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International Conference on Laser and Fiber-Optical Networks Modeling

Nonlinear optical effects in spontaneous and stimulated emission from excited two-band intrinsic semiconductor

Vladislav Cheltsov

Published Dec 22, 2005• 1 citation
Publisher

Abstract

The basic results of theoretical nonperturbative analysis of spontaneous and stimulated emission from two-band excited intrinsic semiconductor interacting with a single mode of radiation field in a lossless micro-cavity are presented. The self-consistent dynamics of the coupled system ''semiconductor + single mode radiation field", accompanied with spontaneous and stimulated emission was investigated as dependent of the initial level of the excitation of semiconductor in the presence initially of the physical field vacuum. Calculations have been carried out with the help of the commutation version of the evolution method without introducing explicitly the phonon mechanisms. The initial non-equilibrium electron and hole populations in the bands have been supposed to be created by ultra-short laser pulses and described by the Fermi-Dirac quasi-equilibrium distributions with the given chemical potentials. The interaction between the electron-hole subsystem and the mode field has been adopted to be switched on suddenly. The calculations have shown that depending on the initial excitation level of electron-hole subsystem three states of the mode field are realized: the equilibrium Bose-Einstein photon distribution with nonzero chemical potential; the quasi-equilibrium distribution with the average number of photons equal to unit and accompanied with their fluctuations, and finally, the state of photon avalanche. The first regime takes the place when the coefficient of the light amplification is negative. Then, the equilibrium between the electron-hole subsystem and arising photons exists until the average number reaches the unit. For negative and =1 the equilibrium still exists but is accompanied with field fluctuations. Finally, when the steady growth arises the lower but stable values are established

