- Email: [email protected]
All-optical logic gates based on metallic waveguide arrays
Accepted Manuscript All-optical logic gates based on metallic waveguide arrays Wu Yang, Xiaoyan Shi, Huaizhong Xing, Xiaoshuang Chen PII: DOI: Reference:
S2211-3797(18)31669-3 https://doi.org/10.1016/j.rinp.2018.10.036 RINP 1738
To appear in:
Results in Physics
Received Date: Revised Date: Accepted Date:
30 June 2018 23 September 2018 22 October 2018
Please cite this article as: Yang, W., Shi, X., Xing, H., Chen, X., All-optical logic gates based on metallic waveguide arrays, Results in Physics (2018), doi: https://doi.org/10.1016/j.rinp.2018.10.036
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
All-optical logic gates based on metallic waveguide arrays Wu Yang,1, * Xiaoyan Shi,1 Huaizhong Xing,2 and Xiaoshuang Chen3 2
1 College of Science, Henan University of Technology, Zhengzhou 450001 China Department of Applied Physics, Donghua University, Ren Min Road 2999, Songjiang District, Shanghai 201620, China 3 National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 500 Yutian Road, Shanghai 200083, China *[email protected]
All-optical logic gates based on metallic waveguide arrays (MWGAs) are proposed. The supermodes of surface plasmon polaritons (SPPs) are excited selectively by different input fields. According to the field distribution of different input fields, the appropriate position of output port is chosen for different logic functions, which the lengths of waveguides are different for different gates: L1=0.68μm is for OR gate and NOT gate; L2=0.38μm is for AND gate; L3=0.32μm is for XOR gate. OR gate and NOT gate can be realized in the same MWGA
choosing different input
waveguides. The intensity contrast ratios between the output logic “1” and “0” are 9.3dB -13.98dB. The
MWGAs can provide a new method for
logic functions in photonic integrated circuits. Keywords: All-optical logic gates; metallic waveguide arrays; surface plasmon polaritons
1. Introduction Surface plasmon polaritons (SPPs), which are localized at the interface of metal and dielectric, are taken as promising candidates in the future photonic circuits because of field confinements. In photonics circuits, plasmonic logic gates have attracted a lot of attentions since they have broad application prospects. Various kinds of logic gates based on plasmonic structures have been proposed, such as silver nanowire network [1,2], plasmonic slot waveguides[3,4], dielectric-loaded waveguides [5], metal-insulator-metal structures[6], and silicon hybrid plasmonic waveguides[7-9]. The logic gates can also been obtained by applying an optical pulse in the cladding region via index modulation [10]. In
addition, Nanostructured metallic waveguide arrays (MWGAs) have also been investigated in the past years due to the special electromagnetic properties, which can used to form negative refraction [11], subwavelength focusing [12], self-imaging [13], and Talbot effect [14]. Recently, we have study the discrete Talbot effect and subwavelength focusing in MWGAs [15,16], where the supermode theory of SPPs is put forward to explain these phenomena. In this paper, we propose all-optical logic gates based on MWGAs. The supermode theory of SPPs mentioned in Ref. 15 and Ref. 16 is used to guide the design of logic gates. In MWGAs, different input fields can excite different SPPs supermodes and the superposition of supermodes can be used to form different logic functions. By choosing an appropriate length of MWGAs and the position of output ports, AND, XOR, NOT, and OR can be realized. The finite-difference time-domain (FDTD) method is used to simulate the field distributions in MWGAs. 1
2. Structure and field distributions Here, we consider a 2D MWGA that contains five metal waveguides (N=5) composed of Ag layers and air layers. A 2D structure was considered mainly because the design of structure is simple and the propagation behavior is similar with a 3D structure [17]. The 2D MWGA structure is shown in Fig. 1(a). The widths of the Ag layer and the air layer are d=20nm and h=30nm, respectively. The relative permittivity of Ag is taken to be the measured value of ε2= 15.7+0.94j at λ=632.8 nm [18]. When the incident fields enter from different positions, different supermodes can be excited and the field distribution of SPPs in the MWGA is a result of superposition of SPPs supermodes[15]. In the MWGA, the total field is formed by the superposition of all supermodes, which can be written as N
( x, z, t ) as H s (x) ei ( t z )
(1)
N H s (x) ei1 z Cs , n n (x, y) eis z n 1
(2)
s
s 1
In the above formula, as is the weighting factor of each excited supermode, Cs,n is the coefficient of wave function in the nth waveguide of the s-order supermode [12]. Cs , n sin
ns N 1
n 1, 2,3,
,N
(3)
The input field can be expressed by { 1 , 2 , 3 , 4 , 5 }, which n is the amplitude value of input fields in the nth waveguide. According to Eq. (1) and Eq. (2), the relations between as and the input field can be obtained, which can be written as 1 C1,1 C 2 1,2 5 C1,5
C5,1 a1 C5,2 a2 C5,5 a5
C2,1 C2,2 C2,5
(4)
