arXiv subjects

Christian Jirauschek

Publications and source records attributed to Christian Jirauschek.

34 records · Page 2Linked to original sources

arXiv2019

Analyzing the Positivity Preservation of Numerical Methods for the Liouville-von Neumann Equation

The density matrix is a widely used tool in quantum mechanics. In order to determine its evolution with respect to time, the Liouville-von Neumann equation must be solved. However, analytic solutions of this differential equation exist only for simple cases. Additionally, if the equation is coupled to Maxwell's equations to model light-matter interaction, the resulting equation set -- the Maxwell-Bloch or Maxwell-Liouville-von Neumann (MLN) equations -- becomes nonlinear. In these advanced cases, numerical methods are required. Since the density matrix has certain mathematical properties, the numerical methods applied should be designed to preserve those properties. We establish the criterion that only methods that have a completely positive trace preserving (CPTP) update map can be used in long-term simulations. Subsequently, we assess the three most widely used methods -- the matrix exponential (ME) method, the Runge-Kutta (RK) method, and the predictor-corrector (PC) approach -- whether they provide this feature, and demonstrate that only the update step of the matrix exponential method is a CPTP map.

quant-ph↗

arXiv2018

Efficient simulation of the swept-waveform polarization dynamics in fiber spools and Fourier domain mode-locked (FDML) lasers

We present a theoretical model and its efficient numerical implementation for the simulation of wavelength-swept waveform propagation in fiber systems such as Fourier domain mode-locked (FDML) lasers, fully accounting for the polarization dynamics in fiber spools and further polarization dependent optical components in the setup. This approach enables us to perform long-time simulations of the FDML laser dynamics over more than 100000 cavity roundtrips, as required for some FDML configurations to ensure convergence to the steady state operating regime. The model is validated against experimental results for single propagation through a fiber spool and for stationary FDML operation. The polarization dynamics due to the fiber spool, inducing polarization-mode dispersion, bending birefringence as well as cross-phase modulation, and other optical components such as the Faraday-rotating mirror used for polarization compensation is thoroughly investigated.

physics.optics↗

arXiv2017

Density matrix Monte Carlo modeling of quantum cascade lasers

By including elements of the density matrix formalism, the semiclassical ensemble Monte Carlo method for carrier transport is extended to incorporate incoherent tunneling, known to play an important role in quantum cascade lasers (QCLs). In particular, this effect dominates electron transport across thick injection barriers, which are frequently used in terahertz QCL designs. A self-consistent model for quantum mechanical dephasing is implemented, eliminating the need for empirical simulation parameters. Our modeling approach is validated against available experimental data for different types of terahertz QCL designs.

cond-mat.mes-hall↗

arXiv2017

Numerical Method for the Maxwell-Liouville-von Neumann Equations using Efficient Matrix Exponential Computations

We present a novel method to solve the Maxwell-Liouville-von Neumann (MLN) equations in an accurate and efficient way without invoking the rotating wave approximation (RWA). The method is a combination of two established concepts, namely the operator splitting method as well as the adjoint representation of the Lie algebra SU(N) (or pseudospin representation). The former concept ensures the accuracy of the approach, but is computationally expensive. The latter concept provides an efficient representation of the problem and two optimization possibilities. We have implemented and verified both optimization approaches and demonstrate that substantial speedup can be achieved.

physics.comp-ph↗

arXiv2014

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 Schrödinger equation and Schrödinger-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.

cond-mat.mes-hall↗

arXiv2011

Photon-induced carrier transport in high efficiency midinfrared quantum cascade lasers

A midinfrared quantum cascade laser with high wall-plug efficiency is analyzed by means of an ensemble Monte Carlo method. Both the carrier transport and the cavity field dynamics are included in the simulation, offering a self-consistent approach for analyzing and optimizing the laser operation. It is shown that at low temperatures, photon emission and absorption can govern the carrier transport in such devices. Furthermore, we find that photon-induced scattering can strongly affect the kinetic electron distributions within the subbands. Our results are validated against available experimental data.

cond-mat.mes-hall↗

arXiv2011

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.

