Accepted Manuscript Title: Implementation of Some High Speed Combinational and Sequential Logic Gates using Micro-Ring Resonator Author: Ajay Kumar Sanjeev Kumar Raghuwanshi PII: DOI: Reference:
S0030-4026(16)30683-0 http://dx.doi.org/doi:10.1016/j.ijleo.2016.06.061 IJLEO 57847
To appear in: Received date: Accepted date:
1-2-2016 14-6-2016
Please cite this article as: Ajay Kumar, Sanjeev Kumar Raghuwanshi, Implementation of Some High Speed Combinational and Sequential Logic Gates using MicroRing Resonator, Optik - International Journal for Light and Electron Optics http://dx.doi.org/10.1016/j.ijleo.2016.06.061 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.
Implementation of Some High Speed Combinational and Sequential Logic Gates using Micro-Ring Resonator Ajay Kumar1 and Sanjeev Kumar Raghuwanshi2 Department of Electronics Engineering Indian School of Mines, Dhanbad-826004, Jharkhand, India Email:
[email protected],
[email protected]
Abstract: All optical logical operation is one of the most important aspects of modern research activity in the optical computing. The paper includes the detailed description of switching phenomena in the Micro-ring resonator (MRR). The Micro-ring resonator is very effective component for the implementation of various combinational and sequential logic devices, because of its small and compact size, immunity to electronic interference, low-attenuation, higher bandwidth and cheap computing. The literature includes the different combination of MRR in order to implement the combinational logic circuits (XOR/XNOR, AND, Full ADDER/SUBTRACTOR) and sequential logic circuits (D Flip-Flops). The results are verified by the MATLAB simulation. Keywords: All optical logic gates, micro-ring resonator, Combinational & Sequential circuits. I.
Introduction
In modern technological scenario, the importance of all optical logic gates has widely increased. A logic gate is a device, which performs the certain and specific Boolean operation on one or more than one input and produces Boolean outputs on the basis of the designed functionality. The logic gate implementation based on the optical computing provides the enormous advantages over electronic computing e.g immunity to electronic interference, more compact system, low-loss transmission, significantly more bandwidth, easier and cheaper computing. However, several techniques has been employed to implement the optical logic gates. Design of XOR, XNOR, NAND and OR gate based on photonic crystal fiber has been described in detail in [1]. The logic gate principle uses the concept of multi-mode interference waveguide. In the same manner the most important logical phenomena such as Binary half adder/Subtractor is implemented using the dark-bright Soliton conversion is explained in [2]. The soliton conversion method shows the great level of accuracy keeping the operation in the optical domain. However lots of effort has been given for the construction of all optical logic gates such as (XOR/XNOR) logic implementation using the dark bright soliton conversion [3], experimental method of construction of all optical logic gate [4]. The concept of optical flip-flop composed of two silicon-on-Insulator coupled to straight waveguides by exploiting the optical bistability behavior due to the nonlinear Kerr effect is explained in [5]. Logic gates based on MMI waveguide for 1
BPSK modulation format in packet switching system is discussed in [6]. Photonic crystals are promising technology in future optical signal processing and optical computing. Design and simulation of novel all-optical fundamental XOR and OR logic gates based on two dimensional photonic crystals utilizing self-collimation and splitting mechanism are reported in [7]. Some experimental method of designing the optical adder can perform the complex binary function. Hence, experimental demonstration of all-optical adder based on bit differential techniques can be obtained in [8]. However, we cannot ignore the importance of sequential circuits. Many researchers has presented the various techniques to implement the sequential logic devices. Optical flip-flops based on the laser diodes (LD) have been extensively investigated in [9]. The design techniques of all-optical S-R and D-flip flop based upon the dark-bright soliton conversion within the optical add/drop filter can be obtain [10]. A scheme to realize all-optical Boolean logic functions AND, XOR and NOT using semiconductor optical amplifiers with quantum-dot active layers is studied [11]. This paper provides the detailed description of various logic gates (combinational and sequential) based on micro-ring resonator structures. Ring resonators are very advantageous because of its small size, less complicity, high free spectral range and high wavelength selectivity. Ring resonators are more suitable for the monolithic integration with some other components and the proposed devices are very much robust with respect to the back reflection. The paper shows the detailed discussion of some combinational (XOR/XNOR, AND Full ADDER/SUBTRACTOR) and sequential logic gate (D flip-flop) with the help of different combination of micro-ring resonator. The section II provides some theoretical background related to micro-ring resonator and its switching phenomena based upon the nonlinear effect. The section III includes structural description of XOR/XNOR logic gate by cascading two similar MRR. The section IV involves the simulation of proposed devices in MATLAB for the given parameters. Section V shows the detailed discussion of Full ADD/SUB circuit with all possible cases of input. The simulation result of Full ADD/SUB device can be shown in section V. Section VI describes the efficient method to construct the optical logic AND gate. Section VII includes description of D-flip flop using the single MRR structure and MATLAB simulation is provided for results verification. II.
