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Annual Meeting Optical Society of America

Brillouin resonances in the interaction of a two-level system with laser radiation

Aharon Postan, Jagdish Rai, C. M. Bowden

Published Jan 1, 1989• 0 citations
Publisher

Abstract

New resonances are predicted in the interaction of a two-level system (TLS) with laser radiation. These resonances are related to the nonlinear coupling between the TLS and Brillouin enhanced acoustic waves driven by the laser radiation. Resonances in phase conjugation by four-wave mixing driven by stimulated Brillouin scattering (SBS) of laser radiation in fluids have been studied elsewhere.1,2 The coupling of such resonances to the TLS interaction with laser radiation influences the spectral behavior of the TLS. Such resonances appear in addition to the Rabi sidebands. The inclusion of these resonances should have important practical implications in processes that depend on accurate spectral behavior such as in the fields of laser spectroscopy, four-wave mixing, and phase conjugation. Here the new resonances are demonstrated for two mutually detuned counterpropagating laser beams interacting with a TLS at frequencies that may be detuned from the TLS spectral line center. The nonlinear Maxwell Bloch equations coupled to the acoustic wave equation are solved numerically. Damping due to viscosity is taken into account. Wave depletion is included and no perturbation theory approximations are assumed in the numerical solution of these equations.

DOI
10.1364/oam.1989.mkk4

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Journal of the Optical Society of America B•Sep 1, 1989•10 citations
New resonances are predicted in the interaction of a two-level system (TLS) with laser radiation. These resonances are related to the nonlinear coupling between the TLS and Brillouin enhanced acoustic waves driven by the laser radiation. Resonances in phase conjugation by four-wave mixing driven by stimulated Brillouin scattering (SBS) of laser radiation in fluids have been studied elsewhere.1,2 The coupling of such resonances to the TLS interaction with laser radiation influences the spectral behavior of the TLS. Such resonances appear in addition to the Rabi sidebands. The inclusion of these resonances should have important practical implications in processes that depend on accurate spectral behavior such as in the fields of laser spectroscopy, four-wave mixing, and phase conjugation. Here the new resonances are demonstrated for two mutually detuned counterpropagating laser beams interacting with a TLS at frequencies that may be detuned from the TLS spectral line center. The nonlinear Maxwell Bloch equations coupled to the acoustic wave equation are solved numerically. Damping due to viscosity is taken into account. Wave depletion is included and no perturbation theory approximations are assumed in the numerical solution of these equations.
Two-photon transitions have provided the basis for numerous useful nonlinear interactions with radiation. In this paper we calculate the absorption and coupling coefficients for one-, two-, and three-wave mixing in two-photon homogeneously broadened media. The resulting field equations form the basis for understanding saturation spectroscopy, phase conjugation,1 and single-mode instabilities2 in lasers and optical bistability in two-photon media. We assume that the wave frequencies are not resonant with any intermediate state j and that the probe and conjugate waves cannot saturate the two-photon transition. This allows us to use the two-photon two-level model and to transfer much of our knowledge of the one-photon two-level systems to the two-photon case. Two major differences occur between the two models. First, dynamic Stark shifts of the active levels play an important role in generating asymmetric spectra and nonzero dispersion (≃ω s T1) at line center. Second, high pump intensities do not bleach the absorption coefficient at the Rabi sidebands.
Frontiers in Guided Wave Optics and Optoelectronics 84 absorption is much too high to render the group effect useful.An exciting breakthrough happened in the early nineties when it was shown that group velocities of few tens of meters per second were possible with nonlinear resonance interactions (Hau et al., 1999).Two important features of nonlinear resonances make this possible: substantially reduced absorption, or even amplification, of radiation at a resonance, and sharpness of such resonances; the sharper a resonance, the higher dn/dω and so the stronger the enhancement of group index, and hence the greater the pulse is delayed.Widely ranging applications for slow light have been proposed, of which those for telecommunication systems and devices (optical delay lines, optical buffers, optical equalizers and signal processors) are currently of most interest (Gauthier, 2005).The essential demand of such devices is compatibility with existing telecommunication systems, that is they must be of wide enough bandwidth (≥10 GHz) and able to be integrated seamlessly into such systems.Of the various nonlinear resonance mechanisms and media, which allow sufficiently long induced delays, stimulated Brillouin and Raman scattering (SBS and SRS) in optical fiber are deemed to be among the