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Optical Precursor Behavior

by LeFew, William R.

Abstract (Summary)
Controlling and understanding the propagation of optical pulses through dispersive

media forms the basis for optical communication, medical imaging, and other modern

technological advances. Integral to this control and understanding is the ability to

describe the transients which occur immediately after the onset of a signal. This

thesis examines the transients of such a system when a unit step function is applied.

The electromagnetic field is described by an integral resulting from Maxwell’s

Equations. It was previously believed that optical precursors, a specific transient effect,

existed only for only a few optical cycles and contributed only small magnitudes

to the field. The main results of this thesis show that the transients arising from this

integral are entirely precursors and that they may exist on longer time scales and

contribute larger magnitudes to the field.

The experimental detection of precursors has previously been recognized only

through success comparison to the transient field resulting from an application of the

method of steepest descent to that field integral. For any parameter regime where

steepest descents may be applied, this work gives iterative methods to determine

saddle points which are both more accurate than the accepted results and to extend

into regimes where the current theory has failed. Furthermore, asymptotic formulae

have been derived for regions where previous attempts at steepest descent have failed.

Theory is also presented which evaluates the applicability of steepest descents in the

represention of precursor behavior for any set of parameters. Lastly, the existence

of other theoretical models for precursor behavior who may operate beyond the

reach of steepest descent is validated through successful comparisons of the transient

prediction of those methods to the steepest descent based results of this work.

Bibliographical Information:

Advisor:Venakides, Stephanos; Trangenstein, John; Mattingly, Jonathan; Witelski, Thomas P.

School:Duke University

School Location:USA - North Carolina

Source Type:Master's Thesis

Keywords:maxwell equations mathematics

ISBN:

Date of Publication:05/07/2007

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