Theory
The micro-ring resonator (MRR) consists of unidirectional coupling between the ring resonator and an input-output waveguide. A basic micro ring resonator consists of a ring waveguide as a resonator cavity closely coupled with either one or two straight waveguides [12]. A fraction (coupling co-efficient between input waveguide and the ring) of the incoming field is transferred to the ring having radius as shown in the Fig. 1. When the optical path length of the round trip is a multiple of the effective wavelength, a constructive interference occurs and hence the MRR is “On resonance”. Therefore, periodic fringes appear at the output ports. At resonance, the drop port shows maximum transmission, since (coupling co-efficient between the ring and output 2
wave guide) of the built up wave inside ring is coupled to this port. In the through port the ring exhibits the minimum at resonance. If the resonator is made of non-linear material, a logic switch can be produce. Through nonlinear effects, the refractive index can be change by the intensity of the light in the resonator. A green laser is use to pump the signal from the top of the ring. Since the optical pulse is almost fully absorbed in the micro-ring waveguide the high density carriers are generated (pumping introduces the extra electron-hole pair). These carriers effectively result in a net decrease of the refractive index of the micro-ring waveguide and cause a temporarily blue shift of the micro-ring resonance wavelength. This changing refractive index will cause the resonant wavelength to vary, which can then in turn be used to switch a signal on or off, or turn the resonance for use of the specific wavelength.
Figure 1: Single ring resonator
), Let us consider the circumference of the ring is L ( is the field coupling coefficients between the input and the ring and is the field coupling coefficients between the ring and the output bus, the intensity attenuation coefficients of the ring is , the intensity insertion loss coefficients is and the wave propagation constant is where ,
is the resonant wavelength of the ring.
,
where and are the linear and nonlinear refractive index, respectively. I and P are the intensity and power of the optical pump signal. We assume and are the input and add port field respectively. We also assume the field at the points and are and can be written as [13], (
)
⁄
*√ √(
)
+
( )
3
(
⁄ )
(
)
⁄
(
( )
*√ )
√(
(
⁄ )
⁄ )
+
(
( )
⁄ )
( )
The field at the through port is given by (
⁄
)
)
*√( +
√
( )
The field at the drop port is given by (
⁄
)
)
*√( +
√
( )
For the simplification let us consider, (
)
⁄
(
) and
Solving Eq. (1) through Eq. (6), we get the through port ( √ √
√
(
√
(
√
√
)
(
( )
(
√
√
) field as
) (
√
) and the drop port (
) (
√ √ √
√
(
√
(
)
( )
The above equations help us to design the ring resonator as a switch and also to help to study the cascaded ring resonator. III.
Design of All optical XOR/XNOR gate
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The circuit consists of two cascaded micro-ring resonator (MRRs) to perform the XOR and XNOR operation. The proposed architecture is shown in the Fig. 2. A continuous optical signal (COS) with the wavelength of is applied to the input of the first ring (MRR1) and is modulated by the optical control pump signal , then the optical signal pulse applied to the input port of the ring resonator appear at the through and drop port of MRR1 as and ̅ respectively. It is assume that the MRR1 resonate at when the optical control pump beam is applied. Here we also assume that no signal is applied to the add port of the MRR1. Through port output of MRR1 acts as input port of the second ring MRR2 and drop port of the output of MRR1 acts as add port of the second ring MRR2. Then both inputs of the ring MRR2 are modulated by the optical signal ̅ ̅ and the optical pulse at Y. Then the optical pulse at the through port of MRR 2 will be ̅ . the drop port of the MRR2 will be ̅
Figure 2: Cascaded micro-ring resonator
IV.
Simulation and Result
The simulation for the cascaded GaAs-AlGaAs micro-ring resonator is done with assumption that there is no optical input in add port and a continuous optical signal with wavelength of is applied to the input of the ring MRR1. Coupling coefficients are taken as , effective cross-sectional area = and resonant wavelength . The simulation result is shown in the Fig.3.
