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Physical review. B, Condensed matter

Theory of coherent propagation of a light wave in semiconductors. II

Zizhao Gan, Guozhen Yang

Published Dec 15, 1982• 5 citations
Publisher

Abstract

This paper contains the second part of a theory of the coherent propagation of a light wave in semiconductors. After considering the interaction among the electrons, we discuss the matter of the interaction of a semiconductor with light and derive equations of motion for the polarization wave of the excitons which have been excited by the light. We show how our equations can be approximated by linear ones and how the exciton polarization wave can be regarded as a Bose field in the limit of low excitation. In this paper we also discuss in detail the problem of the coherent excitation of discrete exciton levels. We show that the coherently excited discrete exciton is approximately equivalent to a two-level atom which is excited by a light wave; the atom energy-level spacing is a function of the degree of excitation, and the density of equivalent "two-level atoms" is determined by features of the exciton-state wave function.

DOI
10.1103/physrevb.26.6833

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•Jan 1, 1992•0 citations
This paper contains the second part of a theory of the coherent propagation of a light wave in semiconductors. After considering the interaction among the electrons, we discuss the matter of the interaction of a semiconductor with light and derive equations of motion for the polarization wave of the excitons which have been excited by the light. We show how our equations can be approximated by linear ones and how the exciton polarization wave can be regarded as a Bose field in the limit of low excitation. In this paper we also discuss in detail the problem of the coherent excitation of discrete exciton levels. We show that the coherently excited discrete exciton is approximately equivalent to a two-level atom which is excited by a light wave; the atom energy-level spacing is a function of the degree of excitation, and the density of equivalent "two-level atoms" is determined by features of the exciton-state wave function.
This paper is the second part of a theory of the coherent propagation of light wave in semiconductors. After considering the interaction between electrons, the problem of a semiconductor interacting with light is discussed and the equation of exciton polarization wave excited by light wave is obtained. We point out that the equation can be approximated by a set of linear ones and the exciton polarization wave can be regarded as a Bose field only in the limit of low excitation. In this paper, the problem of coherent excitation of discrete exciton level is also discussed specifically. It is shown that the discrete exciton level system excited coherently is approximately equivalent to a two-level atom system excited by light wave in which the difference of energy level is dependent on the degree of excitation and the density of equivalent "two-level atoms" is determined by features of the exciton state wave function.
This paper is the third part of a theory of the coherent propagation of light in semiconductors. Based on the previous papers (Ⅰ) and (Ⅱ), the Maxwell-Bloch equation describing the coherent propagation of light in semiconductors is derived; the equation is then used to discuss a number of possible effects of coherent propagation in both interband transitions and exciton transitions. In particular, the phenomena of self-induced transparency are analysed, and it is shown that the phenomena may occur in the above two transitions.
This paper is the third part of a series dealing with the theory of the coherent propagation of light in semiconductors. Based on the results of our previous papers, the "Maxwell-Bloch equations" describing the coherent propagation of light in semiconductors are derived. These equations are used to discuss a number of possible effects of the coherent propagation on both interband and exciton transitions. In particular, we analyze self-induced transparency and show that this effect can occur for both interband and exciton transitions.
A formal, regorous theory of Frenkel excitons interacting with an external electromagnetic field is doveloped within the framework of a two-level-atom model in which the dipole approximation is employed in describing the atom-field (taken as a c-number) interaction. The model exciton Hamiltonian is shown to be identical in form with the Heisenberg model Hamiltonian for S=1/2 spins with anisotropic long-range exchange interactions. Instead of treating excitons as a non-ideal Bose gas, atomic polarization operators and level population defference are taken up as two fundamental quantities to describe Frenkel excitons. A pair of equations satisfied by these two quantities are derived. It is shown that Frenkel excitons are generally expressed as quantum-mechanical nonlinear polarization waves, the nonlinearity being characterized by the level population. A discussion is given on the interrelationship between such polarization waves and those derivable from the classical Drude-Lorentz model. With the aid of several approximation procedures similar to those employed in nonlinear optics, a set of equations describing nonlinear exciton-photon coupled modes are derived. Brief discussion is given on the eigenfrequencies of nonlinear Frenkel excitons and nonlinear polaritons. The existence of nonlinear exciton-photon coupled modes whose properties are different from those of polariton modes is suggested.
The set of phenomenological model equations which we proposed to determine the scaling behavior of the low-density Rabi oscillations [Phys. Rev. B 48, 17 811 (1993)] is justified from the coherent part of the semiconductor Bloch equations in lowest order in the light-matter coupling. In contrast to similar short-time studies, it is shown that for resonant excitation of an excitonic state the Rabi oscillations can be described by a Ginzburg-Landau type equation which includes only the exciton-exciton interaction of the resonantly excited state but no state-filling terms or contributions from detuned excitonic or continuum resonances. Explicit calculations are performed for the bulk two-band jellium model and for a one-dimensional two-band Hubbard model.
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.