**Dr. Manfred Hammer**

Paderborn University

Theoretical Electrical Engineering

Warburger Strasse 100

33098 Paderborn, Germany

Phone: ++49 (0)5251/60-3560

Fax: ++49 (0)5251/60-3524

Building P1, room P1.5.17.1

**Dr. Manfred Hammer**

Universität Paderborn

FG Theoretische Elektrotechnik

Warburger Straße 100

33098 Paderborn

Tel: 05251/60-3560

Fax: 05251/60-3524

Gebäude P1, Raum P1.5.17.1

E-mail: manfred.hammer@uni-paderborn.de

Research topics

Things we have been / are busy with, including a bunch of figures. Keywords: Theoretical photonics, integrated optics, numerical modeling; dielectric waveguide theory, mode solvers, mode expansion modeling, coupled mode theory; interferometric devices, nonreciprocal integrated optical devices; polarizer / isolator / circulator concepts; microresonator simulations, semi-guided waves, ...Publications

References to journal papers, book chapters, and contributions to conference proceedings, a list of talks and poster presentations, and links to online versions of my PhD- and Diploma theses.Teaching

Information about the courses and MSc-, and PhD-projects (finished and upcoming) where I am involved in.Metric

Tools for semianalytic modeling in integrated optics / photonics, simulations of configurations with rectangular refractive index distributions. Includes a mode solver engine for dielectric multilayer slab waveguides, and solvers for scalar and vectorial guided-wave Helmholtz (-scattering) problems based on spectral discretizations along one (BEP: bidirectional eigenmode propagation) or two coordinate axes (QUEP: quadridirectional eigenmode propagation). Extensions concern the angled propagation of plane waves across dielectric multilayer stacks, conventional and hybrid analytical/numerical variants of coupled mode theory, a 2-to-1D effective index treatment of 2D scattering problems, a variational effective-index-like mode solver for 3D channels (with 2D cross sections), the computation of Floquet-Bloch-modes for rectangular periodic structures in 2D, and solvers for the bend modes of curved slab structures, the whispering gallery modes supported by 2-D circular multilayer dielectric cavities, the guided modes of circular multi-step-index optical fibers, and the bound and leaky modes of multilayer structures with complex permittivity, including surface-plasmon-polaritons (SPPs). A series of application examples, embedded in the html manual, complements the downloadable, commented C++ sources.WMM

A quasianalytic mode solver for rectangular dielectric integrated optical waveguide channels (3D configurations with 2D cross sections). Besides the actual procedures for guided mode analysis, the programs provide facilities for the evaluation of perturbational expressions, and an implementation of coupled mode theory. The html manual includes the downloadable, commented C++ sources, accompanied by several application examples.OMS

A mode solver for optical dielectric multilayer slab waveguides with 1D cross sections. For a waveguide defined in terms of refractive indices, layer thicknesses, and a given vacuum wavelength, the script calculates the propagation constants / effective indices of guided modes and allows to inspect the corresponding optical field patterns. Facilities for evaluating simple parameter scans (modal dispersion properties) are provided. The solver is intended as a basic tool for integrated optics design, in particular for purposes of demonstration.EIMS

An approximate, semi-analytic mode solver for dielectric integrated optical waveguides with two-dimensional light confinement and weak lateral guiding. Multilayer step-index waveguides with rectangular, piecewise constant refractive index profiles are addressed. For a waveguide configuration specified in terms of refractive indices, layer thicknesses, slice widths, and the vacuum wavelength, the script calculates the propagation constants / effective indices of guided modes and allows to inspect the corresponding optical field patterns. It is intended as a basic tool for integrated optics design, in particular for purposes of demonstration. Note the remarks on the variant of the effective-index approximation the mode solver relies on.WMMS

Vectorial or semi-vectorial mode analysis of dielectric integrated optical waveguides with two-dimensional light confinement. Multilayer step-index waveguides with rectangular, piecewise constant refractive index profiles are addressed. For a waveguide configuration specified in terms of refractive indices, layer thicknesses, slice widths, and the vacuum wavelength, the online script calculates the propagation constants / effective indices of guided modes and allows to inspect the corresponding optical field patterns. Implementing the wave matching method (WMM), the quasi-analytical solver relies on expansions of the modal fields into locally exact separable solutions of the mode equations, applied piecewise on the rectangular regions that constitute the waveguide cross section.PlasS