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Figure 3: Simulated waveform of proposed all-optical XOR/XNOR gate using micro-ring resonator.
Figure 3 shows the performance of all optical logical gate formed by the combination of the two cascaded ring resonator. The first and second row represents the all possible combination of control input pulse X and Y respectively. The third row and forth row shows the the output waveform for the different combination of input pulse. The third row represents the output for the XOR logic and fourth row represents the output for the XNOR logic. a. Case 1: When the X = logic 0, Y = logic 0 In Fig. 2 when both the pump signals (X, Y) are in the off state, the optical signal which is applied to the input of first micro-ring resonator MRR1 goes to the through port of the MRR 2 as shown by the first column of Fig. 3. b. Case 2: When the X = logic 0, Y = logic 1 When first pump signal (X) is off state and second pump signal (Y) is on state the input signal comes to the drop port of MRR2 which is shown by the second column of Fig. 3. c. Case 3: When X = logic 1, Y = logic 0 When first pump signal (X) is on state and second pump signal (Y) is on state, the input signal comes to the drop port of MRR2 which is shown by the third column of Fig. 3. d. Case 4: When X = logic 1, Y = logic 1
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When both pump signals (X, Y) are on state, the input signal comes to the through port of MRR2, which is shown by the fourth column of Fig 3. V.
All Optical Full-adder and Full-subtractor Circuit
) and gives result in two A full adder circuit adds three single bit binary numbers ( single bit binary outputs, called sum (S) and Carry ( ). The design of full adder circuit using
Figure 4: All optical full adder/subtractor circuit.
Any combinational logic function can be written in a sum-of-products format. Each product is an AND function of the input logic signals, where each input signal appears only once in either its inverted or non-inverted form. The sum is the result of an OR function of all the products [14]. Micro-ring resonator based optical switch is shown in the Fig. 3 [15-16]. Depending upon the ) the output is obtained from one of the eight output state of the variable ( ). The description of all eight possible cases is as following: terminal(
a. Case 1 : First the light from the constant optical source is incident to the input of the first switch . As the control signal is off, the light emerges from the drop port and it acts as input to the switch . If B = 0 the signal appears at the drop port and now it is input to the switch . If the control signal is also absent then signal appears at port . Hence, it acts as optical logic ̅ ̅ ̅
b. Case 2:
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Due to the absence of signal and , the signal appears at the drop port of switch . Due to the presence of the signal , the output signal can be detected at the port 1 through switch . The port 1 can be treated as ̅ ̅ .
c. Case 3: Due to the absence of the signal , the signal appears at the drop port of the switch . The presence of the signal of switch sends the signal at the through port and it acts as the input signal for the switch . Now, due to the absence of the signal the optical signal at the drop port of the switch , which is port . The port can be assumed as ̅ ̅ . d. Case 4: In the same manner the combination of the signal through port of switch . Now, the presence of the signal and it can be treated as ̅ .
, sends the optical signal at the sends the signal at the port
e. Case 5: The specified combination sends the signal at the through port of switch . After that the optical signal appears at the drop port of the switch . Now due to the absence of the signal the signal finally appears at the drop port of switch , which acts as the port ( ̅ ̅ ). f. Case 6 : Due to the presence of the signal A and absence of the signal B, the optical signal appears at the drop port of the switch . Similarly, the appearance of the , shifts the optical signal at the ( ) which gives the result of logical ̅ through port of the switch operation. g. Case 7 : Due to the presence of the signal A and B the optical signal can be obtained at the through port of the switch . The absence of the control signal transfers the optical signal at the port ̅ and it acts as logic signal . Case 8 : The specified combination of the control signal shifts the signal at the port . The port specifies the logic . The following information can be represented in the following tabular manner.
