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All optical NOR and NAND gates using four circular cavities created in 2D nonlinear photonic crystal
Optics and Laser Technology xxx (xxxx) xxxx
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All optical NOR and NAND gates using four circular cavities created in 2D nonlinear photonic crystal Alok Kumar, Sarang Medhekar
⁎
Department of Physics, Central University of Jharkhand, Ranchi 835205, Jharkhand, India
HIGHLIGHTS
photonic crystal NOR and NAND gates are presented. • Novel operating power, good contrast ratio and cascadeble. • Low • Unique in terms of bypass waveguides of the structures. ARTICLE INFO
ABSTRACT
Keywords: Photonic crystal All optical logic gate Circular cavities Kerr effect
The paper presents novel 2D photonic crystal (PhC) structures comprising of four circular cavities (CCs) that mimic NOR and NAND gates. 2D Finite difference time domain (2DFDTD) method is used for simulation and analysis of optical behavior of the proposed structures considering perfectly matched layers (PML) around the simulation region. Photonic band gap (PBG) and projected band diagram are obtained using plane wave expansion (PWE) method. It is shown that both the structures function with optical inputs of same wavelength and intensity. The proposed NOR and NAND gates are having low operating powers and good contrast ratio. Being universal gates, NOR and NAND allows for Boolean completeness. Implementation of bypass waveguides is a unique feature of the structures proposed in this paper. When the output is LOW, most of the optical power channelizes out of the structure through bypass waveguides, which otherwise, would go into the input ports affecting the input devices or would remain trapped inside the structure resulting in heating. This issue is not touched in the previous literature and in our opinion, being addressed for the first time.
1. Introduction
in optical communication and computing system [15]. Various proposals for optical logic gates using linear and nonlinear PhCs are existing in the literature [16,17]. In linear PhCs, all optical logic is obtained using interference effect and thus, require small power [18]. However, desired interference effect requires precise control on phases of the optical inputs, which, in a complex circuitry is challenging and a major limitation in terms of practicability of such devices. Optical logic gates based on nonlinear PhCs, work on optical Kerr or Kerr like effects [19–23]. Such devices require higher operating powers for switching but the control on phase is not an issue and hence, are considered as potential candidates for future optical computing and communication systems. The quest is of their miniaturization and lowering of operating powers. Previously, different structures for obtaining optical logic gate based on Kerr effect have been reported. Man Mohan et al. [24] reported all optical NOT and AND gates using counter propagation beam in nonlinear Mach-Zehnder interferometer made of PhC waveguide which require operating power
Theoretical modeling and fabrication of all optical devices based on photonic crystal (PhC) is of recent interest due to their (PhC’s) unique properties [1]. PhC based optical devices have several advantages over conventional waveguide devices such as compactness and power consumption [2]. PhCs are periodic structures with a period of the order of optical wavelength [3,4]. Photonic bandgap (PBG) originates in PhCs due to periodic distribution of dielectric permittivity. It is the range of frequencies in which the electromagnetic waves propagation is forbidden regardless the wave vector and polarization state [5]. With introducing line and point defect, photonic waveguide and cavity are created in a PhC [6]. Numerous optical devices based on PhC are existing in the literature, such as the optical filter [7], de-multiplexer [8], logic gate [9,10], junction [11], decoder [12], S-R latch [13], and converter [14] etc. Among various optical devices, optical logic gates play important role
⁎
Corresponding author. E-mail addresses: [email protected], [email protected] (S. Medhekar).
https://doi.org/10.1016/j.optlastec.2019.105910 Received 5 May 2019; Received in revised form 26 August 2019; Accepted 16 October 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Alok Kumar and Sarang Medhekar, Optics and Laser Technology, https://doi.org/10.1016/j.optlastec.2019.105910
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Fig. 1. A schematic diagram of the proposed optical NOR gate with parameters as mentioned in the text.
intensity for switching equal to 12.99 × 1014 W/m2 . All optical NOR and NAND gates based on nonlinear photonic crystal ring resonator (PhCRR) were proposed by Hamed Alipour–Banaei et al. [25] which have operating power intensity of 2 kW/ µm2 . Farhad Mehdizadeh et al. reported optical NOR gate [26] that works on operating power intensity of 1 kW/ µ m2 . An ultra-compact all optical OR/NOR gate based on PhCRR was proposed by Aref Rahmani et al. [27] with operating power intensity of 0.25 kW/µ m2 . In the present paper, novel 2D photonic structures comprising of four circular cavities (CCs) are designed that mimic NOR and NAND gates. The functionality of the proposed structure is analysed using two dimensional Finite Difference Time Domain (2DFDTD) [28,29] method. Further, Perfectly Matched Layer (PML) boundary conditions are used to define how the fields behave at the boundaries of the selected domain. PML boundary consists of grid points to the edge of the domain and, for the situations as considered in this paper, is designed to act as highly lossy material that absorbs all incident energy without producing unwanted reflections (a cause of errors in the simulation results). The width of domain is ± 15.4 μm along x- axis and ± 7.4 μm along zaxis. Photonic band gap (PBG) and projected band diagram are obtained using plane wave expansion (PWE) method [30]. It is shown that both the structures function with optical inputs of same wavelength and power intensity (identical operating powers) which is one of the important features required for compatibility and cascadebility. The structures are compact having low operating power and good contrast ratio.
by the coupler waveguide cw1 which is formed by removing thirty dialectic rods along x-axis and inserting ten dielectric rods array (DRA) of radius 100 nm . In exactly same manner CC3 and CC4 are connected to each other by the coupler waveguide cw2. The bias waveguide BS is formed by removing 51 dielectric rods along x-axis and has C and Y as bias and output ports respectively. As shown, two vertical waveguides (made by removing six dielectric rods along z-axis) are connected to CC1 and CC4 and having A and B as the two input ports of the proposed optical NOR gate. Two bypass waveguides BP1 and BP2 are connected to CC1 and CC4 as shown. Fig. 2(a) and (b) show the photonic band diagram and projected band diagram respectively of the structure of optical NOR gate which is obtained by using plane wave expansion (PWE) method. It is clear from the Fig. 2(a) that two PBG exist in the frequency rage a a 0.2817 < < 0.4136 and 0.7154 < < 0.7400 for the TE mode which in terms of wavelength range are 1470 nm < < 2158 nm and 821.5 nm < < 849.8 nm respectively. The guided mode is shown in the projected band diagram (Fig. 2b) that lies in the frequency range of a 0.28 < < 0.41. In principle, the defect waveguides can guide all wavelengths in both the PGBs. However, optical wavelength = 1542 nm is chosen for further investigations as it falls within the wavelength range suitable for optical communication. 2.2. The operation Two-dimensional finite difference time domain (2DFDTD) method is used to simulate/demonstrate NOR function of the proposed structure. The mechanism of switching is straightforward. When total optical power (injected from one or more input ports) is low, the parameters of the structure are so chosen that it does not couple to the bypass waveguides (through connecting waveguides and CCs) and most of the injected optical input appears at the output port Y. However, when the total optical power (injected from one or more input ports) is high, the refractive index of the rods of the structure is changed due to Kerr effect so that most of the injected optical input couples to the bypass waveguides and channelizes out of the structure leaving output port Y with zero or low output.
