Implementation of All-Optical 1x4 memory register unit using the Micro-Ring Resonator Structures

: Implementation of switching activity in the all-optical domain is one of the most important aspects in the field of modern high-speed and secured communication technology. Micro-ring Resonator (MRR) based switching activity can be used to implement all-optical active low tri-state buffer logic and clocked D flip-flop. The paper describes the switching activity of micro-ring resonator structures and the switching activity is further used to implement the effective all-optical 4 − bit memory register using the appropriate arrangement of all-optical tri-state buffers and clocked D flip-flops with the functionality of RD and WR. The complete description of layouts and switching mechanisms of all-optical 4-bit memory registers have been explained and appropriate MATLAB simulation results are presented to observe the suitability of the proposed unit. The analysis shows that implementation of tri-state buffer logic and D flip-flop assisted 4-bit memory register in the all-optical domain includes the considerable advantages of optical communication e.g. immunity to electromagnetic interference, parallel computing, compactness, signal security, etc. The manuscript describes the detailed analysis of performance parameters e. g. extinction ratio, contrast ratio, amplitude modulation, on-off ratio, and switching speed of micro-ring resonator structures to achieve an efficient selection of device parameters and finally describes an efficient technique to implement all-optical MRR based 1 × 4 memory registers.


Introduction
All-optical switching and computations have been widely investigated in optical digital circuits and optical sensors. Optical digital circuits and sensors possess many advantages compared with the conventional electronic circuits and sensors e.g. immunity to electromagnetic interference, parallel computing, compactness, low loss transmission, significantly more bandwidth, easier and cheaper computing, and signal security. However, several techniques have been employed to investigate optical digital computation and sensors. The electro-optic effect-based optical switching logic circuits; optical sensors and delay units have been widely investigated to achieve optimum performance. Reconfigurable optical time delay networks are essential components. A hybrid optical time delay unit using Lithium-Niobate switches and precisely produced fiber loops are one of the most important units is described [1]. The thermal-induced refractive index variation phenomena using the silicon Mach-Zehnder waveguide is investigated. It is observed that optical switches as signal routers can be used efficiently for faster decision-making schemes [2]. The Mach-Zehnder interferometers (MZIs) can be used to perform the optical switching based on the principle of the electro-optic (EO) effect. The electro-optic effect is the phenomena, which are associated with the change in the index of refraction that is proportional to the magnitude of the externally applied electric field. The electro-optic effect-based Mach-Zehnder Interferometer (MZI) structure switching phenomena can be used to design several combinational and sequential circuits [3]- [6]. The semiconductor optical amplifiers are useful building blocks for all-optical gates as wavelength converters and OTDM de-multiplexers. The development of simple gates using the cross gain modulation and four-wave mixing to the integrated interferometric gates using cross-phase modulation is described [7]. Scheme to realize all-optical Boolean logic functions AND, XOR, and NOT using semiconductor optical amplifiers with quantum-dot active layers is studied where nonlinear dynamics including carrier heating and spectral hole-burning are taken into account with the rate equation. The analysis shows that the scheme is suitable for highspeed high-speed Boolean logic function [8]. Implementation of all-optical XOR gate for 160 Gb/s return to zero data signal using a single quantum dot semiconductor optical amplifier are discussed and analyzed in [9]. The scheme involves the detuning optical amplifier, which shows its importance in the field of all-optical signal processing and its application. The nonlinear effect of two-photon absorption (TPA) on the performance of all-optical XOR gates using quantum-dot semiconductor optical amplifier (QDSOA) assisted Mach-Zehnder interferometer is numerically analyzed and investigated at a data rate of 2 Tb/s [10]. The dependence quality factor (QF) on the critical parameters is investigated. Similarly, photonic crystal fibers are one of the advanced technologies and have been a major area of interest for many scientists and researchers. A new set of configurations is proposed to implement simple and highly compact photonic crystalbased all-optical logic AND and OR gates [11]. The design of two types of on-chip logic gates in 2D silicon photonic crystal slab is investigated and the suitable result associated with AND and XOR logic gate