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Table 1: All possible combination of input control signal and the output signal obtained through Fig. 4 Inputs 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
Outputs at different terminals 0 1 0 1 0 1 0 1
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 1
Table 1 shows the all possible combination of input control signal and the output signal obtained at the different output terminals of the structure shown in Fig. 4. As we know that the truth table for the Full adder can be represented by the following table 2. Table 2: Truth table for Full Adder Inputs 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
Outputs Sum 0 1 1 0 1 0 0 1
0 1 0 1 0 1 0 1
Carry 0 0 0 1 0 1 1 1
The table 2 shows that in order to obtain the Sum it must contain the combination of minterms ̅̅ ̅ ̅ ̅ ̅ and . In the same manner the carry term must contain the ̅ and ̅ combination of minterms of ̅ . Hence, Using table 1 we can say that we can obtain the sum by combining the output ports and and the carry term can be obtained by and . We know that the truth table for the Full subtractor can be represented as follow:
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Table 3: Truth table for Full subtractor Inputs 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
Outputs 0 1 0 1 0 1 0 1
Difference 0 1 1 0 1 0 0 1
Borrow 0 1 1 1 0 0 0 1
The table-1 shows that the Difference can be obtained by the same combination of minterms as that of Sum. The Borrow can be obtained by the combination of and . The simulation results for the Full adder and Full subtractor can be represented as follow:
Figure 5: The simulation result of the Full adder
Figure 5 shows simulation result of the specified structure of Fig. 4. The First, second and third row of Fig. 5 represents the all possible combination of and . The fourth and fifth row of 10
Fig. 5 represents the sum and carries for all possible combination of inputs. The result can be verified by the Table 2. In the same manner the result for the full subtractor can be represented as follow:
Figure 6: Simulation result of Full subtractor
Figure 6 describes the simulation result for the all possible combinations of inputs. In the same manner, the first, second and third row of the figure 6 represents all possible combination of the input . The fourth and the fifth rows represent the Difference and Borrow for the full sub-tractor. The simulation results can be verified by the Table 3.
VI.
AND Gate Implementation
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Figure 7 shows the construction of the AND logic implementation using two micro-ring resonator.
Figure 7: All optical AND gate using the two micro-ring resonator.
The Fig 7 shows the clear visualization of optical AND gate. The continuous optical signal is given to the input port of the first ring resonator. The add port is left with zero optical signal all time. The through port output of the first micro-ring resonator is connected to the input port of the second micro-ring resonator. The add port of the second micro-ring resonator is kept with zero optical signal. Hence, we can observe that the optical signal appears at the through port of the second microring resonator only when the control signal A and B attain the value of logic high. In all other case the signal does not appears at the through port of the second micro-ring resonator. Hence, the through port of the second MRR acts as the AND gate. The simulation result can be represented as follow:
Figure 8: Simulation result of the AND logic gate.
Figure 8 shows the simulation result for the all optical AND gate. A first and second row represents the various possible combination of input signal A and B respectively. The third row represents the output of the logical AND gate for the different combination of the inputs. 12
VII.
Construction of Sequential Circuit (D Flip-Flop)
The sequential circuits are some different types of circuit, which can be used to store the binary information up to the desired interval of period. D- flip-flop is special types of sequential device, in which the output follows the input at each clock pulse. That means the device is able to store the binary data up to next clock pulse. Hence, it is widely used for the storing purpose of the bit information. It is interesting to design the optical D-flip-flop, which can able to process the information in a very fast rate. The optical D-flip flop consists of one MRR with a feedback, as shown in the Fig. 9 [17-18].
Figure 9: All optical D-flip flop using single ring resonator.
Figure 9 shows the external feedback from the through port to the add port input. The main objective of the feedback loop to maintain the flip-flops previous state in the absence of the clock input signal. The numerical simulation of the structure can be represented in MATLAB in Fig. 10. The figure shows the proper working of the D flip flop. The figure 10 clearly indicated that this particular arrangement of the micro ring resonator collects the data provides by the sequence D represented in the first row, and the output signal is updated due to the presence of the clock pulse.
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Figure 10: Simulation result of the D-flip flop
According to the result when the input pulse is set to 1, then in the presence of the clock pulse the output terminal ( ) acquires the value of input data (D). After that the output terminals maintains the same output state until the clock signal acquires the value zero. Next the output data is updated at 30 ps, when the clock signal acquires the value 1. This clearly indicates that the following structure is suitable and works as all optical D-flip flop. VIII. Conclusion The theoretical analysis of Micro-ring resonator as an optical switch using the optical pumping method has been explained in detail. We have presented the different types of combination circuits (XOR/XNOR, AND, Full ADDER/SUBTRACTOR) and sequential circuits using the different combination Micro-ring resonator. Each configuration is presented with valuable and considerable MATLAB simulation. The following proposed device can be use for the different coding applications, because of its fast response, small size and larger bandwidth. IX.
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