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A low-power all optical decoder based on photonic crystal nonlinear ring resonators
Accepted Manuscript Title: A Low-Power All Optical Decoder Based on Photonic Crystal Nonlinear Ring Resonators Authors: T. Daghooghi, M. Soroosh, K. Ansari-Asl PII: DOI: Reference:
S0030-4026(18)31239-7 https://doi.org/10.1016/j.ijleo.2018.08.090 IJLEO 61387
To appear in: Received date: Revised date: Accepted date:
31-1-2018 18-7-2018 23-8-2018
Please cite this article as: Daghooghi T, Soroosh M, Ansari-Asl K, A Low-Power All Optical Decoder Based on Photonic Crystal Nonlinear Ring Resonators, Optik (2018), https://doi.org/10.1016/j.ijleo.2018.08.090 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.
A Low-Power All Optical Decoder Based on Photonic Crystal Nonlinear Ring Resonators T. Daghooghi, M. Soroosh*, K. Ansari-Asl
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Department of Electrical Engineering, Shahid Chamran University of Ahvaz, Iran *Corresponding Author Email: [email protected]
Abstract: In this paper, an all-optical 2-to-4 decoder based on photonic crystal nonlinear ring resonators is proposed. The designed decoder has one enable port which can control decoding operation. Using nano-crystal ring resonators, the threshold switching intensity is decreased to 13 W/µm2. The maximum frequency and total size of the device are
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obtained to be 160 GHz and 16×23 µm2 respectively. All output characteristics of the proposed decoder seem to be beneficial for being employed in optical integrated circuits.
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Keywords: Kerr Effect, Optical Decoder, Photonic Crystal, Ring Resonator.
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1. Introduction
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Optical devices play significant roles in communication networking, optical computing and signal processing because of their high operation speed, low signal distortion, low material usage, small
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size, low cost and more importantly immunity to electrical interference, in comparison with conventional electrical devices [1-3]. Photonic crystals (PhCs) are periodic dielectric structures
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which can guide and control the propagation of light. Integration possibility and scalability make PhCs as interesting structures for designing all-optical devices [4]. In recent years, some PhC-
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based optical devices such as optical add/drop filters [5-8], sensors [3,9-10], logic gates and switches [11-23], demultiplexers [24-26], analog to digital converters [27-30], digital to analog
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converters [31], encoders [32-35], adders [36-37] and power splitters [38-40] have been proposed. In optical systems, the number of users sharing one common bus has been increasing and as a result, the receiver should be able to choose appropriate data. Digitizing optical circuits has obliged researchers to design optical logic gates being able to control output ports depending on input states, which is called decoder. Several approaches have been done and various all-optical decoders have recently been proposed [41-45]. The fundamental element in all-optical decoders is 1
an optical switch, capable of controlling output signal via its input and bias signals. Switching operation is accomplished using Kerr nonlinear effect in photonic crystals [46-47]. The first concept in designing all optical decoder was proposed and simulated by Alipour-Banaei et.al in 2014 [41]. Their structure had two lattice constants, one for the main structure and one for the ring resonators. In this structure, the minimum radius of rods is about 120 nm and the proposed decoder
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may not be easily fabricated. In addition, the bias and input intensities are needed for switching operation is 1KW/µm2, which causes high power consumption. Moniem [42] proposed another structure for 2-to-4 decoder using five ring resonators, two T-shape and four Y-shape splitters. Although the decoder was correctly performing at speed of 200 GHz, the structure was too complicated and the radius of rods at splitters were about 40 nm which limits its fabrication possibility. An all-optical decoder was presented by Mehdizadeh et.al at 2015 [43]. Their structure
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consist of five ring resonators and needs three input ports except for bias signal. According to the
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reported results, the minimum intensity needed for switching operation was 2KW/µm2. Another 2-to-4 decoder presented by Mehdizadeh et.al in 2017 [44]. They studied the properties of cavities
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in the decoding operation. Their proposed structure had one enabling port which was not included
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in the previous works. Despite all advantages of their study, the maximum switching frequency of the structure was 20 GHz. Recently, an integrated all-optical decoder has been proposed by
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Khosravi and Zavvari [45]. Three ring resonators have been organized in the manner that three
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input ports were needed. The reported numerical analysis has shown that the normalized power levels for 0 and 1 logics are 0.18Pin and 0.4Pin respectively which gives narrow margin and may
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cause serious problems while coupled to other devices. Investigating all discussed researches, it can be inferred that using ring resonator is beneficial due
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to its high quality factor and high coupling efficiency. The Coupled length and resonance phenomenon in ring resonators assist one to obtain high optical coupling. Amplifying optical signals due to resonance in the ring can decrease the optical power required at input ports in
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comparison with defect based structures. As a result, in this paper, a new structure for all-optical decoder is designed based on 2D square lattice photonic crystals. The switching performance is implemented by using nonlinear ring resonators. Considering high input intensities inevitable effects, silicon nano-crystal ring resonator is used in order to decrease input optical intensity [3044]. In order to control the decoding operation, one enabling port is added to the structure. Propagation of light through the structure is simulated using finite difference time domain (FDTD) 2
method. Time and power analysis have been done and output characteristics of the proposed decoder have been calculated and reported in details. The steady-state time and normalized power levels of the output ports are two important factors because the device should be coupled to other devices in optical integrated circuits (OICs).
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This paper is organized as follows; two structures for optical switch are compared in the next section, a 2-to-4 optical decoder is proposed and finally, the simulation results and output calculated characteristics are presented.
