This book brings together the recent cutting-edge work on computational methods in photonics and their applications. The latest advances in techniques such as the Discontinuous Galerkin Time Domain method, Finite Element Time Domain method, Finite Difference Time Domain method as well as their applications are presented. Key aspects such as modelling of non-linear effects (Second Harmonic Generation, lasing in fibers, including gain nonlinearity in metamaterials), the acousto-optic effect, and the hydrodynamic model to explain electron response in nanoplasmonic structures are included. The application areas covered include plasmonics, metamaterials, photonic crystals, dielectric waveguides, fiber lasers. The chapters give a representative survey of the corresponding area.

Inhalt

Titlle: Recent Trends in Computational Photonics

Editors: Arti Agrawal, Trevor Benson, Richard DeLaRue, Gregory Wurtz

Chapter 1:

Guided wave interaction in photonic integrated circuits - a hybrid analytical / numerical approach to coupled mode theory

By: Manfred Hammer, University of Paderborn Outline:

Computational tools are indispensable in the field of photonic integrated circuits, for specific design tasks as well as for more fundamental investigations. Difficulties arise from the usually very limited range of applicability of purely analytical models, and from the frequently prohibitive effort required for rigorous numerical simulations.Hence we pursue an intermediate strategy. Typically, an optical integrated circuit consists of combinations of elements (waveguide channels, cavities) the simulation and design of which is reasonably well established, usually through more or less mature numerical solvers. What remains is to predict quantitatively the interaction of the waves (modes) supported by these elements. We address this task by a quite general, "Hybrid" variant (HCMT) of a technique known as Coupled Mode Theory. Using methods from the realm of finite-element numerics, the optical properties of a circuit are approximated by superpositions of eigen-solutions for its constituents, leading to good quantitative, reasonably low-dimensional, and easily interpretable models. This chapter describes the theoretical background, explains its limitations, hints at implementational details, and discusses a series of 2-D and 3-D examples that illustrate the versatility of the technique.

Keywords: Photonics, guided wave (integrated) optics, coupled mode theory,

numerical modeling.

Content:

1. Introduction motivation, background

2. Hybrid analytical / numerical coupled mode theory

   setting: frequency domain, 3D / 2D ...

   2.1 Coupled mode field template specifically for an example, general

   2.2 Amplitude discretization specifically for an example, general

   2.3 Projection & algebraic procedure

   2.4 Remarks on theory and implementation avoiding heuristics, relation to numerics, scaling properties, types of basis fields, boundary conditions, spectral scans, material dispersion

   2.5 Eigenfrequencies of composite systems "supermodes"; perturbational analysis

   2.6 Variational approach: restriction of a functional

   3. Examples, 2D 3.1 Basis elements

   modes of straight channels, bend modes, eigenmodes of cavities, WGMs

   3.2 Straight parallel waveguides

   3.2 Waveguide crossing

   3.3 Waveguide Bragg reflector

   3.4 Chains of coupled square cavities

   3.5 Resonators with Ring and disc cavities, bend- and WGM templates

   3.6 Coupled resonator optical waveguide

   4. 3D HCMT

   implementation, first results, outlook

   4.1 ...

   4.2 ...

   5. Concluding remarks brief summary of results, additional comments

   Chapter 2:

   Finite Element Time Domain Method for Photonics

   By: B M A Rahman, R Kabir, A Agrawal, City University London

   Outline:

In this chapter we will discuss the development of a finite element based time domain approach, the use of perforated mesh to increase numerical efficiency and evaluation of numerical dispersions for both 2-D and 3-D photonic devices. Comparison of speed enhancement over the finite difference time domain method will be shown particularly comparing their numerical dispersions. Finally several examples are shown, including waveguide corners, Bragg gratings, and simulation of metamaterials.

Content:

1.1 Introduction 1.2 Time domain approaches

1.3 Finite-Element Time-Domain Method

1.4 Results1.4.1 Mesh representation

1.4.2 Numerical Dispersion in 2-D photonics structures 1.4.3 Numerical Dispersion in 3-D photonic structures

1.4.4 Numerical advantage over FDTD method

1.4.5 Numerical Results

1.5 Conclusions 1.6 References

Chapter 3:

Simulation of Second Harmonic generation of photonic nanostructures using the Discontinuous Galerkin Time Domain method

By: Jens Forstner, University of Paderborn

Outline:

Nonlinear optical properties of photonic nanostructures are of great scientific and technological interest. The problem of numerical simulation of the nonlinear response from such structures is multi-scale that makes it hard for existing numerical methods. Indeed, these are subwavelength metallic objects with sizes ranging from tens to hundreds of nanometers and the mechanisms responsible for the second harmonic generation apparently act on scales of the order of 1 nm. The Discontinuous Galerkin Time Domain (DGTD) method appears to be a good choice here. It is based on the unstructured meshing that simplifies the problem through the local mesh refinement. Second, its nonlinear stability property allows numerical solution of nonlinear PDEs and, correspondingly, construction of a model that describes nonlinear processes in a metal with Maxwell-Vlasov hydrodynamic equation.

Content:

1. Introduction and review of the developments of the DGTD method and its applications in plasmonics

2. Parallel implementation of the DGTD method

3. Incorporation of a nonlinear Maxwell-Vlasov hydrodynamic model

4. Simulation of the second harmonic generation in selected plasmonic nanostructures

   Chapter 4:

   The Modelling of Fibre Lasers for Mid-Infrared Wavelengths

   By: L. Sojka, A. B. Seddon, S. Sujecki, T. M. Benson, University of Nottingham

   Outline:

   Mid-infrared light sources are one of the most intensively developing subjects in the photonic area in recent years. The reason for this is that they can find many applications, for example in remote sensing, medicine, and security and military applications including the sensing of toxic gases, the detection of explosives and infrared counter-measurements.

   Over the past decades silica fibre has revolutionised optical technology. Using a silica-based erbium doped fibre amplifier (EDFA) the signal in an optical network can be amplified and transmitted over several hundreds of kilometres directly in the optical domain. However, the working wavelength bands of commercially available rare earth (RE) doped fibre lasers are from 0.5-3 µm, with a significant spectral gap beyond 3.5 µm. The reason for this gap is the high multi-phonon energy of commercially available glasses (silica, ZBLAN). In order to construct a mid-infrared fibre laser a proper host material, with low multi-phonon energy, has to be manufactured. An ongoing research aim of the authors is to investigate and develop novel materials for near-infrared and mid-infrared fibre lasers based on chalcogenide glasses. Chalcogenide glasses offer significant advantages in the mid-infrared wavelength region. These advantages include the lowest phonon energy, from 400 cm-1 up to 230 cm-1 depending on the glass composition. Consequently, chalcogenide glasses present low non-radiative decay rates and wide infrared transparency. These glasses also have a high refractive index which results in higher absorption and emission cross-sections in the RE doped glasses.

   This chapter describes numerical investigations of some of the possibilit…