Review questions for HW 8


1. The active layer of a LD is 0.2mm long with refractive index of 3 and attenuation coefficient of 1000 (m^{-1}). a) Find mode spacing, b) Find threshold gain coefficient.
a) mode spacing = Delta nu_{FSR} = c/{2nd} = {3 times 10^8} /{2*3*0.2 times 10^{-3}} = 250(GHz)
b) g_{th} = alpha + 1 / (2d} ln(1/{R^2})
R= ((3-1}/{3+1})^2= 0.25
g_(th} = 10 times 3 + {ln (15)}/ {2*0.2 times 10^{-3}}= 7932(1/m)

2. Of the two detection mechanisms, photoconductive and photovoltaic effects, which one is used in optical communication? Why it is being used in optical communication?
Photoconductive effect will be used since it is faster.

3. What factors control the responsivity of a detector? Under what condition, responsivity becomes zero.
wavelength, material, quantum (i.e. absorption) efficiency
If photon energy < Eg, responsivity becomes zero.

4. How should we bias a photodiode?
Reverse bias

5. For a photodiode with responsivity of 0.5 and detection area of 1 mm^2, what is the output photocurrent if a laser beam with an intensity of 100 W/{cm^2} shines on the photodiode, assuming the beam covering the whole detection area.
P_{"in"} = Intensity times area = 100 times 0.1 times 0.1 = 1(W)
I_{ph}= R P_{"in"} => I_ph = 0.5 times 1 = 0.5(A)

6. A single mode communication link has a 10km fiber with D_{"intra"} =20 {ps}/{km-nm}, a detector with a modulation bandwidth of 1GHz and a laser diode with a rise time of 0.3ns and Delta lambda (linewidth) of 1nm. a) Find fiber delay time, b) Find rise time of detector and c) Find the data rate of the system.
a) tau_f = D_{"intra"} times L times Delta lambda = 20 times 10 times 1 = 200 (ps) = 0.2 (ns)

b) tau_r = 0.35 / {10^9} = 0.35 (ns)

c) tau_{sys} = sqrt{ tau_f^2 + tau_r^2 + tau_t^2} = sqrt {0.2^2 + 0.35^2 + 0.3^2} = 0.5025 (ns)
 R_b = 1 / {4 tau_{sys}} = 1 / { 4 times 0.5025} (Gb/s) = 497.5 (Mb/s)

7. What factors control the magnitude of thermal noise? What factors control the magnitude of shot noise?
Thermal noise: Temperature, bandwidth, load resistor
Shot noise: bandwidth, photocurrent

8. What factors control the circuit time of a photodiode? If the transit time of the photodiode is 1ns, what value should be choose for the circuit time so that speed of the photodiode is determined by transit time?
b) V_{rms} = 5 / sqrt(2)= 3.5355(V)