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One-way optical transmission in silicon grating-photoniccrystal
structures
Yanyu Zhang,1 Qiang Kan,2 and Guo Ping Wang1,3,*1School of
Physics and Technology, Wuhan University, Wuhan 430072, China
2Key Laboratory of Semiconductor Materials Science, Institute of
Semiconductors, Chinese Academy of Sciences, Beijing 100083,
China3College of Electronic Science and Technology, Shenzhen
University, Shenzhen 518060, China
*Corresponding author: [email protected]
Received May 14, 2014; revised July 2, 2014; accepted July 15,
2014;posted July 16, 2014 (Doc. ID 212072); published August 15,
2014
One-way optical transmission through a composite structure of
grating-photonic crystal (PC) is presented. This uni-directional
transportation property originates from the diffraction of grating
to change the direction of light incidentinto the PC from
pseudobandgaps to passbands of the PC. Numerical simulation shows
that a light beam in a certainrange of frequencies can transmit the
composite structure when it is incident from the grating interface
but is com-pletely reflected by the structure when it is incident
from the PC interface, which is further verified experimentally.The
present structure may provide another more compact way for
designing on-chip optical diode-like integrateddevices. 2014
Optical Society of America
OCIS codes: (130.3120) Integrated optics devices; (230.5298)
Photonic crystals; (230.1950) Diffraction
gratings.http://dx.doi.org/10.1364/OL.39.004934
Recently, much research has been devoted to all-opticaldevices
due to their important potential applications inoptical
communication and quantum computers [1,2].
A unidirectional transmission device, which allows lightto pass
in one direction but be blocked in the oppositedirection, is a
fundamental element among them. In orderto realize unidirectional
propagation, magneto-optic ma-terials [35], optics nonlinearity
[68], metamaterials[911], and indirect interband photonic
transition [12],etc., have been employed. On the other hand,
structureslike dielectric or metal gratings [1315], parity time
sym-metry waveguides [16,17], plasmonic subwavelength slits[18,19],
and photonic crystals (PCs) with pseudobandg-aps [2022] have been
reported. However, grating andPC slab structures may be a little
more complicated torealize in experiment or have lower one-way
contrastratio and higher loss. Plasmonic subwavelength slits
usu-ally work in a narrow band of frequency. In this Letter,we
present a simple and compact composite structure ofsilicon
grating-PC to realize one-way transmission in awideband range of
frequency with reasonable high-contrast ratio and low loss.
Figure1(a)shows the schematic configuration of thepresent
composite grating-PC structure. It consists of arectangular grating
and a two-dimensional PC with thesame height (h 320 nm). The PC has
a square latticeconstructed with circular silicon rods. The lattice
con-
stant is a 600 nm, and the radius of the silicon rodsis r 225
nm. The thickness of the rectangular silicongrating is t 210 nm,
and the grating constant isag 1800nm, with slit width w 600 nm. The
distancebetween the grating and PC is d, which is a variation inthe
following discussion.
Figure1(b)shows the simulated transmission spectraof a
transverse magnetic (TM) polarized plane light nor-mally incident
from the grating interface (forward, redsolid line) and PC
interface (backward, blue dash line),respectively, by using the
finite-difference time-domain(FDTD) method [23]. In the
simulations, the refractiveindex of silicon is set to 3.49 at 1400
nm and the distance
between grating and PC is d93
nm. From the figure,we can see that there exists an asymmetric
transmissionregion ranging from 1355 to 1375 nm (gray region).For
instance, at wavelength 1360 nm, the forward trans-mission of light
forms a peak with a transmittance T(transmitted light intensity
divided by the incident lightintensity) of about 95% (black arrow),
while the transmit-tance of light in the backward direction is
around 1%, in-dicating that the incident light can only pass
through thecomposite structure in the forward direction.
On the other hand, we can also see that the transmis-sion of
light ranging from 1470 to 1630 nm (green slashedregion) is around
zero from either the forward andbackward direction, which indicates
that light withwavelength falling into this range of frequency
showsno unidirectional transmission.
Figures 1(c) and 1(d) show the simulated electricalfield
intensity distributions of a TM light at 1360 nm in-cident in the
forward [Fig.1(c)] and backward [Fig.1(d)]directions, respectively.
The arrows indicate the direc-tions of the incident light. We can
see that when the lightis incident from the grating interface into
the compositestructure (forward) it can pass through the
grating-PCstructure to the outside [Fig. 1(c)]. However, when
thelight is incident from the PC interface into the
structure(backward), it is reflected back completely by
severallayers of PC [Fig. 1(d)].
