Designing of All Optical Circuit for Two Input Ternary MIN Logical Operation P. Bhowmik1, T. Chattopadhyay2, C. Taraphdar3 and Jitendra Nath Roy1* 1 Department of Physics, National Institute of Technology-Agartala Jirania, Tripura (West), Pin-799055, India 2 Mechanical Operation (Stage – II), Kolaghat Thermal Power Station, West Bengal, India 3 Department of Physics, Bankura Christian College Bankura, Paschim medinipur, W.B.India
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Abstract: The all optical MIN is one of the basic logical operation in superfast multi-valued photonic computing system. Here a Ternary MIN with an optical switch of nonlinear material is proposed and discussed. The inputs of ternary MIN logical gate are represented by different polarization states of light. This model is simple, practical and very much useful for future all optical information processing.
1 Introduction Multi valued logic (MVL) is a non-binary logic which switches between more than two states. In logical operation, depending on the radix and no. of variables, possible Rn
functions are, R where R=radix and n= no. of variables. Keeping the variables constant,if the radix is increased then the no. of possible function will increase. In this sense, MVL(R>2) is preferable than binary logic. MVL can execute arithmetic function faster and with less interconnect than binary logic. Furthermore, the nonbinary data storage requires less physical space than binary data [1]. Many efforts have been made in electronics [1-3], optoelectronics [4] and optics [5-8] for ternary logical operation. Ternary number system is optimum in terms of storage complexity [5]. Binary coded ternary representation[5], optical shadow casting scheme[6] and fringeshifting technique[7] are some of the many techniques proposed in optical computing with ternary logical operations. High speed ultra-fast optical switches have of late resulted in a revolution in optical communication and information processing systems [9-14] . Polarization encoded all-optical logic for optical network offers an exciting scope for research with enormous possibilities of innovation [9-14]. In our proposed alloptical scheme presented in this paper, we have discussed about ternary MIN logical operation with an optical switch of nonlinear material. The ternary logic has three D. Choudhury, G. Lohar (Eds.): Convergence of Optics and Electronics c JIS College of Engineering 2011
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logic states. They are represented by two forms, one is symmetric ternary (ST) and other is ordinary ternary (OT).In polarization encoded logical operation, intensity of the beam does not carry any information. So the strength or weakness of the beam plays no role in the operation of the logic [8]. For the ternary MIN data processing in optics the inputs are represented by three discrete polarized states of light, where forSymmetric MIN:
Ordinary MIN:
0= right circularly polarized light (⥀)
0= right circularly polarized light (⥀)
1= vertically polarized light (↕)
1= vertically polarized light (↕)
1 = horizontally polarized light (•)
2= horizontally polarized light (•)
Table-1: The truth table for (a) symmetric MIN (b) ordinary MIN are given by-
2 Designing of All- Optical Ternary MIN Logic Gate: The design of all optical Ternary logic gates is discussed below in details with proper diagrams. 2.1The Optical Components Used in Proposed Design: The components used in designing the all-optical logic gate for TMIN are as follows2.1.1 Composite Block (CB): The input signal get incident on the composite block (CB) after being expanded by the beam expander (BE). The composite block is made of two layers (shown in Fig-1). 2.1.1.1 Polarization isolator (PI) –Mask: PI mask passes only a specific type of polarized light through it and blocks other types of polarized light. In fig 1, the first layer of the side view is the PI mask of a composite block. The horizontal polarizer isolator (HPI) passes only horizontally polarized light (⦁) and they are placed in a C11, C12 and C13 pixels of the CB.
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The right circular polarizer isolator (RCPI) passes only right circularly polarized light (⥀) and they are placed in C21, C22 and C23 of the CB. The vertical polarizer isolator (VPI) passes vertically polarized light (↕) only and they are placed in C31, C32 and C 33 of the CB. 2.1.1.2 Polarization Converter (PC)– Mask: In Fig-1, the second layer of the side view of composite block is the PC mask and it converts one type of polarized light to another and it’s function can be explained with the help of mathematical analysis of Jones matrix. The Jones vector of three types of polarized light areE•= Jones vector of horizontally polarized light(⦁)
1 0
=
E⥀ = Jones vector of right circularly polarized light (⥀)
=
1 1
2 i
E↕ = Jones vector of vertically polarized light (↕)
=
0 1
Different Types of Polization Converter: Type-1(PC-1) : This type of polarization converter is made of half wave plate (λ/2). The Jones matrix for the half wave plate is
cos(2 ) sin(2 ) J H sin(2 ) cos(2 ) where,
------------------(1)
is the azimuth angle of optic axis. When = then from equn(1) we obtain
the Jones matrix as -
0 1 J H 1 0 ∴
JH.E↕ = E•
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Similarly, JH.E•= E↕ i,e if the optic axis of PC-1 is arranged in 45 with (+x)axis then vertically polarized light (↕) is rotated by 90 and converted to horizontally polarized light (⦁) and vice versa. .
