Koustuban Ravi

A Highly Efficient Computational Model for FDTD Simulations of Ultrafast Electromagnetic Interactions With Semiconductor Media With Carrier Heating/Cooling Dynamics

We report a new computational model to incorporate carrier heating/cooling effects for the finite-difference time-domain (FDTD) simulation of electromagnetic interactions with semiconductor media. The model is formulated to be computationally efficient enough to be applied to FDTD simulations of photonic devices of complex structural geometry. The model developed here is built on top of a previous multi-level multi-electron (MLME) model we presented and the new model is called MLME-dynamical temperature (MLMEDT) model. The key developments here include the following. 1) Intraband transition terms with electron and hole temperature parameters that vary with time and space are introduced. 2) Rate equations for the explicit update of carrier temperature are formulated. A computationally efficient method is used to evaluate these carrier temperature rate equations which circumvent iterative procedures as well as the need to dynamically compute the chemical potential by presolving the relational functions required using dimensionless fitting functions. The temporal update of these fitting functions only needs the total carrier number densities, which are already obtained in the MLME model computation. 3) The changes in the total carrier kinetic energy density and carrier number density due to all interband processes such as stimulated emission/absorption and intraband processes such as free carrier absorption are tracked to drive the carrier temperature rate equations. 4) The thermal relaxation of the electron and hole temperatures to the lattice temperature and the thermal relaxation between electrons and holes are also included. In order to validate the approach, simulations of thermalization of nonequilibrium carrier distributions and nonlinear gain and refractive index dynamics in semiconductor optical amplifiers (SOA) are presented. Quantitative agreement with nonlinear gain dynamics experiments of SOA directly verifies the accuracy of the current approach. Additionally, a 2-D simulation of a microdisk laser is presented to depict how FDTD can be used to visualize the spatial profile of carrier temperatures. The computational time of the MLMEDT model is found to be only ~10% more than that of the MLME model, thus showing high computational efficiency.

Analytical Framework for the Steady State Analysis of Wavelength-Dependent and Intensity-Dependent Interaction of Multiple Monochromatic Beams in Semiconductor Photonic Structures With Multiple Active and Passive Sections

The design, optimization, and parametric studies of photonic integrated circuits typically require steady state optical field profiles. Previously, a planewave-based eigenmode expansion and mode-matching analysis was shown to be an efficient method in calculating the steady-state optical field profile of a monochromatic beam in 2-D/3-D geometries with passive media. In this paper, we extend this approach for steady state analyses of photonic integrated circuits with both passive as well as active media, by enabling the interaction of multiple monochromatic beams with the medium via a self-consistent solution of the Maxwells equations and a modified Bloch equations-based analytical framework. Through the Bloch equations-based framework, we treat the active medium as an ensemble of two-level Bloch atoms with varying density of states to characterize the bandstructure of semiconductors. This enables us to track carrier transitions between conduction and valence bands induced by the light-matter interaction over the entire bandwidth of excited carriers, and yield the correct quasi equilibrium Fermi-Dirac distributions. The numerical solution of obtaining the carrier distributions at each spatial location in active media is simplified by reducing the modified Bloch equations with multiple unknowns to a single equation with just one unknown, to enhance the computational efficiency of the approach. The calculated carrier distributions are then used to evaluate the spatial profile of the complex refractive index seen by each monochromatic beam along with its optical field profile. The applicability of the method to 2-D structures of complex geometry is demonstrated by obtaining the spatial profiles of refractive indices seen by two simultaneously interacting monochromatic beams along with their optical field profiles in a waveguide with multiple passive and active sections.

Complex-envelope alternating-direction-implicit FDTD method for simulating active photonic devices with semiconductor/solid-state media

A complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) approach to treat light-matter interaction self-consistently with electromagnetic field evolution for efficient simulations of active photonic devices is presented for the first time (to our best knowledge). The active medium (AM) is modeled using an efficient multilevel system of carrier rate equations to yield the correct carrier distributions, suitable for modeling semiconductor/solid-state media accurately. To include the AM in the CE-ADI-FDTD method, a first-order differential system involving CE fields in the AM is first set up. The system matrix that includes AM parameters is then split into two time-dependent submatrices that are then used in an efficient ADI splitting formula. The proposed CE-ADI-FDTD approach with AM takes 22% of the time as the approach of the corresponding explicit FDTD, as validated by semiconductor microdisk laser simulations.

