In this paper the possibility of cooperative effects in Cerenkov radiation will be discussed theoretically. A crude sketch is given of a possible capture of photons from a part of the rather broadband Cerenkov spectrum in a high quality resonator. We then introduce a classical Markoffian master equation for the system, accounting for Cerenkov emission as well as reabsorption. Both elementary quantum theory and classical electrodynamics provide us with the same formula for the transition rate of the stimulated Cerenkov process. At present we restrict ourselves to the macroscopic evolutions. The stationary electron distribution is calculated explicitly, as well as the equation governing the photon numbers. A non-equilibrium second order phase transition will be seen to occur for a critical value of the electronic input current density. Rough estimates are presented for threshold parameters. © 1977.In this paper the possibility of cooperative effects in Cerenkov radiation will be discussed theoretically. A crude sketch is given of a possible capture of photons from a part of the rather broadband Cerenkov spectrum in a high quality resonator. We then introduce a classical Markoffian master equation for the system, accounting for Cerenkov emission as well as reabsorption. Both elementary quantum theory and classical electrodynamics provide us with the same formula for the transition rate of the stimulated Cerenkov process. At present we restrict ourselves to the macroscopic evolutions. The stationary electron distribution is calculated explicitly, as well as the equation governing the photon numbers. A non-equilibrium second order phase transition will be seen to occur for a critical value of the electronic input current density. Rough estimates are presented for threshold parameters. © 1977.

Physica C SuperconductivityJan 1, 19760 citations

Cooperative Effects in Matter and Radiation

Charles M. Bowden, D. W. Howgate, H. Robl

Springer eBooksJan 1, 1977116 citations

Cerenkov radiation at the resonance frequency of an amplifying medium

Demosthenes Dialetis

The propagation of C\ifmmode \breve{}\else \u{}\fi{}erenkov radiation through a medium in which the population of two energy levels is inverted has been studied. The population inversion is represented by an imaginary part of the index of refraction of the medium at the resonance frequency. The resonant atoms are embedded in a host medium which has the shape of a slab of finite width $L$ and dielectric constant ${\ensuremath{\epsilon}}_{h}$, which is real and varies slowly for frequencies close to the resonance frequency of the embedded atoms. It is assumed that the host medium and the embedded atoms inside the slab behave as an isotropic noncrystalline medium. The slab is covered by a mirror on each of its surfaces and the medium outside the slab and the mirrors has dielectric constant ${\ensuremath{\epsilon}}_{1}$ (${\ensuremath{\epsilon}}_{1}=1$ for vacuum). While each individual charged particle can stimulate coherent emission by different resonant atoms, the phase of radiation which is due to different particles is uncorrelated. It is shown, however, that radiation of high intensity in the direction of the C\ifmmode \breve{}\else \u{}\fi{}erenkov cone can be produced by highcurrent particle beams. Exact expressions, in integral form, are obtained for the electromagnetic field everywhere in space. Using the method of stationary phase approximate expressions are derived for the C\ifmmode \breve{}\else \u{}\fi{}erenkov fields as well as the radiated energy in the foward and backward direction, far away from the slab.The propagation of C\ifmmode \breve{}\else \u{}\fi{}erenkov radiation through a medium in which the population of two energy levels is inverted has been studied. The population inversion is represented by an imaginary part of the index of refraction of the medium at the resonance frequency. The resonant atoms are embedded in a host medium which has the shape of a slab of finite width $L$ and dielectric constant ${\ensuremath{\epsilon}}_{h}$, which is real and varies slowly for frequencies close to the resonance frequency of the embedded atoms. It is assumed that the host medium and the embedded atoms inside the slab behave as an isotropic noncrystalline medium. The slab is covered by a mirror on each of its surfaces and the medium outside the slab and the mirrors has dielectric constant ${\ensuremath{\epsilon}}_{1}$ (${\ensuremath{\epsilon}}_{1}=1$ for vacuum). While each individual charged particle can stimulate coherent emission by different resonant atoms, the phase of radiation which is due to different particles is uncorrelated. It is shown, however, that radiation of high intensity in the direction of the C\ifmmode \breve{}\else \u{}\fi{}erenkov cone can be produced by highcurrent particle beams. Exact expressions, in integral form, are obtained for the electromagnetic field everywhere in space. Using the method of stationary phase approximate expressions are derived for the C\ifmmode \breve{}\else \u{}\fi{}erenkov fields as well as the radiated energy in the foward and backward direction, far away from the slab.

Physical Review ANov 1, 19781 citation

L

and dielectric constant ${\ensuremath{\epsilon}}_{h}$, which is real and varies slowly for frequencies close to the resonance frequency of the embedded atoms. It is assumed that the host medium and the embedded atoms inside the slab behave as an isotropic noncrystalline medium. The slab is covered by a mirror on each of its surfaces and the medium outside the slab and the mirrors has dielectric constant ${\ensuremath{\epsilon}}_{1}$ (${\ensuremath{\epsilon}}_{1}=1$ for vacuum). While each individual charged particle can stimulate coherent emission by different resonant atoms, the phase of radiation which is due to different particles is uncorrelated. It is shown, however, that radiation of high intensity in the direction of the C\ifmmode \breve{}\else \u{}\fi{}erenkov cone can be produced by highcurrent particle beams. Exact expressions, in integral form, are obtained for the electromagnetic field everywhere in space. Using the method of stationary phase approximate expressions are derived for the C\ifmmode \breve{}\else \u{}\fi{}erenkov fields as well as the radiated energy in the foward and backward direction, far away from the slab.