2009/03/27 by C. P. Dettmann, Carl P. Dettmann, G. V. Morozov +4 · 1 citation
Chemistry · Engineering · Mathematics · Physics and Astronomy · #Chemistry #Complex plane #Condensed matter physics #Dielectric #Eigenvalues and eigenvectors #Mathematical analysis #Mathematics #Mechanical and Optical Resonators #Optics #Photonic Crystals and Applications #Photonic and Optical Devices #Physics #Polarization (electrochemistry) #Quantum mechanics #Refractive index #Total internal reflection #Transcendental equation #physics.optics
paper · pdf · doi:10.1209/0295-5075/87/34003
published as Europhys. Lett. 87 (2009) 34003 · 5 pages, 8 figures, pdflatex
arxiv created 2009/03/27 · openalex publication_date 2009/08/01 · arxiv updated 2010/03/09 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
Circular microresonators (microdisks) are micron size dielectric disks embedded in a material of lower refractive index. They possess modes with complex eigenvalues (resonances) which are solutions of analytically given transcendental equations. The behavior of such eigenvalues in the small opening limit, i.e. when the refractive index of the cavity goes to infinity, is analyzed. This analysis allows one to clearly distinguish between internal (Feshbach) and external (shape) resonant modes for both TM and TE polarizations. This is especially important for TE polarization for which internal and external resonances can be found in the same region of the complex wave number plane. It is also shown that for both polarizations, the internal as well as external resonances can be classified by well-defined azimuthal and radial modal indices.