Next-generation active integrated optic subsystems

Information society technologies programme of the European Commission
Project IST-2000-28018, Workpackage 3: Design

Online collections of illustrative example results

• Power spectrum and related field patterns of a 2D microdisk resonator, a multimode cavity, simulated by a rigorous semianalytical technique (quadridirectional eigenmode propagation, QUEP), see the Metric program collection (Manfred Hammer, MESA+, University of Twente).
• Illustrations and animations concerning guided wave propagation along straight and bent optical waveguides (2D & 3D), related to the development of a 3D FMM bend mode solver (Ladislav Prkna, IREE AS CR).
• An illustration of reciprocal propagation of light through a coupler involving a bent waveguide and a straight waveguide segment; finite-difference time domain simulations (Remco Stoffer, MESA+, University of Twente).
• Comparison of 2D microresonator properties as predicted by finite-difference time domain simulations and by analytic modeling (Remco Stoffer, Kiran Hiremath, MESA+, University of Twente).
• Examples of whispering gallery modes of 2D microring and microdisk cavities, analytical calculations (Ladislav Prkna, Jiri Ctyroky, Milan Hubalek, IREE AS CR).
• Bent slab modes calculated by means of the numerical bend mode solver of the OlympIOs C2V software package (Milan Hubalek & Jiri Ctyroky, IREE AS CR).
• Bent slab modes calculated by means of analytic evaluation (maple) of the bend mode properties in terms of Bessel functions (Kiran Hiremath & Manfred Hammer, MESA+, University of Twente).

Some noncommercial pieces of software that may be of interest for the participating groups

