DESIGNING OF ALL OPTICAL TWO INPUT TERNARY MAX LOGICAL OPERATION Panchatapa Bhowmik1, Jitendranath Nath Roy1 and Tanay Chattopadhyay2 1

Department Of Physics, National Institute Of Technology, Jirania, Tripura(w), Pin-799055 Email: [email protected] , [email protected] 2

Kolaghat Thermal power station, WBPDCL, 721137, Mecheda, West Bengal, India. Email: [email protected]

Abstract: The ternary logical operations are the basic logical operations in superfast photonic computing system. Here an all optical circuit for symmetric TMAX and ordinary TMAX with an optical switch of nonlinear material is proposed and discussed. The gold nanoparticles embedded in optically transparent matrices alumina (Al2O3) is used as the nonlinear material in optical switch at a wavelength of 525nm (radiation from a nanosecond Nd:YAG). The inputs of the logic gates are represented by different polarization states of light. This model is simple, practical and very much useful for future all optical information processing.

Keywords: Nonlinear optics, optical logic, optical system design, photonic component and devices, optical switch, polarization.

1.

INTRODUCTION: With today’s growing dependence on computing technology, the need for high performance computers has significantly increased which can be met only by all optical multi valued logic (MVL) computer. The photon is the ultimate unit of information with unmatched speed and data packaged in a signal of zero mass. Current developments in optical technologies are being directed toward nanoscale devices with sub wavelength dimensions, in which photons are manipulated using nearfield optical phenomena. It is true that light is the fastest means to send information to and from the nanoscale, but there is a fundamental incompatibility between light at the microscale and devices and processes at the nanoscale. In the world of optical computing, though the design of computers began with binary (radix-2) logic system, but the rapid rise in use of computer and of internet give led to the idea of multi valued logic (radix>2), which is the best alternative for increasing the data carrying capacities, large information storage and high speed arithmetic operation

(1)

. By using

ternary notation, we can take advantage of the possibilities lying in the ternary number system. Brian Hayes claims in his article ‘Third base’

(2)

‘Ternary numbering systems are the most efficient of all (3)

integer bases’. In our earlier paper we have designed an all optical circuit for ternary MIN operation

and in this proposed paper, we have designed a circuit for all optical ternary MAX logical operation using optical nonlinear material (OPNLM) based switch, where the nano particle is used as optical

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switch material. 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

(4)

.

For the ternary processing in optics the inputs are represented by different discrete polarized states of light, where for, 1 = horizontally polarized light ( • ), 0 = right circularly polarized light (⥀), 1= vertically polarized light (↕), for symmetric TMAX logical operation and 0 = right circularly polarized light (⥀), 1 = vertically polarized light (↕), 2 = horizontally polarized light ( • ),for ordinary TMAX logical operation respectively.

2.

TERNARY SYMMETRIC LOGICAL OPERATION : Ternary logic are the simplest multi valued logic having radix-3. The number of logical operations in n

MVL can be calculated by using the formula -

R R where, R = radix and n = no.of inputs, so the 2

number of possible two input ternary logical operations will be

33 =19,683, among which Ternary

MAX and Ternary MIN are the main for the both types of ternary logic function as these functions can be implemented in designing the other logical operations. The details of ternary logical operation is discussed in Fig.1.

Fig.1 : what is ternary logic!

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The TMAX logical operation can be defined as -

TMAX (A,B) -

A if A ≥ B Max( A, B) =  B if A < B

Table 1: – Truth table for (a) symmetric ternary MAX, (b) ordinary ternary MAX

(a)

A

1

2

0

0

1

2

1

1

1

1

2

1

2

2

2

2

0

1

1

1

0

1

0

0

0 1

1

1

A

0

1

B

3.

