3. a) Electric field distribution and spectrum response
The most commonly used method of calculating the propagation of light in a structure is the finite difference time domain (FDTD) method [24]. We employed of 1550 nm Gaussian waves as inputs of RSoft software tool to study the propagation of light in eight different cases for our proposed structure based on the truth table of Subtractor (Table 1).
Case 1: when there is no input light, we have no power in the structure, so the outputs are zero. It is equivalent to the first row of Table 1.
Case 2: when "A"="B"=0 and "Bin" =1, is equivalent to the second row of the truth table, the input light from Bin propagates in W4 and W6 waveguides. When the input light reaches to the ring resonator (R1), it cannot provide the power needed for resonance and hence propagates toward the output ports. The normalized power at "D" and "Bout" ports are 83% and 65% respectively and can be considered logically "1". The electric field distribution (EFD) and output spectrum of this case are shown in Figs. 3. (a) and (b) respectively. However, we can see an amount of back propagation light in the input ports as loss.
Case 3: when "A" = "Bin" = 0 and "B"=1, equivalent to the third row of the truth table, and is similar to case 2. The input light from "B" port cannot excite the ring resonator, so propagates toward the output ports. The normalized power at the output ports of "D" and "Bout" are 83% and 65% respectively and can be considered as "1" logic. The EFD and output spectrum of this case are shown in Figs. 4 (a) and (b) respectively.
Case 4: when "A"= 0 and "B" = "Bin" = "1", is equivalent to the 4th row of Table 1. Here, the optical signals from the two input ports propagate in the W3 and W4 waveguides and reach to the ring R1 resonator. Now, the optical intensity is sufficient enough to excite the R1 resonator. It couples the optical signal, both to the output ports and to the W5 and exhaust it from W1 and W2 waveguides. Simultaneously, since the R1 does not fully couple the light and a portion of light propagates to the output ports, the lights interfere destructively and cause no light to propagate to the "D" port. The role of defects, which are named R2, is seen in this case. They are responsible of creation a phase difference and hence constructive interference. Also they act as a filter. Consequently, the output normalized power in "D" and "Bout" output ports are 5% and 92% respectively which can considered as "0" and "1" logically. The EFD and the output spectra in this case are shown in Figs. 5 (a) and (b) respectively.
Case 5: "A" =1 and "B" = "Bin" = 0. This case is equivalent to the 5th row of the Subtractor truth table which the input light propagates through W1 and reaches to W5. Because of its insufficient intensity, cannot excite R1 ring resonator. So 73% of its power is directed to "D" output port and the rest is exhausted from W3 and W4. R2 Defect rods play their filtering role here, too. These rods do not allow the light to propagate in the "Bout" port. It is necessary to mention that the size and the location of these defect rods have been selected after many attempts in a try and error method. As a result, the normalized power in "D" and "Bout" ports are 73% and 5% which can be considered as logically "1" and "0" respectively. The EFD and the spectrum response of this case are shown in Figs. 6 (a) and (b) respectively and verify the simulation.
Case 6: when "A"=1, "B" =0, and "Bin"=1, is equivalent to the 6th row of the Subtractor truth table. In this case, because there are two inputs, the power of media near R1 ring resonator is sufficient enough to resonate. As a result, ring fully couples the light to W3 and it exits from the structure. The normalized power in the "D" and "Bout" are 6% and 2% respectively and can be considered logically "0". The EFD and the spectrum response of this case are shown in Figs. 7 (a) and (b) respectively.
Case 7: if "A"= "B" = "1" and "Bin"=0, is equivalent to the 7th row of the truth table and is similar to case 6. Again we have two inputs and the power is high enough to resonance in the resonator. The ring couples the input optical power to W3 and it exits from the system. As a result, there would be no sufficient power at "D" and "Bout" output ports. They are 6% and 2% respectively which can be considered logically "0". The EFD and spectrum response in this case are shown in the Figs. 8 (a) and (b) respectively.
Case 8: when "A"="B"="Bout"="1", we are in the last row of the truth table. In this case, the electric filed around the ring resonator is high enough. So it can resonate. However, the instructive interference of the coupled light with the third input port causes the light to propagate toward output ports. In this case the output power at the "D" and "Bout" are 65% and 84% respectively and can be considered logically as "1". The EFD and spectrum response in this case are shown in Figs. 9 (a) and (b) correspondingly.
3. b) Time response analysis
Nowadays technologies demand faster and more compact devices. Growing usage of internet at all over the world motivated the designer toward optical systems. As a result, all communications and calculations must be done optically and in a same frequency. The faster devices can improve the optical systems. Time response and device speed are among the criteria used for evaluation of the optical device behavior. The simulation results for seven cases of the proposed all-optical full-Subtractor are shown in Fig. 10
It can be seen from Fig. 10 that the full-Subtractor is very fast. The rise and fall time of Fig. 10 (a) are 2.8 and 0.17 ps respectively. This fast response allows doing more calculations in a specific time. The complete details of rising and falling times for all operation states are listed in Table 2.
The performance of the proposed full-Subtractor can be further investigated by calculating the contrast ratio (CR) which is the ratio of output powers of logic ‘1’ and logic ‘0’ as following [25]:
CR = 10 log (P1 / P0) (3)
where P1 and P0 in the above equation are the power values at the output port for logic ‘1’ and logic ‘0’, respectively. The average CR of the proposed half-Subtractor is greater than 10.35 dB. The details of the CR for all eight states are brought in Table 2.
Table 2. Details of the characteristics of the proposed all-optical Full-Subtractor
A
|
B
|
Bin
|
D%
|
Bout%
|
tr(Ps)
|
tf(Ps)
|
CR(db)
|
Worst Case
|
0
|
0
|
0
|
0
|
0
|
-
|
-
|
-
|
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|
0
|
0
|
1
|
65 ≡ 1
|
72≡ 1
|
2.88
|
0.17
|
-
|
0
|
1
|
0
|
65 ≡ 1
|
72≡1
|
2.88
|
0.17
|
-
|
0
|
1
|
1
|
5 ≡ 0
|
110 ≡ 1
|
2.8
|
0.1
|
13.42
|
1
|
0
|
0
|
156 ≡ 1
|
5 ≡ 0
|
0.93
|
0.08
|
31.93
|
1
|
0
|
1
|
0.8 ≡ 0
|
0.8 ≡ 0
|
0.48
|
0.27
|
-
|
1
|
1
|
0
|
0.8 ≡ 0
|
0.8≡ 0
|
0.47
|
0.27
|
-
|
1
|
1
|
1
|
190 ≡ 1
|
78 ≡ 1
|
2.66
|
0.17
|
-
|
So far, no Full-Subtractor construction or design has been reported, so a comparison has been made between our proposed design and the reported Half-Subtractor or Full-Adders. The results are shown in Table 4. It can be seen that the results of our work are better or comparable to the other reported works
Table 3. Comparison between our proposed Full-Subtractor and some previous presented works.
Device Type
|
Rise time (ps)
|
Fall Time (ps)
|
CR (dB)
|
Ref.
|
Half Sub.
|
0.1
|
-
|
6.28
|
[18]
|
Half Sub.
|
2
|
1
|
7.28
|
[15]
|
Half Sub.
|
1
|
0.6
|
-
|
[27]
|
Full Adder
|
0.6
|
0.36
|
4.77
|
[12]
|
Full Adder
|
3
|
-
|
9.94
|
[28]
|
Full Sub.
|
1.87
|
0.17
|
9.09
|
This work
|