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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Amplifying Sommerfeld precursors and producing a discontinuous index of refraction with gains and losses

Filipe J. Ribeiro, Marvin L. Cohen

Published Sep 19, 2001• 6 citations
Publisher

Abstract

We show that for specially designed linear dispersive media with one absorption line and one gain line the Sommerfeld precursors of a pulse can be amplified leading to an earlier detection of the signal. Also, we show that in some systems with one strong absorption line, a carefully placed gain resonance must induce a discontinuity in the imaginary part of the frequency dependent index of refraction and in the first derivative of its real part.

DOI
10.1103/physreve.64.046602

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Dynamic control of the speed of a light signal, based on stimulated Brillouin scattering in optical fibers, was theoretically studied and also experimentally demonstrated as the core object of this thesis. To date, slow light based on stimulated Brillouin scattering has shown the unmatched flexibility to offer an efficient timing tool for the development of all-optical future router. Nevertheless, the seeming perfect Brillouin slow light suffered from three major obstacles: naturally narrow signal bandwidth, strong change of signal amplitude, and significant signal distortion. The essential contribution of this work has been mostly dedicated to resolve all those impairments so as to make Brillouin slow light a completely operating all-optical delay line for practical applications. Actually, high capability of tailoring the spectral distribution of the effective Brillouin resonance makes possible to resolve partially or completely all those problems. 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We show that for specially designed linear dispersive media with one absorption line and one gain line the Sommerfeld precursors of a pulse can be amplified leading to an earlier detection of the signal. Also, we show that in some systems with one strong absorption line, a carefully placed gain resonance must induce a discontinuity in the imaginary part of the frequency dependent index of refraction and in the first derivative of its real part.
Dynamic control of the speed of a light signal, based on stimulated Brillouin scattering in optical fibers, was theoretically studied and also experimentally demonstrated as the core object of this thesis. To date, slow light based on stimulated Brillouin scattering has shown the unmatched flexibility to offer an efficient timing tool for the development of all-optical future router. Nevertheless, the seeming perfect Brillouin slow light suffered from three major obstacles: naturally narrow signal bandwidth, strong change of signal amplitude, and significant signal distortion. The essential contribution of this work has been mostly dedicated to resolve all those impairments so as to make Brillouin slow light a completely operating all-optical delay line for practical applications. Actually, high capability of tailoring the spectral distribution of the effective Brillouin resonance makes possible to resolve partially or completely all those problems. First of all, a broadband spectral window was passively obtained in between two Brillouin gain/loss resonances by simply appending two segments of fibers showing different Brillouin frequency shifts. The global Brillouin gain of the concatenated fibers manifests a gain/loss doublet resonance showing a broad window in between gain/loss peaks. In practice, this configuration has a crucial advantage that it removes the need of the pump modulation, generally used to create a polychromatic pump source. Therefore, a broadband Brillouin slow and fast light was simple realized with a reduced distortion. Secondly, the signal amplification or attenuation associated to the signal delay was completely compensated by superposing Brillouin gain and loss resonances with identical depth but different width. As a result, the Brillouin gain led to effectively a spectral hole in the center of the broadband absorption and opened a transparent window while the sharp change in the refractive index was preserve. This way it makes possible to realize zero-gain Brillouin slow light. This configuration was also exploited to produce Brillouin fast light with a total absence of signal loss, simply by swapping the spectral position of the two pumps. At last, a signal was continuously delayed through a Brillouin fiber delay line without any distortion. Due to the strong induced dispersion, pulse broadening is a major difficulty in all slow light systems and it is impossible to compensate such broadening using a linear system. Therefore, a conventional Brillouin slow light system was combined with a nonlinear optical fiber loop mirror that gives a nonlinear quadratic transmission. 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In this implementation, a light signal was strongly boosted above the so-called Brillouin threshold, so that most power of the signal was transferred to a backward propagating wave, namely the generation of amplified spontaneous Stokes wave. Since the center frequency of the intense Stokes wave is below the signal frequency by exactly Brillouin shift of the fiber used, this wave led to a Brillouin loss band centered at the signal frequency. Consequently, the signal experienced fast light propagation and the propagation velocity of the signal was self-controlled, simply by varying the signal input power. This technique has many practical advantages such as its high simplicity of the configuration and an invariant signal power in the output of this delay line. Additionally, this system self-adapts the signal bandwidth as the spectrum of the amplified Stokes wave matches the spectral distribution of the signal. An alternative method to generate all-optical delay line was proposed instead of slow light. This scheme makes use of the combination of wavelength conversion and group velocity dispersion. This type of delay line was mainly aimed at improving the storage capability of delaying element. The wavelength of a signal was simply and efficiently converted at a desired wavelength using cross gain modulation in semiconductor optical amplifiers. Then the converted signal was delivered to a high dispersive medium and arrived at the end of the medium with relative time delay due to the group velocity dispersion. A fractional delay of 140 was continuously produced through this delay line for a signal with a duration of 100 ps, preserving signal bandwidth and wavelength. The effect of slow light on linear interactions between light and matter was experimentally investigated to clarify the current scientific argument regarding slow light-enhanced Beer-Lambert absorption. It was predicted that real slowing of the light group velocity could enhance the molecular linear absorptions so as to improve the sensitivity of this type of sensing. However, the experimental results unambiguously show that material slow light (slow light in traveling wave media) does not enhance the Beer-Lambert absorption.
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
It is shown experimentally that a weak optical signal in a Nd:YAG amplifier can have an extraordinarily large gain that is due to transient coherent nonlinear interaction with a strong laser beam. The effect is explained by the diffraction of the strong beam on the dynamic refractive-index grating induced in the interference field of the interacting optical waves and caused by the difference of polarizability of the excited and the unexcited Nd3+ ions. The numerical calculation confirmed the energy transfer from the strong beam to the weak one owing to the predominance of diffraction efficiency of the refractive-index grating over the gain grating in an inverted laser crystal. The investigations give the estimation of the ratio of the real and the imaginary parts of the resonant susceptibility of Nd:YAG at 1064 nm in the range 2–3.