**4. Method of developing frequency encoded different logic operations**

The author was presented a method to develop all optical frequency encoded binary logic gates such as NOT, AND, OR, NAND, NOR, EX-OR etc. based on the conjugate beam generation technique by PPLN waveguide and subsequently frequency routing by add/drop multiplexers and frequency conversion using reflecting semiconductor optical amplifiers (RSOA)[Garai S.K., Samanta D.,et.al.,.(2008), Garai S.K., Mukhopadhyay S.,2009a,2011]. Conversion efficiency of conjugate beam generation by PPLN is not high enough and considerable amount of energy is lost to implement the logic operation. This problem was undertaken by the author and he tried to avert the intermediate conjugate beam generation, as a consequence he has supplanted the method by a new one. In this section, the author has presented a novel method to design all optical frequency encoded different logic gates exploiting the principle of nonlinear rotation of the state of polarization rotation (SOP) of the probe beam in semiconductor optical amplifier in the presence of pump beam of specific intensity ranges. Here conjugate beam generation is

Now the mode of conversion of the decimal number '0' and '13' into its frequency encoded

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

X1 and therefore, all these switches will remain in ON state and the amplified probe beam of

Hence at the output end, one will obtain the binary form of frequency encoded data

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

2 at each of the output end Y3, Y2 and Y0. Remaining PSW1 units will not get any pump

terminal Y1. Thus, the binary number corresponds to the decimal number '13' is

Similarly the conversion of all other decimal number to its binary form can be explained

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

The author was presented a method to develop all optical frequency encoded binary logic gates such as NOT, AND, OR, NAND, NOR, EX-OR etc. based on the conjugate beam generation technique by PPLN waveguide and subsequently frequency routing by add/drop multiplexers and frequency conversion using reflecting semiconductor optical amplifiers (RSOA)[Garai S.K., Samanta D.,et.al.,.(2008), Garai S.K., Mukhopadhyay S.,2009a,2011]. Conversion efficiency of conjugate beam generation by PPLN is not high enough and considerable amount of energy is lost to implement the logic operation. This problem was undertaken by the author and he tried to avert the intermediate conjugate beam generation, as a consequence he has supplanted the method by a new one. In this section, the author has presented a novel method to design all optical frequency encoded different logic gates exploiting the principle of nonlinear rotation of the state of polarization rotation (SOP) of the probe beam in semiconductor optical amplifier in the presence of pump beam of specific intensity ranges. Here conjugate beam generation is

**4. Method of developing frequency encoded different logic operations** 

1 will appear at the output end of each polarization switch. Now all the

/ and PSW0/ unit and one will obtain the amplified probe beam of frequency

/ to PSW3/ will get the pump beam from previous PSWs as well

<sup>2</sup> from common supply X2. Combination of the pump

/.

<sup>1</sup> from common source

/ ) to OFF

/ to PSW3

1 at the output

1 after passing through

binary number are explained with the help of Fig. 3(b).

frequency

PSW3/, PSW2

' 1 1 1 

' 2 2 1 <sup>2</sup> '.

polarization switches PSW0

as the probe beams of frequency

with the help of Fig.2(b) and Table-2.

beam. All these switches will get only the probe beam of frequency

state. Fractional parts of the output beam of PSWs of frequency

bypass path of PSW/s will appear at output end of PSW0/ to PSW3

<sup>1</sup> ', for input decimal number '0'.

explained in details in the work of Garai S.K.,2011a.

beam and the probe beam will drive all the polarization switches (PSW0

beam and according to its function, one will get optical beam of frequency

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 presented in Table-3.


