PHOTONICS-2008: International Conference on Fiber Optics and Photonics December 13-17, 2008, IIT Delhi, India

POLARIZATION ENCODED ALL-OPTICAL QUATERNARY MAX GATE J. N. Roy 1 , T.Chattopadhyay1 , S.Manna2 and G.K.Maity2 1

Department of Physics, College of Engineering & Management, Kolaghat, KTPP T/S, Purbamedinipur 721171, W.B. India 2

Calcutta Institute of Technology, Uluberia , Howrah, W.B. India Email :[email protected] ,[email protected] ,

Abstract: An all-optical scheme of polarization encoded quaternary (4-valued) MAX logic gate with the help of Terahertz Optical Asymmetric Demultiplexer (TOAD) based fiber interferometric switch is proposed and described. For the quaternary data processing in optics, the quaternary number (0, 1, 2, 3) can be represented by four discrete polarized state of light.

1. INTRODUCTION

an additional, intra loop 2×2 coupler, and a nonlinear

Multi-valued logic can be viewed as an alternative

element (NLE) that is offset from the loop’s midpoint

approach to solve many problems in transmission,

by a distance x as shown in fig.1 (a) [8].

storage

and

processing

of

large

amount

of

information in digital signal processing [1-7]. In this paper, first time to our knowledge we propose and describe

an

all-optical

scheme

for

designing

polarization encoded quaternary MAX logic gate with the help of nonlinear material based fiber interferometric switches. For the quaternary data processing in optics, the quaternary number (0, 1, 2, 3) can be represented by four discrete polarized state of light. In optical implementation we can consider the set of quaternary logic states {0, 1, 2, 3} as shown below:

In the absence of a control signal, data signal

0 = No light (null). 1 = vertically polarized light (

Fig.1 (a): TOAD-based optical switch

(incoming signal) enters the fiber loop, pass through

)

the semiconductor optical amplifier (SOA) at

2 = horizontally polarized light ( • ) 3 = partially polarized or Un-polarized light (

)

2. TOAD-BASED OPATICAL SWITCH

different times as they counter-propagate around the loop, and recombine interferometrically at the coupler. Since both signals see the same medium as they propagate around the loop, the data is reflected back toward the source. When a control signal is injected into the loop, it saturates the SOA and

[8-13]

TOAD based gate has added a new

momentum in the field of all-optical logic and data processing. The TOAD consists of a loop mirror with

changes its index of refraction. As a result, a differential phase shift can be achieved between the

two counter-propagation data signal to switch the

gates in quaternary world. Quaternary MAX gate is

data signal to the counter port (output port). A

equivalent OR gate in binary world.

polarization or wavelength filter may be used at the

The QMAX operation is shown in the equation no

output to reject the control and pass the input signal.

(1), the operator ‘ ∨ ’ is QMAX operation

The

control

pulse

has

sufficient

energy

QMAX ( X , Y ) = X ∨ Y

to

significantly modify the optical properties of the NLE, but the clock wise and counter clock wise

(1)

A QMAX (X, Y) function is shown in the Table-1. And the optical circuit is shown in the Fig.2.

signal pulses do not. Even if the NLE has a slow nonlinearity, a very short control pulse can modify its optical properties on a time scale of a picoseconds or less. The incoming and control signals are to be adjusted in such a way that the input signal enters the SOA at about the same time as the control signal.

Table-1: Truth table of Quaternary MAX gate X 0 1 2 3 Y 0 0 1 2 3 1 1 1 2 3 2 2 2 2 3 3 3 3 3 3 Here X and Y are two quaternary input and can take any one of the four logic state. X and Y passed through PBS1 and PBS2 respectively, where it splits into two components. X1 & Y1 are the vertically polarized light component. X2 & Y2 are the horizontally polarized light component, which are

Fig.1 (b): Schematic diagram of TOAD-based optical switch

passed

through

a

polarization

converter

PC

(polarization converter, which is preferably half wave plate; converts vertically polarized light to horizontal one and vice versa). In fig-2 they are indicated by X21

Now it is clear that in the absence of control signal,

& Y21 respectively. Now these two rays are fed to the

the incoming signal exits through input port of

two TOAD based switches S1 and S2 respectively as

TOAD and reaches to the output port-2 as shown in

incoming signal. The control signals of these

Fig. 1 (a). In this case no light is present in the output

switches are taken from X1 and Y1 after passing

port-1. But in the presence of control signal, the

through WC (wavelength converter) and EDFA (Er+3

incoming signal exits through output port of TOAD

doped fiber amplifiers. Beam combiner BC2 joints

and reaches to the output port-1 as shown in Fig.1

one part of Y21 & Y1. The combined beam Y3 is

(a). In this case no light is present in the output port-

directed to another beam combiner BC1, where X21 &

2. In the absence of incoming signal, port-1 and port-

X1 are jointed. The combined beam, I3 is directed to

2 receives no light as the filter blocks the control

another switch S3 as incoming signal. Now another

signal. Schematic block diagram is shown in Fig.1

part of X21 & Y21 are combined by beam combiner

(b).

