Reconfigurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals
Introduction
Photonic crystals are alternating structures whose electric or electromagnetic permittivity coefficient changes, alternatively. If this coefficient changes in two dimensions (i.e. x and z directions) and stays constant in the third dimension (y direction), a two-dimensional photonic crystal is formed [1], [2].
The most important characteristic of alternation in the structure is the formation of frequency ranges in which waves cannot be propagated. This range is called the Photonic Band Gap (PBG) [3], [4]. Using the PBG characteristics, light can be guided in specific paths, called defects. Defect paths can be formed by changing the alternating structure. For example, some rods can be eliminated (line defect) or the radius be changed (point defect) [5], [6], [7].
For realizing logic gates, first the inputs and outputs are specified. Then, some defects are formed in the paths of light from the input to the output. Logical “0” and “1” are defined based on the optical power; if the optical power is low at a point, a logical “0” and if the optical power is close to the power of the light source, a logical “1” is considered [8], [9].
Many gates, such as NOT, OR, AND, NOR, NAND, XOR, and XNOR have been designed and simulated based on two-dimensional photonic crystals In some of them, the structure is used as multiple logical gates [10], [11], [12], [13], [14], [15], [16]. In some designs, ring resonators are used that in addition to increasing the size of the circuit, increase the time delay, due to light coupling within the resonator [17], [18], [19], [20].
One of the parameters that should be considered in design is the interval between the values of logical “0” and “1”. Increasing this interval causes a decrease in the identification error at the output. A criterion for comparing this interval is using the parameter Contrast Ratio (CR), which is defined as follows [21]:
In Equation (1), the value of P0 is the optical power for logical “0” and P1 is the optical power for logical “1”. Considering the fact that there may be several logical “0” and “1” cases, the worst condition is used for the calculation of CR. In other words, the maximum power that signifies a logical “0” and the minimum power that signifies a logical “1” are considered.
In this article, a structure for the use of the three logical gates (NOT, XOR, and NOR) is proposed. This structure consists of three inputs and one output (specific inputs are used for every logic gate). Characteristics of light interference at the junction of the defects form the desired outputs.
In most of the previous works, the dimensions of the structure are large and the output in logic “0” is relatively high which reduces CR. Also, in some of them, the ring resonators are used that leads to increasing the dimensions of the circuit and delay time.
In this design, an attempt has been made to use a small structure. Furthermore, since ring resonators have not been used and only simple defect paths are considered, the delay time will be much lower. One of the other parameters considered in this design is CR. For the XOR gate, a high value of CR had been obtained. This increase in CR will reduce the identification error for sensing high and low logical states.
In comparison with previous works, it can be worthy mentioning that the advantages of the proposed structure are low dimensions, simple structure, low optical output power in logic “0” state and consequently higher CR.
In Section 2, the NOT, XOR, and NOR logical gates are briefly described. In Section 3, logical gates are designed using photonic crystals. First the NOT and the XOR gates are designed and simulated, then the NOR gate is simulated and the results are discussed. Finally, in Section 4, conclusions are presented.
Section snippets
NOT, XOR, and NOR logic gates
The NOT logic gate has one input and one output which is the complement of the input. The accuracy table and the circuit symbol of the NOT logic gate is shown in Fig. 1.
The XOR logic gate has two inputs and one output. The output is a logical “1” when the inputs are not equal. The accuracy table and the circuit symbol of the XOR logic gate is shown in Fig. 2.
Considering the accuracy table of the XOR logic gate, if the port A is a logical “1” and port B is considered to be the input, it acts
Realizing optical logic gates using photonic crystals
In this research, a photonic crystal structure is used for implementing the three logic gates described. In other words, using the one structure and just by selecting the appropriate inputs (or with phase differences) the desired logic gate is created. This makes it possible to use one manufacturing process for all the three gates.
Photonic crystals can be used in two structures. In the first scheme, the holes in the dielectric substrate and in the second one, dielectric rods in the air are
Conclusion
In this study, the NOT, XOR, and NOR logic gates were designed and simulated using two dimensional photonic crystals. The structure used for all the three gates is the same and according to the input selection, the desired gate is created. The optical sources used are at a frequency of , which is in the range of the PBG of the structure and light can be guided in the defect paths. In designing logic gates, low delay time, small dimensions of the structure, and high contrast ratio are
Acknowledgment
The authors would like to thank the Kermanshah Branch, Islamic Azad University for the financial support of this research project.
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