# Manfred HammerUniversität Paderborn | UPB · Department of Electrical Engineering and Information Technology

Manfred Hammer

PhD, Theoretical Physics

## About

134

Publications

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Introduction

Additional affiliations

May 2000 - August 2014

## Publications

Publications (134)

The 3D implementation of a hybrid analytical/numerical variant of the coupled-mode theory is discussed. Eigenmodes of the constituting dielectric channels are computed numerically. The frequency-domain coupled-mode models then combine these into fully vectorial approximations for the optical electromagnetic fields of the composite structure. Follow...

We show how to optically connect guiding layers at different elevations in a 3-D integrated pho-tonic circuit. Transfer of optical power carried by planar, semi-guided waves is possible without reflections, without radiation losses, and over large vertical distances. This functionality is realized through simple step-like folds of high-contrast die...

Whispering gallery modes supported by open circular dielectric cavities are embedded into a nonparametric two-dimensional frequency domain hybrid coupled mode theory framework. Regular aggregates of these cavities, including straight access channels, are investigated. The model enables convenient studies of the guided wave scattering process, the r...

Magneto-optical garnets combine high Faraday rotation with low optical losses in the near-infrared region where optical communication through glass fiber is established. In this spectral range, garnets are the only materials discussed to realize nonreciprocal devices as optical isolators and circulators. Although such devices are available as micro...

The propagation of guided and nonconfined optical waves at fixed frequency through dielectric structures with piecewise constant, rectangular permittivity is considered in two spatial dimensions. Bidirectional versions of eigenmodes, computed for sequences of multilayer slab waveguides, constitute the expansion basis for the optical electromagnetic...

Lithium niobate on insulator (LNOI) has a great potential for photonic integrated circuits, providing substantial versatility in design of various integrated components. To properly use these components in the implementation of different quantum protocols, photons with different properties are required. In this paper, we theoretically demonstrate a...

Lithium niobate on insulator (LNOI) has a great potential for photonic integrated circuits, providing substantial versatility in design of various integrated components. To properly use these components in the implementation of different quantum protocols, photons with different properties are required. In this paper, we theoretically demonstrate a...

We demonstrate the integration of amorphous tungsten silicide superconducting nanowire single-photon detectors on titanium in-diffused lithium niobate waveguides. We show proof-of-principle detection of evanescently-coupled photons of 1550nm wavelength using bidirectional waveguide coupling for two orthogonal polarization directions. We investigate...

A stepwise angular spectrum method (SASM) for curved interfaces is presented to calculate the wave propagation in planar lens-like integrated optical structures based on photonic slab waveguides. The method is derived and illustrated for an effective 2D setup first and then for 3D slab waveguide lenses. We employ slab waveguides of different thickn...

A dielectric step-index optical fiber with tube-like profile is considered, being positioned with a small gap on top of a dielectric slab waveguide. We propose a 2.5-D hybrid analytical/numerical coupled mode model for the evanescent excitation of the tube through semi-guided waves propagating in the slab at oblique angles. The model combines the d...

We investigate optical microresonators consisting of either one or two coupled rectangular strips between upper and lower slab waveguides. The cavities are evanescently excited under oblique angles by thin-film guided, in-plane unguided waves supported by one of the slab waveguides. Beyond a specific incidence angle, losses are fully suppressed. Th...

Radiation losses at a junction of high-contrast Si/SiO2 slabs of different thicknesses can be avoided, if, for excitation by semi-guided waves, the angle of incidence is raised beyond a critical angle. By introducing an additional short waveguide segment of intermediate thickness at the junction, reflections can be suppressed; our simulations predi...

A rectangular dielectric strip at some distance above an optical slab waveguide is being considered, for evanescent excitation of the strip through the semi-guided waves supported by the slab, at specific oblique angles. The 2.5-D configuration shows resonant transmission properties with respect to variations of the angle of incidence, or of the ex...

Oblique propagation of semi-guided waves across slab waveguide structures with bent corners is investigated. A critical angle can be defined beyond which all radiation losses are suppressed. Additionally an increase of the curvature radius of the bends also leads to low-loss configurations for incidence angles below that critical angle. A combinati...

Frequently, optical integrated circuits combine elements (waveguide channels, cavities), the simulation of which is well established through mature numerical eigenproblem solvers. It remains to predict the interaction of these modes. We address this task by a general, “Hybrid” variant (HCMT) of Coupled Mode Theory. Using methods from finite-element...

The modal properties of curved dielectric slab waveguides are investigated. We consider quasi-confined, attenuated modes that propagate at oblique angles with respect to the axis through the center of curvature. Our analytical model describes the transition from scalar 2-D TE/TM bend modes to lossless spiral waves at near-axis propagation angles, w...

DNA sequencing by microchip capillary electrophoresis (CE) enables cheap, highspeed analysis of low reagent volumes. One of its potential applications is the identification of genomic deletions or insertions associated with genetic illnesses. Detecting single base-pair insertions or deletions from DNA fragments in the diagnostically relevant size r...