Introducing n and Cs,n into Eq. (4), we can obtain the value of as and the field distribution theoretically[16]. Eq. (4) shows that different incident fields { 1 , 2 , 3 , 4 , 5 } can excite different weighting factor of supermodes, which means the superposition field of SPPs supermodes is different. So we can choose appropriate field distributions in the MWGA by incident fields. We numerically simulate the propagation behavior of SPPs by the commercial software EastFDTD, which is based on FDTD method. The grid size is dx=dz=2nm and the time increment is Δt=Δs/2c, where c is the velocity of light in vacuum. Around the computational domain, a perfectly matching layer is adopted to absorb the outgoing electromagnetic wave. The simulated field distribution is presented in Fig. 1(b)-(d), where the amplitude values of input fields, { 1 , 2 , 3 , 4 , 5 }, are {1, 0, 0, 0, 0}, {0, 0, 0, 0, 1}, {1, 0, 0, 0, 1}, respectively. By the theory of SPP supermodes mentioned in Ref. 2
15 and Ref. 16, the field distributions in Fig. 1(b)-(d) can be interpreted reasonably, which are the result of superposition of SPPs supermodes. By applying the method of Ref. 15, the field distributions of the SPPs supermodes are shown in Fig. 2 (a) – (e), which correspond to the 1st–5th supermodes. When one or more input fields are incident on waveguides of the MWGA, the supermodes are excited [15,16]. The total field intensity distribution is formed by the superposition of these supermodes, as shown in Fig. 1(b)-(d). In other words, Fig. 1(b)-(d) are the results of the superposition of the 1st–5th supermodes with different weight coefficient [15,16]. It can be seen from Fig. 1(b) and Fig. 1(c) that the input fields can propagate to adjacent waveguides with the increase of transmission distance. Fig. 1(d) is the superposition of Fig. 1(b) and Fig. 1(c), which the maximum value of transmission field appears at about z=0.68μm indicated by the green dashed line.
Fig.1 (a) The MWGA of five adjacent two-dimensional metal waveguides, which composed of Ag layers and air layers. The numerical simulation results of field distributions in the MWGA, which the input fields are located at (b) the 1st waveguide, (c) the 5th waveguide, (d) the 1st and 5th waveguides.
Fig.2 The field distributions of individual supermodes in the MWGA. (a) The 1st supermode; (b) The 2nd supermode; (c) The 3rd supermode; (c) The 4th supermode; (e) The 5th supermode.
3
3. Design and simulation results According the field distributions in Fig. 1(b)-(d), OR gate can be obtained if we set the output port at z=0.68μm in the 3rd waveguide. The scheme was shown in Fig. 3(a), where the 1st, 2nd, 4th, and 5th waveguides are closed by Ag layers at the end of the MWGA and only the 3rd waveguide is open. The 1st and 5th waveguides are input ports, which are labeled with A and B. The end of the 3rd waveguide is the output port labeled with O. By applying the method of Ref. 15, the length of waveguides is choose to L1=0.68μm, which is determined by the field distributions of the superposition of SPPs supermodes in Fig. 1(b)-(d).
Fig.3 (a) The scheme of OR gate, L1=0.68μm. The numerical simulation results of field distributions, which the input fields are located at (b) the 1st waveguide, (c) the 5th waveguide, (d) the 1st and 5th waveguides. The simulated results are shown in Fig. 3(b)-(d), where the input signals are incident from B port, A port, A and B ports, respectively. By the normalization, the amplitude of input signal is 1. In Fig. 3(b), A=1, B=0, the amplitude value of output signal is 0.45, which corresponds to O=1. Then the logic state of “0 OR 1=1” is obtained. Fig. 3(c) is similar to Fig. 3(b), which corresponds to the logic state of “1 OR 0=1”. In Fig. 3(c), the amplitude value of output signal is 0.90, which corresponds to the logic state of “1 OR 1=1”. The operating principle of the OR gate is shown in Table1. Table 1 The operating principle of the OR gate amplitude of
amplitude of
input field
output field
logical output
intensity contrast ratio (dB)
Port A
Port B
Port O
OR
0
0
0
0
0
1
0.45
1
1
0
0.45
1
1
1
0.90
1
4
>20
Similarly, NOT gate can be obtained according the field distribution in Fig. 1(b) and Fig. 1 (d). The scheme was shown in Fig. 4(a), where port A is the input port and port B is the control port. The output port O is at the end of the 1st waveguide. The length of waveguides is the same with Fig. 4(a), L1=0.68μm. The amplitude of control signal is the same with input signal. The simulated results are shown in Fig. 4(b) and(c), which the input port is off and on, respectively. By defining an appropriate threshold value, the logic gates of “0” and “1” can then be realized. In Fig. 4(b), the amplitude value of output port is 0.14. In Fig. 4(c), the amplitude of output port is 0.028. We set 0.1 for the threshold value (0.028<0.1<0.14), which the signal is “0” when the amplitude value is no more than 0.1 and the signal is “1” when the amplitude value is more than 0.1. By the definition of threshold value, Fig. 4(b) (0.14>0.1) is corresponding to the logic state of “NOT 0=1” and Fig. 4(c) (0.028<0.1) is corresponding to the logic state of “NOT 1=0”. NOT operation is achieved. The operating principle of the NOT gate is shown in Table2. The intensity contrast ratio between the output logic “1” and “0” is 13.98dB, which is calculated from 10log(I1/I0). (I1 and I0 are the signal intensities of logic “1” and “0”, respectively.) It should be pointed out that the signal strength of “1” is weak (the amplitude value is 0.14) and the reflection rate of NOT gate is high. This is because the field strength of output port is weak by the superposition of SPPs supermodes [15].
