40 research outputs found
Accuracy of transfer matrix approaches for solving the effective mass Schr\"{o}dinger equation
The accuracy of different transfer matrix approaches, widely used to solve
the stationary effective mass Schr\"{o}dinger equation for arbitrary
one-dimensional potentials, is investigated analytically and numerically. Both
the case of a constant and a position dependent effective mass are considered.
Comparisons with a finite difference method are also performed. Based on
analytical model potentials as well as self-consistent Schr\"{o}dinger-Poisson
simulations of a heterostructure device, it is shown that a symmetrized
transfer matrix approach yields a similar accuracy as the Airy function method
at a significantly reduced numerical cost, moreover avoiding the numerical
problems associated with Airy functions
Modeling techniques for quantum cascade lasers
Quantum cascade lasers are unipolar semiconductor lasers covering a wide
range of the infrared and terahertz spectrum. Lasing action is achieved by
using optical intersubband transitions between quantized states in specifically
designed multiple-quantum-well heterostructures. A systematic improvement of
quantum cascade lasers with respect to operating temperature, efficiency and
spectral range requires detailed modeling of the underlying physical processes
in these structures. Moreover, the quantum cascade laser constitutes a
versatile model device for the development and improvement of simulation
techniques in nano- and optoelectronics. This review provides a comprehensive
survey and discussion of the modeling techniques used for the simulation of
quantum cascade lasers. The main focus is on the modeling of carrier transport
in the nanostructured gain medium, while the simulation of the optical cavity
is covered at a more basic level. Specifically, the transfer matrix and finite
difference methods for solving the one-dimensional Schr\"odinger equation and
Schr\"odinger-Poisson system are discussed, providing the quantized states in
the multiple-quantum-well active region. The modeling of the optical cavity is
covered with a focus on basic waveguide resonator structures. Furthermore,
various carrier transport simulation methods are discussed, ranging from basic
empirical approaches to advanced self-consistent techniques. The methods
include empirical rate equation and related Maxwell-Bloch equation approaches,
self-consistent rate equation and ensemble Monte Carlo methods, as well as
quantum transport approaches, in particular the density matrix and
non-equilibrium Green's function (NEGF) formalism. The derived scattering rates
and self-energies are generally valid for n-type devices based on
one-dimensional quantum confinement, such as quantum well structures
Gaussian pulse dynamics in gain media with Kerr nonlinearity
Using the Kantorovitch method in combination with a Gaussian ansatz, we
derive the equations of motion for spatial, temporal and spatiotemporal optical
propagation in a dispersive Kerr medium with a general transverse and spectral
gain profile. By rewriting the variational equations as differential equations
for the temporal and spatial Gaussian q parameters, optical ABCD matrices for
the Kerr effect, a general transverse gain profile and nonparabolic spectral
gain filtering are obtained. Further effects can easily be taken into account
by adding the corresponding ABCD matrices. Applications include the temporal
pulse dynamics in gain fibers and the beam propagation or spatiotemporal pulse
evolution in bulk gain media. As an example, the steady-state spatiotemporal
Gaussian pulse dynamics in a Kerr-lens mode-locked laser resonator is studied
Linear circuit models for on-chip quantum electrodynamics
We present equivalent circuits that model the interaction of microwave
resonators and quantum systems. The circuit models are derived from a general
interaction Hamiltonian. Quantitative agreement between the simulated resonator
transmission frequency, qubit Lamb shift and experimental data will be shown.
We demonstrate that simple circuit models, using only linear passive elements,
can be very useful in understanding systems where a small quantum system is
coupled to a classical microwave apparatus