Maxwell-Bloch Model Research Articles

Chirped excitation of optically dense inhomogeneously broadened media using Eu^3+:Y_2SiO_5

We describe experimentally accessible diagnostics for the excitation of optically dense frequency-selective media by linear frequency-chirped pulses using a sensitive pump–probe technique on the 7F0 to 5D0 transitions of 1.0% Eu3+:Y2SiO5. Distinct features within a transmitted cw probe pulse are used to identify the combination of linear chirp rate and optical power needed to produce an average Bloch-vector rotation of 90°. The resulting superposition state is thus an equal mixture of the ground and excited states on average. We find experimentally a linear relationship between the applied chirp-pulse intensity and chirp rate required to produce this half-inversion, a conclusion supported by both analytical calculations made using a Landau–Zener approach, and detailed computer simulations using the Maxwell–Bloch model. The numerical simulations predict experimentally observed phenomena such as the reshaping of probe pulses by stimulated emission or absorption. Finally, we quantify the relationship between chirp rate and optical power for half-inversion as a function of the optical density of the medium. The pump–probe experimental techniques and simulation analysis techniques developed here can be extended to produce an arbitrary mixture of ground and excited states, on average, in media spanning a wide range of optical density. Preparation of such media by chirped pulses for applications in quantum computing, photon-echo-based time-domain storage, and signal processing will be aided by these techniques.

A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP

This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell's equations for the wave field coupled with a version of Bloch's equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material.

Computational modeling of ultrashort powerful laser pulses in a nonlinear crystal

This article presents a scheme for a semi-classical model of electromagnetic wave propagation in a non-centro-symmetric crystal of KDP. The model was throughfully described in [A Maxwell–Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP (submitted)]. It uses Maxwell's equations to describe the wave field and Bloch's equations for the medium at the quantum-mechanical level. We extend the Yee [Computational Electrodynamics: The Finite-difference Time-domain Method, second ed., Artech House, Boston, MA, 2000; IEEE Trans. Antennas Propag. AP-14 (1966) 302] scheme, in the undimensional case, used for isotropic media to treat the case of a KDP crystal, while ensuring an accurate scheme. Finally, several numerical simulations are performed.

High-frequency modulation of segmented-contact semiconductor lasers

Simulations of the high-frequency modulation characteristics of semiconductor lasers with segmented contacts predict a pronounced resonance-like modulation response that is beyond five times the original cut-off modulation frequency. Based on an effective multi-mode Maxwell–Bloch model, the simulations reveal the underlying phenomena. They show that the high-frequency response is a direct consequence of the particular spatio-temporal and multi-mode dynamics induced by the segmented-contact laser geometry.

Dispersive optical bistability in cold atomic vapours

We present an analysis of dispersive optical bistability in a system of cold atoms enclosed in a bidirectional ring cavity. This analysis is carried out using a system of equations which extend the so-called Maxwell–Bloch model to self-consistently include atomic centre-of-mass motion. When the atomic sample is sufficiently cold and dense, the atomic centre-of-mass motion causes the low pump transmission state to become unstable when the pump is blue-shifted with respect to the atomic resonance. This recoil-induced instability results in the exponential growth of the radiation field counterpropagating to the pump and an atomic density grating. The density grating strongly influences the dispersive properties of the atomic sample and causes the pump transmission to jump from the low transmission state to the high transmission state. It is expected that these effects should be observable in a cold ( T<30 μ K), dense ( n∼10 11 cm −3) sample of Rb, enclosed in a high quality ring cavity ( R≈99%).

Net Coherent Optical Gain in Strongly Pumped Semiconductor Microcavities

We study the subpicosecond gain dynamics in a high-finesse semiconductor microcavity containing quantum wells by means of degenerate pump–probe spectroscopy. Tuning the optical excitation in resonance with both the exciton and the cavity modes, at high pump fields the probe pulses are strongly amplified near the energy of the empty-cavity mode. At zero probe delay, integration of the probe spectrum yields a net gain of several percents. The coherent nature of the gain is demonstrated by its oscillatory behavior versus probe delay. A dynamical Maxwell-Bloch model for semiconductors reproduce well the experimental findings and gives insight into the microscopic origin of the coherent gain.

Recoil-induced effects in absorptive optical bistability

We present an analysis of absorptive optical bistability in a system of cold atoms enclosed in a bidirectional ring cavity. This analysis is carried out using a system of equations that extends the so-called Maxwell-Bloch model to self-consistently include atomic center-of-mass motion. The analysis predicts an instability resulting in the simultaneous generation of an atomic density grating and a coherently backscattered radiation field. The formation of the density grating arises from a modulation of the radiation pressure forces exerted on the atoms. A consequence of this instability is that the lower transmission branch of the usual bistability curve, where atomic motion is neglected, can become unstable and the system switches to the upper transmission branch destroying the bistability.

