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Optik 122 (2011) 1284–1288

Contents lists available at ScienceDirect

Optik

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method of implementation of frequency encoded all optical logic gates basedn non-linear total reflectional switch at the interface

ousik Mukherjee ∗

G and UG Dept. of Physics, B.B. College, Asansol 713303, West Bengal, India

r t i c l e i n f o

rticle history:eceived 17 February 2010ccepted 9 August 2010

a b s t r a c t

A novel method of implementation of frequency encoded logic gates NOT, OR, AND, NOR, NAND, X-OR,X-NOR is discussed. The frequency sources and physical requirements for the implementation are alsodiscussed. The non-linear material (liquid) suitable for these operations to be performed should be of

eywords:ll opticalogic gateson-linear total reflectional switch

large non-linear coefficient, high reverse saturation absorption, large thermo-optic coefficient and lowviscosity. The input controlling beams used to induce non-linearity in the switch are either of frequency�1 or �2 and the probe beam is a mixed signal of frequencies �1 and �2. Depending on the nature of thecontrolling inputs the output conditions of the probe can be adjusted to get different logic gates.

© 2010 Elsevier GmbH. All rights reserved.

requency encoding

. Introduction

Optics has a potential and strong role in signal processing,omputation, image processing and communication due to sev-ral advantages over electronic. In respect to speed, a photon is auitable signal carrier and a variety of information processors haveeen proposed in the last few decades [1–4]. All optical parallelomputation is the key technology for all optical networks and allptical logic gates are the essential parts of the optical computer.ecently, research on quantum information and computation hasttracted a large community of scientists, but has many difficul-ies to overcome, among them decoherence is the important one5,6]. Because of these difficulties in quantum computation tra-itional optical computation is still an emerging field of researchsing non-linear effect [7–14]. In most of these proposals, the statesf information are represented by intensity encoding technique orolarization encoding technique. In intensity encoding the state ‘1’

s represented by the presence of photon whereas ‘0’ is by absencef photon. This technique have many drawbacks namely, inten-ity loss dependent problems. In intensity encoding a particularalue of the signal intensity level must be maintained. In transmis-ion, reflection or refraction the intensity of the signals changesnd problems are created in the channel selection. This is because

non-linear media directs signals of different intensities in dif-

erent direction. As an alternative technique one can say aboutolarization encoding [15–17] but this scheme also have draw-

∗ Corresponding author.E-mail address: lipton007@indiatimes.com.

030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2010.08.017

back of changing state of polarization on reflection refraction ortransmission. So some polarization control mechanism is required.

Recently frequency encoding technique [18–20] and hybridencoding technique [21] free from intensity loss dependent prob-lem and polarization dependent problem are proposed. In thiscommunication the frequency encoding technique is utilized toimplement different logic gates using total reflectional opticalswitch.

2. The principle of the scheme

The working of the proposed logic gates is based on the fre-quency encoding and optical routing based on total reflectionalswitches.

2.1. Frequency encoding

In the frequency encoding scheme, the states of information ‘0’and ‘1’ are represented by signals of frequencies �1 and �2 respec-tively. Using this encoding technique the truth table of differentall optical logic gates are shown in Table 1 (NOT gate) and Table 2(other gates) below.

Thus it is clear from Tables 1 and 2 that the information coded interms of frequencies can be an efficient way to represent differentlogical input and output conditions.

2.2. Optical switching and routing

The optical switching and routing is based on the non-linearityinduced by the input beams and depending on that the variation

K. Mukherjee / Optik 122 (2011) 1284–1288 1285

Table 1Truth table of the NOT gate.

Input OutputA Ã

�1 (0) �2 (1)�2 (1) �1 (0)

Table 2Truth table of OR, AND, NOR, NAND, X-OR, X-NOR gates.

Inputs Outputs

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

0 (�1) 0 (�1) 0 (�1) 0 (�1) 1 (�2) 1 (�2) 0 (�1) 1 (�2)0 (�1) 1 (�2) 1 (�2) 0 (�1) 0 (�1) 1 (�2) 1 (�2) 0 (�1)1 (�2) 0 (�1) 1 (�2) 0 (�1) 0 (�1) 1 (�2) 1 (�2) 0 (�1)1 (�2) 1 (�2) 1 (�2) 1 (�2) 0 (�1) 0 (�1) 0 (�1) 1 (�2)

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Fig. 1. Optical switch.

n the propagation of the probe beams in a 1 × 2 total internaleflectional switch shown in Fig. 1. It consists of a pair of rectan-ular prisms with a non-linear medium (NLM) between them. As aon-linear medium a liquid of refractive index nl can be used. Theefractive index of the material of the prism np is so chosen suchhat in normal conditions np = nl.

