Formation of optical fields of stimulated Raman scattering with a resolution beyond the Abbe diffraction limit by spherical microlens cavities with whispering gallery modes: Near-field approximation

We consider a significant lowering of the threshold of stimulated Raman scattering in solid fused silica spherical microlenses cavities that is caused by an increase in the integral overlap factor of whispering gallery modes. The structure of focal regions of a microlens is shown to have the shape of honeycombs, forming a photonic crystal or a photonic nanojet. We show that, at comparatively small numerical apertures NA = 0.7–0.8, which correspond to hemispherical microlenses, a spherical microlens cavity exhibits the possibility of focusing laser radiation beyond the Abbe diffraction limit. This enables the possibility of wide practical applications of microspheres as a focusing element the resolving power of which exceeds the Abbe diffraction limit in the near field. The whispering-gallery-mode spherical microlens cavity makes it possible to perform laser generation with a duration of a coherent pulse in the subfemtosecond range and to form a subwavelength focal region of the near field. This ensures the possibility of detecting single molecules of a substance in the subwavelength range in the near field and can be used to increase the sensitivity of intracavity spectroscopy methods and as microlasers for excitation of molecules in metal molecular nanoswitches and semiconductor heterostructures. From an array of microlens cavities, metamaterials with a negative refractive index can be formed.     

Electrothermal automodulation in incipient ferroelectric whispering-gallery microwave resonators at 4.2 K

Threshold conditions for electrothermal automodulation instability in high-Q ferroelectric microwave cryogenic resonators operating in the two-mode regime are investigated. The dependence of the electrothermal automodulation frequency on the numbers of interacting modes for different combinations of thermal modes and surface electromagnetic whispering-gallery modes is presented. The threshold power exciting the electrothermal automodulation of the oscillation of the partial mode electromagnetic amplitudes is compared with the threshold power of strictional parametric excitation of acoustic oscillations in the resonator. It is shown that the electrothermal automodulation in the two-mode regime may take place at an excitation power from 10 to 120 μW depending on the combination of interacting thermal and electromagnetic surface modes. Calculated threshold powers are low, which makes it possible to apply the electrothermal automodulation for improving the sensitivity of resonance bolometers and distributed microwave antennas with basic elements built around nonlinear microwave resonators. In addition, the electrothermal automodulation could be applied in developing novel microwave metamaterials. Nonlinear microwave whispering-gallery cryogenic resonators can be used as elements increasing the sensitivity of EPR spectroscopy methods.     

Electron transport in a double quantum dot governed by a nuclear magnetic field

We investigate theoretically electron transfer in a double dot in a situation where spin blockade is lifted by nuclear magnetic field: this has been recently achieved in experiment [F. Koppens, Science 309, 1346 (2005)]. We show that for a given realization of nuclear magnetic field spin blockade can be restored by tuning external magnetic field; this may be useful for quantum manipulation of the device.     

THE MITRA‐WAN FORESTRY MODEL: A DISCRETE‐TIME OPTIMAL CONTROL PROBLEM

In this paper, we present some new properties of the Mitra‐Wan forestry model written as a discrete‐time optimal control problem. For this problem, the set of stationary states is characterized. For the optimal long‐run management, we consider the following optimality criteria: average optimality, good control policies, bias optimality, and overtaking optimality. We establish relationships between these criteria and show that the value of average optimal policies is constant and equals the value in the optimal stationary state.     

Efficient magnetization reversal with noisy currents

We propose to accelerate reversal of the ferromagnetic order parameter in spin valves by electronic noise. By solving the stochastic equations of motion we show that the current-induced magnetization switching time is drastically reduced by a modest level of externally generated current (voltage) noise. This also leads to a significantly lower power consumption for the switching process.