Fig.4 (a) The scheme of NOT gate, L1=0.68μm. The numerical simulation results of field distributions, which the input fields are located at (b) the 5th waveguide, (c) the 1st and 5th waveguides.
Table 2 The operating principle of the NOT gate amplitude of
Control
amplitude of
input field
port
output field
Logical Output
Port A
Port B
Port O
NOT
0
1
0.14
1
1
1
0.028
0
5
intensity contrast ratio (dB) 13.98
In order to achieve AND logic functions, the input fields are placed in the 1st, 3rd, and 5th waveguides in the MWGA. Four different combinations of input fields are employed: {0,1,0}, {1,1,0}, {0,1,1}, {1,1,1}, which correspond to the amplitudes of input fields in the 1st, 3rd, and 5th waveguides. The field distributions can be interpreted by the superposition of SPP supermodes [15,16]. The simulated field distribution is presented in Fig. 5(a) - (d). By observing the field distribution in Fig. 5(a) - (d), we notice that when z=0.38μm (green dashed line), the amplitude of the 3rd waveguide in Fig. 5(a) is almost zero and the amplitudes of the 3rd waveguide in Fig. 5(b) - (d) are significantly stronger. If setting the output port at the position of z=0.38μm in the 3rd waveguide, AND gate can be obtained. The scheme was shown in Fig. 6(a), where L2=0.38μm. Port A and B are input ports. Port C is the control port and Port O is the output port. The simulated fields are shown in Fig. 6(b)-(e), which the amplitude values of output ports are 0.086, 0.12, 0.12, and 0.35. If setting 0.12 for the threshold value, which the signal is “0” when the amplitude value is no more than 0.12, AND operation can be achieved. The operating principle of the AND gate is shown in Table3. The intensity contrast ratio between the output logic “1” and “0” is 9.3dB.
Fig.5 The numerical simulation results of field distributions in the MWGA, which the input fields are located at (a) the 3rd waveguide (b) the 1st and 3rd waveguides, (c) the 3rd and 5th waveguides, (d) the 1st, 3rd and 5th waveguides.
6
Fig.6 (a) The scheme of AND gate, L2=0.38μm. The numerical simulation results of field distributions, which the input fields are located at (a) the 3rd waveguide (b) the 1st and 3rd waveguides, (c) the 3rd and 5th waveguides, (d) the 1st, 3rd and 5th waveguides.
amplitude of input
Table 3 The operating principle of the AND gate Control port amplitude of Logical
field
output field
Output
Port A
Port B
Port C
Port O
AND
0
0
1
0.086
0
0
1
1
0.12
0
1
0
1
0.12
0
1
1
1
0.35
1
intensity contrast ratio (dB) 9.3
To realize XOR logic functions, the input fields are placed in the 2nd and 4th waveguides. The simulated field distributions are presented in Fig. 7(a) - (d). In Fig. 7(a), the amplitude of input field in the 2nd waveguide is 1 and the amplitude in input field of the 4th waveguide is 0. In Fig. 7(b), the amplitude of input field in the 2nd waveguide is 0 and the amplitude of input field in the 4th waveguide is 1. In Fig. 7(c), the amplitudes of input fields are both 1. When z=0.32μm (green dashed line), the amplitude of the 2nd waveguide in Fig. 7(c) is almost zero and the amplitudes of the 2nd waveguide in Fig. 7(a) - (b) are significantly stronger. If we set the output port at z=0.32μm in the 2nd waveguide, XOR gate can be obtained. The scheme was shown in Fig. 8(a), where L3=0.32μm. Port A and B are input ports and Port O is the output port. The simulated field distributions are shown in Fig. 8(b)-(d), which the amplitude values of output ports are 0.17, 0.16, and 0.05. If setting 0.05 for the threshold value, which the signal is “0” when the amplitude value is no more than 0.05, AND operation can be achieved. The operating principle of the XOR gate is shown in Table4. The intensity contrast ratio between the output logic “1” and “0” is 10.1dB.
