This document proposes and analyzes photonic NOT and NOR logic gates based on a single photonic crystal ring resonator (PCRR). The PCRR is formed by removing rods along the ΓM direction in a square lattice photonic crystal structure. Beam interference theory and 2D FDTD simulations are used to analyze the logic gate behavior. The simulations show the gates can function as NOT and NOR gates without requiring nonlinear materials. An output intensity greater than 50% is defined as logic 1, and less than 50% as logic 0. This approach could potentially be used to integrate photonic logic circuits on a chip.

1. Photonic NOT and NOR gates based on a single
compact photonic crystal ring resonator
Jibo Bai,1
Junqin Wang,2
Junzhen Jiang,1
Xiyao Chen,3
Hui Li,1
Yishen Qiu,1
and Zexuan Qiang1,
*
1
School of Physics and Optoelectronics Technology, Fujian Normal University, Fuzhou 35007, China
2
College of Chemistry and Material Science, Fujian Normal University, Fuzhou 35007, China
3
Department of Physics and Electronic Information Engineering, Minjiang University,
Fuzhou 350108, China
*Corresponding author: qiangzx@fjnu.edu.cn
Received 10 August 2009; revised 26 October 2009; accepted 9 November 2009;
posted 16 November 2009 (Doc. ID 115473); published 10 December 2009
New all-optical NOT and NOR logic gates based on a single ultracompact photonic crystal ring resonator
(PCRR) have been proposed. The PCRR was formed by removing the line defect along the ΓM direction
instead of the conventional ΓX direction in a square-pattern cylindrical silicon-rod photonic crystal struc-
ture. The behavior of the proposed logic gates is qualitatively analyzed with the theory of beam inter-
ference and then numerically investigated by use of the two-dimensional finite-difference time-domain
method. No nonlinear material is required with less than a 2:2 μm effective ring radius. The wavelengths
of the input signal and the probe signal are the same. This new device can potentially be used in on-chip
photonic logic-integrated circuits. © 2009 Optical Society of America
OCIS codes: 130.3750, 230.1150, 230.5298, 140.4780.
1. Introduction
All-optical logic gates have attracted increased at-
tention mainly due to their potential application in
all-optical signal processing such as addressing,
switching, header recognition, odd and even parity
checks, data encoding, and encryption, all of which
will lead to the development of all-optical ultra-
high-speed communication networks and next-
generation optical computers. Work reported to date
is mostly based on traditional technologies including
optical fibers [1], waveguide interferometers [2],
semiconductor optical amplifiers [3], and microreso-
nators [4]. However, the traditional technologies
have the disadvantage of intrinsic limitations. For
example, fiber-based logic gates are difficult to use
for chip-scale integration. Waveguide interferometer
based gates usually require complicated configura-
tions and a reduction in size is also a challenge. Semi-
conductor optical amplifiers and microresonators are
limited by their inevitable spontaneous emission
noise [5].
Photonic crystals (PCs), on the other hand, offer
great promise in ultracompact all-optical integrated
circuits with ultrafast switching and significant re-
duction in the size and power consumption. Recently,
various photonic logic gates based on a photonic crys-
tal platform have been reported [6–10]. Most of the
reported research was based on nonlinear optical ef-
fects, which typically require relatively large power
consumption operating in a narrow frequency range
and have difficulty in integrating with silicon-based
optical devices. Very recently, photonic logic gates
based on photonic crystal ring resonators (PCRRs)
[11,12] were demonstrated since PCRRs can provide
scalable ring sizes and flexible mode coupling config-
urations and present a potential solution to overcome
the scaling obstacle of traditional microring resona-
tors [13,14]. However, they still require a significant
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© 2009 Optical Society of America
20 December 2009 / Vol. 48, No. 36 / APPLIED OPTICS 6923

2. amount of power consumption, e.g., 330 W=μm re-
ported in Ref. [11]. In addition, they require two non-
linear PCRRs and the wavelengths of the probe
signal and the input signal differ, which increases
the complexity of the operation and the size of the
device.