2. Optical switch
The fundamental structure is 31×31 square lattice of silicon rods in air. The refractive index of the
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dielectrics is 3.48 and the radius of rods are 0.19a, where a is the lattice constant. In 2D photonic
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crystal based structures, the height of the dielectric rods in air is typically assumed to be 0.2a [48]. To have the optical confinement in third dimension, rods are placed between two layers (or rods)
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with low refractive index [48]. According to the total internal reflection (TIR), one can confine the
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input signal in two dimensions. We use plane wave expansion (PWE) method to calculate the band structure. The band structure of the proposed PhC includes two bandgaps at TE mode. According
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to the lattice constant of 630 nm, the first gap is equal to 1480nm≤ λ ≤2180nm and seems to be
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suitable for optical communication systems. To form the optical switch, input and output ports were created by removing rows of rods in both
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x and z directions. The designed structure has one enabling port (E) which enables the structure to operate as an optical switch. Two ring resonators are placed in center of the switch as shown in
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Fig. 1. Since the optical switch is a nonlinear device, the optimum optical intensity needed for switching application is an important issue. The refractive index of materials (n) depends on the light intensity and is known as Kerr effect. This effect can be used in ring resonators for achieving
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switching applications. Generally, n=n1+n2I is defined for Kerr effect where n1 and n2 are linear refractive index and nonlinear coefficient respectively and I is the light power intensity [49]. It can be inferred that the needed input intensity for switching depends on the nonlinear coefficient of the ring resonator. In the majority of reviewed papers, the chalcogenide glass is used instead of silicon because of higher nonlinear refractive index [50]. In the proposed switch, silicon nanocrystal rods have been used for ring resonators in which the linear refractive indices are 1.5 [4]. 3
But the most important advantage of using this ring is its nonlinear coefficient. According to the Kerr effect, the greater nonlinear coefficient, the lower input intensity needed for switching application. The nonlinear coefficient of the silicon nano-crystal and chalcogenide glass are 10-16 m2/W and 9×10-17 m2/W, respectively [4,50]. In order to compare the presented switch with that of previously reported, two structures for the optical switch are introduced in the following.
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Structure 1 includes 7×7 square-shaped ring of silicon nano-crystal which is shown in yellow in Fig. 1.a. and the radii of rods are the same as the fundamental structure. The other structure as shown in Fig. 1.b is formed by omitting 24 rods around the center of the switch, which is shown in blue for both structures. In the structure 2, 9×9 square-shaped ring of chalcogenide glass is placed, which is coloured in green. In both structures, for better coupling, extra rods are added at
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the corners.
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Fig. 1. Two proposed structures for optical switch, (a) structure 1, and (b) structure 2.
According to Kerr effect, threshold optical intensity needed for switching application should be
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realized. Different input intensities are scanned and output power levels at both ports are simulated. The transmission ratio versus input intensity for both structures are presented in Fig. 2. Ratio of output to input optical intensities is defined as the transmission ratio of the switch [51]. As shown
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in Fig. 2(a), the threshold intensity needed for switching effect is about 13 W/μm2 for the first structure while it is increased to 1KW/μm2 in the second structure.
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(a)
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Fig. 2. Transmission ratio versus input intensity for two proposed switches, (a) structure 1, and (b) structure 2.
It is clear that, when port E is OFF, none of the output ports can be ON either input A is ON or
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OFF. In contrast, if port E is ON, or in the other words, enabling signal is coupled through port E,
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output ports can be ON depending on input A. In case logic 0 (or A=0), enable signal coupled
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through the ring resonator will appear through port O1. If both enable and input signals are coupled through ring resonator (or A=1), the resonance wavelength will be altered due to Kerr effect and
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refractive index modification. As a result, enable signal propagates through port O2. The electric field distribution for both structures 1 and 2 are shown in Fig. 3 and Fig. 4 respectively. The
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diagrams are obtained by solving Maxwell’s equations using FDTD method. In this method, two
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stability conditions must be carefully studied. First is known as the Courant condition and in twodimensional simulation, it is described as follows [52]: 𝟏 √(
𝟏 𝟏 + ) ∆𝒙𝟐 ∆𝒛𝟐
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𝒄∆𝒕 <
(1)
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where c is the speed of light in vacuum, Δt is the time step, and Δx and Δz are mesh sizes in both directions. The second condition is about the grid spacing that should be less than λ/10, where λ is
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the wavelength.
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Fig. 3. The electric field distribution into structure 1 for (a) A=0 and (b) A=1.
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Fig. 4. The electric field presentation for structure 2 in two cases (a) A=0 and (b) A=1.
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Although switching operation of both structures are the same, there are major differences in power and time analysis. Time response simulation for the proposed switches are depicted in Fig. 5 and
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Fig. 6. For better evaluation, output characteristics of them are summarized in table 1. The maximum steady-state time for structure 2 is about 2 ps while it increases to 4 ps for structure 1. Steady state time is the time that output signal oscillates within a certain error band. In the majority
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of reported oscillation systems, error bands 2% and 5% are concerned [53]. In this paper, error band 5% is selected. The normalized power intensity levels for logics 0 and 1 in structure 1 are equal to 0.05 and 0.86 respectively while the margins in structure 2 are obtained to 0.2 and 0.79.
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Fig. 5. The normalized output power intensity for structure 1, (a) A=0 and (b) A=1.
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Fig. 6. The normalized power intensity at ports O1 and O2 for structure 2, (a) A=0 and (b) A=1.
State
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Normalized power level
Steady-state time (ps)
Input intensity (W/µm2)
Logic 0
Logic 1
A=0
0.04
0.96Pin
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0
A=1
0.05
0.86Pin
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13
A=0
0.08
0.92Pin
2
0
A=1
0.2
0.79Pin
2
1500
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Structure
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Table 1. The calculated characteristics of two proposed structures.