Coherent exciton—photon dynamics in high-quality II–VI semiconductor microcavities

Results are presented of both linear optical transmission and femtosecond four-wave mixing measurements, on a II–VI semiconductor microcavity into which three quantum wells have been inserted. The excitons (Xs) confined in the wells are strongly coupled to the photons, and at resonance the transmission spectra reveal two polariton peaks of less than 2 meV width, and a Rabi splitting of 11.5 meV, demonstrating the high quality of the sample. The nonlinear emission shows strong and well-resolved beats at the Rabi frequency, that occur both for positive and negative time delays. These features are similar to those observed in a good-quality III–V microcavity. On the basis of a semiclassical Maxwell—Bloch model, they are attributed to the strong X-photon coupling causing oscillations in the X population during the coherent transient. The slightly longer decay time of the lower polariton branch observed at resonance is related to the dephasing properties of localised X states.

The incorporation of microscopic material models into the FDTD approach for ultrafast optical pulse simulations

We are developing full-wave vector Maxwell equation solvers for use in studying the physics and engineering of linear and nonlinear integrated photonics systems. Particular emphasis has been given to the interaction of ultrafast optical pulses with nonresonant and resonant optical materials and structures. Results are reviewed that simulate the interaction of ultrafast optical pulses with structures (e.g., gratings of finite length) filled with materials exhibiting resonant loss or gain. In particular, we consider structures loaded with atomic media resonant at or near the frequency of the incident optical radiation. Interest in these problems follows from our desire to design micron-sized linear and nonlinear guided-wave couplers, modulators, and switches. These resonant problems pose interesting FDTD modeling issues because of the many time and length scales involved. To understand the physics underlying the small-distance scale and short-time scale interactions, particularly in the resonance regime of the materials and the associated device structures, a first principles approach is desirable. Thus, the results presented are based upon a quantum mechanical two-level atom model for the materials. The resulting Maxwell-Bloch model requires a careful marriage between microscopic (quantum mechanical) material models of the resonant material systems and the multidimensional, macroscopic Maxwell's equations solver. The FDTD numerical issues are discussed. Examples are given to illustrate the design and control of these resonant large-scale optical structures. An optical triode is designed and characterized with the FDTD Maxwell-Bloch simulator.

Observation in the two-level spatial Maxwell-Bloch model of the anomalously large first peak as seen in experimental Lorenz-like spiral chaos from the 15NH 3 laser

The experimentally observed Lorenz like chaos from the isotopic ammonia 15NH 3 laser is modeled using a set of two-level Maxwell-Bloch laser equations with a radially varying gain profile. The model is sufficient to predict a particular feature of the ammonia laser, namely the anomalously large first peak of each chaotic spiral. The numerical model is shown to compare favorably with the experimental results.

Space-time dynamics of wide-gain-section lasers.

The space-time behavior of a wide-gain-section, single-longitudinal-mode laser is investigated. Analysis of the full Maxwell-Bloch model in one transverse spatial dimension identifies a traveling-wave solution beyond the first laser threshold, for positive detuning from resonance, which appears to be a globally attracting state of the laser. On the negative-detuning side we observe an initial bifurcation to a homogeneous plane-wave state. A second instability threshold can be identified by linearizing about the respective solutions for both positive and negative detuning. We also find that the standard approach to adiabatic elimination, whereby the polarization equation is adiabatically eliminated, can lead to a spurious high-transverse-wave-number instability in the reduced equations. The derivation of an adiabatically reduced set of equations to remove the instability on the positive-detuning side is a nontrivial matter.

Infinite multilevel system coupled to a quantum-field mode

We investigate a multilevel system coupled to a quantum-field mode, neglecting the damping. The model is shown to be exactly solvable in the case of equal couplings and detunings. The eigenvalues and eigensolutions are calculated. We compute the time evolution of the level populations. The behavior is compared with that of the corresponding exactly solvable semiclassical model, in which the quantum mode is replaced with an external classical field, and with that of the Maxwell–Bloch model, in which the ladder and field variables are decorrelated in the lowest nontrivial order. The semiclassical limit of the quantum system is also studied.

Dynamics of a monovelocity beam maser

It is shown that the dynamics of a monovelocity beam maser differs substantially from the dynamics of a maser (laser) described using the Maxwell–Bloch model.

Optical vortices

It is shown that laser cavities with large Fresnel number can exhibit a state which bears some analogy with a superfluid vortex. This optical vortex is studied in the framework of a Maxwell-Bloch model.

Evidence that transverse effects cause an instability in a single-mode CO2 laser.

We show experimental evidence of spontaneous oscillations in a single-transverse and single-longitudinal mode ${\mathrm{CO}}_{2}$ laser under conditions for which the plane-wave Maxwell-Bloch model predicts stable laser operation. These instabilities seem to result from transverse structure in the mode, as a model which accounts for the transverse profile of the field in the cavity predicts behavior in close agreement with our experimental results.