Review questions for HW 6

1. What are the factors that determine the effective strength of nonlinear effect?
Intensity, length of medium (fiber), nonlinear coefficient.

2. What are the use of nonlinearity?
Making devices, such as laser, mixer and compensating for dispersion

3. What are the undesirable effects of nonlinearity?
Cross talk, interference, robbing power from the desired channel.

4. What are the relative magnitudes of the pump and output frequency of nonlinear smatterings (such as SRS, SBS)?
Pump freq (photon energy) should be higer than out freq (photon energy).

5. Which nonlinear scattering (SRS or SBS) has larger threshold power? Which nonlinear scattering (SRS or SBS) has wide bandwidth? Which nonlinear scattering (SRS or SBS) has detrimental effect on optical communication?
SRS
SRS
SRS

6. A system with 1000 channels versus a system with 10 channels, which system has stronger SRS? Explain your answer.
1000 channel system is more susceptible to SRS since it can easily reach the threshold power for SRS.

7. What is the frequency relation for FWM?
f_1+f_2-f_3

8. How to avoid FWM?
Increase channel spacing, use nonuniform channel spacing, decease channel power, use nonzero dispersion fiber, use fiber with larger core size (decrease intensity), use a long piece of fiber to avoid pulse overlapping.

9. Consider FWM of 2 channels with frequencies f_a and f_b. List all possible frequencies.
f_a=f_a+f_a-f_a, f_b=f_b+f_b-f_b, 2f_a-f_b, 2f_b-f_a

10. What is the meaning of chirp factor >0? Which polarity of D_{"intra"} does it correspond to?
chirp factor >0 means the high frequency having longer delay at the trailing edge of a pulse. It can be cancelled with D_{"intra"} > 0 (or k''<0) which makes long wavlength (low frequency) to have longer delay.

11. What is SPM? What is XPM? What are their effects?
SPM: f_a+f_a-f_a causes nonlinear change in refractive index that is induced by an optical beam itself. XPM: f_a+f_b-f_b causes nonlinear change in refractive index that is induced by other beams. SPM and XPM cause phase modulation and widening of signal bandwidth. XPM also introduces cross talk.

12. For a medium with nonlinear refractive index coefficient >0, sketch the frequency chirp induced by SPM on a Gaussian pulse.
dI/dt vs t has positive values on the negative t while negative value on the positive t.
Since n_2 >0, delta omega (freq chirp) vs t has negative freq (red shift) on the negative t while positive freq (blue shift) on the positive t.
That means longer wavelength having smaller delay.

13. What polarity of D_{"intra"} can cancel the frequency chirp in question 12.?
D_{"intra"} > 0 has opposite freq arrangement of question 12 and hence compensate for the freq chirp.

14. What is a soliton?
Soliton is a pulse that will not dissipate even after traveling for a long distance.

15. If you can generate solitons with pulse width of 10ps when the optical power is 10mW, how much power is required to generate soliton with width of 1ps?
10*sqrt(10)=1*sqrt(P)=>P=1000mW=1W.