	A simulator for 3D circular microresonators based on numerically computed profiles for vectorial modes of bent and straight optical channels. A variant of coupled mode theory is used to evaluate the evolution of an arbitrary number of modes that couple as they propagate along a set of waveguides. The C++ implementation includes a reasonably comfortable user interface, in which the structure can be defined, calculations are done, and fields may be visualized. Mode field calculations are not fully integrated so far: Basis mode profiles are computed externally (FMM or OlympIOs) and imported from files in a discretized format. Two coupler configurations are combined with the bends of the ring or disk cavity to compute the wavelength response of the full microresonator. After a license agreement with the University of Twente, the company C2V will take care of the further distribution and support of the programs. Please contact Remco Stoffer, UT-MESA+
	Circurs: A semianalytical 2D microresonator model. Analytical solutions for modes supported by bend segments and straight channels are combined in a framework of frequency domain coupled mode theory. The resonator is functionally decomposed into two bent-straight waveguide couplers, which are connected to each other by segments of bent waveguides. The C++ implementation provides objects for straight and bent waveguides, coupler configurations, and full microresonator structures. The latter includes methods for the evaluation of the power transmission, the free spectral range, the width of the resonances, and, for given vacuum wavelength, of the full (2D) optical fields. Scans over the wavelength parameter permit to compute the spectral response of the microresonator device. A preliminary version of an online manual is available, including the C++ code and a few example driver files. Please contact Kiran Hiremath, UT-MESA+
	Mode solvers for bent waveguides and ringresonators in 2D and 3D, related to the implementation of a 3D Film Mode Matching technique: 2D mode solver for slab waveguides (multilayers). Accepts both lossless and lossy layers. Uses either transfer matrix, impedance or reflectance method and bracketing of effective indices for lossless and contour integral evaluation or mode tracking for lossy structures. The waveguide is enclosed with artificial magnetic or electric walls (optionally PMLs) - this discretization of the continuous spectrum allows to locate not only guided but radiation modes, too. 2D mode solver for planar microresonators. Both microring and microdisk structures are supported. The propagation constant (here a natural number to meet the resonant condition) is estimated from the mode of a 2D bent waveguide with the same parameters. A contour line integral method is then used to search the complex plane of frequency for zeros of the dispersion equation, which holds for microresonators as well as for bent waveguides. 3D mode solver for straight waveguides, semivectorial Film Mode Matching approach for lossless waveguides with step-index cross-section. Each slice (horizontally uniform segment - multilayer) is characterized by a set of eigenmodes. These are used to establish the dispersion relation horizontally. The structure is vertically enclosed with suitable boundary conditions to discretize the continuous spectrum of the multilayers. 3D mode solver for bent waveguides, semivectorial Film Mode Matching approach for waveguides with step-index cross-section, provides complex root tracking of bend modes. Taking a straight waveguide mode as initial guess, a complex zero of the dispersion equation of a bent waveguide with long radius is polished. The stepwise decrease of the bend radius yields the mode evolution of a structure being bent. 3D mode solver for microresonators, semivectorial Film Mode Matching approach for microrings and microdisks with step-index cross-section, intended as a different approach to microresonator modeling. If circular symmetry is considered, a microresonator is characterized as a lossy resonant structure with complex eigenfrequencies. Somewhat more time consuming as the slices' eigenmodes must be recomputed for each trial frequency. Ladislav Prkna, IREE Prague
	The AAMP Finite Difference Time Domain program provides an environment to perform two-dimensional electromagnetic simulations on non-dispersive, linear, nonabsorbing and nonamplifying materials with arbitrary shapes. Perfectly Matched Layers (PML's) are employed to absorb radiation leaving the calculation domain. Input fields can either be generated from behind the PML's, or inside the window by means of the Total Field / Scattered Field approach. Analysis can be performed on e.g. waveguide mode powers in a wide spectral range; fields can be saved to files at arbitrary times. A preliminary version of the FDTD program for MS Windows and a brief user manual are available online. Please contact Remco Stoffer, UT-MESA+
	A semianalytical 2D bend mode solver, implemented in C++, based on field matching at radial interfaces of different materials. In the present state, the mode solver is limited to structures with at most one guiding layer. For given real frequency / vacuum wavelength, the program computes complex valued mode profiles and the corresponding complex propagation constants, or effective mode indices and attenuation constants, respectively. Mode profiles are represented in terms of Bessel and Hankel functions with complex order, which are evaluated using their "uniform asymptotic expansions". A secant method is used to find complex roots that correspond to valid propagation constants. Further details are available in a research report. The programs have been included in the Circurs subroutine collection. Please contact Kiran Hiremath, UT-MESA+
	Metric: Tools for semianalytic modeling in integrated optics / photonics, simulations of lossless 2D configurations with rectangular refractive index distributions. Includes a mode solver engine for dielectric multilayer slab waveguides, and solvers for guided-wave Helmholtz (-scattering) problems based on spectral discretizations along one (BEP: bidirectional eigenmode propagation) or two coordinate axes (QUEP: quadridirectional eigenmode propagation). A series of application examples, embedded in the html manual, complements the downloadable, commented C++ sources. Manfred Hammer, UT-MESA+
	A quasianalytic mode solver for dielectric integrated optical waveguides with rectangular 2D cross sections (Wave Matching Method). The html-manual includes the downloadable, commented C++ sources, accompanied by several application examples. Although the programs are designed for straight waveguides only, the included features of perturbation theory may prove to be useful when dealing with lossy or anisotropic materials. A collection of additional application files extends the WMM coupled mode theory implementation to adiabatic, threedimensional directional couplers. Accepting the - admittedly crude - approximation of the bend mode of a ring cavity by a profile that corresponds to a straight waveguide with analogous cross section, these procedures can provide a computationally cheap means to tackle the problem of coupling the cavity loop in a cylindrical microresonator to a straight port waveguide. Several documents reporting on the evaluation of this model for the configurations considered in NAIS can be found in the workplace section of the NAIS website. Manfred Hammer, UT-MESA+
	Modal analysis of multilayer and graded index waveguides with 1D cross sections. Specifically: (1)  Modal analysis of a general 1D multilayer waveguide (propagation constants and mode field distributions). Complex refractive indices are allowed. In open waveguides, both guided and leaky modes can be calculated. Method used: transfer matrix method. (2)  Modal analysis of a general 1D graded-index waveguide (propagation constants and mode field distributions). Complex refractive indices are allowed. Method used: transversal impedance method using Runge-Kutta 3-th and 4-th order integration. (3)  Modal analysis of a general 1D multilayer waveguide (propagation constants and mode field distributions) of waveguides containing metal layers with negative real part of permittivity that support surface plasmons. Method used: transfer matrix method. Please contact Jiri Ctyroky, IREE Prague
	Online mode solvers (Java applets), directly executable in your web browser. A 1D multilayer slab waveguide mode solver and a 2D effective index multilayer waveguide mode solver are available. The programs are meant as a kind of pocket calculator for rough and quick assessment of problems involving slab waveguides, and for purposes of demonstration. The limited functionality is hardly sufficient for more extensive design tasks, where one should resort to other computational means. Analogous C++ programs (Metric) are available as well, without a graphical user interface, but applicable to a substantially larger variety of problems. Manfred Hammer, UT-MESA+
	Uni- and bidirectional eigenmode propagation simulations for segmented planar waveguide structures. More specifically: (1)  Modally resolved transmission and reflection in a 1D (planar) waveguide consisting of a concatenation of an arbitrary number of sections of longitudinally uniform multilayer waveguides. Complex refractive indices are allowed. Method used: Bidirectional mode expansion and propagation method with PMLs. (2)  Modally resolved transmission in a 1D (planar) waveguide consisting of a concatenation of a several sections of longitudinally uniform multilayer waveguides. One section can contain metal layer supporting propagation of surface plasmons. Complex refractive indices are allowed. Method used: Unidirectional option of a bidirectional mode expansion and propagation method with PMLs. (3)  Modally resolved transmission and reflection in a 1D (planar) waveguide consisting of a concatenation of periodically repeated longitudinally uniform sections of multilayer waveguides. Complex refractive indices are generally allowed. Method used: Bidirectional mode expansion and propagation method combined with the Bloch-Floquet theorem and PMLs. Please contact Jiri Ctyroky, IREE Prague