2. Optical NOR gate 2.1. The design Fig. 1 shows a schematic diagram of the proposed optical NOR gate. A 51 × 25 2D square lattice PhC platform is considered for designing it. The PhC is composed of Silicon dielectric rods of refractive index equal m2
to 3.46 and nonlinear Kerr coefficient equal to 1.5 × 10 17 W embedded in air. Radius of the rods is 0.2 × a , where a(=608 nm ) is the lattice constant. Four circular cavities CC1, CC2, CC3 and CC4 are formed by removing nine dielectric rods and inserting a central rod Rc (of radius 200 nm ) as shown. CC1 and CC2 are optically connected to each other
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Fig. 3. (a) Device characteristics is obtained by gradually increasing power intensity at C in the range zero to1080 W/ µm2 , and recording normalized output at the port Y using power monitor. (b) Normalized output power at the port Y is recorded by keeping CW bias of 360 W/ µ m2 at C and gradually increasing input power intensity at the port A in the range 0 to 800 W/ µm2 . Fig. 2. (a) Photonic band diagram of the structure of optical NOR gate obtained by using plane wave expansion (PWE) method. Two PBG exist in the frequency a a rage 0.2817 < < 0.4136 and 0.7154 < < 0.7400 for the TE mode which in
It should function with same inputs at all input ports (identical operating powers) and (iii) should have good contrast ratio. Keeping above mentioned in mind, we explore for that power intensity of continuous wave (CW) optical inputs (of = 1542 nm ) which when injected at all input ports of the proposed structure, NOR operation is obtained. For this purpose, in the first step, we plot device characteristics by gradually increasing power intensity at C in the range zero to1080 W/ µm2 , and recording normalized output at the port Y using power monitor. The result is as shown in Fig. 3(a). It may be noted in the figure that output remains high for lower levels of input and drops sharply at the higher sides. It is obvious from the characteristics that the structure offers high transmission (i.e. small losses) in a vide range of input power intensity. It is worth to mention here that after repeated explorations, we intuitively focused at the intensity level of 360 W/ µm2 for further investigations. Choice of 360 W/ µm2 results in 78%
1470nm < < 2158 nm terms of wavelength range are and 821.5nm < < 849.8 nm respectively. (b) Projected band diagram guided a mode exists in frequency range of 0.28 < < 0.41 as shown.
We stress here that the implementation of bypass waveguides is a unique feature of the structures proposed in this paper. One can note that when output at Y is LOW, most of the optical power (which is not going to Y) is channelized out of the structure through bypass waveguides BP1 and BP2, which otherwise, would go into the input ports affecting the input devices or would remain trapped inside the structure resulting in heating. This issue is not touched in the previous literature and in our opinion, being addressed here for the first time. Before going further, it is worth to mention that we look for three desired features in our proposed gates; (i) It should have small losses (ii)
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Fig. 4. (a) Case of ʻ00’ state is shown in which both inputs A and B are OFF (zero W/ µ m2 ). Y is considered as ON as 78% of the CW bias (i. e. ,280 W/ µm2) reaches to the output port Y. (b) Case of ‘10’ state in which input port A is ON and port B is OFF. The output at Y becomes OFF (18 W/ µm2) . (c) For the case of ‘01’ state, the result is same that of case ‘10’. (d) Case of ʻ11’ state in which port A is ON (360 W/ µm2) and port B is ON (360 W/ µm2) , the output port Y is become OFF (18 W/ µm2) ,
Therefore, by compromising a little on transmission, we have retained a feature of high importance, i.e., identical input powers or identical powers for all inputs. Further, sudden deep drop in normalized output for higher input power intensities suggests possibility of switching with high contrast ratio. In the next step, we keep CW bias of 360 W/ µm2 at C and gradually increase input intensity at the port A in the range 0 to 800 W/ µm2 and record normalized output power at the port Y. The result is shown in the Fig. 3(b). It is obvious form the figure that if any intensity level of 300 W/ µm2 or more is chosen as input at port A, the output would switch down to a very low value (i.e. OFF state) and very good switching could be obtained. However, for the sake of equality of all inputs, we choose 360 W/ µm2 as input level for the port A out of many other possibilities. At 360 W/ µm2 , the normalized output switches down to 5% (18 W/ µm2) which is quite low. There will not be any difference if we interchange ports A and B, therefore, input level for port B is also chosen as 360 W/ µm2 making all inputs (A, B and C) equal.
Table 1 The working states of optical NOR gate. Bias Port C 1
Input Port A 0
Input Port B 0
Output Port Y 1
1
1
0
0
1
1
1
0
1
0
1
0
Power intensity at output Port Y
280 W/ µm2 18 W/µm2 18 W/µm2 18 W/µm2
(280 W/µ m2) output of 360 W/ µm2 . Off course, Fig. 3(a) suggests that any power level less than 360 W/ µm2 would result in even higher transmission. However, if we chose lower power level, for example 300 W/ µm2 , the transmission would be slightly higher, however, the other input ports (A and B) would then need higher powers (more than 360 W/ µm2 ) for accomplishing switching operation and then the desired feature of equality of all input powers (identical inputs) will be lost.
