Pixelated phase masks and their synthesis

Parametric excitation of temperature oscillations in a high-Q dielectric microwave resonator in liquid helium vapor

“…In this work, we will employ equations from [8], using the same notations. The initial equations for describing oscillations in a dielectric resonator are the Maxwell equations and the heat conduction equation [13,14].…”

“…. [12], and the parametric excitation of temperature relaxation oscillations at the frequency Ω T with the appearance of the electromagnetic combination frequency ω s = ω p ±Ω a (the effect of electrothermal excitation of temperature oscillations) [8]. The existence of the effect of electrothermal excitation of temperature oscillations is caused by the presence of thermal feedback, when the effective temperature of a ferroelectric resonator is determined by the level of scattered power of forced electromagnetic oscillations whose amplitude, in turn, depends on the system tuning and, correspondingly, the effective temperature.…”

“…The electric displacement and the distribution functions of temperature fields in the resonator are represented as series in terms of normalized eigenfunctions of Helmholtz's equations and the Laplacian with homogeneous boundary conditions of the first kind [14]. In [8], shortened chains of oscillation equations were obtained, which represented the electrothermal processes in the resonator as interactions of a set of nonlinearly connected oscillators and temperature relaxation links. Information on the influence of spatial distributions of electric and temperature fields is comprised in integral coefficients.…”

“…The initial analysis showed that the best conditions for observing temperature oscillations exist in spherical dielectric microwave resonators made of virtual ferroelectrics SrTiO 3 and KTaO 3 at a liquid-helium temperature of 4.2 K. The threshold power of excitation of thermal oscillations should be rather low and amount to 10 −3 W or less [8]. It is the purpose of this paper to determine the threshold conditions for excitation of temperature oscillations in spherical ferroelectric resonators.…”

“…Electrothermal excitation of thermal oscillations is a result of the presence of thermal feedback: the effective temperature of a ferroelectric resonator is determined by the level of scattered power of the forced electromagnetic oscillations whose amplitude, in turn, depends on the tuning of the system and, specifically, on the effective temperature. The thermal feedback in parametric resonant oscillatory systems with a temperature-sensitive dielectric leads to the effects of multistability and self-modulation instability [8,9].…”