To have the instructive interferences and high optical coupling between waveguide and resonator three aspects should be considered: coupling length, distance and effective refractive index of resonator. The close distance between them and using the desired nonlinear materials for rods 7
result in enhancing optical coupling for both resonant ring and cavity. Coupling length of the ring is an efficient parameter to increase the quality factor. It has been demonstrated that if the coupling length is increased the quality factor can be enhanced [54]. This issue can encourage one to use the resonant ring than the resonant cavity. So, one can design high quality factor ring resonators for dropping applications. Quality factor indicates rate of energy loss of the resonator and is
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defined as Q=λ/Δλ, where Δλ is the resonance bandwidth [55]. Numerical simulations have shown that quality factor of structure 1 is 1065 while it is decreased to 322 for structure 2.
In nonlinear optical devices, high input intensities may impose inevitable deconstructive effects. So decreasing optical intensity will improve the application of these devices. The most important advantage of structure 1 in comparison to another is the minimum power needed for switching application. According to table 1, using silicon nano-crystal for ring resonator, the input and bias
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powers are decreased from 1500 W/µm2 to 13 W/µm2. So, we use the structure 1 for designing the
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proposed decoder.
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3. All-optical 2-to-4 decoder
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In the proposed structure, four ring resonators are used, as shown in Fig. 7. It has one enable port labelled as port E, two input ports labelled as port X and Y and four output ports named O0, O1,
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O2, and O3.
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At first, electric field distribution for four decoding states should be investigated. The FDTD simulation results for the proposed decoder are presented in Fig. 8. Four decoded cases as
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summarized in the truth table 2, are described as follows:
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Case Ⅰ (X=Y=0): the enable signal is coupled to rings 1 and 2, and then output O0 will be on. Case Ⅱ (X=0, Y=1): the enable signal is coupled to ring 1 but it will not be coupled to ring 2
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because Y value is equal to logic 1. Therefore, output O1 will be on. Case Ⅲ (X=1, Y=0): the enable signal is coupled to ring 3 and 4 and output O2 will be on. Case Ⅳ (X=Y=1): because X=Y=1, the enable signal cannot be coupled to neither ring 1 nor ring 4. So output signal will appear at port O3. It should be stated that four discussed cases are true if enable port is ON. On condition that port E=0, input signals X and Y will not couple through their designed direction and decoding operation will not be reached. 8
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Fig. 7. The schematic of the proposed structure for 2-to-4 decoder.
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Fig. 8. Electric field distribution of the proposed decoder (a) X=Y=0, (b) X=0 Y=1, (c) X=1 Y=0, and (d) X=Y=1.
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The proposed structure can be performed as all-optical decoder, but it should be coupled to other devices while integrating into optical circuits and systems. So, output characteristics of the decoder should be investigated. Time response and normalized light power at output ports are shown in Fig. 9. For better evaluation, power levels of four outputs and steady-state time
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of each state are summarized in table 2.
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Fig. 9. The normalized power intensity versus time for (a) X=Y=0, (b) X=0 Y=1, (c) X=1 Y=0, and (d) X=Y=1. Table 2. The truth table for the proposed decoder.
Inputs Y 0 1 0 1
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X 0 0 1 1
O0 1 0 0 0
Outputs Logic O1 0 1 0 0
O2 0 0 1 0
O3 0 0 0 1
O0 86 5 0.01 5
Normalized power (%) O1 O2 3.8 0.01 68 10 7 63 0.01 4
O3 1.9 1.2 2 63
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In multiple coupling, output and input power levels for logics 0 and 1 are extremely needed. Output power margins for both 0 and 1 should be carefully investigated. Other output characteristics of the proposed decoder including contrast ratio, cross-talk, and insertion loss should be carefully calculated [56-57]. Contrast ratio, defined as Plogic1/Plogic0, indicates the power margin between logics 1 and 0. The optical insertion loss is one of the most challengeable characteristics for low power devices which is defined by 10log((Pin-Pout)/Pin). 10
The other dominant parameter in multiple port optical devices is cross-talk, which shows the effects of ports on each other and defined as 10log(Plow/Phigh) where Plow and Phigh are the lowest and the highest power levels obtained at output ports for each logic state. The above mentioned characteristics are reported in table 3. As it can be concluded, the minimum contrast ratio of the proposed decoder is about 7 and the maximum one is more than 28.7 and the insertion loss is varied from -4.31 dB to -8.54 dB. The maximum cross-talk is between -17.53dB and -39.34dB. In this structure, threshold power intensity of ring resonators
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for switching is 13 W/µm2, while in the most of previous researches the threshold varies from 1 KW/µm2 to 2 KW/µm2 [41, 43, 45]. Although the operation speed of the proposed decoder
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is nearly the same as other reviewed researches, low power intensity of bias and input ports
can prevent other inevitable nonlinear optical properties occur at high input intensities. Low insertion loss at output ports is beneficial while integrating optical devices. In addition, power margins of logics 0 and 1 are large enough and as a result possible misunderstandings can be
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prevented, especially in multiple couplings.
Insertion loss (dB) -8.54 -4.95 -4.31 -4.31
Maximum crosstalk (dB) -39.34 -17.53 -37.99 -37.99
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contrast ratio 28.7 6.8 9 12.6
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Output ports O0 O1 O2 O3
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Table 3. The calculated characteristics of the proposed decoder. Steady-state time (ps) 6.3 3.96 6.4 4.2
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As a final analysis, periodic pulses are launched at input ports A and B then normalized output powers are investigated in Fig. 10. As it is shown, all four output ports are ON or OFF
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depending on input logic states. The pulse width of input signals is 8 ps. Since the maximum steady-state time of the decoder is about 6.3ps, it will be guaranteed that the pulse response of all states will be correct. Data rate is referred to the speed at which data is transferred and can
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be calculated using the time response of the output signal, as described in [58-59] in details. Data rate is the reciprocal of the steady state time. So, the maximum data rate is calculated
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about 160 Gb/s.