Generally, there are two representative PC groups,
airhole type and dielectric-rod type. While it has
been argued that hole-type PCs are relatively easier
to fabricate than rod types by using traditional litho-
graphy and etching methods, recently, with bottom-
up fabrication techniques, it is more attractive and
natural to grow rod-type PCs [15]. So far, much re-
search related to rod-type PCs has been theoretically
and experimentally demonstrated [15–19], which
does not present only a successful practical realiza-
tion of the rod PC structures, but also reports trans-
mission efficiencies and out-of-plane radiation losses
comparable with hole geometry [20]. Additionally,
dielectric-rod-type PC waveguides can be easily oper-
ated in single mode while airhole-type PC wave-
guides tend to be multimode without any other
structure modification.
We propose and discuss photonic NOT and NOR logic
gates based on one single-ring two-dimensional
PCRR composed of cylindrical silicon rods in air.
The new configuration of PCRR is based on
square-lattice PC pattern by forming the ring resona-
tor along ΓM direction (45° PCRR) instead of our pre-
viously demonstrated ΓX direction [13]. Only one
wavelength is considered for both probing signal
and input signal in this work. In Section 2 we briefly
describe the characteristics of a 45° PCRR. In Sub-
section 3.A we discuss the schematic of the proposed
photonic logic gates with qualitative analysis based
on the principle of beam interference. The behavior of
new logic gates is numerically analyzed in Subsec-
tion 3.B by using a two-dimensional (2D) finite-differ-
ence time-domain (FDTD) technique. The definitions
of logic 0 and 1 are also introduced, and the photonic
NOT and NOR gates are discussed in detail. Finally, we
present our conclusions in Section 4.
2. 45° Photonic Crystal Ring Resonators
The schematic of a 45° PCRR is shown in Fig. 1(a),
and consists of a square lattice of silicon rods in
air with refractive indices of nSi ¼ 3:48 and
nair ¼ 1. The incident port and exit ports are labeled
as A, B, C, and D, respectively. The surrounding per-
iods of the W1 bus waveguide (one line of rods re-
moved along the ΓX direction) and ring resonator
are 4 and 22, i.e., d ¼ 4a and L ¼ 22a, respectively.
The coupling strength, Lc, defined as the number
of coupling periods between the bus waveguide
and the PCRRs, is Lc ¼ 0a. The ratio of rod radius
r to lattice period a is 0.1. If the height of the silicon
rods is chosen to be greater than 2λ (λ is the wave-
length of interest, e.g., 1:55 μm), the structure can
be considered infinite in the vertical direction and
the light leakage is sufficiently suppressed [21], even
though the real structure would, in practice, require
a 3D FDTD numerical analysis, which typically
means computation time and amount of memory
used. In addition, this 2D approach can offer design
trade-offs and guidelines for a 3D approach. There-
fore, for simplicity, here we discuss only a 2D PC con-
figuration. From the simulated dispersion plots of
TM polarization along the ΓX and the ΓM directions
shown in Figs. 1(b) and 1(c), respectively, a shared
broadband single-mode frequency (normalized) ex-
ists that ranges from 0:395 a=λ to 0:505 a=λ. For
the 1550 nm communication window, a is set as
685 nm. Based on the concept of effective ring radius
Reff [14], the Reff in Fig. 1(a) is
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
32a2
=π
p
, approxi-
mately 2:186 μm. Note that an additional eight of
the same Si scatterers labeled S in Fig. 1(a) are in-
troduced in the center of its four nearest-neighbor
rods to improve spectral selectivity and to obtain a
high dropped efficiency [13], which will be discussed
subsequently.
The transmission characteristics were then simu-
lated with a free open 2D FDTD technique using per-
fectly matched layers as the absorbing boundary
condition [22]. A Gaussian TM polarization optical
pulse, covering the whole frequency range of interest,
is launched at input port A. Power monitors were
placed at each of the other three ports (B, C, D) to
collect the transmitted spectral power density after
Fourier transformation. All the transmitted spectral
power densities were normalized to the incident light
spectral power density from input port A. For fair
comparison, here a conventional 5 × 5 PCRR [13] is
Fig. 1. (Color online) (a) Schematic of proposed 45° single PCRR with coupling section Lc ¼ 0a. (b), (c) Dispersion plot and the corre-
sponding bus–waveguide mode along ΓX and ΓM, where the radius and the refractive index of the Si rod are 0:1a and 3.48, respectively.