best candidates.Currently SBS is the most actively investigated and many experimental and theoretical papers on pulse delaying via SBS in optical fiber have been published in the last few years, see the review paper (Thevenaz, 2008) and references therein.In this process the pulse to be delayed is a frequency down-shifted (Stokes) pulse.This is transmitted through an optical fiber through which continuous wave (CW) pump radiation is sent in the opposite direction to prime the delay process.It is supposed that the Stokes pulse is amplified by parametric coupling with the pump wave and a material (acoustic) wave in the medium (Kroll, 1965), and the amplification is characterised by a resonant-type gain profile.The dispersion of refractive index associated with this profile (which is similar to that in Fig. 1) can then be used to increase the group index for optical pulses at the Stokes frequency (Zeldovich, 1972).Along with obvious device compatibility, there are several other advantages of the SL via SBS approach for optical communications systems: slow-light resonance can be created at any wavelength by changing the pump wavelength; use of optical fibre allows for long interaction lengths and thus low powers for the pump radiation, the process runs at room temperature, it uses off the shelf telecom equipment, and SBS works in the entire transparency range of fibers and in all types of fiber.Currently a main obstacle to applications of this approach is the narrow SBS gain spectral bandwidth, (Thevenaz, 2008), which is typically ≈ 120-200 MHz in silica fiber in the spectral range of telecom optical radiation (~1.3-1.6 μm) (Agrawal, 2006).This chapter reviews our ongoing work on the physical mechanisms that give rise to pulse delay in SBS.In section 2 the theoretical background of the SBS phenomenon is given and the main working equations describing this nonlinear interaction are presented.In section 3 ways by which the SBS spectral bandwidth may be increased are addressed.Waveguide induced spectral broadening of SBS in optical fibre is considered as a means of increasing the bandwidth to the multi-GHz range.An alternative way widely discussed in the literature, (Thevenaz, 2008), is based on spectral broadening of the pump radiation.However it is shown through analytic analysis of the SBS equations converted to the frequency domain that pump radiation broadening by any reasonable amount has only a negligible effect on increasing the SBS bandwidth.Importantly in this section we show that, irrespective of the nature of the broadening considered, the SBS gain bandwidth remains www.intechopen.
In this paper we report on the study of two and multi-level atoms interacting with multiple laser beams. The semi-classical approach is used to describe the system in which the atoms are treated quantum mechanically via the density matrix operator, while the laser beams are treated classically using Maxwells equations. We present results of a two level atom interacting with single and multiple laser beams and demonstrate Rabi oscillations between the levels. The effects of laser modulation on the dynamics of the atom (atomic populations and coherences) are examined by solving the optical Bloch equations. Plots of the density matrix elements as a function of time are presented for various parameters such as laser intensity, detuning, modulation etc. In addition, phase-space plots and Fourier analysis of the density matrix elements are provided. The atomic polarization, estimated from the coherence terms of the density matrix elements, is used in the numerical solution of Maxwells equations to determine the behaviour of the laser beams as they propagate through the atomic ensemble. The effects of saturation and hole-burning are demonstrated in the case of two counter propagating beams with one being a strong beam and the other being very weak. The above work is extended to include four-wave mixing in four level atoms in a diamond configuration. Two co-propagating beams of different wavelengths drive the atoms from a ground state |1〉 to an excited state |3〉 via an intermediate state |2〉. The atoms then move back to the ground state via another intermediate state |4〉, resulting in the generation of two additional correlated photon beams. The characteristics of these additional photons are studied.
Investigations of self-pumped phase conjugation using Brillouin-enhanced four-wave mixing in TiCl4 at 1 μm are presented. We have (1) observed both forward and backward Brillouin scattering into the optical cavity used for self-pumped phase conjugation during a single pump laser pulse and enhanced the forward-scattered component relative to the backward-scattered component by changing the angle of incidence of the pump beam, (2) demonstrated up to 80% coupling of pump radiation into cavity radiation, (3) examined quenching of the radiation in the optical cavity and eliminated both multiple Stokes orders from Brillouin scattering and Raman scattering as possible mechanisms, (4) observed mode beating in the cavity intensity profile coincident with the quenching, and (5) studied ring-resonator geometries, demonstrating both forward and backward scattering, unidirectional oscillation, and bidirectional oscillation leading to a triple-shifted phase conjugate.