Review questions for HW 9

1. What are disadvantages of surface emitting lasers? How to compensate for these disadvantages?
Reduction in d and higher threshold current
Use multilayer mirror to increase R and special structure to enhance stimulated emission

2. What other device is similar to a waveguide grating router (WGR)?
MZ interferometer

3. What are advantages of WGR comparing to DFB laser array?
Frequency spacing is fixed and independent on temperature, low loss

4. What is the upper limit for direct modulation?
40 Gb/s

5. What is the difference between APD and PIN diode?
APD has a current gain region

6. An APD with responsivity=0.3A/W, M=30, I_d = 2nA, P_{"in"}= {10^{-5}} /3 (mW). Find a) I_{apd}, b) mean square value of shot noise for the APD if Delta f = 20MHz and F_{apd} =1, and c) mean square value of thermal noise if Delta f=20MHz and F=1, T=300K and R_L= 500 Ohm.
a) I_{apd} = M times R times I_{ph} = 30 times 0.3 times 0.333 times 10^{-5}=30(nA)
b) \bar {i_S^2}  = 2q (R P_"in" + I_d) Delta f times M^2 times F _{apd} = 1.728 times 10^{-17}(A^2)
c) \bar {i_T^2}  = {4 kT Delta f times F}/{R_L} = 6.656 times 10 ^{-16} (A^2)

7. Under what condition, you will get shot noise (quantum) limited detection.
Current gain tends to infinity

8. Why digital systems perform better than analog systems? What is their trade-off?
The requirement on SNR is low for reasonable BER but it requires more bandwidth.

9. For a thermal-noise limited digital system, we have SNR=17dB. a) What is its BER? b) What should be the minimum receiver power if the mean square current of thermal noise is 10^{-15} (A^2) for a detector with responsivity=0.5A/W.
SNR = 10^{-17/10} = 50.12
x = 0.354 times sqrt{SNR} = 2.506
BER = 0.5 times (1-erf(x)) = 0.5 times (1-0.99959) = 2.05 times 10^{-4}
b) What should be the minimum receiver power if the mean square current of thermal noise is 10^{-15} (A^2) for a detector with responsivity=0.5A/W.
For NEP calculation, SNR=1 but this problem gives SNR=17dB = 50.12. We need to use this SNR.
I_{ph}^2 = SNR times 10^{-15} = 5.012 times 10^{-14} (A^2)
P_{"in"} = I_{ph}/R = 2 I_{ph} = 4.48 times 10^{-7} (W)

10. Name one factor that limits the maximum number of channels in using a prism as a multiplexer/demultiplexer.
The beam divergence limits the max. number of channels.

Last Modified: April 18, 2018
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