Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Three-dimensionalab initioinvestigation of light-matter interaction in Mie lasers

Andrea Fratalocchi, Claudio Conti, Giancarlo Ruocco

Published Jul 2, 2008• 58 citations
Publisher

Abstract

We report on an ab initio investigation of light-matter interactions in a spherical Mie laser. We derive a three-dimensional vector set of Maxwell-Bloch (MB) equations and solve them by the finite-difference time-domain (FDTD) method. Parallel MB-FDTD simulations are employed to study the nonlinear behavior of these nanosized lasers with a varying geometry and different material parameters. The retrieved electromagnetic resonances are consistent with those expected from Mie theory. The lasing regime is characterized by a rich physical scenario, including mode competition and dynamical frequency pulling effects. Application of these dynamics could favor the realization of nonlinearly controlled highly tunable nanolaser devices.

DOI
10.1103/physreva.78.013806

Related papers

Light-matter interaction in Mie nanolasers

Claudio Conti, Andrea Fratalocchi, Giancarlo Ruocco

By deriving a three dimensional vector set of Maxwell-Bloch equations, we report on an ab-initio investigation of a spherical Mie nanolaser. Parallel numerical simulations predict a rich physical scenario, ranging from a nontrivial vectorial energy-matter interplay in the initial stage of evolution to mode competition and dynamical frequency pulling effects. Application of these effects could favor the realization of nonlinearly-controlled largely-tunable nanolaser devices.

arXiv:0709.1442•Sep 10, 2007•0 citations

Simulation of coherent responses of resonant media excited by a series of ultrashort laser pulses

Alexey Tiranov, Каримуллин Камиль Равкатович, В. В. Самарцев

A technique for the numerical simulation of coherent optical responses of the photon echo type formed in resonance media with strong inhomogeneous broadening under the action of femtosecond laser pulses is developed. This approach is based on solving the Maxwell-Bloch equations using the finite-difference time-domain (FDTD) method without application of a fast rotating field and slowly varying envelope approximations. The method can be used to simulate coherent responses in different resonance media with a complex structure of energy levels. The technique was validated using the example of describing experiments on narrowing a photon echo pulse and femtosecond echo processing.

Bulletin of the Russian Academy of Sciences Physics•Mar 1, 2012•1 citation

Computational Modeling of Ultrashort Pulse Propagation in Nonlinear Optical Materials

Peter M. Goorjian, Govind Prasad Agrawal

Recent progress in ultrafast technology has led to the generation of optical pulses as short as 8 fs. The propagation of such short pulses in nonlinear optical media requires new computational techniques in which the standard approximations such as the slowly-varying envelope approximation (SVEA) and rotating-wave approximation (RWA) are not made while using the Maxwell-Bloch equations [1]. Previous calculations, which used the finite-difference time-domain (FDTD) method, found that for a a Kerr-like instantaneous nonlinearity [2] significant differences can occur when the full vector Maxwell equations are used instead of the nonlinear Schrodinger equation. Recently, the FDTD method has been extended to the case of a homogeneously broadened two-level atomic system [3].

