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Journal of Experimental and Theoretical Physics

Photoinduced phase transitions in a system with a transformable electron spectrum

A. L. Semenov

Published Jun 1, 1997• 1 citation
Publisher

Abstract

An electron theory of photoinduced phase transitions and cavityless optical bistability in a light field with a finite optical-spectrum width is constructed. The Liouville equation for the density matrix is used to derive the existence criteria and calculate the main characteristics of the given phenomena. Broadening of the optical spectrum is shown to reduce the possibility of observing critical features (the existence criterion becomes more stringent and the hysteresis-loop area becomes smaller). Finally, results are compared with experimental data for CdS and amorphous GeS 2 .

DOI
10.1134/1.558255

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An electron theory of photoinduced phase transitions and cavityless optical bistability in a light field with a finite optical-spectrum width is constructed. The Liouville equation for the density matrix is used to derive the existence criteria and calculate the main characteristics of the given phenomena. Broadening of the optical spectrum is shown to reduce the possibility of observing critical features (the existence criterion becomes more stringent and the hysteresis-loop area becomes smaller). Finally, results are compared with experimental data for CdS and amorphous GeS 2 .
Abstract Optical bistability (OB) is a phenomenon that describes a light induced phase transition in the non-equilibrium state. It is vital for all-optical computing and communication, serving as the basis for switches, logic gates, transistors, and memory. By enabling two stable light states, OB allows storage and fast switching, making high-speed, energy-efficient data processing possible. In this work we study the phenomenon in a two-band semiconductor in an optical cavity. Starting from a many-body Hamiltonian of optically generated electrons, holes and light-semiconductor interaction and Coulomb electron–electron, hole–hole and electron–hole interactions, we obtain the optical Bloch equations, in the mean field approximation, where relaxation is included phenomenologically. We obtain expressions for particle density, excitonic pair density and output intensity as non-linear functions of input light intensity. All these quantities show bistable behaviour, with two stable phases, and hysteresis in the non-equilibrium state. Equilibrium is ensured by introducing damping terms for the particle density amplitude, excitonic density amplitude, and cavity photon amplitude phenomenologically. The electron–hole pairs increase with light intensity, shows bistable features and then disappears with further increase in the input light intensity. The bistable behaviour becomes pronounced as we pass from low Coulomb interaction strengths to high Coulomb interaction strengths between electrons and holes. For sub-bandgap excitations, the output light versus incident light shows a complex behaviour.
Relaxation cavityless optical bistability is studied when a semiconductor is exposed to light quanta with an energy exceeding the transition energy and the free-electron relaxation time depends on temperature. The numerical analysis of dynamic equations for temperature and free-electron density demonstrates that 11 regimes of light-semiconductor interaction are possible. The regimes are classified in terms of the features of temperature-intensity characteristic curves, namely, by the number and arrangement of instability and quasistability segments and by the presence or absence of bistability. It is found that both the upper and the lower branch of a bistable characteristic curve may be unstable, which results in spontaneous switchings between the respective states. Similarly, if the upper state is unstable and the lower state is stable, a small perturbation of the parameters (free-electron temperature and density) near the former causes the transition to the oscillatory regime. If the upper state is unstable and a small perturbation of the lower (stable) state excites a damped oscillation, spontaneous switchings result if the fluctuating temperature exceeds some critical value for the lower state.
The purpose of this work is to study the behavior of atomic fluctuations and the spectrum of transmitted light by a nonlinear medium with absorption and dispersion. The authors make use of the system-size expansion and apply it to the quantum-mechanical Langevin's equations for the atomic operators and obtain the characteristic curves for bistable behavior, macroscopic atomic expectation values, and the spectrum of the atomic fluctuations. The calculated spectrum of transmitted light exhibits line narrowing near bistable thresholds, discontinuous formation of bands along the high-transmission bistable branch, and hysteresis effects, etc., for detuning $|\ensuremath{\delta}|$ less than a critical value ${\ensuremath{\delta}}_{c}$. For $|\ensuremath{\delta}|>{\ensuremath{\delta}}_{c}$, the discontinuous character of all the physical variables of the system vanishes; the system no longer exhibits bistable behavior. The system, however, still shows cooperative and single-atom behavior separated by a critical value of the intensity of the incident coherent pump at which a critical slowing down of the medium occurs, exhibiting a phase transition.
An exciton-phonon mechanism for producing cavityless optical bistability is suggested. We consider the influence of the oscillating subsystem of a crystal on the absorption process of a laser wave in the region of exciton frequencies. It is shown that exciton-phonon interaction leads to nonlinear dependence of the absorption coefficient on the density of the exciton gas. The increase of absorption with increasing exciton density, however, is possible only in the frequency region on the long-wavelength tail of the exiton band. As a result, the exciton density of the crystal becomes a hysteresis function of external parameters (intensity of the incident wave, temperature, etc.). We calculate the absorption coefficient of excitons and define the frequency and temperature regions where optical bistability may exist. We analyze different relaxation mechanisms of excitons and explain the experimental results of observing optical bistability in different semiconductor crystals.
Within the framework of a simple numerical model, we investigate the optical properties of a laser-excited direct-band-gap semiconductor (CdS) in the case when both free and bound electron-hole pairs are present. At low temperatures the ionization of excitons proceeds via a first-order phase transition, which is closely related to the Mott transition, and we argue that in direct-band-gap semiconductors it is not suppressed by the electron-hole liquid condensation, as it is in indirect-band-gap materials. The existence of the two corresponding ionization phases with different optical properties is shown to result in optical bistability (OB), which is quite similar to the increasing-absorption (resonatorless) OB but has some peculiarities of its own. Our model also predicts another optical manifestation of this ionization phase transition---the possibility of absorption oscillations at resonant excitation of excitons.