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Fig. 5. Schematic diagram of proposed optical NAND gate which is designed by making some modifications in the structure of optical NOR gate of Fig. 1. Port B and associated waveguide is removed. Input port A is replaced by two input ports A1 and A2 by properly designing and implementing a twobeam combiner. The beam combiner consists of three rods (P1, P2, P3) of radius 50 nm as shown. The output port is Y and bias port is C.
z x We once again stress here, and obvious from device characteristics that choice of input intensity of any value lower than 360 W/ µm2 at port C would result in slightly higher normalized output, further, choice of input intensity of any value higher than 360 W/ µm2 at input port A or B would result in slightly better contrast, yet for the sake of equality of all inputs, we fix value of input power intensity at A, B and C equal to 360 W/ µm2 . Further, from the Fig. 3(a) and (b) one can anticipate that by fixing optical inputs of 360 W/ µm2 , other two desired features, i.e., small losses and very good contrast ratio are obtainable. In what follows, we confirm the anticipations mentioned above; The proposed optical NOR gate has two inputs, we therefore investigate the operation of four input states ʻ00’, ‘10’, ‘01’ and ‘11’. The bias port C is always injected with the CW optical input of 360 W/ µm2 . The snapshots of simulations for different input states are illustrated in the Fig. 4. Fig. 4(a) shows the state ʻ00’ in which both inputs A and B are OFF (zero W/ µm2 ). In this case, the 78% of the CW bias, i.e., 280 W/ µ m2 reaches to the output port Y and hence, output port Y is considered as ON. As shown in Fig. 4(b), when port A is ON and port B is OFF (‘10’ state), the output at Y becomes OFF (18 W/ µm2) . This is because combined intensity (of A and C) changes the refractive index of central cavities rod and DRA due to Kerr effect to an extent that most of the injected optical power couple to cw1, cw2 and CCs, and pass through bypass waveguides leaving Y OFF. For the same reason the output port Y remains OFF (18 W/ µm2) in the states ʻ01’ [Fig. 4(c)] and in the state ‘11’ [Fig. 4(d)]. All working states are summarized in Table 1. Y (ON ) The contrast ratio (CR) = 10log Y (OFF ) [31] of proposed optical NOR gate is calculated as 11.91dB .
three rods (P1, P2, P3) of radius 50 nm as shown. The output port Y and bias port C remain same as earlier structure. 3.2. The operation To examine the performance of the structure, we plot three curves of Fig. 6. Fig. 6(a) is obtained by varying CW optical input in the range of 0to1080 W/ µm2 at C and recording normalized output power at Y. As can be seen in the figure, the normalized output is 75% (270 W/µ m2) when the input is 360 W/ µm2 which is fairly high. Input of 360 W/ µm2 is our focus for the sake having input levels equal to that of the NOR gate. In the Fig. 6(b), CW optical bias of 360 W/ µm2 is injected at C and optical input is varied at A1 in the range 0 to 720 W/ µm2 . The recorded output at Y is as shown. It may be noted that input of 360 W/ µm2 at port A1 results in 58% (208.80 W/µ m2) normalized output at Y. Same result would be obtained if optical input of 360 W/ µm2 is injected at A2 in place of A1. In the last step, keeping optical bias of 360 W/ µm2 at C, we gradually increase optical inputs at A1 and A2 simultaneously in range of 0 to 500 W/ µm2 and record at the output at port Y by using power monitor. The result is shown in the Fig. 6(c). It is obvious in the figure that when inputs at both A1 and A2 reaches at 360 W/ µm2 , the output power drop to 3% (10.8 W/µ m2) . The Fig. 7 show the snapshots of simulation for different operation cases of optical NAND gate. The bias port C is always ON (360 W/µ m2) . For the input state ʻ00’, the ports A1 and A2 are OFF (zero W/ µm2 ) as shown in the Fig. 7(a). The output port Y in this case is ON (270 W/µ m2) . The Fig. 7(b) shows the ʻ10’ state in which port A1 is ON (360 W/µ m2) and port A2 is OFF (zero W/ µm2 ). In this case, 58% of the input reaches at the output port Y and Y may be considered as ON (208.80 W/µ m2) . For ʻ01’ state in which port A1 is OFF (zero W/ µm2 ) and port A2 is ON (360 W/µ m2) , the result is same that of the case ‘10’ as shown in the Fig. 7(c). The Fig. 7(d) shows the last case ʻ11’ in which both port A1 and A2 are ON (360 W/µ m2) . The output port Y becomes OFF (10.8 W/µ m2) , All working states are summarized in Table 2. The CR of proposed optical NAND gate is 13.97 dB.
3. Optical NAND gate 3.1. The design As shown in Fig. 5, optical NAND gate is designed by making some modifications in the structure of optical NOR gate of Fig. 1. As can be seen, port B and associated waveguide is removed. Further, input port A is replaced by two input ports A1 and A2 by properly designing and implementing a two-beam combiner. The beam combiner consists of
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Fig. 6. (a) The graph is obtained by varying CW optical input in the range of 0 to 1080 W/ µ m2 at C and recording normalized output power at Y. The normalized output is 75% (270 W/ µm2) when the input is 360 W/ µ m2 . (b) Output at Y is as shown when CW optical bias of 360 W/ µ m2 is injected at C and optical input is varied at A1 in the range 0 to 720 W/ µm2 . Input of 360W/ µ m2 at port A1 results in 58% (208.80 W/ µm2) normalized output at Y. Same result would be obtained if optical input of 360 W/ µ m2 is injected at A2 in place of A1. (c) Output at port Y, when optical bias is kept at 360 W/ µ m2 at C and optical inputs at A1 and A2 are simultaneously increased in range of 0 to 500 W/ µm2 . When inputs at both A1 and A2 reaches at 360 W/ µ m2 , the output power drops to 3% (10.8 W/ µm2) .
Size, Kerr coefficient, operating powers and contrast ratio of the proposed structures and other structures available in the literature are presented in Table 3 for ready reference. It is worth to mention here that the Kerr coefficient used in simulations of our paper is much smaller, If larger Kerr coefficient is used, much smaller operating powers would be obtained.
injected with optical power. As bias waveguides of both NOR and NAND are exactly same in structure, the transmission curves obtained for both gates are the same. The analysis of transmission T (normalized output power intensity) with variation in the structure parameters has been carried out for three cases; Case (i): Variation of T for % variation of the radius of fundamental dielectric rods of the structure ( ) in the range −2% to +2% (keeping defect rods unchanged). The result is as shown in Fig. 8(a). Case (ii): Variation of T for % variation of the radius of defect dielectric rods of the structure ( ) in the range −2% to +2% (keeping fundamental rods unchanged). The result is as shown in Fig. 8(b).
