Abstract
To study the effects of a finite turn-on time on the transient phenomena associated with dispersive pulse propagation, we consider the propagated field in a Lorentz medium due to an input hyperbolic-tangent modulated signal f(t) = u (t) sin(ωct) of carrier frequency ωc with initial pulse envelope where the parameter β, which is indicative of the rapidity of turn-on of the signal, is real and positive. In the limit as β → ∞ this initial envelope function approaches a unit step function. The dynamic evolution of the propagated field is described via the dynamics of the saddle points in the complex ω plane that are associated with the complex phase function appearing in the integral representation of the propagated field and their interaction with the simple pole singularities of the spectrum ũ (ω − ωc) of the intial pulse envelope function. This analysis shows that the precursor fields that are characteristic of the input unit step-function modulated signal will persist nearly unchanged for the input hyperbolic-tangent modulated signal for values of β of the order of δ or greater, where δ is the damping constant of the Lorentz model medium. As β decreases below δ, the precursor fields become less important and the field becomes quasimonochromatic.
© 1986 Optical Society of America
PDF ArticleMore Like This
Shioupyn Shen and Kurt Edmund Oughstun
WG30 OSA Annual Meeting (FIO) 1986
Kurt E. Oughstun
THF4 OSA Annual Meeting (FIO) 1987
Kurt E. Oughstun and Judith Laurens
TUF3 OSA Annual Meeting (FIO) 1989