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Title of Dissertation:    & {\large  NONLINEAR PULSE PROPAGATION }\\
&                     {\large  THROUGH AN OPTICAL FIBER:} \\
&                     {\large  THEORY AND EXPERIMENT} \\
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&                          {\large  Bhaskar Khubchandani} \\
&                           {\large Doctor of Philosophy, 2004} \\
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Dissertation Directed by: & {\large  Professor Rajarshi Roy} \\
&               {\large  Department of Physics } \\
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{\color{red}NOTE:   Proquest no longer requires a limit to the
length of the Abstract.}

 Pulse propagation through optical
fibers is studied for two different phenomena: (i) the evolution
of four-wave-mixing and (ii) the interplay between self- and
cross-phase modulation for ultra-short pulses in a polarization
maintaining fiber.

For the four-wave-mixing case, we present the results of a study
of the dynamical evolution of multiple four-wave-mixing processes
in a single-mode optical fiber with spatially and temporally
$\delta$-correlated phase noise. A nonlinear Schr\"odinger
equation (NLSE) with stochastic phase fluctuations along the
length of the fiber is solved using the Split-Step Fourier method.
Good agreement is obtained with previous experimental and
computational results based on a truncated-ODE model in which
stochasticity was seen to play a key role in determining the
nature of the dynamics. The full NLSE allows for simulations with
high frequency resolution (60\,MHz) and frequency span (16\,THz)
compared to the truncated ODE model (300\,GHz and 2.8\,THz), thus
enabling a more detailed comparison with observations.
Fluctuations in the refractive index of the fiber core are found
to be a possible source for this phase noise. It is found that
index fluctuations as small as 1 part per billion are sufficient
to explain observed features of the evolution of the
four-wave-mixing sidebands. These measurements and numerical
models thus may provide a technique for estimating these
refractive index fluctuations which are otherwise difficult to
measure.

For the case of self- and cross-phase modulation, the evolution of orthogonal polarizations of asymmetric femtosecond pulses (810\,nm) propagating through  a birefringent single-mode optical fiber (6.9\,cm) is studied both experimentally (using GRENOUILLE) and numerically (using a set of coupled NLSEs). A linear optical spectrogram representation is derived from the electric field of the pulses and juxtaposed with the optical spectrum and optical time-trace. The simulations are
in good qualitative agreement with the experiments. Input temporal pulse asymmetry is found to be the dominant cause of output spectral asymmetry. The results indicate that it is possible to modulate short pulses both temporally and spectrally by passage through polarization maintaining optical fibers with specified orientation and length.