4. Tolerance analysis of optical NOR and NAND gates The tolerance analysis is carried out by giving HIGH (360 W/ µm2 ) input at the bias port and LOW (zero ) at the both input ports [16] of NOR and NAND gates, in other words, only bias waveguides are
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Fig. 7. Snapshots of simulation for different operation cases of optical NAND gate. The bias port C is always ON (360 W/ µm2) . (a) Result of the nput state ʻ00’ is shown. The ports A1 and A2 are OFF (zero W/ µ m2 ). The output port Y in this case is ON (270 W/ µm2) . (b) Figure shows the case of ʻ10’ state in which port A1 is ON (360 W/ µm2) and port A2 is OFF (zero W/ µ m2 ). In this case, 58% of the input reaches at the output port Y and may be considered as ON (208.80 W/ µm2) . (c) For ʻ01’ state in which port A1 is OFF (zero W/ µ m2 ) and port A2 is ON (360 W/ µm2) , the result is same that of the case ‘10’ as shown. (d) figure shows the last case ʻ11’ in which both port A1 and A2 are ON (360 W/ µm2) . The output at port Y becomes OFF (10.8 W/ µm2) ,
5. Conclusions
Table 2 The working states of optical NAND gate. Bias Port C
Input Port A1
Input Port A2
Output Port Y
Power intensity at output Port Y
1
0
0
1
270 W/ µm2
1
0
1
1
1 1
1 1
0 1
1 0
In conclusion, novel 2D photonic crystal (PhC) structures are proposed comprising of four circular cavities (CCs). The structures mimic NOR and NAND gates at operating wavelength that falls in the range of communication wavelength. 2D Finite difference time domain (2DFDTD) method is used for simulation and analysis of optical behavior of the proposed structures considering perfectly matched layers (PML) around the simulation region. Photonic band gap (PBG) and projected band diagram are obtained using plane wave expansion (PWE) method. Operating power intensity is same (360 W/µ m2) for both the structures which is quite low compared to previously reported structures. Contrast ratio of optical NOR and NAND gates are 11.91dB and 13.97 dB respectively which are better compared to previously reported structures. Further, proposed NOR and NAND gates with single input mimic an optical NOT gate. Being universal gates, NOR and
208.80 W/µm2 208.80 W/µm2
10.8 W/µm2
Case (iii): Variation of T for % variation of the radius of defect dielectric rods as well as fundamental rods of the structure ( ) in the range −2% to +2%. The result is as shown in Fig. 8(c). It is evident from the figures that performance of the considered structure would be fairly tolerant for −0.2% to 0% variation of the structure parameters as mentioned in above three cases.
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Table 3 presents size, Kerr coefficient, operating powers and contrast ratio of the proposed structures and other structures available in the literature. Sl. No.
Reference
Size of structure in µm2
Kerr coefficient
1
This paper
471.32
1.5 × 10
2
[26]
1534.80
9 × 10
17
9 × 10
17
3
[25]
750.53
4
[22]
394.60
5
[23]
487.58
1.0 × 10
6
[21]
382.46
9 × 10
7
[20]
268.09
8
[27]
299.41
17
17
NOR: 11.91 dBNAND: 13.97 dB
1 kW/µm2
11.46 dB
W m2
2 kW/µm2
–
–
9.54 dB
–
11.19 dB
1.5 kW/ µm2
–
330 W/ µm
6.93 dB
m2 W m2
17
1.0
W m2 W
16
1.0 × 10 9 × 10
360 W/ µm2
W
16
CR
m2 W m2
14
1.4 × 10
Operating Power
m2 W 2 m W
0.5
19.8 dB
kW/µm2
0.8
0.8 0.6
T
T
0.6 0.4
0.2
0.2 0.0
0.4
-2
-1
0
1
0.0
2
-2
-1
0
1
2
β
(a)
(b) 1.0 0.8
T
0.6 0.4 0.2 0.0
-2
-1
0
1
2
(c) Fig. 8. To examine the fabrication tolerance of optical NOR and NAND gates, the analysis of transmission T (normalized output power intensity) with variation in the structure parameters has been carried out for three cases; (a) Variation of T with % variation of the radius of fundamental dielectric rods of the structure ( ) in the range −2% to +2% (keeping defect rods unchanged). (b) Variation of T with % variation of the radius of defect dielectric rods of the structure ( ) in the range −2% to +2% (keeping fundamental rods unchanged). (c) Variation of T with % variation of the radius of defect dielectric rods as well as fundamental rods of the structure ( ) in the range −2% to +2%.
NAND allows for Boolean completeness. Moreover, implementation of bypass waveguides is a unique feature of the structures proposed in this paper. When the output is LOW, most of the optical power is channelizes out of the structure through bypass
waveguides, which otherwise, would go into the input ports affecting the input devices or would remain trapped inside the structure resulting in heating. This issue is not touched in the previous literature and in our opinion, being addressed for the first time.