For information on the C2V software products (OlympIOs), please consult the C2V website directly.

Selected research reports / drafts

• Coupled mode theory simulations of microresonators with multimode cavities, summarized on a research poster (Kiran Hiremath, Remco Stoffer, & Manfred Hammer, MESA+, University of Twente).
• "System" simulation of pulse propagation in a microresonator device, summarized on a research poster (Milan Hubalek & Jiri Ctyroky, IREE AS CR).
• Analytical modeling of 2D cylindrical integrated optical microresonators, summarized in a detailed research report, (Kiran Hiremath, MESA+, University of Twente).
• Sketch of a simple coupled mode model for 3D directional couplers involving bent and straight waveguides, NAIS internal note, September 2002 (Manfred Hammer, MESA+, University of Twente). See the NAIS workplace for detailed drafts that report on the evaluation of the model for the parameter sets that are relevant for NAIS.
• Standard ringresonator model, a summary of the basis for most present discussions on optical ringresonators, NAIS internal note, April 2003 (Manfred Hammer, MESA+, University of Twente).
• Bent slab mode computations and 2D coupler simulations by coupled mode theory and FDTD, presented on two research posters (Kiran Hiremath, et al., MESA+, University of Twente).

Journal articles and contributions to conference proceedings related to WP3 of NAIS

