arXiv subjects

Jakob Rosenkrantz de Lasson

Publications and source records attributed to Jakob Rosenkrantz de Lasson.

9 recordsLinked to original sources

arXiv2018

Benchmarking five numerical simulation techniques for computing resonance wavelengths and quality factors in photonic crystal membrane line defect cavities

We present numerical studies of two photonic crystal membrane microcavities, a short line-defect cavity with relatively low quality ($Q$) factor and a longer cavity with high $Q$. We use five state-of-the-art numerical simulation techniques to compute the cavity $Q$ factor and the resonance wavelength $λ$ for the fundamental cavity mode in both structures. For each method, the relevant computational parameters are systematically varied to estimate the computational uncertainty. We show that some methods are more suitable than others for treating these challenging geometries.

physics.comp-ph↗

arXiv2017

Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates

Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform $k$-space discretization was introduced for rotationally symmetric structures providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A 33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier $k$ space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence enabling more accurate and efficient modeling of open 3D nanophotonic structures.

physics.optics↗

arXiv2017

On the theory of coupled modes in optical cavity-waveguide structures

Light propagation in systems of optical cavities coupled to waveguides can be conveniently described by a general rate equation model known as (temporal) coupled mode theory (CMT). We present an alternative derivation of the CMT for optical cavity-waveguide structures, which explicitly relies on the treatment of the cavity modes as quasinormal modes with properties that are distinctly different from those of the modes in the waveguides. The two families of modes are coupled via the field equivalence principle to provide a physically appealing yet surprisingly accurate description of light propagation in the coupled systems. Practical application of the theory is illustrated using example calculations in one and two dimensions.

physics.optics↗

arXiv2016

Open geometry Fourier modal method: Modeling nanophotonic structures in infinite domains

We present an open geometry Fourier modal method based on a new combination of open boundary conditions and an efficient $k$-space discretization. The open boundary of the computational domain is obtained using basis functions that expand the whole space, and the integrals subsequently appearing due to the continuous nature of the radiation modes are handled using a discretization based on non-uniform sampling of the $k$-space. We apply the method to a variety of photonic structures and demonstrate that our method leads to significantly improved convergence with respect to the number of degrees of freedom, which may pave the way for more accurate and efficient modeling of open nanophotonic structures.

physics.comp-ph↗

arXiv2015

Semi-analytical quasi-normal mode theory for the local density of states in coupled photonic crystal cavity-waveguide structures

We present and validate a semi-analytical quasi-normal mode (QNM) theory for the local density of states (LDOS) in coupled photonic crystal (PhC) cavity-waveguide structures. By means of an expansion of the Green's function on one or a few QNMs, a closed-form expression for the LDOS is obtained, and for two types of two-dimensional PhCs, with one and two cavities side-coupled to an extended waveguide, the theory is validated against numerically exact computations. For the single cavity, a slightly asymmetric spectrum is found, which the QNM theory reproduces, and for two cavities a non-trivial spectrum with a peak and a dip is found, which is reproduced only when including both the two relevant QNMs in the theory. In both cases, we find relative errors below 1% in the bandwidth of interest.

physics.optics↗

arXiv2015

Impact of slow-light enhancement on optical propagation in active semiconductor photonic crystal waveguides

We derive and validate a set of coupled Bloch wave equations for analyzing the reflection and transmission properties of active semiconductor photonic crystal waveguides. In such devices, slow-light propagation can be used to enhance the material gain per unit length, enabling, for example, the realization of short optical amplifiers compatible with photonic integration. The coupled wave analysis is compared to numerical approaches based on the Fourier modal method and a frequency domain finite element technique. The presence of material gain leads to the build-up of a backscattered field, which is interpreted as distributed feedback effects or reflection at passive-active interfaces, depending on the approach taken. For very large material gain values, the band structure of the waveguide is perturbed, and deviations from the simple coupled Bloch wave model are found.

physics.optics↗

arXiv2014

Calculation, normalization and perturbation of quasinormal modes in coupled cavity-waveguide systems

We show how one can use a non-local boundary condition, which is compatible with standard frequency domain methods, for numerical calculation of quasinormal modes in optical cavities coupled to waveguides. In addition, we extend the definition of the quasinormal mode norm by use of the theory of divergent series to provide a framework for modeling of optical phenomena in such coupled cavity-waveguide systems. As an example, we apply the framework to study perturbative changes in the resonance frequency and Q value of a photonic crystal cavity coupled to a defect waveguide.

physics.optics↗

arXiv2014

A roundtrip matrix method for calculating the leaky resonant modes of open nanophotonic structures

We present a numerical method for calculating quasi-normal modes of open nanophotonic structures. The method is based on scattering matrices and a unity eigenvalue of the roundtrip matrix of an internal cavity, and we develop it in detail with electromagnetic fields expanded on Bloch modes of periodic structures. This procedure is simpler to implement numerically and more intuitive than previous scattering matrix methods, and any routine based on scattering matrices can benefit from the method. We demonstrate the calculation of quasi-normal modes for two-dimensional photonic crystals where cavities are side-coupled and in-line-coupled to an infinite W1 waveguide and show that the scattering spectrum of these types of cavities can be reconstructed from the complex quasi-normal mode frequency.

physics.optics↗

arXiv2013

Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states and quasinormal modes

We present a numerical formalism for solving the Lippmann-Schwinger equation for the electric field in three dimensions. The formalism may be applied to scatterers of different shapes and embedded in different background media, and we develop it in detail for the specific case of spherical scatterers in a homogeneous background medium. In addition, we show how several physically important quantities may readily be calculated with the formalism. These quantities include the extinction cross section, the total Green's tensor, the projected local density of states and the Purcell factor as well as the quasinormal modes of leaky resonators with the associated resonance frequencies and quality factors. We demonstrate the calculations for the well-known plasmonic dimer consisting of two silver nanoparticles and thus illustrate the versatility of the formalism for use in modeling of advanced nanophotonic devices.

physics.optics↗