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Springer eBooks

Diagrammatic Methods for Nonlinear Response of a System Dressed by Resonant External Fields

Manoj Kumar, G. S. Agarwal

Published Jan 1, 1989• 0 citations
Publisher
DOI
10.1007/978-1-4613-0847-8_114

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Diagrammatic methods for the calculation of the nonlinear response of a system that is dressed by resonant external fields are developed. The double-sided diagrams used earlier by Prior [IEEE J. Quantum Electron. QE-20, 37 (1984)] for the calculation of nonlinear susceptibilities in the presence of weak fields are generalized. Additional types of double-sided diagrams are given that incorporate explicitly (a) the relaxation-induced population transfers among the dressed levels and (b) the effects of the nonvanishing of the diagonal elements of the dipole operator in the dressed-state basis. The rules for the diagrams are worked out from the analytical structure of the nonlinear response. Applications of the diagrammatic techniques to several intense-field phenomena are discussed.
External fields modify the confinement potential and electronic structure in a multiple quantum well system, affecting the light–matter interaction. Here, we present a theoretical study of the modulation of the nonlinear optical response simultaneously employing an intense non-resonant laser field and an electric field. Considering four occupied subbands, we focus on a GaAs/AlGaAs symmetric multiple quantum well system with five wells and six barriers. By solving the Schrödinger equation through the finite element method under the effective mass approximation, we determine the electronic structure and the nonlinear optical response using the density matrix formalism. The laser field dresses the confinement potential while the electric field breaks the inversion symmetry. The combined effect of both fields modifies the intersubband transition energies and the overlap of the wave functions. The results obtained demonstrate an active tunability of the nonlinear optical response, opening up the possibility of designing optoelectronic devices with tunable optical properties.
A diagrammatic density matrix technique is developed and applied to study nonlinear optical processes involving responses from weak probe fields interacting with a system under strong excitation. These diagrams consist of lowest-order double-Feynman diagrams which represent the density matrix perturbation terms describing the system response to the weak probe fields1,2 combined with dressed propagators which represent the density matrix elements of the system under strong excitation. The dressed propagators are described by a set of linear equations which, in most cases, may be derived in inspection. The methodology is similar to the bare-atom approach.2 The advantages of using this diagrammatic technique are that (1) it allows one to select and express analytically the dominant and appropriate density matrix elements (diagrams and dressed propagators); (2) analytical expressions may be constructed directly from the diagrams and thus lengthy calculations needed to obtain closed-form solutions are greatly reduced; (3) it provides a physical interpretation for the density matrix solutions and nonlinear optical processes; and (4) it may be generalized to more complicated, multilevel systems. We demonstrate the application of this technique to describe gain saturation, Stark splitting, and Raman scattering.