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Journal of the Optical Society of America B

Optical precursors in a weakly dispersive double narrow-resonance dielectric

Heejeong Jeong, Chang‐Won Lee, Andrew M. C. Dawes, Daniel J. Gauthier

Published Nov 7, 2019• 3 citations
Publisher

Abstract

We investigate optical precursors transmitted through a double-Lorentz dielectric consisting of two adjacent narrow resonances. Compared to the patterns in a single-Lorentz dielectric, the transmitted envelope shows additional modulation that oscillates at the separation frequency between two resonances, corresponding to the doublet frequency separation. We use the weakly dispersive, narrow-resonance condition to analyze it, which compares favorably to our observations. This work will be meaningful to identify dielectric properties by analyzing multi-resonant media for application of optical communication.

DOI
10.1364/josab.36.003282

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We investigate optical precursors transmitted through a double-Lorentz dielectric consisting of two adjacent narrow resonances. Compared to the patterns in a single-Lorentz dielectric, the transmitted envelope shows additional modulation that oscillates at the separation frequency between two resonances, corresponding to the doublet frequency separation. We use the weakly dispersive, narrow-resonance condition to analyze it, which compares favorably to our observations. This work will be meaningful to identify dielectric properties by analyzing multi-resonant media for application of optical communication. © 2019 Optical Society of America

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We investigate optical precursors transmitted through a double-Lorentz dielectric consisting of two adjacent narrow resonances. Compared to the patterns in a single-Lorentz dielectric, the transmitted envelope shows additional modulation that oscillates at the separation frequency between two resonances, corresponding to the doublet frequency separation. We use the weakly dispersive, narrow-resonance condition to analyze it, which compares favorably to our observations. This work will be meaningful to identify dielectric properties by analyzing multi-resonant media for application of optical communication.
We investigate optical precursors transmitted through a double-Lorentz dielectric consisting of two adjacent narrow resonances. Compared to the patterns in a single-Lorentz dielectric, the transmitted envelope shows additional modulation that oscillates at the separation frequency between two resonances, corresponding to the doublet frequency separation. We use the weakly dispersive, narrow-resonance condition to analyze it, which compares favorably to our observations. This work will be meaningful to identify dielectric properties by analyzing multi-resonant media for application of optical communication. © 2019 Optical Society of America
We study theoretically the propagation of a step-modulated optical field as it passes through a dispersive dielectric made up of a dilute collection of oscillators characterized by a single narrow-band resonance. The propagated field is given in terms of an integral of a Fourier type, which cannot be evaluated even for simple models of the dispersive dielectric. The fact that the oscillators have a low number density (dilute medium) and have a narrow-band resonance allows us to simplify the integrand. In this case, the integral can be evaluated exactly, although it is not possible using this method to separate out the transient part of the propagated field known as optical precursors. We also use an asymptotic method (saddle-point method) to evaluate the integral. The contributions to the integral related to the saddle points of the integrand give rise to the optical precursors. We obtain analytic expressions for the precursor fields and the domain over which the asymptotic method is valid. When combined to obtain the total transient field, we find that the agreement between the solutions obtained by the asymptotic and the exact methods is excellent. Our results demonstrate that precursors can persist for many nanoseconds and the chirp in the instantaneous frequency of the precursors can manifest itself in beats in the transmitted intensity. Our work strongly suggests that precursors have been observed in many previous experiments.
We observe interference between the optical precursors and the main signal for small optical depth α0 L ∼ 1, in which the main signal cannot be entirely absorbed. Since the main signal oscillates at the carrier frequency of the input pulse and precursors oscillate at medium resonance frequency, in our case carrier frequency dependence of the total transmitted field is observed as a form of modulation patterns oscillating at the detuning frequency. To distinguish between the Sommerfeld and Brillouin precursors for the case of weakly dispersive off-resonance medium, we utilize asymptotic precursor theory under the assumption of small detuning.
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.
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.
The appearance of optical precursors in the transient response of linear dielectric media is elucidated by combining temporal and spectral analysis. Numerical calculations show that it is feasible to detect experimentally the precursors in the transient responses of excitonic resonances to picosecond excitation. A novel experiment is proposed in which precursors are spatially separated from the main part of the signal in a thin-prism sample. Some features of the transients in reflection are analyzed.