BC3 and it is fed to S3 switch as control signal

3. ALL-OPTICAL QUATERNARY MAX GATE Like binary world there are also numbers of basic

through WC and EDFA. Now the upper output channels of S3 (after passing through PC) (S3U), S1 (S1U), S2 (S2U) and lower output channels of S3 (S3L)

are combined by beam combiner BC4 to get the final output. Now the operation of this quaternary MAX

(e)

this case. Hence the final output is 3 ( ). When X=1, Y=0. So X1=1 ( ), X21= Y1=Y21=0

gate is described below:

So I3=1, C3=0.

(a)

output is 1 (

When X=Y=0, then only no light is put to the inputs of all switches. Hence no light is found at

(f)

(b) When X=0, Y=1. So X1=X21=Y21=0 and Y1=1 (

).

When X=Y=1. Then X1=Y1=1 & X21=Y21=0. So I3=1, C3=0.

the final output i.e. the logical state 0.

Hence S3L=1 (as incoming

signal is present but control signal is absent of S3). So the final output is 1 (

). Then only S3 switch get vertically

polarized light as incoming. But C3=0. So,

Hence S3L=1. So the final

(g)

).

When X=1, Y=2. Then X1=1 & X21= 0, Y1=0 &

S3L=1 & S3U=0 (as incoming signal is present

Y21=1. So I3=1, C3=1. Hence S3U=2 ( • ) (as

but control signal is absent of S3). Other

both incoming and control signal of S3 are

switches are inactive. Hence the final output is

present). Other gates are inactive in this case.

1(

Hence the final output is 2 ( • ).

).

(h) When X=1, Y=3. Then X1=1 & X21= 0, Y1= Y21=1. The same thing is happened as case- (d). So the final output is 3 ( (i)

).

When X=2, Y=0. Then X1=0 & X21=1, Y1= Y21=0. The same thing is happened as case- (c). So the final output is 2 ( • ).

(j)

When X=2, Y=1. Then X1=0 & X21= 1, Y1=1 & Y21=0. So I3=1, C3=1. Hence S3U=2 ( • ) (as both incoming and control signal of S3 are present). No light is found to the other outputs

Fig-2: All optical circuit for Quaternary MAX gate PC: Polarization Converter ( λ / 2 plate);

i.e. S1U, S2U and S3L. Hence the final output is 2 ( • ).

BC: WC :

(k) When X=Y=2. Then X1=0 & X21=1, Y1=0 &

Wavelength converter. S1, S2, S3 are interferometric

Y21=1. So I3=1, C3=1. Hence only S3U=2 ( • )

switches.

(as both incoming and control signal of S3 are

Beam combiner;

(c)

BS: Beam splitter;

present). Hence the final output is 2 ( • ).

When X=0, Y=2 ( • ). So X1=X21=Y1=0 and Y2=1 (

). Hence S2U=0 (as incoming signal is

present but control signal of S2 is absent). Also C3=1, I3=1. So S3U=2 ( • ) (as both incoming and control signal of S2 are present). And S1 switch is inactive. Hence the final output is 2 ( • ).

(l)

When X=2, Y=3. Then X1=0 & X21=1, Y1= Y21=1. The same thing is happened as case- (d). So the final output is 3 (

).

(m) When X=3, Y=0. Then X1=X21=1, Y1=Y21=0. Hence, S1U=1 (

) and S3U=2 ( • ) (as both

(d) When X=0, Y=3 ( ). So X1=X21=0 and Y2= Y1=1 ( ). Hence S2U=1 ( ) and S3U=2 ( • ) (as

incoming and control signal of S2 and S3 are

both incoming and control signal of S2 and S3

(n) When X=3, Y=1. Then X1=X21=1, Y1=1 &

are present). And S1 switch is also inactive in

Y21=0. The same thing is happened as case-

present). Hence the final output is 3 (

).

(m). So the final output is 3 ( (o)

[7] ! "

).

When X=3, Y=2. Then X1=X21=1, Y1=0, Y21=1.

)

The same thing is happened as case- (m). So the

,

final output is 3 ( ). (p) When X=Y=3. Then X1=X21=Y1=Y21=1 ( ). Hence, S1U=1 (

), S2U=1 (

), S3U=2 ( • ) and

S3L=0 (as both incoming and control signal of

#$ % & *

' (

+

! +

. Journal of Nonlinear

Optical Physics and Materials /

01 2 3345

[8] J. P. Sokoloff, P. R. Prucnal , I. Glesk and M.

S1, S2 and S3 are present). Hence the final

Kane,

output after BC4 is 3 (

demultiplexer (TOAD)”, IEEE Photon. Technol.

).

“A

terahertz

optical

asymmetric

Lett., 5(7), 787-790, (1993). 4. CONCLUSION

[9] Y. K. Huang, I. Glesk, R. Shankar and

Here, the first time we have proposed and described

P.R.Prucnal,

“Simultaneous

all-optical

3R

an all-optical circuit for some basic quaternary logic

regeneration scheme with improved scalability

operations like QMAX.

using TOAD”, Optics Express, 14(22), 1033910344, (2006)

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