![superluminal group velocity superluminal group velocity](https://aip.scitation.org/action/showOpenGraphArticleImage?doi=10.1063/1.4928893&id=images/medium/1.4928893.figures.f5.gif)
A pulse passing through the grating obtains hyperbolic spectral support with respect to the direction of the grating surface. The scheme for generating pulsed wave field with the hyperbolic spectral support by means of cylindrical grating can be generalized to a better one consisting of a conical diffraction grating and a conical mirror as depicted in Fig.
#SUPERLUMINAL GROUP VELOCITY FREE#
In the following we deduce the requirement for the distribution in the momentum space.Ī general solution to the free space scalar wave equation depends on 4 coordinates Ψ = Ψ( x, y, z, t). To generate a nonspreading wave packet one must be able to form certain specific spatial distribution of the plane wave constituents. It is instructive here to start with treatment of ultrawideband localized waves as superpositions of monochromatic plane waves with various frequencies and propagation directions. Section snippets Formation of the support of the spectrum Generalized optical scheme is introduced in Section 3 and studied in detail in Section 4 which presents also a numerical example. In Section 2 the basic idea of generating the suitable spatial distribution of the plane wave constituents by means of diffraction grating is introduced. In this paper we present a generalized optical scheme and analyze the formation of SpLW-s by means of an enhanced practical scheme.
#SUPERLUMINAL GROUP VELOCITY GENERATOR#
The simplest generator of a SpLW is cylindrical diffraction grating. The motivation of this paper is to elaborate methods for obtaining exact spatial distribution of plane wave constituents of superluminally propagating localized waves (SpLW). More complex LW called focus wave mode which belongs to family of luminal LW-s has been obtained by approximating the resulting angular dispersion curve of optical elements to that required for the LW. Despite a number of experiments have been carried out on LW-s in acoustics, optics and microwave domain in free space and in dispersive media, ,, , the task has been satisfactorily solved only for simplest superluminal pulses – the so-called X- or Bessel-X waves which can be generated from an ultrashort pulse by conical optics or annular slit and convergent lens. There are four families of LW-s distinguished by the shape of the support of the distribution of the plane waves in the momentum space and, correspondingly, by their superluminal, luminal or subluminal group velocity along the propagation axis.
![superluminal group velocity superluminal group velocity](https://slidetodoc.com/presentation_image/2e6dc10859af7470baa4868b5b662b33/image-22.jpg)
However, a real breakthrough here requires development of practical methods of generation of LW-s.ĭue to the sophisticated non-separable temporal and spatial dependencies in the wavefunctions of LW-s, in order to generate them in reality the first task is to form a specific quasi-singular spatial distribution of the plane wave constituents of the wave field. Optical LW-s are prospective in many areas of application – particle manipulation, trapping and acceleration, imaging, ultrafast spectroscopy, quantum optics and, especially, in nonlinear optics (see, e.g. Physical nature of the localized waves (LW) has been put to solid terms, ,, ,, , and number of different localized wave solutions to the scalar wave equation has been derived during the last quarter of century (see, and overviews, , ). Localized waves (also known as nondiffracting or undistorted progressive waves) are ultrawideband wave packets with both spatially and temporally highly localized instantaneous intensity distribution propagating without any spread or distortion in free space or in linear media.