A Novel Design for an Ultracompact Optical Majority Gate based on Ring Resonator on Photonic Crystals Substrate

doi:10.21203/rs.3.rs-2231762/v1

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A Novel Design for an Ultracompact Optical Majority Gate based on Ring Resonator on Photonic Crystals Substrate

https://doi.org/10.21203/rs.3.rs-2231762/v1

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published 14 Feb, 2023

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This paper tries to design and simulate a majority gate with three inputs based on the resonance ring of 2D photonic crystals. In the design of this gate, a resonator gate and 4 waveguides in a square lattice have been used. This structure is simple and small with dielectric rods of silicon on an air substrate. Low and high logics are defined based on the optical sources being on or off. The large interval between 0 and 1 at the output demonstrates high accuracy of this optical gate. The operating wavelength of this optical majority gate is 1.55µm, which is in the photonic band-gap calculated for the gate structure. Calculations are carried out in the TM mode using the FDTD numerical method.

majority gate

resonance ring

photonic crystals

photonic band-gap

In order to increase the digital information exchange speed in electronic circuits, transistor dimension reduction is used. But the transistor dimension reduction trend has recently slowed down because semiconductors of nano-dimensions have been constructed and fundamental technological changes are required. Thus, the researchers look for a novel technology to increase the speed of electronic devices [1–9].

Photonic crystals are structures of high capacity in the design of various optical gates. The photonic band-gap in these structures is used to design various gates, circuits, fibers, and sensors. By creating resonance rings and waveguides in the crystal structures, the desired circuit is designed and simulated. The operating wavelength of each circuit is in the range of the photonic band gap, which is determined considering characteristics of the designed structure, including network constant, radius of the rods or holes, and the refraction index [10–19].

Photonic crystals are structures of dielectric rods in air or holes in a dielectric material in which the refraction index changes periodically. The refraction index might change in one, two, or three directions regarding the structure design, developing 1D, 2D or 3D photonic crystals [20–23]. 2D photonic crystals are widely used in the design of all-optical logic gates. Various logic gates have been developed based on this structure so far. Also, combinational and sequential logic circuits have been designed using photonic crystals, which are faster than electronic gates and circuits [24–42].

The majority gate is one of the most applied gates in telecommunication and electronic circuits. More than half of the inputs being 1, the output is 1. The number of inputs in these gates is usually an odd number with one output. If the number of inputs is even, if the number of 0s and 1s is the same, the output would be unknown. Thus, this gate is usually designed such that the number of inputs is odd. In this paper, an optical majority gate based on photonic crystals with three inputs using one resonator ring is designed and simulated. In the following, the operation of the majority gate is described. Then, a photonic crystal with square lattice is defined and the band structure calculations are carried out to determine the frequency performance. Then, the waveguide paths for light propagation are created and time simulation for light propagation is carried out.

The majority gate is a circuit with multiple inputs (an odd number) and one output. If more than half of the inputs are 1, the output would be 1; otherwise, it would be zero. Usually, in order to prevent the number of 0s and 1s being equal, an odd number of inputs is selected. In this paper, a majority gate with three inputs and one output is designed. The truth table of this optical gate is given in Table 1. Considering the truth table, if more than one input is 1, the output would be 1. If two or three inputs are 1, the output would be 1. If all inputs are 0 or only one of the inputs is 1, the output would be 0.

Table 1: The truth table of 3×1 majority gate.
Inputs			output
A	B	C	output
0	0	0	0
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	1

Block diagram of a majority gate with 3 inputs in shown in Fig. 1.

Considering the truth table of the majority gate, the output function can be described as follows:

1) M = A. B + A. C + B. C + A. B. C

The optical majority gate is designed based photonic crystals in a 13×13 square structure with silicon rods with a refraction index of 3.4 in an air background (refraction index of 1). As shown in Fig. 2, this gate has 4 waveguides and one resonance ring, including three inputs and one output. The radius of the rods is 0.18a and the lattice constant is a = 0.64. Also, the radius of the 4 rods have decreased at the point where the waveguides are connected to the resonance ring. Two rods are reduced to 0.6r, one is reduced to 0.7r, and the output waveguide rod is reduced to 0.56r. The input optical source (B) has a phase difference of -20. The simulations demonstrated that such a phase difference improves the simulation results.

The operating wavelength of this gate is 1.55um. Since the photonic crystals operate based on the photonic band-gap, this wavelength is in the range of the photonic band-gap of this gate. Figure 3 shows the photonic band-gap diagram of the majority gate. As can be seen, there are two forbidden wavelength intervals, where 1.55 is in the range of 1.39 to 1.88µm.

According to the truth table, 8 states can be defined for this gate, which are studied here.

If all three inputs are 0, since no source is on, the output would be 0. If any of the inputs becomes 1, while the other two inputs are 0, the output remains 0. Figures 4 to 6 show these three states. In these figures, part “a” shows the optical power distribution and part “b” shows the optical power transmitted to the output. As can be seen in Fig. 4, if A = 1, B = 0, C = 0, the output is 0.16, which is close to 0 and can be considered as the logical value of 0.

When A = 0, B = 1, C = 0, the output is about 0.18. Figure 5 shows the power distribution and output power in this state. This value is considered as 0 logic.

Figure 6 also shows power distribution and output power for A = 0, B = 0, and C = 1. In this state, the output power is 0.16, which is equal to logic 0.

According to the truth table, if more than 1 input is 1, the output would be 1, and 4 states can be defined in this case. If A = B = 1, C = 0, the output is 0.65, as shown in Fig. 7. In this state, the output is 1.

If A = C = 1, B = 0, the output is 0.7, which can be considered as the logic 1. Figure 8(a) shows power distribution and Fig. 8(b) shows the output power.

If A = 0, B = C = 1, the output is 0.7, which is equal to the logic 1. Figure 9 shows simulation results and the output values.

It is obvious that if all inputs become 1 simultaneously, the output would be 1. Simulation results for A = B = C = 1 are given in Fig. 10. As can be seen in Fig. 10(b), the output power in this state is about 1.8, which can be considered as logic 1.

According to the simulation results, the above structure behaves according to the truth table; in all states that the output in the truth table is 0, the output power is very low, and in all states that the output in the truth table is 1, the output power is high. Therefore, this structure can be used as a majority gate with three inputs. The results show that the power in logics 0 and 1 is low and high, respectively. Therefore, this optical gate has a high accuracy in detecting logical values. Among other advantages of this structure, its small size can be mentioned, which makes it suitable for optical integrated circuits.

The majority gate detects if more than half of the inputs are 1. In this paper, an optical majority gate based on 2D photonic crystals was designed and simulated. 4 waveguides and one resonance ring in a 13×13 square structure has been used in this structure. The large distance between the calculated values for logics 0 and 1 shows high accuracy of this optical gate. This gate is suitable for integrated circuits due to its small dimension, high speed and accuracy.

Conflict of Interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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You are reading this latest preprint version

A Novel Design for an Ultracompact Optical Majority Gate based on Ring Resonator on Photonic Crystals Substrate

Status:

Journal Publication

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Abstract

Figures

1. Introduction

2. The Majority Gate’s Performance

3. Design Of An Optical Majority Gate

4. Conclusion

Declarations

References

Status:

Journal Publication

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