7
Fig.7 The numerical simulation results of field distributions in the MWGA, which the input fields are located at (a) the 2nd waveguide, (b) the 4th waveguide, (c) the 2nd and 4th waveguides.
Fig.8 (a) The scheme of XOR gate, L3=0.32μm. The numerical simulation results of field distributions, which the input fields are located at (b) the 2nd waveguide, (c) the 4th waveguide, (d) the 2nd and 4th waveguides.
Table 4 The operating principle of the XOR gate amplitude of input field
amplitude
of
Logical
intensity
output field
Output
contrast ratio
Port A
Port B
Port O
XOR
0
0
0
0
1
0
0.17
1
0
1
0.16
1
1
1
0.05
0
8
(dB) 10.1
4. Conclusion We propose new schemes of
MWGAs. By applying the method of Ref. 15, the
field distributions of the SPPs supermodes in MWGAs are obtained. According to the field distribution, OR, AND, NO, and XOR logic functions can be achieved by choosing the appropriate length of MWGAs, specific input fields, output ports and suitable threshold value. The lengths of waveguides are different for different gates: L1=0.68μm is for OR gate and NOT gate; L2=0.38μm is for AND gate; L3=0.32μm is for XOR gate. The intensity contrast ratios between the output logic “1” and “0” are 9.3dB -13.98dB in these
. OR gate and NOT gate can be realized in the same MWGA
choosing different input waveguides. Due to its simple structure and controllability, the MWGAs can provide a new method for logic functions in photonic integrated circuits. It should be pointed out that these schemes are not unique. If the number of waveguides in MWGAs is increased, the field distributions will be changed and the waveguide lengths, input fields, output ports and suitable threshold value need to be reselected. By a similar analysis, OR, AND, NO, and XOR logic gates can also be obtained. Acknowledgment This work is supported by Doctoral Foundation of Henan University of Technology (2016BS010), the Fundamental Research Funds for Henan Provincial Colleges and Universities in Henan University of Technology (2016QNJH13), the Henan Province Education Department Natural Science Research Programs (17A140006), and the Natural Science Foundation of Henan Province (182300410195). References 1. H. Wei, Z. Li, X. Tian, Z. Wang, F. Cong, N. Liu, S. Zhang, P. Nordlander, N. J. Halas, H. Xu, uantum Dot-Based Local Field Imaging Reveals Plasmon-Based Interferometric Logic in Silver Nanowire Networks, Nano Lett. 11 (2011) 471. 2. H. Wei, Z. X. Wang, X. R. Tian, M. Kall, H. X. Xu, Cascaded logic gates in nanophotonic plasmon networks, Nat. Commun. 2 (2011) 387. 3. Y. Fu, X. Hu, C. Lu, S. Yue, H. Yang, Q. Gong, All-Optical Logic Gates Based on Nanoscale Plasmonic Slot Waveguides, Nano Lett. 12 (2012) 5784. 4. D. Pan, H. Wei, H. Xu, Optical interferometric logic gates based on metal slot waveguide network realizing whole fundamental logic operations, Opt. Express 21 (2013) 9556. 5. M. Ota, A. Sumimura, M. Fukuhara, Y. Ishii, M. Fukuda, Plasmonic-multimode interference-based logic circuit with simple phase adjustment. Sci. Rep. 6 (2016) 24546 6. Y. Bian, Q. Gong, Compact all-opticalinterferometriclogicgatesbased on one-dimensional metal– insulator–metal structures. Opt. Commun. 313 (2014) 27 7. L. Cui, L. Yu, Multifunctional logic gates based on silicon hybrid plasmonic waveguides. Mod. Phys. Lett. B 32 (2018) 1850008 8. N. Gogoi , P. P. Sahu, All-optical tunable power splitter based on a surface plasmonic two-mode interference waveguide, Appl. Opt. 57 (2018) 2715. 9. P. P. Sahu, Theoretical Investigation of All optical switch based on compact surface plasmonic two mode interference coupler, J. Lightw.Technol. 34 (2016) 1300. 10. N. Gogoi , P. P. Sahu, All optical compact surface plasmonic two mode interference device for optical logic gates, Appl. Opt. 54(2015) 1051.
