Stimulated Raman and Brillouin scattering (SRS and SBS) phenomena have been investigated analytically with use of density-matrix formulations and assuming parity indefiniteness for the eigenfunctions of the energy eigenstates of a two-level system in noncentrosymmetric (NCS) crystals. In crystals, when a molecule is excited, the disturbance travels through the crystal as a vibrational wave (phonon mode). We have considered the scattering of the incident electromagnetic wave by phonon modes on a common footing, assuming that vibrations should correspond to optical phonons for SRS and to acoustic phonons for SBS. The retardation effect due to finite ${\ensuremath{\chi}}^{(2)}$ in NCS crystals is found to play a more significant role in the case of SRS than for SBS. The classical differential polarizability (\ensuremath{\partial}\ensuremath{\alpha}/\ensuremath{\partial}u${)}_{0}$ that causes SRS has been determined from the present formulations in terms of the material constants of the crystal and the photon pump energy. Applying Heisenberg's uncertainty relation, we have also obtained a general formula for the determination of the electrostrictive coefficient \ensuremath{\gamma} that is responsible for SBS in crystals. We find (\ensuremath{\partial}\ensuremath{\alpha}/\ensuremath{\partial}u${)}_{0}$/\ensuremath{\gamma}\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}8}$ with \ensuremath{\gamma}\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}10}$--${10}^{\mathrm{\ensuremath{-}}11}$ mks units for important III-V semiconductors. Both Raman and Brillouin gain constants are studied over a wide frequency spectrum in the semiconductors. The ratio between the two gain constants indicates that for the same pump intensity SBS exhibits higher gain than SRS by a magnitude \ensuremath{\sim}${\ensuremath{\omega}}_{\mathrm{OP}/{\ensuremath{\omega}}_{\mathrm{AP}}}$. .AE
Stimulated Raman and Brillouin scattering (SRS and SBS) phenomena have been investigated analytically with use of density-matrix formulations and assuming parity indefiniteness for the eigenfunctions of the energy eigenstates of a two-level system in noncentrosymmetric (NCS) crystals. In crystals, when a molecule is excited, the disturbance travels through the crystal as a vibrational wave (phonon mode). We have considered the scattering of the incident electromagnetic wave by phonon modes on a common footing, assuming that vibrations should correspond to optical phonons for SRS and to acoustic phonons for SBS. The retardation effect due to finite \ensuremathχ(2) in NCS crystals is found to play a more significant role in the case of SRS than for SBS. The classical differential polarizability (\ensuremath{\partial}\ensuremath{\alpha}/\ensuremath{\partial}u)0 that causes SRS has been determined from the present formulations in terms of the material constants of the crystal and the photon pump energy. Applying Heisenberg's uncertainty relation, we have also obtained a general formula for the determination of the electrostrictive coefficient \ensuremath{\gamma} that is responsible for SBS in crystals. We find (\ensuremath{\partial}\ensuremath{\alpha}/\ensuremath{\partial}u)0/\ensuremath{\gamma}\ensuremath{\sim}10\ensuremath−8 with \ensuremath{\gamma}\ensuremath{\sim}10\ensuremath−10--10\ensuremath−11 mks units for important III-V semiconductors. Both Raman and Brillouin gain constants are studied over a wide frequency spectrum in the semiconductors. The ratio between the two gain constants indicates that for the same pump intensity SBS exhibits higher gain than SRS by a magnitude \ensuremath{\sim}\ensuremathωOP/\ensuremathωAP. .AE
We study the stimulated Raman scattering (SRS) of light from an atomic system embedded in a photonic crystal and coherently pumped by a laser field. In our study, the electromagnetic field is treated classically and the atomic system is described quantum mechanically. Considering a decomposition of the pump and Stokes fields into the Bloch modes of the photonic crystals and using a multiscale analysis, we derive the Maxwell-Bloch equations for SRS in photonic crystals. These equations contain effective parameters that characterize the SRS gain, the nonlinear atomic response to the electromagnetic field, and the group velocity and that can be calculated in terms of the Bloch modes of the unperturbed photonic crystal. We show that if the pump laser frequency is tuned near a photonic band edge and the atomic system is carefully chosen such that the Stokes mode matches another photonic band edge, low-threshold, enhanced Raman amplification is possible. Possible physical realizations of SRS in photonic crystals are also discussed.