Fig-1: Composite Block (CB-Block) Type-2 (PC-2): This type of polarization converter is made of quater-wave plate (λ/4) and the Jones matrix of this type is–
J
Q
i e
4
2
i 4 2 cos e sin 2.i sin cos
2.i sin cos -----(2)
i 4 2 i 4 2 e cos e sin
Where, =azimuth angle of optical axis. When, =
then the equu (2) becomes-
JQ
1 2
1 i i 1
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∴ JQ.E⦁ = E⥀ Similarly, JQ.E↕ = E⥀ i,e PC-2,converts both vertical(↕) and horizontally polarized light (⦁) into right circularly polarized light (⥀) . 2.1.2 OPNLM Matrix: The optical nonlinear material (OPNLM) matrix is an optical switch which works on the principle of four wave mixing phenomena.Here nine numbers of OPNLM pixels are placed in (3 3) matrix form.
OPNLM
2.2 Function of OPNLM-Based Switching System: The working principle of OPNLM optical switch is discussed below in details with diagram-
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The fig 3 shows a set up for phase conjugation to creat a light beam .Here two light beams 1 and 2 (having same frequency and states of polarization),preferably laser are allowed to incident from two opposite sides on the OPNLM, which have at least a cubic type of nonlinearity. A third beam ( known as probe beam ) having the same frequency is allowed to fall on the point of intersection of the two read beams on the OPNLM,after being partially reflected from the beam splitter. Then this incident beam reflects back from the incident point,following the same path in opposite direction to give the output beam .The output beam will emerge only if the states of polarzation of the three interacting beams are identical and both of the read beams are present. 2.3 All Optical Symmetric Ternary MIN Logical Operation: In the circuit for TMIN logical operation , CB-2 is oriented by 90 w.r.t CB-1 in anticlockwise direction. Light from two coherent sources (inputs A and B) will incident on both CB-1 and CB-2 . A horizontally polarized light will emerge from both the blocks and get incident on OPNLM. A probe beam(horizontally in nature) is allowed to fall on the same point of intersection in the OPNLM. According to the switching mechanisim,a light of same state of polarization(horizontal) will come out from the OPNLM and will pass through PCM(type-2).The output of this PCM will give the result of TMIN logical operation. 1)When A = 1 and B = 1 (horizontally polarized light), then horizontally polarized light (⦁) emerges from C11, C12 and C13 pixels of both CB-1 and CB-2 blocks and they will meet at O11 of OPNLM. The reflected probe beam from O11 will pass through P11 of PCM (type 2) matrix and will give the output 1 , logical state. 2)When A = 0 (right circularly polarized light) and B = 1 (horizontally polarized light), then horizontally polarized light (⦁) emerges from C21, C22 and C23 pixels of CB-1 and C11, C12 and C13 of CB-2 block and they will meet at O21 of OPNLM. The reflected probe beam from O21 will pass through P21 of PCM (type 2) matrix and will give the output 1 , logical state
Fig-4: PCM (type-2) matrix for (a) symmetric MIN (b) ordinary MIN
3)When A = 1 (vertically polarized light) and B = 0 (right circularly polarized light), then horizontally polarized light (⦁) emerges from C31, C32 and C33 pixels of CB-1 and C21, C22 and C23 of CB-2 block and they will meet at O32 of OPNLM. The reflected
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probe beam from O32 will pass through P32 of PCM (type 2) matrix and will give the output 0, logical state. All these output of PCM (type 2) matrix satisfy the truth table of symmetric TMIN logical operation. 2.4 All Optical Ordinary Ternary MIN Logical Operation: Just by changing the PCM(type-2) matrix (given in fig.4) in fig.5 ordinary TMIN can be performed as follows1) When A = 2 and B = 2 (horizontally polarized light), then horizontally polarized light (⦁) emerges from C11, C12 and C13 pixels of both CB-1 and CB-2 blocks and they will meet at O11 of OPNLM. The reflected probe beam from O11 will pass through P11 of PCM (type 2) matrix and will give the output 2 , logical state. 2) When A = 0 (right circularly polarized light) and B = 2 (horizontally polarized light), then horizontally polarized light (⦁) emerges from C21, C22 and C23 pixels of CB-1 and C11, C12 and C13 of CB-2 block and they will meet at O21 of OPNLM. The reflected probe beam from O21 will pass through P21 of PCM (type 2) matrix and will give the output 0, logical state.
