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Optics Express

Amplification and attenuation of light in a waveguide modulated by a travelling wave

M. Sumetsky

Published Mar 9, 2026• 1 citation
Publisher

Abstract

Light propagating in an optical waveguide can gain or lose power through interaction with a travelling acoustic wave or radio-frequency modulation of permittivity. Here, we model this propagation by considering an optical wave interacting with a weak travelling-wave permittivity perturbation whose frequency is much smaller than the optical frequency and whose amplitude decays exponentially along the propagation direction. Four modulation cases are analyzed: instantaneous modulation, synchronous modulation, and the Stokes and anti-Stokes resonances. For these cases, simple expressions are obtained for the carrier and sideband transmission and reflection powers as well as for the total gain and loss powers. Although the achievable total gain remains small for realistic modulation and waveguide parameters, the anti-Stokes resonance is identified as the most promising condition for observing modulation-induced light amplification.

DOI
10.1364/oe.592420

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Light propagating in an optical waveguide can gain or lose power through interaction with a travelling acoustic wave or radio-frequency modulation of permittivity. Here, we model this propagation by considering an optical wave interacting with a weak travelling-wave permittivity perturbation whose frequency is much smaller than the optical frequency and whose amplitude decays exponentially along the propagation direction. Four modulation cases are analyzed: instantaneous modulation, synchronous modulation, and the Stokes and anti-Stokes resonances. For these cases, simple expressions are obtained for the carrier and sideband transmission and reflection powers as well as for the total gain and loss powers. Although the achievable total gain remains small for realistic modulation and waveguide parameters, the anti-Stokes resonance is identified as the most promising condition for observing modulation-induced light amplification.
Light propagating in an optical waveguide can gain or lose power through interaction with a travelling acoustic wave or radio-frequency modulation of permittivity. Here, we model this propagation by considering an optical wave interacting with a weak travelling-wave permittivity perturbation whose frequency is much smaller than the optical frequency and whose amplitude decays exponentially along the propagation direction. Four modulation cases are analyzed: instantaneous modulation, synchronous modulation, and the Stokes and anti-Stokes resonances. For these cases, simple expressions are obtained for the carrier and sideband transmission and reflection powers as well as for the total gain and loss powers. Although the achievable total gain remains small for realistic modulation and waveguide parameters, the anti-Stokes resonance is identified as the most promising condition for observing modulation-induced light amplification.
The behavior of electromagnetic waves in a medium modulated in time and space, largely investigated decades ago, has recently attracted renewed interest. Here, we address an intriguing problem of this research: can light with an initial frequency ω 0 be amplified solely pumped by a traveling wave with a much lower frequency ω p ≪ ω 0 ? Generally, the bandwidth of the modulation-induced optical frequency comb spectrum can be substantially broadened when the phase velocity of the traveling wave, v p , approaches the phase velocity of light, v 0 . However, in realistic photonic waveguides, the amplification effect remains small due to the unfeasible modulation and waveguide parameters required. In contrast, we demonstrate that modulating an optical resonator by a traveling wave having the frequency ω p and phase velocity v p much smaller than the frequency ω 0 and phase velocity v 0 of light can result in large light amplification accompanied by conversion to multiple comb lines within a relatively small frequency band.
The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.
The process of an optical signal undergoing a transition between two modes of a photonic structure is referred to as a photonic transition. We show that a signal wave interacting with a free carrier front in a slow light waveguide experiences indirect photonic transitions leading to transmission or reflection from the moving front. Theory and experimental results are presented. The front induced dynamic frequency conversion is also compared to the frequency shifting based on other nonlinear effects like cross-phase modulation and four wave mixing.
We experimentally investigated optical pulse propagation through an amplifying ring resonator, in which a semiconductor optical amplifier was used as a loss or gain medium. Initially, the transmission intensity showed resonance dips as a function of laser frequency. These dips were gradually filled and transformed into resonance peaks as the amplification gain increased. A Gaussian-shaped temporal pulse was either advanced by −7.3 ns at low amplification gain or delayed up to 45 ns at high gain. System operation was classified into a complete set of the four regions depending on the gain parameter, and experimental delay times were analyzed based on relevant system dispersion.