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Acknowledgment
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Alok Kumar acknowledges University fellowship from Central University of Jharkhand, Ranchi-835205, INDIA. Authors thank the anonymous reviewer for his critical comments and suggestions. References [1] T.A. Monem, All optical active decoder using integrated 2D square lattice photonic crystals, J. Mod. Opt. 62 (2015) 1643–1649. [2] T. Baba, Slow light in photonic crystals, Nature Photon. 2 (2008) 465–471. [3] E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics, Phys. Rev. Lett. 58 (1987) 2059–2062. [4] S. John, Strong localization of photons in certain disordered dielectric super lattices, Phys. Rev. Lett. 58 (1987) 2846–12489. [5] C.G. Bostan, R.M.D. Ridder, Design of photonic crystal slab structures with absolute gaps in guided modes, J. Optoelectron. Adv. Mater. 4 (2002) 921–928. [6] J.D. Joannopoulos, G. Steven, J.N. Winn, R.D. Meade, Photonic Crystal: Modeling the Flow of Light, Princeton University Press, 2008 P. Copyright. [7] A. Taalbi, G. Bassou, M.Y. Mahmoud, New design of channel drop filters based on photonic crystal ring resonators, Optik 124 (2013) 824–827. [8] M.F. Monifi Djavid, A. Ghaffari, M.S. Abrishanmian, Hetrostructure wavelength division multiplexers using photonic crystals ring resonators, Opt. Comm. 28 (2008) 4028–4032. [9] A. Kumar, M.M. Gupta, S. Medhekar, All optical NOT and AND gates based on 2D nonlinear photonic crystal ring resonant cavity, Optik 167 (2018) 164–169. [10] A.M. Bahabady, S. Olyaee, All-optical NOT and XOR logic gates using photonic crystal nano – resonator and based on an interference effect, IET Optoelectron. 12 (2018) 191–195. [11] M.M. Gupta, S. Medhekar, A versatile optical junction using photonic band-gap guidance and self- collimation, Appl. Phys. Lett. 105 (2014) 131104. [12] A. Banaei, H. Mehdizadeh, F. Serajmohammadi, S.H. Kashtiban, A 2*4 all optical decoder switch based on photonic crystal ring resonators, J. Mod. Opt. 62 (2015) 430–434. [13] J. Zhong, J.S. Li, Photonic crystal based waveguide terahertz wave Set-Reset latch, Optik 145 (2017) 49–55. [14] T.A. Moniem, E.S.E. Din, Design of intregated all optical digital to analog converter
9
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Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
All optical NOR and NAND gates using four circular cavities created in 2D nonlinear photonic crystal Alok Kumar, Sarang Medhekar
⁎
Department of Physics, Central University of Jharkhand, Ranchi 835205, Jharkhand, India
HIGHLIGHTS
photonic crystal NOR and NAND gates are presented. • Novel operating power, good contrast ratio and cascadeble. • Low • Unique in terms of bypass waveguides of the structures. ARTICLE INFO
ABSTRACT
Keywords: Photonic crystal All optical logic gate Circular cavities Kerr effect
The paper presents novel 2D photonic crystal (PhC) structures comprising of four circular cavities (CCs) that mimic NOR and NAND gates. 2D Finite difference time domain (2DFDTD) method is used for simulation and analysis of optical behavior of the proposed structures considering perfectly matched layers (PML) around the simulation region. Photonic band gap (PBG) and projected band diagram are obtained using plane wave expansion (PWE) method. It is shown that both the structures function with optical inputs of same wavelength and intensity. The proposed NOR and NAND gates are having low operating powers and good contrast ratio. Being universal gates, NOR and NAND allows for Boolean completeness. Implementation of bypass waveguides is a unique feature of the structures proposed in this paper. When the output is LOW, most of the optical power channelizes out of the structure through bypass waveguides, which otherwise, would go into the input ports affecting the input devices or would remain trapped inside the structure resulting in heating. This issue is not touched in the previous literature and in our opinion, being addressed for the first time.
1. Introduction
in optical communication and computing system [15]. Various proposals for optical logic gates using linear and nonlinear PhCs are existing in the literature [16,17]. In linear PhCs, all optical logic is obtained using interference effect and thus, require small power [18]. However, desired interference effect requires precise control on phases of the optical inputs, which, in a complex circuitry is challenging and a major limitation in terms of practicability of such devices. Optical logic gates based on nonlinear PhCs, work on optical Kerr or Kerr like effects [19–23]. Such devices require higher operating powers for switching but the control on phase is not an issue and hence, are considered as potential candidates for future optical computing and communication systems. The quest is of their miniaturization and lowering of operating powers. Previously, different structures for obtaining optical logic gate based on Kerr effect have been reported. Man Mohan et al. [24] reported all optical NOT and AND gates using counter propagation beam in nonlinear Mach-Zehnder interferometer made of PhC waveguide which require operating power
Theoretical modeling and fabrication of all optical devices based on photonic crystal (PhC) is of recent interest due to their (PhC’s) unique properties [1]. PhC based optical devices have several advantages over conventional waveguide devices such as compactness and power consumption [2]. PhCs are periodic structures with a period of the order of optical wavelength [3,4]. Photonic bandgap (PBG) originates in PhCs due to periodic distribution of dielectric permittivity. It is the range of frequencies in which the electromagnetic waves propagation is forbidden regardless the wave vector and polarization state [5]. With introducing line and point defect, photonic waveguide and cavity are created in a PhC [6]. Numerous optical devices based on PhC are existing in the literature, such as the optical filter [7], de-multiplexer [8], logic gate [9,10], junction [11], decoder [12], S-R latch [13], and converter [14] etc. Among various optical devices, optical logic gates play important role
⁎
Corresponding author. E-mail addresses: [email protected], [email protected] (S. Medhekar).
https://doi.org/10.1016/j.optlastec.2019.105910 Received 5 May 2019; Received in revised form 26 August 2019; Accepted 16 October 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: Alok Kumar and Sarang Medhekar, Optics and Laser Technology, https://doi.org/10.1016/j.optlastec.2019.105910
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Fig. 1. A schematic diagram of the proposed optical NOR gate with parameters as mentioned in the text.
intensity for switching equal to 12.99 × 1014 W/m2 . All optical NOR and NAND gates based on nonlinear photonic crystal ring resonator (PhCRR) were proposed by Hamed Alipour–Banaei et al. [25] which have operating power intensity of 2 kW/ µm2 . Farhad Mehdizadeh et al. reported optical NOR gate [26] that works on operating power intensity of 1 kW/ µ m2 . An ultra-compact all optical OR/NOR gate based on PhCRR was proposed by Aref Rahmani et al. [27] with operating power intensity of 0.25 kW/µ m2 . In the present paper, novel 2D photonic structures comprising of four circular cavities (CCs) are designed that mimic NOR and NAND gates. The functionality of the proposed structure is analysed using two dimensional Finite Difference Time Domain (2DFDTD) [28,29] method. Further, Perfectly Matched Layer (PML) boundary conditions are used to define how the fields behave at the boundaries of the selected domain. PML boundary consists of grid points to the edge of the domain and, for the situations as considered in this paper, is designed to act as highly lossy material that absorbs all incident energy without producing unwanted reflections (a cause of errors in the simulation results). The width of domain is ± 15.4 μm along x- axis and ± 7.4 μm along zaxis. Photonic band gap (PBG) and projected band diagram are obtained using plane wave expansion (PWE) method [30]. It is shown that both the structures function with optical inputs of same wavelength and power intensity (identical operating powers) which is one of the important features required for compatibility and cascadebility. The structures are compact having low operating power and good contrast ratio.