Nonlinear Optics•Jan 1, 1996•0 citations

HIGH FREQUENCY BEHAVIOR OF THE MAXWELL–BLOCH MODEL WITH RELAXATION: CONVERGENCE TO THE SCHRÖDINGER-RATE SYSTEM

François Castella, Éric Dumas

We study the Maxwell–Bloch model, which describes the propagation of a laser through a material and the associated interaction between laser and matter (polarization of the atoms through light propagation, photon emission and absorption, etc.). The laser field is described through Maxwell's equations, a classical equation, while matter is represented at a quantum level and satisfies a quantum Liouville equation known as the Bloch model. Coupling between laser and matter is described through a quadratic source term in both equations. The model also takes into account partial relaxation effects, namely the trend of matter to return to its natural thermodynamic equilibrium. The whole system involves 6 + N(N + 1)/2 unknowns, the six-dimensional electromagnetic field plus the N(N + 1)/2 unknowns describing the state of matter, where N is the number of atomic energy levels of the considered material. We consider at once a high frequency and weak coupling situation, in the general case of anisotropic electromagnetic fields that are subject to diffraction. Degenerate energy levels are allowed. The whole system is stiff and involves strong nonlinearities. We show the convergence to a nonstiff, nonlinear, coupled Schrödinger-rate model, involving 3 + N unknowns. The electromagnetic field is eventually described through its envelope, one unknown vector in ℂ3. It satisfies a Schrödinger equation that takes into account propagation and diffraction of light inside the material. Matter on the other hand is described through a N-dimensional vector describing the occupation numbers of each atomic level. It satisfies Einstein's rate equation that describes the jumps of the electrons between the various atomic energy levels, as induced by the interaction with light. The rate of exchange between the atomic levels is proportional to the intensity of the laser field. The whole system is the physically natural nonlinear model. In order to provide an important and explicit example, we completely analyze the specific (two-dimensional) Transverse Magnetic case, for which formulae turn out to be simpler. Technically speaking, our analysis does not enter the usual mathematical framework of geometric optics: it is more singular, and requires an ad hoc Ansatz.

Journal of Hyperbolic Differential Equations•Sep 1, 2012•0 citations

The Interaction Between Light and Matter

Jerome V. Moloney, Alan C. Newell

A detectable nonlinear response between light and matter depends on one of two key ingredients: Either there is a resonance between the light wave and some natural oscillation mode of the material, or the light is sufficiently intense. In this chapter, the authors let the matter variables themselves play active roles and derive coupled nonlinear differential equations for the electric and matter fields. They outline the use of Schrodinger's equation to derive the Bloch equations, which describe the dynamics of the oscillators of matter and help to derive the Maxwell equation for the envelope of an almost monochromatic electromagnetic wave. The authors analyse the case of two distinct co- or counter-propagating waves interacting with a three-level medium where both waves excite separate quantum transitions sharing a common level. They also help to derive an effective two-level atom model that describes two-photon absorption and stimulated Raman scattering.

