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Reconﬁgurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals Fariborz Parandin a, *, M. Reza Malmir b, Mosayeb Naseri c, Abdulhamid Zahedi d a

Department of Electrical Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran Young Researchers and Elite Club, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran c Department of Physics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran d Department of Electrical Engineering, Kermanshah University of Technology, Kermanshah, Iran b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 September 2017 Received in revised form 3 December 2017 Accepted 4 December 2017 Available online xxx

Photonic crystals can be considered as one of the most important basis for designing optical devices. In this research, using two-dimensional photonic crystals with triangular lattices, ultra-compact logic gates are designed and simulated. The intended structure has the capability to be used as three logical gates (NOT, XOR, and NOR). The designed structures not only have characteristics of small dimensions which make them suitable for integrated optical circuits, but also exhibit very low power transfer delay which makes it possible to design high speed gates. On comparison with the previous works, our simulations show that at a wavelength of 1:55 mm, the gates indicate a time delay of about 0.1 ps and the contrast ratio for the XOR gate is about 30 dB, i.e., the proposed structures are more applicable in designing low error optical logic gates. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Photonic crystals Optical logic gates Defect

1. 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) [5e7]. 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 twodimensional photonic crystals In some of them, the structure is used as multiple logical gates [10e16]. In some designs,

* Corresponding author. E-mail address: [email protected] (F. Parandin). https://doi.org/10.1016/j.spmi.2017.12.005 0749-6036/© 2017 Elsevier Ltd. All rights reserved.

Please cite this article in press as: F. Parandin et al., Reconﬁgurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals, Superlattices and Microstructures (2017), https://doi.org/10.1016/j.spmi.2017.12.005

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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 [17e20]. 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]:

CR ¼ 10 log

P1 P0

(1)

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. 2. 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 similar to a NOT logic gate. This characteristic can be used to design an XOR logic gate using a NOT gate. Fig. 3 shows the accuracy table and the circuit symbol of the NOR logic gate. As we can see in Fig. 3, the output of the NOR gate is “1” only when both the inputs are “0”.

Fig. 1. a) circuit symbol and b) accuracy table of the NOT logic gate.

Please cite this article in press as: F. Parandin et al., Reconﬁgurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals, Superlattices and Microstructures (2017), https://doi.org/10.1016/j.spmi.2017.12.005

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Fig. 2. a) circuit symbol and b) accuracy table of the XOR logic gate.

3. 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.

Fig. 3. a) circuit symbol and b) accuracy table of the NOR logic gate.

Please cite this article in press as: F. Parandin et al., Reconﬁgurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals, Superlattices and Microstructures (2017), https://doi.org/10.1016/j.spmi.2017.12.005

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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 used. The former is used for the control of electric modes and the latter is used for magnetic modes. In this paper the second structure is implemented. For obtaining the desired optical logic gates, ﬁrst a structure of triangular photonic crystals is formed. This structure consists of dielectric rods with a refractive index of 3, which are placed next to each other in an air background setting. The area of the structure consisting of 17*17 rods is about 104:8 mm2 . The lattice constant of the structure is a ¼ 0:64 mm and the radiuses of the rods are r ¼ 0:18a. The band structure calculations are performed using the Plane Wave Expansion (PWE) method within the RSoft software. Results show that a PBG is created at a wavelength of 1:26 mm to 1:92 mm. In this interval, no wavelength can be propagated in the structure and is reﬂected after hitting the crystal. Furthermore, the inputs and outputs of the gates should be speciﬁed in the structure and using defects, a path for transferring light from the inputs to the outputs should be created. For this purpose, a combination of line and point defects are used. Fig. 4 shows the placement of defect paths. As shown in Fig. 4, the defect paths at the three inputs are linear and all three paths intersect at one location. At that location, the three point defects are used such that the radiuses of the rods are ra ¼ rb ¼ rc ¼ 0:5r. Further, three coherent light sources are placed at the inputs; their wavelengths are considered to be 1:55 mm. For the light to be guided in the defect paths and not propagated in the other parts of the structure, the wavelengths of the sources are selected within the PBG interval. Also, the C input has a phase difference of 100 with the other two inputs. To create the phase difference between the input waves, it is assumed that the sources are coherent and the difference in path length from source to input port can leads to different phases of inputs. The coherent sources can be generated that, for example all the input waves may come from one main source and the path traversed by the input waves is not the same. In the function of the structure as XOR gate, the propagated light waves from the sources have been collided in the defect rods. The waveguide lengths and the radius of defect rods are so selected that light wave interference be destructive for equal inputs and the transmitted power to the output is very low. When the structure is used as a NOR gate, according to the light paths and defects, if at least one input is on, the interference of the input waves and the control wave leads to a destructive interference and the transmission power to the output will be low. 3.1. NOT and XOR optical logic gates In order to use the structure as an XOR gate, the source at port B is considered off and ports A and C are selected as inputs. When A ¼ C ¼ 0, since all sources are turned off, no optical power is transferred to the output and the output is at a logical “0” state. Fig. 5 depicts the distribution of the optical waves for different inputs. Results show that when the two input sources are off (A ¼ C ¼ 0) there is no optical wave distribution in the output, which will further be in a “0” logical state. If one input is “0” and the other is “1” (A ¼ 0, C ¼ 1 or A ¼ 1, C ¼ 0), the optical wave distribution in the output will be signiﬁcant and in this case, the output will be equal to “1” logic. When two input sources are on (A ¼ C ¼ 1), coherence of the sources and differences in the optical paths will cause destructive interferences to occur in the wave incidence area and the optical wave distribution in the output will be very low and the logic state will be “0”. Fig. 6 shows the normalized optical power at the output for different inputs of the XOR gate. The range of the optical power is normalized and is considered in relation to the power of a light source in the “on” position.