by the coupler waveguide cw1 which is formed by removing thirty dialectic rods along x-axis and inserting ten dielectric rods array (DRA) of radius 100 nm . In exactly same manner CC3 and CC4 are connected to each other by the coupler waveguide cw2. The bias waveguide BS is formed by removing 51 dielectric rods along x-axis and has C and Y as bias and output ports respectively. As shown, two vertical waveguides (made by removing six dielectric rods along z-axis) are connected to CC1 and CC4 and having A and B as the two input ports of the proposed optical NOR gate. Two bypass waveguides BP1 and BP2 are connected to CC1 and CC4 as shown. Fig. 2(a) and (b) show the photonic band diagram and projected band diagram respectively of the structure of optical NOR gate which is obtained by using plane wave expansion (PWE) method. It is clear from the Fig. 2(a) that two PBG exist in the frequency rage a a 0.2817 < < 0.4136 and 0.7154 < < 0.7400 for the TE mode which in terms of wavelength range are 1470 nm < < 2158 nm and 821.5 nm < < 849.8 nm respectively. The guided mode is shown in the projected band diagram (Fig. 2b) that lies in the frequency range of a 0.28 < < 0.41. In principle, the defect waveguides can guide all wavelengths in both the PGBs. However, optical wavelength = 1542 nm is chosen for further investigations as it falls within the wavelength range suitable for optical communication. 2.2. The operation Two-dimensional finite difference time domain (2DFDTD) method is used to simulate/demonstrate NOR function of the proposed structure. The mechanism of switching is straightforward. When total optical power (injected from one or more input ports) is low, the parameters of the structure are so chosen that it does not couple to the bypass waveguides (through connecting waveguides and CCs) and most of the injected optical input appears at the output port Y. However, when the total optical power (injected from one or more input ports) is high, the refractive index of the rods of the structure is changed due to Kerr effect so that most of the injected optical input couples to the bypass waveguides and channelizes out of the structure leaving output port Y with zero or low output.
2. Optical NOR gate 2.1. The design Fig. 1 shows a schematic diagram of the proposed optical NOR gate. A 51 × 25 2D square lattice PhC platform is considered for designing it. The PhC is composed of Silicon dielectric rods of refractive index equal m2
to 3.46 and nonlinear Kerr coefficient equal to 1.5 × 10 17 W embedded in air. Radius of the rods is 0.2 × a , where a(=608 nm ) is the lattice constant. Four circular cavities CC1, CC2, CC3 and CC4 are formed by removing nine dielectric rods and inserting a central rod Rc (of radius 200 nm ) as shown. CC1 and CC2 are optically connected to each other
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Fig. 3. (a) Device characteristics is obtained by gradually increasing power intensity at C in the range zero to1080 W/ µm2 , and recording normalized output at the port Y using power monitor. (b) Normalized output power at the port Y is recorded by keeping CW bias of 360 W/ µ m2 at C and gradually increasing input power intensity at the port A in the range 0 to 800 W/ µm2 . Fig. 2. (a) Photonic band diagram of the structure of optical NOR gate obtained by using plane wave expansion (PWE) method. Two PBG exist in the frequency a a rage 0.2817 < < 0.4136 and 0.7154 < < 0.7400 for the TE mode which in
It should function with same inputs at all input ports (identical operating powers) and (iii) should have good contrast ratio. Keeping above mentioned in mind, we explore for that power intensity of continuous wave (CW) optical inputs (of = 1542 nm ) which when injected at all input ports of the proposed structure, NOR operation is obtained. For this purpose, in the first step, we plot device characteristics by gradually increasing power intensity at C in the range zero to1080 W/ µm2 , and recording normalized output at the port Y using power monitor. The result is as shown in Fig. 3(a). It may be noted in the figure that output remains high for lower levels of input and drops sharply at the higher sides. It is obvious from the characteristics that the structure offers high transmission (i.e. small losses) in a vide range of input power intensity. It is worth to mention here that after repeated explorations, we intuitively focused at the intensity level of 360 W/ µm2 for further investigations. Choice of 360 W/ µm2 results in 78%
1470nm < < 2158 nm terms of wavelength range are and 821.5nm < < 849.8 nm respectively. (b) Projected band diagram guided a mode exists in frequency range of 0.28 < < 0.41 as shown.
We stress here that the implementation of bypass waveguides is a unique feature of the structures proposed in this paper. One can note that when output at Y is LOW, most of the optical power (which is not going to Y) is channelized out of the structure through bypass waveguides BP1 and BP2, which otherwise, would go into the input ports affecting the input devices or would remain trapped inside the structure resulting in heating. This issue is not touched in the previous literature and in our opinion, being addressed here for the first time. Before going further, it is worth to mention that we look for three desired features in our proposed gates; (i) It should have small losses (ii)
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Fig. 4. (a) Case of ʻ00’ state is shown in which both inputs A and B are OFF (zero W/ µ m2 ). Y is considered as ON as 78% of the CW bias (i. e. ,280 W/ µm2) reaches to the output port Y. (b) Case of ‘10’ state in which input port A is ON and port B is OFF. The output at Y becomes OFF (18 W/ µm2) . (c) For the case of ‘01’ state, the result is same that of case ‘10’. (d) Case of ʻ11’ state in which port A is ON (360 W/ µm2) and port B is ON (360 W/ µm2) , the output port Y is become OFF (18 W/ µm2) ,
Therefore, by compromising a little on transmission, we have retained a feature of high importance, i.e., identical input powers or identical powers for all inputs. Further, sudden deep drop in normalized output for higher input power intensities suggests possibility of switching with high contrast ratio. In the next step, we keep CW bias of 360 W/ µm2 at C and gradually increase input intensity at the port A in the range 0 to 800 W/ µm2 and record normalized output power at the port Y. The result is shown in the Fig. 3(b). It is obvious form the figure that if any intensity level of 300 W/ µm2 or more is chosen as input at port A, the output would switch down to a very low value (i.e. OFF state) and very good switching could be obtained. However, for the sake of equality of all inputs, we choose 360 W/ µm2 as input level for the port A out of many other possibilities. At 360 W/ µm2 , the normalized output switches down to 5% (18 W/ µm2) which is quite low. There will not be any difference if we interchange ports A and B, therefore, input level for port B is also chosen as 360 W/ µm2 making all inputs (A, B and C) equal.
