Abstract Refractive index N(t) = N0-CKd(t) Phase ?(t) =

Abstract The report describes about develop an opticalswitching simulation based on Mach-Zehnder interferometer. Interferometeris a device used to measure relative phase shift between two parallel beams thesource and used to measure the optical path length by splitting a single sourcelight into two beams that travel in different path and then combined again toproduce interference. //A comprehensive study has been made on the effect ofinput optical signals on the switching properties with reference to the opticalfield propagation and refractive index propagation.// The overview of theinvestigation on static and dynamic performances of Mach-Zehnder interferometerhas been discussed in this report. MATLAB is used for develop time basedoptical switching simulation. The detailed description on the development of the simulator and thenthe results produced are discussed in this report.  Overview of the investigation The optical switching performance can beinvestigated in two ways, one is static performance, where the refractive indexbetween D1 and D2 and the relative phase shift with respect to d(t0)is calculated by substituting given parameters in to the formula.

Other way isthe dynamic performance, where an optical signal is applied to one of theinput, transfer over the switch’s and phase shifter to the output. The initialsimulationparameters are given in table 1.   Investigatingstatic performance. For investigating static performance, the relativerefractive index and phase shift between D1 and D2 calculated for a value ofd(t0) =1×1024, 1.25×1024 , 1.5×1024 withK = 2×10-26 m3. Refractive index N(t) = N0-CKd(t) Phase  ?(t) = /  From the static performance investigation, For the value of d(t0) = 1´1024, N(t) = 2.9970 and ?(t) = 6.

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2769e+03. For the value of d(t0) = 1.25´1024, N(t) = 2.9963 and ?(t) = 6.2753e+03 For the value of d(t0) = 1.5´1024, N(t) = 2.

9955 and ?(t) = 6.2738e+03. Thus, it can beshown that there is not much of a difference in values of N(t) and ?(t) fordifferent values of d(t0). Investigatingdynamic performance.

    Coupler 1 1    Coupler 2 2    D1    P1   Dl    D2    P2    P3    P4   Fig. 1 In dynamic performance, anoptical data signal is input to port 1 with no input to port 2. The devices D1 and D2 in figure (1), have an identical controlsignal applied to them at the same instance in time such that d(t) variesaccording to the data given in the spreadsheet assignment.A particular value of d(t) can be considered to act along the whole length ofthe device at that time instance. For the simplicity, it is assumed thatoptical field input to port 1 has an intensity that does not affect d(t) in D1or D2. To evaluate the switching operation the most intuitive way is toconsider the phase shift experienced by all possible light paths from input tooutput. The operation of the device is such that a signal input to port 1splits into two (by power) at coupler 1.

The two components travel alongdifferent paths. Assuming the actual physical length is the same then thepresence of the phase shifter will delay the signal passing through it withrespect to the other signal and cause a relative phase between them. Thesignals will add together at coupler 2. The way they add depends on the phaseshifts imposed onto them by the various paths.Assuming a signal is input is toport 1 only. A number of paths can be identified, and these are:Path 1.Port 1 straight through coupler 1, through the phase shifter D1, straightthrough coupler 2 and out through port 3.

Path 2.Port 1 straight through coupler 1, through the phase shifter D1, cross over atcoupler 2 and out through port 4.Path 3.

Port 1 cross over at coupler 1, through the phase shifter D2, cross over atcoupler 2 and out through port 3.Path 4.Port 1 cross over at coupler 1, through the phase shifter D2, straight throughcoupler 2 and out through port 4.

 Phase shift imposed on a signalwhen passing straight through a coupler is 0. Phase shift imposed on a signalwhen crossing over at coupler is d.It is assumed in this analysis that the coupler phase shift d= p/2. Phase shift imposed by phaseshifter is q. This effectively gives fourwaveforms at the output (two at each output port). The waves and their relativephase shifts are summed to give the waveform at each output.