Nonlinear Optics•May 4, 2018•1 citation

Nonlinear dynamics in a single mode three-level laser without inversion

A. G. Vladimirov, Paul Mandel, Susanne F. Yelin +2 more

We characterize analytically the nature of the lasing solutions of a laser operating without population inversion. We consider models involving three-level media interacting with a strong driving field and a lasing field in the vicinity of the lasing threshold. We assess the influence of different relaxation and pumping schemes on the dynamics of these lasers. We use the atom-field detuning, the cavity detuning, and the linear gain as bifurcation parameters. Depending on their values, the stable lasing solution is shown to be cw or self-pulsing. We show that the optimal lasing operation is achieved if both the driving field frequency and the cavity frequency are out of resonance with the atomic frequencies. Physically, the lasing regimes arise from nonlinearly interacting sidebands induced in the lasing medium by atomic interference.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Feb 1, 1998•9 citations
We report on an ab initio investigation of light-matter interactions in a spherical Mie laser. We derive a three-dimensional vector set of Maxwell-Bloch (MB) equations and solve them by the finite-difference time-domain (FDTD) method. Parallel MB-FDTD simulations are employed to study the nonlinear behavior of these nanosized lasers with a varying geometry and different material parameters. The retrieved electromagnetic resonances are consistent with those expected from Mie theory. The lasing regime is characterized by a rich physical scenario, including mode competition and dynamical frequency pulling effects. Application of these dynamics could favor the realization of nonlinearly controlled highly tunable nanolaser devices.
A technique for the numerical simulation of coherent optical responses of the photon echo type formed in resonance media with strong inhomogeneous broadening under the action of femtosecond laser pulses is developed. This approach is based on solving the Maxwell-Bloch equations using the finite-difference time-domain (FDTD) method without application of a fast rotating field and slowly varying envelope approximations. The method can be used to simulate coherent responses in different resonance media with a complex structure of energy levels. The technique was validated using the example of describing experiments on narrowing a photon echo pulse and femtosecond echo processing.
Recent progress in ultrafast technology has led to the generation of optical pulses as short as 8 fs. The propagation of such short pulses in nonlinear optical media requires new computational techniques in which the standard approximations such as the slowly-varying envelope approximation (SVEA) and rotating-wave approximation (RWA) are not made while using the Maxwell-Bloch equations [1]. Previous calculations, which used the finite-difference time-domain (FDTD) method, found that for a a Kerr-like instantaneous nonlinearity [2] significant differences can occur when the full vector Maxwell equations are used instead of the nonlinear Schrodinger equation. Recently, the FDTD method has been extended to the case of a homogeneously broadened two-level atomic system [3].
We study the Maxwell–Bloch model, which describes the propagation of a laser through a material and the associated interaction between laser and matter (polarization of the atoms through light propagation, photon emission and absorption, etc.). The laser field is described through Maxwell's equations, a classical equation, while matter is represented at a quantum level and satisfies a quantum Liouville equation known as the Bloch model. Coupling between laser and matter is described through a quadratic source term in both equations. The model also takes into account partial relaxation effects, namely the trend of matter to return to its natural thermodynamic equilibrium. The whole system involves 6 + N(N + 1)/2 unknowns, the six-dimensional electromagnetic field plus the N(N + 1)/2 unknowns describing the state of matter, where N is the number of atomic energy levels of the considered material. We consider at once a high frequency and weak coupling situation, in the general case of anisotropic electromagnetic fields that are subject to diffraction. Degenerate energy levels are allowed. The whole system is stiff and involves strong nonlinearities. We show the convergence to a nonstiff, nonlinear, coupled Schrödinger-rate model, involving 3 + N unknowns. The electromagnetic field is eventually described through its envelope, one unknown vector in ℂ3. It satisfies a Schrödinger equation that takes into account propagation and diffraction of light inside the material. Matter on the other hand is described through a N-dimensional vector describing the occupation numbers of each atomic level. It satisfies Einstein's rate equation that describes the jumps of the electrons between the various atomic energy levels, as induced by the interaction with light. The rate of exchange between the atomic levels is proportional to the intensity of the laser field. The whole system is the physically natural nonlinear model. In order to provide an important and explicit example, we completely analyze the specific (two-dimensional) Transverse Magnetic case, for which formulae turn out to be simpler. Technically speaking, our analysis does not enter the usual mathematical framework of geometric optics: it is more singular, and requires an ad hoc Ansatz.
A detectable nonlinear response between light and matter depends on one of two key ingredients: Either there is a resonance between the light wave and some natural oscillation mode of the material, or the light is sufficiently intense. In this chapter, the authors let the matter variables themselves play active roles and derive coupled nonlinear differential equations for the electric and matter fields. They outline the use of Schrodinger's equation to derive the Bloch equations, which describe the dynamics of the oscillators of matter and help to derive the Maxwell equation for the envelope of an almost monochromatic electromagnetic wave. The authors analyse the case of two distinct co- or counter-propagating waves interacting with a three-level medium where both waves excite separate quantum transitions sharing a common level. They also help to derive an effective two-level atom model that describes two-photon absorption and stimulated Raman scattering.
We characterize analytically the nature of the lasing solutions of a laser operating without population inversion. We consider models involving three-level media interacting with a strong driving field and a lasing field in the vicinity of the lasing threshold. We assess the influence of different relaxation and pumping schemes on the dynamics of these lasers. We use the atom-field detuning, the cavity detuning, and the linear gain as bifurcation parameters. Depending on their values, the stable lasing solution is shown to be cw or self-pulsing. We show that the optimal lasing operation is achieved if both the driving field frequency and the cavity frequency are out of resonance with the atomic frequencies. Physically, the lasing regimes arise from nonlinearly interacting sidebands induced in the lasing medium by atomic interference.