Review questions for HW 7


1. A piece of etalon is made of glass (n=1.5). It is 1mm thick. Find a) free spectral range of the etalon, b) power reflectivity between air and glass and c) Finesse of the etalon.
n=({1.5-1}/{1.5+1})^2=0.04
F= pi sqrt{R}/{1-R}=0.6545

2. Name 3 ways that can modify the free spectral range or resonant frequency of a FP cavity.
Change, n, d, and angle.

3. We consider to use an etalon as a filter for a multichannels optical communication system. If the etalon has a free spectral range of 100 GHz and Finesse of 50. Estimate the maximum number of channels that can be used with this filter and the bandwidth of each channel.
Max number of channels = 50
Channel bandwidth = 100/50 = 2(GHz)

4. Consider the etalon in question 1. we target it to operate at a wavelength of 1550 nm, find the harmonic m (an integer) that is closest to the targeted operation wavelength and determine the actual operation wavelength.
d = m lambda / (2 n)
m = "int"(2*1.5*10^-3/{1550 times 10^{-9}})=1935
actual wavelength = 2*1.5*10^-3/1935 = 1550.3 (nm)

5. What is the output wavelength and direction of a fiber Bragg grating (FBG)?
Propagation in backward direction
lambda = Lambda*n*2/m with m=1 usually and Lambda is the grating period.

6. Name 3 methods for tuning a FBG.
Thermal expansion, mechanical force, electro-optic effect

7. What is the resonant condition for a acousto-optics filter? Please include the polarization condition.
lambda = (Delta n)*"acoustic wavelength"
Polarization rotation by 90 deg, e.g. TE to TM or TM to TE

8. For a directional coupler, what is the phase change from input port 1 to output port 1 and what is phase change from input port 1 to output port 2?
input port 1 to output port 1 -- 0 deg
input port 1 to output port 2 -- 90 deg

9. We originally design a MZ filter for channel spacing of 100 GHz with path difference (Delta L) being 10 micron. If we decrease the channel spacing to 10 GHz, what should be the path difference (Delta L)?
It is a reciprocal relationship between Delta f and Delta L. Delta L = 100 mu m

10. How many 2x2 MZ filters are required for construction of a 1x4 filter?
3 MZ filters since there are 2 layers or stages.

11. At what region is the light of a LED or laser diode (LD) generated?
Depletion or active layer

12. How should LED or LD be biased for light emitting?
Forward biased

13. What are the 3 radiative processes that happen in a laser? Which one is responsible for lasing?
Spontaneous emission, stimulated emission and absorption
Stimulated emission for laser.

14. What are the 3 components (requirements) for lasing?
A pumping source (current injection), positive feedback (FP cavity) and special device structure to enhance stimulated e mission

15. How do the spectral width and peak freq of a LED change with increasing temperature?
Spectral width = {3.3 kT}/h, peak freq = {Eg+kT}/h

16. What factors control the mode spacing of a laser? What factors control the threshold current or gain?
Mode spacing: Cavity length, refractive index
Threshold: Attenuation coefficient of the semiconductor, mirror reflectivity, cavity length

17. What material parameter determines the output wavelength of a LD or LED?
Bandgap energy E_g