If a controlling signal is made incident on the liquid the liquidhould be converted to gas such that the refractive index of theLM decreases [17]. If nl = np sin �input is maintained, then the probe

ignal will be total internally reflected from the non-linear mediumNLM) prism interface and changes its path. So the control signalsnduce a non-linearity and controls the path of propagation of therobe beam.

The simplest way to achieve this type of non-linearity is to useerr effect [22,23] but the effect is too weak. So alternatively onean use quartz as optical refractive media and fullerenes as the non-inear medium [18]. When there is no controlling signal signingn the non-linear medium nfullerenes = nquartz = 1.46, which can bebtained by properly adjusting the proportion of fullerenes andoluene, the probe signal will be transmitted without changing theath of propagation. Now shining controlling signal on the non-

inear medium converts it into gas and the refractive index of the◦

on-linear medium becomes nfullerenes = nquartz sin 45 = 1.03. In this

ondition, the probe signal will be reflected at the interface and theropagation direction will be changed. The structure of the opti-al router is shown in Fig. 2. The router consists of a pair of total

Fig. 2. Optical router.

Fig. 3. The optical router.

internal reflectional switches. The controlling signals (X, Y) are firstcoupled and then divided equally. One part is passed through thefilter F1 (�1 pass) and focusing lens L1 and another part throughfilter F2 (�2 pass) and focusing lens L2. The routing of the probesignal depends on the conditions of the input controlling signals.This type of optical switch is independently realized by Lawson andMichael [24] and a similar one using Kerr effect by Deshazer et al.[25].

3. Scheme of generation of different logic gates

The scheme of generation of different logic gates is based onfrequency encoding and frequency routing by the total reflectionalswitches. In the scheme, the input controlling beams are passedthrough two filters F1 (�1 pass) and F2 (�2 pass) corresponding toswitches S1 and S2 respectively. So the non-linearity is induced inthe switch S1 by signal of frequency �1 and in the S2 the signal offrequency �2 induces the non-linearity. Depending on the condi-tion of the controlling beam the path of the probe beams are shownin Fig. 3.

In Fig. 3, there are three different paths A, B and C of the probebeams depending on the conditions of the input controlling beams.When both the controlling inputs X and Y are signals of frequency�1, the non-linearity is only induced in the switch S1 and thecorresponding path of the probe beam is A due to total internalreflection at S1 (Fig. 3a). Similarly when the inputs are signals offrequency �1 and �2 (either X = �1 and Y = �2 or X = �2 and Y = �1)the non-linearity is induced on both the switches S1 and S2. The cor-responding path of the probe light is B due total internal reflectionon both the switches S1 and S2 (Fig. 3b). When both the controllinginputs X and Y are signals of frequency �2, the non-linearity is onlyinduced in the switch S2 and the corresponding path of the probebeam is C due to transmission through the switch S1 (Fig. 3c).

3.1. Implementation of the NOT gate

A NOT gate is a single input gate, and the output is the com-plement of the input. Thus if the controlling beam is of frequency�1, then the output will be a signal of frequency �2, which willbe extracted from the probe beam. Similarly for input controllingbeam of frequency �2, the output should be a signal of frequency�1, extracted from the probe. In Fig. 4, propagation of probe beamand extraction of the outputs are shown corresponding to the NOTgate is shown.

In Fig. 4, when the controlling input is a signal of frequency�1 (i.e. LOW), then the path of the probe signal will be along A.and in the path A, a �2 pass filter is used to extract output signal

at frequency �2 (i.e. HIGH) from the probe beam. This is the NOToperation corresponding to

0 (�1) → 1 (�2)

1286 K. Mukherjee / Optik 122 (2011) 1284–1288

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in these conditions. So the operations

0 (�1) NAND 0 (�1) → 1 (�2)

Fig. 4. NOT gate.