DOI
10.1109/lfnm.2005.1553210

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The basic results of theoretical nonperturbative analysis of spontaneous and stimulated emission from two-band excited intrinsic semiconductor interacting with a single mode of radiation field in a lossless micro-cavity are presented. The self-consistent dynamics of the coupled system ''semiconductor + single mode radiation field", accompanied with spontaneous and stimulated emission was investigated as dependent of the initial level of the excitation of semiconductor in the presence initially of the physical field vacuum. Calculations have been carried out with the help of the commutation version of the evolution method without introducing explicitly the phonon mechanisms. The initial non-equilibrium electron and hole populations in the bands have been supposed to be created by ultra-short laser pulses and described by the Fermi-Dirac quasi-equilibrium distributions with the given chemical potentials. The interaction between the electron-hole subsystem and the mode field has been adopted to be switched on suddenly. The calculations have shown that depending on the initial excitation level of electron-hole subsystem three states of the mode field are realized: the equilibrium Bose-Einstein photon distribution with nonzero chemical potential; the quasi-equilibrium distribution with the average number of photons equal to unit and accompanied with their fluctuations, and finally, the state of photon avalanche. The first regime takes the place when the coefficient of the light amplification is negative. Then, the equilibrium between the electron-hole subsystem and arising photons exists until the average number reaches the unit. For negative and =1 the equilibrium still exists but is accompanied with field fluctuations. Finally, when the steady growth arises the lower but stable values are established
The behavior of a single mode of radiation field coupled to an excited two band intrinsic semiconductor has been investigated with the help of the commutator version of evolution operator method. As dependent on the excitation level three states of the field has been shown to exist: the equilibrium with the number of photons determined by the Bose–Einstein distribution with nonzero chemical potential; the quasi-equilibrium with the average number of photons equal to unity and accompanied by fluctuations; the state of photon avalanche.
The nonperturbative theory of the cooperative spontaneous emission from a two level atom trapped in one-dimentional damped nanocavity with a single resonance mode is presented. The time-dependent spectral properties and nonlinear dynamics of a separate photon emission by the micro-molecular-like system "excited atom coupled to a resonance decaying mode" have been analyzed. The investigation has been carried out by solving the Schrödinger equation in the interaction picture with the help of the Green functions method in the Heitler-Ma's form. The formalism was supplemented with the novel algorithm in operating causal singular functions and with fundamentals of the theory of quasi-stationary systems. The proposed theory accounts automatically of both reabsorptions of emitted photon and its simultaneous escaping out of the cavity. Solutions of the wave equation were found without using intermediate virtual states and series expansions. In accordance with the theory of quasi-stationary systems the field of mode decaying exponentially in the empty nanocavity was represented with the Lorenz-shaped packet of stationary photonic states (quasi-modes). The electro-dipolar interaction between the atom and the mode field was adopted to be switched on suddenly. The expressions and plots of emission probabilities spectral densities together with photon emission probability dynamics as functions of time for various ratios Γ/4g of photon escaping rate Γ and coupling constant g are presented. For Γ/4g <1 the transient emission spectrum reveals the presence of two symmetrical side-bands and of the central peak, the latter decaying in time at the rate ∝ Γ/2 so that the final spectrum is a doublet. In this case the photon emission probability is described by decaying oscillations. On the contrary for Γ/4g ≥ 1 the spectrum is a singlet and the emission occurs in exponentially decaying ways.
Spontaneous emission from a two-level atom embedded in photonic crystals was investigated in this paper. Due to the photon localization and the quantum interference between the two dressed states, some changes in the radiation field take place: when the excited level moves from the gap to the band, the energy of the localized field is transferred to the propagating field through the diffusion field. If the localized field and the propagating field could coexist, the population evolution in the excited level would exhibit quasi-oscillation behavior. If they could not coexist, there would be no quasi-oscillation. The steady-state trapped atom population in the excited level is changed also. All these characteristics depend not only on the relative position δ of the excited level ω _1 with respect to the band-edge ω _c but also on the photon density of states ρ(ω_k) (or the band-edge smoothing parameter e ) near the band edge.
Spontaneous emission competes with stimulated emission in many interactions of light with matter. In the usual analyses which describe the interaction of an atom with a coherent optical field, the spontaneous emission characteristics, e.g., probability and spectral distribution, are not determined. The spontaneous emission from an atom which interacts with a coherent light wave is considered. The competition between coherent photons and spontaneous photons is treated in detail for a system consisting of a stationary atom, an open cavity and spatial fields. In the model chosen, a multilevel atom which spontaneously decays by interacting with spatial fields has two nondegenerate states coupled by an interaction with a single mode of the cavity. The Laplace-transformed Schrodinger equation is solved for specified initial conditions of the system. It is found that the interaction with the coherent field modifies the spectral distribution of spontaneous radiation from the atom. For spontaneous transitions involving an atomic state which interacts with the coherent field, the spectral distributions can no longer be described by Lorentzian functions. The new distributions exhibit a broadening and splitting for strong interactions between the atom and the coherent field. It is shown that the qualitative features of these distributions can be predicted from the energy-level diagram of the atom-cavity system. The net probability of the system gaining a coherent or cavity photon is calculated by integrating over the emitted spontaneous frequencies. The equivalence of this approach to the method of computing probabilities by integrating over time is demonstrated by using Parseval's theorem.
We theoretically study quantum-optical properties of one- and two-dimensional semiconductor nanostructures, where the electronic band structure is described by a two-band tight-binding model. Since the focus of our work is on analyzing quantum-optical effects of systems with a continuous band structure, many-body processes like electron-electron and electron-phonon interactions are neglected. The quantum-optical interband excitations are fully incorporated and described by a Jaynes-Cummings-type model. The exciting quantum light can be a state with arbitrary photon statistics. For simplicity, the results discussed here are limited to single-photon and two-photon Fock states. Our analytical approach is based on the eigenvalue problem and can be utilized to obtain explicit expressions for the steady-state properties of the system. Numerical simulations are based on solutions of the equations of motion and allow for a more precise analysis of the dynamics and nonresonant excitations of the system. We demonstrate that during the interaction process, a collective excitation of the conduction band is formed. For nonresonant excitations, this collective dynamics results in interesting steady states, in which the resonantly addressed eigenstates are occupied. The presented model provides a framework for microscopic simulations of quantum-optically excited extended semiconductor nanostructures.
Summary form only given. Optical interactions in semiconductor microcavities embedded with quantum wells enter a nonperturbative regime when the dipole coupling rate between the exciton and the cavity mode exceeds relevant decay rates. In this regime, coherent energy exchange between the exciton and the cavity mode, i.e. normal mode oscillation (NMO), takes place when the cavity mode is excited impulsively by a short laser pulse. Similar coherent oscillations have also been observed in transient four-wave mixing (FWM) responses. In this paper, we present experimental and theoretical studies on the nature of oscillations in these transient FWM responses. We show that, in contrast to earlier beliefs, oscillations in time-integrated transient FWM do not correspond to NMO of the exciton or photon populations. Theoretical studies further reveal that FWM arising from different physical mechanisms including band filling, excitation-induced dephasing, and renormalized electric fields is characterized by highly distinct coherent dynamics. Oscillations in transient FWM reflect interference between these coherent optical processes and can be used as a unique probe for exciton many-body interactions in the nonperturbative regime.