[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

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Table Of Integrals Series And Products

Microwave photonics with superconducting quantum circuits

In the past 20 years, impressive progress has been made both experimentally and theoretically in superconducting quantum circuits, which provide a platform for manipulating microwave photons. This emerging field of superconducting quantum microwave circuits has been driven by many new interesting phenomena in microwave photonics and quantum information processing. For instance, the interaction between superconducting quantum circuits and single microwave photons can reach the regimes of strong, ultra-strong, and even deep-strong coupling. Many higher-order effects, unusual and less familiar in traditional cavity quantum electrodynamics with natural atoms, have been experimentally observed, e.g., giant Kerr effects, multi-photon processes, and single-atom induced bistability of microwave photons. These developments may lead to improved understanding of the counterintuitive properties of quantum mechanics, and speed up applications ranging from microwave photonics to superconducting quantum information processing. In this article, we review experimental and theoretical progress in microwave photonics with superconducting quantum circuits. We hope that this global review can provide a useful roadmap for this rapidly developing field.

Nonlinear dynamics of the Frenkel-Kontorova model

Currently, cylindrical beams with radial or azimuthal polarization are being used successfully for the optical manipulation of micro- and nano-particles as well as in microscopy, lithography, nonlinear optics, materials processing, and telecommunication applications. The creation of these laser beams is carried out using segmented polarizing plates, subwavelength gratings, interference, or light modulators. Here, we demonstrate the conversion of cylindrically polarized laser beams from a radial to an azimuthal polarization, or vice versa, by introducing a higher-order vortex phase singularity. To simultaneously generate several vortex phase singularities of different orders, we utilized a multi-order diffractive optical element. Both the theoretical and the experimental results regarding the radiation transmitted through the diffractive optical element show that increasing the order of the phase singularity leads to more efficient conversation of the polarization from radial to azimuthal. This demonstrates a close connection between the polarization and phase states of electromagnetic beams, which has important implications in many optical experiments.

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Polarization conversion when focusing cylindrically polarized vortex beams.

We have investigated macroscopic quantum tunneling in Bi(2)Sr(2)CaCu(2)O(8 + delta) intrinsic Josephson junctions at millikelvin temperatures using microwave irradiation. Measurements show that the escape rate for uniformly switching stacks of Nu junctions is about Nu(2) times higher than that of a single junction having the same plasma frequency. We argue that this gigantic enhancement of the macroscopic quantum tunneling rate in stacks is boosted by current fluctuations which occur in the series array of junctions loaded by the impedance of the environment.

Enhanced macroscopic quantum tunneling in Bi2Sr2CaCu2O8 + delta intrinsic Josephson-junction stacks.

This paper uses the integral Rayleigh–Sommerfeld transformation of the first type and an expansion in plane waves to investigate the nonparaxial phenomena that appear when optical elements are combined (using the lensacon as an example) even with a low numerical aperture. The contribution of various components of the vector field when high-aperture optical elements are used in tandem was also taken into account. Based on our studies, it is shown that, in the case of radial polarization, supplementing a lens with an axicon makes it possible to substantially strengthen the contribution of the longitudinal component and to overcome the diffraction limit in the overall intensity by a method that is an alternative to using an annular stop.

The lensacon: nonparaxial effects

Airy beams possess a number of properties that ensure their multifunction and high relevance in many applications. This fact stimulates scientists to search for new modifications and generalizations of classical Airy beams. Several generalizations of the Airy functions are known, on the basis of both the modification of the differential equation and the variations in the integral representation. In this paper we propose and investigate a new type of Airy beams—fractional Airy beams (FrAiB). They are based on the generalization of the integral representation and are close to the Olver functions, but we are considering a wider range of the power-law dependence of the argument, including non-integer (fractional) values of the power. A theoretical and numerical analysis of the FrAiBs, as well as their symmetrized variants, was performed. The properties of FrAiBs, such as being non-diffracting and autofocusing, were numerically investigated by means of the fractional Fourier transform, describing the beam transformations by paraxial optical systems. We believe that new beams can be useful for laser manipulation techniques and lensless laser patterning.

Fractional Airy beams.

We report the formation of a negative energy flux in the case of tight focusing of an arbitrary-order radially polarized annular beam. We consider not only the longitudinal component of the Poynting vector (energy flux density) and the region of its negative values, but also the local inverse energy flux as an integral characteristic over the region of negative values. Theoretically, the Richards-Wolf formulas in the Debye approximation are used to maximize the negative value of the energy flux density on the optical axis in the focal region for the second-order radial polarization ($m=2$). In this case, the local inverse energy flux, an integral characteristic in the bulk region of negative values, increases with increasing radial polarization order, i.e., for $mg2$. Jones matrices are employed to show that the result obtained will be valid for azimuthal polarization, as well as for a circularly polarized vortex beam. The results of numerical simulation are in good agreement with theoretical calculations. In addition, taking into account the approximate nature of the Richards-Wolf formulas, we also additionally model the tight focusing of a circular beam based on the solution of Maxwell's equation using the finite element method. It is shown that the local inverse energy flux in the case of the second-order radial polarization will be 1.5 times less than that in the case of the third-order radial polarization. In turn, the use of the fourth-order radial polarization makes it possible to increase the local inverse energy flux by a factor of 2.

Andrey V. Ustinov

Papers

Polarization conversion when focusing cylindrically polarized vortex beams.

Enhanced macroscopic quantum tunneling in Bi2Sr2CaCu2O8 + delta intrinsic Josephson-junction stacks.

The lensacon: nonparaxial effects

Fractional Airy beams.

Inverse energy flux of focused radially polarized optical beams