Table 3. Truth table of frequency encoded different logic units

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 for reflected frequency ' <sup>1</sup> ' by the application of proper biasing current of SOAs in 'ADMs' [Garai S.K., Mukhopadhyay S., 2009, 2009b; Garai S.K., 2011c ]. The reflected signal of frequency ' <sup>1</sup> ' from 'ADM1' is dropped down by circulators 'C1' and then power of the 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 'SOA2'. The reflected signal of frequency ' <sup>1</sup> ' from 'ADM 2' is dropped down by circulator '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 for SOA3. The destination of the input beam 'A' of frequency 2 as the pump beam after passing through ADM1 is given by { SOA3, SOA4} and that of the input beam 'B' of frequency 2 as the pump beam after passing through ADM2 is given by { SOA2, SOA4}. X1 and X2 are two linearly polarized input probe beams of frequency ' <sup>1</sup> ' and ' <sup>2</sup> ' respectively. 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. Now the NAND logic operation is explained with the help of Fig3.

A Novel Method of Developing Frequency Encoded

**Case-2: Input pump beam 'A' is of frequency '**

Now the destination of the input beam 'A' of frequency

**Case-3: Input pump beam 'A' is of frequency '**

beam of 'SOA3' will give the beam of frequency

**Case-4: Both the pump beams are of frequency '**

input probe beam 'X1' of frequency

probe beams SOA1 and SOA4 unit be

<sup>1</sup> ) and X2(

optical arithmetic logic unit [Garai S.K.(2011c)].

Thus using input pump beams of frequencies

beam of frequency

circuit.

probe beams X1(

Now the destination of the input beam 'A' of frequency

<sup>1</sup> at the output end.

all other logic gates can be developed using NAND gates only.

<sup>1</sup> **' i.e. at '0' state** 

Now the destination of the input beam 'A' of frequency

**'**

<sup>2</sup> **' i.e. at '1' state** 

beam 'X2' of frequency

<sup>2</sup> .

frequency

frequency

**frequency '**

Different Optical Logic Processors Using Semiconductor Optical Amplifier 59

reflecting back by ADM1 is given by { SOA1, SOA2} and that of the input beam 'B' of

Under this situation 'SOA2' only will get both the pump beams at the same time. These two pump beams can significantly rotate the state of polarization of input probe

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

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

the pump beam after reflecting back by ADM2 is given by {SOA3, SOA4}. Thus both the input pump beams are injected at 'SOA4' whereas other SOAs get at most one pump beam. Therefore both the pump beams of 'SOA4' can significantly rotate the state of polarization of

> 1 and

frequency encoded NAND logic operation. NAND logic gate is the universal logic gate and

The utility of the above mentioned scheme is that the same circuit can be used to implement any one out of the 16 binary logic operations, only by properly selecting the frequency of the probe beam of the four SOA units. As for example, if the frequency of the

then it is possible to execute frequency encoded X-OR logic operation using the same

The block diagram of frequency encoded different logic units with proper distribution of

The above mentioned scheme may be extended to design all optical multiplexer and demultiplexer [Garai S.K., Mukhopadhyay S.(2009)], data comparator[Garai S.K.(2011)] multivalued logic unit such as trinary [Garai S.K., 2010], quaternary etc. logic gates and all

SOA2, SOA3 and SOA4, designated by 1,2,3 and 4 respectively are as shown in Fig.4.

the pump beam after reflecting back by ADM2 is given by { SOA1, SOA3}. Therefore under this situation 'SOA3' only will get both the pump beams. These pump beams can significantly rotate the state of polarization of the probe beam 'X2' and as a result output

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

<sup>1</sup> **' i.e. at '0' state and the B is of frequency** 

1 as the pump beam after

2 as the pump beam after passing

2 as the pump beam after passing

<sup>2</sup> as input data, it is possible to get a

1 as

2 as

<sup>2</sup> (X2),

<sup>2</sup> **' i.e. at '1' state and the 'B' is of** 

<sup>2</sup> and as a result output beam of 'SOA2' will give a beam of

<sup>2</sup> at the output end of PBS.