6924 APPLIED OPTICS / Vol. 48, No. 36 / 20 December 2009

3. also considered where Reff is
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
36a2
=π
p
, approxi-
mately 2:318 μm. All the results are shown in Fig. 2,
where the left and right panels show the normalized
intensity spectra and their corresponding ideal
cavity resonant wavelengths and quality factor Q.
Figures. 2(a) and 2(b) show the new proposed 45°
PCRRs with and without scatterers, respectively;
Fig. 2(c) shows our early reported 5 × 5 PCRR with
scatterers. Other parameters such as L, d, and Lc
for three PCRRs are the same as 22a, 4a, and 0a, re-
spectively. Clearly, for a 45° ring cavity without scat-
terers, three very close resonant modes, M3, M4, and
M5, exist; M4 is shown in the inset of Fig. 2(b). The
modes interact with each other and finally result in a
low dropped efficiency with poor spectral selectivity.
By simply introducing eight scatterers, the number
of modes reduce and significantly improve spectral
selectivity, with an approximately 90% dropped effi-
ciency and 840-Q at the 1550 nm channel (port D),
where Q is defined as the ratio of δλ (FWHM) to
the center wavelength λ of the dropped channel.
By comparing new and early PCRRs, as shown in
Figs. 2(a) and 2(c), the spectral selectivity of the
new proposed PCRR is higher than its forerunner.
It is worth mentioning that the discrepancy between
the ideal PCRR Q and the CDF (channel drop filter)
Q is mainly caused by coupling strength Lc in the
coupling sections between the W1 waveguide and
the PCRR [13].
3. All-Optical NOT and NOR Logic Gates
A. Structure Design and Qualitative Analysis
It is well known that a Y branch waveguide is an es-
sential configuration for construction of various PC
devices. Recently, an XOR logic gate based on a PC
Y branch was demonstrated. However, its size is rela-
tively large and its performance is determined by its
length and width [10]. According to the principle of
beam interference, it would be feasible to demon-
strate a new PC logic gate integrating the aforemen-
tioned 45° PCRR and Y branches, which would be
achieved by forming one additional W1 waveguide
at the horizontal mirror plane of the 45° PCRR as
shown in Fig. 3(a), where ports 1 and 5 are input logic
signals A and B, port 4 is the probe signal, and port 3 is
used to record the output to determine the states of
the logic gate. Note that only one single ring is consid-
ered here without any nonlinear material introduced
in comparison with the early reported PCRR-based
Fig. 2. (Color online) Left: intensity at output ports B, C, and D;
right: corresponding cavity resonant wavelengths and quality fac-
tor Q: (a) 45° PCRR with scatterers (S); (b) 45° PCRR without S;
(c) conventional 5 × 5 PCRR with S, where Lc ¼ 0a, d ¼ 4a, and
L ¼ 22a, respectively.
Fig. 3. (Color online) (a) Schematic of our proposed photonic crystal logic gate and (b) (from top to bottom: Media 1, Media 2, and Media 3)
propagating field intensity distribution, where the arrow represents the direction of the incident light.
20 December 2009 / Vol. 48, No. 36 / APPLIED OPTICS 6925

4. logic gate [11]. All the physical parameters are kept
the same as the ones used in Fig. 1(a). As discussed
above, when the input wavelength of signal A is away
from the dropping channel, e.g., 1560 nm, most of the
light will pass straight through port 2. When the
wavelength of input A approaches the dropping chan-
nel, 1550 nm, the light will drop into port 5, as shown
by the dashed flow arrow. Furthermore, owing to the
existence of an additional W1 waveguide along ports 3
and 4, it will result in weak confinement of the propa-
gating field and can also be guided into the other three
remaining ports 2, 4, and 6. The function of Y
branches dominates when the incident light is input
from port 4. The probe signal is mostly guided into
ports 1, 3, and 5 marked by the solid arrow. Finally,
the probe signals will interfere with each other at
the output port when one of the input signals or both
are on. It is thus feasible to realize a new PC logic gate
with various combinations of input signals A and B,
that is, on and off.