function at different frequencies are verified [12]. The technique is based on the scheme that, center directional emitting cavity and different input/output direction can lead to different logic operations without nonlinearity and magnetism. All-optical clocked J-K flip-flop, SR, and T flop is proposed and described using silicon waveguide-based optical micro-ring resonator (OMRR) [13]. Similarly, four-wave mixing-based switching is one of the important mechanisms to implement logical functionality. A high-speed all-optical NAND logic gate is proposed and experimentally demonstrated using four-wave mixing Bragg scattering in highly nonlinear fiber [14]. The scheme describes the implementation at two wavelengths by encoding logic inputs on two pumps via on-off keying. Similarly, the possibility of effective creation of quantum gates based on polarization photon qubits using a Kerr non-linear medium in a cavity is described [15]. It describes the mechanism to implement the four-wave mixing technique for the creation quantum C-NOT gate. Similarly, the electro-optic effect-based logic gates using a single micro-ring resonator structure is one of the efficient techniques. A novel technique to realize directed optical digital logic gate based on the structure-based free carrier distribution principles, changes in the refractive index of the waveguide, and the scattering analysis on the micro-ring resonator coupling region, are clearly described [16]. A novel analysis of a micro-ring resonator structure is presented, which includes the mathematical as well as simulation analysis on the modulated signals in [17]. In the analysis of [17], simulation results are generated to investigate some important parameters e. g. the full width at half-maximum, quality factor (Q-factor), and depth of the resonance at the different modulated voltage. Simulation and analysis of the digital and photonic positive edgetriggered JK flip-flop using a single micro-ring resonator as basic building blocks are investigated in [18]. In this scheme, the basic single micro-ring resonator structure uses free-carrier plasma dispersion electro-optic effect properties in its ring waveguide, which is structured as a PIN diode. A novel design technique to implement the photonic D-type flip-flop based on silicon micro-ring resonator as basic building blocks are investigated and it was observed that, carrier injection forward-biased PIN waveguide resonance phenomena can be used to generate the logic of D flip-flops [19]. A novel Micro-ring resonator-based switching activity can be effectively used for several optical logic computations and sensor design. Micro-ring resonator switching activity has been efficiently used for the implementation of the all-optical gray code converter [20], NAND logic gate, Half-adders [21], and some well-known combinational and sequential circuits [22]. The manuscript describes a theoretical mechanism to implement the all-optical 1 × 4 memory register using the ultra-fast switching activity of the micro-ring resonator (MRR) structure. In section 1, the relevant introduction associated with the modern optical switching schemes and related technology is discussed. Section 2 includes the basic idea of 1 bit and 4 bits memory registers, which includes the specific arrangement of clocked D flip-flop and active low tri-state buffers. In this section, we have shown the implementation of micro-ring resonator structure as powerful all-optical switches. The device parameters are analyzed in detail, which show the suitability of the proposed unit in the all-optical domain. The important performance effecting parameters e. g. free spectral range, 3-dB bandwidth (FWHM), Finesse, Quality factor, On-off ratio, Extinction ratio (ER), Contrast ratio (CR), Amplitude modulation (AM), and switching speed are optimized by selecting the appropriate values of the most important device parameter of MRR, which is coupling coefficients (k 1 ,k 2 ) and radius of MRR. Now, based on the parameter analysis, the basic idea of optically clocked D flip-flop and all-optical active low tri-state buffer is described. Finally, the layout of the proposed MRR switchingbased all-optical 1 × 4 memory registers is discussed. In section 2, it is observed that the selected device parameters provide the suitable result and it is verified using the appropriate MATLAB simulation result and proper mathematical modeling. The suitability of the results is also represented in a tabular manner. The design technique involves the additional advantage of all-optical units. The proposed scheme represents the WRITE, READ, and MEMORY-related operation without the conversion of signals from optical to electrical and electrical to optical. It completely resolves the complexities related to optical to electrical and electrical to optical conversions. Hence, the proposed scheme theoretically describes the application of an ultra-fast MRR based memory register which provides the optimum results including the additional advantage of all-optical switching phenomena.
