**3. Conversion of decimal number to frequency encoded binary data**

To implement the frequency encoded all-optical arithmetic logic (ALU) processors, generation of frequency encoded binary data is very important. In this section the author has first mentioned a method of generating intensity encoded binary data to frequency encoded binary data and subsequently explained the scheme of conversion of decimal data to frequency encoded binary data using the above mentioned action of PSW made of SOA.

 

to superscript TM and TE represent the parameters for TM mode and TE mode of propagation respectively. At the PBS, the two modes coherently combine. If the phase

then at the output port-2 no beam will appear. In this case the output from port-2 will be

power of input pump beam as well as choosing the suitable parameters and length of SOA

Thus in the absence of pump beam, probe beam will appear at port-2 (ON-state) and in the presence of the pump beam of specific intensity, the probe beam will be suppressed in port-2(OFF-state). Obviously the state of port-1 will be complementary with respect to port-2 i.e.,

field for TE mode, *TE* is the confinement factor, *TE g* is the real gain function , *TE*

*TE TE TE TM TM TM*

 

*g g <sup>L</sup>*

*<sup>g</sup> v* is the group velocity of the envelop of the optical electric

*int* is the modal loss. All the parameters corresponding

**,** the angle of rotation of the beam after combination of

(3)

is the

 */* 2 and

is controlled by the

*TE TM g g*

*v v*

1 2

suppressed i.e. switched off. Here the induced phase difference

in the presence of the pump beam, power will develop at port-1.

TE and TM mode (having almost same amplitude) at output end of SOA is

**3. Conversion of decimal number to frequency encoded binary data** 

To implement the frequency encoded all-optical arithmetic logic (ALU) processors, generation of frequency encoded binary data is very important. In this section the author has first mentioned a method of generating intensity encoded binary data to frequency encoded binary data and subsequently explained the scheme of conversion of decimal data to frequency encoded binary data using the above mentioned action of PSW made of SOA.

*TE TM*

 

is an odd multiple of

(intensity > 0.4 mW) [Garai S.K.,2010,2011a].

Fig. 1(c). SOA acting as a polarization switch

where L is the length of SOA, *TE*

difference

phase modulation parameter and *TE*

The scheme of conversion of all optical decimal data to frequency encoded binary data works based on the principle of frequency conversion by polarization switches (PSW) and it is explained with the help of Fig.2(a) [Garai S.K.,2010,2011a]. The optical circuit comprises two polarization switches PSW1 and PSW2. Major part of the output beam of PSW1 is applied as the input pump beam of PSW2 and the rest part is coupled with the output beam of PSW2. The probe beam X1 of PSW1 is of frequency ν1 and the probe beam of PSW2 is X2 of frequency ν2.

Fig. 2(a). Optical circuit for converting decimal to frequency encoded binary data


Table 1. Decimal numbers and their corresponding frequency encoded binary numbers

In the absence of input pump beam 'A', the PSW1 will be in ON state which in turn will suppress PSW2. The least fraction of the output beam of PSW1 of frequency ν1 will appear at the output. In the presence of the input beam A, the PSW1 will be in OFF state which in turn

A Novel Method of Developing Frequency Encoded

converted binary number.

Optical beam

connecting

terminal

3 D3 2 PSW0

5 D5 2 PSW0

6 D6 2 PSW1

9 D9 2 PSW0

10 D10 2 PSW1

12 D12 2 PSW2

7 D7 3

11 D11 3

13 D13 3

14 D14 3

15 D15 4

No of split up

parts of beam

Connected to

PSW switches

as pump beam

0 D0 NIL None All None None All

1 D1 No PSW0 1,2,3 0 0 1,2,3

2 D2 No PSW1 0,2,3 1 1 0,2,3

4 D4 No PSW3 0,1,2 3 3 0,1,2

PSW0 PSW1 PSW3

PSW0 PSW1 PSW3

PSW0 PSW2 PSW3

PSW1 PSW2 PSW3

PSW0 PSW1 PSW2 PSW3

Table 2. Decimal to binary conversion scheme in tabular form

8 D8 No PSW3 0,1,2 3 3 0,1.2

Decimal Number

Different Optical Logic Processors Using Semiconductor Optical Amplifier 55

binary number in sequence 'Y3Y2Y1Y0' corresponding to the input decimal number. Here Y3 represents the most significant bit (MSB) and Y0 represents the least significant bit (LSB) of the

