Phenomenon Of Parametric Amplification Research Articles

Parametric amplification and instability in time-periodic dielectric slabs.

We study the phenomenon of parametric amplification in the context of time-periodic dielectric slabs. These structures show particular promise inasmuch as they are capable of very large amplifications when illuminated by an electromagnetic wave of half the modulation frequency. Successive studies have corroborated this finding but none have yet been able to ascertain the nature of amplification in such devices. On top of that, some studies have raised speculations regarding the instability of a time-periodic slab which are off the mark. The problem lies in the poor understanding (or lack thereof) of the mathematical devices necessary to tackle such problems. We successfully carry out the tasks by tapping into the rich mathematical theory of Hill's equation. Specifically, we make use of the Folquet's theorem in its complete form which brings to light novel physical phenomena that the more prevalent simplified form fails to account for. Also, useful mathematical concepts such as coexistence are employed which to the best of our knowledge have not yet been applied in the field of time-varying optics. Our analytical method proves an effective means of assessing the amplifier's performance, e.g., estimating how long it takes for the device to reach steady state. We further delineate the link between amplification and instability and correct the misconceptions surrounding the subject by presenting a rigorous analysis of the instability problem in such structures.

Analytical study of two-frequency interaction between waves in a nonlinear radiating electromagnetic crystal

Two-frequency interaction between electromagnetic waves in a nonlinear radiating 2D electromagnetic crystal is analyzed under the conditions of the spatial synchronism of the forward wave at the fundamental frequency and the backward wave at the second harmonic of the fundamental frequency. The mathematical model of a radiating electromagnetic crystal is formulated as a system of differential equations. An approximate analytical solution describing the effect of generation of the second harmonic in the case of excitation of the analyzed structure by a free-space plane wave is obtained. The phenomenon of parametric amplification in the case of simultaneous excitation of the electromagnetic crystal by a signal from free space at the fundamental frequency and a planar-waveguide mode at the doubled frequency is analytically studied.

Numerical analysis of two-frequency interaction between waves in a nonlinear radiating electromagnetic crystal

Two-frequency interaction between electromagnetic waves in a 2D nonlinear radiating electromagnetic crystal under the conditions of the spatial synchronism of the forward wave at the fundamental frequency and the backward wave at the second harmonic of the fundamental frequency is analyzed. The mathematical model of a 2D radiating electromagnetic crystal is built. The effect of generation of the second harmonic in the case of excitation of this structure by a free-space plane wave is analyzed. The phenomenon of parametric amplification in the case of simultaneous excitation of the electromagnetic crystal by a signal with the fundamental frequency arriving from free space and a planar-waveguide mode with the doubled frequency is studied. The possibility of narrowing the radiation pattern of the structure by means of generation of the second harmonic is shown.

Exploring the parametric amplification phenomenon for energy harvesting

Due to inherent system nonlinearities, many vibratory excitation sources possess a frequency spectrum which contains energy components at multiple integers of the fundamental frequency of the source. In this paper, we theoretically explore the prospect of enhancing the transduction of a vibratory energy harvester (VEH) by utilizing the parametric amplification phenomenon to channel energy from one of these superharmonics, namely the one at twice the fundamental frequency, to a purely resistive load. Towards that end, we consider a piezoelectric cantilevered-type bimorph harvester and show that by tilting the axis of the beam through a proper angle with respect to the direction of excitation, it is possible to utilize a parametric pump to enhance the output power at the fundamental frequency. Percentage improvement in the output power depends on the excitation’s parameters and the mechanical damping ratio. It is observed that when the mechanical damping ratio is small, significant enhancement in the output power is attainable even when the magnitude of the superharmonic is small when compared to the fundamental frequency. Such findings reveal that, under certain conditions, parametric amplification can be utilized to enhance the output power of a VEH especially for microscale applications where the damping ratio can be easily controlled.

Parametric amplification of waves during gravitational collapse: a first investigation

We study the dynamical evolution of perturbations in the gravitational field of a collapsing fluid star. Specifically, we consider the initial value problem for a massless scalar field in a spacetime similar to the Oppenheimer–Snyder collapse model, and numerically evolve in time the relevant wave equation. Our main objective is to examine whether the phenomenon of parametric amplification, known to be responsible for the strong amplification of primordial perturbations in the expanding Universe, can efficiently operate during gravitational collapse. Although the time-varying gravitational field inside the star can, in principle, support such a process, we nevertheless find that the perturbing field escapes from the star too early for amplification to become significant. To put an upper limit on the efficiency of the amplification mechanism (for a scalar field) we furthermore consider the case of perturbations trapped inside the star for the entire duration of the collapse. In this extreme case, the field energy is typically amplified at the level ∼1% when the star is about to cross its Schwarzschild radius. Significant amplification is observed at later stages when the star has an even smaller radius. Therefore, the conclusion emerging from our simple model is that parametric amplification is unlikely to be of significance during gravitational collapse. Further study, based on more realistic collapse models, is required in order to fully assess the astrophysical importance of parametric amplification.

Cosmological reheating and self-interacting final state bosons

We consider inflaton decay to final state bosons with self-interactions of moderate strength. We find that such final state self-interactions qualitatively alter the reheat dynamics. In the case of narrow-band resonance decay, where a quantitative analysis is possible, we show that these final state interactions regulate the decay rate. The phenomenon of parametric amplification is then effectively suppressed, and does not drastically enhance the decay rate and reheat the temperature. Detailed applications of our results to realistic classes of inflationary models will be considered elsewhere.

On nonlinear parametric amplification of Rayleigh waves

The phenomenon of parametric amplification of a weak Rayleigh surface acoustic wave of frequency ω 0 by a strong pump Rayleigh wave of frequency 2ω 0 is considered using the system of nonlinear evolution equations derived by Parker [Int. J. Eng. Sci. 26 (1988) 59] and modified to take into account the usual material dissipation and additional selective damping of certain wave harmonics. It is shown that introducing selective dissipation on both the third and fourth harmonics results in an essential increase of parametric amplification.

Parametric amplification of ion-acoustic and Alfven waves

The phenomenon of parametric amplification of propagating ion-acoustic wave and Alfven wave in a finite resistivity and low beta plasma, due to a modulated magnetic field, has been investigated using single mode theory. It is found that the ion-acoustic wave is not amplified in such a medium. For the Alfven waves it is found that the expression for growth rate and the threshold modulation are the same for high resistivity plasma as those for a low resistivity plasma.

Amplitude Modulation of a Forced System by Parameter Variation

Classical (primary) parametric amplification is reviewed. This phenomenon is known to occur for a parametric variation with a frequency of twice that of a harmonic input in the neighborhood of a system’s characteristic frequency. A higher-order phenomenon that is identified as secondary parametric amplification (or attenuation), is discussed in detail and solutions related to Mathieu’s equation are presented. Its occurrence is characterized by a frequency of the parametric variation that is of the order of 2α/n (where n = 1, 2, 3, …, and α is the undamped characteristic frequency of the system) and a harmonic input of a much lower frequency. The amplification (or attenuation) resulting from the secondary parametric amplification phenomenon is manifested in an overmodulated response that must be low-pass filtered to recover the desired low frequency response.