Controlled transition between parametric and Raman oscillations in ultrahigh-Q silica toroidal microcavities

A controllable and reversible transition between parametric and Raman oscillations in an ultrahigh-Q silica toroidal microcavity is experimentally demonstrated and theoretically analyzed. By direct change of cavity loading and indirect adjustment of frequency detuning, parametric and/or Raman oscillation can be accessed selectively without modification of cavity geometry in a toroidal microcavity with a large enough aspect ratio. Based on an effective cavity gain theory, this transition is analyzed in terms of cavity loading and frequency detuning leading to a better understanding of the combined effects of parametric and Raman processes in silica microcavities

Perturbative analytic theory of an ultrahigh-Q toroidal microcavity

A perturbation theoretic approach is proposed as an efficient characterization tool for a tapered fiber coupled ultrahigh-quality factor (Q) toroidal microcavity with a small inverse aspect ratio. The Helmholtz equation with an assumption of quasi-TE/TM modes in local toroidal coordinates is solved via a power series expansion in terms of the inverse aspect ratio and the expanded eigenmode solutions are further manipulated iteratively to generate various characteristic metrics of the ultrahigh-Q toroidal microcavity coupled to a tapered fiber waveguide. Resonance wavelengths, free spectral ranges, cavity mode volumes, phase-matching conditions, and radiative Q factors are derived along with a mode characterization given by a characteristic equation. Calculated results are in excellent agreement with full vectorial finite-element simulations. The results are useful as a shortcut to avoid full numerical simulation, and also render intuitive insight into the modal properties of toroidal microcavities

Ellsberg Paradox and Second-order Preference Theories on Ambiguity: Some New Experimental Evidence

We study the two-color problem by Ellsberg (1961) with the modification that the decision maker draws twice with replacement and a different color wins in each draw. The 50-50 risky urn turns out to have the highest risk conceivable among all prospects including the ambiguous one, while all feasible color distributions are mean-preserving spreads to one another. We show that the well-known second-order sophisticated theories like MEU, CEU, and REU as well as Savage’s first-order theory of SEU share the same predictions in our design, for any first-order risk attitude. Yet, we observe that substantial numbers of subjects violate the theory predictions even in this simple design.Ellsberg paradox, Ambiguity, Second-order risk, Second-order preference theory, Experiment

Dynamical thermal behavior and thermal self-stability of microcavities

As stability and continuous operation are important for almost any use of a microcavity, we demonstrate here experimentally and theoretically a self-stable equilibrium solution for a pump-microcavity system. In this stable equilibrium, intensity- and wavelength-perturbations cause a small thermal resonant-drift that is enough to compensate for the perturbation (noises); consequently the cavity stays warm and loaded as perturbations are self compensated. We also compare here, our theoretical prediction for the thermal line broadening (and for the wavelength hysteretic response) to experimental results