• R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, J. Ctyroky
  Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory
  Optics Communications 256 (1-3), 46-67 (2005)
• K. R. Hiremath, R. Stoffer, M. Hammer
  Modeling of circular integrated optical microresonators by 2-D frequency-domain coupled mode theory
  Optics Communications 257 (2), 277-297 (2006)
• J. Ctyroky, L. Prkna, M. Hubalek, F. Ondracek
  Modelling of guided-wave optical microresonators
  Proceedings of the 12th European Conference on Integrated Optics ECIO'05, Grenoble, France, 359-366 (2005)
• K. R. Hiremath, M. Hammer
  Perturbational evaluation of bend mode phase shifts for the tuning of cylindrical microresonators
  Proceedings of the 12th European Conference on Integrated Optics ECIO'05, Grenoble, France, 367 (2005)
• R. Stoffer, K. R. Hiremath, M. Hammer, L. Prkna, J. Ctyroky
  Simulations of vertically-coupled microdisk-resonators by 3-D vectorial coupled mode theory
  Proceedings of the 12th European Conference on Integrated Optics ECIO'05, Grenoble, France, 372-375 (2005)
• K.R. Hiremath, R. Stoffer, M. Hammer
  Multimode circular integrated optical microresonators: Coupled mode theory modeling
  IEEE/LEOS Benelux Chapter, Proceedings of the 9th Annual Symposium, Ghent, Belgium, 79-82 (2004)
• L. Prkna, M. Hubalek, J. Ctyroky
  Field modelling of circular microresonators by film mode matching
  Journal of Selected Topics on Quantum Electronics 11 (1), 217-223 (2005)
• K. R. Hiremath, M. Hammer, R. Stoffer, L. Prkna, J. Ctyroky
  Analytical approach to dielectric optical bent slab waveguides
  Optical and Quantum Electronics 37 (1-3), 37-61 (2005)
• L. Prkna, M. Hubalek, J. Ctyroky
  Vectorial eigenmode solver for bent waveguides based on mode matching
  IEEE Photonics Technology Letters 16, 2057-2059 (2004)
• L. Prkna, J. Ctyroky, M. Hubalek
  Ring microresonator as a photonic structure with complex eigenfrequency
  Optical and Quantum Electronics 36 (1-3), 259-269 (2004)
• M. Hammer, D. Yudistira, R. Stoffer
  Modeling of grating assisted standing wave microresonators for filter applications in integrated optics
  Optical and Quantum Electronics 36 (1-3), 25-42 (2004)
• M. Hammer, K.R. Hiremath, R. Stoffer
  Analytical approaches to the description of optical microresonator devices
  in M. Bertolotti, A. Driessen, and F. Michelotti, eds., Microresonators as building blocks for VLSI photonics, AIP Conference Proceedings, Melville, New York, vol. 709, 48-71 (2004); Proceedings of the International School of Quantum Electronics, 39th course, Erice, Sicily (October 2003)
• J. Ctyroky, L. Prkna, M. Hubalek
  Guided-wave optical microresonators: Calculation of eigenmodes
  in M. Bertolotti, A. Driessen, and F. Michelotti, eds., Microresonators as building blocks for VLSI photonics, AIP Conference Proceedings, Melville, New York, vol. 709, 72-90 (2004); Proceedings of the International School of Quantum Electronics, 39th course, Erice, Sicily (October 2003)
• R. Stoffer, K.R. Hiremath, M. Hammer
  Comparison of coupled mode theory and FDTD simulations of coupling between bent and straight optical waveguides
  in M. Bertolotti, A. Driessen, and F. Michelotti, eds., Microresonators as building blocks for VLSI photonics, AIP Conference Proceedings, Melville, New York, vol. 709, 366-377 (2004); Proceedings of the International School of Quantum Electronics, 39th course, Erice, Sicily (October 2003)
• K.R. Hiremath, R. Stoffer, M. Hammer
  Coupled Mode Theory and FDTD Simulations of the Coupling Between Bent and Straight Optical Waveguides
  IEEE/LEOS Benelux Chapter, Proceedings of the 8th Annual Symposium, Enschede, The Netherlands, 33-36 (2003)
• M. Hammer, D. Yudistira
  Grating assisted rectangular integrated optical microresonators
  in J. Ctyroky, M. Hubalek, F. Ondracek, eds., Proceedings of the 11th European Conference on Integrated Optics ECIO'03, ISBN 80-01-02729-5, Vol. 1, 357-360 (2003)

... and two theses

• K.R. Hiremath
  Coupled Mode Theory Based Modeling and Analysis of Circular Optical Microresonators
  Department of Applied Mathematics, University of Twente, Enschede, The Netherlands, October 2005
• L. Prkna
  Rotationally symmetric resonant devices in integrated optics
  Faculty of Mathematics and Physics, Charles University, Prague, and Institute of Radio Engineering and Electronics, Academy of Sciences of the Czech Republic, Prague, July 2004

 Manfred Hammer   (11.2005, adapted 11.2021)