High-Nonlinearity in Glass Fibers and Cross-Phase Modulation - Optical Signal Processing by Silicon Photonics - page 61

Fig. 5.4 Peak gain variation
versus the ratio of power i.e.,
P 2 / P 1 for different GVM [ 13 ]

6

P1= 100w

8=1Ps/m

3

2

4

1

0

2

0

0.2 0.4 0.6 0.8 1

P2/ P1

wavelengths a few nanometers separated. The parameter δ = 2-5 ps/m for a wave-
length in the range 5-10 nm, the peak gain nearly equal to 6 1/m can be expected
for approximately equal powers of 100 W as shown in the Fig. 5.4 .
Optical spectra of both the beams that are propagating in response to modula-
tion instability have to be divided into side-bands present with a frequency separa-
tion on both sides as given in Eq. ( 5.17 ). When δ = 2 ps/m and β = 0.06 ps 2 /m,
the frequency is about Vm = 5 THz which is nearly equal to 5 nm at 0.53 μ m. The
side-bands produced as a result of modulation are because of input noise amplifi-
cation provided by vacuum fluctuations or spontaneous emission with a peak gain
of about 6 1/m, the amplification factor of exp(6 L ) for length L meter optical fiber.
Hence, a few build-ups of side-bands are expected for a fiber having few meters in
length. As far as time-domain response is concerned, both the propagating beams
perform amplitude modulation with period 1/Vm in femto-second range which is
200 fs in the example mentioned above.
Therefore, unstable modulation manifest itself as breaking each beam of cw
into a stream of extremely short pulses with repetition rate of some tera hertz.
Taking the scenario of conventional modulation that is not stable [ 9 , 10 ] experi-
mental observation of modulation instability produced by XPM, requiring the
optical pulses to stop SBS. So the overlap of both pulses will occur throughout the
fiber length if τ >> δ L .
So far the assumption has been made that both the propagating beams are
happening, respectively, over the optical fiber but there is another important
option that if the other beam is produced as a result of SRS. In case of silica fib-
ers, stoke shift is of 13 THz i.e., (at λ = 0.53 μ m, 12 nm) and the mismatched
group velocity that lies between the stoke waves and pump is δ nearly equal to
5 ps/m. However, the analysis described here is not relevant and can not be applied
directly because if the effect of Raman gain is not included, possibly the quali-
tative feature of XPM based modulation instability is there and from Eq. ( 5.17 ),
modulation frequency is also about 14 m i.e., nearly 13 THz for a 0.53 μ m pump.
Hence modulation side-bands will appear at a number of Stoke shift thereby mak-
ing it difficult identifying existence of Stoke lines of higher order.