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Reconﬁgurable design of logic gates based on a two-dimensional photonic crystals waveguide structure Yu-Chi Jiang a,b, Shao-Bin Liu a,n, Hai-Feng Zhang a, Xiang-Kun Kong a a Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b School of Physics and Electronic Engineering, Changshu Institute of Technology, Changshu 215500, China

art ic l e i nf o

a b s t r a c t

Article history: Received 18 March 2014 Received in revised form 8 July 2014 Accepted 11 July 2014 Available online 23 July 2014

In this paper, a particular two-dimensional photonic crystal reconﬁgurable structure is designed to realize different logic functions based on the theory of light beam interference effect, and the distribution of the electric ﬁeld is computed by the ﬁnite-difference time-domain (FDTD) method. The results show that ﬁve types of logic gates such as NOR, OR, XNOR, Aþ B, NOT can be realized by choosing different input and reference port in a two-dimensional PCs waveguide conﬁguration. It is noticed that the logic state of “1” and “0” at output port are deﬁned as the transmission is larger than 0.5 and less than 0.1, respectively. Crown Copyright & 2014 Published by Elsevier B.V. All rights reserved.

Keywords: Photonic crystals Waveguide Reconﬁgurable logic gate Finite-difference time-domain method

1. Introduction The Photonic crystals(PCs) were ﬁrst proposed dependently by Yablonovitch [1] and John [2] almost at the same time in 1987 which are composed of mediums with different refractive index in spatial periodic arrangement. The photonic band gap (PBG) is always observed in the PCs which can control the propagation of the electromagnetic wave, and PBG has very interesting properties of light conﬁnement and localization [3,4]. Many researchers focus on modifying large PBG by covering the rods with other materials [5], changing the rod with different shapes [6] or hybrid scatterers [7]. If one point defect is introduced in the twodimensional PCs, some frequencies in the PBG are no longer prohibited and the defect mode can be formed in the PCs [8,9]. If one line or several lines of rods are removed in two-dimensional PCs, line defect channel also called waveguide is formed. Waveguide has been extensively studied for applications in wavelength division multiplexer [10], ultrahigh-contrast alloptical diode [11], ultra-fast all-optical switching [12] and logic gate [13]. In recent years, the great efforts have been made to the design and application of logic gates. Fu et al. design different all-optical logic gates [14] with different structure design in two-dimensional (2D) PCs and obtain high contrast ratio between the logic state of

n

Corresponding author. E-mail address: [email protected] (S.-B. Liu).

http://dx.doi.org/10.1016/j.optcom.2014.07.038 0030-4018/Crown Copyright & 2014 Published by Elsevier B.V. All rights reserved.

“1“and “0”. An all-optical AND gate based on a 2D PCs can operate at various wavelength, which has more ﬂexibility in the applications of logic gate in the optical processing [15]. A new topology for “AND” logic gate with ultra-short transition and delay time is proposed while Kerr nonlinear medium is introduced into 2D triangular PCs [16]. NOR logic gate is realized based on nonlinear PCs micro ring resonators to obtain the higher light contrast ratio between logic state “1” and “0” [17]. However, in these reports, one logic gate is realized with one conﬁguration, which restricts the design and integration of the optical device. Although AND & XOR logic gates are presented based on nonlinear PCs ring resonator [18] and two output ports are used for signal propagating simultaneously, the scheme only can realize two logic gates functions. In this paper, ﬁve types of logic gates are realized based on the theory of light beam interference effect with a same topology by choosing different reference light beam port and input port, meanwhile, the distribution of the electric ﬁeld is simulated by the FDTD method. The results show that this reconﬁgurable design of logic gates has the advantages of compactness and potential for photonic device integration and design.

2. Physical model The x–y plane diagram of our model is presented in Fig. 1(a), and the inserted silicon rod (marked with white circle in Fig. 1(a)) with axis along z is surrounded by air background (marked with

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Fig. 1. (a) the schematic structure of the 2D photonic crystals waveguide (b) the simpliﬁed computing model (c) Band diagram of triangular lattice of inﬁnite silicon rods embedded in air substrate.