quant-ph↗

arXiv2011

Carrier-envelope phase sensitive inversion in two-level systems

We theoretically study the carrier-envelope phase dependent inversion generated in a two-level system by excitation with a few-cycle pulse. Based on the invariance of the inversion under time reversal of the exciting field, parameters are introduced to characterize the phase sensitivity of the induced inversion. Linear and nonlinear phase effects are numerically studied for rectangular and sinc-shaped pulses. Furthermore, analytical results are obtained in the limits of weak fields as well as strong dephasing, and by nearly degenerate perturbation theory for sinusoidal excitation. The results show that the phase sensitive inversion in the ideal two-level system is a promising route for constructing carrier-envelope phase detectors.

physics.atom-ph↗

arXiv2011

Temperature performance analysis of terahertz quantum cascade lasers: Vertical versus diagonal designs

Resonant phonon depopulation terahertz quantum cascade lasers based on vertical and diagonal lasing transitions are systematically compared using a well established ensemble Monte Carlo approach. The analysis shows that for operating temperatures below 200 K, diagonal designs may offer superior temperature performance at lasing frequencies of about 3.5 THz and above; however, vertical structures are more advantageous for good temperature performance at lower frequencies.

cond-mat.mes-hall↗

arXiv2011

Accuracy of transfer matrix approaches for solving the effective mass Schrödinger equation

The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schrödinger 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 Schrödinger-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.

cond-mat.mes-hall↗

arXiv2011

Monte-Carlo-based spectral gain analysis for THz quantum cascade lasers

Employing an ensemble Monte Carlo transport simulation, we self-consistently analyze the spectral gain for different THz quantum cascade laser structures, considering bound-to-continuum as well as resonant phonon depopulation designs. In this context, we investigate temperature dependent gain broadening, affecting the temperature performance of THz structures. Furthermore, we discuss the influence of the individual scattering mechanisms, such as electron-electron, impurity and interface roughness scattering. A comparison of the simulation results to experimental data yields good agreement.

cond-mat.mes-hall↗

arXiv2011

Modeling bound-to-continuum terahertz quantum cascade lasers: The role of Coulomb interactions

Based on an ensemble Monte Carlo analysis, we show that Coulomb interactions play a dominant role in bound-to-continuum terahertz quantum cascade lasers and thus require careful modeling. Coulomb interactions enter our simulation in the form of space charge effects as well as Coulomb scattering events. By comparison to a full many-subband Coulomb screening model, we show that simplified approaches produce considerable deviations for such structures. Also the spin dependence of electron-electron scattering has to be adequately considered. Moreover, we demonstrate that iterative Schrödinger-Poisson and carrier transport simulations are necessary to correctly account for space charge effects.

cond-mat.mes-hall↗

arXiv2011

Monte Carlo study of carrier-light coupling in terahertz quantum cascade lasers

We present a method for self-consistently including the optical cavity field into Monte Carlo-based carrier transport simulations. This approach allows for an analysis of the actual lasing operation in quantum cascade lasers, considering effects such as gain saturation and longitudinal mode competition. Simulation results for a terahertz quantum cascade laser are found to be consistent with experiment.

cond-mat.mes-hall↗

arXiv2011

Semianalytic theory of self-similar optical propagation and mode locking using a shape-adaptive model pulse

A semianalytic theory for the pulse dynamics in similariton amplifiers and lasers is presented, based on a model pulse with adaptive shape. By changing a single parameter, this test function can be continuously tweaked between a pure Gaussian and a pure parabolic profile and can even represent sech-like pulses, the shape of a soliton. This approach allows us to describe the pulse evolution in the self-similar and other regimes of optical propagation. Employing the method of moments, the evolution equations for the characteristic pulse parameters are derived from the governing nonlinear Schrödinger or Ginzburg-Landau equation. Due to its greatly reduced complexity, this description allows for extensive parameter optimization, and can aid intuitive understanding of the dynamics. As an application of this approach, we model a soliton-similariton laser and validate the results against numerical simulations. This constitutes a semianalytic model of the soliton-similariton laser. Due to the versatility of the model pulse, it can also prove useful in other application areas.

physics.optics↗

arXiv2011

Comparative analysis of resonant phonon THz quantum cascade lasers

We present a comparative analysis of a set of GaAs-based THz quantum cascade lasers, based on longitudinal-optical phonon scattering depopulation, by using an ensemble Monte Carlo simulation, including both carrier-carrier and carrier-phonon scattering. The simulation shows that the parasitic injection into the states below the upper laser level limits the injection efficiency and thus the device performance at the lasing threshold. Additional detrimental effects playing an important role are identified. The simulation results are in reasonable agreement with the experimental findings.

cond-mat.mes-hall↗

arXiv2011

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.

physics.optics↗