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Journal of Communications Technology and Electronics

The character of the dispersion of the refractive index near an isolated spectral line

Nikolai S. Bukhman, Anastasia Kulikova

Published May 1, 2015• 4 citations
Publisher

Abstract

An approximate analog of the Kramers-Kronig relationships for an isolated spectral line is proposed. Expressions are obtained for the real part of the dielectric susceptibility of a substance near a spectral line for collisional, Doppler, and time-of-flight spreading of the spectral line. It is shown that, generally, the imaginary part of the complex form-factor of the spectral line attenuates very slowly, namely, according to the hyperbolic law, as the deviation from the center frequency grows. Therefore, even in the case when practically there is no radiation absorption beyond the spectral line, the influence of this spectral line on the refractive index of the substance manifests itself rather far from it.

DOI
10.1134/s1064226915030080

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An approximate analog of the Kramers-Kronig relationships for an isolated spectral line is proposed. Expressions are obtained for the real part of the dielectric susceptibility of a substance near a spectral line for collisional, Doppler, and time-of-flight spreading of the spectral line. It is shown that, generally, the imaginary part of the complex form-factor of the spectral line attenuates very slowly, namely, according to the hyperbolic law, as the deviation from the center frequency grows. Therefore, even in the case when practically there is no radiation absorption beyond the spectral line, the influence of this spectral line on the refractive index of the substance manifests itself rather far from it.
When the real and imaginary parts of the susceptibility, χ′ and χ″ respectively, of narrow saturated absorption lines are of Lorentzian form, it is shown that a constant A can always be found such that χ′ and A χ″ are a Kronig-Kramers transform pair. Lines made up of weighted linear super-positions of Lorentzian lines having the same shape and the same saturation behaviour also possess this property, as do certain continuous distributions of narrow Lorentzian lines. The Kronig-Kramers calculation of a saturated absorption lineshape from a saturated dispersion signal is therefore very likely to yield the true lineshape.
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.
The response of a medium to radiation with a complex frequency corresponding to an exponential time decrease in the radiation amplitude has been analyzed. The effect of complex resonance has been demonstrated when the real and imaginary parts of the complex radiation frequency approach the real and imaginary parts of the complex frequency of damping natural oscillations of medium oscillators. In resonance itself, the absolute value of the refractive index is divergent and radiation is completely reflected from the medium boundary. It has been shown that scanning of not only the real part, but also the imaginary part of the probe radiation frequency expands the capabilities of spectroscopy and makes it possible to, e.g., distinguish resonances even with coinciding (real) frequencies and close (of the same order of magnitude) widths.
The propagation of narrow packets of electromagnetic waves (EMWs) in frequency dispersive medium with the consideration of the complex refractive index is studied. It is shown that counting in the dispersion of the complex refractive index within the context of the conventional expression of the group velocity of narrow wave packets of EMWs propagating in a dispersive medium results in the appearance of additional constraints on the group velocity, which dictates that the physically acceptable group velocity can only be realized in the case of a negligible imaginary part of the group index. In this paper, the conditions that allow one to realize the physically acceptable group velocity are formulated and analyzed numerically for the relevant model of the refractive index of a system of two-level atoms in the optical frequency range. It is shown that in the frequency band where superluminal light propagation is expected, there is a strong dispersion of the refractive index that is accompanied with strong absorption, resulting in a strongly attenuated superluminal light.