TY - JOUR AB - 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. Following a discretization of amplitude functions by 1D finite elements, pro- cedures from the realm of finite-element numerics are applied to establish systems of linear equations for the then- discrete modal amplitudes. Examples substantiate the functioning of the technique and allow for some numerical assessment. The full 3D simulations are highly efficient in memory consumption, moderately demanding in com- putational time, and, in regimes of low radiative losses, sufficiently accurate for practical design. Our results include the perturbation of guided modes by changes of the refractive indices, the interaction of waves in parallel, horizontally or vertically coupled straight waveguides, and a series of crossings of potentially overlapping channels with fairly arbitrary relative positions and orientations. AU - Hammer, Manfred AU - Alhaddad, Samer AU - Förstner, Jens ID - 3828 IS - 3 JF - Journal of the Optical Society of America B KW - tet_topic_waveguide KW - tet_topic_numerics SN - 0740-3224 TI - Hybrid coupled-mode modeling in 3D: perturbed and coupled channels, and waveguide crossings VL - 34 ER - TY - JOUR AB - 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, with a continuum of vectorial attenuated spiral modes in between. Modal solutions are characterized in terms of directional wavenumbers and attenuation constants. Examples for vectorial mode profiles illustrate the effects of oblique wave propagation along the curved slab segments. For the regime of lossless spiral waves, the relation with the guided modes of corresponding dielectric tubes is demonstrated. AU - Ebers, Lena AU - Hammer, Manfred AU - Förstner, Jens ID - 3830 IS - 4 JF - Optical and Quantum Electronics KW - tet_topic_waveguide SN - 0306-8919 TI - Spiral modes supported by circular dielectric tubes and tube segments VL - 49 ER - TY - CONF AU - Hildebrandt, Andre AU - Alhaddad, Samer AU - Hammer, Manfred AU - Förstner, Jens ED - Broquin, Jean-Emmanuel ED - Nunzi Conti, Gualtiero ID - 3543 KW - tet_topic_waveguide T2 - Integrated Optics: Devices, Materials, and Technologies XX TI - Oblique incidence of semi-guided waves on step-like folds in planar dielectric slabs: Lossless vertical interconnects in 3D integrated photonic circuits ER - TY - CONF AB - 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 finite-element numerics, the optical properties of a circuit are approximated by superpositions of eigen-solutions for its constituents, leading to quantitative, low-dimensional, and interpretable models in the frequency domain. Spectral scans are complemented by the direct computation of supermode properties (spectral positions and linewidths, coupling-induced phase shifts). This contribution outlines the theoretical background, and discusses briefly limitations and implementational details, with the help of an example of a 2-D coupled-resonator-optical-waveguide configuration. AU - Hammer, Manfred ED - Broquin, Jean-Emmanuel ED - Nunzi Conti, Gualtiero ID - 3934 IS - 9750 KW - tet_topic_waveguide KW - tet_topic_numerics T2 - Integrated Optics: Devices, Materials, and Technologies XX TI - Wave interaction in photonic integrated circuits: Hybrid analytical / numerical coupled mode modeling ER - TY - JOUR AB - 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 the light to the receiver waveguides, which relies on total internal reflection at the interface between two such regions. These regions are connected adiabatically to prevent unwanted mode conversion and loss at the edges of the prism. The structure can be fabricated with two wet etching steps. The paper presents basic theory and a general approach for device optimization. The latter is illustrated with a numerical example assuming SiON technology. AU - Civitci, F. AU - Hammer, Manfred AU - Hoekstra, H.J.W.M. ID - 3845 JF - Optics Communications KW - tet_topic_waveguide SN - 0030-4018 TI - Planar prism spectrometer based on adiabatically connected waveguiding slabs VL - 365 ER - TY - JOUR AB - 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 are still subject to pronounced reflection and polarization conversion. A system of two corners can be viewed as a structure akin to a Fabry-Perot-interferometer. By adjusting the distance between the two partial reflectors, here the 90-degree corners, one identifies step-like configurations that transmit the semi-guided plane waves without radiation losses, and virtually without reflections. Simulations of semi-guided beams with in-plane wide Gaussian profiles show that the effect survives in a true 3-D framework. AU - Hammer, Manfred AU - Hildebrandt, Andre AU - Förstner, Jens ID - 3847 IS - 3 JF - Journal of Lightwave Technology KW - tet_topic_waveguide SN - 0733-8724 TI - Full Resonant Transmission of Semiguided Planar Waves Through Slab Waveguide Steps at Oblique Incidence VL - 34 ER - TY - JOUR AB - We show how to optically connect guiding layers at different elevations in a 3-D integrated photonic circuit. Transfer of optical power carried by planar, semi-guided waves is possible without reflections or radiation losses, and over large vertical distances. This functionality is realized through simple step-like folds of high-contrast dielectric slab waveguides, in combination with oblique wave incidence, and fulfilling a resonance condition. Radiation losses vanish, and polarization conversion is suppressed for TE wave incidence beyond certain critical angles. This can be understood by fundamental arguments resting on a version of Snell’s law. The two 90° corners of a step act as identical partial reflectors in a Fabry–Perot-like resonator setup. By selecting the step height, i.e., the distance between the reflectors, one realizes resonant states with full transmission. Rigorous quasi-analytical simulations for typical silicon/silica parameters demonstrate the functioning. Combinations of several step junctions can lead to other types of optical on-chip connects, e.g., U-turn- or bridge-like configurations. AU - Hammer, Manfred AU - Hildebrandt, Andre AU - Förstner, Jens ID - 3894 IS - 16 JF - Optics Letters KW - tet_topic_waveguide SN - 0146-9592 TI - How planar optical waves can be made to climb dielectric steps VL - 40 ER - TY - JOUR AB - The incidenceofthin-film-guided, in-planeunguidedwavesatobliqueanglesonstraightdiscontinuities of dielectricslabwaveguides,anearlyproblemofintegratedoptics,isbeingre-considered.The3-D frequencydomainMaxwellequationsreducetoaparametrizedinhomogeneousvectorialproblemona 2-D computationaldomain,withtransparent-influx boundaryconditions.Weproposearigorousvec- torial solverbasedonsimultaneousexpansionsintopolarizedlocalslabeigenmodesalongthetwo orthogonal crosssectioncoordinates(quadridirectionaleigenmodepropagationQUEP).Thequasi-ana- lytical schemeisapplicabletoconfigurations with — in principle — arbitrary crosssectiongeometries. Examples forahigh-contrastfacetofanasymmetricslabwaveguide,forthelateralexcitationofa channel waveguide,andforastepdiscontinuitybetweenslabwaveguidesofdifferentthicknessesare discussed. AU - Hammer, Manfred ID - 3890 JF - Optics Communications KW - tet_topic_waveguide KW - tet_topic_numerics SN - 0030-4018 TI - Oblique incidence of semi-guided waves on rectangular slab waveguide discontinuities: A vectorial QUEP solver VL - 338 ER - TY - JOUR AB - 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 discussion on how group delay and sensitivity are interrelated and can be converted into each other and which physical quantities are relevant for high sensitivity. As a by-product of the theory presented, a general expression relating group delay and the ratio of the time-averaged optical energy and the input power is presented. AU - Hoekstra, Hugo J. W. M. AU - Hammer, Manfred ID - 3937 IS - 7 JF - Journal of the Optical Society of America B KW - tet_topic_waveguide SN - 0740-3224 TI - General relation for group delay and the relevance of group delay for refractometric sensing VL - 31 ER -