Again when the input control beam is a signal of frequency2 (i.e. HIGH), then the path of the probe signal will be along C.nd in the path C, a �1 pass filter is used to extract output signalt frequency �1 (i.e. LOW) from the probe beam. This is the NOTperation corresponding to

(�2) → 0 (�1)

Thus the switches S1 and S2 along with filters �1 pass and �2ass operate like a NOT gate.

.2. Implementation of the OR gate

An OR gate gives output high when any one of the input is highnd low only when both the inputs are low. The module describinghe propagation of probe beam and extraction of different outputsorresponding to the OR gate is shown in Fig. 5.

When both the input controlling beams are of frequency �1LOW), the path of the probe beam is A. The use of �1 pass filtern the path A makes the output a signal of frequency �1 (LOW). Sohe operation, 0 (�1) OR 0 (�1) → 0 (�1) is achieved.

Similarly when the inputs are signals of frequency �1 and �2either X = �1 and Y = �2 or X = �2 and Y = �1), the path of the probeeam is along B. The corresponding outputs are signals of frequency2 (HIGH) through the �2 pass filter placed in the path B, so the ORperations 0 (�1) OR 1 (�2) → 1 (�2) and 1 (�2) OR 0 (�1) → 1 (�2)re achieved.

Now when the input controlling beams are both signals of fre-uency �2, the corresponding path of the probe signal is along C.he �2 pass filter in the path C generates an output signal at fre-uency �2. So the operation 1 (�2) OR 1 (�2) → 1 (�2) is achieved.o the OR gate can be achieved using the optical router and threelters only.

.3. Implementation of AND gate

The output of an AND gate is high only when both the inputs areigh. In the module of the AND gate the filters in the paths A andare �1 pass and the filter in the path C is a �2 pass as shown in

ig. 6.When the input control signals are both of frequency �1, the

robe beam propagates along the path A and give rises to outputignal at frequency �1 (LOW) after the �1 pass filter. So we gothe operation 0 (�1) AND 0 (�1) → 0 (�1). In the conditions whennputs are signals of frequency �1 and �2 (either X = �1 and Y = �2

Fig. 5. OR gate.

Fig. 6. AND gate.

or X = �2 and Y = �1), the path of the probe beam is along B. Thecorresponding outputs are signals of frequency �1 (LOW) throughthe �1 pass filter placed in the path B, so the AND operations 0 (�1)AND 1 (�2) → 0 (�1) and 1 (�2) AND 0 (�1) → 0 (�1) are achieved.

When both input controlling beams are of frequency �2, theprobe beam propagates along the path C and the output is a sig-nal of frequency �2 through the �2 pass filter in the path C. Thiscorresponds to the operation 1 (�2) AND 1 (�2) → 1 (�2).

3.4. Implementation of the NOR gate

The NOR gate has high output only when both the inputs arelow, otherwise the output is low. This can be achieved by using themodule shown in Fig. 7.

When the input control signals are both of frequency �1, theprobe beam propagates along the path A and give rises to out-put signal at frequency �2 (HIGH) after the �2 pass filter. So wegot the operation 0 (�1) NOR 0 (�1) → 1 (�2). In the conditionswhen inputs are signals of frequency �1 and �2 (either X = �1 andY = �2 or X = �2 and Y = �1), the path of the probe beam is alongB. The corresponding outputs are signals of frequency �1 (LOW)through the �1 pass filter placed in the path B, so the AND opera-tions 0 (�1) NOR 1 (�2) → 0 (�1) and 1 (�2) NOR 0 (�1) → 0 (�1)are achieved. When both input controlling beams are of frequency�2 (HIGH), the probe beam propagates along the path C and theoutput is a signal of frequency �1 through the �1 pass filter in thepath C. This corresponds to the operation 1 (�2) AND 1 (�2) → 0(�1).

3.5. Implementation of the NAND gate

NAND gate generates a low output only when both the inputsignals are high otherwise generates high outputs. The modulecorresponding to the NAND gate is shown in Fig. 8.

In the conditions when either one of the inputs is low, i.e. signalof frequency �1, the path of the probe beams are along A or B. Inboth of these paths �2 pass filters are present giving a high outputs

Fig. 7. NOR gate.

K. Mukherjee / Optik 122 (2011) 1284–1288 1287

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Fig. 8. NAND gate.

