Optoelectronic device simulations based on macroscopic Maxwell-Bloch equations

Abstract

Due to their intuitiveness, flexibility and relative numerical efficiency, the macroscopic Maxwell-Bloch (MB) equations are a widely used semiclassical and semi-phenomenological model to describe optical propagation and coherent light-matter interaction in media consisting of discrete-level quantum systems. This review focuses on the application of this model to advanced optoelectronic devices, such as quantum cascade and quantum dot lasers. The Bloch equations are here treated as a density matrix model for driven quantum systems with two or multiple discrete energy levels, where dissipation is included by Lindblad terms. Furthermore, the one-dimensional MB equations for semiconductor waveguide structures and optical fibers are rigorously derived. Special analytical solutions and suitable numerical methods are presented. Due to the importance of the MB equations in computational electrodynamics, an emphasis is placed on the comparison of different numerical schemes, both with and without the rotating wave approximation. The implementation of additional effects which can become relevant in semiconductor structures, such as spatial hole burning, inhomogeneous broadening and local-field corrections, is discussed. Finally, links to microscopic models and suitable extensions of the Lindblad formalism are briefly addressed.

54 pages, 23 figures

References in corpus (24)

• Environment-Assisted Quantum Transport
• Linear and nonlinear optical spectroscopy of a strongly-coupled microdisk-quantum dot system
• Resonance fluorescence from a coherently driven semiconductor quantum dot in a cavity
• Modeling techniques for quantum cascade lasers
• Non-Markovian generalization of the Lindblad theory of open quantum systems
• Genuine quantum trajectories for non-Markovian processes
• All-Optical Delay of Images using Slow Light
• Staying positive: going beyond Lindblad with perturbative master equations
• Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation
• A phenomenological position and energy resolving Lindblad approach to quantum kinetics
• Self-generation of optical frequency comb in single section Quantum Dot Fabry-Perot lasers: a theoretical study
• Density-matrix theory of the optical dynamics and transport in quantum cascade structures: The role of coherence
• Failure of the α-factor in describing QD laser dynamical instabilities and chaos
• Elimination of the Diffraction of Arbitrary Images Imprinted on Slow Light
• Cavity-coupled double-quantum dot at finite bias: analogy with lasers and beyond
• Derivation of nonlinear single-particle equations via many-body Lindblad superoperators: A density-matrix approach
• Density matrix Monte Carlo modeling of quantum cascade lasers
• Density matrix theory of transport and gain in quantum cascade lasers in a magnetic field
• An extended density matrix model applied to silicon-based terahertz quantum cascade lasers
• Temperature Dependence and Screening Models in Quantum Cascade Structure
• Femtosecond pulses in a dense two-level medium: Spectral transformations, transient processes, and collisional dynamics
• Finite-difference time-domain formulation of stochastic noise in macroscopic atomic systems
• Time-dependent transport in open systems based on quantum master equations
• Non-Markovian Dynamics of Charge Carriers in Quantum Dots