2. Design of all-optical 4-bit memory register using the optical active low tri-state buffer logic and clocked D flip-flops 2.1 Introduction to 1 bit and combined 4-bit memory register Memory registers are one of the most essential parts of complex and sequential digital circuits. The memory registers play a vital role in the storing mechanism of bit information. Mainly, the R/W memory shows wide applications in the field of combinational and sequential computation. The R/W memory comprises a group of flipflops or field-effect transistors, which stores bits of information [23]. Flip-flop or latch can be used as the basic memory element. The basic block diagram of the 1-bit storing memory element can be represented in fig. (1). Active low tri-state buffers are associated with the input and output terminals of clocked D-flip flop, which provides controlled R/W operation. The input bits can be read-only, if the output buffer is enabled, otherwise the output Q and output terminal D out remains isolated. Similarly, one active low tri-state buffer logic gate can be associated with the input segment of the clocked D flip-flop. The data can be written at the input terminal by enabling the input buffer. Hence, figure 1 shows the simple layout of the one-bit R/W memory cell. The single-bit memory cell can be arranged to implement the controlled 4-bit storing mechanism, as shown in fig. 2. It behaves as 4 bit or 1 × 4 bit memory register, which consists of 4 I/O lines and two control line RD ̅̅̅̅ and WR ̅̅̅̅̅ . Fig 2 shows that controlling terminals of all the four input buffers are combined, which provides controlled writing. Similarly, controlled reading can be observed in the form of combined output buffer control terminals. However, In this paper we have represented an ideal technique to implement the alloptical 1 × 4 R/W memory register, using a simple micro-ring resonator structure as a switching element.

The Micro-Ring Resonator Structure as Basic Switching Element
Now a day, the micro-ring resonator (MRR) structures are widely used for several alloptical signal processing e.g. filtering, multiplexing, de-multiplexing, switching, etc. The MRR as a switch finds wide application in the field of all-optical computational and decision-making units. The basic MRR structures are mainly associated with the ring waveguide, which is closely coupled with one or two waveguides. In fig. 3, the fraction k 1 and k 2 represents the fraction of the incoming field transferred to the ring. 'R' is the radius of the circle. Constructive interference of the signal can be observed if the total optical path length is an integral multiple of the effective wavelength. The phenomenon is termed as the "On resonance", which can be observed as multiple fringes at the output ports. Hence, resonance shows the maximum transmission at the drop port and minimum at the through the port. The introduction of non-linear material can open the door to logical switching phenomena. The non-linear effect leads to an appreciable change in the effective refractive index due to the appropriate introduction of a green laser as a control pump signal. A green laser control pump signal is applied from the top of the ring, which introduces the change in the effective index of the ring resonator section. Change in the effective index causes the temporary blue shift phenomena on the microring resonance wavelength. Hence, the change in the effective index phenomena invokes appropriate switching activity at the specific resonance wavelength. In fig. 3, ′R′ is the radius of the ring, k 1 and k 2 is the coupling coefficient between the ring structure and the straight waveguide section. The effective index of the ring structure can be represented as n eff = n 0 + n 2 . I = n 0 + n 2 A eff P. n 0 and n 2 are the linear and non-linear refractive index, respectively. I and P are the intensity and power of the optical pump signals. In figure 3 symbols E i1 and E i2 are the input and add the port field, respectively. Now, the electric field at points a, b, c, and d are E ra , E rb , E rc and E rd can be written as following [24]: 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 ϕ = k n L 2 Solving Eq. (1) -Eq. (6), we get the through port (TP) and the drop port (DP) field as In the eq. (1) -(8), γ and α are the insertion loss coefficient and attenuation coefficient of the ring, respectively. In the same manner, k n = 2π λ n eff is the propagation constant, where is the resonant wavelength of the ring. Eq. (7) - (8) can be used to show the implementation of the ring resonator structure as a perfect all-optical switch. The MATLAB simulation result is performed to show the perfect switching activity of MRR structures. To obtain the proper switching activity, the specific device parameters are considered based on the performance analysis of MRR structures, which are represented as shown in table 1. The MATLAB simulation result can be observed in fig.  4, which describes the switching activity. Figure 4 describes the switching of an optical signal with the application of the control signals. It is observed that the absence of the control signal shifts the signal from through port to the drop port. Similarly, as we apply the optical control pump signal vertically to the ring resonator, the gradual shifting of an optical signal from the drop port to the through the port, can be observed. Figure 5 shows the graphical representation of the transfer function of a single Micro-ring resonator (MRR) at the through and drop port. The figure shows the significant switching at the specified wavelength of 1550nm. Figure 5 describes the temporary blue shift of the micro-ring resonator wavelength. Some important parameters are assigned for the occurrence of appropriate blue shift phenomena. The parameters can be represented in table 3. Based on the specified parameters, the MATLAB simulation result can be observed in fig. 5, which shows the perfect switching activity with appreciable optical signal strength at the output ports. However, the analysis of the transfer function involves the computation refractive index change (∆n), which can be represented by the eq. (9) [25].
