Abstract

The report describes to develop

an optical switching simulation based on Mach-Zehnder interferometer. The interferometer is a device used

to measure the relative phase shift

between two parallel beams the source and used to measure the optical path

length by splitting a single source light into two beams that travel in a different path and then combined again to

produce interference. The report describe the effect of input optical signals

on the switching properties with reference to the optical field propagation and

refractive index propagation. The overview of the investigation on static and

dynamic performances of Mach-Zehnder interferometer has been discussed in this

report. MATLAB programming is employed develop time based optical switching

simulation.

The detailed description of the development of the simulator and then the

results produced are discussed in this report.

Overview of the

investigation

The optical switching

performance can be investigated in two ways, one is static performance, where

the refractive index between D1 and D2 and the relative phase shift with

respect to d(t0) is calculated by substituting given parameters in

to the formula. Another way is the

dynamic performance, where an optical signal is applied to one of the input,

transfer over the switches and phase

shifter to the output. The initial simulation parameters are given in below table 1.

Investigating

static performance.

For investigating static

performance, the relative refractive index and phase shift between D1 and D2

calculated for a value of d(t0) =1×1024, 1.25×1024 ,

1.5×1024 with K = 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) = 6.2769e+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 be shown that there is not much of a difference

in values of N(t)

and ?(t) for

different values of d(t0).

Investigating

dynamic performance.

Coupler 1 1

Coupler 2 2

D1

P1

Dl

D2

P2

P3

P4

Fig. 1

In

dynamic performance, an optical data

signal is input to port 1 with no input

to port 2. The devices D1 and

D2 in figure (1), have an identical control signal applied to them at the same

instance in time such that d(t) varies according to the data given in the

spreadsheet assignment. A particular

value of d(t) can be considered to act along the whole length of the device at

that time instance. For the simplicity, it is assumed that optical field input

to port 1 has an intensity that does not affect d(t) in D1 or D2. To evaluate

the switching operation the most intuitive way is to consider the phase shift experienced

by all possible light paths from input to output. The operation of the device

is such that a signal input to port 1 splits into two (by power) at coupler 1.

The two components travel along different paths. Assuming the actual physical

length is the same then the presence of the phase shifter will delay the signal

passing through it with respect to the other signal and cause a relative phase

between them. The signals will add together at coupler 2. The way they add

depends on the phase shifts imposed onto

them by the various paths.

Assuming

a signal is input is to port 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, straight through coupler 2 and out through

port 3.

Path

2. Port 1 straight through coupler

1, through the phase shifter D1, cross over at coupler 2 and out through port

4.

Path

3. Port 1 cross over at coupler 1,

through the phase shifter D2, cross over at coupler 2 and out through port 3.

Path

4. Port 1 cross over at coupler 1,

through the phase shifter D2, straight through coupler 2 and out through port

4.

Phase

shift imposed on a signal when passing straight through a coupler is 0. Phase

shift imposed on a signal when crossing over at coupler is d.

It is assumed in this analysis that the coupler phase shift d

= p/2. Phase shift imposed by phase shifter is q.

This effectively gives four waveforms at the output (two at each output port).

The waves and their relative phase shifts are summed to give the waveform at

each output. It is easier to consider only the phase shifts and assume that

when waves add together that are in anti-phase they cancel and produce no

signal. Waves that add together that are in phase produce a signal.

Consider

when the phase shifter imposes no phase shift

–

Consider

first the waves output from port 3.

Path

1 the phase shifts imposed on a signal is 0 + 0 = 0 (no cross over at the

coupler).

Path

2 the phase shifts imposed on a signal is p/2

and p/2 (two cross overs at the coupler) =p.

Effectively

this is two waves one with 0 phase shift and one with p

phase shift, anti-phase signals. Adding these two waves amounts to two waves p

radians (180°) out of phase, the waves cancel, with no output from port

3.

Consider

the waves output from port 4.

Path

3 the phase shifts imposed on a signal is 0 + p/2

= p/2 (one coupler cross over).