ON state

OFF state

PSW1 2,3 0,1 0,1 2,3

PSW3 1,2 0,3 0,3 1,2

PSW3 0,2 1,3 1,3 0,2

PSW3 1,2 0,3 0,3 1,2

PSW3 0,2 1,3 1,3 0,2

PSW3 0,1 2,3 2,3 0,1

2 0,1.3 0,1,3 2

2 0,1.3 0,1,3 2

1 0,2,3 0,2,3 1

0 1,2,3 2,2,3 0

None All All None

PSW in PSW/ in Output

OFF state

ON state

Y3 Y2 Y1 Y0

 1111 

 1112 

 1121 

 1122 

 1211 

 1212 

 1221 

 1222 

 2111 

 2112 

 2121 

 2122 

 2211 

 2212 

 2221 

 2222 

will switch the PSW2 in ON state and thereby the beam of frequency ν2 will be obtained at the output end.

The above mentioned technique has been exploited for the conversion of decimal (0 to 15) to binary data and it is explained with the help of Fig.2(b).

Fig.2(b) comprises four frequency converter units made of polarization switches (PSW0, PSW0/), (PSW1, PSW1/), (PSW2, PSW2/) and (PSW3, PSW3 /). PSW0, PSW1, PSW2 and PSW3 have their common probe beam 'X1' of frequency <sup>1</sup> , whereas another four prime polarization switches (PSW0 / to PSW3 /) have their common probe beam 'X2' of frequency <sup>2</sup> . D0, D1, D2…..D15 are sixteen input terminals corresponding to decimal numbers 0,1,2,3,….,15 respectively, through which optical beam of specific power is to be applied to convert a specific decimal number(corresponding to terminal number) into its binary form. For example, to convert the decimal number '9' to its binary form, a laser source of specific power [Garai S.K.,2011a] is to be applied in the terminal D9 by means of an optical switch. The beam after entering via the terminal D9 will split up into two equal parts and serve as the pump beam of PSW3 and PSW1. The beam entering via the terminal D13 will serve as the pump beam of PSW3, PSW2 and PSW0, the beam entering via the terminal D15 will act as the pump beam for all four polarization switches PSW3, PSW2, PSW1 and PSW0 and so on. The splitting of the beams after entering through the sixteen terminals ( 0 to 15) and their function as the pump beam for different PSWs are presented in Table-2. The terminal D0 has no internal connection to any of the polarization switches. The output ends of the combination of polarization switch (PSW3, PSW3 / ), (PSW2, PSW2 /), (PSW1, PSW1 /) and (PSW0, PSW0 / ) are designated as Y3,Y2,Y1 and Y0 respectively and these will give the frequency encoded

Fig. 2(b). Decimal to frequency encoded binary data conversion scheme

will switch the PSW2 in ON state and thereby the beam of frequency ν2 will be obtained at

The above mentioned technique has been exploited for the conversion of decimal (0 to 15) to

Fig.2(b) comprises four frequency converter units made of polarization switches (PSW0, PSW0/), (PSW1, PSW1/), (PSW2, PSW2/) and (PSW3, PSW3/). PSW0, PSW1, PSW2 and PSW3

D0, D1, D2…..D15 are sixteen input terminals corresponding to decimal numbers 0,1,2,3,….,15 respectively, through which optical beam of specific power is to be applied to convert a specific decimal number(corresponding to terminal number) into its binary form. For example, to convert the decimal number '9' to its binary form, a laser source of specific power [Garai S.K.,2011a] is to be applied in the terminal D9 by means of an optical switch. The beam after entering via the terminal D9 will split up into two equal parts and serve as the pump beam of PSW3 and PSW1. The beam entering via the terminal D13 will serve as the pump beam of PSW3, PSW2 and PSW0, the beam entering via the terminal D15 will act as the pump beam for all four polarization switches PSW3, PSW2, PSW1 and PSW0 and so on. The splitting of the beams after entering through the sixteen terminals ( 0 to 15) and their function as the pump beam for different PSWs are presented in Table-2. The terminal D0 has no internal connection to any of the polarization switches. The output ends of the combination

/ ), (PSW2, PSW2

Fig. 2(b). Decimal to frequency encoded binary data conversion scheme

designated as Y3,Y2,Y1 and Y0 respectively and these will give the frequency encoded

/), (PSW1, PSW1

/) have their common probe beam 'X2' of frequency

<sup>1</sup> , whereas another four prime

/) and (PSW0, PSW0

<sup>2</sup> .

/ ) are

binary data and it is explained with the help of Fig.2(b).

have their common probe beam 'X1' of frequency

/ to PSW3

the output end.

polarization switches (PSW0

of polarization switch (PSW3, PSW3

binary number in sequence 'Y3Y2Y1Y0' corresponding to the input decimal number. Here Y3 represents the most significant bit (MSB) and Y0 represents the least significant bit (LSB) of the converted binary number.