The device principle of a prism-based on-chip spectrometer for TE polarization is introduced. The spectrometer exploits the modal dispersion in planar waveguides in a layout with slab regions having two different thicknesses of the guiding layer. The set-up uses parabolic mirrors, for the collimation of light of the input waveguide and focusing of...

Semi-guided light propagation across linear folds of slab waveguides is being considered. Radiation losses vanish beyond certain critical angles of incidence, as can be understood by arguments resembling Snell's law. One thus realizes lossless propagation through 90-degree corner configurations, where the remaining guided waves are still subject to...

Typical optical integrated circuits combine elements, like straight and curved waveguides, or cavities, the simulation and design of which is well established through numerical eigenproblem-solvers. It remains to predict the interaction of these modes. We address this task by a ”Hybrid” variant (HCMT) of Coupled Mode Theory. Using methods from fini...

Sheets of slab waveguides with sharp corners are investigated. By means of
rigorous numerical experiments, we look at oblique incidence of semi-guided
plane waves. Radiation losses vanish beyond a certain critical angle of
incidence. One can thus realize lossless propagation through 90-degree corner
configurations, where the remaining guided waves...

DNA sequencing in a lab-on-a-chip aims at providing cheap, high-speed analysis of low reagent volumes to, e.g., identify genomic deletions or insertions associated with genetic illnesses. Detecting single base-pair insertions/deletions from DNA fragments in the diagnostically relevant range of 150-1000 base-pairs requires a sizing accuracy of S < 1...

The incidence of thin-film-guided, in-plane unguided waves at oblique angles on straight discontinuities of dielectric slab waveguides, an early problem of integrated optics, is being re-considered. The 3-D frequency domain Maxwell equations reduce to a parametrized inhomogeneous vectorial problem on a 2-D computational domain, with transparent-inf...

The relevance of our definition for sensitivity in refractometric sensing, being the relative change in the transmittance of a certain output channel of an optical device over the change in the refractive index of the probed material, is discussed. It is compared to one based on spectral shift per refractive index unit change. Further, there is dis...

The non-normal incidence of semi-guided plane waves on step-like or tapered transitions between thin film regions with different thicknesses, an early problem of integrated optics, is being reconsidered. As a step beyond the common effective index picture, we compare two approaches on how this problem can be tackled—at least approximately—by nowada...

A flexible and efficient method for fully vectorial modal analysis of 3D
dielectric optical waveguides with arbitrary 2D cross-sections is proposed. The
technique is based on expansion of each modal component in some a priori
defined functions defined on one coordinate axis times some unknown
coefficient-functions, defined on the other axis. By app...

Outline of a quite general, hybrid analytical / numerical variant of coupled mode theory, accompanied by a series of examples form integrated optics.

At the Integrated Optical Microsystems (IOMS) Group of the University of Twente, we are working towards setting the basis for the future of on-chip nanophotonics. In the following sections, our work on on-chip lasers and amplifiers, optical waveguide devices for different applications such as medical imaging and sensing as well as photonics-electro...

Circuits of dielectric integrated optical microring resonators are addressed through a two-dimensional hybrid analytical/numerical coupled mode theory (HCMT) model. Analytical modes of all straight and curved cores form templates for the optical fields of the entire circuits. Our variational technique then generates solutions for the amplitude func...

This chapter discusses an ab initio frequency domain model of circular microresonators, built on the physical notions that
commonly enter the description of the resonator functioning in terms of interaction between fields in the circular cavity
with the modes supported by the straight bus waveguides. Quantitative evaluation of this abstract model r...

This paper describes a simulation method for 2D frequency domain scattering problems in
photonics. The technique reduces the spatial dimensionality of the problem by means of
global, continuous mode expansion combined with a variational formalism; the resulting
equations are solved using a finite element method. Transparent influx boundary conditio...

Recent Near-field Scanning Optical Microscopy (NSOM) experiments with slit metal coated probes claim to measure the out-of-plane optical magnetic field around a dielectric sample waveguide [1]. The observations can also be explained by mode overlap calculations.

The spatial dimensionality of vectorial 3D frequency domain optical scattering problems is reduced by means of a global expansion of the field in one direction in slab modes of some reference slice(s). A variational formalism yields the equations in the other two directions. These coupled partial differential equations are solved using a Finite Ele...

Chains of coupled square dielectric cavities are investigated in a 2-D setting, by means of a quasi-analytical eigenmode expansion
method. Resonant transfer of optical power can be achieved along quite arbitrary, moderately long rectangular paths (up to
9 coupled cavities are considered), even with individual standing-wave resonators of limited qua...

To assess the quality of effective index approximations for photonic crystal slabs, we consider a reduction of 2-D problems for waveguide Bragg gratings to 1-D, and compare with rigorous 2-D solutions. A variational procedure permits to establish reasonable effective indices even if locally no guided modes exist. Summary The propagation of light th...

The optical properties of slab-like photonic crystals are often discussed on the basis of effective index (EI) approximations,
where a 2-D effective refractive index profile replaces the actual 3-D structure. Our aim is to assess this approximation
by analogous steps that reduce finite 2-D waveguide Bragg-gratings (to be seen as sections through 3-...