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Fig. 10. The normalized power intensity for input pulse with 8 ps and different states A=0 B=0, A=0 B=1,
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A=1 B=0, A=B=1 at (a) port O0 (b) port O1 (c) port O2 (d) port O3, respectively.
For better evaluation, all mentioned output characteristics are compared with other previous
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researches and results are presented in table 4. Since some of the features were not reported, the character “–” is placed instead. As it can be inferred, the insertion loss and input intensity
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of the proposed decoder is sufficiently decreased in comparison with other pervious researches [42-45]. The operation speed of the proposed decoder is greater than that of reported in Ref.
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[44]. Although the operation speed is not improved in comparison with Ref. [42], the total size of the proposed decoder is definitely smaller than the size of the discussed decoder [42]. Table 4. Comparison of the obtained results in this work with other works. Input intensity (KW/µm2)
Insertion loss (dB)
Size (µm2)
Ref [42]
160
-
-
40×38
Ref [44]
2
0.02
-3.42
-
Ref [45]
-
1
-2.20
-
This work
160
0.015
-4.31
16×23
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Operation speed (GHz)
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Considering some fabricated devices [60-65], semiconductors fabrication confinements are concerned. The minimum diameter of the rods and lattice constant of the fundamental structure are 240 nm and 630 nm, respectively. It can be concluded that the proposed decoder is potentially applicable in real time implementations.
4. Conclusion
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High-speed performance, low power consumption, and suitable output power margins are three important factors in evaluating optical devices. Considering all mentioned issues, in this paper,
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an integrated all-optical 2-to-4 decoder was proposed. Numerical simulation results have been
done and output diagrams were presented. In order to reduce the input power intensity, nanocrystal rings, which have high Kerr coefficient, are placed in the center of all-optical switches. Thus, the required optical intensity was reduced to 13 W/µm2. The operation speed of the
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decoder is about 160 GHz. The worst output power levels for logics 0 and 1 are 0.1Pin and 0.63Pin, respectively. The maximum insertion loss is -4.31dB, which occurs in two cases. The
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maximum calculated cross-talk for case II is -17.53 dB. Since the total size of the structure is
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16 × 23 µm2, it can be a suitable candidate for compact optical circuits. Taking to account all
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above characteristics, the proposed decoder is capable of employing as a part of all-optical integrated circuits.
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[32] T. A. Moniem, All-optical digital 4×2 encoder based on 2D photonic crystal ring resonators, Journal of Modern Optics 63 (2015) 735-741. [33] I. Quahab Rafah, A novel all optical 4×2 encoder switch based on photonic crystal ring resonators, Optik 127 (2016) 7835-7841. [34] M. Hassangholizadeh-Kashtiban, R. Sabbaghi-Nadooshan, H. Alipour-Banaei, A novel all optical reversible 4×2 encoder based on photonic crystals, Optik 126 (2015) 2368-2372. [35] F. Mehdizadeh, M. Soroosh, H. Alipour-Banaei, A proposal for 4-to-2 optical encoder based on photonic crystals, IET Optoelectronics 11 (2017) 29-35. [36] M. Neisy, M. Soroosh, K. Ansari-asl, All optical half adder based on photonic crystal resonant cavities, Photonic Network Communications 35 (2018) 245-250. [37] F. Cheraghi, M. Soroosh, G. Akbarizadeh, An ultra-compact all optical full adder based on nonlinear photonic crystal resonant cavities, Superlattices and Microstructures 113 (2018) 359-365. [38] H. Razmi, M. Soroosh, Y. Seifi-Kavian, A new proposal for ultra-compact polarization independent power splitter based on photonic crystal structures, Journal of Optical Communications, (2017) https://doi.org/ 10.1515/joc-2017-0021. [39] R. Chavidel, A. Andalib, H. Alipour-Banaei, A new design of photonic crystal filter and power splitter based on ring resonators, Journal of Intelligence in Electrical Engineering 2 (2013) 5-8. [40] A. Tavousi, M. A. Mansouri-Birjandi, Study on the similarity of photonic crystal ring resonator cavity modes and whispering-gallery-like modes in order to design more efficient optical power dividers, Photonic Network Communications 32 (2016) 160-170. [41] H. Alipour-Banaei, F. Mehdizadeh, S. Serajmohammadi, M. Hassangholizadeh-Kashtiban, A 2*4 all optical decoder switch based on photonic crystal ring resonators, Journal of Modern Optics 62 (2014) 430-434. [42] T. A. Moniem, All optical active high decoder using integrated 2D square lattice photonic crystals, Journal of Modern Optics 62 (2015) 1643-1649. [43] F. Mehdizadeh, M. Soroosh, H. Alipour-Banaei, A novel proposal for optical decoder switch based on photonic crystals ring resonators, Optical and Quantum Electronics 48 (2016) 20-29. [44] F. Mehdizadeh, H. Alipour-Banaei, S. Serajmohammadi, Study of the role- of non-linear resonant cavities in photonic crystal-based decoder switches, Journal of Modern Optics 64 (2017) 1233-1239. [45] Khosravi Sh., Zavvari M. (2017). Design and analysis of integrated all-optical 2×4 decoder based on 2D photonic crystals, Photon Netw. Commun. https://doi.org/10.1007/s11107-017-0724-x [46] M. Tajaldini, M. Jafri, An optimum multimode interference coupler as an all-optical switch based on nonlinear modal propagation analysis, Optik 126 (2015) 436-441. [47] S. Serajmohammadi, H. Alipour-Banaei, F. Mehdizadeh, All optical decoder switch based on photonic crystal ring resonators, Optical and Quantum Electronics 47 (2015) 1109-1115. [48] S. G. Johnson, Photonic Crystals: from theory to practice, Doctoral thesis at Massachusetts institute of technology (2001). [49] G. Fibich, A. L. Gaeta, Critical power for self-focusing in bulk media and in hallow waveguides, Optics Letters 25 (2000) 335-337. [50] K. Ogusu, J. Yamasaki, Sh. Maeda, Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching, Optics Letters 29 (2004) 265-267. [51] P. M. Costas and M. Soukoulis, Wave Propagation; From Electrons to Photonic Crystals and LeftHanded Materials, Princeton University Press, 2008. [52] DM Sullivan, “Electromagnetic simulation using the FTDT method”, IEEE press, 2013. [53] T. T. Tay, I. Mareels and J. B. Moore, High performance control, Birkhäuser (1997).