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11. X. B. Fan, G. P. Wang, J. C. W. Lee, C. T. Chan, All-Angle Broadband Negative Refraction of Metal Waveguide Arrays in the Visible Range: Theoretical Analysis and Numerical Demonstration. Phys. Rev. Lett. 97 (2006) 073901. 12. X. B. Fan, G. P. Wang, Nanoscale metal waveguide arrays as Plasmon lenses. Opt. Lett. 31 (2006) 1322. 13. G. D. Valle, S. Longhi, Subwavelength diffraction control and self-imaging in curved plasmonic waveguide arrays. Opt. Lett. 35 (2010) 673. 14. Y. Wang, K. Zhou, X. Zhang, K. Yang, Y. Wang, Y. Song, S. Liu, Discrete plasmonic Talbot effect in subwavelength metal waveguide arrays. Opt. Lett. 35 (2010) 685. 15. X. Shi, W. Yang, H. Xing, X. Chen. Subwavelength focusing by a sheltered metallic waveguide array, Opt. Commun. 349 (2015) 151 16. X. Shi, W. Yang, H. Xing, X. Chen. Discrete plasmonic Talbot effect in finite metal waveguide arrays, Optics Letters 40 (2015) 1635 17. A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, S. Linden. Bloch oscillations in plasmonic waveguide arrays. Nat Commun. 5: 3843 (2014) 18. E. D. Palik, Handbook of Optical Constants of Solids, (Academic, 1985).
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S2211-3797(18)31669-3 https://doi.org/10.1016/j.rinp.2018.10.036 RINP 1738
To appear in:
Results in Physics
Received Date: Revised Date: Accepted Date:
30 June 2018 23 September 2018 22 October 2018
Please cite this article as: Yang, W., Shi, X., Xing, H., Chen, X., All-optical logic gates based on metallic waveguide arrays, Results in Physics (2018), doi: https://doi.org/10.1016/j.rinp.2018.10.036
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
All-optical logic gates based on metallic waveguide arrays Wu Yang,1, * Xiaoyan Shi,1 Huaizhong Xing,2 and Xiaoshuang Chen3 2
1 College of Science, Henan University of Technology, Zhengzhou 450001 China Department of Applied Physics, Donghua University, Ren Min Road 2999, Songjiang District, Shanghai 201620, China 3 National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, 500 Yutian Road, Shanghai 200083, China *[email protected]
All-optical logic gates based on metallic waveguide arrays (MWGAs) are proposed. The supermodes of surface plasmon polaritons (SPPs) are excited selectively by different input fields. According to the field distribution of different input fields, the appropriate position of output port is chosen for different logic functions, which the lengths of waveguides are different for different gates: L1=0.68μm is for OR gate and NOT gate; L2=0.38μm is for AND gate; L3=0.32μm is for XOR gate. OR gate and NOT gate can be realized in the same MWGA
choosing different input
waveguides. The intensity contrast ratios between the output logic “1” and “0” are 9.3dB -13.98dB. The
MWGAs can provide a new method for
logic functions in photonic integrated circuits. Keywords: All-optical logic gates; metallic waveguide arrays; surface plasmon polaritons
1. Introduction Surface plasmon polaritons (SPPs), which are localized at the interface of metal and dielectric, are taken as promising candidates in the future photonic circuits because of field confinements. In photonics circuits, plasmonic logic gates have attracted a lot of attentions since they have broad application prospects. Various kinds of logic gates based on plasmonic structures have been proposed, such as silver nanowire network [1,2], plasmonic slot waveguides[3,4], dielectric-loaded waveguides [5], metal-insulator-metal structures[6], and silicon hybrid plasmonic waveguides[7-9]. The logic gates can also been obtained by applying an optical pulse in the cladding region via index modulation [10]. In
addition, Nanostructured metallic waveguide arrays (MWGAs) have also been investigated in the past years due to the special electromagnetic properties, which can used to form negative refraction [11], subwavelength focusing [12], self-imaging [13], and Talbot effect [14]. Recently, we have study the discrete Talbot effect and subwavelength focusing in MWGAs [15,16], where the supermode theory of SPPs is put forward to explain these phenomena. In this paper, we propose all-optical logic gates based on MWGAs. The supermode theory of SPPs mentioned in Ref. 15 and Ref. 16 is used to guide the design of logic gates. In MWGAs, different input fields can excite different SPPs supermodes and the superposition of supermodes can be used to form different logic functions. By choosing an appropriate length of MWGAs and the position of output ports, AND, XOR, NOT, and OR can be realized. The finite-difference time-domain (FDTD) method is used to simulate the field distributions in MWGAs. 1
