Annual Meeting Optical Society of America

Optical pulse propagation in a multiple resonant dispersive Lorentz medium

Shioupyn Shen, Kurt Edmund Oughstun

Published Jan 1, 1986• 1 citation

Abstract

To obtain a more complete understanding of the effects of temporal dispersion on the propagation dynamics of optical pulses in a physically realistic medium, we have examined the classical problem of dispersive pulse propagation in a Lorentz model medium that is characterized by two separate resonance frequencies. Both an input delta-function pulse and an input unit step-function modulated signal with carrier frequency ωc are considered. In each case the dynamic evolution of the propagated field is described in terms of 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 field. The appearance of a new precursor field, separate from the well-known Sommerfeld and Brillouin precursor fields, is shown to appear when the two resonance frequencies of the medium are sufficiently separated. Finally, the signal velocity that is characteristic of the field contribution oscillating at the applied carrier frequency ωc is obtained. These results are illustrated with numerical solutions that depict the entire evolution of the propagated field.

DOI: 10.1364/oam.1986.wg30

Related papers

Uniform asymptotic description of ultrashort rectangular optical pulse propagation in a linear, causally dispersive medium

Kurt Edmund Oughstun, George C. Sherman

The uniform asymptotic description of the propagation of an input rectangle-modulated harmonic signal of fixed angular frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ and initial pulse width T into the half-space z>0 that is occupied by a single-resonance Lorentz medium is presented. The asymptotic description is developed by representing the input rectangular pulse as the difference between two Heaviside-unit-step-function-modulated signals that are separated in time by the initial pulse width T. This representation clearly shows that the resultant pulse distortion in the dispersive medium is primarily due to the Sommerfeld and Brillouin precursor fields that are associated with the leading and trailing edges of the input pulse. The dynamical pulse evolution with increasing propagation distance z>0 is completely described for both long and very short initial pulse widths T. In both cases it is shown that the pulse distortion becomes severe when the propagation distance z is such that the precursor fields associated with the trailing edge of the pulse interfere with the precursor fields associated with the leading edge. Finally, the asymptotic theory clearly shows that the main body of the pulse propagates with the signal velocity in the dispersive medium.

Physical Review AJun 1, 199057 citations

Uniform asymptotic description of ultrashort optical pulses

Kurt Edmund Oughstun

The uniform asymptotic description of the propagation of an input rectangle-modulated harmonic signal of angular frequency ω c and initial pulse width T into the half-space z ᐳ 0 that is occupied by a single resonance Lorentz medium is described. The asymptotic description is developed by representing the input rectangular pulse as the difference between two Heaviside unit step-function modulated signals that are separated in time by the initial pulse width T. This representation clearly shows that the resultant pulse distortion in the dispersive medium is solely due to the Sommerfeld and Brillouin precursor fields that are associated with the leading and trailing edges of the input pulse. The dynamic evolution of the pulse with increasing propagation distance z ᐳ 0 is described for both long and very short initial pulse widths T. In both cases it is shown that the pulse distortion becomes severe when the propagation distance z is such that the precursor fields associated with the trailing edge of the pulse interfere with the precursor fields associated with the leading edge.

Annual Meeting Optical Society of AmericaJan 1, 19870 citations

Dispersive pulse propagation in a double-resonance Lorentz medium

Shioupyn Shen, Kurt Edmund Oughstun

The propagation of electromagnetic pulses in a linear, dispersive Lorentz medium with two isolated resonance frequencies is presented within the context of the classical theory due to Sommerfeld and Brillouin. Particular attention is given to the modification of the dynamical field evolution when one proceeds from a single-resonance to a double-resonance medium. The appearance of a new field structure in the precursor field evolution is obtained, and the conditions for its evolution are described. The signal velocity for a pulsed field is obtained and compared with the energy-transport velocity in a double-resonance medium both when the conditions for the evolution of the modified precursor field structure are satisfied as well as when they are not satisfied and it is absent from the total propagated field structure.

Journal of the Optical Society of America BMay 1, 198960 citations

Uniform asymptotic description of ultrashort Gaussian pulse dispersion

Kurt Edmund Oughstun, Judith E. K. Laurens

The uniform asymptotic description of the propagation of an input Gaussian modulated harmonic signal of fixed angular frequency ω c and initial pulse width T into the half-space z > 0 that is occupied by a single resonance Lorentz medium is described. The asymptotic theory shows that the propagated field can be expressed solely in terms of a generalized Sommerfeld and Brillouin precursor field structure. If the applied signal frequency ω c is either below or near the medium resonance frequency, the propagated field is found to be dominated by the generalized Brillouin precursor field, while if ω c is well above the medium resonance frequency it is dominated by the generalized Sommerfeld precursor field. The resultant pulse distortion in the dispersive medium is shown to be due solely to the manner in which the initial Gaussian pulse envelope spectrum modifies the precursor field amplitude. Finally, the frequency dependence of the pulse velocity in the single resonance Lorentz medium is described.

Annual Meeting Optical Society of AmericaJan 1, 19890 citations

Group-velocity description of the arrival of the Brillouin precursor in a dispersive medium with absorption

George C. Sherman, Kurt Edmund Oughstun

The propagation of short pulses in a dispersive medium can be described in simple physical terms by employing the concept of the group velocity provided the medium is lossless. When the medium is absorbing, the group velocity description breaks down. In a previous paper,1 we presented a similar description employing the velocity of energy of monochromatic waves in place of the group velocity which is valid for a particular dispersive medium with absorption known as the Lorentz medium. That model describes the entire dynamics of the pulse as it propagates with the exception of the early stages of the evolution of the second precursor (otherwise known as the Brillouin precursor). Since that region contains the peak values of the pulse, it is important to include it in the model. The present paper describes the arrival of the Brillouin precursor in terms of the group velocity of a propagating field of the form exp [ωttω z] where ω and kω are real and positive.

Annual Meeting Optical Society of AmericaJan 1, 19900 citations

Asymptotic description of wave propagation in an active Lorentzian medium

Reza Safian, Mohammad Mojahedi, Costas D. Sarris

In a causally dispersive medium the signal arrival appears in the dynamical field evolution as an increase in the field amplitude from that of the precursor fields to that of the steady-state signal. The interrelated effects of phase dispersion and frequency dependent attenuation and/or amplification alter the pulse in such a fundamental way that results in the appearance of precursor fields. Although superluminal group velocities have been found in various dispersive media, the pulse "front" and associated precursors will never travel faster than c , and hence these are the vehicles through which relativistic causality is preserved. While many rigorous studies of wave propagation and associated abnormal group velocities in passive Lorentzian media have been performed, the corresponding problem in active media has remained theoretically unexplored. This problem is addressed in the present paper, by employing the steepest descent method for the determination of the response of an active Lorentzian medium to a step modulated pulse. The steepest descent method provides a detailed description of the propagation of the pulse inside the dispersive medium in the time domain. Moreover, the evolution of the saddle points illuminates the relation between the medium parameters and the temporal evolution of the propagating pulse within the medium. Hence, useful physical insights are obtained and the interesting differences between the passive and active case are deduced.

Physical Review EJun 26, 200717 citations