Polarization Mode Dispersion
A Program for the Simulation of Polarization Mode Dispersion
- 1. Download PMdisp.zip by clicking here.
- 2. Unzip the PMdisp.zip file.
(Go to www.WinZip.com if you do not have an unzipping program installed.)
- 3. Run Setup.exe and follow the on-screen instructions.
- 4. Run PMfiber from the CIRL software program group of the Start menu.
This model uses the same mode coupling calculations as PMfiber and
Cascade. PMFiber is a model for illustrating the state of polarization
along a PM fiber, based on the division of the propagating path into
small slices which are rotated in small increments. The new state of
polarization is calculated after each discontinuity. The light is
assumed coherent and CW resulting in a unique output state of
polarization. A similar program (Cascade) is used for a string of PM
components along a PM fiber where the new state of polarization is
calculated after a cross coupled component.
In the case of polarization mode dispersion where the light is a pulse
propagating along a fiber we consider the phase difference introduced by
the small difference in the propagation constants of the birefringent
axes of the fiber created by manufacturing methods, bends and stress
effects. It is convenient to treat the fiber as successive lengths of
weakly birefringent fiber with a specified rotation between each length.
The rotation can be selected to be random, or a small incremental change
to illustrate a slowly rotating fiber. The pulse travels along the
birefringent axes and after each rotation of the next fiber length
results in a new state of polarization and a distribution of different
states along the pulse due to displacement. Depending on the model input
parameters, it can be shown that the pulse simply broadens in both
principal axes or there is significant displacement between axes with
The PMD model
The figure shows a pulse *E* resolved into components *E_x * and *E_y *
on the axes of a PM fiber. The pulse propagates a distance along the
fast and slow z axes such that a displacement Dz occurs and the
components have a new phase f_x and f_y (strictly at the leading edge).
At this distance there is a rotation of the axes from X-Y to P-Q, and a
new refractive index set N_x and N_y . The modified pulse in the P and Q
axes has three distinct parts in each of the P and Q axes. It can be
seen that the first part has phase f_x with amplitudes E_p1 and E_q1 ,
there being no overlap with the f_y component. Similarly the last part
has phase f_y with amplitude E_p3 and E_q3 . The mid part has a
combination of f_x and f_y resulting in f_p and f_q with amplitudes E_p2
The new pulse is propagated a second distance to the next set of rotated
axes with similar changes in N_x and N_y and this results in a pulse
with up to five different phase and amplitude parts. Propagation for
further distances (the number of iterations) gives the final graphical
outputs as shown in the display.
In this model the pulse is divided into a number of segments. The pulse
is propagated a relatively large distance along a weakly birefringent
fiber such that the displacement of the components is an integral number
of the segments. The segments are made small enough to allow a large
range of phase differences for each displacement. The parts of the pulse
that result from several iterations can be numerous due to random
displacements giving rise to many edges, or can be relatively small if
the displacements are constant.
Click here to see a screen-shot of the PM Dispersion Program.
- Resize and reposition the *pmd* and *Plot *windows to suit your desktop.
- All of the parameters can be varied by editing the current values.
NOTE:values less than unity are preceded by 0, i.e. 0.1.
- Clicking *Defaults* will load the default values.
- Clicking *OK* will execute the program and will redraw the plot.
- Clicking *Cancel* exits the program.
The plot window displays three separate graphs. The first plot, Rotation
and Displacement, is a representation of the displacements (shown in
green) and rotations (shown in red) used in the successive PMD
iterations. A flat line indicates a constant value throughout all
The second plot, Power and Normalized Phase along Pulse, plots the power
(in green) and the normalized phase (in red) over each segment of the
The third plot, Pulse Intensity Ep Es, plots the intensity of both
output components over each segment of the pulse.
||The number of successive lengths of fiber (each length is 100m)
||Displacement of the pulse for each iteration, m easured in pulse sgements.
||Range (2 to 12)
||If checked, randomizes the displacement range. (Default randomizes between 2 and 12)
||The width of the input pulse in mm.
|Number segments per mm
||The number of segments per mm. (Resolution)
||The wavelength in microns
||The input angle of the initial pulse with respect to the weakly birefringent axes of the fiber. (In degrees)
||Attenuation of the pulse in parts per million per meter along the X axis.
||Attenuation of the pulse in parts per million per meter along the Y axis.
||The angle of rotation between successive axes. (In degrees)
|Random Axes Rotation
||Range (-180 to 180)
||If checked, randomizes the angle of rotation between successive axes. (Default randomizes between -180 and 180 degrees)