A unified spectral and temporal representation is introduced for nondiffracting waves. We consider a set of elementary broadband X waves that spans the commonly considered nondiffracting wave solutions. These basis X waves have a simple spectral representation that leads to expressions in closed algebraic form or, alternatively, in terms of hypergeometric functions. The span of the X waves is also closed with respect to all spatial and temporal derivatives and, consequently, they can be used to compose different types of waves with complex spectral and spatial properties. The unified description of Bessel-based nondiffracting waves is further extended to include singular Neumann and Hankel waves, or Y waves. We also discuss connections between the different known nondiffracting wave solutions, and their relations to the present unified approach.

We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal with arbitrary correlation functions. The formalism proves useful, e.g., in view of recent developments in full counting statistics of charge transfer, where detecting schemes have been proposed for measurement of frequency dependent spectra of higher moments. Some of these schemes are different from the well-known fictitious spin detector and therefore generally involve calculation of non-Keldysh-contourordered correlation functions. As an illustration of the approach we consider various third order correlation functions of current, including the usual third cumulant of current statistics. We investigate the frequency dependence of these correlation functions explicitly in the case of energy-independent scattering. The results can easily be generalized to the calculation of arbitrary nth order correlation functions, or to include the effect of interactions.

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We consider propagation of a two-level atom coupled to one electro-magnetic mode of a high-Q cavity. The atomic center-of-mass motion is treated quantum mechanically and we use a standing wave shape for the mode. The periodicity of the Hamiltonian leads to a spectrum consisting of bands and gaps, which is studied from a Floquet point of view. Based on the band theory we introduce a set of effective mass parameters that approximately describe the effect of the cavity on the atomic motion, with the emphasis on one associated with the group velocity and on another one that coincides with the conventional effective mass. Propagation of initially Gaussian wave packets is also studied using numerical simulations and the mass parameters extracted thereof are compared with those predicted by the Floquet theory. Scattering and transmission of the wave packet against the cavity are further analyzed, and the constraints for the effective mass approach to be valid are discussed in detail.Comment: 16 pages, 15 figures, accepted in Phys Rev

Holograms-diffractive elements-are designed and fabricated for shaping millimetre-wave radio fields. Methods for the synthesis of hologram elements are discussed and several beam shapes are tested: plane waves, radio-wave vortices and Bessel beams. Here we present an overview of the methods applied and results obtained with quasi-optical hologram techniques using both amplitude and phase holograms.