Docstoc

Ultra Fast Computing Using Photonic Crystal Based Logic Gates

Document Sample
Ultra Fast Computing Using Photonic Crystal Based Logic Gates Powered By Docstoc
					                                                               (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




                                                                      152                               http://sites.google.com/site/ijcsis/
                                                                                                        ISSN 1947-5500
                                                             (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




                                                                    153                                http://sites.google.com/site/ijcsis/
                                                                                                       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



                                                                           154                                     http://sites.google.com/site/ijcsis/
                                                                                                                   ISSN 1947-5500
                                                                        (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.




                                                                                155                                     http://sites.google.com/site/ijcsis/
                                                                                                                        ISSN 1947-5500