer thicknesses (d), grating
fill factor (f ), and grating period (Λ), as depicted in Fig.
1.
The subscripts are c for cover layer, g for grating layer, w
for waveguide layer, gra for GRIN, and s for substrate.
The refractive index variation throughout the physical
thickness of the GRIN layer is described by
n
gra
yn
0
αy 0 ≤ y ≤ d
gra
; (1)
where n
0
is chosen as 1.5, α is gradient coefficient, and y
is the relative thickness of GRIN layer (whose range is
0 ≤ y ≤ d
gra
). This kind of linearly graded layer can be
Fig. 1. Scheme of the designed GMRF with a GRIN layer.
October 15, 2014 / Vol. 39, No. 20 / OPTICS LETTERS 5929
0146-9592/14/205929-04$15.00/0 © 2014 Optical Society of America