7. A 1550 directly modulated laser diode has the following parameters :
Active area width
w 3 microns
Active area thickness d
0.3 microns
Length
L
500 microns
Confinemen t factor 
0.3
Time constant  r
1 ns
Gain cross - section  g
2.0 10 -20 m 2
Threshold density n
0.8 10 24 m 3
th
Cavity loss  cav
50m 1
Refractive index  3.5
(a) Assume a drive current of 200 mA (constant). Solve the diode rate equations
numericall y and show that the steady state optical power generated is accurately
predicted by the steady state analytic solution of the rate equation.
(b) Assume a NRZ bit sequence of 101101 as input current to the laser diode. The peak
current is 200 mA. Assume that current is zero for a bit '0'.Bit rate is 300 Mb/s.
1. Find the LP modes of a triangular core fiber with its refractive index given by the
following formula:
n(r )  n1  (n1  n2 )r / a for r  a
 n2
for r  a
where n 2 is cladding index = 1.45, n1 is core index at the center = 1.455.
(a) Choose a such that the fiber supports at least three modes at 1550 nm. Calculate
the effective indices and plot the mode profile as a function of radius r.
(b) Choose a such that the fiber is single-moded at 1550 nm. Plot the mode profile
as a function of radius r. Calculate the cut-off wavelength.
2. Find the LP modes of a parabolic index fiber with its refractive index given by the
following formula:
n(r )  n1  (n1  n2 )( r / a ) 2 for r  a
 n2
for r  a
where n 2 is cladding index = 1.45, n1 is core index at the center = 1.455.
(a) Choose a such that the fiber supports at least three modes at 1550 nm. Calculate
the effective indices and plot the mode profile as a function of radius r.
(b) Choose a such that the fiber is single-moded at 1550 nm. Plot the mode profile
as a function of radius r. Calculate the cut-off wavelength.
3. Find the LP modes of a two segmented fiber with its refractive index given by
following formula:
n(r)  n1
 n2
 n3
for r  a
for b  r  a
for r  b
where n3 is cladding index = 1.45, n1 = 1.455 , n2 =1.453, a=1 micron.
(a) Choose b such that the fiber supports at least three modes at 1550 nm. Calculate
the effective indices and plot the mode profile as a function of radius r.
(b) Choose a such that the fiber is single-moded at 1550 nm. Plot the mode profile
as a function of radius r. Calculate the cut-off wavelength.
4. Find the LP modes of a triangular core fiber with its refractive index given by the
following formula:
n(r )  n1  (n1  n2 )r / a for r  a
 n2
for r  a
where n 1 is core index at the center = 1.46. Maximum index change = 0.5 %.
(a) Choose a such that the fiber supports at least three modes at 1550 nm. Calculate
the effective indices and plot the mode profile as a function of radius r.
(b) Choose a such that the fiber is single-moded at 1550 nm. Plot the mode profile
as a function of radius r. Calculate V and b parameters.
5.
Find the LP modes of a parabolic index fiber with its refractive index given by
the following formula:
n(r )  n1  (n1  n2 )( r / a ) 2
for r  a
 n2
for r  a
where n 1 is core index at the center = 1.46. Maximum index change = 0.5 %.
(a)Choose a such that the fiber supports at least three modes at 1550 nm. Calculate
the effective indices and plot the mode profile as a function of radius r.
(b)Choose a such that the fiber is single-moded at 1550 nm. Plot the mode profile
as a function of radius r. Calculate V and b parameters.
6. Find the LP modes of a two segmented fiber with its refractive index given by
following formula:
n(r)  n1 for r  a
 n2
 n3
for b  r  a
for r  b
where n3 is cladding index = 1.46, n1 = 1.465 , n2 =1.463, a=1.5 micron.
(c) Choose b such that the fiber supports at least three modes at 1550 nm. Calculate
the effective indices and plot the mode profile as a function of radius r.
(d) Choose a such that the fiber is single-moded at 1550 nm. Plot the mode profile
as a function of radius r. Calculate V and b parameters.
Design an EDFA to have a gain in the range of 5-20 dB. Assume the following
parameters:
Cross section area of the pump and signal = 4 micron2 .
Pump transition cross-section
= 2e-25 m2.
Signal transition cross-section
= 4.2e-25 m2.
Spontaneous life time
=12 ms.
Total atomic density
= 9.28e23 m-3.
Pump wavelength
= 1480 nm.
Signal wavelength
= 1530 nm.
Signal power input
= 0.5 mW.
Fiber loss at pump wavelength
= 2 dB/km.
Fiber loss at signal wavelength
= 0.2 dB/km.
(a) Choose the length of the fiber such that gain of EDFA is 10 dB. Assume
input pump power of 10 mW.
(b) Plot gain as a function of pump power in the range of 2 to 10 mW for different
lengths of EDFA (2 m to 15 m).
Design a photonic system with the following parameters:
Transmitter parameters:
The average output power = 5 dBm, bit rate = 10 Gb/s, duty cycle = 25%, extinction
ratio = infinite (dB), modulation format = RZ, assume Gaussian pulses, wavelength =
1550 nm. Assume a bit sequence : 01110110.

Fiber parameters:
Fiber loss=0.2 dB/km, dispersion 2 = -21 ps2/km.
EDFA parameters:
Amplifier gain = 4 dB, Noise Figure = 12 dB.
Photo detector parameters:
Responsivity R = 1 A/W, noise bandwidth = 0.7*bit rate,
Load resistance = 1000 ohm.
Assume that transmitter output is fiber input and output of the fiber is amplified by
EDFA and then, it is coupled to a photo-detector.
(a) Simulate the fiber propagation and plot the optical power launched to the fiber
and the optical power after amplification as a function of time. Ignore amplifier
noise.
(b) Calculate the mean current of ‘1’ and ‘0’ from the simulation (Note: mean
current of ‘0’ may be zero because of inifinite extinction ratio).. Calculate the
standard deviation of ‘1’ and ‘0’ analytically. (Note : std. deviation of ‘0’ due to
shot noise and ASE are zero because of infinite extinction ratio). Calculate Qfactor and BER.
(c) Assume that you are free to choose different parameters listed above. Identify all
the parameters that if changed would reduce BER.