(�1) NAND 1 (�2) → 1 (�2)

(�2) NAND 0 (�1) → 1 (�2) are achieved.

When both the controlling inputs are signals of frequency �2,he path of the probe beam is along C in which a �1 pass filter isresent. So the output in this condition is signal of frequency �1,

.e. low. So the operation 1 (�2) NAND 1 (�2) → 0 (�1) is achieved.

.6. Implementation of the X-OR gate

An X-OR gate gives output high when both the inputs are notame, i.e. one is low and another is high. The X-OR gate based onotal reflectional switch is shown in Fig. 9.

In the paths A and C of the probe beams corresponding to theonditions when both the controlling inputs are signals of fre-uency �1 or �2 respectively, �1 pass filters are used. So in theseonditions signal of frequency �1 (LOW) is detected in the output.o the operations

(�1) X-OR 0 (�1) → 0 (�1)

(�2) X-OR 1 (�2) → 0 (�1) are achieved.

Now when the controlling inputs are signals of two differentrequencies �1 and �2, the path of the probe beam is along B inhich a �2 pass filter is used. This give rises to the output signal at

requency �2, i.e. high. So the X-OR operations

(�1) X-OR 1 (�2) → 1 (�2)

(�2) X-OR 0 (�1) → 1 (�2) are achieved.

.7. Implementation of the X-NOR gate

The output of an X-NOR gate is high only when both the inputsre either low or high, otherwise the outputs are low. In Fig. 10, theodule of the X-NOR gate is shown.

In the paths A and C of the probe beams corresponding to the

onditions when both the controlling inputs are signals of fre-uency �1 or �2 respectively, �2 pass filters are used. So in these

Fig. 9. X-OR gate.

Fig. 10. X-NOR gate.

conditions signal of frequency �2 (HIGH) is detected in the output.So the operations

0 (�1) X-NOR 0 (�1) → 1 (�2)

1 (�2) X-NOR 1 (�2) → 1 (�2) are achieved.

Now when the controlling inputs are signals of two differentfrequencies �1 and �2, the path of the probe beam is along B inwhich a �1 pass filter is used. This gives rises to the output signalat frequency �1 (i.e. LOW). So the X-NOR operations

0 (�1) X-NOR 1 (�2) → 0 (�1)

1 (�2) X-NOR 0 (�1) → 0 (�1) are achieved.

4. Discussion and conclusions

The all optical logic gates NOT, OR, AND, NOR, NAND, X-OR, X-NOR are implemented in a single optical routing system using totalreflectional switches for the first time in frequency encoded format.The basic physical requirement for the logic gates are discussedbelow:

(1) Sources of two frequencies �1 and �2 preferably in the C bandsuitable for all optical communication.

(2) Filters which can pass frequencies �1 and �2.(3) Non-linear optical switches.(4) Focusing lenses.(5) Coupler and beam splitters.

The non-linear material suitable for the implementation of thegates should have the following properties [17]:

(1) Large non-linear coefficient,(2) High reverse saturation absorption,(3) Large thermo-optic coefficient, and(4) Low viscosity.

The input controlling beams can be taken to be of wavelengths1540 nm and 1550 nm in the C band corresponding to the frequen-cies �1 and �2 respectively. These signals can be extracted froma mode locked fiber laser (MLFL) by spectral slicing method [26].The probe beam is a mixer of signals of frequency �1 and �2. Theintensity of the controlling signals is so adjusted that they cancause pronounced non-linearity in the optical switches. The speedof operation of the gates is limited by the time taken in transmis-sion of the signal and the gates have ultrafast speed of operation.Among the implemented gates NAND and NOR gates are universaland one can generate any logical and functional devices by cascad-

ing these gates. The X-OR gate is an integral part of a binary halfadder, comparator and also finds application in header recognitionscheme which will be future communications of the author. Mostimportantly since frequency encoding technique is used, the logic

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288 K. Mukherjee / Opti

ates do not have the drawback of intensity loss dependent prob-ems or polarization sensitiveness. For these reasons the hardwareecomes simpler. The main challenge of the scheme to be realizable

s to find out an appropriate liquid, which gets converted into gashen illuminated by controlling signals. So further research in thiseld is necessary to find out a suitable non-linear material and theuthor believes that the technique and device has the potential ofecoming the essential part of future all optical computation andommunication network.

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