High-Nonlinearity in Glass Fibers and Cross-Phase Modulation - Optical Signal Processing by Silicon Photonics - page 55

5.4.2 Pulse Broadening

Another issue in nonlinear fiber devices is the temporal broadening of the control
pulse caused by GVD. Even though the control and signal pulses have the same
group velocities, if the control pulse has high GVD, the temporal broadening of
the control pulse reduces the switching time of devices. A shorter control pulse
width exhibits faster response time, but it is often limited due to GVD. The disper-
sion length LD is already defined and the critical pulse width, τ , is defined as: [ 1 ]

[τ c ] 2 = 4ln ( 2 |β 2 | L )

where β 2 is the dispersion parameter and L is the fiber length. Over a propagating
length L , an optical pulse broadens by a factor of 2 when L = LD. Therefore, to
avoid the pulse broadening effect, the following condition should be satisfied.

L
L D

≪ 1

and the output pulse width τ o given by

2

τ c
i

2 2

[τ o ] =[τ i ] 1 +

should be nearly equal to the input pulse width τ i .
Usually, nonlinear fiber devices require long device-lengths to induce a suffi-
cient nonlinear phase shift at lower optical powers due to the low nonlinearities of
silica fibers. Furthermore, since the minimum switching time is limited by the con-
trol pulse width; a short control pulse is required to achieve much faster switching.
These requirements of long device length, which increases the walk-off parameter
and GVD, and short control pulse in nonlinear fiber devices make the switching
performance much worse because a short pulse is broadened even more for a given
fiber length. Therefore, the device length should be short enough to minimize the
walk-off parameter and pulse broadening due to GVD. This can be achieved by
introducing HNL glasses since they can increase the nonlinear-index coefficient
and decrease the effective mode area, thus resulting in extremely short devices.

5.4.3 Polarization Sensitivity

The fluctuation of SOP severely degrades the performance of nonlinear fiber
devices because SOP is very critical to the operation of almost all nonlinear fiber
devices. Therefore, polarization controllers or PMFs are usually used in order to
control the SOP of an optical pulse, since the SOP in standard fibers changes ran-
domly as the pulse propagates along the fiber. However, it is not efficient to adjust