Manoukian, E.B.

Suranaree University of Technology Intellectual Repository

*Corresponding author.Physica B 269 (1999) 115}122C[ erenkov radiation in discontinuous media: a quantumview-pointE.B. Manoukian*, P. BantitadawitSchool of Physics, Suranaree University of Technology, Nakhon Ratchasima 30000, ThailandReceived 12 November 1998; accepted 6 January 1999AbstractThe photon propagator in the C[ erenkov radiation o! a charged particle moving in a dielectric slab immersed withinanother dielectric medium is derived. From the vacuum-to-vacuum transition amplitude, an explicit expression isobtained for the photon number density of given frequency of photons radiated per unit path length of the particle. Inparticular, it is shown that near threshold, the density behaves like sin h#rather than of the well known behavior of sin2 h#for uniformly extended media and may be of interest experimentally, where h#is the C[ erenkov-cone half-angle. Thederived expression is applied to the visible region. The analysis is given from a "eld-theory view-point. ( 1999Published by Elsevier Science B.V. All rights reserved.PACS: 41.60.Bq; 12.20.Ds; 11.10.!z; 03.50.!zKeywords: C[ herenkov radiation; Quantum electrodynamics; Field theory1. IntroductionThere has been much interest recently[1}4,14}16] in the classic C[ erenkov radiation [5,6]and its experimental veri"cation has been repeatedmany times over the years (cf. [7}9,17,18]). Its nu-merous applications in particle detection, in nu-clear and cosmic ray physics, in high-energyphysics and tests of properties of materials havebeen well documented (cf. [10,19,20]). The purposeof this work is to carry out a systematic analysis ofC[ erenkov radiation o! a charged particle movingin a plane homogeneous isotropic dielectric slab ofpermitivity i1with the latter immersed in anotherhomogeneous isotropic dielectric medium of per-mitivity i2'i1via the Green's function (propaga-tor) of the photon. With the physical problem inmind, a direct derivation is given for the latter andthen we use the vacuum-to-vacuum transitionamplitude (e.g., [1,11,14]) to obtain an explicit ex-pression for the number [1,12,14,21,22] density ofphotons radiated within a given frequency range asthe particle transverses a unit distance parallel tothe surface of the slab and, for simplicity, at mid-point. Of particular interest in our results are thatnear threshold for emission, the density behaveslike sin h#rather than of the well known behavior of0921-4526/99/$ - see front matter ( 1999 Published by Elsevier Science B.V. All rights reserved.PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 1 0 1 - 5

Cerenkov radiation in discontinuous media: a quantum view-point

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Cerenkov radiation in discontinuous media: a quantum view-point

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