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Physical Review A

Origin of spectral hole burning in Brillouin fiber amplifiers and generators

L. Stépien, Stéphane Randoux, J. Zemmouri

Published May 3, 2002• 26 citations
Publisher

Abstract

We show theoretically that the spectral hole burning recently observed in Brillouin fiber amplifiers and generators can be interpreted without invoking an inhomogeneous broadening of the Brillouin line. By using the three-wave model of stimulated Brillouin scattering (SBS), we first investigate the linear response of a Brillouin fiber amplifier to a weak amplitude modulation of the injected signal wave. The transfer functions that fully characterize this response are analytically calculated. The fact that they may exhibit a dip is shown to be due both to the gain saturation and to the coupling between the pump and signal perturbations that counterpropagate around the steady-state intensity profiles. These transfer functions also appropriately characterize the way through which noisy perturbations are filtered in SBS fiber generators. The spectral hole burning observed in generators is thus simply connected to spectral hole burning studied in SBS amplifiers.

DOI
10.1103/physreva.65.053812

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We show theoretically that the spectral hole burning recently observed in Brillouin fiber amplifiers and generators can be interpreted without invoking an inhomogeneous broadening of the Brillouin line. By using the three-wave model of stimulated Brillouin scattering (SBS), we first investigate the linear response of a Brillouin fiber amplifier to a weak amplitude modulation of the injected signal wave. The transfer functions that fully characterize this response are analytically calculated. The fact that they may exhibit a dip is shown to be due both to the gain saturation and to the coupling between the pump and signal perturbations that counterpropagate around the steady-state intensity profiles. These transfer functions also appropriately characterize the way through which noisy perturbations are filtered in SBS fiber generators. The spectral hole burning observed in generators is thus simply connected to spectral hole burning studied in SBS amplifiers.
We observe spectral hole burning in a room-temperature optical fiber pumped by a spectrally broadened pump beam. This beam drives the stimulated Brillouin process, creating an inhomogeneously broadened resonance in the material whose shape can be engineered by tailoring the beam's spectrum. A monochromatic saturating beam "burns" a narrow spectral hole that is approximately 10(4) times narrower than the inhomogeneous width of the resonance. This research paves the way toward agile optical information processing and storage using standard telecommunication components.
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. Using this configuration, the inevitable pulse broadening was completely compensated at the output of the loop and a signal was delayed up to one symbol without any distortion. Brillouin slow light systems were further studied in the spectral domain. For a given Brillouin resonance the spectrum of a light pulse was optimized to better match the Brillouin bandwidth. When the time envelope of a pulse was properly shaped, it was clearly observed that the spectral width of the pulse became minimized while preserving the pulse duration. This way the maximum time delay through Brillouin slow light could be enhanced for a fixed pulse width. Brillouin fast light was even realized in total absence of any pump source, which is a plain requirement for the generation of Brillouin slow or fast light. This self-generated delay line, key contribution of this thesis, relies on both spontaneous and stimulated Brillouin scattering in optical fibers. 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.
Erbium-Doped Fiber Amplifiers can present holes in spectral gain in Wavelength Division Multiplexing operation. The origin of this inhomogeneous saturation behavior is still a subject of controversy. In this paper we present both an experimental methods and a gain's model. Our experimental method allow us to measure the first homogeneous linewidth of the 1.5μ\muμm erbium emission with gain spectral hole burning consistently with the other measurement in the literature and the model explains the differences observed in literature between GSHB and other measurement methods.
Gain-difference spectra are used to show that 980-nm band pump wavelength changes can significantly effect spectral-hole burning (SHB) in erbium-doped fiber amplifiers (EDFAs). Gain measurements made using a number of different signal and pump wavelengths help to characterize the underlying inhomogeneous spectral properties of EDFAs and a framework for modeling these effects is presented. Despite the difficulty of obtaining the needed subpopulation specific cross section spectra, this model can be used to explain seemingly anomalous changes in the gain spectra of EDFA as a result of changes in signal or pump wavelength.
We study theoretically and experimentally the spectral properties of low-frequency transmitted intensity noise induced by stimulated Brillouin scattering in optical fibers. In fibers with a length of 25 km the Brillouin scattering induces transmitted intensity noise with a bandwidth on the order of tens of kHz. The power spectral density of the noise can be stronger than the shot noise in the photo-detector even when the optical power is significantly lower than the Brillouin threshold. The low-frequency transmitted intensity noise is caused due to depletion of the pump wave by the stochastic Brillouin wave. Since pump depletion occurs over a long distance, noise with a narrow bandwidth is generated in the transmitted wave. When the pump power is high enough, the spectrum of the induced noise contains features such as hole at low frequencies and ripples. Good quantitative agreement between theory and experiments is obtained. Low-frequency intensity noise induced by Brillouin scattering may limit the generation of ultra-low noise signals in optoelectronic oscillators and may limit the transfer of ultra-low noise signals in fibers.