Equation (1)   However, to achieve optimum performance of the proposed 1 × 4 memory register, the performance parameters of the micro-ring resonator structure are analyzed and the appropriate values of some important parameters e. g. coupling co-efficient (k 1 , k 2 ) and ring radius is obtained. The detailed analysis of parameters can be represented as follow.
The coupling coefficient k 1 and k 2 are key design parameters of a micro-ring resonator (MRR) for the proper functioning of an MRR as an optical switch. In a single ring resonator, if the control signal is not applied then, the input optical signal will appear at the drop port of MRR and in the presence of the control signal, the input signal will be directed towards through the port of MRR. In this way, the MRR is working as an optical switch and for obtaining the switching of MRR, the optimum values of k 1 and k 2 should be selected. Hence, to select the optimum values of k 1 and k 2 , simulation is performed for a different combination of these coupling coefficients and the obtained results are shown in fig. 7 and fig. 8, respectively.  and in the absence of a control pump signal, the through port intensity is 0.347, which is very high. Similarly, by analyzing all the readings of table 1, we have selected the values of coupling coefficients k 1 = k 2 = 0.25 as an optimum value for the proper working of a micro-ring resonator as an optical switch.
The radius of the ring is also a very important parameter for the switching operation of an MRR. By using the suitable value of ring radius, the output signals can be optimized accordingly. The wave propagates within the system acquires phase shift, as it travels along the radius of curvature of the ring. The relative phase of the traveling wave determines whether the light interferes constructively or destructively with the input signals. This phenomenon directly influences the output signal of the system. To obtain the most suitable value of the radius, simulation is performed by considering all the other parameters of MRR as constant, and the radius of the ring is varied from 1 to 10 µm. The effects of the ring radius towards the through port and drop port intensities of MRR are presented in fig. 9 and fig. 10. The fig. 9 shows the variation of through port and drop port intensity with the variation of radius R of a micro-ring resonator in the absence of a control pump signal while fig.  10 shows the variation of through port and drop port intensity for radius R of a microring resonator in the Presence of the control pump signal. In the absence of a control pump signal, we are getting seven minima values of through port intensity at a different value of R and seven maxima values of drop port intensity of the optical signal for the respective values of R. All the values of through port minima and drop port maxima at their corresponding values of radius, are shown by the column 2 and column 1 of Table 2. Now in the presence of the control pump signal, from fig. 10, we are taking values of through port and Drop port intensity for the respective values of radius R as given by the first column of Table 2. These values of through port and Drop port intensity of the signal are noted in the third column of Table 2. As per the basic working principle of ring resonator as an optical switch, in the absence of control signal through port must be at the minimum intensity, and Drop port must be at the maximum intensity of input optical signal and vice versa in the presence of control signal. So, from the obtained data of table 5, it can be concluded that the best value for the ring radius of the system is at R = 7.08 µm.