2. Structure and field distributions Here, we consider a 2D MWGA that contains five metal waveguides (N=5) composed of Ag layers and air layers. A 2D structure was considered mainly because the design of structure is simple and the propagation behavior is similar with a 3D structure [17]. The 2D MWGA structure is shown in Fig. 1(a). The widths of the Ag layer and the air layer are d=20nm and h=30nm, respectively. The relative permittivity of Ag is taken to be the measured value of ε2= 15.7+0.94j at λ=632.8 nm [18]. When the incident fields enter from different positions, different supermodes can be excited and the field distribution of SPPs in the MWGA is a result of superposition of SPPs supermodes[15]. In the MWGA, the total field is formed by the superposition of all supermodes, which can be written as N
( x, z, t ) as H s (x) ei ( t z )
(1)
N H s (x) ei1 z Cs , n n (x, y) eis z n 1
(2)
s
s 1
In the above formula, as is the weighting factor of each excited supermode, Cs,n is the coefficient of wave function in the nth waveguide of the s-order supermode [12]. Cs , n sin
ns N 1
n 1, 2,3,
,N
(3)
The input field can be expressed by { 1 , 2 , 3 , 4 , 5 }, which n is the amplitude value of input fields in the nth waveguide. According to Eq. (1) and Eq. (2), the relations between as and the input field can be obtained, which can be written as 1 C1,1 C 2 1,2 5 C1,5
C5,1 a1 C5,2 a2 C5,5 a5
C2,1 C2,2 C2,5
(4)
Introducing n and Cs,n into Eq. (4), we can obtain the value of as and the field distribution theoretically[16]. Eq. (4) shows that different incident fields { 1 , 2 , 3 , 4 , 5 } can excite different weighting factor of supermodes, which means the superposition field of SPPs supermodes is different. So we can choose appropriate field distributions in the MWGA by incident fields. We numerically simulate the propagation behavior of SPPs by the commercial software EastFDTD, which is based on FDTD method. The grid size is dx=dz=2nm and the time increment is Δt=Δs/2c, where c is the velocity of light in vacuum. Around the computational domain, a perfectly matching layer is adopted to absorb the outgoing electromagnetic wave. The simulated field distribution is presented in Fig. 1(b)-(d), where the amplitude values of input fields, { 1 , 2 , 3 , 4 , 5 }, are {1, 0, 0, 0, 0}, {0, 0, 0, 0, 1}, {1, 0, 0, 0, 1}, respectively. By the theory of SPP supermodes mentioned in Ref. 2
15 and Ref. 16, the field distributions in Fig. 1(b)-(d) can be interpreted reasonably, which are the result of superposition of SPPs supermodes. By applying the method of Ref. 15, the field distributions of the SPPs supermodes are shown in Fig. 2 (a) – (e), which correspond to the 1st–5th supermodes. When one or more input fields are incident on waveguides of the MWGA, the supermodes are excited [15,16]. The total field intensity distribution is formed by the superposition of these supermodes, as shown in Fig. 1(b)-(d). In other words, Fig. 1(b)-(d) are the results of the superposition of the 1st–5th supermodes with different weight coefficient [15,16]. It can be seen from Fig. 1(b) and Fig. 1(c) that the input fields can propagate to adjacent waveguides with the increase of transmission distance. Fig. 1(d) is the superposition of Fig. 1(b) and Fig. 1(c), which the maximum value of transmission field appears at about z=0.68μm indicated by the green dashed line.
Fig.1 (a) The MWGA of five adjacent two-dimensional metal waveguides, which composed of Ag layers and air layers. The numerical simulation results of field distributions in the MWGA, which the input fields are located at (b) the 1st waveguide, (c) the 5th waveguide, (d) the 1st and 5th waveguides.
Fig.2 The field distributions of individual supermodes in the MWGA. (a) The 1st supermode; (b) The 2nd supermode; (c) The 3rd supermode; (c) The 4th supermode; (e) The 5th supermode.
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3. Design and simulation results According the field distributions in Fig. 1(b)-(d), OR gate can be obtained if we set the output port at z=0.68μm in the 3rd waveguide. The scheme was shown in Fig. 3(a), where the 1st, 2nd, 4th, and 5th waveguides are closed by Ag layers at the end of the MWGA and only the 3rd waveguide is open. The 1st and 5th waveguides are input ports, which are labeled with A and B. The end of the 3rd waveguide is the output port labeled with O. By applying the method of Ref. 15, the length of waveguides is choose to L1=0.68μm, which is determined by the field distributions of the superposition of SPPs supermodes in Fig. 1(b)-(d).
