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Optik 122 (2011) 321–323

Contents lists available at ScienceDirect

Optik

journa l homepage: www.e lsev ier .de / i j leo

mplementation of a novel hybrid encoding technique and realization of allptical logic gates exploiting difference frequency generation alone

ousik Mukherjeeept. of Physics (PG&UG), BB College, Asansol, Burdwan, West Bengal 713303, India

r t i c l e i n f o

rticle history:

a b s t r a c t

A novel hybrid encoding technique scheme is proposed. Using this technique and difference frequency

eceived 2 July 2009ccepted 28 February 2010

eywords:ybrid encoding

generation different all optical logic gates NOT, OR, AND, NAND, NOR, and X-OR are realized.© 2010 Elsevier GmbH. All rights reserved.

ifference frequency generationogic gates

. Introduction

Optics has a strong and potential role in signal processing, com-utation, image processing, and communication due to severaldvantages over electronics. In respect to speed photon is a suit-ble information carrier. A variety of optical data and informationrocessor have been proposed over the last few decades [1–4].

n most of the cases the states of information are represented byntensity encoding i.e. the presence of photon ‘1’ and absence ‘0’,nd for this reasons there are several difficulties [5–14]. Intensityncoding has main drawback of intensity loss dependent problem.ecently frequency encoding technique has been developed [15,16]nd has no intensity loss dependent problem. But frequency encod-ng scheme [17] requires two different frequencies to representhe states or a wide band of frequency is required for its imple-

entation. But one can utilize the simplicity of intensity encodinglong with advantages of frequency encoding scheme by a hybridncoding technique which is proposed in this paper. In this com-unication the author wish to implement all optical logic gates

amely NOT, OR, AND, NAND, NOR, and X-OR exploiting differencerequency generation alone and hybrid encoding technique.

. Working principle

The working of the all optical logic gates depends on the mea-urement of frequency of a photon and the difference frequencyeneration.

E-mail address: lipton007@indiatimes.com.

030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2010.02.013

2.1. Hybrid encoding technique

In hybrid encoding technique, the states of the binary logic‘0’ and ‘1’ are represented by the absence of photon [property ofintensity encoding] and by a photon of frequency ‘�’ [property offrequency encoding]. While representing the state ‘0’ we are usingintensity encoding as the frequency detector will read nothing inthis condition but the detector will record the frequency whenthere will be photon of a particular frequency � irrespective of theintensity of the beam. This removes the intensity loss dependentproblem. So we do not have to maintain an intensity level of thelight beams. Use of a single frequency to represent the binary statesmakes the hardware simpler than that of frequency encoding.

2.2. Difference frequency generation

If two frequencies signals of frequencies �1 and �2 interactsinside a nonlinear medium, they can give rise to a signal of fre-quency (�1 − �2) in such a way that the phase matching conditionk(�1) − k(�1) = k(�1 − �2) is satisfied. In Fig. 1 the frequency sub-traction unit is shown which will be used to generate differencefrequency.

In the hybrid encoding technique one can select �1 equal to �and �2 equal to either � or zero, so that the output of the differencefrequency generation will be zero or � depending on the value of�2, respectively.

3. Operating principle of different logic gates

The truth table for different logic gates is shown in Tables 1 and 2.

322 K. Mukherjee / Optik 122 (2011) 321–323

Fig. 1. Difference frequency generation [DGG unit].

Fig. 2. NOT gate.

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Fig. 4. AND gate.

Fig. 3. OR gate.

.1. NOT gate

The performance of the difference frequency generator unit isothing but that of a NOT gate as shown in Fig. 2.

When A = 0, the difference is � − 0 = 0. This is the A = 1 and when= � the difference is � − � = 0 i.e. A = 0 i.e. operation of a NOT gate.

.2. OR gate

The OR operation is obtained by just coupling two beams withach other as in the case of intensity encoding. This is anotherdvantage over frequency encoding where to get OR operation aot of active devices are required. The hybrid encoded OR gate ishown in Fig. 3.

When either one of the inputs A or B is � then the output is �nd when both A and B are zero the output is zero as in the ORperation.

Table 1Truth table of the NOT gate.

A A

0 � (1)� (1) 0

able 2ruth table of the OR, AND, NAND, NOR, X-OR and X-NOR gates.

A B OR AND NAND NOR X-OR X-NOR

0 0 0 0 � (1) � (1) 0 � (1)0 � (1) � (1) 0 � (1) 0 � (1) 0� (1) 0 � (1) 0 � (1) 0 � (1) 0� (1) � (1) � (1) � (1) 0 � (1) 0 � (1)

Fig. 5. NAND gate.

3.3. AND gate

The AND operation can be expressed as so it can be representedby NOT of (A + B) = AB realized by using three DFG units as shownin Fig. 4.

When any one of the inputs A or B is 0, then the input to theDFG unit III is � giving the output 0. When both the inputs are �,the input of the DFG unit III is 0 and the output is �. This is nothingbut AND operation.

3.4. NAND gate

We can express the NAND operation as A NAND B =NOT of (AB) = A + B. This can be implemented using two differencefrequency generation units as shown in Fig. 5.

When any one of the input is 0 then any one of the DFG unitoutput is � giving the output �. Again when both the inputs A and Bare � then the output of the both gates are 0 resulting in a 0 output.This operation is similar to a NAND gate.

3.5. NOR gate

The NOR gate output is given by

A NOR B = NOT of (A + B) = AB

This can be implemented using hybrid scheme and exploiting dif-ference frequency generation as shown in Fig. 6.

