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Frequency combs, invented in 2000, have revolutionized frequency measurement and thereby impacted a host of applications. These include applications to military systems, medicine, environmental sensing, astrophysics, and basic physics. The sources have improved dramatically in the past decade, evolving from laboratory-size lasers to fiber lasers to microresonators on a chip. However, the theoretical input to these developments has been surprisingly small. The key problem in designing frequency combs is to determine where in the experimentally-adjustable parameter space stable solutions exist, to determine how to access them, and to determine the impact that noise has on them. While analytical approaches to answer these questions exist, computational tools to implement these approaches in realistic settings have been lacking. Our research has developed computational tools to address these issues, focusing on fiber laser and microresonator combs. In this talk, we will review our progress to date and discuss open problems. 

Abstract We have studied optical properties of single-layer and multi-fold nanoporous gold leaf (NPGL) metamaterials and observed highly unusual transmission spectra composed of two well-resolved peaks. We explain this phenomenon in terms of a surface plasmon absorption band positioned on the top of a broader transmission band, the latter being characteristic of both homogeneous “solid” and inhomogeneous “diluted” Au films. The transmission spectra of NPGL metamaterials were shown to be controlled by external dielectric environments, e.g. water and applied voltage in an electrochemical cell. This paves the road to numerous functionalities of the studied tunable and active metamaterials, including control of spontaneous emission, energy transfer and many others. 

We have studied emission kinetics of HITC laser dye on top of glass, smooth Au films, and randomly structured porous Au nanofoams. The observed concentration quenching of luminescence of highly concentrated dye on top of glass (energy transfer to acceptors) and the inhibition of the concentration quenching in vicinity of smooth Au films were in accord with our recent findings. Intriguingly, the emission kinetics recorded in different local spots of the Au nanofoam samples had a spread of the decay rates, which was large at low dye concentrations and became narrower with increase of the dye concentration. We infer that in different subvolumes of Au nanofoams, HITC molecules are coupled to the nanofoams weaker or stronger. The inhibition of the concentration quenching in Au nanofoams was stronger than on top of smooth Au films. This was true for all weakly and strongly coupled subvolumes contributing to the spread of the emission kinetics. The experimental observations were explained using theoretical model accounting for change in the Förster radius caused by the strong energy transfer to metal. 

We study soliton frequency combs generated in dual microresonators with different group velocity dispersion. We obtain stable bright and dark solitons at different pump amplitudes. 

We present a method to deterministically obtain broad bandwidth frequency combs in microresonators. These broadband frequency combs correspond to cnoidal waves in the limit when they can be considered soliton crystals or single solitons. The method relies on moving adiabatically through the (frequency detuning)×(pump amplitude) parameter space, while avoiding the chaotic regime. We consider in detail Si₃N₄microresonators with small or intermediate dimensions and an SiO₂microresonator with large dimensions, corresponding to prior experimental work. We also discuss the impact of thermal effects on the stable regions for the cnoidal waves. Their principal effect is to increase the detuning for all the stable regions, but they also skew the stable regions, since higher pump power corresponds to higher power and hence increased temperature and detuning. The change in the detuning is smaller for single solitons than it is for soliton crystals. Without temperature effects, the stable regions for single solitons and soliton crystals almost completely overlap. When thermal effects are included, the stable region for single solitons separates from the stable regions for the soliton crystals, explaining in part the effectiveness of backwards-detuning to obtaining single solitons.

 

We have studied optical properties of single and multi-fold nanoporous gold leaf metamaterials and demonstrated that they can be controlled with applied voltage and dielectric environment.