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

In this paper, a quantum mechanical model is proposed to describe the basic features of stimulated Cherenkov radiation in the small-signal low-gain regime. In this model, the electron is described by a wavepacket 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 match with other classical and quantum approaches based on different theoretical concepts.