Fig.3 (a) The scheme of OR gate, L1=0.68μm. The numerical simulation results of field distributions, which the input fields are located at (b) the 1st waveguide, (c) the 5th waveguide, (d) the 1st and 5th waveguides. The simulated results are shown in Fig. 3(b)-(d), where the input signals are incident from B port, A port, A and B ports, respectively. By the normalization, the amplitude of input signal is 1. In Fig. 3(b), A=1, B=0, the amplitude value of output signal is 0.45, which corresponds to O=1. Then the logic state of “0 OR 1=1” is obtained. Fig. 3(c) is similar to Fig. 3(b), which corresponds to the logic state of “1 OR 0=1”. In Fig. 3(c), the amplitude value of output signal is 0.90, which corresponds to the logic state of “1 OR 1=1”. The operating principle of the OR gate is shown in Table1. Table 1 The operating principle of the OR gate amplitude of
amplitude of
input field
output field
logical output
intensity contrast ratio (dB)
Port A
Port B
Port O
OR
0
0
0
0
0
1
0.45
1
1
0
0.45
1
1
1
0.90
1
4
>20
Similarly, NOT gate can be obtained according the field distribution in Fig. 1(b) and Fig. 1 (d). The scheme was shown in Fig. 4(a), where port A is the input port and port B is the control port. The output port O is at the end of the 1st waveguide. The length of waveguides is the same with Fig. 4(a), L1=0.68μm. The amplitude of control signal is the same with input signal. The simulated results are shown in Fig. 4(b) and(c), which the input port is off and on, respectively. By defining an appropriate threshold value, the logic gates of “0” and “1” can then be realized. In Fig. 4(b), the amplitude value of output port is 0.14. In Fig. 4(c), the amplitude of output port is 0.028. We set 0.1 for the threshold value (0.028<0.1<0.14), which the signal is “0” when the amplitude value is no more than 0.1 and the signal is “1” when the amplitude value is more than 0.1. By the definition of threshold value, Fig. 4(b) (0.14>0.1) is corresponding to the logic state of “NOT 0=1” and Fig. 4(c) (0.028<0.1) is corresponding to the logic state of “NOT 1=0”. NOT operation is achieved. The operating principle of the NOT gate is shown in Table2. The intensity contrast ratio between the output logic “1” and “0” is 13.98dB, which is calculated from 10log(I1/I0). (I1 and I0 are the signal intensities of logic “1” and “0”, respectively.) It should be pointed out that the signal strength of “1” is weak (the amplitude value is 0.14) and the reflection rate of NOT gate is high. This is because the field strength of output port is weak by the superposition of SPPs supermodes [15].
Fig.4 (a) The scheme of NOT gate, L1=0.68μm. The numerical simulation results of field distributions, which the input fields are located at (b) the 5th waveguide, (c) the 1st and 5th waveguides.
Table 2 The operating principle of the NOT gate amplitude of
Control
amplitude of
input field
port
output field
Logical Output
Port A
Port B
Port O
NOT
0
1
0.14
1
1
1
0.028
0
5
intensity contrast ratio (dB) 13.98
In order to achieve AND logic functions, the input fields are placed in the 1st, 3rd, and 5th waveguides in the MWGA. Four different combinations of input fields are employed: {0,1,0}, {1,1,0}, {0,1,1}, {1,1,1}, which correspond to the amplitudes of input fields in the 1st, 3rd, and 5th waveguides. The field distributions can be interpreted by the superposition of SPP supermodes [15,16]. The simulated field distribution is presented in Fig. 5(a) - (d). By observing the field distribution in Fig. 5(a) - (d), we notice that when z=0.38μm (green dashed line), the amplitude of the 3rd waveguide in Fig. 5(a) is almost zero and the amplitudes of the 3rd waveguide in Fig. 5(b) - (d) are significantly stronger. If setting the output port at the position of z=0.38μm in the 3rd waveguide, AND gate can be obtained. The scheme was shown in Fig. 6(a), where L2=0.38μm. Port A and B are input ports. Port C is the control port and Port O is the output port. The simulated fields are shown in Fig. 6(b)-(e), which the amplitude values of output ports are 0.086, 0.12, 0.12, and 0.35. If setting 0.12 for the threshold value, which the signal is “0” when the amplitude value is no more than 0.12, AND operation can be achieved. The operating principle of the AND gate is shown in Table3. The intensity contrast ratio between the output logic “1” and “0” is 9.3dB.
Fig.5 The numerical simulation results of field distributions in the MWGA, which the input fields are located at (a) the 3rd waveguide (b) the 1st and 3rd waveguides, (c) the 3rd and 5th waveguides, (d) the 1st, 3rd and 5th waveguides.
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Fig.6 (a) The scheme of AND gate, L2=0.38μm. The numerical simulation results of field distributions, which the input fields are located at (a) the 3rd waveguide (b) the 1st and 3rd waveguides, (c) the 3rd and 5th waveguides, (d) the 1st, 3rd and 5th waveguides.
amplitude of input
Table 3 The operating principle of the AND gate Control port amplitude of Logical
field
output field
Output
Port A
Port B
Port C
Port O
AND
0
0
1
0.086
0
0
1
1
0.12
0
1
0
1
0.12
0
1
1
1
0.35
1
intensity contrast ratio (dB) 9.3
To realize XOR logic functions, the input fields are placed in the 2nd and 4th waveguides. The simulated field distributions are presented in Fig. 7(a) - (d). In Fig. 7(a), the amplitude of input field in the 2nd waveguide is 1 and the amplitude in input field of the 4th waveguide is 0. In Fig. 7(b), the amplitude of input field in the 2nd waveguide is 0 and the amplitude of input field in the 4th waveguide is 1. In Fig. 7(c), the amplitudes of input fields are both 1. When z=0.32μm (green dashed line), the amplitude of the 2nd waveguide in Fig. 7(c) is almost zero and the amplitudes of the 2nd waveguide in Fig. 7(a) - (b) are significantly stronger. If we set the output port at z=0.32μm in the 2nd waveguide, XOR gate can be obtained. The scheme was shown in Fig. 8(a), where L3=0.32μm. Port A and B are input ports and Port O is the output port. The simulated field distributions are shown in Fig. 8(b)-(d), which the amplitude values of output ports are 0.17, 0.16, and 0.05. If setting 0.05 for the threshold value, which the signal is “0” when the amplitude value is no more than 0.05, AND operation can be achieved. The operating principle of the XOR gate is shown in Table4. The intensity contrast ratio between the output logic “1” and “0” is 10.1dB.