It is easier toconsider only the phase shifts and assume that when waves add together that arein anti-phase they cancel and produce no signal. Waves that add together thatare in phase produce a signal.  Consider when the phase shifterimposes no phase shift – Consider first the waves outputfrom port 3.Path 1 the phase shifts imposed ona signal is 0 + 0 = 0 (no cross over at the coupler).Path 2 the phase shifts imposedon a signal is p/2 and p/2(two cross overs at the coupler) =p.Effectively this is two waves onewith 0 phase shift and one with pphase shift, anti-phase signals.

Adding these two waves amounts to two waves pradians (180°) out of phase, the waves cancel,with no output from port 3.Consider the waves output fromport 4.Path 3 the phase shifts imposedon a signal is 0 + p/2 = p/2(one coupler cross over).Path 4 the phase shifts imposedon a signal is p/2 + 0 = p/2.

These two waves undergo the samephase shift and constructively interfere gives an output at port 4. Thus, nooutput at 3 but an output at 4. Consider when the phase shifterimposes p phase shift -Consider the waves output fromport 3.Path 1 the phase shifts imposedon a signal is 0 + p + 0 = p.Path 2 the phase shifts imposedon a signal is p/2 + p+ p/2 = 2p.Effectively this is two waves onewith p phase shift and one with 2pphase shift, anti-phase signals.

Adding these two waves amounts to two waves pradians (180°) out of phase, the waves cancel,with no output from port 3.Consider the waves output fromport 4.Path 3 the phase shifts imposedon a signal is 0 + p + p/2= 3p/2.Path 4 the phase shifts imposedon a signal is p/2 + p+ 0 = 3p/2.

These two waves undergo the samephase shift and constructively interfere gives an output at port 4. Thus, nooutput at 3 but an output at 4. Note the imposing of a phase shift of pby the phase shifter has effectively not switched the signal from port 4 toport 3. From this above analysis we can find that there is no output producedin port 3. Therefore, in order to switch the signals from port 4 to port 3, thephysical separation between the phase shifter devices be of magnitude ?l. Thiswould produce the delayed version of signals in the output ports.

  Description of the simulator Thetime based optical switching simulator is implemented in the MATLAB as show inthe above fig1. The coupler is used to split and combine optical signal. It canbe described as a device that split the input signal equally, in terms of powerat the output.

The coupler can be expressed in terms of power/ intensityfunction given by.                                      Where h(m, n) represents the power couplingcoefficient between ports m and n. P3, P4 are the outputports and P1, P2 are input ports (Optical Networks, 2010). Asinusoidal signal is generated to propagate through devices D1 and D2 which areelectronic in origin and are based on a parameter, d(t), in the device, whichis based on a control affects the field propagating through the switch and thusthe Refractive index.The relative refractive indexbetween D1 and D2 based on d(t) is                         where N0 is arefractive index constant, C a factor that affects propagation, K the                       dependence of refractiveindex on d(t) and Dt the propagation delay between D1and D2. Phase.    Relative phase change betweensignal propagating through D1 and D2 (this is                    appropriate for switchingapplications such as this) L is the length of D1 or D2, lthe signal wavelength.

 The waveguides form theintersection of the inputs, couplers, devices and outputs and serve to guidethe fields along. Duringthe implementation of MATLAB simulation, the devices D1 and D2 are imposed withdensity of charge d(t) varied with time. The data is imported into the MATLABfrom excel sheet. The time delay is calculated for the device D1.

So, that thesignal is in constructive. In the simulator electric charge is applied for bothnonlinear devices D1 and D2 which changes the refractive indices N1(t) and N2(t).it is expressed as. N2(t)= N1(t- ?l/c) Where?l is the length between the devices andC is the speed of light, it shows that signal arrives at device D1 earlier thanthe signal travel through the D2 device.

The phase shift at each branch iscalculate by   In order to operate the switchoperation a simple modulation and amplitude shift keying is used forimplementing a transmitter and Matlab programming. The transmitter prepares arandom bit stream. The optical signal cannot be effectively transmitted becauseits main frequency is far away from the optimal frequency. The signal ismodulated by the carrier signal of Matlab progrmming help complex exponentialform with frequency f=c/ . Where,  is the wave length of the input signal.

