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

Abstract

The report describes about develop an optical
switching simulation based on Mach-Zehnder interferometer. Interferometer
is a device used to measure 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 different path and then combined again to
produce interference. //A comprehensive study has been made on 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 is used for develop time based
optical switching simulation. The detailed description on the development of the simulator and then
the results produced are discussed in this report.

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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. Other way is
the dynamic performance, where an optical signal is applied to one of the
input, transfer over the switch’s and phase shifter to the output. The initial
simulation
parameters are given in 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 evaluate the feasibility of employing the proposed device
as an optical switch. 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
outputs.

Fig. 2

Figure (3a & 3b)
shows the effects of transmitting a pure sinusoid through our 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, E3intermediate and E4intermediate.
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 coursework
an optical switch based on the Mach-Zehnder interferometer has been evaluated.
In the development of this report, the overview of investigation on
Mach-Zehnder interferometer was given, then the description of the simulator
for a single-mode switch operation using a simple amplitude-shift keying
modulator/demodulator was given. In the result analysis it was shown that the
switch’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 of
the devices better switching could be achieved when the intended output is port
3. If the physical design of the switch renders such a change, it is
suggested to cascade a clamping device that attenuates the port 4 signal once
it 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. (21st
December 2017). In Wikipedia.

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.