N. B. Abraham

Polarization properties of vertical-cavity surface-emitting lasers

Polarization-state selection, polarization-state dynamics, and polarization switching of a quantum-well vertical-cavity surface-emitting laser (VCSEL) for the lowest order transverse spatial mode of the laser is explored using a recently developed model that incorporates material birefringence, the saturable dispersion characteristic of semiconductor physics, and the sensitivity of the transitions in the material to the vector character of the electric field amplitude. Three features contribute to the observed linearly polarized states of emission: linear birefringence, linear gain or loss anisotropies, and an intermediate relaxation rate for imbalances in the populations of the magnetic sublevels. In the absence of either birefringence or saturable dispersion, the gain or loss anisotropies dictate stability for the linearly polarized mode with higher net gain; hence, switching is only possible if the relative strength of the net gain for the two modes is reversed. When birefringence and saturable dispersion are both present, there are possibilities of bistability, monostability, and dynamical instability, including switching by destabilization of the mode with the higher gain to loss ratio in favor of the weaker mode. We compare our analytical and numerical results with recent experimental results on bistability and switchings caused by changes in the injection current and changes in the intensity of an injected optical signal.

Calculating the dimension of attractors from small data sets

Abstract Calculations of the order-2 information dimension for data sets generated from numerical simulations as well as from an experiment show that it is possible to distinguish between periodic, chaotic and random signals, as well as to characterize different kinds of chaotic behavior using relatively small, noisy data sets.

Overview of transverse effects in nonlinear-optical systems

Beams of light interacting with nonlinear-optical materials naturally form complex transverse profiles. Self-focusing, filamentation, modulational instabilities, spontaneous pattern formation and symmetry breaking, nonlinear waveguiding, and transverse mode excitation are but some of the many phenomena that are observed in lasers, in optical bistability, and in the free interaction of beams. As an introduction to a special issue of the Journal of the Optical Society of America B on transverse effects in nonlinear-optical systems, we provide this overview of history and current work.

Overview of instabilities in laser systems

This paper contains a brief overview of the main types of instability in laser systems. The topics being discussed include the early spiking in solid-state lasers, single-mode lasers with homogeneous and inhomogeneous broadening, the effect of noise and modulation, multimode operation, and a brief survey of nonlinear dynamics.

On chaos in lasers with modulated parameters: A comparative analysis

Abstract Modulation of the laser excitation rate and modulation of the cavity losses are shown to result in the same dynamical phenomena for lasers in which the polarization can be adiabatically eliminated. However, to obtain the same results, the degree of modulation of the excitation must be larger than the degree of modulation of the looses.

Differences in polarization dynamics of the electromagnetic field in xenon and neon lasers

Abstract We have experimentally observed the appearance of oscillations in the state of polarization of a constant-total-intensity, quasi-isotropic, HeXe, single-“geometrical”-mode laser operating at λ = 3.51 μm. Similar oscillations, accompanied by oscillations in the total intensity, have been detected also in a HeNe laser operating at λ = 3.3922 μm under the same experimental conditions. While the oscillations in the HeXe laser are understandable in terms of competition between the field amplitudes of two modes of different polarization, those in the HeNe may involve the atomic dynamics as well.

Experimentally accessible periodic pulsations of a single-mode homogeneously broadened laser (the Lorenz model)

Abstract We discuss the appearance of stable pulsation patterns and hysteresis effects in a single-mode, homogeneously broadened ring laser for values of the pump parameter both near and below the instability threshold. These periodic solutions develop when the ratio of the population decay rates is sufficiently smaller than unity. Their pulsation frequency is calculated analytically with very good accuracy.

Polarization state selection and stability in a laser with a polarization-isotropic resonator ; an example of no lasing despite inversion above threshold

Abstract Different models are considered for the study of dynamical instabilities of lasers with a transversally isotropic resonator operating on a single longitudinal mode coupled to a homogeneously broadened J = 1 → J = 0 material transition. We devise a model of intermediate complexity which retains the dynamics of the atomic variables and which has the experimentally required linearly or circularly polarized steady state solutions with their relative stability near threshold depending on the difference of certain collisionally enhanced relaxation rates. Stability analysis of these steady states in this model provides second thresholds above which the polarization state is time dependent. The stable operation of polarized output states is interpreted in terms of coherence induced absorption or transparency even though the population inversion exceeds the lasing threshold on the transition which drives the orthogonally polarized field. A more general model of the field-atom dynamics than those previously considered is also constructed and analyzed for the stability of its steady states. The fundamental physical condition on the ratio of certain relaxation rates of previous models for stability of circular or linearly polarized solutions is unchanged.

Lasers and Brains: Complex Systems with Low-Dimensional Attractors

The quantification of complex dynamical phenomena associated with motions on strange attractors has made available a tool of considerable power for the analysis of systems which display aperiodic or apparently random temporal behavior. Until recently, aperiodic phenomena were described primarily in terms of snapshots of time sequences, power spectra, or correlation functions. These made possible some qualitative or pictorial analyses but did not provide simple numerical criteria suitable for more quantitative studies. During the past decade, spectral studies have made possible the identification of a few characteristic routes to apparently chaotic behavior in hydrodynamic[l–3], chemical [4], optical [5–7, 16, 29], and electronic [8, 9] systems. There were very strong indications that the complex motions, characterized by broadband spectra, to which these routes led, were in fact motions on strange attractors.

Deterministic mode alternation, giant pulses and chaos in a bidirectional CO2 ring laser

Abstract A CO 2 ring laser with a single longitudinal mode propagating in each direction shows a variety of stable, periodic, and aperiodic phenomena depending on gas pressure, cavity detuning and relative excitation. Three distinct low frequency time scales for dynamical behavior are observed and are explained by numerical solutions of an appropriate model.