<sup>2</sup> **' i.e. both are at '1' state** 

1 and as a result output beam of 'SOA4' will give a

<sup>1</sup> (X1) and that of SOA2 and SOA3 unit be

<sup>2</sup> ) in four probe beam terminals of SOA units i.e., SOA1,

Fig. 3. Scheme of implementing frequency encoded NAND logic operation

#### **Case-1: Both the input pump beams A and B are of frequency '**<sup>1</sup> **' i.e. both are at '0' state**

Now both the pump beams of frequency ' <sup>1</sup> ' will be reflected from 'ADM1' and 'ADM2' and dropped down by circulators 'C1 and C2 respectively'. The destination of the input beam 'A' of frequency 1 as the pump beam is given by { SOA1, SOA2} and that of the input beam 'B' of frequency 1 as the pump beam is given by { SOA1, SOA3}.Thus SOA1 will get both the input pump beams whereas all other 'SOAs' get at most one pump beam at a time. Therefore both the pump beams of SOA1 can significantly rotate the state of polarization of input probe beam 'X2'of frequency 2 and an polarization beam splitter(PBS) at the output end can detect the nonlinear polarization rotation in terms of intensity difference. As a result output beams of 'SOA1' will give a beam of frequency <sup>2</sup> at the cost of the input pump beam each of frequency<sup>1</sup> .

Fig. 3. Scheme of implementing frequency encoded NAND logic operation

and dropped down by circulators 'C1 and C2 respectively'. The destination of the input

both the input pump beams whereas all other 'SOAs' get at most one pump beam at a time. Therefore both the pump beams of SOA1 can significantly rotate the state of polarization of

end can detect the nonlinear polarization rotation in terms of intensity difference. As a result

2 and an polarization beam splitter(PBS) at the output

1 as the pump beam is given by { SOA1, SOA2} and that of the input

1 as the pump beam is given by { SOA1, SOA3}.Thus SOA1 will get

<sup>1</sup> ' will be reflected from 'ADM1' and 'ADM2'

<sup>1</sup> **' i.e. both are at '0' state** 

<sup>2</sup> at the cost of the input pump beam

**Case-1: Both the input pump beams A and B are of frequency '**

Now both the pump beams of frequency '

output beams of 'SOA1' will give a beam of frequency

input probe beam 'X2'of frequency

<sup>1</sup> .

beam 'A' of frequency

beam 'B' of frequency

each of frequency

#### **Case-2: Input pump beam 'A' is of frequency '** <sup>1</sup> **' i.e. at '0' state and the B is of frequency '**<sup>2</sup> **' i.e. at '1' state**

Now the destination of the input beam 'A' of frequency 1 as the pump beam after reflecting back by ADM1 is given by { SOA1, SOA2} and that of the input beam 'B' of frequency 2 as the pump beam after passing through ADM2 is given by { SOA2, SOA4}. Under this situation 'SOA2' only will get both the pump beams at the same time. These two pump beams can significantly rotate the state of polarization of input probe beam 'X2' of frequency <sup>2</sup> and as a result output beam of 'SOA2' will give a beam of frequency<sup>2</sup> .

#### **Case-3: Input pump beam 'A' is of frequency '** <sup>2</sup> **' i.e. at '1' state and the 'B' is of frequency '**<sup>1</sup> **' i.e. at '0' state**

Now the destination of the input beam 'A' of frequency 2 as the pump beam after passing through ADM1 is given by { SOA3, SOA4} and that of the input beam 'B' of frequency 1 as the pump beam after reflecting back by ADM2 is given by { SOA1, SOA3}. Therefore under this situation 'SOA3' only will get both the pump beams. These pump beams can significantly rotate the state of polarization of the probe beam 'X2' and as a result output beam of 'SOA3' will give the beam of frequency<sup>2</sup> at the output end of PBS.