Efficient FDTD Simulation of Active Photonic Devices With Multiple Temporal Resolutions

A computational method to reduce computational time for finite-difference time-domain simulations of active photonic devices by using different temporal resolutions for the update of Maxwells equations and active-medium (AM) equations are presented. A larger temporal resolution for the update of AM equations is used due to their slower evolution in comparison to the electromagnetic fields. Slow varying envelope approximation in the carrier rate equations are avoided. The method is easy to implement and is validated through numerical examples of semiconductor microdisk lasers. A speed enhancement of between two to threefold can be obtained without loss in accuracy.

A multi-band, multi-level, multi-electron model for efficient FDTD simulations of electromagnetic interactions with semiconductor quantum wells

We report a new computational model for simulations of electromagnetic interactions with semiconductor quantum well(s) (SQW) in complex electromagnetic geometries using the finite-difference time-domain method. The presented model is based on an approach of spanning a large number of electron transverse momentum states in each SQW sub-band (multi-band) with a small number of discrete multi-electron states (multi-level, multi-electron). This enables accurate and efficient two-dimensional (2-D) and three-dimensional (3-D) simulations of nanophotonic devices with SQW active media. The model includes the following features: (1) Optically induced interband transitions between various SQW conduction and heavy-hole or light-hole sub-bands are considered. (2) Novel intra sub-band and inter sub-band transition terms are derived to thermalize the electron and hole occupational distributions to the correct Fermi-Dirac distributions. (3) The terms in (2) result in an explicit update scheme which circumvents numerically cumbersome iterative procedures. This significantly augments computational efficiency. (4) Explicit update terms to account for carrier leakage to unconfined states are derived, which thermalize the bulk and SQW populations to a common quasi-equilibrium Fermi-Dirac distribution. (5) Auger recombination and intervalence band absorption are included. The model is validated by comparisons to analytic band-filling calculations, simulations of SQW optical gain spectra, and photonic crystal lasers.

CE-ADI-FDTD method for active photonic device simulation with semiconductor/solid-state media

This paper presents a complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) method to treat light-matter interaction self-consistently with electromagnetic field evolution for efficient simulations of active photonic devices. The active medium (AM) is modeled using an efficient multi-level system of carrier rate equations. To include AM in the CE-ADI formulation, a 1st-order differential system composed of CE fields in AM is first set up. The system sub-matrices are then determined and used in an efficient ADI splitting formula. From microdisk laser simulations, the proposed method is shown to consume 22% of the explicit FDTD CPU time.

Novel design framework for photonic integrated circuits (PICs) with active and passive sections

Novel design framework for PICs with active-passive sections embeds semiconductor bandstructure in active sections to self-consistently evaluate the spatial profiles of each optical field and permittivity seen by it in presence of multi-fields interaction.

A computationally efficient, non-equilibrium, carrier temperature dependent semiconductor gain model for FDTD simulation of optoelectronic devices

We report a Finite Difference Time Domain (FDTD) model incorporating carrier heating/cooling for the first time. The proposed model thermalizes non equilibrium carrier distributions through carrier temperature dependent intraband transition terms. This multi-level, multi-electron model is formulated to be computationally efficient despite its physical complexity and hence presents potential for the development of powerful general optoelectronic device simulators for devices of arbitrary geometry. Results of carrier distribution thermalization and comparisons to non linear gain experiments are provided to validate the model.

Spatial temporal simulation of active optoelectronic and plasmonic devices using a multi-level multi-electron FDTD model

We introduce a recently developed general computational model for the electromagnetic simulations of complex atomic, molecular, or semiconductor media using the finite difference time domain (FDTD) method based on a multi-level multi-electron (MLME) system. We show how this MLME-FDTD model can be used for spatial-temporal simulation of a wide range of active optoelectronic and plasmonic devices. Realistic simulations ranging from semiconductor lasers, to plasmonic lasers, and semiconductor optical amplifiers are illustrated.