black part) in the 2D PCs. The structure is composed of triangular lattice arrays of silicon which can provide a considerably large band gap and be used in many studies as all-optical logic gates [13–15]. The dielectric constant of the dielectric rods is set to 11.56. The radius of the cylindrical rod is 247.5 nm and the lattice constant is 1000 nm. The ports A, B, C could be chosen as the input port or the reference port into which the reference light beam is injected, and the port D is the output port. A continuous wave (CW) light source at a wavelength of 2040 nm further investigated in the part 3.1 is used as the input source in the following calculations. Here, we propose that the input wave excited at any input port has the electrical ﬁeld amplitude of 100 V/m and original phase of 0. The signal light injected into the input port or reference port is considered as TM wave where the electrical ﬁeld is kept parallel of the z-axis. The distribution of the electric ﬁeld intensity is simulated and the transmission is computed by the FDTD method. Fig. 1(b) refers to the simpliﬁed computing model. The computing space is composed of 28 28

lattices in the x axis and y axis and each lattice includes 20 Yee cells. Port D is assumed as the output port. According to the courant stability condition of FDTD method [19,20], time interval (Δt) is 2.2458 10 15 S and spatial interval along x axis (Δx) and y axis (Δy) is 50 nm. The boundary absorption condition is considered as the perfectly matched layer (PML) which is 20 layers. The normalized frequency of PBG marked by red zone is 0.475(a/λ) 0.58(a/λ) according to the band diagram shown in Fig. 1(c) which is obtained by the plane wave expansion (PWE) method [21].

3. Simulation and results According to the wave optics theory [14], if the phase difference between two light beams is 2kπ (k ¼0,1,2…), the constructive interference will occur, and the output light will have high power (corresponding to logic state of “1”). On the contrary, if the phase

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difference is (2kþ 1)π (k ¼0,1,2…), the destructive interference will occur, and the output light power will approximately zero (corresponding to the logic state of “0”). The 2D PCs waveguide structure designed in this paper is based on this wave optics theory and different logic gates could be realized by controlling the phase difference between two input light beam through choosing different input ports.

either port A or port C, no signal light is found at the output port. The distribution of the electric ﬁeld simulated in the above three conditions is shown in Fig. 2(a)–(c). The truth table for the logic gate is shown in Table 1. It can be concluded that only when the signal light at the port A is different from that at the port B, and the signal light intensity is large at the output port. Therefore, the XOR logic gate can be realized by this scheme.

3.1. Realization of XOR logic gate

3.2. Realization of OR logic gate

We consider port C as an idle port, the port A and B are regarded as input ports. Here, the light path length difference between AD and BD is about one lattice constant which produces the phase difference between the two input light beams of π . Selection of the input light wavelength as 2040 nm which is about the twice of the light path length difference between AD and BC can result in the destructive interference and the corresponding normalized frequency of 0.49 also falls into the photonic band gaps, which makes the input wave propagation in the waveguide with little light consumption. If the input waves are excited at both A and B port, the transmission is 0.07. If the light beam is input into the port A, and no signal light is injected into port B, the transmission is 0.55. In the similar case, if the light beam is input into the port B, and no signal light is injected into port A, the transmission is 0.6. It is obvious that if no signal is injected in

If the port B and C are input ports with the port A as an idle port, the distribution of the electrical ﬁeld is shown in Fig. 3(a)–(c). While the signal is injected into both A and B port, the transmission is 0.9 due to the constructive interference. If the light beam is only injected into the port B, the transmission is about 0.6. In the similar case, if the signal is only injected into the port C, the transmission is about 0.52. The truth table for the logic gate is shown in Table 2. It is obvious that once the light signal is excited into any input port or two ports, the high output transmission can be obtained. Thus, the logic function of OR logic gate can be realized. 3.3. Realization of XNOR logic gate We consider the port A as the reference port into which the light beam is injected into, while the port B and C are input

Fig. 2. (a) Field distribution as EA ¼ EB ¼ E (b) ﬁeld distribution as EA ¼E, EB ¼0 (c) ﬁeld distribution as EA ¼0, EB ¼ E.

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Table 1 Truth table for XOR logic gate. Input A

Input B

Logic output

Output D (transmission)

1 1 0 0

1 0 1 0

0 1 1 0

0.07 0.55 0.6 0

Fig. 3. (a) Field distribution as EB ¼EC ¼E (b) ﬁeld distribution as EB ¼E, EC ¼ 0 (c) ﬁeld distribution as EB ¼ 0, EC ¼E.