Path

4 the phase shifts imposed on a signal is p/2

+ 0 = p/2.

These

two waves undergo the same phase shift and constructively interfere gives an

output at port 4. Thus, no output at 3 but an output at 4.

Consider

when the phase shifter imposes p phase shift –

Consider

the waves output from port 3.

Path

1 the phase shifts imposed on a signal is 0 + p

+ 0 = p.

Path

2 the phase shifts imposed on a signal is p/2

+ p + p/2 = 2p.

Effectively

this is two waves one with p phase shift and one with 2p

phase shift, anti-phase signals. Adding these two waves amounts to two waves p

radians (180°) out of phase, the waves cancel, with no output from port

3.

Consider

the waves output from port 4.

Path

3 the phase shifts imposed on a signal is 0 + p

+ p/2 = 3p/2.

Path

4 the phase shifts imposed on a signal is p/2

+ p + 0 = 3p/2.

These

two waves undergo the same phase shift and constructively interfere gives an

output at port 4. Thus, no output at 3 but an output at 4. Note the imposing of

a phase shift of p by the phase shifter has effectively not switched the

signal from port 4 to port 3. From this above analysis

we can find that there is no output produced in port 3. Therefore, in order to

switch the signals from port 4 to port 3, the physical separation between the

phase shifter devices be of magnitude ?l. This would produce the delayed

version of signals in the output ports.

Description of the

simulator

The

time based optical switching simulator is implemented in the MATLAB as show in the above fig1. The coupler is used to

split and combine optical signal. It can be described as a device that split

the input signal equally, in terms of power at the output. The coupler can be

expressed in terms of power/ intensity function given by.

Where h(m,

n) represents the power coupling coefficient between ports m and n. P3, P4 are the

output ports and P1, P2 are input ports (Optical

Networks, 2010).

A

sinusoidal signal is generated to propagate through devices D1 and D2 which are

electronic in origin and are based on a parameter, d(t), in the device, which

is based on a control affects the field propagating through the switch and thus

the Refractive index.

The relative refractive index between D1 and D2 based on

d(t) is

where N0 is a refractive index constant, C a

factor that affects propagation, K the dependence of

refractive index on d(t) and Dt

the propagation delay between D1 and D2.

Phase.

Relative phase change between signal propagating through D1

and D2 (this is appropriate

for switching applications such as this)

L is the length of D1 or D2, l the signal wavelength.

The waveguides form the intersection of the inputs, couplers,

devices and outputs and serve to guide the fields along.

During

the implementation of MATLAB simulation, the devices D1 and D2 are imposed with

density of charge d(t) varied with time. The data is imported into the MATLAB

from excel sheet. The time delay is calculated for the device D1. So, that the

signal is in constructive. In the simulator electric charge is applied for both

nonlinear 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 and C is the speed of light, it shows that signal

arrives at device D1 earlier than the signal travel through the D2 device. The

phase shift at each branch is calculate by

In order to operate the switch operation a simple modulation

and amplitude shift keying is used for implementing a transmitter and Matlab

programming. The transmitter prepares a random bit stream. The optical signal

cannot be effectively transmitted because its main frequency is far away from

the optimal frequency. The signal is modulated by the carrier signal of Matlab

progrmming help complex exponential form with frequency f=c/

. Where,

is the wave length of the input signal. At

the output the signal is demodulated by the complex conjugate (Proakis

2008).

To recover the bit stream from demodulation received signal, Matlab uses Integrator

function intdump() to add up everyspb samples.it declares that the value above

zero represent a symbol ‘1’ and a ‘0’ otherwise.

Results and

discussion

The purpose of

this simulation is to understand the process of optical switching. Hence, we

need to check to what extent is the input signal present at each of the output

ports in steady state and in transient charge density in devices D1 and D2. First, we analyse the effective phase shift introduced by D1

and D2. Figure (2) shows the phase shift (in radians) that a signal passing

through each of these devices undergoes. The effective phase shift ??(t) = ?1(t)

– ?2(t) defines the switching behaviour. When it is flat, the input field

appears at one of two outputs; during transient periods there will be

electrical energy at both output.