The stimulated Raman scattering (SRS), arising from the interaction between molecules of a medium and two strong light fields - a resonant field and a pumping field - is studied theoretically. The transitions of molecules between a given pair of levels is assumed to be both Raman active and infrared active. A semiclassical approach, in which the density matrix method is used for the quantum mechanical description for the medium, is employed. We expand the density matrix in various orders within which the zeroth-order is referred to as the solution of the equation of motion of the density matrix when only the resonant field is applied. -- We obtain a set of equations in second order of the density matrix element p₁₀⑵ (ω) from which the gain function can be derived. This set of equations in the special case of steady state is accidentally similar to those obtained by Mollow in his study of the power spectrum of a strong driven two-level system. We have shown that the SRS in the steady state under the resonant field interaction, is drastically reduced in general. When the flopping frequency is larger than the relaxation constants (Ω > r), we find there appears both weak positive and weak negative gains on both sides of the ordinary SRS components. Since we retain our second-order equations in a general form rather than the form for steady state, we are able to take account of the dependence on the transient zeroth solution. By employing the Laplace transform technique with the help of convolution products, we are able to solve for ρ₁₀⑵(ω) in the stationary flopping state. When the intensity of the resonant field is high, we have found theoretically that both the Stokes and anti-Stokes component become doublets and equally displaced by the amount of the flopping frequency, Ω, on the opposite sides of ordinary Stokes and anti-Stokes components, respectively. The gain maxima are approximately the order of Ω/4r times the ordinary gain of the Stokes component, where Ω/r >> 1 if the flopping exists. The gains are therefore large in comparison with the ordinary gain for SRS in the steady state.
The polarization-related properties of stimulated Brillouin scattering (SBS) processes in long, randomly birefringent, standard optical fibers are examined. Evolution equations for the pump and signal waves, in the presence of both birefringence and SBS, are provided in Jones and Stokes spaces. It is shown that in the undepleted pump regime, the amplification of the SBS signal wave is equivalent to that of a linear medium with polarization-dependent gain. The process is associated with a pair of orthogonal states of polarizations (SOPs) of the signal wave, which undergo maximum and minimum amplification. In long, standard fibers, the Jones vector of the probe SOP which corresponds to maximum amplification is aligned with the complex conjugate of the pump wave Jones vector. The maximum and minimum SBS gain coefficients in such fibers equal two-thirds and one-third of the gain coefficient that is predicted by scalar theory, respectively. The large differential gain of the SBS process gives rise to an effective pulling of the amplified Stokes probe wave SOP, towards that of maximum amplification. Lastly, Stokes wave pulses that are aligned for maximum and minimum amplification experience different group delays, which manifest as polarization-related distortions in SBS slow light setups.
Abstract Laser Stimulated Scattering and Multiphoton Excitation is the first book that comprehensively covers the following three major areas: (1) Quantum electrodynamic theory of stimulated scattering and multiphoton excitation processes; (2) Various stimulated scattering effects, including the early discovered stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS), the later investigated stimulated Kerr scattering (SKS), and the recently developed stimulated Rayleigh–Bragg scattering (SRBS) and stimulated Mie scattering (SMS); (3) Multiphoton excitation-based nonlinear optical effects, photoelectric effects, atomic and molecular ionization effects, and molecular dissociation effects. Each chapter covers: (i) the concept and mechanism description, (ii) the necessary theoretical formulation, (iii) the experimental research achievements, and (iv) the scientific/technological applications. Laser Stimulated Scattering and Multiphoton Excitation is useful and suitable for academics, experts, and students working or interested in the areas of nonlinear optics, nonlinear photonics, laser spectroscopy, physical optics, physical chemistry, and optoelectronic engineering.
A theory of stimulated Raman scattering (SRS) is presented which treats in a unified manner the buildup of SRS from spontaneous Raman scattering and the spatial propagation which leads to gain. Maxwell-Bloch equations describe the coupling between the Stokes field operator and the collective atomic operators, which are driven by a classical laser field under low-signal-gain conditions, where the atomic ground states and laser field remain undepleted. An analytic expression is derived for the forward-propagating Stokes field operator in a one-dimensional spatial approximation when the Fresnel number of the excited medium is unity. Steady-state and transient Stokes intensities are evaluated under low-gain (spontaneous) and high-gain (stimulated) conditions. The Stokes intensity is found to be exactly independent of a laser bandwidth arising solely from phase fluctuations. The power spectrum of steady-state SRS is evaluated, giving a gain-narrowed spectral profile when the laser is narrow band, and a spectrum identical to the laser spectrum when the laser is broad band. A strong analogy between SRS and two-level superfluorescence is found; in both cases the macroscopic, collective dipole moment is initiated by quantum fluctuations.
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.