Atthe output the signal is demodulated by the complex conjugate (Proakis 2008).To recover the bit stream from demodulation received signal, Matlab uses Integratorfunction intdump() to add up everyspb samples.it declares that the value abovezero represent a symbol ‘1’ and a ‘0’ otherwise.

  Results and discussion The purpose ofthis simulation is to evaluate the feasibility of employing the proposed deviceas an optical switch. Hence, we need to check to what extent is the inputsignal present at each of the output ports in steady state and in transientcharge density in devices D1 and D2. First, weanalyse the effective phase shift introduced by D1 and D2. Figure (2) shows thephase shift (in radians) that a signal passing through each of these devicesundergoes. The effective phase shift ??(t) = ?1(t) – ?2(t) defines theswitching behaviour. When it is flat, the input field appears at one of twooutputs; during transient periods there will be electrical energy at bothoutputs.

  Fig. 2 Figure (3a & 3b)shows the effects of transmitting a pure sinusoid through our system. Forillustrative purposes, the sinusoid shown has much lower frequency than thespecified carrier with.

From these plots we can understand the function of theswitch. The input field E1switch has its energyevenly split by the first coupler into two signals, E3intermediate and E4intermediate.The latter is delayed by a quarter-wavelength. After passing through theelectronic devices and, the respective signals appear stretched in time in thetransient charge period.  This is due to the time-varying phase delayintroduced by the devices. After the device charge settles, the output signalhas the same wavelength as at the beginning.

Finally, at the outputs of coupler2 we observe the switching behaviour. When, all the input power goes to port 4of coupler 2; when most of the input power goes to port 3.   Fig. 3a       Fig. 3b The switch doesnot exhibit ideal behaviour when diverting the input signal to port 3 ofcoupler 2. When input power is switched to output 3, output 4 continues to emitabout 10% of the signal power. Figure (4) shows the power of the electricfields at each of these ports over time.

  Fig. 4 Figure(5) shows the transmitted and recovered bitstreams from the experiment with azero bit-error rate. As Figure shows, the non-ideality of this switch issignificant. As designed, the switch is insecure, because it broadcasts theinput signal to one of the output ports at all times and inefficient, becauseit does not transmit all the input power to the desired output when port 3 isselected.  Fig.

5  Conclusion In this courseworkan optical switch based on the Mach-Zehnder interferometer has been evaluated.In the development of this report, the overview of investigation onMach-Zehnder interferometer was given, then the description of the simulatorfor a single-mode switch operation using a simple amplitude-shift keyingmodulator/demodulator was given. In the result analysis it was shown that theswitch’s non-ideality allows the recovery of the input bit stream from the”off” port. Further, it was suggested that by increasing the charge density ofthe devices better switching could be achieved when the intended output is port3. If the physical design of the switch renders such a change, it issuggested to cascade a clamping device that attenuates the port 4 signal onceit falls below 10% of nominal power to ensure data security.  References       1       Proakis, J. G.

Digital communications.1995. McGraw-Hill, New York.

       2       Mach-Zehnder Interferometer. (21stDecember 2017). In Wikipedia.Retrieved from https://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer        3       Mehra, R., Shahani, H.

, & Khan, A. (2014).Mach Zehnder interferometer and its applications. Int. J.

Comput. Appl,31-36.       4       Singh, G., Yadav, R. P., Janyani, V., &Ray, A. (2008).

Design of 2× 2 optoelectronic switch based on MZI and study theeffect of electrode switching voltages. Journal of World Academy ofScience, Engineering and Technology, 39, 401-407.       5       Rajiv Ramaswami, Kumar N. Sivarajan, Galen H. Sasaki(2010).Optical Networks 3rdedition, Chapter 3 Components.coupler, Retrieved from http://www.sciencedirect.com.lcproxy.shu.ac.uk/science/article/pii/B9780123740922500114