Circular Integrated Optical Microresonators: Analytical Methods and Computational Aspects

  • Kirankumar Hiremath
  • Manfred Hammer
Part of the Springer Series in Optical Sciences book series (SSOS, volume 156)


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.


Cavity Mode Transverse Electric Finite Difference Time Domain Couple Mode Theory Slab Waveguide 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer-Verlag US 2010

Authors and Affiliations

  1. 1.Department of Mathematics, Institute for Scientific Computing and Mathematical ModelingUniversity of KarlsruheKarlsruheGermany
  2. 2.Department of Applied Mathematics, MESA+ Institute for NanotechnologyUniversity of TwenteEnschedeThe Netherlands

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