Review questions for HW 5

1. Why a graded index fiber has a smaller dispersion than a multimode step index fiber?
The graded index allows the shortest path to have slowest speed wile the longest path to have fastest speed. Hence, differences in delay among modes are reduced.

Consider a 5km long optical communication system with D_{"modal"}=1ns/km, D_{"int"ra}=2ps/km-nm and using a laser with linewidth of 3nm for question 2 and 3.
2. If we use an appropriate wavelength, we can choose the system to have V=2.3. Which dispersion parameter should be used? What is the time delay for the system that is introduced by the fiber?
D_{"intra"} should be used
Delta tau = 2*5*3 = 30(ps)

3. If we choose a wrong wavelength, we have V=10. What is the time delay for the system that is introduced by the fiber?
D_{"modal"} should be used
Delta tau = 1 times 5 = 5(ns)

4. For chromatic dispersion, which mode are we considering?
LP_{01} or HE_{11} mode.

5. What is the mean of D_{"intra"} < 0?
The longer wavelength has smaller delay, i.e. high freq is faster.

6. A fiber with n_1=1.5, n_2=1.49, operation wavelength of 1.4 micron, core radius a = 2 micron, zero dispersion wavelength of 1.31 micron and dispersion slope at zero dispersion wavelength = 0.08 (ps) /(km-nm^2), find its D_{"intra"}.
D_{"intra"} = S_0 lambda ( 1 - ( lambda_0 / lambda )^4)/4
= 0.08 times 1400 ( 1 - (1.31/1.4)^4)/4 = 6.535({ps}/{km-nm})

7. What is a dispersion-shifted fiber? What is the principle behind?
Dispersion-shifted fiber has its zero dispersion wavelength close to 1.55 micron. By reducing core radius, D_{waveguide} becomes larger and cancel D_{material} at longer wavelength.

8. A step index fiber with Delta = 0.008 and a = 3 micron.
a) What dispersion should be considered if it operates at lambda=1.5 micron. Justify your answer.
b) What dispersion should be considered if it operates at lambda = 0.8 micron. Justify your answer.
NA = 1.5 sqrt ( 2 times 0.008) = 0.1897
a) V = 2 pi a {NA} / {lambda} = 2.38 < 2.405=> D_{"intra"}
b) With lambda decreased to 0.8 micron, V increases further and > 2.405 => D_{"modal"}.

9. For the fiber in 8. with additional condition that it is also a dispersion shifted fiber. Write down the formula for dispersion a) lambda = 1.5 micron and b) lambda = 0.8 micron.
a) D = S_0 times (1.5 - lambda_0 )
b) D_{"modal"} = n times Delta / c = {1.5 times 0.008} / {3 times 10^8} =4 times 10^{-11}(s/m)=40({ns}/{km})

10. At what wavelength does the glass fiber have minimum attenuation?
1.55 micron

11. A laser has power of 3mW. The fiber link has 1dB loss for attenuation and 2dB loss of connectors.
a) Find laser power in dBm.
b) Total losses in dB.
c) Received power at the other end of the fiber link in dBm.
d) Express answer for c) in mW.
a) 10 log (3) = 4.77(dBm)
b) -3dB
c) P_{rec} = 4.77 -3 = 1.77 (dBm)
d) P_{rec} = 10^0.177 = 1.503 (mW)`

12. What are the structural features of a polarization maintaining fiber?
The fiber has elliptical core or/and cladding.

13. How many windows of transmission are possible for glass fiber now? What are their wavelengths?
5 windows: 0.8 micron, 1.33 micron (O band), 1.55 micron (C band), 1.6 micron (L band), 1.4 micron(S band).