1. 1. For a resonant cavity shown below, the transmission matrix can be written as below
Z=0
Z=L
Prove that the E field is continuous at the interfaces, z=0 and z=L.

2. What’s the coupling length needed to have 20% splitting ratio?
2. Splitter
(20%)
 = 1µm-1
 = 0.2µm-1 1 3
For A1(0) = A1, A2(0) =0
A1(z)
A2(z)
Un-connected port 4
What’s the coupling length needed to have 20% splitting ratio?

3. 3. Waveguide gratings (20%)
A1(z)|z=0 = A1(0)
A1(z)
 = 0.1µm-1
n1 = 1.5
A2(z) )|z=L = 0
A2(z)
(a) What’s the length of the grating needed to achieve 98% reflections?
(b) (Optional for undergraduate, required for graduate students)
Describe how we can reduce the length of the grating while keeping the same 98% reflections, and why?

4. 4. (20%) For an optical amplifier, when the input signal is 2
4. (20%) For an optical amplifier, when the input signal is 2.0mW, the output signal is 40mW.
When the input is –28dBm, the output power is -7dBm. Determine:
(a) The saturation power Psat;
(b) What’s the maximum power can be extracted from the amplifier?
(c) What’s the input power to the get the maximum power.
(d) Explain why the gain saturation happens?

5. 5. (20%) For an EDFA, using the two-energy-level model
5. (20%) For an EDFA, using the two-energy-level model. If the gain of the EDFA is measured to be 20dB, find out the noise figure of the EDFA, assuming the population inversion factor is 2?