Single-Course English 5 ECTS

# Numerical methods in photonics

## Overall Course Objectives

To make the participants familiar with modeling of modern photonics components using the finite-difference method in the time and frequency domains. The participants will also learn to model the propagation of pulses over long distances in optical fibers under the influence of nonlinearity by using the split-step Fourier method. Finally stationary mode-structures will be calculated by solving the equivalent boundary-value problem.

Learning Objectives

• write down the second and forth order finite-difference schemes for numerical solution of Maxwell’s equations
• analyse numerical dispersion and stability criteria of the finite-difference time-domain method in 1D, 2D and 3D
• implement a MATLAB realization of the finite-difference time-domain method in 1D and analyse the propagation of pulses in multilayer dielectric media (reflection and transmission spectra, group velocities and field amplitudes)
• describe the conditions and approximations under which full-vectorial and scalar wave equations in the frequency domain for guided modes in straight waveguides may be derived
• recast the wave equations as a matrix eigenvalue problem using the finite-difference technique, and implement a numerical tool in MATLAB to solve this eigenvalue problem
• utilize mirror symmetries to formulate the waveguide finite-difference problem in a reduced calculation domain
• use the MATLAB code to determine propagation constants and mode profiles in various types of straight waveguides, and ascertain that the results are well-converged in resolution and domain size
• implement a split-step Fourier method in MATLAB for modeling nonlinear pulse propagation and interaction in optical fibres and perform all necessary validations
• find conserved quantities and symmetry properties of the integrable and extended nonlinear Schrödinger equations to use for validity tests of the code
• analyse numerically a range of important nonlinear effects in optical fibers, such as solitons and their interaction, modulational instability,and Raman red-shift

Course Content

Modern photonics research and technology is increasingly reliant on efficient numerical methods for accurate modeling of the optical properties of advanced components such as high-index waveguides, microstructured fibres, microresonators or nanostructured systems such as metamaterials, photonic crystals, etc. There is also an increasing interest in using nonlinear effects for all-optical signal processing so a basic knowledge of numerical modeling tools for both linear and nonlinear optical phenomena is important for anyone doing photonics research and development. This course aims to give its participants a basic understanding of common numerical methods, emphasizing both the underlying mathematics, algorithmic issues encountered in their implementation, and their performance in solving important photonics problems. The following numerical methods are studied during the course: finite-difference time-domain method, finite-difference frequency-domain method and split-step Fourier method.

Recommended prerequisites

10036/31400/10370/34041, Knowledge of Matlab is an advantage.

Teaching Method

Lectures with computer based exercises.

Faculty

Remarks

Other teachers:
Ole Bang, Lyngby Campus, building 343
oban@fotonik.dtu.dk
Phone: 45 25 63 73

See course in the course database.

## Registration

Language English 13 weeks Electro DTU Lyngby Campus 34053 Candidate Week 5 Week 19 Mon 13-17
Price 7.500,00 DKK