Fig. 4. Creating defect paths for transferring light from inputs to the output.

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Fig. 5. Distribution of optical waves in optical XOR gate for: a) A ¼ C ¼ 0, b) A ¼ 0, C ¼ 1, c) A ¼ 1, C ¼ 0 and d) A ¼ C ¼ 1.

When both the sources are active, i.e. A ¼ C ¼ 1, light waves intersect at the crossing point of the defects and considering the differences in the input paths and the phase difference of source C, the waves have different phases and the interference is destructive. In this case, the waves cancel each other out and a very small power is transferred to the output.

Fig. 6. Normalized optical power at the output for XOR gate.

Please cite this article in press as: F. Parandin et al., Reconﬁgurable all-optical NOT, XOR, and NOR logic gates based on two dimensional photonic crystals, Superlattices and Microstructures (2017), https://doi.org/10.1016/j.spmi.2017.12.005

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F. Parandin et al. / Superlattices and Microstructures xxx (2017) 1e8 Table 1 Normalized output optical power for XOR gate. A

C

Normalized output

Logic Value

0 0 1 1

0 1 0 1

0.00 0.62 0.70 0.0006

0 1 1 0

Fig. 6 shows that the time delay of the XOR gate is about 0.1 ps. Furthermore, the diagrams show that if the inputs are equal, the optical power at the output is very little and close to zero, which causes an increase in CR. Table 1 shows the normalized power at the output for different inputs to the XOR gate. As shown in Table 1, the worst output value in the logical “0” condition is associated with the case where A ¼ 1 and C ¼ 1, which is very small, approximately 0.0006. In this case, CR ¼ 30 dB, which is large compared to previous works. This XOR structure can be used as a NOT gate. For this purpose, port A is considered as a bias and port C is considered to be the input. If the source at the bias port is active, when C ¼ 0, the normalized output power is 0.7 (logical “1”) and when C ¼ 1, the output power is 0.0006 (logical “0”). In this case, for a NOT logic gate, a value of CR ¼ 30 dB is obtained. 3.2. NOR optical logic gate For using the proposed structure as a NOR gate, port C is considered as a bias and ports A and B are considered to be the inputs. Considering the fact that when both the inputs are “0” the output should be a “1”, a bias source is required to supply the necessary power when the inputs are “0”. Therefore, the bias source should be turned on when using the structure as a NOR gate. Results of simulation for different inputs are shown in Fig. 7. Fig. 7 shows that when the two input sources are off (A ¼ B ¼ 0), the light from bias source is transmitted to the output, which further will be in “1” logical state.

Fig. 7. Distribution of optical waves in optical NOR gate for: a) A ¼ B ¼ 0, b) A ¼ 0, B ¼ 1, c) A ¼ 1, B ¼ 0 and d) A ¼ B ¼ 1.

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Fig. 8. Normalized optical power at the output for NOR gate.

Table 2 Normalized output optical power for NOR gate. A

B

Normalized output

Logic Value

0 0 1 1

0 1 0 1

0.62 0.11 0.0006 0.13

1 0 0 0

Even if one input is “1” (A ¼ 0, B ¼ 1, A ¼ 1, B ¼ 0 or A ¼ B ¼ 1), the phase difference and the differences in the optical paths will cause destructive interferences in the incident waves and the optical wave distribution in the output will be very low and the output will be equal to “0” logic. Fig. 8 shows the normalized optical power at the output, for different inputs of the NOR gate. Fig. 8 shows that when A ¼ B ¼ 0, the output is at logical “1”, where the output power is supplied by the bias source. In other cases, the output power is very little (logical “0”). The defect path and the phase difference of the source at bias port C is such that if each or both of the A and B inputs is “1” logic, destructive interferences occur at the intersection of the waves and the power transferred to the output is very low (logical “0”). The delay time of an NOR gate is measured to be about 0.1 ps. Table 2 shows the value of the optical power at the output of the NOR gate and their logical equivalents. These values are further normalized. Table 2 shows that the normalized power at “1” logic state is equal to 0.62 in association with A ¼ B ¼ 0. In the other three cases, the output is logical “0”. For calculating CR, the worst case should be considered. The output power in the worst case is about 0.13, with CR ¼ 6.8 dB. 4. 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 1:55 mm, 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 considered. Acknowledgment The authors would like to thank the Kermanshah Branch, Islamic Azad University for the ﬁnancial support of this research project. References [1] J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton University Press, Princeton, 1995. [2] E. Yablonovitch, Photonic crystals: semiconductors of light, Sci. Am. (Dec. 2001) 46e55.

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