Image Processing Reference
In-Depth Information
logarithmic step size
constant step size
power
power
length
length
digital backward propagation (DBP)
Fig. 6. Comparison of DBP algorithms based on constant step-size method and logarithmic
step-size method. The red curves show the power dependence along per-span length.
discussed for forward simulation of optical communication systems. These techniques can be
investigated to implement DBP in future. In this section we will discuss the figure of merit for
different step-size distribution techniques.
3.3.1 Non-linear phase rotation method
In this method step-size is chosen so that the phase change due to non-linearities
φ NL does
not exceed a certain limit (Sinkin et al., 2003). In Eq. 9 the effect of non-linear operator ( N )is
to increase the non-linear phase shift
φ NL for a specific step-size ( h ) by an amount as given in
Eq. 17.
2 h
φ NL
= γ |
E
|
(17)
max
NL
An upper-limit for the phase rotation
φ
is ensured for this method is the step-size h fulfills
Eq. 18.
max
NL
γ|
φ
h
(18)
|
2
E
This step-size selection method is mainly used for soliton transmission.
3.3.2 Walk-off method
Walk-off method of implementing SSFM is suitable for investigating the WDM (Mateo et
al., 2010) transmission systems. In these systems the wavelengths cover a braod spectrum
due to which the interplay of chromatic dispersion and intra-channel cross phase modulation
(XPM) plays dominant degradation role in system performance. In this method step-size is
determined by the largest group velocity difference between channels. The basic intention is
to choose the step size to be smaller than a characteristic walk-off length. The walk off length
is the length of fiber required for the interacting channels to change their relative alignment
by the time duration that characterizes the intensity changes in the optical signals. This length
can be determined as: L wo
t /
(
D
λ )
,where D is chromatic dispersion and
λ
is the
channel spacing between the interacting channels.
 
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