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[54] D. Goldring, U. Levy and D Mendlovic, Highly dispersive micro-ring resonator based on one dimensional photonic crystal waveguide design and analysis, Optics Express 15 (2007), 3156-3168. [55] A. Salmanpour, Sh. Mohammadnejad, A. Bahrami, Photonic crystal logic gates: an overview, Optical and Quantum Electronics 47 (2015) 2249-2275. [56] Z. Chen, Z. Li, B. Li, A 2-to-4 decoder switch in SiGe/Si multimode interference, Optics Express 14 (2006) 2671–2678. [57] S. Zhang, Traveling-Wave Electroabsorption Modulators, PhD Thesis, University of California, Santa Barbara, 1999.
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[58] H. Veenstra and J. R. Long, Circuit and Interconnect Design for RF and High Bit-Rate Applications, Springer Science (2008). [59] R. M. Younis, N. F. Areed, S. A. Obayya, Fully Integrated AND and OR Optical Logic Gates, IEEE Photonics Technology Letter 26 (2014) 1900–1903. [60] L. O’Faolain, T. P. White, D. O’Brien, X. D. Yuan, M. D. Settle, and T. F. Krauss, Dependence of extrinsic loss on group velocity in photonic crystal waveguides, Optics Express 15 (2007) 13129– 13138. [61] D. M. Beggs, L. O’Faolain, and T. F. Krauss, Accurate determination of the functional hole size in photonic crystal slabs using optical methods, Photonics Nanostructure: Fundamentals and applications, 6 (2008) 213–218. [62] A. Spott, T. Baehr-Jones, R. Ding, Y. Liu, R. Bojko, T. O’Malley, A. Pomerene, C. Hill, W. Reinhardt, M. Hochberg, Photo-lithographically fabricated low-loss asymmetric silicon slot waveguides, Optics Express 19 (2011) 10950-10958. [63] S. Rahimi, A. Hosseini, X. Xu, H. Subbaraman, R. T. Chen, Group-index independent coupling to band engineered SOI photonic crystal waveguide with large slow-down factor, Optics Express 19 (2011) 21832-21841. [64] A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Lukyanchuk, Optically resonant dielectric nanostructures, Science 354 (2016) 846. [65] U. Zywietz, A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, Laser printing of silicon nanoparticles with resonant optical electric and magnetic responses, Nature Communications 5 (2014) 3402.
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S0030-4026(18)31239-7 https://doi.org/10.1016/j.ijleo.2018.08.090 IJLEO 61387
To appear in: Received date: Revised date: Accepted date:
31-1-2018 18-7-2018 23-8-2018
Please cite this article as: Daghooghi T, Soroosh M, Ansari-Asl K, A Low-Power All Optical Decoder Based on Photonic Crystal Nonlinear Ring Resonators, Optik (2018), https://doi.org/10.1016/j.ijleo.2018.08.090 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.
A Low-Power All Optical Decoder Based on Photonic Crystal Nonlinear Ring Resonators T. Daghooghi, M. Soroosh*, K. Ansari-Asl
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Department of Electrical Engineering, Shahid Chamran University of Ahvaz, Iran *Corresponding Author Email: [email protected]
Abstract: In this paper, an all-optical 2-to-4 decoder based on photonic crystal nonlinear ring resonators is proposed. The designed decoder has one enable port which can control decoding operation. Using nano-crystal ring resonators, the threshold switching intensity is decreased to 13 W/µm2. The maximum frequency and total size of the device are
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obtained to be 160 GHz and 16×23 µm2 respectively. All output characteristics of the proposed decoder seem to be beneficial for being employed in optical integrated circuits.
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Keywords: Kerr Effect, Optical Decoder, Photonic Crystal, Ring Resonator.
