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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 2, 2010
Ultra Fast Computing Using Photonic Crystal Based
Logic Gates
X.Susan Christina A.P.Kapilan P. Elizabeth Caroline
Dept. of ECE Dept. of ECE Dept. of ECE
Mookambigai College of Engg. Chettinad College of Engg & Tech JJ College of Engg &Tech,
Trichy- 622 502, India. Karur,. 639114. India. Trichy –620 009,India.
fab_jesu@yahoo.co.in apkabilan@yahoo.co.in becaroline05@yahoo.com
Abstract— A Novel design of all-optical fundamental NAND Photonic Crystals (PC) are produced by artificially imparting
and XNOR logic gates based on two dimensional photonic periodic change of the refractive index of a structure which
crystals has been presented in this paper. In a photonic has a band gap that prevents propagation of certain frequency
crystal self collimated beams are partially transmitted and range of light. But the propagation of light inside the PC can
partially reflected with a phase lag at line defect in Γ-X be controlled by different propagation mechanisms such as
direction. By employing a appropriate phase shifter, the negative refraction, super prism and self collimated beam
reflected and transmitted input beams are interfered propagation. When non linear effect is applied to the photonic
constructively or destructively to obtain the required logic crystal it requires high intensity incident light for its
outputs. The operation of the logic gates is simulated using propagation and the balance between diffraction and focusing
two dimensional Finite Difference Time Domain (FDTD) easily collapses due to the absorption. In self-collimating
method.
effect, the collimated light beam insensitive to the divergence
Keywords-optical computing; logic gated; photonic crystal; self of the incident beam without applying a nonlinear effect [11].
collimated beam; FDTD In this paper we propose NAND and XNOR gates realization.
The paper is organized as follows, In Section II, photonic
I. INTRODUCTION crystal theory is described. In Section III, structural and
The demand for bandwidth in worldwide networks numerical analysis is explained. Section IV presents the
continues to increase due to growing internet usage and high proposed scheme of logic gates. Results and related
bandwidth applications. Optical computing is one of promising discussions are presented in section V. Finally, conclusions are
technique to meet all the necessary requirements such as high summarized in section VI.
speed, high speed, supporting high data rate and ultra fast
performance [1,2]. All optical logic gates are the key element II. PHOTONIC CRYSTAL THEORY
in next generation optical computing and in networking to
perform optical signal processing such as binary addition, Photonic crystals (PC) are composed of periodic dielectric
header reorganization, parity checking, optical bit pattern materials. In PC, for some frequency ranges the light waves are
recognition addressing, demultiplexing, regenerating and not propagating through the structure such frequency range is
switching. In order to realize the gates, various configurations called forbidden gap photons. The doping of impurity or
have been reported that utilize the nonlinear properties of the creating defects will allow a perfect control of light
optics. All-optical gates reported in the literature [3-8] could propagation and radiation. Introducing line defects in PC
be achieved with a semiconductor laser amplifier loop mirror results in a photonic crystal waveguide. Line defects can be
(SLALOM), a semiconductor optical amplifier- (SOA-) based formed in photonic crystal either by reducing the radii of PC
Mach-Zehnder interferometer (SOA-MZI), a SOA based ultra rods or by eliminating them partially. When the self-collimated
fast nonlinear interferometer (UNI), cross-polarization beam is incident at the line defect the beam is splitted [12, 13].
modulation, and four-wave mixing (FWM) in SOAs, SOA with It is evident that there is a phase difference between the
Optical filter, Periodically Poled Lithium Noibate (PPLN) transmitted and the reflected beams. If the rod radii of the line
waveguide . These schemes suffered from certain fundamental defect are smaller than that of the host rod radii, the reflected
limitations such as spontaneous emission noise, power wave lag the transmitting wave by π/2 else the phase difference
consumption and size. is - π/2 [14]. If another self- collimated beam with appropriate
phase is launched, the reflected and transmitted beams may
In recent years, optical waveguide element employing interfere constructively or destructively. This phenomenon is
photonic crystals have been received lot of attention because used to realize logic gates functions.