To understand the physics underlying the above one-way
transportation of light, we calculate the TM-modeband structure of
the PC (see Fig. 2) by using the
plane-wave expansion method [24]. The frequency is nor-malized
by, where is the incident wavelength.a From theband structure, we
can see that there exists a directionalbandgap (gray region)
between the third and fourthbands, ranging from 2c 0.4428 to
2c0.4086 (from 1355 to 1470 nm in wavelength). Such agap stops the
propagation of light along the X direc-tion but allows the
propagation of light along the Mdirection. Therefore, by using a
grating to change the di-rection of light (ranging from 1355 to
1375 nm) incident
4934 OPTICS LETTERS / Vol. 39, No. 16 / August 15, 2014
0146-9592/14/164934-04$15.00/0 2014 Optical Society of
America
http://dx.doi.org/10.1364/OL.39.004934http://dx.doi.org/10.1364/OL.39.004934http://localhost/var/www/apps/conversion/tmp/scratch_10/
8/11/2019 Optical Diode
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region). Figure 3(b) shows the measured transmissionspectra of
light incident into the composite structure withd 93 nm in the
forward (red circle, solid line) andbackward directions (blue x
dashed line). For compari-son, the simulated transmission of light
beam from theforward (red solid line) and backward directions
(bluedashed line) are also presented in the figure. We see that,at
wavelength 1360 nm, nearly 75% of the incident light is
passed through the grating-PC structure in the forward
direction, while only around 1% of the light can transmitthe
structure as it is incident in the backward direction,indicating
that the light can propagate through the struc-ture in one incident
direction, but will be reflected in theopposite direction. The
difference between the experi-mental measurement and numerical
simulation [95%transmittance of light in the forward direction;
seeFig. 1(b)] can be attributed to the fact that a part ofthe
incident light is leaked out from the structure surfacein
experiments.
We also measured the transmission spectra of the in-cident light
ranging from 1470 to 1500 nm (within the fullbandgap of the PC)
[see inset of Fig. 3(b)]. We can seethat it does not matter whether
the illumination is inthe forward or backward directions, the
transmittanceof the light is no more than 2%, indicating that the
lightshows no one-way transmission but instead is
completelyforbidden by the composite structure in both forwardand
backward directions.
We also investigate the effect of distance d betweengrating and
PC on the one-way transmission. We intro-duce a one-way contrast
ratio Cs as Cs TF TBTFTB [25], where TF and TB are the forward
andbackward transmittances, respectively. Figure 3(c)shows the Cs
dependence on d as the incident light isset at three wavelengths.
We can see from the figure thatthe one-way contrast ratio shows
little dependence onthe distance between grating and PC when the
incidentlight is at different wavelengths. For example, as the
in-cident light is at 1360 nm, theCs is around 0.73 and 0.75as d
170 nm and 93 nm, respectively (red square,dotted line). From this,
we can conclude that the
present composite grating-PC structure shows goodproperties in
one-way transmission as the distance be-tween grating and PC is
changed within a certain valueof ranges.
On the other hand, when the thickness of grating ischanged, it
mainly influences the transmittance of theunidirectional
transmission of the structure. This is be-cause the thickness of
gratings will, in general, affect
the diffraction efficiency of light, so as to change the
in-tensity of light incident into the PC. While the grating
con-stant is changed, it will change the direction anddiffraction
efficiency of illumination light incident intothe PC. If it makes
the wave vector of light into thePC still fall in the stopband of
the PC after diffractedby the grating, the structure will show no
unidirectional
propagation. Otherwise, unidirectional transmission ap-pears.
Our calculations (not shown here) reveal that,although some grating
constants still make the one-way transmission of structure work, it
may reduce thetransmittance of the structure. This means that
thegrating constant may affect both the function of
unidirectional transmission and the transmittance ofgrating-PC
structures.
When the light source is tilted, it may fall into the pass-band
of the PC. Hence, even when there is no grating infront of the PC,
light may pass through the structure nomatter what (forward or
backward) direction of light isincident, indicating that one-way
transmission phenome-non will disappear. In the case of grating
being present,tilted illumination will affect the contrast ratio of
one-
way transmission and even destroy the
unidirectionaltransmission, because it will modulate the direction
oflight incident into the PC. This is in principle similarto the
case where grating constant in front of PC ischanged.
In conclusion, we have demonstrated both numericallyand
experimentally a simple and compact grating-PCstructure for
wideband and high-contrast asymmetricoptical transmission. Such a
unidirectional optical trans-
portation property originates from the role the gratingplayed in
changing the direction of light incident intothe PC from the
pseudobandgap to the passbands ofthe PC. The present structure may
provide another moreeffective way for designing on-chip optical
diode-likeintegrated devices.
This work was supported by 973 Program(2011CB933600) and
National Natural Science Founda-tion of China (Grant 11274247).
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