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1. Introduction
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Optical devices play significant roles in communication networking, optical computing and signal processing because of their high operation speed, low signal distortion, low material usage, small
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size, low cost and more importantly immunity to electrical interference, in comparison with conventional electrical devices [1-3]. Photonic crystals (PhCs) are periodic dielectric structures
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which can guide and control the propagation of light. Integration possibility and scalability make PhCs as interesting structures for designing all-optical devices [4]. In recent years, some PhC-
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based optical devices such as optical add/drop filters [5-8], sensors [3,9-10], logic gates and switches [11-23], demultiplexers [24-26], analog to digital converters [27-30], digital to analog
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converters [31], encoders [32-35], adders [36-37] and power splitters [38-40] have been proposed. In optical systems, the number of users sharing one common bus has been increasing and as a result, the receiver should be able to choose appropriate data. Digitizing optical circuits has obliged researchers to design optical logic gates being able to control output ports depending on input states, which is called decoder. Several approaches have been done and various all-optical decoders have recently been proposed [41-45]. The fundamental element in all-optical decoders is 1
an optical switch, capable of controlling output signal via its input and bias signals. Switching operation is accomplished using Kerr nonlinear effect in photonic crystals [46-47]. The first concept in designing all optical decoder was proposed and simulated by Alipour-Banaei et.al in 2014 [41]. Their structure had two lattice constants, one for the main structure and one for the ring resonators. In this structure, the minimum radius of rods is about 120 nm and the proposed decoder
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may not be easily fabricated. In addition, the bias and input intensities are needed for switching operation is 1KW/µm2, which causes high power consumption. Moniem [42] proposed another structure for 2-to-4 decoder using five ring resonators, two T-shape and four Y-shape splitters. Although the decoder was correctly performing at speed of 200 GHz, the structure was too complicated and the radius of rods at splitters were about 40 nm which limits its fabrication possibility. An all-optical decoder was presented by Mehdizadeh et.al at 2015 [43]. Their structure
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consist of five ring resonators and needs three input ports except for bias signal. According to the
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reported results, the minimum intensity needed for switching operation was 2KW/µm2. Another 2-to-4 decoder presented by Mehdizadeh et.al in 2017 [44]. They studied the properties of cavities
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in the decoding operation. Their proposed structure had one enabling port which was not included
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in the previous works. Despite all advantages of their study, the maximum switching frequency of the structure was 20 GHz. Recently, an integrated all-optical decoder has been proposed by
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Khosravi and Zavvari [45]. Three ring resonators have been organized in the manner that three
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input ports were needed. The reported numerical analysis has shown that the normalized power levels for 0 and 1 logics are 0.18Pin and 0.4Pin respectively which gives narrow margin and may
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cause serious problems while coupled to other devices. Investigating all discussed researches, it can be inferred that using ring resonator is beneficial due
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to its high quality factor and high coupling efficiency. The Coupled length and resonance phenomenon in ring resonators assist one to obtain high optical coupling. Amplifying optical signals due to resonance in the ring can decrease the optical power required at input ports in
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comparison with defect based structures. As a result, in this paper, a new structure for all-optical decoder is designed based on 2D square lattice photonic crystals. The switching performance is implemented by using nonlinear ring resonators. Considering high input intensities inevitable effects, silicon nano-crystal ring resonator is used in order to decrease input optical intensity [3044]. In order to control the decoding operation, one enabling port is added to the structure. Propagation of light through the structure is simulated using finite difference time domain (FDTD) 2
method. Time and power analysis have been done and output characteristics of the proposed decoder have been calculated and reported in details. The steady-state time and normalized power levels of the output ports are two important factors because the device should be coupled to other devices in optical integrated circuits (OICs).
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This paper is organized as follows; two structures for optical switch are compared in the next section, a 2-to-4 optical decoder is proposed and finally, the simulation results and output calculated characteristics are presented.
2. Optical switch
The fundamental structure is 31×31 square lattice of silicon rods in air. The refractive index of the
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dielectrics is 3.48 and the radius of rods are 0.19a, where a is the lattice constant. In 2D photonic
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crystal based structures, the height of the dielectric rods in air is typically assumed to be 0.2a [48]. To have the optical confinement in third dimension, rods are placed between two layers (or rods)
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with low refractive index [48]. According to the total internal reflection (TIR), one can confine the
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input signal in two dimensions. We use plane wave expansion (PWE) method to calculate the band structure. The band structure of the proposed PhC includes two bandgaps at TE mode. According
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to the lattice constant of 630 nm, the first gap is equal to 1480nm≤ λ ≤2180nm and seems to be
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suitable for optical communication systems. To form the optical switch, input and output ports were created by removing rows of rods in both
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x and z directions. The designed structure has one enabling port (E) which enables the structure to operate as an optical switch. Two ring resonators are placed in center of the switch as shown in
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Fig. 1. Since the optical switch is a nonlinear device, the optimum optical intensity needed for switching application is an important issue. The refractive index of materials (n) depends on the light intensity and is known as Kerr effect. This effect can be used in ring resonators for achieving
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switching applications. Generally, n=n1+n2I is defined for Kerr effect where n1 and n2 are linear refractive index and nonlinear coefficient respectively and I is the light power intensity [49]. It can be inferred that the needed input intensity for switching depends on the nonlinear coefficient of the ring resonator. In the majority of reviewed papers, the chalcogenide glass is used instead of silicon because of higher nonlinear refractive index [50]. In the proposed switch, silicon nanocrystal rods have been used for ring resonators in which the linear refractive indices are 1.5 [4]. 3
But the most important advantage of using this ring is its nonlinear coefficient. According to the Kerr effect, the greater nonlinear coefficient, the lower input intensity needed for switching application. The nonlinear coefficient of the silicon nano-crystal and chalcogenide glass are 10-16 m2/W and 9×10-17 m2/W, respectively [4,50]. In order to compare the presented switch with that of previously reported, two structures for the optical switch are introduced in the following.
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Structure 1 includes 7×7 square-shaped ring of silicon nano-crystal which is shown in yellow in Fig. 1.a. and the radii of rods are the same as the fundamental structure. The other structure as shown in Fig. 1.b is formed by omitting 24 rods around the center of the switch, which is shown in blue for both structures. In the structure 2, 9×9 square-shaped ring of chalcogenide glass is placed, which is coloured in green. In both structures, for better coupling, extra rods are added at
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the corners.
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Fig. 1. Two proposed structures for optical switch, (a) structure 1, and (b) structure 2.
