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Journal of the Optical Society of America B

Coupling effects of signal and pump beams in three-level saturable-gain media

Yuri Mitnick, Moshe Horowitz, Baruch Fischer

Published Sep 1, 1998• 2 citations
Publisher

Abstract

We theoretically investigate new coupling and indirect wave-mixing effects formed in a three-level atomic gain medium that is optically pumped by two mutually coherent beams that propagate in opposite directions. The interference of the pump beams and the saturation effects caused by the signal waves periodically modulate the gain along the amplifier that is due to spatial hole burning. In cases when the interference patterns of the pump and the signal waves are spatially synchronized, the signal gain becomes dependent on the frequencies and the optical phases of the pump and the signal waves. This dependence can be used for obtaining controllable narrow-band filters and for obtaining single-mode operation in lasers.

DOI
10.1364/josab.15.002433

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We theoretically investigate new coupling and indirect wave-mixing effects formed in a three-level atomic gain medium that is optically pumped by two mutually coherent beams that propagate in opposite directions. The interference of the pump beams and the saturation effects caused by the signal waves periodically modulate the gain along the amplifier that is due to spatial hole burning. In cases when the interference patterns of the pump and the signal waves are spatially synchronized, the signal gain becomes dependent on the frequencies and the optical phases of the pump and the signal waves. This dependence can be used for obtaining controllable narrow-band filters and for obtaining single-mode operation in lasers.
Summary form only given. We investigate special coupling effects in an Er-doped optical fibre amplifier, of which the gain medium is optically pumped by two mutually coherent counterpropagating pump waves that interfere inside the amplifier. The result is a unique filtering behavior where the signal gain becomes dependent on the wavelength and on the optical phases of the pump waves. This effect can be used for obtaining filters and single-mode operation of lasers. The wavelength of such a laser can be controlled by changing the wavelength or the phases of the pump waves. We have also shown previously that bidirectional pumping may cause bistability.
We analyze the gain behavior of an optical amplifier that is optically pumped by two counterpropagating beams that are mutually coherent. The pump beams interfere inside the amplifier, resulting in a nonuniform distribution of the pumping. In the low-pump-intensity regions of the amplifier, the medium absorbs, and in the high-pump-intensity regions amplification can be obtained. The combination of the absorbing regions and the amplifying can lead to bistable behavior inside a resonator. The effect was analyzed for three-level gain media applicable to erbium-doped fiber amplifiers and lasers.
We investigate the interplay between the two components of the four-wave mixing (FWM) beams in a ladder-type three-level atomic system. The interplay, including the shift and splitting of the two FWM beams and their intensity modulation, depends on the frequency detuning and the angles as well as the powers of the pump fields. The x-directional splitting due to the cross-phase modulation and y-directional splitting because of electromagnetically induced gratings of FWM beams are investigated. Both the theoretical and experimental results exhibit that the spatial separation and the number of the FWM signals can be well controlled by additional dressing laser beams. Such studies not only can be very useful in better understanding the formation of spatial solitons but also have potential applications in signal processing.
In this study, we extended the observation of the effect of the coherence of a laser field to four-wave mixing interactions in atomic media. These measurements will help us understand quantitatively recent techniques employing broad-band nanosecond laser pulses for measurements of sub-picosecond dipole relaxation lifetimes in a variety of media. The coherence of the laser field in this work is controlled using random phase/frequency modulation techniques, creating a field in the laboratory known as the phase diffusion field. The four-wave mixing signal is generated by an ensemble of two-level atoms (Na) interacting with degenerate broad-band, correlated, pump and probe fields. This two-level system is produced by optically pumping the sodium atoms into a single hyperfine component of the ground state. Data sets were taken without and with noise applied to the optical field. For the latter, we measured the dependence of the power of the four-wave mixing signal on the delay times between the pump and probe beams. These data sets were compared with the computer simulation results.
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].
The nonlinear response of a two-level system interacting with two pump beams of different frequencies is studied with a view to examine several recent experiments on nonlinear mixing of high orders, instabilities in homogeneously broadened lasers, and holes in homogeneous lines. Such a nonlinear response is calculated with use of the continued fractions given in our earlier work [J.Opt. Soc. Am. 81, 164 (1984)]. Saturation effects lead to the appearance of many structures at submultiples of the Rabi frequency. The origin of these subharmonics in nonlinear-response functions is explained. It is shown that collisions not only lead to hole burning at the line center for weak fields but can also lead in moderate fields to the appearance of structures at subharmonics of the Rabi frequency. Existence of collision-induced coherences similar to those in four-wave mixing is shown in six-wave mixing. Exact results for the degenerate nonlinear mixing of arbitrary order are presented for arbitrary values of field strengths. Saturating fields create holes at the line center of such nonlinear mixing signals. Gain profiles of two modes symmetrically displaced from line center are also given. Numerical results, with complete account of saturation and collisions, for a variety of nonlinear-response functions are presented.