Figure of Merits
The radius of the ring R and coupling coefficients (k 1 and k 2 ) of a ring resonator are very crucial parameters and from our analysis, we have chosen their optimum values as k 1 = k 2 = 0.25 & R = 7.08 µm. Now, we are going to calculate the values of different performance parameters of the ring resonator from the simulation result and also verify that, we are getting the optimum value of performance parameters at the mentioned values of coupling coefficients/radius of the ring. The performance of each ring resonator can be measured in terms of the free spectrum range (FSR), 3-dB bandwidth or full width at half maximum (FWHM), Finesse (F), Q factor, on-off ratio (OOR), extinction ratio (ER), contrast ratio (CR), amplitude modulation (AM) and switching speed. The output of the simulation result is shown in Fig. 11. It shows the variation of normalized output intensity of through port and drop port for the wavelength of the input optical signal in the presence and absence of optical control pump signal. Free spectrum range (FSR): It is the frequency spacing between two resonance peaks of the drop port signal which is shown in fig. 6. For the calculation of FSR, let us consider k as the phase constant which corresponds to Φ = 2mπ and k+Δk as the phase constant which corresponds to Φ = (2+1) mπ where m is an integer and Δk is the phase constant. The frequency and phase shifts are denoted by Δf and Δ and can be written as [26], Now the FSR in terms of frequency (f) and wavelength ( ) is expressed as: -∆f = c n gr . L (12) ∆λ = |− λ 2 n gr . L | Where n gr is the group refractive index and it is defined as, n gr = n eff − λ dn eff dλ (14) In fig 11, the FSR of the proposed MRR structure is computed as 43 nm.
The full width at half maximum (FWHM): -The bandwidth of the ring resonator is given by the full width at half maximum (FWHM) of the ring intensity resonance or its 3-dB bandwidth. It is a measure of the sharpness of the resonance [26]- [27]. The resonance bandwidth determines how fast the optical data can be processed by a ring resonator. The FWHM, in terms of frequency (f) and wavelength ( ) can be expressed as: FWHM(λ) = λ 2 F n gr . L (16) Where F denotes finesse of ring resonator. In the fig. 11, the computed value of FWHM is 2 nm.
Finesse: -The finesse, F of the resonator is defined as the ratio of the free spectral range (FSR) to the full width at half maximum (FWHM) of a micro-ring resonator.
Now, computing the values of FSR and FWHM using the fig. 11, the value of Finesse is computed as 21.5.
Quality factor: -The quality factor or Q factor of an optical waveguide is due to its energy stored and the power lost per optical cycle. The Q factor is defined as: The Q factor of a ring resonator can be defined as The shape and bandwidth of the ring resonator output are determined by the Q factor. A high value of the Q factor is required for all-optical signal processing applications [26]. According to the suggested parameters of the proposed unit, the Q factor of the proposed unit is computed as 750.

On-off ratio (OOR): -
The ON-OFF ratio for the throughput and drop port, which is the ratio of the on-resonance intensity to the off-resonance intensity, is given by [26]- [27]: On − off Ratio = T max (through port) T min (drop port) (20) A high value of the ON-OFF ratio is required for designing the high-performance micro ring resonator system and it should be more than 20 dB [28]. From fig. 11, the obtained value of the ON-OFF ratio is 41.0490 dB.

Extinction ratio (ER): -
The extinction ratio is defined as, [26]- [27], Where P min 1 and P max 0 are the minimum and maximum values of the peak intensity of high ('1') and low ('0') respectively. The high value of extinction ratio distinguishes the high level (1) from the low level (0) very clearly. The impact of the variation of coupling coefficient on ER is represented in fig. 12 and the impact of the variation of ring radius on ER is shown in fig. 13. From these two graphs, it can be seen that at coupling coefficient k 1 = k 2 = 0.25 and ring radius = 7.08 µm, we are getting the maximum value of extinction ratio as 18.98 dB. Therefore, this result justifies that we have selected optimum values of coupling coefficient and ring radius.

