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Circular Integrated Optical Microresonators: Analytical Methods and Computational Aspects

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Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 156))

Abstract

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 requires propagation constants associated with the cavity/bend segments, and scattering matrices, that represent the wave interaction in the coupler regions. These quantities are obtained by an analytical (2-D) or numerical (3-D) treatment of bent waveguides, along with spatial coupled mode theory (CMT) for the couplers. The required CMT formulation is described in detail. Also, quasi-analytical approximations for fast and accurate computation of the resonator spectra are discussed. The formalism discussed in this chapter provides valuable insight into the functioning of the resonators, and it is suitable for practical device design.

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Notes

  1. 1.

    In the time domain, the Q factor \(Q = \omega/(2\delta\omega)\) is defined as the ratio of the optical power stored in the cavity to the cycle averaged power radiated out of the cavity [42]. The larger the Q factor, the longer the optical field is trapped inside the cavity.

  2. 2.

    The arbitrariness in the choice of R renders the actual value of \(\gamma\) virtually meaningless [19]. Only the product \(\gamma R\) is relevant.

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Acknowledgments

This work was carried out as a part of the project “NAIS” (IST-2000-28018), funded by the European Commission. K. R. Hiremath also acknowledges support by the DFG (German Research Council) Research Training Group “Analysis, Simulation and Design of Nanotechnological Processes,” University of Karlsruhe. The authors thank R. Stoffer for his hard work on the 3-D simulations. They are grateful to H. J. W. M. Hoekstra, E. van Groesen, and their colleagues in the NAIS project for many fruitful discussions.

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Authors and Affiliations

  1. Department of Mathematics, Institute for Scientific Computing and Mathematical Modeling, University of Karlsruhe, Karlsruhe, Germany

    Kirankumar Hiremath

  2. Department of Applied Mathematics, MESA+ Institute for Nanotechnology, University of Twente, Enschede, The Netherlands

    Manfred Hammer

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  1. Kirankumar Hiremath
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Correspondence to Kirankumar Hiremath .

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Editors and Affiliations

  1. , School of Electrical and, National Technical University, Athens, 157 80, Greece

    Ioannis Chremmos

  2. Dept. Electrical & Computer Engineering, Concordia University, Maisonneuve Blvd. West, EV005.126 1455, Montreal, H3G 1M8, Canada

    Otto Schwelb

  3. , School of Electrical and, National Technical University, Athens, 157 80, Greece

    Nikolaos Uzunoglu

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Hiremath, K., Hammer, M. (2010). Circular Integrated Optical Microresonators: Analytical Methods and Computational Aspects. In: Chremmos, I., Schwelb, O., Uzunoglu, N. (eds) Photonic Microresonator Research and Applications. Springer Series in Optical Sciences, vol 156. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1744-7_2

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