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Fig.7 The numerical simulation results of field distributions in the MWGA, which the input fields are located at (a) the 2nd waveguide, (b) the 4th waveguide, (c) the 2nd and 4th waveguides.
Fig.8 (a) The scheme of XOR gate, L3=0.32μm. The numerical simulation results of field distributions, which the input fields are located at (b) the 2nd waveguide, (c) the 4th waveguide, (d) the 2nd and 4th waveguides.
Table 4 The operating principle of the XOR gate amplitude of input field
amplitude
of
Logical
intensity
output field
Output
contrast ratio
Port A
Port B
Port O
XOR
0
0
0
0
1
0
0.17
1
0
1
0.16
1
1
1
0.05
0
8
(dB) 10.1
4. Conclusion We propose new schemes of
MWGAs. By applying the method of Ref. 15, the
field distributions of the SPPs supermodes in MWGAs are obtained. According to the field distribution, OR, AND, NO, and XOR logic functions can be achieved by choosing the appropriate length of MWGAs, specific input fields, output ports and suitable threshold value. The lengths of waveguides are different for different gates: L1=0.68μm is for OR gate and NOT gate; L2=0.38μm is for AND gate; L3=0.32μm is for XOR gate. The intensity contrast ratios between the output logic “1” and “0” are 9.3dB -13.98dB in these
. OR gate and NOT gate can be realized in the same MWGA
choosing different input waveguides. Due to its simple structure and controllability, the MWGAs can provide a new method for logic functions in photonic integrated circuits. It should be pointed out that these schemes are not unique. If the number of waveguides in MWGAs is increased, the field distributions will be changed and the waveguide lengths, input fields, output ports and suitable threshold value need to be reselected. By a similar analysis, OR, AND, NO, and XOR logic gates can also be obtained. Acknowledgment This work is supported by Doctoral Foundation of Henan University of Technology (2016BS010), the Fundamental Research Funds for Henan Provincial Colleges and Universities in Henan University of Technology (2016QNJH13), the Henan Province Education Department Natural Science Research Programs (17A140006), and the Natural Science Foundation of Henan Province (182300410195). References 1. H. Wei, Z. Li, X. Tian, Z. Wang, F. Cong, N. Liu, S. Zhang, P. Nordlander, N. J. Halas, H. Xu, uantum Dot-Based Local Field Imaging Reveals Plasmon-Based Interferometric Logic in Silver Nanowire Networks, Nano Lett. 11 (2011) 471. 2. H. Wei, Z. X. Wang, X. R. Tian, M. Kall, H. X. Xu, Cascaded logic gates in nanophotonic plasmon networks, Nat. Commun. 2 (2011) 387. 3. Y. Fu, X. Hu, C. Lu, S. Yue, H. Yang, Q. Gong, All-Optical Logic Gates Based on Nanoscale Plasmonic Slot Waveguides, Nano Lett. 12 (2012) 5784. 4. D. Pan, H. Wei, H. Xu, Optical interferometric logic gates based on metal slot waveguide network realizing whole fundamental logic operations, Opt. Express 21 (2013) 9556. 5. M. Ota, A. Sumimura, M. Fukuhara, Y. Ishii, M. Fukuda, Plasmonic-multimode interference-based logic circuit with simple phase adjustment. Sci. Rep. 6 (2016) 24546 6. Y. Bian, Q. Gong, Compact all-opticalinterferometriclogicgatesbased on one-dimensional metal– insulator–metal structures. Opt. Commun. 313 (2014) 27 7. L. Cui, L. Yu, Multifunctional logic gates based on silicon hybrid plasmonic waveguides. Mod. Phys. Lett. B 32 (2018) 1850008 8. N. Gogoi , P. P. Sahu, All-optical tunable power splitter based on a surface plasmonic two-mode interference waveguide, Appl. Opt. 57 (2018) 2715. 9. P. P. Sahu, Theoretical Investigation of All optical switch based on compact surface plasmonic two mode interference coupler, J. Lightw.Technol. 34 (2016) 1300. 10. N. Gogoi , P. P. Sahu, All optical compact surface plasmonic two mode interference device for optical logic gates, Appl. Opt. 54(2015) 1051.
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