(b)

B

DESIGNING OF ALL OPTICAL CIRCUIT FOR TERNARY MAX LOGICAL OPERATION:

The block diagram of all optical circuit for ternary MAX logical operation is given in fig-4. The details of the circuit components used in the diagram is already discussed in a earlier paper(5).The light from the source first get incident on a beam expander (BE) and then falls on the composite block. The composite block is made of two layers - the polarization isolator mask (PI-mask) and the polarization converter mask (PC-mask). In fig -2, the first layer of the side view is the PI-mask where nine numbers of polarization isolator are placed in a (3X3) matrix - the first row of the PI-matrix contains Horizontal polarization isolator (HPI), second row contains Right circular polarization isolator (RCPI) and the third row contains Vertical polarization isolator (VPI) respectively .The second layer of side view of the composite block is PC-mask which is also a (3X3) matrix ,made of different types of polarization converter. The details mathematical analysis of polarization converter is already given in the earlier paper(5). In our proposed circuit we have used only three types of polarization converter and these are (a) PC-1: It converts the vertically polarized light (↕) into horizontally polarized light ( • ) and vice versa.

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0

1

0

(b) PC-2: It converts the both vertical (↕) and horizontally polarized light ( • ) into right circularly polarized light ( ). (c) PC-3:

It converts right circularly polarized light ( ) into horizontally polarized light ( • ) and

vertically polarized light (↕) into right circularly polarized light ( ).

Fig . 2 - Composite block (CB-block)

3.1 PRINCIPLE OF WORKING OF THE PROPOSED CIRCUIT: Optical phase conjugation is a mechanism of creating a beam from another beam with equal frequency, but in opposite phase. Mixing of four waves is mainly used to generate the phase conjugate wave. A forward and a backward propagating pump beam interact in an OPNLM, which has at least a cubic type of nonlinearity. When the third probe beam is introduced at an angle, a reflected conjugate beam is generated. The total field of the nonlinear medium is (6) E(t) ∞

 

 f + Eb + Ep + complex conjugate]3

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The pump beam has the high power while the probe is weak and the energy of the pump beam is transferred to the conjugate probe beam as a multiplicative gain term. When two pump beams are made collinear, the reflected beam exactly retraces the path of the probe beam.

Pump wave E1 (

Phase conjugate waveE4(

Z-axis Signal waveE3(

Pump wave E2 (

Z=0

Z=l

Fig .3 - Working principle of an OPNLM based switching system

Light from the source first falls on the beam expander (BE) and then being expanded get incident on composite block. In PI-mask of CB-block, the first row receives right circularly polarized light (RCPL), second row receives vertically polarized light (VPL) and the third row receives the horizontally polarized light (HPL) respectively. Then the light passes through the PC-mask and only the horizontally polarized light comes out from all pixels of CB – block. In fig-4, [O] is the optical switch which is a 3X3 matrix, made of optical nonlinear material (the nanoparticle, Au, embedded in Alumina,Al2O3). As shown in the figure-4 , the two inputs A and B of logic function are allowed to fall on OPNLM block after passing through the two blocks CB-1 and CB-2 respectively, where CB-2 is oriented by 90° in anti-clockwise direction with respect to CB-1. Now the probe beam (horizontally polarized light) from constant light source (CLS) is allowed to fall on the OPNLM block. According to the switching mechanism, discussed earlier, the conjugate beam reflected out from OPNLM will be also horizontal in nature and then this beam is allowed to pass through a PCM (type-2) matrix. The light coming out from PCM (type-2) is considered as the output of logical operations. PCM (type-2) matrix is different for symmetric ternary MAX and ordinary ternary MAX operation. The PCM (type-2) matrix for both types of ternary MAX operations are given in fig.-5. By placing the proper PCM (type-2) matrix in the circuit of fig-4, we can get the output of the respective logical operation.