According to Kerr effect, threshold optical intensity needed for switching application should be
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realized. Different input intensities are scanned and output power levels at both ports are simulated. The transmission ratio versus input intensity for both structures are presented in Fig. 2. Ratio of output to input optical intensities is defined as the transmission ratio of the switch [51]. As shown
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in Fig. 2(a), the threshold intensity needed for switching effect is about 13 W/μm2 for the first structure while it is increased to 1KW/μm2 in the second structure.
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(a)
(b)
Fig. 2. Transmission ratio versus input intensity for two proposed switches, (a) structure 1, and (b) structure 2.
It is clear that, when port E is OFF, none of the output ports can be ON either input A is ON or
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OFF. In contrast, if port E is ON, or in the other words, enabling signal is coupled through port E,
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output ports can be ON depending on input A. In case logic 0 (or A=0), enable signal coupled
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through the ring resonator will appear through port O1. If both enable and input signals are coupled through ring resonator (or A=1), the resonance wavelength will be altered due to Kerr effect and
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refractive index modification. As a result, enable signal propagates through port O2. The electric field distribution for both structures 1 and 2 are shown in Fig. 3 and Fig. 4 respectively. The
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diagrams are obtained by solving Maxwell’s equations using FDTD method. In this method, two
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stability conditions must be carefully studied. First is known as the Courant condition and in twodimensional simulation, it is described as follows [52]: 𝟏 √(
𝟏 𝟏 + ) ∆𝒙𝟐 ∆𝒛𝟐
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𝒄∆𝒕 <
(1)
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where c is the speed of light in vacuum, Δt is the time step, and Δx and Δz are mesh sizes in both directions. The second condition is about the grid spacing that should be less than λ/10, where λ is
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the wavelength.
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(a)
(b)
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Fig. 3. The electric field distribution into structure 1 for (a) A=0 and (b) A=1.
(b)
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Fig. 4. The electric field presentation for structure 2 in two cases (a) A=0 and (b) A=1.
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Although switching operation of both structures are the same, there are major differences in power and time analysis. Time response simulation for the proposed switches are depicted in Fig. 5 and
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Fig. 6. For better evaluation, output characteristics of them are summarized in table 1. The maximum steady-state time for structure 2 is about 2 ps while it increases to 4 ps for structure 1. Steady state time is the time that output signal oscillates within a certain error band. In the majority
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of reported oscillation systems, error bands 2% and 5% are concerned [53]. In this paper, error band 5% is selected. The normalized power intensity levels for logics 0 and 1 in structure 1 are equal to 0.05 and 0.86 respectively while the margins in structure 2 are obtained to 0.2 and 0.79.
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(a)
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Fig. 5. The normalized output power intensity for structure 1, (a) A=0 and (b) A=1.
(b)
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Fig. 6. The normalized power intensity at ports O1 and O2 for structure 2, (a) A=0 and (b) A=1.
State
1
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2
Normalized power level
Steady-state time (ps)
Input intensity (W/µm2)
Logic 0
Logic 1
A=0
0.04
0.96Pin
4
0
A=1
0.05
0.86Pin
2
13
A=0
0.08
0.92Pin
2
0
A=1
0.2
0.79Pin
2
1500
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Structure
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Table 1. The calculated characteristics of two proposed structures.
To have the instructive interferences and high optical coupling between waveguide and resonator three aspects should be considered: coupling length, distance and effective refractive index of resonator. The close distance between them and using the desired nonlinear materials for rods 7
result in enhancing optical coupling for both resonant ring and cavity. Coupling length of the ring is an efficient parameter to increase the quality factor. It has been demonstrated that if the coupling length is increased the quality factor can be enhanced [54]. This issue can encourage one to use the resonant ring than the resonant cavity. So, one can design high quality factor ring resonators for dropping applications. Quality factor indicates rate of energy loss of the resonator and is
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defined as Q=λ/Δλ, where Δλ is the resonance bandwidth [55]. Numerical simulations have shown that quality factor of structure 1 is 1065 while it is decreased to 322 for structure 2.
In nonlinear optical devices, high input intensities may impose inevitable deconstructive effects. So decreasing optical intensity will improve the application of these devices. The most important advantage of structure 1 in comparison to another is the minimum power needed for switching application. According to table 1, using silicon nano-crystal for ring resonator, the input and bias
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powers are decreased from 1500 W/µm2 to 13 W/µm2. So, we use the structure 1 for designing the
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proposed decoder.
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3. All-optical 2-to-4 decoder
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In the proposed structure, four ring resonators are used, as shown in Fig. 7. It has one enable port labelled as port E, two input ports labelled as port X and Y and four output ports named O0, O1,
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O2, and O3.
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At first, electric field distribution for four decoding states should be investigated. The FDTD simulation results for the proposed decoder are presented in Fig. 8. Four decoded cases as
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summarized in the truth table 2, are described as follows:
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Case Ⅰ (X=Y=0): the enable signal is coupled to rings 1 and 2, and then output O0 will be on. Case Ⅱ (X=0, Y=1): the enable signal is coupled to ring 1 but it will not be coupled to ring 2
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because Y value is equal to logic 1. Therefore, output O1 will be on. Case Ⅲ (X=1, Y=0): the enable signal is coupled to ring 3 and 4 and output O2 will be on. Case Ⅳ (X=Y=1): because X=Y=1, the enable signal cannot be coupled to neither ring 1 nor ring 4. So output signal will appear at port O3. It should be stated that four discussed cases are true if enable port is ON. On condition that port E=0, input signals X and Y will not couple through their designed direction and decoding operation will not be reached. 8
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Fig. 7. The schematic of the proposed structure for 2-to-4 decoder.
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(c)
(d)
Fig. 8. Electric field distribution of the proposed decoder (a) X=Y=0, (b) X=0 Y=1, (c) X=1 Y=0, and (d) X=Y=1.
