国際交流・公開研究セミナーのお知らせ(電気:時間領域モデリング分野)
講 演 者:Dr. Nataliya K. Sakhnenko, Associate Professor
Department of Mathematics, Kharkov National University of Radio Electronics, Kharkov, Ukraine
講演題目:TIME DOMAIN MODELLING OF TRANSIENTS IN MICROCAVITIES
Sakhnenko博士(ウクライナ,ハリコフ国立電波エレクトロニクス大学准教授)が来日される機会に、最近その応用が注目されている時間領域モデリングに関してご講演をお願いしました。是非ご参集ください。
アブストラクト:
The strong interest in circular optoelectronic components, e.g. whispering gallery mode (WGM) resonators, is due to their wide range of potential applications, including low-threshold micro-lasers and bio-sensors. Optically active and tunable devices are of great importance for all-optical data processing and switching purposes. For these applications accurate time domain modelling is of great importance. Besides, photonic dynamic systems with time-varying material properties demonstrate features that can not be achieved in static ones. Permittivity modulation within micro-cavities has been shown to exhibit new physical effects associated with the stopping and time reversal of light pulses. Modulation of permittivity in photonic crystals leads to changes of light colour and reversed Doppler shifts.
As known, for thin dielectric resonators full 3-D electromagnetic problems can be approximately reduced to the 2-D problems in the median plane of the resonator using the effective refractive index concept. We present a computationally straightforward and efficient method for obtaining the transient fields due to pulse excitation of the 2-D stand-alone and optically coupled WGM resonators or time variation of material properties. The method is based on obtaining an analytical solution of the Maxwell equations in the Laplace transform domain and recovering of the time domain fields by virtue of the computation of the inverse Laplace transform via the residue evaluation at singular points and a rapidly convergent integral along the branch cut in the complex plane. This approach guarantees accurate back transformation of the functions and allows us to gain understanding and insight into the fundamental processes occurring in microcavities.
Theoretical studies of the motion of optical pulse travelling inside and scattering out of a circular dielectric resonator will be presented. Using the pulse of sufficiently long duration with a spectrum narrow enough leads to the observation of the transient field beating. The transient effect of a repetition in the wave shape after a few round-trips occurs. This method provides detailed information about the process of propagation of optical pulses through the system of coupled resonators as well.
In general, there are two aspects in the consideration of the time domain problems that concern (i) time non-harmonic fields, and (ii) time-varying materials. The approach above gives accurate results for both kinds of problems and leads to understanding of rich variety of physical phenomena. What is also important is the ability of the method to provide detailed information on the electromagnetic field evolution in the ‘early’ time of transients as well as in the ‘late’ time intervals.
In practice, the temporal change in the material refractive index can be realized by varying the input signal in a nonlinear structure; by voltage control; by focused laser beam as a local heat source or else by a free-carrier plasma injection. It will be shown that a variation in time of the refractive index in the cavity can be exploited to achieve a fast frequency shift of the WGM that does not depend on the initial light intensity and is proportional to the fractional change of the refractive index.
The frequency shift can be enhanced in a linear chain of resonators with time varying permittivity. The optical energy transport between the WGM micro-resonators in a chain and the sensitivity of such a transport to the material time variation of individual resonator will be discussed.
This approach is valid for a wide range of materials (e.g. transient plasma) and different geometries. Numerical results will be presented.
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