The output power is calculated at the output port with respect to the input signal using the following equation.
(1)
where, T(f) represents the normalized transmission, p(f) represents the pointing vector and dS represents the surface normal.
The Perfect Matched Layer (PML) is incorporated to minimize to reflection which is an artificial boundary layer to support the simulation in open boundary condition. It strongly absorbs all the incident waves in all directions, without any reflection inside the PC lattice.
(2)
where Δt denotes the step time, C denotes the speed of light in free space, respectively.
The Gaussian optical signal is applied to the four input ports, namely A0, A1, A2, and A3. The 1mW of input power is applied at 1550nm for simulation. The proposed encoder structure is simulated using the 2D FDTD method and the performance parameters are examined. In the proposed structure, the nano coupling rods (N1, N2, N3, N4) are working as a digital switch between input and output waveguides which in turn enhancing the coupling between the input and output ports. In this simulation, the input power is considered Pi, the output power is Po, and normalized power is treated as Pn = Po/Pi. In this case, the normalized power level at the output port is resulted the logical level, such as, ‘ON’ or ‘OFF’ state. If Po is underneath 0.25mW, it is treated as logic '0' and the Po is directly above the level of 0.25mW that is assumed as logic '1'.
State 1: For a given logic input of 1000, A0=1 i.e. is ‘ON’ and A1, A2, A3 are ‘OFF’, the Gaussian input signal is not entered inside the waveguide. In this case, the input signal is entered into A0 input port and signal is blocked due to the arrangement waveguide A0. Hence, there is no power is directed to the output port B0 and B1 (00) as shown in Fig. 4(a). The output power Po is 0.0062 at B0 and 0.0001 at B1, hence, the normalized transmission power is 0%. The electromagnetic field distribution is displayed as inset in Fig. 4(a).
State 2: For the logic input of 0100, A1 input is ‘ON’, and A0, A2, A3 inputs are ‘OFF’ state. Then input signal is passed into the A1 input port and the signal is coupled through the N1 Nano coupling rods. Hence the output port B0 is ‘ON’ and B1 is ‘OFF’ state as shown in Fig. 4(b). The normalized power level at output port B0 is around 99.8% and 0.0052% power level obtained in another output port B1 and the field distribution is displayed as inset in Fig. 4(b).
State 3: The logic input 0010 is given, the input port A2=1 is ‘ON’ state and the other inputs are retained in ‘OFF’ condition. The input power applied to port A2 and then the input signal is coupled through the N4 coupling rods in the B1 output port and the encoder generates the output 01 as depicted in Fig. 4(c). The power level at B0 is 0.0052% and 99.8% of power level is obtained in output port B1. The inset in Fig. 4(c) shows the field distribution when the input is 0010.
State 4: For logic input 0001, A3 is ‘ON’ and A0, A1, A2 inputs are in ‘OFF’ condition. Then input signal is applied to port A3 and then the light propagates in both Y shaped waveguides and the input signal is coupled through the N2 and N3 coupling rods which generate high output power in both output ports B0 and B1 as depicted in Fig. 4(d) inset. In this case, the encoder generates the output 11 as shown in Fig. 4(d). As displayed in Fig. 4(d), the normalized power level at B0 is 0.5311Pi and B1 is 0.5311 Pi and the normalized transmission power is 53.11%.
The contrast ratio of the nano-optical encoder is defined by taking logarithmic function of the normalized output power of logic 1 to logic 0 as follows,
(3)
For different logic combination, the simulation of signal propagation is providing analytical graph with power versus time. And this process is used to find the functional parameters, such as, normalized output power, contrast ratio, response time and bit rate. The P1 and P0 indicate the normalized power of logic ‘1’ and logic ‘0’, respectively.