A Novel Method of Developing Frequency Encoded

Table 3. Truth table of frequency encoded different logic units

for SOA3. The destination of the input beam 'A' of frequency

and X2 are two linearly polarized input probe beams of frequency '

Now the NAND logic operation is explained with the help of Fig3.

'SOA2'. The reflected signal of frequency '

presented in Table-3.

for reflected frequency '

frequency '

frequency

Different Optical Logic Processors Using Semiconductor Optical Amplifier 57

not required. Hence the conversion efficiency and speed of operation are higher compared to the earlier method. The truth table of frequency encoded different logic gates are

The scheme of the experiment for implementing frequency encoded NAND logic operation exploiting the nonlinear rotation of the state of polarization of the probe beam is shown in Fig.3. 'A' and 'B' are two input terminals through which frequency encoded pump beams are applied. 'ADM1' and 'ADM2' are the optical add and drop multiplexers which are tuned

[Garai S.K., Mukhopadhyay S., 2009, 2009b; Garai S.K., 2011c ]. The reflected signal of

beam is divided into two equal parts by means of 'beam splitter'(BS) .One part of the beam is injected as the pump beam for 'SOA1' and another part is injected as pump beam for

'C2' and then the beam is divided into two equal parts by means of beam splitter(BS). One of the beams is injected as the pump beam of SOA1 and another part is injected as pump beam

passing through ADM1 is given by { SOA3, SOA4} and that of the input beam 'B' of

The state of polarizations are maintained by polarization controllers(PC).The beam X2 is split up into three equal parts which are serving as the weak probe beam of SOA1, SOA2 and SOA3 respectively. Output of each 'SOA' is selected by an optical filter each having pass frequency equal to its corresponding input probe beam frequency. The final output is 'Y' which is obtained by connecting the output of each SOA after passing through polarization beam splitters (PBS). Initially the state of polarization of input probe beams are oriented in such a way that output from each PBS is zero in the absence of pump beams.

<sup>1</sup> ' from 'ADM1' is dropped down by circulators 'C1' and then power of the

2 as the pump beam after passing through ADM2 is given by { SOA2, SOA4}. X1

<sup>1</sup> ' by the application of proper biasing current of SOAs in 'ADMs'

<sup>1</sup> ' from 'ADM 2' is dropped down by circulator

<sup>1</sup> ' and '

2 as the pump beam after

<sup>2</sup> ' respectively.

Now the mode of conversion of the decimal number '0' and '13' into its frequency encoded binary number are explained with the help of Fig. 3(b).

To convert the decimal number '0' to its binary form, the laser beam is to be connected to the input terminal D0. As the terminal D0 has no internal connection to any of the polarization switch, therefore, polarization switches PSW0, PSW1, PSW2 and PSW3 will not get any pump beam. All these switches will get only the probe beam of frequency <sup>1</sup> from common source X1 and therefore, all these switches will remain in ON state and the amplified probe beam of frequency 1 will appear at the output end of each polarization switch. Now all the polarization switches PSW0 / to PSW3/ will get the pump beam from previous PSWs as well as the probe beams of frequency <sup>2</sup> from common supply X2. Combination of the pump beam and the probe beam will drive all the polarization switches (PSW0 / to PSW3 / ) to OFF state. Fractional parts of the output beam of PSWs of frequency 1 after passing through bypass path of PSW/s will appear at output end of PSW0 / to PSW3 /.

Hence at the output end, one will obtain the binary form of frequency encoded data ' 1 1 1 <sup>1</sup> ', for input decimal number '0'.

To convert decimal number '13' into its binary form, the laser beam is to be connected to X13 terminal. After entering through D13, it will split up into three equal parts. Here the three successive spilt up parts will act as pump beam for PSW3, PSW2 and PSW0 unit respectively. The pump beams in these three units will switch off the PSWs which in turn will switch on PSW3/, PSW2 / and PSW0/ unit and one will obtain the amplified probe beam of frequency 2 at each of the output end Y3, Y2 and Y0. Remaining PSW1 units will not get any pump beam and according to its function, one will get optical beam of frequency 1 at the output terminal Y1. Thus, the binary number corresponds to the decimal number '13' is ' 2 2 1 <sup>2</sup> '.

Similarly the conversion of all other decimal number to its binary form can be explained with the help of Fig.2(b) and Table-2.

The above mentioned scheme may be extended to convert decimal numbers to binary coded decimal numbers and gray code and vice versa exploiting the above principle and that are explained in details in the work of Garai S.K.,2011a.