Table 1 The working states of optical NOR gate. Bias Port C 1
Input Port A 0
Input Port B 0
Output Port Y 1
1
1
0
0
1
1
1
0
1
0
1
0
Power intensity at output Port Y
280 W/ µm2 18 W/µm2 18 W/µm2 18 W/µm2
(280 W/µ m2) output of 360 W/ µm2 . Off course, Fig. 3(a) suggests that any power level less than 360 W/ µm2 would result in even higher transmission. However, if we chose lower power level, for example 300 W/ µm2 , the transmission would be slightly higher, however, the other input ports (A and B) would then need higher powers (more than 360 W/ µm2 ) for accomplishing switching operation and then the desired feature of equality of all input powers (identical inputs) will be lost.
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Fig. 5. Schematic diagram of proposed optical NAND gate which is designed by making some modifications in the structure of optical NOR gate of Fig. 1. Port B and associated waveguide is removed. Input port A is replaced by two input ports A1 and A2 by properly designing and implementing a twobeam combiner. The beam combiner consists of three rods (P1, P2, P3) of radius 50 nm as shown. The output port is Y and bias port is C.
z x We once again stress here, and obvious from device characteristics that choice of input intensity of any value lower than 360 W/ µm2 at port C would result in slightly higher normalized output, further, choice of input intensity of any value higher than 360 W/ µm2 at input port A or B would result in slightly better contrast, yet for the sake of equality of all inputs, we fix value of input power intensity at A, B and C equal to 360 W/ µm2 . Further, from the Fig. 3(a) and (b) one can anticipate that by fixing optical inputs of 360 W/ µm2 , other two desired features, i.e., small losses and very good contrast ratio are obtainable. In what follows, we confirm the anticipations mentioned above; The proposed optical NOR gate has two inputs, we therefore investigate the operation of four input states ʻ00’, ‘10’, ‘01’ and ‘11’. The bias port C is always injected with the CW optical input of 360 W/ µm2 . The snapshots of simulations for different input states are illustrated in the Fig. 4. Fig. 4(a) shows the state ʻ00’ in which both inputs A and B are OFF (zero W/ µm2 ). In this case, the 78% of the CW bias, i.e., 280 W/ µ m2 reaches to the output port Y and hence, output port Y is considered as ON. As shown in Fig. 4(b), when port A is ON and port B is OFF (‘10’ state), the output at Y becomes OFF (18 W/ µm2) . This is because combined intensity (of A and C) changes the refractive index of central cavities rod and DRA due to Kerr effect to an extent that most of the injected optical power couple to cw1, cw2 and CCs, and pass through bypass waveguides leaving Y OFF. For the same reason the output port Y remains OFF (18 W/ µm2) in the states ʻ01’ [Fig. 4(c)] and in the state ‘11’ [Fig. 4(d)]. All working states are summarized in Table 1. Y (ON ) The contrast ratio (CR) = 10log Y (OFF ) [31] of proposed optical NOR gate is calculated as 11.91dB .
three rods (P1, P2, P3) of radius 50 nm as shown. The output port Y and bias port C remain same as earlier structure. 3.2. The operation To examine the performance of the structure, we plot three curves of Fig. 6. Fig. 6(a) is obtained by varying CW optical input in the range of 0to1080 W/ µm2 at C and recording normalized output power at Y. As can be seen in the figure, the normalized output is 75% (270 W/µ m2) when the input is 360 W/ µm2 which is fairly high. Input of 360 W/ µm2 is our focus for the sake having input levels equal to that of the NOR gate. In the Fig. 6(b), CW optical bias of 360 W/ µm2 is injected at C and optical input is varied at A1 in the range 0 to 720 W/ µm2 . The recorded output at Y is as shown. It may be noted that input of 360 W/ µm2 at port A1 results in 58% (208.80 W/µ m2) normalized output at Y. Same result would be obtained if optical input of 360 W/ µm2 is injected at A2 in place of A1. In the last step, keeping optical bias of 360 W/ µm2 at C, we gradually increase optical inputs at A1 and A2 simultaneously in range of 0 to 500 W/ µm2 and record at the output at port Y by using power monitor. The result is shown in the Fig. 6(c). It is obvious in the figure that when inputs at both A1 and A2 reaches at 360 W/ µm2 , the output power drop to 3% (10.8 W/µ m2) . The Fig. 7 show the snapshots of simulation for different operation cases of optical NAND gate. The bias port C is always ON (360 W/µ m2) . For the input state ʻ00’, the ports A1 and A2 are OFF (zero W/ µm2 ) as shown in the Fig. 7(a). The output port Y in this case is ON (270 W/µ m2) . The Fig. 7(b) shows the ʻ10’ state in which port A1 is ON (360 W/µ m2) and port A2 is OFF (zero W/ µm2 ). In this case, 58% of the input reaches at the output port Y and Y may be considered as ON (208.80 W/µ m2) . For ʻ01’ state in which port A1 is OFF (zero W/ µm2 ) and port A2 is ON (360 W/µ m2) , the result is same that of the case ‘10’ as shown in the Fig. 7(c). The Fig. 7(d) shows the last case ʻ11’ in which both port A1 and A2 are ON (360 W/µ m2) . The output port Y becomes OFF (10.8 W/µ m2) , All working states are summarized in Table 2. The CR of proposed optical NAND gate is 13.97 dB.
3. Optical NAND gate 3.1. The design As shown in Fig. 5, optical NAND gate is designed by making some modifications in the structure of optical NOR gate of Fig. 1. As can be seen, port B and associated waveguide is removed. Further, input port A is replaced by two input ports A1 and A2 by properly designing and implementing a two-beam combiner. The beam combiner consists of
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Fig. 6. (a) The graph is obtained by varying CW optical input in the range of 0 to 1080 W/ µ m2 at C and recording normalized output power at Y. The normalized output is 75% (270 W/ µm2) when the input is 360 W/ µ m2 . (b) Output at Y is as shown when CW optical bias of 360 W/ µ m2 is injected at C and optical input is varied at A1 in the range 0 to 720 W/ µm2 . Input of 360W/ µ m2 at port A1 results in 58% (208.80 W/ µm2) normalized output at Y. Same result would be obtained if optical input of 360 W/ µ m2 is injected at A2 in place of A1. (c) Output at port Y, when optical bias is kept at 360 W/ µ m2 at C and optical inputs at A1 and A2 are simultaneously increased in range of 0 to 500 W/ µm2 . When inputs at both A1 and A2 reaches at 360 W/ µ m2 , the output power drops to 3% (10.8 W/ µm2) .