#### **Case-4: Both the pump beams are of frequency '**<sup>2</sup> **' i.e. both are at '1' state**

Now the destination of the input beam 'A' of frequency 2 as the pump beam after passing through ADM1 is given by {SOA3, SOA4} and that of the input beam 'B' of frequency 2 as the pump beam after reflecting back by ADM2 is given by {SOA3, SOA4}. Thus both the input pump beams are injected at 'SOA4' whereas other SOAs get at most one pump beam. Therefore both the pump beams of 'SOA4' can significantly rotate the state of polarization of input probe beam 'X1' of frequency 1 and as a result output beam of 'SOA4' will give a beam of frequency <sup>1</sup> at the output end.

Thus using input pump beams of frequencies 1 and <sup>2</sup> as input data, it is possible to get a frequency encoded NAND logic operation. NAND logic gate is the universal logic gate and all other logic gates can be developed using NAND gates only.

The utility of the above mentioned scheme is that the same circuit can be used to implement any one out of the 16 binary logic operations, only by properly selecting the frequency of the probe beam of the four SOA units. As for example, if the frequency of the probe beams SOA1 and SOA4 unit be <sup>1</sup> (X1) and that of SOA2 and SOA3 unit be <sup>2</sup> (X2), then it is possible to execute frequency encoded X-OR logic operation using the same circuit.

The block diagram of frequency encoded different logic units with proper distribution of probe beams X1( <sup>1</sup> ) and X2( <sup>2</sup> ) in four probe beam terminals of SOA units i.e., SOA1, SOA2, SOA3 and SOA4, designated by 1,2,3 and 4 respectively are as shown in Fig.4.

The above mentioned scheme may be extended to design all optical multiplexer and demultiplexer [Garai S.K., Mukhopadhyay S.(2009)], data comparator[Garai S.K.(2011)] multivalued logic unit such as trinary [Garai S.K., 2010], quaternary etc. logic gates and all optical arithmetic logic unit [Garai S.K.(2011c)].

A Novel Method of Developing Frequency Encoded

Fig. 5. Frequency encoded single bit memory circuit

Fig.6. Here the frequency of optical signal '

0 state and the frequency

The operation of the frequency encoded memory unit is now explained with the help of

If the input beam 'A' be of frequency ν1(0), then it will pass through ADM and behaves as the pump beam for polarization switch PSW1. As the probe beam X2 of PSW1 is of frequency ν2, therefore, by the joint action of pump and probe beam the PSW1 goes to switch off state i.e. output of PSW1 will give no signal (zero). Now the polarization switch PSW2 will get only probe beam signal X1 of frequency ν1 and according to the action of polarization switch

1 (corresponding wavelength

<sup>2</sup> ) as the state 1.

<sup>1</sup> ) is encoded as

<sup>2</sup> (corresponding wavelength

coupler (B.C.).

Different Optical Logic Processors Using Semiconductor Optical Amplifier 61

The basic building blocks of the memory unit consists of three polarization switches PSW1 and PSW2 [Garai S.K., 2010, 2011a], an isolator, two input sources X2 and X1 giving the probe beams having frequencies ν2 and ν1 respectively and one add/drop multiplexer, ADM as shown in Fig.5. The beam obtaining from output port-2 of PSW1 splits up into two parts by means of beam splitter B.S. One part of the beam is coupled as the input pump beam for polarization switch PSW2 and another part is serving as the output data (Y). Similarly, the output beam from port-2 of PSW2 is split up into two parts. One part is serving as the probe beam of PSW3 switch via an attenuator AT and another part is viewed as output at Y terminal via the attenuator. The low intensity input probe beam of PSW3 switch is controlled by the isolator. The function of the isolator is that it allows the part of the output beam of PSW2 to appear at Y end but prevents the output of PSW1 to appear at the input end of PSW3. 'A' is the input pump beam terminal of switch PSW1. The input pump beam is injected to PSW1 via add/drop multiplexer ADM. The ADM is tuned for reflection frequency ν2. The reflected beam of frequency ν2 is reflected back by ADM and drop down by circulator and injected as the pump beam (control beam) for PSW3. The beam obtained at the output port-2 of PSW3 is coupled with input pump beam 'A' by a beam

Fig. 4. Block diagram of different logic units
