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.
Supercontinuum generating sources, which incorporate a non-linear medium that can generate a wideband intensity spectrum under high-power excitation, are ideal for many applications of photonics such as spectroscopy and imaging. Supercontinuum generation using ultra-miniaturized devices is of great interest for on-chip imaging, on-chip measurement, and for future integrated photonic devices. In this study, semiconductor nano-antennas are proposed for ultra-broadband supercontinuum generation via analytical and numerical investigation of the electric field wave equation and the Lorentz dispersion model, incorporating semiconductor electron dynamics under optical excitation. It is shown that by a rapid modulation of the carrier injection rate for a semiconductor nano-antenna, one can generate an ultra-wideband supercontinuum that extends from the far-infrared (Far-IR) range to the deep-ultraviolet (Deep-UV) range for an infrared excitation of arbitrary intensity level. The modulation of the injection rate is achieved by high-intensity pulsed-pump irradiation of the nano-antenna, which has a fast nonradiative electron recombination mechanism that is on the order of sub-picoseconds. It is shown that when the pulse period of the pump irradiation is of the same order with the electron recombination time, rapid modulation of the free electron density occurs and electric energy accumulates in the nano-antenna, allowing for the generation of a broad supercontinuum. The numerical results are compared with the semiempirical second harmonic generation efficiency results for validation and a mean accuracy of 99.7% is observed. The aim of the study is to demonstrate that semiconductor nano-antennas can be employed to achieve superior supercontinuum generation performance at the nanoscale and the process can be programmed in an adaptive manner for continuous spectral shaping via tuning the pulse period of the pump irradiation.
Optical amplification of the input wave by mixing the pump wave within a nonlinear interaction medium offers high gain for a variety of applications. In real life studies, the interaction mediums which allow the optical amplification of the input wave have many resonance frequencies. However, the computational expense for tuning the pump frequency to yield the optical amplification of the input wave increases with the number of resonance frequencies within the interaction mediums. Here, we present a Fletcher-Reeves based algorithm for parametric amplification in micro-resonators having multiple resonance frequencies. Using our novel mathematical formulations, we obtained a gain of 4.7x10 7 for the input wave at 640 THz and a gain of 1.5x10 8 for the input wave at 100 THz within the micro-resonators. Moreover, the performance of our algorithm is verified by the well know mathematical expression, and we achieved more than 99% accuracy in computation of optical amplification. To our knowledge, this is the first study where Fletcher-Reeves algorithm is used for the parametric amplification. Our methodology can be accompanied to design optical parametric amplifiers for applications of high-speed optical communications, photonic circuits, and ultrafast lasers.
This paper computationally investigates the effect of the polarization decay rate (γ), and the peak resonance frequency (f0) on optical parametric amplification inside a low-loss micro resonator. It is found that, for lower values of the polarization decay rate and the peak resonance frequency, the magnitude of amplification can be significantly higher. However, it was also observed that beyond a certain threshold value of the polarization decay rate, the gain factor of the amplification sharply reduces to a negligible value. This suggests that the polarization decay rate of a material has a more profound effect on wave attenuation for the case of nonlinear wave propagation as compared to the case of linear wave propagation. This gain enhancing effect of the low polarization decay rate requires the resonator walls to be highly reflective. We found that below a certain value of the mean reflection coefficient of the resonator walls, the amplification becomes insignificant regardless of the value of the polarization decay rate. Numerical simulations are performed using the finite difference time domain method and the resulting gain variations are plotted and tabulated with respect to the polarization decay rate, peak resonance frequency, and the mean reflection coefficient of the micro resonator to illustrate this drastic gain enhancement.
Semiconductor optical amplifiers (SOAs) often exhibit pronounced phase noise owing to their inherently high linewidth enhancement factor (LWEF). The signal to noise ratio of a semiconductor optical amplifier is often decreased due to refractive index fluctuations in the gain medium causing distorted phase relationship between the generated photons, which is quantified by the LWEF. A simple and precise theoretical model that offers a prescription for minimizing the LWEF in SOAs is unavailable in the literature. In this study, we have developed an inclusive yet simple algorithmic model that aims to both represent the variation and to provide a strategy for minimizing the LWEF in multiple-quantum-well (MQW) based SOAs. The results of the presented model were verified via a reasonable agreement with experimental results. This study provides a theoretical description of how to adjust the linewidth enhancement factor through tuning of the most critical MQW SOA parameters in the design stage.
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