3) When A = 1 (vertically polarized light) and B = 0 (right circularly polarized light), then horizontally polarized light (⦁) emerges from C31, C32 and C33 pixels of CB-1 and C21, C22 and C23 of CB-2 block and they will meet at O32 of OPNLM. The reflected
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probe beam from O32 will pass through P32 of PCM (type 2) matrix and will give the output 0, logical state. All these output of PCM (type 2) matrix satisfy the truth table of symmetric TMIN logical operation. 3 Conclutions: In this paper,we have discussed an all optical tristate logical operation of Ternary MIN in both symmetric and ordinary mode.TMIN is a fundamental logic gateWe can implement this idea to design the others circuits like ternary multiplexer, adder,subtractor etc.In our next papers we will try to design the circuits for these logical operations.This proposed scheme,is easily practicable as the components like light source,optical switch,BS,PC etc.are technically highly devoloped and widely used in optical communication. 4 References: 1. K.C.Smith, “The prospects for Multivalued Logic: A Technology and Applications View”,IEEE Transactions computers, C-30, 619-634 (1981). 2. C.Y.Wu, H.Y.Huang, IEEE Journal of solid-state circuits, 28(8), 895-906(1993). 3. A.Stakhov, The computer Journal, 45, 221-236 ( 2002). 4. S.Liu, C.Li, J.Wu and Y.Liu, “Optoelectronic multiple-valued logic implementation”, Optics letters, 14, 713-715 (1989). 5. G.Eichmann, Y.Li and R.R.Alfano, Applied Optics, 25, 3113-3121(1986). 6. A.A.S.Awwal, M.A.Karim and A.K.Cherri, “Polarization-encoded optical shadow-casting scheme: design of multioutput trinary combinational logic units”, Applied Optics, 26, 274-277(1987). 7. Y.Imai and Y.Ohtsuka, “Optical multiple-output and multiple-valued logic operation based on fringe shifting techniques using a spatial light modulator”, Applied Optics, 26, 274-277(1987). 8. Jin Yi, He Huacan and Lu Yangtian, “Ternary Optical Computer Architecture”, Physica Scripta. Vol. T118, 98–101 (2005) 9. J.P.Sokoloff, P.R.Prucnal , I..Glesk and M.Kane, “A terahertz optical asymmetric demultiplexer (TOAD)”, IEEE Photon. Technol. Lett., 5, 787-790 (1993). 10. B.C.Wang, V.Baby, W.Tong, L.Xu, M.Friedman, R.J.Runser, I.Glesk and P.R.Prucnal, “A novel fast optical switch based on two cascaded terahertz optical asymmetric demultiplexers (TOAD)”, Optics Express, 10, 15-23 (2002). 11. D.K.Gayen and J.N.Roy, “All-Optical Arithmetic Unit with the help of Terahertz Optical Asymmetric Demultiplexer (TOAD) based Tree Architecture”, Applied Optics, 47, 933-943 (2008). 12. J.N.Roy, G.K.Maity, D.K.Gayen and T.Chattopadhyay, “Terahertz optical asymmetric demultiplexer based tree-net architecture for all-optical conversionscheme from binary to its other 2n radix based form”, Chin. Optics Letter, 6, 536-540 (2008). 13. A.P.Vandevendar and P.G. Kwiat, High speed transparent switch via frequency up conversion Optics express, 15, 4677-4683(2007). 14. Z. Li, and G. Li, “Ultrahigh-speed reconfigurable logic gates based on four-wave mixing in a semiconductor optical amplifier,” IEEE Photon. Technol. Lett. 18, 1341-1343 (2006).