Fig. 2

Figure (3a & 3b)

shows the effects of transmitting a pure sinusoid through the system. For

illustrative purposes, the sinusoid shown has much lower frequency than the

specified carrier with. From these plots we can understand the function of the

switch. The input field E1switch has its energy evenly split by the

first coupler into two signals, E3 intermediate and E4

intermediate. The latter is delayed by a quarter-wavelength. After

passing through the electronic devices and, the respective signals appear

stretched in time in the transient charge period. This is due to the

time-varying phase delay introduced by the devices. After the device charge

settles, the output signal has the same wavelength as at the beginning.

Finally, at the outputs of coupler 2 we

observe the switching behaviour. When,

all the input power goes to port 4 of coupler 2; when most of the input power

goes to port 3.

Fig. 3a

Fig. 3b

The switch does

not exhibit ideal behaviour when diverting the input signal to port 3 of

coupler 2. When input power is switched to output 3, output 4 continues to emit

about 10% of the signal power. Figure (4) shows the power of the electric

fields at each of these ports over time.

Fig. 4

Figure

(5) shows the transmitted and recovered bitstreams from the experiment with a

zero bit-error rate. As Figure shows, the non-ideality of this switch is

significant. As designed, the switch is insecure, because it broadcasts the

input signal to one of the output ports at all times and inefficient, because

it does not transmit all the input power to the desired output when port 3 is

selected.

Fig. 5

Conclusion

In

this work an optical switch based on the

Mach-Zehnder measuring system has been evaluated. Within

the development of this report, the summary of investigation on

Mach-Zehnder interferometer was given, then the outline of

the simulator for a single-mode switch operation using a simple amplitude-shift

keying modulator/demodulator was given. In the result

analysis it had been shown that the switch’s

non-ideality permits the recovery of the input bit stream from the

“off” port. Further, it had been prompt that by increasing the

charge density of the devices higher switch might

be achieved once the supposed output is port 3.

References

1

Proakis, J. G. Digital

communications. 1995. McGraw-Hill, New York.

2

Mach-Zehnder Interferometer.

(21st December 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 the effect of electrode switching voltages. Journal of

World Academy of Science, Engineering and Technology, 39, 401-407.

5

Rajiv Ramaswami, Kumar N.

Sivarajan, Galen H. Sasaki(2010).Optical Networks 3rd edition, Chapter 3 Components.

coupler, Retrieved from

http://www.sciencedirect.com.lcproxy.shu.ac.uk/science/article/pii/B9780123740922500114.

MATLAB code

clear;

close all;

clc;

% retrieving data from

excelsheet

data = xlsread(‘assignment.xls’);

figure(1);

plot(data(:,1),data(:,2));

title(‘assignment.xls’)

xlabel(‘t/s’)

ylabel(‘d(t)/(per metre cubed)’)

t = data(:,1); %s

– time

d = data(:,2); %C/m^3

– charge density

t(1) = 0;

%% Prepare constants

% Constants

c = 3e8; %m/s – speed of light

L = 500e-6; %m

K = 2e-26; %m^3

N0 = 3; – D1 and D2 initial index of refraction

C = 0.15;

lambda = 1.5e-6; %m

– Optical carrier wavelength

n = 1.0; – waveguide index of

refraction

delta_l = 1;

%% Calculate phase change

due to D1 and D2

N1 = N;

N(end)*ones(dl_over_c,1); %- ind. of refraction at D1

N2 = N(1)*ones(dl_over_c,1);

N; %- ind. of refraction at D2

% Extend time axis

dt = t(2)-t(1);

t = t(1):dt:length(N1)*dt-dt;

phi1 = 2*pi*L*(N1-N1(1))/lambda; %rad – phase

shift through D1

phi2 = 2*pi*L*(N2-N2(1))/lambda; %rad – phase

shift through D2

%% Signal generator

f = c/lambda;

