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’)