B. Numerical Results and Discussion
We first apply only one continuous wave (cw) with
1560 (1550 nm) at input A and 1550 nm at the prob-
ing input, respectively. The results of animated field
propagation are shown in Fig. 3(b) (from top to bot-
tom: Media 1, Media 2, and Media 3) and prove the
above assumptions. Then, to analyze this logic gate, a
pulse-pattern input light with the same center wave-
length, covering range, phase, and polarization was
first considered where the probe signal is always
launched from port 4. Note that either input signal
A or B is on, and some portion of light will be coupled
into port 4 as aforementioned. Thus we first need to
consider only one simple W1 straight waveguide with
the same bus–waveguide length and record the input
power of the probe signal, Pprobe. Then the normal-
ized intensity of the logic gate at the output port
can be obtained by normalizing the measured power
at port 3 to Pprobe as shown in Fig. 4(a), where L, d,
and phase difference φ between the signal A (B) and
the probe signal are 22a, 4a, and 0 deg, respectively.
From Fig. 4(a), the output intensity of the A off, B off
case is always higher than when either one of them
or both are on. This is caused by beam interference. It
is interesting that two distinguished states exist
when the operating wavelength approaches
1553:4 nm. In this case, when inputs A and B are
off, the output intensity at port 3 is greater than
Fig. 4. (Color online) (a) Behavior of our proposed PC logic gate
with various combinations of input signals where φ ¼ 0, L ¼ 22a,
and d ¼ 4a; (b) definition of logic levels 0 and 1; (c) output inten-
sity changes with L where φ ¼ 0 and d ¼ 4a; (d) output intensity
changes with φ, where L ¼ 32a and d ¼ 4a.
Table 1. Truth Table for Our PC Gates
Input A Input B Probe Output
0 0 1 1
1 0 1 0
0 1 1 0
1 1 1 0
Fig. 5. (Color online) Field distribution to demonstrate the performance of proposed NOT and NOR gates where the operating wavelength
is 1553:4 nm.
6926 APPLIED OPTICS / Vol. 48, No. 36 / 20 December 2009

5. 70%, defined as logic 1, as shown in Fig. 4(b). While
input A and/or B are individually or simultaneously
on, the output intensity is always less than 35%, de-
fined as logic 0. Note that the defined logic 1 and 0
can be further improved by engineering the same
change in L and relative phase φ at each input port.
Figure 4(c) shows the result of the change in L where
phases φ and d are 0 and 4a, respectively. The output
intensity for the A off, B off case experiences a slight
increase, a fast increase, and almost saturation with
the increase in L, whereas the output intensity of the
other three cases continues to increase. If we set L as
17a, logic 1 and 0 can be defined as greater than 70%
and less than 25%, respectively. The results caused
by phase change φ are also shown in Fig. 4(d), where
the L and d are 32a and 4a, respectively. It is clear
that the intensity of the A off, B off case will not
change while others will vary in sine profile ranging
from −180° to 180°. We can again define logic 1 and 0
as greater than 82% and less than 41%, respectively.
A truth table for our proposed PC gates is summar-
ized in Table 1, which shows that there is no doubt
that the device can first operate as a NOR gate for in-
puts A and B simultaneously. Furthermore, the de-
vice can individually operate as a NOT gate for
either A or B. The behavior of the proposed logic
gates is shown in Fig. 5, where the incident light
is cw with a 1553:4 nm wavelength, and the L and
d are 22a and 4a, respectively. The simulation results
further proved that this new configuration can really
function as NOT and NOR gates, respectively.
4. Conclusion
In conclusion, a new 45° PCRR has been proposed
and numerically demonstrated in two-dimensional
square lattice silicon rods. By combining the func-
tions of Y branches and a PCRR, new ultracompact
photonic crystal logic NOR and NOT gates have been
demonstrated. Only one single ring is required with
less than 2:2 μm for a 1550 nm optical communica-
tion window. The definitions of logic 1 and 0 were also
introduced. These findings make PCRRs potentially
usable for all-optical logic circuits and ultracompact
high density photonic integration.
The authors appreciate the partial support from
the Natural Science Foundation of Fujian Province
of China under grants 2009J05140 and 2009J01012.
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