Resonances in Axially Symmetric Dielectric Objects

A high-order convergent and robust numerical solver is constructed and used to find complex eigenwavenumbers and electromagnetic eigenfields of dielectric objects with axial symmetry. The solver is based on Fourier-Nyström discretization of combined integral equations for the transmission problem and can be applied to demanding resonance problems at microwave, terahertz, and optical wavelengths. High achievable accuracy, even at very high wavenumbers, makes the solver ideal for benchmarking and for assessing the performance of general-purpose commercial software.

[1]  Nico M. Temme,et al.  Numerical methods for special functions , 2007 .

[2]  L. Felsen,et al.  Creeping waves and resonances in transient scattering by smooth convex objects , 1983 .

[3]  Anders Karlsson,et al.  Determination of Normalized Magnetic Eigenfields in Microwave Cavities , 2014, IEEE Transactions on Microwave Theory and Techniques.

[4]  Per-Gunnar Martinsson,et al.  A high-order Nyström discretization scheme for boundary integral equations defined on rotationally symmetric surfaces , 2011, J. Comput. Phys..

[5]  Anders Karlsson,et al.  Determination of normalized electric eigenfields in microwave cavities with sharp edges , 2016, J. Comput. Phys..

[6]  Matthew R Foreman,et al.  Whispering gallery mode sensors. , 2015, Advances in optics and photonics.

[7]  N. Yu,et al.  Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators , 2010 .

[8]  Michael T. Heath,et al.  Scientific Computing: An Introductory Survey , 1996 .

[9]  Ahmed A. Kishk,et al.  Conical dielectric resonator antennas for wide-band applications , 2002 .

[10]  Jan Wiersig.  Boundary element method for resonances in dielectric microcavities , 2003 .

[11]  Francesco Stellacci,et al.  A Study of the Surface Plasmon Resonance of Silver Nanoparticles by the Discrete Dipole Approximation Method: Effect of Shape, Size, Structure, and Assembly , 2010 .

[12]  P. Yla-Oijala,et al.  Well-conditioned Muller formulation for electromagnetic scattering by dielectric objects , 2005, IEEE Transactions on Antennas and Propagation.

[13]  B. Sturman,et al.  Whispering gallery modes at the rim of an axisymmetric optical resonator: analytical versus numerical description and comparison with experiment. , 2013, Optics express.

[14]  M. Oxborrow.  Traceable 2-D Finite-Element Simulation of the Whispering-Gallery Modes of Axisymmetric Electromagnetic Resonators , 2006, IEEE Transactions on Microwave Theory and Techniques.

[15]  Trevor M. Benson,et al.  Nystrom method for the Muller boundary integral equations on a dielectric body of revolution: axially symmetric problem , 2015 .

[16]  I. Reaney,et al.  Microwave Dielectric Ceramics for Resonators and Filters in Mobile Phone Networks , 2006 .

[17]  Staffan Ström,et al.  The null-field approach to electromagnetic resonance of composite objects , 1991 .

[18]  Anders Holst,et al.  Variants of an explicit kernel-split panel-based Nyström discretization scheme for Helmholtz boundary value problems , 2013, Adv. Comput. Math..

[19]  J. Swinburne.  Electromagnetic Theory , 1894, Nature.

[20]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[21]  M. Ferrando-Bataller,et al.  Overcoming Low-Frequency Breakdown of the Magnetic Field Integral Equation , 2013, IEEE Transactions on Antennas and Propagation.

[22]  M. Taskinen,et al.  Current and charge Integral equation formulation , 2006, IEEE Transactions on Antennas and Propagation.

[23]  Tatsuo Itoh,et al.  Dielectric materials, devices, and circuits , 2002 .

[24]  A. Matsko,et al.  Optical resonators with whispering-gallery modes-part I: basics , 2006, IEEE Journal of Selected Topics in Quantum Electronics.

[25]  Claus Müller,et al.  Foundations of the mathematical theory of electromagnetic waves , 1969 .

[26]  Lan Yang,et al.  Whispering gallery microcavity lasers , 2013 .

[27]  Yuxiang Liu,et al.  Efficient numerical solution of acoustic scattering from doubly-periodic arrays of axisymmetric objects , 2015, J. Comput. Phys..

[28]  T. Kippenberg,et al.  Microresonator-Based Optical Frequency Combs , 2011, Science.

[29]  H. Cohl,et al.  A Compact Cylindrical Green’s Function Expansion for the Solution of Potential Problems , 1999 .

[30]  D. Blair,et al.  Microwave characterisation of BaCe2Ti5O15 and Ba5Nb4O15 ceramic dielectric resonators using whispering gallery mode method , 2000 .

[31]  M. Ganesh,et al.  An all-frequency weakly-singular surface integral equation for electromagnetism in dielectric media: Reformulation and well-posedness analysis , 2014 .

[32]  Anders Karlsson,et al.  An explicit kernel-split panel-based Nyström scheme for integral equations on axially symmetric surfaces , 2013, J. Comput. Phys..