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C11 C21 C31

C12 C22 C32

OPNLM matrix

C13 C23 C33

O11 O21

O12 O22

O31

O32

CB-2 block

O13 C13

O23

C12

O33

C32

C22

C11

Probe

C33

C23

C21

C31

Light from Input B through Beam Expander

Light from Input A through Beam Expander

CB-1 block

BS

P11 P21 P31

P12 P22 P32

P13

PCM(type-2)

P23

([P] matrix )

P33

Output (Y)

Fig .4 - Two input all optical Tri-state logical operation

Ternary MAX (radix=3) operation :

Symmetric TMAX and ordinary TMAX logical operations are discussed below-

A. Symmetric Ternary MAX : a. When A = 1 and B = 1 (vertically polarized light), then horizontally polarized light ( • ) emerges from C31 , C32 and C33 pixels of both CB-1 and CB-2 blocks and they will meet at O33 of OPNLM. The reflected probe beam from O33 will pass through P33 of PCM (type 2) matrix and will give the output 1, logical state. b. When A =

1 (horizontally polarized light) and B = 0 (right circularly polarized light), then horizontally

polarized light ( • ) emerges from C11 , C12 and C13 pixels of CB-1 and C21 , C22 and C23 pixels of CB-2 block and they will meet at O12 of OPNLM. The reflected probe beam from O12 will pass through P12 of PCM (type 2) matrix and will give the output 0, logical state. Similarly we can get the output of other combinations also.

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PC-2

PC-1

PC-2

PC-1

PC-2

PC-2

PC-1

PC-1

PC-1

PC-1

PC-1

PC-1

(a)

(b)

Fig-5 : PCM (type-2) matrix for (a) symmetric TMAX (b) ordinary TMAX

B. Ordinary Ternary MAX : a. When A = 0 (right circularly polarized light) and B = 1 (vertically polarized light), then horizontally polarized light ( • ) emerges from C21 , C22 and C23 pixels of CB-1 and C31 , C32 and C33 pixels of CB-2 block respectively and they will meet at O23 of OPNLM. The reflected probe beam from O23 will pass through P23 of PCM (type 2) matrix and will give the output 1, logical state. b. When A = 2 (horizontally polarized light) and B = 1 (vertically polarized light), then horizontally polarized light ( • ) emerges from C11 , C12 and C13 pixels of CB-1 and C31 , C32 and C33 pixels of CB-2 block and they will meet at O13 of OPNLM. The reflected probe beam from O13 will pass through P13 of PCM (type 2) matrix and will give the output 2, logical state. Similarly we can get the output of other combinations also. All the outputs of the logical operations of the circuit given in fig.-4 satisfy the theoritical truth tables given in table-1.

4.

CONCLUSIONS : In this paper we have presented an idea to design a dynamic all optical circuit using OPNLM switch for realizing two input basic Ternary MAX logical operations. Gold nano particles embedded in alumina (Au:Al2O3) is used as the nonlinear material of the switch. The advantageous properties of the circuit is it amplifies the intensity of input beam and the logic system has a better flexibility in circuit design, more storage capacity and utilization of newer semiconductor technologies. This circuit may be useful in future all-optical logical computing system.

.

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5.

REFERENCES : 1. Smith KC. The prospects for multi valued logic : a technology and applications view. IEEE Transactions on Computers 1981 ; C-30 (9): 619-34 2. B. Hayes, “Third base”, American scientist, vol. 89, number 6, pp. 490-494, Nov-Dec 2001 3. P.Bhowmik, Jitendranath Roy, T. Chattopadhyay and C. Taraphder “Designing of All Optical Circuit for Two Input Ternary MIN Logical Operation”, COE’11 ,march,2011 4. Jin Yi, He Huacan and Lu Yangtian, “Ternary Optical Computer Architecture”, Physica Scripta. Vol. T118, 98–101 (2005) 5. Tanay Chattopadhyay, Goutam Kumar Maity and Jitendra Nath Roy, “Designing of all-optical tri-state logic system with the help of Optical Nonlinear material” J of Nonlinear optical physics and materials, vol 17, no. 3 (2008) 315-328. 6. Optical computing-an introduction By Mohammad A. Karim and Abdul A.S.Awwal, Chapter 10

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