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Physical Review E

Semiclassical model of stimulated Raman scattering in photonic crystals

Lucia Florescu, Xiang Zhang

Published Jul 13, 2005• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.72.016611

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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.
We present a theoretical analysis of laser action within the bands of propagating modes of a photonic crystal. Using Bloch functions as carrier waves in conjunction with a multiscale analysis, we derive the generalized Maxwell–Bloch equations for an incoherently pumped atomic system in interaction with the electromagnetic reservoir of a photonic crystal. These general Maxwell–Bloch equations are similar to the conventional semiclassical laser equations but contain effective parameters that depend on the band structure of the linear photonic crystal. Through an investigation of steady-state laser behavior, we show that, near a photonic band edge, the rate of stimulated emission may be enhanced and the internal losses are reduced, which leads to an important lowering of the laser threshold. In addition, we find an increase of the laser output along with an additional narrowing of the linewidth at a photonic band edge.
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.
Recent advances in generating light in specific quantum states facilitate new sensing applications and enhance or revitalize established measurement and sensing techniques. Stimulated Raman spectroscopy (SRS), a measurement modality based on Raman scattering, could benefit from tuning the quantum properties of the pump and the Stokes lights or the properties of quantum states of the stimulating and excitation fields. Additionally, this modality could also benefit from field enhancement accompanied by plasmon excitation in the surface regions of metal nanoparticles. We present a theoretical investigation of stimulated Raman scattering involving squeezed states of light. The concept of surface- and quantum-enhanced stimulated Raman scattering is introduced. Furthermore, expressions for the respective SRS transition rates are derived, and their dependence on the quantum states of the optical field is discussed, with particular emphasis on the squeezing parameters characterizing these states. For cases involving surface enhancements, we also employ classical computational electrodynamics to guide our exploration of atomically large systems that support plasmon excitation.
We demonstrate both theoretically and numerically that slow light can enhance the stimulated emission of four-level atomic systems in photonic crystals. By applying the Bloch-Floquet formalism and the semiclassical physical model of harmonic oscillators coupled to electromagnetic fields, we develop a formalism that relates the group velocity of slow light to the conversion rate between the electric field and atomic potential energy. From our numerical study of the stimulated emission in fiber Bragg gratings (FBGs) and nongrating fiber, a ninefold enhancement of stimulated emission is observed in a FBG over the nongrating fiber when pumping at the band edge, while a 20-fold enhancement of is observed when the frequency of the stimulated emission approaches the band edge.
Stimulated Raman scattering of femtosecond pulses in a photonic crystal consisting of alternating quarter-wave dielectric layers and layers of a nonlinear-scattering medium is calculated taking into account the quantum fluctuations of the medium polarisation. Analysis of the calculations showed that the Stokes pulse duration and intensity depend substantially on the statistic properties of polarisation. The efficient SRS conversion in a photonic crystal occurs under certain dispersion conditions providing the minimum difference between dispersions of the pump and Stokes frequencies, which are determined by the length and the number of periods of the photonic crystal.