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Register a new userVarying the medium surrounding an optical resonator: An efficient and rigorous way to calculate its spectral changes
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Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications. Computationally, it presents, however, a fundamental challenge owing to the nature of the eigenstates of an open system lacking completeness outside it. We solve this challenge by making a linear transformation of Maxwells equations which maps perturbations of the surrounding medium onto effective perturbations within the system where the resonant states are complete. By treating such perturbations with the rigorous resonant state expansion, we find the modified modes of the system for arbitrary perturbations of the medium with any required accuracy. Numerically efficient single and few mode approximations are shown to be precise in practically important cases of, respectively, plasmonic nanoparticles and dielectric micro resonators.
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The interaction of a cavity with an external field is symmetric under time reversal. Thus, coupling to a resonator is most efficient when the incident light is the time reversed version of a free cavity decay, i.e. when it has a rising exponential shape matching the cavity lifetime. For light entering the cavity from only one side, the maximally achievable coupling efficiency is limited by the choice of the cavity mirrors reflectivities. Such an empty-cavity experiment serves also as a model system for single-photon single-atom absorption dynamics. We present experiments coupling exponentially rising pulses to a cavity system which allows for high coupling efficiencies. The influence of the time constant of the rising exponential is investigated as well as the effect of a finite pulse duration. We demonstrate coupling 94% of the incident TEM00 mode into the resonator.
The availability of a robust and efficient routine for calculating light curves of a finite source magnified due to bending its light by the gravitational field of an intervening binary lens is essential for determining the characteristics of planets in such microlensing events, as well as for modelling stellar lens binaries and resolving the brightness profile of the source star. However, the presence of extended caustics and the fact that the images of the source star cannot be determined analytically while their number depends on the source position (relative to the lens system), makes such a task difficult in general. Combining the advantages of several earlier approaches, an adaptive contouring algorithm is presented, which only relies on a small number of simple rules and operations on the adaptive search grid. By using the parametric representation of critical curves and caustics found by Erdl & Schneider (1993), seed solutions to the adaptive grid are found, which ensures that no images or holes are missed.
In this paper, an efficient algorithm to find the center of the biggest circle inscribed in a given polygon is described. This work was inspired by the publication of Daniel Garcia-Castellanos & Umberto Lombardo and their algorithm used to find a landmass poles of inaccessibility. Two more efficient algorithms were found, one of them only applicable when the problem can be described as a linear problem, like in the case of a convex polygon. Keywords: distance geometry, euclidean distance, inscribed circle, irregular polygon, algorithm, mathematical optimization, Monte Carlo, linear programming, maximin
Linking classical microwave electrical circuits to the optical telecommunication band is at the core of modern communication. Future quantum information networks will require coherent microwave-to-optical conversion to link electronic quantum processors and memories via low-loss optical telecommunication networks. Efficient conversion can be achieved with electro-optical modulators operating at the single microwave photon level. In the standard electro-optic modulation scheme this is impossible because both, up- and downconverted, sidebands are necessarily present. Here we demonstrate true single sideband up- or downconversion in a triply resonant whispering gallery mode resonator by explicitly addressing modes with asymmetric free spectral range. Compared to previous experiments, we show a three orders of magnitude improvement of the electro-optical conversion efficiency reaching 0.1% photon number conversion for a 10GHz microwave tone at 0.42mW of optical pump power. The presented scheme is fully compatible with existing superconducting 3D circuit quantum electrodynamics technology and can be used for non-classical state conversion and communication. Our conversion bandwidth is larger than 1MHz and not fundamentally limited.
In this work, we present the design and fabrication of a packaged whispering gallery mode (WGM) device based on an optical nanoantenna as the coupler and a glass microsphere as the resonator. The microspheres were fabricated from SiO$_2$ fiber or Er$^{3+}$-doped fiber, the latter creating a WGM laser with a threshold of 93 $mu$W at 1531 nm. The coupler-resonator WGM device is packaged in a glass capillary. The performance of the packaged microlaser is characterized, with lasing emission both excited in and collected from the WGM cavity via the nanoantenna. The packaged system provides isolation from environmental contamination, a small size, and unidirectional coupling while maintaining a high quality (Q-) factor ($sim$10$^8$). It opens up new possibilities for practical applications of WGM microdevices in a variety of fields such as low threshold lasers, filters, and sensors.
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