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The longitudinal component of radially polarized electric field in the focal region has attracted particular attention in the laser optics due to its several special characteristics, namely, the directional characteristic on propagation axis, strong intensity and small focal size when tightly focused with high-numerical-aperture optical system, which find applicationssuch as particle acceleration, molecule microscopy, material processing, and particle trapping. It has been proposed and experimentally demonstrated that paraboloidal reflector creates smaller focal size compared with lens.Comparatively little attention has been paid to its microwave version since, in microwave regime, the directional property in focal region has not been the main interest. Only very recently, after the introduction of planar slot antenna which can generate microwaves with focusing for near field scanning, the longitudinal component of radially polarized microwavewith the slot antenna has been experimentally investigated. However, the focusing of radially polarized microwave with paraboloidal reflector is much more versatile in applications as in the optical regime.The experimental observation of this longitudinal component is newly performed in this work with a configuration of two-paraboloidal-mirror system. This longitudinal field of microwave and the two-mirror system can also be exploited in some applications such as microwave scanning, microwave acceleration in free space, and creating Bessel-like beamwhich can be used in high resolution tomography, micro-manipulation in optical regime and long range communication in microwave regime. Two applications, microwave particle acceleration and quasi Bessel beam, are investigated in this work. A new method of ultratight focusing acceleration is proposed and a more precise analysis of quasi Bessel beam with variable cone angles is demonstrated.

A thought experiment is proposed to demonstrate the existence of a gravitational, vector Aharonov-Bohm effect. A connection is made between the gravitational, vector Aharonov-Bohm effect and the principle of local gauge invariance for nonrelativistic quantum matter interacting with weak gravitational fields. The compensating vector fields that are necessitated by this local gauge principle are shown to be incorporated by the DeWitt minimal coupling rule. The nonrelativistic Hamiltonian for weak, time-independent fields interacting with quantum matter is then extended to time-dependent fields, and applied to problem of the interaction of radiation with macroscopically coherent quantum systems, including the problem of gravitational radiation interacting with superconductors. But first we examine the interaction of EM radiation with superconductors in a parametric oscillator consisting of a superconducting wire placed at the center of a high Q superconducting cavity driven by pump microwaves. We find that the threshold for parametric oscillation for EM microwave generation is much lower for the separated configuration than the unseparated one, which then leads to an observable dynamical Casimir effect. We speculate that a separated parametric oscillator for generating coherent GR microwaves could also be built., 25 pages, 5 figures, YA80 conference (Chapman University, 2012)