An analytic solver for the 1-D eigenmodes of optical multilayer step-index slab waveguides made from media with in general complex refractive index and complex permittivity. Given a potentially guiding configuration defined in terms of refractive index and/or permittivity, layer thicknesses, if applicable, and the vacuum wavelength, the script calculates the complex effective indices of the modes supported by the structure, or their phase propagation and attenuation constants, respectively, and allows to inspect the corresponding optical field patterns. Bound and leaky modes of structures with loss or gain can be identified, as well as the bound solutions related to the propagation of surface-plasmon-polaritons (SPPs) along metal-dielectric interfaces.FiMS

An online solver for the guided modes supported by circular dielectric optical fibers with radially piecewise constant refractive index profiles. For a fiber problem defined in terms of vacuum wavelength, core radius, refractive indices, and thicknesses of intermediate layers, the script calculates the effective mode indices and propagation constants of the vectorial, hybrid guided modes supported by the fiber. TE- and TM-modes can be identified, as well as orbital-angular-momentum (OAM) modes of different angular and radial orders; modes of EH- and HE-type are found as superpositions of the latter. Facilities for detailed inspection of the mode profiles, and for exporting data and figures, are provided.MuLS

A solver for problems of plane wave reflection from dielectric multilayer systems at oblique incidence. Given the stack definition in terms of refractive indices, layer thicknesses, vacuum wavelength, and the angle of incidence, the script calculates reflectance and transmittance properties for s- and p-polarized waves, and allows to inspect the corresponding optical fields. Facilities for evaluating parameter scans / spectra are available. The script can serve as a basic tool for the design of dielectric multilayer coatings / reflectors / filters, in particular for purposes of demonstration.BendS

A mode solver for bent integrated optical multilayer slab waveguides and curved dielectric interfaces with 1-D cross sections. For a bend configuration defined in terms of bend radius, refractive indices, layer thicknesses, if applicable, and the vacuum wavelength, the script calculates the complex effective indices of the leaky modes supported by the bend, or their phase propagation and attenuation constants, respectively, and allows to inspect the corresponding bend mode profiles. Optical field patterns associated with the bend mode propagation can be visualized directly.WGMs

An online solver for the whispering gallery resonances of microdisks, microrings, or more general circular 2-D dielectric multilayer cavities in integrated optics / photonics. Following the structure definition in terms of cavity radius, refractive indices, and layer thicknesses, if applicable, and the specification of a target vacuum wavelength or of an interval of potential resonance wavelengths, the script calculates the complex angular eigenfrequencies of the (leaky) whispering gallery modes supported by the cavity, and their resonance wavelengths and linewidths, resonance frequencies, cavity lifetimes, and quality (Q-) factors, respectively. Facilities for detailed inspection of the corresponding mode profiles and resonant field patterns, and for exporting data and figures, are provided.QuEPS

A frequency domain solver for 2-D rectangular optical guided-wave scattering problems. The scalar polarized 2-D Helmholtz equations are addressed, on a rectangular computational domain with transparent boundary conditions that permit guided wave in- and outflux. Given a problem specification in terms of interface positions, a matrix of refractive index values, polarization and wavelength parameters, and guided wave input, the script determines modal output amplitudes (elements of the scattering matrices), and the power levels associated with guided and nonguided directional outgoing waves (transmittances / reflectances, power balance). Facilities for detailed inspection of the optical electromagnetic field are provided, including animations of the harmonic oscillations in time, with options for exporting figures and data.Epsilon

Linear anisotropic media are considered from a viewpoint of not necessarily crystal-aligned external device coordinates. The script calculates optical axes and effective refractive index eigenvalues associated with a general optical permittivity, and provides controls for arbitrary 3-D rotations of the tensor. Facilities for the rudimentary illustration of the wave propagation through the oriented crystalline medium are available.WaFE

Conversion between quantities that characterize the propagation of harmonic electromagnetic waves in vacuum. This concerns wavelength, wavenumber, spectroscopic wavenumber, frequency, angular frequency, time period, and photon energy, (mostly) in SI units.Fig3

A simple drawing tool for the programmatic generation of 3D figures, on the basis of the Three.js library and standard Javascript code. Emphasis is on schematics and line drawings with partly transparent solids, of modest complexity, and accompanied by annotations and labels, as seen frequently in more technical scientific articles. Images are exported in vector format.Plot-It

An online function and data plotter. Features: graphs of functions of one variable, data curves, parametrized functions, families of functions, cubic spline interpolation, linear regression; export to svg-images, aims at a close-to-scientific appearance of the figures.Teval

A script that can evaluate simple C-style expressions. The script knows about the numerical values of some common physical constants, hence it is in particular useful for a certain class of basic exercises in physics courses ...Bookmarks

Links to online content that I find nice or useful or that I once found nice or useful.