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The proposed structure can be performed as all-optical decoder, but it should be coupled to other devices while integrating into optical circuits and systems. So, output characteristics of the decoder should be investigated. Time response and normalized light power at output ports are shown in Fig. 9. For better evaluation, power levels of four outputs and steady-state time
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of each state are summarized in table 2.
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Fig. 9. The normalized power intensity versus time for (a) X=Y=0, (b) X=0 Y=1, (c) X=1 Y=0, and (d) X=Y=1. Table 2. The truth table for the proposed decoder.
Inputs Y 0 1 0 1
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X 0 0 1 1
O0 1 0 0 0
Outputs Logic O1 0 1 0 0
O2 0 0 1 0
O3 0 0 0 1
O0 86 5 0.01 5
Normalized power (%) O1 O2 3.8 0.01 68 10 7 63 0.01 4
O3 1.9 1.2 2 63
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In multiple coupling, output and input power levels for logics 0 and 1 are extremely needed. Output power margins for both 0 and 1 should be carefully investigated. Other output characteristics of the proposed decoder including contrast ratio, cross-talk, and insertion loss should be carefully calculated [56-57]. Contrast ratio, defined as Plogic1/Plogic0, indicates the power margin between logics 1 and 0. The optical insertion loss is one of the most challengeable characteristics for low power devices which is defined by 10log((Pin-Pout)/Pin). 10
The other dominant parameter in multiple port optical devices is cross-talk, which shows the effects of ports on each other and defined as 10log(Plow/Phigh) where Plow and Phigh are the lowest and the highest power levels obtained at output ports for each logic state. The above mentioned characteristics are reported in table 3. As it can be concluded, the minimum contrast ratio of the proposed decoder is about 7 and the maximum one is more than 28.7 and the insertion loss is varied from -4.31 dB to -8.54 dB. The maximum cross-talk is between -17.53dB and -39.34dB. In this structure, threshold power intensity of ring resonators
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for switching is 13 W/µm2, while in the most of previous researches the threshold varies from 1 KW/µm2 to 2 KW/µm2 [41, 43, 45]. Although the operation speed of the proposed decoder
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is nearly the same as other reviewed researches, low power intensity of bias and input ports
can prevent other inevitable nonlinear optical properties occur at high input intensities. Low insertion loss at output ports is beneficial while integrating optical devices. In addition, power margins of logics 0 and 1 are large enough and as a result possible misunderstandings can be
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prevented, especially in multiple couplings.
Insertion loss (dB) -8.54 -4.95 -4.31 -4.31
Maximum crosstalk (dB) -39.34 -17.53 -37.99 -37.99
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contrast ratio 28.7 6.8 9 12.6
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Output ports O0 O1 O2 O3
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Table 3. The calculated characteristics of the proposed decoder. Steady-state time (ps) 6.3 3.96 6.4 4.2
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As a final analysis, periodic pulses are launched at input ports A and B then normalized output powers are investigated in Fig. 10. As it is shown, all four output ports are ON or OFF
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depending on input logic states. The pulse width of input signals is 8 ps. Since the maximum steady-state time of the decoder is about 6.3ps, it will be guaranteed that the pulse response of all states will be correct. Data rate is referred to the speed at which data is transferred and can
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be calculated using the time response of the output signal, as described in [58-59] in details. Data rate is the reciprocal of the steady state time. So, the maximum data rate is calculated
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about 160 Gb/s.
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(c)
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Fig. 10. The normalized power intensity for input pulse with 8 ps and different states A=0 B=0, A=0 B=1,
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A=1 B=0, A=B=1 at (a) port O0 (b) port O1 (c) port O2 (d) port O3, respectively.
For better evaluation, all mentioned output characteristics are compared with other previous
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researches and results are presented in table 4. Since some of the features were not reported, the character “–” is placed instead. As it can be inferred, the insertion loss and input intensity
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of the proposed decoder is sufficiently decreased in comparison with other pervious researches [42-45]. The operation speed of the proposed decoder is greater than that of reported in Ref.
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[44]. Although the operation speed is not improved in comparison with Ref. [42], the total size of the proposed decoder is definitely smaller than the size of the discussed decoder [42]. Table 4. Comparison of the obtained results in this work with other works. Input intensity (KW/µm2)
Insertion loss (dB)
Size (µm2)
Ref [42]
160
-
-
40×38
Ref [44]
2
0.02
-3.42
-
Ref [45]
-
1
-2.20
-
This work
160
0.015
-4.31
16×23
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Operation speed (GHz)
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Considering some fabricated devices [60-65], semiconductors fabrication confinements are concerned. The minimum diameter of the rods and lattice constant of the fundamental structure are 240 nm and 630 nm, respectively. It can be concluded that the proposed decoder is potentially applicable in real time implementations.
4. Conclusion
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High-speed performance, low power consumption, and suitable output power margins are three important factors in evaluating optical devices. Considering all mentioned issues, in this paper,
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an integrated all-optical 2-to-4 decoder was proposed. Numerical simulation results have been
done and output diagrams were presented. In order to reduce the input power intensity, nanocrystal rings, which have high Kerr coefficient, are placed in the center of all-optical switches. Thus, the required optical intensity was reduced to 13 W/µm2. The operation speed of the
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decoder is about 160 GHz. The worst output power levels for logics 0 and 1 are 0.1Pin and 0.63Pin, respectively. The maximum insertion loss is -4.31dB, which occurs in two cases. The
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maximum calculated cross-talk for case II is -17.53 dB. Since the total size of the structure is
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16 × 23 µm2, it can be a suitable candidate for compact optical circuits. Taking to account all
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above characteristics, the proposed decoder is capable of employing as a part of all-optical integrated circuits.
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