QUEEN’S UNIVERSITY AT KINGSTON
Department of Electrical and Computer Engineering
ELEC–486 Fiber-Optic Communications
Assignment 3, Winter 2013
1. The chirp of a lithium niobate modulator for dual drive (push-pull) modulation is
dV2 (t) dV1 (t)
+
:
dt
dt
(1)
Vm cos (! m t + ) and V2 (t) = Vb2 + Vm cos (! m t)
(2)
(t) =
1
4V
Using
V1 (t) = Vb1
(1) yields,
(t) =
=
=
,
=
!m
[ Vm sin(! m t) + Vm sin(! m t + )]
4V
! m Vm
[ sin(! m t) + sin(! m t) cos + cos(! m t) sin ]
4V
! m Vm
[( 1 + cos ) sin(! m t) + sin cos(! m t)]
4V
! m Vm
[A cos(! m t) B sin(! m t)]
4V
! m Vm p 2
A + B 2 cos (! m t + )
4V
(3)
where
= tan 1 (B=A), A = sin and B = 1 cos .
p
A2 + B 2 can be simpli…ed (although it’s not necessary)
p
A2 + B 2 =
=
(sin )2 + (1
(sin )2 + (cos )2 + 1
= [2
p
(t) =
cos )2
1=2
2 cos
1=2
2 cos ]1=2
2! m Vm
[1 cos ]1=2 cos (! m t + ) :
4V
1
(4)
As expected, the special case
pp
= 0 yields
(t) = 0. The peak-to-peak chirp is
p
2! m Vm
=
[1 cos ]1=2
2V
p
2 fm Vm
=
[1 cos ]1=2
V
p
=
2 1010 (0:1) [1 cos( =10)]1=2
= 0:98 GHz.
(5)
2A. For a single-drive lithium niobate Mach-Zehnder modulator, the output signal is given
by
V1 (t)
2 V
V1 (t)
1 + cos
V
I(t) = = E02 cos2
E02
2
=
(6)
:
(7)
The applied voltage is a Gaussian pulse
V1 (t) = Vb + Vm exp
(t=T )2
(8)
where Vb is the bias voltage and Vm is the modulation voltage. The chirp is given by
1 dV1 (t)
4V
dt
Vm t
exp
=
2V T 2
(t) =
(t=T )2 :
(9)
The -parameter is given by
d chirp
d(ln I)
d chirp =dt
= 2
d(ln I)=dt
2
(t)
= 2
d(ln I)=dt
(t)
= 4 I
dI=dt
= 2
(10)
Substituting (6) and (9) in (10), and using (8) yields
=
V1 (t)
2 V
cot
2
:
(11)
Chirp for a Gaus s ian Pulse
Chirp (GHz)
5
0
-5
-100
-80
-60
-40
-20
0
Tim e (ps )
20
40
60
80
100
pi
Power (mW) and Voltage (V/V )
Applied Voltage and Output Power for a Gauss ian Pulse
2
Power
Applied Voltage
1.5
1
0.5
0
-100
-80
-60
-40
-20
0
Tim e (ps )
20
40
60
80
100
Figure 1: Chirp, power and applied voltage for Vb = Vm = V .
B. For T = 50 ps, V = 4 V, a CW input optical power of 1 mW, and Vb = Vm = V , the
chirp, power, and applied voltage are shown in Figure 1. For these values of Vb and Vm , the
noninverting case is obtained and the modulator is changed from o¤ to on during the rising
edge of the voltage pulse. The optical pulse di¤ers from the applied voltage pulse due to the
transfer characteristic of the modulator; the optical pulse has sharper edges. The chirp is
positive for single-drive modulation of arm 1 with V2 = 0 V. The peak-to-peak chirp is about
9 GHz. The -parameter
is shown in Figure 2. The half-power points of the output pulse
p
occur for t =
ln(2)T = 41:63 ps. The -parameter at these points is 1, as expected
since the simple expression for the -parameter obtained in class is for this point. Over the
duration of the pulse, the -parameter varies from being close to zero to being in…nitely
large for t = 0 since dI=dt = 0.
3
Alpha Param eter for a Gaus s ian Pulse
10
9
8
Alpha Parameter
7
6
5
4
3
2
1
0
-100
-80
-60
-40
Figure 2:
-20
0
Tim e (ps )
20
40
-parameter for Vb = Vm = V .
