**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`.
**

Last Modified: March 6, 2018

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