Ph.D.,
Department of Applied Mathematics ,
University of Colorado at Boulder.
Thesis title:
"Collision-induced timing jitter and four-wave
mixing in wavelength-division multiplexing soliton systems" (postscript file)
Thesis advisor: Mark J. Ablowitz
1.
"The effects of weak randomness on pulse interactions and four-wave mixing products"
with T. Schafer and C.K.R.T. Jones, accepted to Physica D, special ed.
(2004)
2. "A (Very) brief introduction to soliton theory in
a class of nonlinear pdes" , submitted to the Conference for
African-American Researchers in the Mathematical Sciences proceedings,
(2002)
3.
"Four wave mixing in dispersion-managed return-to-zero systems"
with M.J. Ablowitz, G. Biondini and S. Chakravarty, J. Opt. Soc.
Am. B, 20, pp. 831-845 (2003)
4.
"A comparison between lumped and distributed filter models in
wavelength-division multiplexed soliton systems" with
M.J. Ablowitz, G. Biondini and S. Chakravarty, Opt. Commun., 172,
pp. 211-227 (1999)
5.
"On Timing Jitter in Wavelength-Division Multiplexed Soliton Systems"
with M.J. Ablowitz, G. Biondini and S. Chakravarty, Opt. Commun.,
150, pp. 305-318 (1998)
I am currently examining the effects of weak randomness on four- wave mixing product growth. We consider FWM product growth which arises from pairwise interactions of pulses ("solitons") in nonlinear optical fibers. The randomness comes into play via the dispersion profile. This approximates impurities in the fiber line.
Another topic of interest is the study of FWM product growth in the vector
Nonlinear Schrodinger equation and its variants (i.e., Manakov type system). We develop
a theory concerning this growth where polarization of the pulses are included in the analysis.
Here's a copy of my current research statement in either pdf format
or postscript format (last updated in November 2004).
Here's a copy of my teaching statement in either
pdf format or postscript format (last updated in November 2004).