Super-Gain Optical Parametric Amplification in Dielectric Micro-Resonators via BFGS Algorithm-Based Non-Linear Programming

Abstract

The goal of this paper is to show that super-gain optical parametric amplification can be achieved even in a small micro-resonator using high-intensity ultrashort pump waves, provided that the frequencies of the ultrashort pulses are tuned to maximize the intracavity magnitude of the wave to be amplified, which we call the stimulus wave. In order to accomplish this, we have performed a dispersion analysis via computational modeling of the electric polarization density in terms of the non-linear electron cloud motion and we have concurrently solved the electric polarization density and the wave equation for the electric field. Based on a series of non-linear programming-integrated finite difference time-domain simulations, we have identified the optimal pump wave frequencies that simultaneously maximize the stored electric energy density and the polarization density inside a micro-resonator by using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization algorithm. When the intracavity energy and the polarization density (which acts as an energy coupling coefficient) are simultaneously high, an input wave can be strongly amplified by efficiently drawing energy from a highly energized cavity. Therefore, we propose that micrometer-scale achievement of super-gain optical parametric amplification is possible in a micro-resonator via high-intensity ultrashort “pump wave” pulses, by determining the optimal frequencies that concurrently maximize the stored electric energy density and the polarization density in a dielectric interaction medium.

High-Fidelity Harmonic Generation in Optical Micro-Resonators Using BFGS Algorithm

“…The intended description for the cost function can be stated as where is the bandwidth around the target frequency. A certain target harmonic can be programmed to be maximized because the process of nonlinear wave mixing generates many new harmonics as a result of supercontinuum generation [ 20 , 21 , 22 , 23 , 24 , 25 , 26 ], which arise from high stored energy. What we intended to do is to program the microcavity to concentrate the supercontinuum spectral density around the target frequency.…”

“…A computational study that is based on maximizing the harmonic generation efficiency via a nonlinear programming algorithm is lacking [ 6 , 7 , 8 ]. Experimental studies usually focus on finding new techniques to increase the second and the third harmonic generation efficiency and there are relatively few experimental studies that have demonstrated a minor increase in the harmonic generation or conversion efficiency via certain experimental configurations and setups [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 ]. Some computational studies have focused on increasing the computation efficiency of harmonic generation problems rather than proving that the harmonic generation efficiency itself can actually be increased.…”

“…These include the studies mentioned in [ 6 , 7 , 8 ], which have managed to increase the efficiency of the nonlinear Finite-Difference-Time-Domain (FDTD) method by decreasing the dispersion error. The current literature of harmonic generation via nonlinear wave mixing is dominated by increasing the efficiency of the second/third harmonic generation rather than increasing the efficiency of an arbitrary harmonic [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 ]. There are currently no known techniques in the literature that reported a high-efficiency in the microscale for an arbitrary harmonic generation (not necessarily the second harmonic) under monochromatic optical excitation [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 30 , 31 , 32 , 33 , …”

Design of Ultra-High Gain Optical Micro-Amplifiers via Smart Non-Linear Wave Mixing

“…Optical parametric amplification via nonlinear wave mixing has been extensively studied [1][2][3][4][5][6][7] and can be used for a variety of applications such as photonic integrated circuits 8 , high-speed optical comunications 9 , piezoelectric MEMS device 10 , and development of powerful ultrafast lasers 11 . Optical parametric amplification is achieved via mixing a non-linearity inducing high-intensity pump wave with an input wave of low intensity, during which the low-intensity input wave gets amplified by absorbing energy from the high-intensity pump wave 12,13 .…”

“…Optical parametric amplification is mostly studied experimentally 10, [19][20][21][22] . There are a few computational studies where optimization of pump frequency is investigated 5,6,14,23 , but the interaction mediums have a single resonance frequency. However, in real applications, the interaction mediums of nonlinear wave mixers have multiple resonance frequencies which causes high computation cost.…”