In order to reduce the computational effort we develop a method for 3D-to-2D dimensionality reduction of scattering problems in photonics. Contrary to the 'standard' Effective Index Method the effective parameters of the reduced problem are always rigorously defined using the variational technique, based on the vectorial 3D Maxwell equations. Resul...

We analyze coupled optical defect cavities realized in finite one-dimensional photonic crystals (PC). Viewing these as open systems, where waves are permitted to leave the structures, one obtains eigenvalue problems for complex frequencies (eigenvalues) and quasi-normal modes (QNM) (eigenfunctions). Single-defect structures (PC atoms) can be viewed...

A variational vectorial mode solver for 3-D dielectric waveguides with arbitrary 2-D cross-sections is proposed. It is based on expansion of each component of a mode profile as a superposition of some a priori defined functions defined on one coordinate axis times some unknown continuous coefficient functions, defined on the other axis. By applying...

A general variant of coupled-mode-theory for frequency domain guided wave problems in integrated optics is discussed. Starting point is a physically reasonable field template, that typically consists of a few known, most relevant modes of the optical channels in the structure, superimposed with coefficient functions of the respective - in principle...

By combining Dirichlet to Neumann (DtN) operators and perfectly matched layers (PMLpsilas) as boundary conditions on a rectangular domain on which the Helmholtz equation is solved, the disadvantages of both methods are greatly diminished. Due to the DtN operators, light may be accurately fluxed into the domain, while the PMLpsilas absorb light that...

Quasi-normal modes are used to characterize transmission resonances in 1D optical defect cavities and the related field approximations. We specialize to resonances inside the bandgap of the periodic multilayer mirrors that enclose the defect cavities. Using a template with the most relevant QNMs a variational principle permits to represent the fiel...

We investigate the thermal antenna behavior of emissive/absorptive substrates coated by passive optical multilayer systems that contain negative refractive index metamaterials (NIM). Spectral and angular distributions of the thermal radiation emittance for periodic defect-containing multilayer with NIM is addressed. We analyze realistic finite stru...

We analyze coupled optical defect cavities realized in finite one-dimensional Photonic Crystals. Viewing these as open systems where waves are permitted to leave the structures, one obtains eigenvalue problems for complex frequencies (eigenvalues) and Quasi-Normal-Modes (eigenfunctions). Single defect structures (photonic crystal atoms) can be view...

1 Chains of square 2D microcavities Coupled-resonator optical waveguides (CROWs) have been discussed already for some years [1] as a means to realize waveguiding along paths with small-size bends. Con-cepts based on series of microring resonators or sequences of defects in photonic crystal slabs [2] exist. As an alternative, we consider chains of s...

A variational method for the fully vectorial mode analysis of lossless dielectric waveguides with piecewise constant rectangular refractive index distributions is proposed. Summary An extension of the scalar Mode Expansion Mode Solver [1] to fully vectorial simulations is discussed. The method uses a six component variational formulation of the Max...

Microresonator filters, which are realized by evanescent coupling of circular cavities with two parallel bus waveguides, are promising candidates for applications in dense wavelength-division multiplexing. Tunability of these filters is an essential feature for their successful deployment. In this paper, we present a framework for modeling of tunin...

In this paper, a general version of coupled-mode theory for frequency-domain scattering problems in integrated optics is proposed. As a prerequisite, a physically reasonable field template is required, that typically combines modes of the optical channels in the structure with coefficient functions of in principle arbitrary coordinates. Upon 1D dis...

A variational approach for the semivectorial modal analysis of dielectric waveguides with arbitrary piecewise constant rectangular
2D cross-sections is developed. It is based on a representation of a mode profile as a superposition of modes of constituting
slab waveguides times some unknown continuous coefficient functions, defined on the entire co...

We analyze coupled optical defect cavities realized in finite one-dimensional Photonic-Crystals. Viewing these as open systems where waves are permit-ted to leave the structures, one obtains eigenvalue prob-lems for complex frequencies (eigenvalues) and Quasi-Normal-Modes (eigenfunctions) [1-2]. QNMs are field profiles in which the leaky structure...

Boundary conditions for a 2D finite element Helmholtz solver are derived, which allow scattered light to leave the calculation domain in the presence of outgoing waveguides. Influx of light, through a waveguide or otherwise, can be prescribed at any boundary. In the simulation of integrated optical structures, the boundaries of the calculation wind...

A functional of the six electromagnetic components is proposed as a variational basis for 3-D frequency domain problems in integrated optics. Stationarity implies that the Maxwell equations in the interior of the domain of interest and transparent influx conditions for incoming waveguides on its boundary port planes are satisfied.

Slow light (SL) states corresponding to wavelength regions near the bandgap edge of grated structures are known to show strong
field enhancement. Such states may be excited efficiently by well-optimized adiabatic transitions in grated structures, e.g.,
by slowly turning on the modulation depth. To study adiabatic excitations, a detailed research in...

Circular integrated optical (ring or disk) microresonators are increasingly employed as compact and versatile wavelength filters. In this paper, we investigate a 2-D frequency domain model for these devices, based on spatial coupled mode theory. The microresonators are functionally represented in terms of two couplers with appropriate connections u...