4
60
80
100
3. EAM
Eye Diagram Analyzer
Optical Time Domain Visualizer
Dbl Click On Objects to open properties. Move Objects w ith Mouse Drag
0
0.5
1
0
0.5
Tim e (bit period)
1
0.0008
1m
0.0006
800 µ
0.0004
Amplitude (a.u.)
600 µ
0.0002
400 µ
193.08 T
193.1 T
Frequency (Hz)
193.12 T
193.14 T
200
210
Tim e (bits)
0
0
0
200 µ
20 G
0
10 G
Frequency (Hz)
-20 G
200 µ
-80
-100
193.06 T
-10 G
400 µ
Power (W)
600 µ
Power (dBm)
-60
-40
800 µ
-20
1m
0
Dbl Click On Objects to open properties. Move Objects w ith Mouse Drag
Tim e (bits)
200
210
220
0.001
Optical Spectrum Analyzer
Dbl Click On Objects to open properties. Move Objects w ith Mouse Drag
220
MQW MZM SR = 1.
Eye Diagram Analyzer
Optical Time Domain Visualizer
Dbl Click On Objects to open properties. Move Objects w ith Mouse Drag
0
0.5
1
0
0.5
Tim e (bit period)
1
0.0007
1m
0.0005
800 µ
0.0003
Amplitude (a.u.)
600 µ
400 µ
0.0001
200 µ
20 G
0
10 G
Frequency (Hz)
-20 G
200 µ
193.08 T
193.1 T
Frequency (Hz)
193.12 T
193.14 T
200
210
Tim e (bits)
0
0
-80
-100
193.06 T
-10 G
400 µ
Power (W)
600 µ
Power (dBm)
-60
-40
800 µ
-20
1m
0
Dbl Click On Objects to open properties. Move Objects w ith Mouse Drag
Tim e (bits)
200
210
220
0.0009
Optical Spectrum Analyzer
Dbl Click On Objects to open properties. Move Objects w ith Mouse Drag
220
MQW MZM SR = 1:3.
Optical Spectrum Analyzer
Eye Diagram Analyzer
Optical Time Domain Visualizer
Dbl Click On Objects to open properties. Move Objects w ith Mouse Drag
Tim e (bits)
200
210
220
Dbl Click On Objects to open properties. Move Objects w ith Mouse Drag
0
0.5
1
0
0.5
Tim e (bit period)
1
0.0008
1m
0.0006
800 µ
0.0004
Amplitude (a.u.)
600 µ
0.0002
400 µ
193.08 T
193.1 T
Frequency (Hz)
193.12 T
193.14 T
200
210
Tim e (bits)
5
220
0
0
0
200 µ
20 G
0
10 G
Frequency (Hz)
-20 G
200 µ
-80
-100
193.06 T
-10 G
400 µ
Power (W)
600 µ
Power (dBm)
-60
-40
800 µ
-20
1m
0
Dbl Click On Objects to open properties. Move Objects w ith Mouse Drag
The spectra are all quite similar. Since these are time-averaged results they do not
reveal the distinct properties of the modulator chirp. By comparing the results with a
directly modulated laser (DML), adiabatic chirp (as exhibited by a DML) changes the
modulated signal spectrum from that of ideal ASK more so than the transient chirp.
The chirp of the EAM is negative and then positive because of the voltage-dependent
properties of the
parameter. The chirp of the MQW MZM is negative.
The peak-to-peak chirp is about 36 GHz for the EAM, 11 GHz for MQW MZM SR = 1,
and 22 GHz for MQW MZM SR = 1:3.
The MQW MZM SR = 1 has better extinction (smaller output signal in the o¤-state)
than the MQW MZM SR = 1:3. With the
phase shift design and 0 V applied to
each arm, the signals are out-of-phase with the same amplitude for the MQW MZM
SR = 1 but not for the MQW MZM SR = 1:3. This is seen the time-dependence of
the optical power and the eye diagrams. Otherwise, the eye diagrams are similar, but
di¤erent due to the principles of operation: all three modulators are intended for 10
Gb/s intensity modulation.
The peak-to-peak chirp of the MQW MZM SR = 1:3 is larger than that of the MQW
MZM SR = 1 since more power is launched into the arm that contributes negative
chirp to the output signal.
6