Complex resonance in Fresnel reflection of radiation pulses
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Complex Resonance in Fresnel Reflection of Radiation Pulses N. N. Rosanov1 Vavilov State Optical Institute, St. Petersburg, 199034 Russia St. Petersburg State University of Information Technologies, Mechanics, and Optics, St. Petersburg, 197101 Russia email: [email protected] Received October 27, 2009
Abstract—The Fresnel reflection of radiation pulses with an exponential temporal amplitude profile is ana lyzed. The conditions for the relevance of the concept of reflectance at a complex frequency, the imaginary part of which determined the rate of time variation of the amplitude, are specified. For the radiation pulses under study, we demonstrate a complex resonance, i.e., an increase in the magnitude of reflectance for the complex frequency of incident radiation (trailing edge of a pulse) that approaches the complex frequency of natural oscillations of oscillators in the medium. DOI: 10.1134/S106377611010002X 1
1. INTRODUCTION The resonance in oscillatory systems, i.e., an increase in the amplitude of induced oscillations of the system for the frequency of an external periodic action approaching the frequency of natural oscillations of the system, takes place both in micro and in mac roobjects and plays an important role in nature, sci ence, and engineering [1]. The increase in the ampli tude in the vicinity of resonance is limited by dissipa tion (damping) in the system [2]. Since oscillations are damped, the frequency of natural oscillations is complexvalued, which indi cates an exponential decrease with time of the ampli tude of oscillations of the oscillators forming the oscil latory system. For this reason, it is natural to expect the effect of complex resonance, i.e., an increase in the amplitude of induced oscillations of an oscillator when not only the real, but also the imaginary part of the complex frequency of the external action approach the real and imaginary parts of the natural frequency of the oscillator, respectively [3]. Complex resonance can be attained for an external action with a varying expo nential decrease in the amplitude with time. In com plex resonance, the amplitude of the response is not limited by the rate of damping of oscillators any longer. Complex resonance can apparently be demon strated easily for an electric circuit consisting of series connected capacitance, inductance, and resistance and subjected to the action of a pulse of an external electromotive force (emf) with controllable (real) fre quency and the rate of exponential decrease of the amplitude at the trailing edge of the pulse with time. The electrodynamics of continuous media, in which analytic properties of permittivity as a function of the
1 In the list of references, the author appears as Rozanov.
complex frequency are well known, is even more informative [4]. Complex resonance in the reflection of radiation from a medium with frequency dispersion of the Lorentz type was briefly analyzed in [3]. In this case, the conditions for the applicability of these con cepts as the coeffi
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