Contrast ratio (CR):
The output contrast ratio (CR) is defined as the ratio of the mean value of output intensity for '1' (P mean 1 ) to the mean output intensity for '0' (P mean 0 ) and given as [29], For optimum performance, the CR must be as high as possible so that the main fraction of input can exist at the output. Variation of contrast ratio with the variation of coupling coefficient is given in fig. 14 and the variation of contrast ratio for the radius of the ring is given by fig. 10. In fig. 14  and P min 1 are the maximum and minimum values of intensity at a high (1) level. As we know that, the typical value of AM must be less than 1dB [32]. The simulation results for determining the optimum value of amplitude modulation (AM) are shown graphically in fig. 16 and fig. 17. The effect of the variation of coupling coefficients on AM is shown in fig. 16 and from the figure it can be observed that the lowest value of AM is 0.0165 dB and it is obtained at 0.25 of coupling coefficient. Hence, the result shows that we have selected the most suitable value of the coupling coefficient. Figure 17 shows the impact of the variation of radius of the ring (R) on amplitude modulation (AM). We can observe from fig. 17 that, the lowest value of AM (0.0166 dB) is obtained at R = 7.08 µm.
Switching speed: -In a micro-ring resonator, the output optical signal is switched on and off by the application of continuous optical input signal and control pump signal. As a result of this ultra-fast rising and falling edges can be observed. When the input signal is applied across the ring resonator in the presence of the control pump signal, the output signal starts to rise and in the absence of the control signal, the output signal falls to a low level. The rise and falling time of the micro ring resonator is shown below in fig.18 (a) & 18 (b).  fig. 18 (a), the switching speed for rise time is taken as the time required to reach the output optical signal from 10% to 90% of its magnitude. Similarly, from the fig.18 (b), the switching speed for fall time is taken as the time required to reach the output optical signal from 90% to 10% of its magnitude. Hence, the obtained values of rise time and fall time are 2.531ps and 2.52ps, respectively. Based on the investigated parameter, the proposed 1 × 4 memory register is simulated, and suitable results are obtained. The final result is represented using tables (4)- (6). Hence, the above analysis shows the suitability of the selected parameters for the proposed all-optical memory registers. Based on the parameter analysis, we have suggested some optimum device parameters as shown in table 1. The optimum parameters are used to design the proposed unit and the optimum result can be observed as shown in the fig. (26)- (28).  Fig. 19 All-optical clocked D flip-flop using the feedback assisted micro-ring resonator structure In figure 19, the design of the optical clocked D flip-flop using the micro-ring resonator structure is discussed. The proposed Optical clocked D flip-flop can be used to store the optical data up to the desired duration of time-based on an optically controlled pump signal [22]. The layout consists of feedback assisted micro-ring resonator structure. The main objective of feedback is to maintain the previous state of the flip-flop in the absence of the controlled pump signals. The suitability of the layout can be verified by the MATLAB simulation result as shown in fig. 20. Figure 20 shows the proper working of clocked assisted all-optical clocked D flip-flop. The first row indicates the presence of data bits in the form of the presence and absence of the optical signal.   fig. 21 provides the controlling mechanism to implement the READ/WRITE operation [23]. The layout of active low tristate buffer logic comprises two micro-ring resonators (MRR) structures. The first MRR is responsible for the presence of the optical signal at the input port of the second MRR. The switching of the first MRR can be controlled using the vertically applied optical signal EN. In the absence of EN, the optical signal can be observed at the drop port of the first MRR, which is directly connected to the input port of the second MRR. Hence, in the absence of EN, the optical signal can be observed at the input port of the second MRR structure. The second MRR can be controlled by the optical control pump signal 'IN'. Hence, the presence of an optical signal at the through port of the second MRR depends upon the status of the input signal. Similarly, if the EN acquires the high value the optical signal switches to through port of the first MRR. Hence, the status of IN signal will not change the status of the through the port of the second MRR.