of their dimension, low loss structure of less than 2 dB/cm [9]
and high speed with data rate of 120 GB/s [10]. Normally
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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 2, 2010
III. STRUCTURAL AND NUMERICAL ANALYSIS IV. PROPOSED SCHEME OF LOGIC GATES
To realize the operation of the all optical logic gates, a 2D
A. Schematic of XNOR Gate
square lattice PC composed of silicon dielectric rods in air is
considered. The size of the PC is 6.4 x 6.4 μm. The refractive Logic gates function can be realized by introducing a
index of the silicon rod is 3.5. The radius and the dielectric certain phase difference between the input beams. To realize
constant of rods are ‘r’ =0.35a and ‘ε’ = 12.0 respectively [12], XNOR gate along with two input beams, the third reference
where ‘a’ is the lattice constant and its value is 0.365 µm. The input beam is also incident on the PC. The inputs I1 and I2 are
line defect is formed by reducing the silicon rod radii = 0.274a launched at the input face 1 and the third reference beam is
of 15 rods aligned in the Γ-X direction. Self collimation applied to the input face 2. The optical phase shifter is
phenomena occurs when lights of frequencies around f = 0.194 connected at the reference input to obtain appropriate phase
c/a [12] where ‘c’ is the speed of light in free space propagate shift. The phase difference between the inputs I1 and I2 are
along the direction of Γ-M. Fig 1 shows the schematic diagram zero i.e. φ1- φ2= 0 and the phase difference between inputs
of the Photonic crystal. In this structure there are four faces, and the reference input φ1- φ3 is set as π/2. The XNOR output
two of them are consider as input and remaining two are as is taken from the output face 2.
output.
Figure 3. Schematic of XNOR gate.
B. Schematic of NAND Gate
Figure 1. Schematic diagram of photonic
crystal. The gate NAND can be realized by applying the input
beams I1 and I2 on input face 1 and the reference beam is
To analysis photonic crystal, FDTD with perfectly
matched layer boundary condition method is used in this launched at input face 2. The inputs powers consider in this
paper. It solves Maxwell's equations by first discretizing the case are half of the reference input power. The phase
equations via central differences in time and space and then difference between the inputs I1 and I2 is zero i.e. φ1- φ2= 0
numerically solving these equations. Since the whole and the phase difference between inputs and the reference
calculation region is divided into very small uniform cells, the input φ1- φ3 set as π/2. The NAND output is taken from the
accuracy of this technique can be improved. Photonic wave output face 2.
guides are very small due to the frequency of light. It is both
expensive and complicated to construct these. Therefore
FDTD simulation is a great interest to analysis. Fig. 2 depicts
the band diagram of the PC using FDTD simulation.
Figure 4. Schematic of NAND gate.
V. RESULTS AND DISCUSSIONS
In the XNOR gate when two input beams and the reference
input with the phase difference π/2 are introduced, the output
Figure 2. Band diagram of photonic crystal.
light will be at the face O2. If only one input with reference
input is applied, there is no output at the face O2. Table 1 gives
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ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 2, 2010
the functions of the XNOR gate and Fig. 5 shows the field various input combinations are shown in Fig. 6 and Table 2
distributions of TE mode for various input combinations. gives the functions of the NAND gate.
TABLE I. FUNCTIONS OF XNOR GATE TABLE II. FUNCTIONS OF NAND GATE
Signal XNOR for φ1- φ2= 0 & φ1- φ3= π/2 Signal NAND gate for φ1- φ2 =0 & φ1- φ3 =π/2
Descriptions and the input powers I1=I2= I3 Descriptions and the input powers I1/2=I2/2= I3
Input signal (I1) 0 0 1 1 Input signal (I1) 0 0 1 1
Input signal (I2) 0 1 0 1 Input signal (I2) 0 1 0 1
Control signal (I3) 1 1 1 1 Control signal (I3) 1 1 1 1
Output O2 1 0 0 1 Output O2 1 1 1 0
Figure 5a) Simulated field distribution when both inputs are Figure 6a) Simulated field distribution when both inputs are high.
high.
Figure 5b) Simulated field distribution when one of the input is Figure 6b) Simulated field distribution when one of the input is high.
high.
VI. CONCLUSION
The design of novel all-optical logic gates consisting of
phase shifter and photonic crystal with a line defect in the Γ-X
direction is proposed. The self-collimated optical beams are
applied at a line defect of the photonic crystal that are partially
transmitted and reflected with a phase lag. If the intensities of
the input beams are chosen in appropriate proportions and
opposite phase difference between the input signals, the
Figure 5c) Simulated field distribution when both inputs are overlapping of transmitted and reflected beams interfere either
low. constructively or destructively giving a logic output. Based on
these phenomena the XNOR and NAND gates functions are
realized. The steady state field distributions at different input
In the NAND gate when two input beams whose powers states are obtained by FDTD simulation. The results indicate
are half of the reference input power is introduced, no output that photonic crystals are potential candidature for optical
signal is from the face O2. If only one input with reference digital integrated circuits which are used for optical
input or only reference input is applied, there is an output
computing.
signal in the face O2. The TE mode field distributions for
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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 2, 2010
REFERENCES [13] S.G.Lee, S.S.Oh, J.E.Kim, H.Y.Park and C.S.Kee, “Line-defect-
induced bending and splitting of self-collimated beams in two-
dimensional photonic crystal,” Appl. Phys. Lett., vol. 87, 181106-3,
[1] J.M. Martinez,J.Herrera, F.Ramos and J. Marti, “ All-Optical Address 2005.