Table 2 Truth table for OR logic gate. Input B

Input C

Logic output

Output D (transmission)

1 1 0 0

1 0 1 0

1 1 1 0

0.9 0.6 0.52 0

ports with the same electrical ﬁeld amplitude and original phase as that of the reference port. If the signal is injected into both two input ports, the transmission is 0.55. If the signal light is injected only into the port B or into the port C, the transmission is 0.07 and 0.09, respectively. However, the reference light

beam could also propagate without any signal light injected into the input ports and the transmission is 0.52. The distribution of the electric ﬁeld simulated in the above four conditions is shown in Fig. 4(a)–(d). It is shown that only if the electrical ﬁeld of the input light at the port B is same with that of the port

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propagation. The distribution of the electric ﬁeld simulated in the above four conditions is shown in Fig. 5(a)–(d). It is obvious that this waveguide structure realizes the logic function of A þ B according to the truth table shown in Table 4.

C, could the high transmission be obtained. The scheme implements the logic function of XNOR according to the truth table shown in Table 3. 3.4. Realization of A þ B logic gate

3.5. Realization of NOT logic gate We consider port C as the reference port, meanwhile, port A and B are regarded as input ports. We assume that if the signal light beams are injected into both input ports, the transmission of 0.55 is obtained. If the signal is injected only into the port A, the transmission is 0.09, while only into the port B, the transmission is 0.9. Even if no signal is injected into any input port, the transmission of 0.52 could also be obtained for reference light wave

If port A is considered as the input port and port B as the reference port, the transmission of 0.07 and 0.6 could be obtained when the input port A with or without signal light, respectively. The distribution of the electric ﬁeld is shown in Fig. 6(a)–(b). Therefore, the NOT logic gate can be realized according to the truth table in Table 5.

Fig. 4. (a) Field distribution as EB ¼ EC ¼E (b) ﬁeld distribution as EB ¼ E, EC ¼0 (c) ﬁeld distribution as EB ¼0, EC ¼ E (d) ﬁeld distribution as EB ¼ 0, EC ¼ 0.

Table 3 Truth table for XNOR logic gate. Input B

Input C

Logic output

Output D (transmission)

1 1 0 0

1 0 1 0

1 0 0 1

0.55 0.07 0.09 0.52

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Fig. 5. (a) Field distribution as EA ¼ EB ¼E (b) ﬁeld distribution as EA ¼E, EB ¼ 0 (c) ﬁeld distribution as EA ¼ 0, EB ¼E (d) ﬁeld distribution as EA ¼ 0, EB ¼0.

Table 4 Truth table for A þ B logic gate. Input A

Input B

Logic output

Output D (transmission)

1 1 0 0

1 0 1 0

1 0 1 1

0.55 0.09 0.9 0.52

4. Conclusion In summary, based on the reconﬁgurable design of the 2D photonic crystals waveguide structure, ﬁve types of logic gates such as NOR, OR, XNOR, A þ B, NOT are realized by choosing the different input port and reference port, and the higher contrast between logic state of “1” and “0” can be obtained by the FDTD method. The results show that this compact 2D PCs waveguide topology takes good advantages of the optical device design because of its reconﬁgurable character. Therefore, the design is valuable in optical device integration which is helpful and signiﬁcant to the application of 2D PCs waveguide in optical communications.

However, all above investigations are with the consideration of no phase difference between two input light beams. If taking the phase difference into account in the all optical logic gate design, the electrical ﬁeld distribution of the two light beams interference is altered. For example in the part 3.1, if the two input light beams has the phase difference of π and the optical path difference is also considered, the two output light beams will have the same phase and high transmission of 0.9 can be obtained. The electrical ﬁeld distribution when the two input light beams have the phase difference of π is shown in Fig. 7 compared with that of no phase difference shown in Fig. 2(a), which will be studied in detail in our following work.

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Fig. 6. (a) Field distribution as EA ¼ E (b) ﬁeld distribution as EA ¼ 0.

Table 5 Truth table for NOT logic gate. Input A

Logic output

Output D (transmission)

1 0

0 1

0.07 0.6

Foundation (Grant no. BK2011727), the Foundation of Aeronautical Science (no. 20121852030) and Open Research Program in Jiangsu Key Laboratory of Meteorological Observation and Information Processing (Grant no. KDXS1207).

References

Fig. 7. Field distribution as EA ¼ EB ¼ E, while the phase difference of the two input light beams equals to π

Acknowledgements This work was supported by the supports from the National Natural Science Foundation of China (Grant no. 61307052), Chinese Specialized Research Fund for the Doctoral Program of Higher Education (grant no. 20123218110017), the Jiangsu Province Science

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