Stephan W Koch

Optical Nonlinearities and Instabilities in Semiconductors

The main mechanisms for the observed large optical nonlinearities in semiconductors are briefly discussed and illustrated for the example of the exciton ionization by plasma screening. These nonlinearities cause various types of optical bistability, either of intrinsic nature or evoked by an additional resonator feedback. Under certain operation conditions also higher instabilities such as oscillations and chaos can be obtained. As an example, the self-pulsing of an induced absorber in a ring cavity is treated. The resulting locked oscillations are shown to follow a Farey-tree scenarium.

Subband-level renormalization and absorptive optical bistability in semiconductor multiple quantum well structures☆

Abstract A microscopic theory of many-body effects in the lowest subbands of semiconductor multiple quantum well structures is presented. The renormalized subband levels are calculated for a broad temperature range and optical bistability due to induced absorption is predicted.

Nonequilibrium properties of electron-hole plasma in direct-gap semiconductors

The gain spectra of the electron-hole plasma recombination in CdS are investigated as a function of the excitation conditions and of the lattice temperature. From a lineshape analysis which includes such many-body effects as collision broadening, single-particle energy renormalization and excitonic enhancement, average plasma parameters are obtained. In contrast to the predictions of quasi-equilibrium theory, one finds that the electron-hole plasma does not reach a full thermal quasi-equilibrium in direct-gap materials because of the short lifetimes of the carriers. The nonequilibrium effects are shown to lead to the formation of electron-hole plasma density fluctuations. No well-defined coexistence region exists. The experimental results in the phase transition region can consistently be explained by theoretical treatments of this nonequilibrium phase transition.

Spatial and temporal phase coexistence in optical bistability

Optical bistability is a first-order nonequilibrium phase transition, which is characterized by the spatial or temporal coexistence of two phases. In systems with resonators this phase coexistence can be realized in the form of transverse patterns of high and low intensity values, whereas in a resonatorless optical bistability the phase coexistence becomes manifest in a longitudinal intensity variation. In systems in which strong diffusion of the elementary excitations suppresses spatial phase coexistence, random fluctuations establish at least in principal a temporal phase coexistence by stochastic switching between the two bistable states.

Optical bistability due to a two-photon absorption resonance with fluctuations

Using the intensity-dependent complex dielectric function for a two-photon absorption resonance we derive the Langevin equation for the fluctuating light-field in the non-linear resonator. The corresponding Fokker-Planck equation is solved by expanding the distribution function in terms of products of trigonometric functions and generalized Laguerre polynomials. The expansion coefficients are calculated using the method of matrix continued fractions. Numerical results for the stationary case are given.

Calculation of the intensity-dependent changes of the index of refraction in GaAS

Abstract In order to explain the recently observed optical bistability in GaAs we calculate the intensity-dependent changes of the index of refraction on the basis of the previously developed many-body theory of the gain and absorption spectra of highly excited direct-gap semiconductors.

On the electron-hole plasma phase transition in direct and indirect gap semiconductors☆

Abstract We show that the electron-hole droplet nucleation can be a first- or second-order nonequilibrium phase transition, depending on the lifetime of the electronic excitations. The phase transition is known to be of first order for Ge, but for GaAs and CdS it is shown to be of second order.

Deterministic chaos and noise in optical bistability

The time-dependent solutions of the mean-field Maxwell-Bloch equations for optical bistability are studied numerically for the deterministic equations and the stochastic equations with additional noise sources. From the solutions of the deterministic equations, a discrete map is constructed showing that the periodic and chaotic solutions form a Feigenbaum scenarium. Inclusion of noise sources leads to a finite lifetime of the states in the upper bistable branch and to destabilization of higher periodic solutions.

Electron-hole droplet condensation - A phase transition in an open system

Abstract We derive from hydrodynamical equations a generalized Ginzburg-Landau potential for the amplitude of the u stable mode, which describes a first order phase transition in the electron-hole plasma.