Recognition Scheme for Label-Swapping Networks,” IEEE Photonics [14] D. D. Zhao, J. Zhang, P. Yao, X. Jiang, and X. Chen,“ Photonic crystal
Technology Letters, vol. 18, no.1, pp. 151-153,2006. Mach - Zehnder interferometer based on self-collimation,” Appl. Phys.
[2] T.Fujiswa and M. Koshiba, “Finite-Element Modelling of non linear Lett., vol.90, 231114-1, 2007.
Mach-Zehnder interferometers based on photonic crystal wave guides
for All-Optical signal Processing,” Journal of Lightwave Technology,
vol. 24, no. 1pp. 617-623, 2006. AUTHORS PROFILE
[3] A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All optical X. Susan Christina pursuing her Doctorate in Optical Computing at Anna
full adder with Bit-differential delay,” Opt.Commun., vol.156, pp.22-26, University, Trichy, India. She has 13 years of teaching experience. She has
1998. been working as a Professor and Head of the Department of Electronics and
Communication Engineering at Anna University, Trichy. Her research
[4] A. J. Poustie, K. J. Blow, A. E. Kelly, and R. J. Manning, “All optical interests in the area of digital signal processing, optical signal processing and
parity checker with bit-differential delay,”Opt. Commun., vol.162, optical computing. She has published fifteen papers in National, International
pp.37-43, 1999. conferences proceedings and Journals. She is a life member of ISTE.
[5] H. Avramopoulos, “Optical TDM devices and their applications,” Dr. A.P. Kabilan has a Doctorate in Microwave Engineering from Patrice
Optical Fiber Communication, vol. 54, 2001. Lumumba University, Moscow, Russia and has 25 years of experience in
[6] H. Soto, C. A. Díaz, J. Topomondzo, D. Erasme, L. Schares and G. teaching and research. He is a dynamic academician with 26 international
Guekos, “All-Optical AND gate implementation using cross polarization publications and eight national ones. He worked as a Professor and Head of
modulation in a semiconductor optical amplifier,” IEEE Photon. the Department of Electronics and Communication Engineering at Anna
Technol. Lett.,vol. 14, pp.498-500, 2002. University, Coimbatore for the past ten years. At present, he is the Principal of
[7] D. Nesset, M. C. Tatham, and D. Cotter, “All Optical gate operating 10 Chettinadu College of Engineering and Technology, Karur, and Tamil Nadu
Gbits/s signals at the same wavelength using four-wave mixing in a India. He is an active member of IEEE and a life member of ISTE. He has a
semiconductor laser amplifier”, Electronics Letters, vol.31, no. 31, strong background in microwave, optical and antenna engineering.
pp.896-897, 1995. P. Elizabeth Caroline is pursuing her Doctorate in Optical Signal Processing
at Anna University, India. She has 16 years of teaching experience. She has
[8] J.Wang, J.Sun and Q.Sun “PPLN based Flexible Optical Logic AND
gate,” IEEE Photon Tech Lett. vol. 20, pp. 211-213, 2008. been working as a Professor and Head of the Department of Electronics and
Communication Engineering at Anna University, Trichy. She has a strong
[9] E. Kuromochi, M. Notomi, S.Hughes et al, “Disorder-induced scattering background in signal processing and optical computing. She has presented
loss of the line defect waveguides in photonic crystal slabs,” Phys. papers in international IEEE conferences and national conferences. She is an
Rev.B, vol.72, 161318(R), 2005. active member of IEEE and a life member of ISTE.
[10] Parisa Andalip and Nosratollah Granpayeh, “All-Optical ultra-compact
photonic crystal AND based on nonlinear ring resonators,” Journal of
Opticla Society of America B, vol.26, no.1,pp. 10-16, 2009.
[11] H.Kosaka, T.Kawashima, A.Tomita, M.Notomi, T.Tamamura, T.sato
and S.Kawakami, “Self-collimatin phenomena in photonic crystal’,
Appl.Phys.Lett.,vol.74, pp.1212-1214, 1999.
[12] X. Yu and S. Fan, “Bends and splitters for self-collimated beams in
photonic crystals,” Appl. Phys. Lett., vol. 83, 3pp. 251-3253, 2003.
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