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Physical Review

Influence of a Resonant Absorber whose Thickness Varies Linearly with Time on the Spectral Shape of an Incident Lorentzian Wave Packet

I. Nowik

Published Jun 1, 1962• 2 citations
Publisher

Abstract

The influence of a resonant absorber whose thickness varies linearly with time on the spectral shape of an incident Lorentzian wave packet is discussed, using classical dispersion theory. The resonant line is broadened and, for high enough velocities with which the thickness of the absorber changes, the line is split into two bands with a minimum at the resonant frequency ${\ensuremath{\omega}}_{0}$.

DOI
10.1103/physrev.126.1878

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The influence of a resonant absorber whose thickness varies linearly with time on the spectral shape of an incident Lorentzian wave packet is discussed, using classical dispersion theory. The resonant line is broadened and, for high enough velocities with which the thickness of the absorber changes, the line is split into two bands with a minimum at the resonant frequency \ensuremathω0{\ensuremath{\omega}}_{0}\ensuremathω0​.
A new approach is suggested for dealing with the many-body aspects of resonance broadening of spectral lines in gases. A Liouville-space formalism is used in which the absorption by NNN identical molecules undergoing resonance-exchange collisions is described by an NNN-dimensional projection operator in Liouville space. In the impact approximation, under conditions in which the Doppler shift of resonance frequencies can be neglected, it is shown that the effect of resonance collisions is to modify the linewidth expression obtained by ordinary foreign-gas-type theories. The shape of isolated lines remains, however, Lorentzian. Only a combined effect of Doppler and collision broadening causes appreciable deviations from the Lorentzian shape near the line center, but these deviations are not peculiar to resonance broadening.
Light propagation behavior in a resonantly absorbing waveguide array is analyzed. Both a Lorentzian line shape and an inhomogeneous broadened absorbing line shape are considered, with their imaginary and real part of the refractive index determined by a Kramers-Kronig relationship. The diffracted wave is shown to have the frequency spectra determined by the material absorption, dispersion as well as the waveguide structure. An interesting phenomenon is that a spectral hole is produced and becomes deeper in the diffraction spectrum as the thickness of the resonantly absorbing waveguide array increases. The experimental measurements conducted in a waveguide array are found to be in good agreement with the numerical results.
It is shown that the velocity of propagation of a frequency-modulated wave packet through a strongly dispersive absorbing medium can be significantly different from (either higher or lower than) that of a non-frequency-modulated wave packet. This difference is attributed to the absorption dispersion of the medium. The easiest way to take the absorption dispersion into account is to use the formalism of the complex group velocity of a wave packet. This paper considers the propagation of a linear frequency-modulated wave packet, whose carrier frequency is close to the frequency of a spectral absorption line of the medium.