Supercontinuum Generation by Nonlinear Optics - Optical Signal Processing by Silicon Photonics - page 72

Two basic structures of nonlinear PCFs are: Multimode fibers with
microstructure like a cobweb and having extremely small core, Single - mode fibers
with smaller holes, slightly larger cores, and engineered zero dispersion [ 19 ].

6.4 Numerical Modeling of SC Generation

In optical fibers spectral broadening of incident pulses or SC generation is gov-
erned by nonlinear effects like SPM, SRS, and FWM. Figure 6.3 shows the spec-
tral broadening. In this incident pulse (blue) is launched into photonic crystal fiber
and result in SC generation (red line).
The numerical modeling of SC can be done by solving the nonlinear
Schrödinger equation (NLS). To include intrapulse Raman scattering and disper-
sive effect, the following is the equation of pulse evolution inside single mode fib-
ers can be used [ 20 ].

∂ 2 A
∂ T 2 −

∂ 3 A
∂ T 3

∂ A
∂ Z

1
2 (α(ω O ) + I α 1

∂
∂ T

∂ A
∂ T

I β 2
2

β 3
6

+ ) A + β 1 +

(6.1)

∞

∂
∂ T

R ( T ′ )| A Z , T − T ′ | 2 D T ′ = I γ (ω O ) + I γ 1 A ( Z , T )

0

where amplitude of pulse envelope is presented by A ( z , t ), β 2 is group velocity
dispersion (GVD) parameter is nonlinear parameter responsible for SPM, the
integral is representation of energy transfer in intrapulse Raman scattering. For

Fig. 6.3 Spectral broadening
( red line ) by launching
incident pulse ( blue line ) in
photonic crystal fiber [ 20 ]