The loss of high-Q whispering-gallery modes (WGMs) with lower azimuthal mode number [m~(9-12)] in a circular cavity have been analyzed by using a two-dimensional finite-difference time domain method (2D FDTD) method employing Cartesian gridding and staircase approximation. The FDTD simulated Q-factors of these WGMs are generally lower than those of theoretical expectations. The variations of FDTD simulated Q-factors with spatial-calculation step size indicate that the FDTD results do not simply approximate to their theoretical expectation but jump unstably under the expectation. A loss estimation method similar to volume current method (VCM) is developed to explain the FDTD results and instability. This method calculates the “incoherent” scattering field of a scattering source under influence of cavity. Theoretical results coincident with the FDTD simulation are obtained, especially for transverse magnetic modes. As based on the developed method, the energy loss is affected by only a few harmonics of boundary fluctuation that cause the FDTD loss instability.
© 2009 Optical Society of America
Optics at Surfaces
Original Manuscript: April 6, 2009
Revised Manuscript: June 24, 2009
Manuscript Accepted: June 24, 2009
Published: August 4, 2009
Shan-Liang Qiu and Yong-Ping Li, "Q-factor instability and its explanation in the staircased FDTD simulation of high-Q circular cavity," J. Opt. Soc. Am. B 26, 1664-1674 (2009)