T = 2*pi/f;

Spb = 400;

nbits = floor(length(t)/spb);

b = randi(2,1,nbits)-1;

p = ones(1,spb);

% Convert bit sequence b to

sample sequence d

d = zeros(size(phi1));

for n=0:nbits-1

d(1+n*spb:(n+1)*spb)= b(n+1)*p;

end

%%

%% Prepare transmission

signal

x = exp(2i*pi*f*t/2300); % Pure sinusoid

%% Execute simulation

E1_switch = x; % Input E field at switch 1

(top branch)

E2_switch = E1_switch; % Input E field at switch 2 (bottom branch)

% E fields after first

coupler

E3_intermediate = E1_switch.*(0.7071);

E4_intermediate =

E2_switch.*(0.7071i);

% E fields after D1 and D2

E1_intermediate =

E3_intermediate.*exp(-1i*phi1)’; % top branch

E2_intermediate =

E4_intermediate.*exp(-1i*phi2)’; % bottom branch

% E fields at output

E3_switch = E1_intermediate.*(0.7071);

E4_switch =

E2_intermediate.*(0.7071i);

%%

%% Figure – phase shift at

D1, D2 and effective phase shift

figure(2);

subplot(2,1,1)

plot(t,phi1,t,phi2);

grid on

xlabel(‘Time (s)’);

ylabel(‘Phase shift (radians)’)

legend(‘D1′,’D2′,’Location’,’NorthWest’)

subplot(2,1,2)

grid on

plot(t,phi1-phi2);

xlabel(‘Time (s)’);

ylabel(‘Deltaphi(t) (radians)’)

%%

%% Figure – simulator

performance with sinusoidal input

figure(3)

subplot(2,1,1)

plot(t, real(E1_switch), t,

real(E2_switch))

title(‘Input E-fields’)

xlabel(‘Time (s)’)

legend(‘E1_{switch}’, ‘E2_{switch}’, ‘Location’,’northoutside’,’Orientation’,’horizontal’)

subplot(2,1,2)

plot(t, real(E3_intermediate), t,

real(E4_intermediate))

title(‘Coupler 1 Outputs’)

xlabel(‘Time (s)’)

legend(‘E3_{intermediate}’, ‘E4_{intermediate}’, ‘Location’,’northoutside’,’Orientation’,’horizontal’)

figure(4)

subplot(2,1,1)

plot(t, real(E1_intermediate), t,

real(E2_intermediate))

title(‘D1 and D2 Output’)

xlabel(‘Time (s)’)

legend(‘E1_{intermediate}’, ‘E2_{intermediate}’, ‘Location’,’southoutside’,’Orientation’,’horizontal’)

subplot(2,1,2)

plot(t, real(E3_switch), t,

real(E4_switch))

title(‘Coupler 2 Outputs’)

xlabel(‘Time (s)’)

legend(‘E3_{switch}’,’E4_{switch}’, ‘Location’,’southoutside’,’Orientation’,’horizontal’)

%% Figure – Non-ideal

switching performance at coupler 2 outputs

figure(5)

plot(t, abs(E3_switch), t,

abs(E4_switch))

title(‘Coupler 2 Output Power’)

xlabel(‘Time (s)’)

legend(‘E3_{switch}’,’E4_{switch}’, ‘Location’,’southoutside’,’Orientation’,’horizontal’)

%% Figure – zero bit-error

rate

figure(6);

% Trim E4_switch

E4_t =

E4_switch(1:end-mod(length(E4_switch),10));

b_recovered =

abs(intdump(real(E4_t.^2), spb))>0;

hold on;

stem(b)

stem(0.5*b_recovered)

fprintf(‘Bit error rate: %f

‘,

sum(b-b_recovered)/length(b));

legend(‘Transmitted’, ‘Recovered (scaled)’)

title(‘Zero bit-error rate’)

xlabel(‘Index’)

ylabel(‘Symbol’)