Fig. 22: MATLAB simulation result of the proposed optical active low tri-state buffer
The MATLAB simulation result of the all-optical tri-state buffer is represented as shown in fig. 22. The first row of the simulation result represents the status of the first MRR control signal EN. The second and third-row describes the status of the Input signal and Output signal, respectively. The Output signal can be observed at the through-port of the second MRR. The MATLAB simulation result is obtained using the eq. (1) -(8). Figure 22 represents that, in the absence of signal EN, the second MRR simply transfers the input optical signal to the through port whereas, if the EN signal is made high the output signal can be observed as low, irrespective of any status of the control signal 'IN' i.e. input signal. In the presence of the clock signal, the optical data bits D 0 , D 1 , D 2 and D 3 can be observed at the respective output ports in the form of Q 0 , Q 1 , Q 2 and Q 3 , respectively. In the absence of a clock signal, it maintains the previous output through the feedback path for a small duration. The fourth column of the proposed layout ensures the controlled READ operation. The switching activity in each MRR of the fourth column (MRR13-MRR16) can be controlled by the common vertically applied optical RD signal. For the low value of RD signal, the optical signals Q 0 , Q 1 , Q 2 and Q 3 can be observed at the corresponding drop port of the respective MRR in the form of D OUT 0 , D OUT 1 , D OUT 2 and D OUT 3 . The simultaneous application of optical control pump signal is very important in the proposed unit. In the proposed unit, an all-optical control pump signal is applied in the form of a green laser from the top of the ring. The control pump signal (2.552mW) enables the switching from the drop port to the through-port under the process of blue shift phenomena. However, the simultaneous application of control pump signals e.g. WR, D in0 − D in1 , CLK and RD signal can be applied using the approach of diffractive beam splitter techniques. The unit involves the splitting of the laser into multiple beams and simultaneously focusing on multiple points by combining lenses or focusing lenses. It can be used with multi-mode and single-mode lasers. It provides the facility of easy alignment and in this technique, splitting characteristics remain independent of beam incidence position. The collimated laser beam is allowed to pass through the beam splitter with the prespecified separation angle. The well-focused spots can be achieved with precise and certain distance by adding a focusing lens after the diffractive beam splitter. The selection of lens can be performed on the basis eq. (24)

d = tan(θ s ) × EFL (24)
The minimum input beam size can be decided by the fact, that it should be at least 3 times the size of the period in the DOE. The period is given by the grating equation (25). The system modeling and simulation process of the proposed unit can be divided into four groups. The first group (MRR1-MRR4) is associated with the WRITE operation, which enables the write operation based on the status of the optical control pump signal (WR). Figure 23 suggests that, if the status of (WR) is '0', which means WR ̅̅̅̅̅ =1, optical input signal can be observed at the drop port of the MRR1-MRR4. The mathematical expression of the output signal intensity at the drop port of MRR1-MRR4 can be represented using the equation (26). Where, the parameters D, k 1 , k 2 , x are having the usual meaning as described in the equation (1) - (8), in the segment of mathematical analysis of a single MRR structure. The expression for ϕ MRR1 − ϕ MRR4 can be represented using the equation (27).
where, n eff(MRR1) n eff(MRR2) n eff(MRR3) n eff(MRR4) } = n 0 + n 2 . I WR = n 0 + n 2 A eff P WR (27) Where, I WR and P WR is the intensity and power associated with the optical control pump signal WR. In equation (31), the value of ( 0 − 3 ) can be taken from the eq. (29). The values of ( 9 − 12 ) can be represented by the eq. (32) Where, and is the intensity and power associated with the optical control pump signal . The final and fourth stage shows the READ operation of the proposed 1 × 4 memory register. The MRR13-MRR16 switches the optical input signal ( 0 − 3 ) to specified output ports ( 0 − 3 ) based on the status of the control pump signal RD. In fig. 23, it is visible that, the absence of control pump signal RD (RD=0 or ̅̅̅̅ = 1) switches the optical signal ( 0 − 3 ) to the specified output port of ( 0 − 3 ). Finally, the mathematical expression for the status of the output port ( 0 − 3 ) can be represented using the equation (33). The status of the optical data bits can be observed in the second row. The 3 rd and 4 th row show the previous and present status of the output signals, respectively. Similarly, the 5 th and 6 th row shows the status of the control signal RD and output signals ( 0 , 1 , T 2 and 3 ), respectively. It can be observed that, in fig. 26, as the status of the WR signal is low, the status of 2 nd row ( 0 1 2 3 → 0110) is written to the 4 th row (through-port of each feedback-assisted optical clocked D flip-flop). As for the simulation, we have made the clock signal high, hence the through ports of (MRR9-MRR12) ( 0 1 2 3 → 0000) is completely independent of the previous state of the output at the D-flip flop( 0 . In the fourth row, the RD is made high, hence at the output port 0 , 1 , 2 and 3 the READ operation cannot be observed. Basically, in fig. 26, the write operation has been performed.    