Size, Kerr coefficient, operating powers and contrast ratio of the proposed structures and other structures available in the literature are presented in Table 3 for ready reference. It is worth to mention here that the Kerr coefficient used in simulations of our paper is much smaller, If larger Kerr coefficient is used, much smaller operating powers would be obtained.
injected with optical power. As bias waveguides of both NOR and NAND are exactly same in structure, the transmission curves obtained for both gates are the same. The analysis of transmission T (normalized output power intensity) with variation in the structure parameters has been carried out for three cases; Case (i): Variation of T for % variation of the radius of fundamental dielectric rods of the structure ( ) in the range −2% to +2% (keeping defect rods unchanged). The result is as shown in Fig. 8(a). Case (ii): Variation of T for % variation of the radius of defect dielectric rods of the structure ( ) in the range −2% to +2% (keeping fundamental rods unchanged). The result is as shown in Fig. 8(b).
4. Tolerance analysis of optical NOR and NAND gates The tolerance analysis is carried out by giving HIGH (360 W/ µm2 ) input at the bias port and LOW (zero ) at the both input ports [16] of NOR and NAND gates, in other words, only bias waveguides are
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Fig. 7. Snapshots of simulation for different operation cases of optical NAND gate. The bias port C is always ON (360 W/ µm2) . (a) Result of the nput state ʻ00’ is shown. The ports A1 and A2 are OFF (zero W/ µ m2 ). The output port Y in this case is ON (270 W/ µm2) . (b) Figure shows the case of ʻ10’ state in which port A1 is ON (360 W/ µm2) and port A2 is OFF (zero W/ µ m2 ). In this case, 58% of the input reaches at the output port Y and may be considered as ON (208.80 W/ µm2) . (c) For ʻ01’ state in which port A1 is OFF (zero W/ µ m2 ) and port A2 is ON (360 W/ µm2) , the result is same that of the case ‘10’ as shown. (d) figure shows the last case ʻ11’ in which both port A1 and A2 are ON (360 W/ µm2) . The output at port Y becomes OFF (10.8 W/ µm2) ,
5. Conclusions
Table 2 The working states of optical NAND gate. Bias Port C
Input Port A1
Input Port A2
Output Port Y
Power intensity at output Port Y
1
0
0
1
270 W/ µm2
1
0
1
1
1 1
1 1
0 1
1 0
In conclusion, novel 2D photonic crystal (PhC) structures are proposed comprising of four circular cavities (CCs). The structures mimic NOR and NAND gates at operating wavelength that falls in the range of communication wavelength. 2D Finite difference time domain (2DFDTD) method is used for simulation and analysis of optical behavior of the proposed structures considering perfectly matched layers (PML) around the simulation region. Photonic band gap (PBG) and projected band diagram are obtained using plane wave expansion (PWE) method. Operating power intensity is same (360 W/µ m2) for both the structures which is quite low compared to previously reported structures. Contrast ratio of optical NOR and NAND gates are 11.91dB and 13.97 dB respectively which are better compared to previously reported structures. Further, proposed NOR and NAND gates with single input mimic an optical NOT gate. Being universal gates, NOR and
208.80 W/µm2 208.80 W/µm2
10.8 W/µm2
Case (iii): Variation of T for % variation of the radius of defect dielectric rods as well as fundamental rods of the structure ( ) in the range −2% to +2%. The result is as shown in Fig. 8(c). It is evident from the figures that performance of the considered structure would be fairly tolerant for −0.2% to 0% variation of the structure parameters as mentioned in above three cases.
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Table 3 presents size, Kerr coefficient, operating powers and contrast ratio of the proposed structures and other structures available in the literature. Sl. No.
Reference
Size of structure in µm2
Kerr coefficient
1
This paper
471.32
1.5 × 10
2
[26]
1534.80
9 × 10
17
9 × 10
17
3
[25]
750.53
4
[22]
394.60
5
[23]
487.58
1.0 × 10
6
[21]
382.46
9 × 10
7
[20]
268.09
8
[27]
299.41
17
17
NOR: 11.91 dBNAND: 13.97 dB
1 kW/µm2
11.46 dB
W m2
2 kW/µm2
–
–
9.54 dB
–
11.19 dB
1.5 kW/ µm2
–
330 W/ µm
6.93 dB
m2 W m2
17
1.0
W m2 W
16
1.0 × 10 9 × 10
360 W/ µm2
W
16
CR
m2 W m2
14
1.4 × 10
Operating Power
m2 W 2 m W
0.5
19.8 dB
kW/µm2
0.8
0.8 0.6
T
T
0.6 0.4
0.2
0.2 0.0
0.4
-2
-1
0
1
0.0
2
-2
-1
0
1
2
β
(a)
(b) 1.0 0.8
T
0.6 0.4 0.2 0.0
-2
-1
0
1
2
(c) Fig. 8. To examine the fabrication tolerance of optical NOR and NAND gates, the analysis of transmission T (normalized output power intensity) with variation in the structure parameters has been carried out for three cases; (a) Variation of T with % variation of the radius of fundamental dielectric rods of the structure ( ) in the range −2% to +2% (keeping defect rods unchanged). (b) Variation of T with % variation of the radius of defect dielectric rods of the structure ( ) in the range −2% to +2% (keeping fundamental rods unchanged). (c) Variation of T with % variation of the radius of defect dielectric rods as well as fundamental rods of the structure ( ) in the range −2% to +2%.
NAND allows for Boolean completeness. Moreover, implementation of bypass waveguides is a unique feature of the structures proposed in this paper. When the output is LOW, most of the optical power is channelizes out of the structure through bypass
waveguides, which otherwise, would go into the input ports affecting the input devices or would remain trapped inside the structure resulting in heating. This issue is not touched in the previous literature and in our opinion, being addressed for the first time.
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Acknowledgment
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