Advancements in Silicon Photonics - Optical Signal Processing by Silicon Photonics - page 38

where ε 0 is the vacuum permittivity and χ ( J ) is j th order susceptibility. In general,
χ ( J ) is a tensor of rank j + 1. The linear susceptibility χ (1) represents the dominant
contribution to P . Its effects are incorporated through the refractive index n and
the attenuation coefficient α .

10
L

P T
P O

α dB =− (4.2)

log

The second-order susceptibility χ (2) is responsible for such nonlinear effects
as second-harmonic generation and sum-frequency generation. However, it is
nonzero only for media that lack inversion symmetry at the molecular level. As
SiO 2 is a symmetric molecule, χ (2) vanishes for silica glasses. As a result, optical
fibers do not normally exhibit second-order nonlinear effects (Fig. 4.6 ).
In nonlinear optics (NLO) we come to know that how light behaves at very
high intensities, and also how to take advantage of this behavior to gain remark-
able control over light. Basically, nonlinearity is very important phenomenon
because it allows light to interact with the light. In a system where electric polari-
zation is only proportional to the electric field, the waveforms that can be super-
posed exclusive of any change to the dynamics of the individual components. If
two waveforms interact, they will cleanly pass through one another. Consequently,
if a light is passed with a specified set of frequency in the course of a linear
medium, then we can only ever get those frequencies exposed. When the optical
nonlinearity is present, conversely the waveforms can mix or self-interact to con-
struct a completely new waveform. Examples of nonlinear phenomena consist of:

(a) In second-harmonic generation where the photons are fundamentally com-
bined to give photons with twice of the energy [ 15 ].
(b) For four wave mixing in which three frequency components interact to each
other and then construct or amplify a fourth wave [ 16 , 17 ].
(c) The light with a very broad frequency spectrum that can be generated from a
narrow spectrum pulse in super continuum generation [ 18 , 19 ].

Polarization Mode Dispersion

Optical
Pulse

Differential Group Delay

Fig. 4.6 Optical pulse propagation [ 15 ]