When both A and B are 0, the output is � and for all other cases(i.e. either any one of A or B is �) the input to the DFG unit is � andhence the output is 0 as in the case of a NOR gate.

3.6. X-OR gate

The output of an X-OR gate is AB + AB. The implementation ofthe gate exploiting only difference frequency is shown in Fig. 7.

K. Mukherjee / Optik 122

Fig. 6. NOR gate.

Fig. 7. X-OR gate.

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generation (SFG + DFG) in LiNbO3 waveguides, Opt. Express 13 (19) (2005)7405–7414.

[17] S.K. Garai, S. Mukhopadhyay, A method of optical implementation of frequencyencoded different logic operations using second harmonic and difference fre-quency generation technique in non linear material, Opt. Int. J. Light Electron.

Fig. 8. X-NOR gate.

When both A and B are zero, the output of the DFG units I andI are �. So the inputs of the units III and IV are also �. This gives anal output zero by difference frequency generation.

When both A and B are � then the inputs to both III and IV arelso � due to coupling of A and B with the outputs of units II and, respectively. The difference frequency generation in the units IIInd IV results in output zero in the final stage.

When one of the inputs A is zero and another B is �, then thenput to the unit III is always � and the input to the unit IV is alwaysero. This condition generates final output �. Similarly when A is �nd B is zero, the input to the unit III is zero and that to the unit IVs � giving the final output �. So it is clear that this gate behaves like

n X-OR gate.

(2011) 321–323 323

3.7. X-NOR gate

The performance of an X-NOR gate is given by AB + AB. The gateis implemented using four DFG units as shown in Fig. 8.

When both A and B are zero, the input to the units I, II and III arezero. So the input to the unit IV is � and the final output � from theoutput of unit I.

When both A and B are �, the inputs to the units I, II, and III areall �, thus their output are zero. So the final output is � from theoutput of unit IV.

When A is zero and B is � the inputs of units I, II, and III are �,zero, and �, respectively. The corresponding outputs are zero, �, andzero, respectively. Hence the input of unit IV is � and the output atthe final stage is zero. Similarly when A is � and B is zero, the finaloutput is zero. This gives the operation of an X-NOR gate.

4. Conclusion

The hybrid encoding technique is simple in realization and hasno disadvantage of intensity loss dependent problem. So the powerof the input beams do not require to be maintained at a particularintensity level. The realization of the logic gates is simpler in thesense that here only difference frequency generation is used andno other principle is involved. In this communication the NANDgate is realized which is universal and can be the building blockof any combinational or sequential logic like half adder, full adder,subtractor, Flip Flop, and many more which will be the author’sfuture communications.

References

[1] A.A. Sawchuk, T.C. Strand, Digital optical computing, Proc. IEEE 72 (1984)758–779.

[2] M.T. Fatehi, K.C. Wasmundt, S.A. Collins, Optical flip flops and sequential logiccircuits using a liquid crystal light valve, Appl. Opt. 23 (1984) 2163–2171.

[3] S. Mukhopadhyay, An optical conversion system: from binary to decimal anddecimal to binary, Opt. Commun. (Neth.) 76 (5–6) (1990) 309–312.

[4] J.N. Roy, S. Mukhopadhyay, A minimization scheme of optical space variantlogic operations in a combinational architecture, Opt. Commun. 119 (1995)499–504.

[5] S. Dhar, S. Mukhopadhyay, All optical decoding method for ASCII coded datausing non linear material based switching, Opt. Eng. (USA) 45 (11) (2006),115201-1–115201-4.

[6] S. Mukhopadhyay, D.N. Das, N. Pahari, An optical method for addition of binarydata by non linear material, Appl. Opt. (USA) 43 (33) (2004) 6147–6150.

[7] S. Mukhopadhyay, Binary optical data subtraction using ternary digital repre-sentation technique in optical arithmetic problems, Appl. Opt. (USA) 31 (1992)4622–4623.

[8] S. Mukhopadhyay, D.N. Das, P.P. Das, P. Ghosh, Implementation of all opticaldigital matrix multiplication scheme with non linear material, Opt. Eng. 40 (9)(2001) 1998–2002.

[9] K. Roychowdhury, P.P. Das, S. Mukhopadhyay, All optical time domainmultiplexing–demultiplexing scheme with non linear material, Opt. Eng. 44(3) (2005), 035201-1–035201-5.

10] W. Wu, S. Campbell, S. Zhou, P. Yeh, Polarisation encoded optical logic operationin photorefractive media, Opt. Lett. 18 (1993) 1742–1744.

11] S. Mukhopadhyay, Optical computation and parallel processing, in: ClassiqueBook, 2000, ISBN 81-87616-01-6.

12] S.D. Smith, Lasers, nonlinear optics and optical computers, Nature 316 (6026)(1985) 319–324.

13] G. Li, L. Liu, Optical one rule symbolic substitution for pattern processing, Opt.Commun. 101 (3–4) (1993) 170–174.

14] M.S. Alan, Efficient trinary signed digit symbolic arithmetic, Opt. Lett. 19 (5)(1994) 353–355.

15] S.K. Garai, D. Samanta, S. Mukhopadhyay, All optical implementation of inver-sion logic operation by second harmonic generation and wave mixing characterof some nonlinear material, Opt. Optoelectron. Technol. China 6 (4) (2008)43–46.

16] J. Wang, J. Sun, C. Luo, Q. Sun, Experimental demonstration of wavelengthconversion between ps-pulses based cascaded sum and difference frequency

Opt. 121 (8) (2010) 715–721.