The response time and data rate are primarily calculated from the time-evolving curve as in Figs. 4(a) − 4(d). The response time is expressed as the time taken for the output signal to reach a quarter of the power range in the time response of the normalized curve. The data rate is calculated as the reciprocal of the response time. When the input is either 1000 or 0001, the output for ‘ON’ & ‘OFF’ state is remaining same, hence, the contrast ratio is estimated for the input 0100 and 0010. For different logic level outputs are achieved from the input level of 0100 and 0010 and the output power level of 0.9980 and 0.0052 are examined and the contrast ratio is 22.83 dB, respectively. The logic output 01 and 10, the response time and data rate are 0.228ps and 4.38Tbps, respectively. Another logic output 11, the response time and data rate are 0.235ps and 4.25Tbps, respectively. From Table 2, the minimum contrast ratio, maximum delay time and the minimum data rate of the proposed optical encoder is 22.83 dB, 0.235ps and 4.25Tbps, respectively, which are listed in Table 2.
Table 2. Logic input, Output power, Response time Bit rate and Contrast ratio of proposed 4x2 encoder
Input Ports
|
Output Ports
|
Response Time (ps)
|
Data rate (Tbps)
|
Contrast
Ratio (dB)
|
A0
|
A1
|
A2
|
A3
|
B0
|
B1
|
1
|
0
|
0
|
0
|
0.0062
|
0.0001
|
**
|
**
|
**
|
0
|
1
|
0
|
0
|
0.9980
|
0.0052
|
0.228
|
4.38
|
22.83
|
0
|
0
|
1
|
0
|
0.0052
|
0.9980
|
0.228
|
4.38
|
22.83
|
0
|
0
|
0
|
1
|
0.5311
|
0.5311
|
0.235
|
4.25
|
**
|
Table 3. Functional parameters comparison of proposed encoders with reported encoders
References
|
Lattice
|
Defects
|
Contrast Ratio (dB)
|
Response Time (ps)
|
Bit Rate (Tbps)
|
Footprint in µm2
|
[28]
|
Cubic/Square
|
Circular Ring resonator
|
05.86
|
3
|
3.3
|
612
|
[29]
|
Cubic/Square
|
Square Ring resonator
|
17.78
|
1
|
1
|
1927
|
[30]
|
Cubic/Square
|
Line and Point defect
|
07.30
|
0.2
|
4.1
|
880
|
[31]
|
Cubic/Square
|
Circular Ring resonator
|
07.11
|
**
|
**
|
128.5
|
[32]
|
Cubic/Square
|
Circular Ring resonator
|
12.80
|
***
|
***
|
1794
|
[33]
|
Hexagonal
|
Line and Point
defect
|
03.71
|
1.40
|
0.71
|
3795
|
[34]
|
Hexagonal
|
Circular Ring resonator
|
11.80
|
0.70
|
1.42
|
625.0
|
[35]
|
Cubic/Square
|
Square Ring resonator
|
09.54
|
***
|
***
|
240.5
|
[36]
|
Hexagonal
|
Circular Ring resonator
|
05.70
|
1.00
|
1.00
|
218.6
|
[37]
|
Cubic/Square
|
Square Ring resonator
|
09.24
|
1.80
|
0.84
|
795.6
|
Proposed work
|
Hexagonal
|
Line and Point
defect
|
22.83
|
0.235
|
4.34
|
178.1
|
The primary parameters of the encoder, such as, type of lattice, type of defects, contrast ratio, response time, bit rate and foot print of the proposed encoders is compared with the reported encoders which are listed in Table 3. The encoders are devised using cubic or hexagonal lattice. The ring resonator and point and line defect mechanism are predominantly incorporated. The contrast ratio, bit rate and size of the proposed encoder is 22.83dB, 4.34Tbps and 178.1 µm2 which is better than the reported one. In Ref. 30, the response time is 0.2ps, however, the contrast ratio is lower and the size is larger. Typically, in the reported encoders, if the contrast ratio is increased, the response time is decreased. On the other hand, if the response time is improved, it confines the contrast ratio. In addition, if the contrast ratio, bit rate and response time are superior, the size of the encoder is larger. However, the proposed encoder provides significant improvement in all the parameters with the compact size than the reported encoders. Hence, the proposed encoders are used for high speed computing photonic integrated circuits.