Table 4 shows the tabular validation of WRITE operation of the all-optical memory register, where the data provided in the form of 0 − 3 can be written at the through-port of optically clocked D flip flop, which can be observed as 0 − 3 .  fig. 27 represents all-optical READ operation. The first row shows the WR signal is high, which ensures that the write operation is disabled. In fig. 27, although the second row is loaded with the optical data 0 1 2 3 → 0111, but in the absence of a clock signal the device maintains the previous optical data Q prev0 , Q prev1 , Q prev2 and Q prev3 → 0110 at the output of each optical clocked D flip-flop Q 0 Q 1 Q 2 Q 3 → 0110. In the 4 th row of fig. 27, as the RD signal is maintained at the low, hence at the output port of the proposed device is observed as the D OUT 0 D OUT 1 D OUT 2 D OUT 3 → 0110, which clearly shows the optical READ operation.  The tabular representation of the READ operation can be verified using table 5. The table shows the validity of the proposed unit, with the selected value operating parameter as shown in table 3, which is obtained by the parameter analysis. Figure 28 shows, we have made the READ and WRITE operation disabled. The MATLAB simulation clearly shows the memory-mode of the unit, where both WR and RD are maintained at the logic high. In this case, although the optical data bits are given as D IN 0 D IN 1 D IN 2 D IN 3 → 1001 but the output ports is associated with Q 0 Q 1 Q 2 Q 3 → 0111, which is the same as the previous data Q prev0 , Q prev1 , Q prev2 and Q prev3 → 0111. Since we have disabled the READ operation by making RD signal as logic high, hence we are not observing the output at the output terminals. Figure 28 shows the memorymode of the 4-bit all-optical memory register. The tabular representation of memory mode can be represented using table 6, where we can find the previous output at the through-port of optically clocked D flip-flop, with some power loss. The loss analysis for the three different modes i.e. READ, WRITE, and MEMORY mode of the proposed memory register are as follows. The loss factor for the cascaded Micro-ring resonator can be represented using the eq. (35) [27], Loss Factor = 20 log ( Output Intensity Input Intensity ) Based on the eq. (35) the loss factor is computed for the proposed unit, which can be represented as follow, Fig. 29: Average Loss factor for the cascaded Micro-ring resonator structure Fig. 29 suggests the average loss factor of all the four output data ports in the state of READ, WRITE, and MEMORY mode for 1 clock duration. The analysis shows that the average loss factor is -3.487dB, -2.901dB, and -2.703dB for the READ, WRITE, and MEMORY modes.

Conclusion
In this paper, we have described one of the applications of the switching activity of the micro-ring resonator structure. The paper shows the efficient application of appropriate numbers of MRR structures to implement the all-optical 1x4 memory register. The different segment of the proposed unit is described. The paper shows the complete mathematical description of the switching activity of the micro-ring resonator structure. The paper describes the requirement of the average amount of controlled power to perform the appropriate switching activity at the wavelength of 1550nm. In this paper, we have performed the complete parameter analysis to optimize the performance effecting parameter of the proposed memory register. The important device parameter of the switching unit e.g. coupling coefficients and radius of MMR structures are investigated to optimize various performance effecting parameters e.g. extinction ratio, on-off ratio, contrast ratio, amplitude modulation, and switching time. The different segments used to implement the proposed unit e.g. optical clocked D flip-flop, all-optical active low tri-state buffers are discussed and the corresponding MATLAB simulation result is described. Finally, 16 identical MRR assisted complete 1 × 4 memory register layout is described completely with the detailed mathematical modeling and simulation process. The proposed unit is verified using the appropriate MATLAB simulation result, where READ and WRITE, and MEMORY mode of operations are represented.