Quantum characteristics of stimulated Cherenkov radiation in dielectric-lined waveguide operating at optical wavelengths

Abstract

In this paper, a quantum mechanical model is proposed to describe the basic features of stimulated Cerenkov radiation in the small-signal gain regime. In this model, the electron is described by a wave packet with finite spreading length and the electron wave function is a solution of the Schrödinger equation. We show that the quantum effects are manifested when the spreading length of the electron wave is much longer than the electromagnetic (EM) wavelength such as in the optical wavelength range. The effect of electron relaxation due to Coulomb's collisions with neighboring electrons is introduced to characterize the damping of the vibration of the electron wave with time. When the relaxation effect is neglected, we prove that our essential results matches with other classical and quantum approaches based on different theoretical concepts.

A quantum mechanical analysis of Smith–Purcell free-electron lasers

“…The theoretical analysis was performed basing on the density matrix formalism which is a quantum statistical treatment [24]− [26]. In the theoretical model of [23,27,28], the electron is represented by an electron wave with a finite spreading length.…”

Space-charge effects and gain in Cherenkov free-electron lasers

“…The presence of the positive ions in (or around) the electron beam greatly influences the electron relaxation. In the current quantum mechanical analysis, the electron relaxation process is viewed as a phase distortion in the electron wave and represents the Coulomb repulsion forces between electrons [29][30][31].…”

On the small-signal theory of stimulated Cherenkov emission in dielectric-lined waveguides

“…Assuming for simplicity a device without a vacuum gap between the beam and the waveguide (b ¼ a), and using the continuity of the tangential component of the electric field (Ẽ ðIÞ z ÀẼ ðIIÞ z ¼ 0 at y ¼ a) with the help of Eqs. (9) and (15), we can get in the beam region in the limit of small perturbation of electrons (i.e., when x p ( x) T ðIIÞ z ðyÞ ¼ A 0 sinðp y aÞe Àk y ðyÀaÞ ; T ðIIÞ y ðyÞ ¼ ðÀjb=k y ÞA 0 sinðp y aÞe Àk y ðyÀaÞ : (20) In Eq. (20),…”

“…(9) and (15), we can get in the beam region in the limit of small perturbation of electrons (i.e., when x p ( x) T ðIIÞ z ðyÞ ¼ A 0 sinðp y aÞe Àk y ðyÀaÞ ; T ðIIÞ y ðyÞ ¼ ðÀjb=k y ÞA 0 sinðp y aÞe Àk y ðyÀaÞ : (20) In Eq. (20),…”