Yan Kaganovsky

Wave analysis of Airy beams

The Airy beams are analyzed in order to provide a cogent physical explanation to their intriguing features which include weak diffraction, curved propagation trajectories in free-space, and self healing. The asymptotically exact analysis utilizes the method of uniform geometrical optics (UGO), and it is also verified via a uniform asymptotic evaluation of the Kirchhoff-Huygens integral. Both formulations are shown to fully agree with the exact Airy beam solution in the paraxial zone where the latter is valid, but they are also valid outside this zone. Specifically it is shown that the beam along the curved propagation trajectory is not generated by contributions from the main lobe in the aperture, i.e., it is not described by a local wave-dynamics along this trajectory. Actually, this beam is identified as a caustic of rays that emerge sideways from points in the initial aperture that are located far away from the main lobe. The field of these focusing rays, described here by the UGO, fully agrees with the Airy beam solution. These observations explain that the “weak-diffraction” and the “self healing” properties are generated, in fact, by a continuum of sideways contributions to the field. The uniform ray representation provides a systematic framework to synthesize aperture sources for other beam solutions with similar properties in uniform or in non-uniform media.

Nonparaxial wave analysis of three-dimensional Airy beams.

The three-dimensional Airy beam (AiB) is thoroughly explored from a wave-theory point of view. We utilize the exact spectral integral for the AiB to derive local ray-based solutions that do not suffer from the limitations of the conventional parabolic equation (PE) solution and are valid far beyond the paraxial zone and for longer ranges. The ray topology near the main lobe of the AiB delineates a hyperbolic umbilic catastrophe, consisting of a cusped double-layered caustic. In the far zone this caustic is deformed and the field loses its beam shape. The field in the vicinity of this caustic is described uniformly by a hyperbolic umbilic canonical integral, which is structured explicitly on the local geometry of the caustic. In order to accommodate the finite-energy AiB, we also modify the conventional canonical integral by adding a complex loss parameter. The canonical integral is calculated using a series expansion, and the results are used to identify the validity zone of the conventional PE solution. The analysis is performed within the framework of the nondispersive AiB where the aperture field is scaled with frequency such that the ray skeleton is frequency independent. This scaling enables an extension of the theory to the ultrawideband regime and ensures that the pulsed field propagates along the curved beam trajectory without dispersion, as will be demonstrated in a subsequent publication.

Airy pulsed beams.

The Airy beams (AiBs) have attracted a lot of attention recently because of their intriguing features, the most distinctive one is the propagation along curved trajectories in free-space. These beams are also weakly diffractive along their trajectories, i.e., they retain their structure and remain essentially diffraction-free for distances that are much longer than Gaussian beams with the same width. We have previously shown that the AiB is in fact a caustic of rays that radiate from the periphery of the aperture. In the present paper we derive ultra wideband (UWB) Airy Pulsed Beams (AiPBs), which are the extension of the AiBs into the time domain. We introduce a frequency scaling of the initial aperture field that renders the ray skeleton of the field, including the caustic, frequency independent, thus ensuring that all the frequency components propagate along the same curved trajectory, so that the AiPB does not disperse due to the wide frequency band. The resulting AiPBs preserve the intriguing features of the time-harmonic AiBs discussed above. Closed form solutions for the AiPBs are derived using the Spectral Theory of Transients (STT). The STT solution also explains how the strong pulsed field is formed in regions near the caustic, including its shadow side.

Analysis of Radiation From a Line Source in a Grounded Dielectric Slab Covered by a Metal Strip Grating

In this paper, we present a study of the radiation from a line source located inside a grounded dielectric slab covered by a metal strip grating. The array scanning method was applied to enable an efficient ldquounit cellrdquo formulation. The numerical solution was obtained with the use of the spectral method of moments. Both TM and TE cases were solved. The effects of the geometrical parameters on the propagation of guided modes and their excitation are studied.

Wave analysis of airy beams

The Airy beams are analyzed in order to provide a cogent physical explanation to their intriguing features which include weak diffraction, curved propagation trajectories in free-space, and self healing. The asymptotically exact analysis utilizes the method of uniform geometrical optics (UGO), and it is also verified via a uniform asymptotic evaluation of the Kirchhoff-Huygens integral. Both formulations are shown to fully agree with the exact Airy beam solution in the paraxial zone where the latter is valid, but they are also valid outside this zone. Specifically it is shown that the beam along the curved propagation trajectory is not generated by contributions from the main lobe in the aperture, i.e., it is not described by a local wave-dynamics along this trajectory. Actually, this beam is identified as a caustic of rays that emerge sideways from points in the initial aperture that are located far away from the main lobe. The field of these focusing rays, described here by the UGO, fully agrees with the Airy beam solution. These observations explain that the “weak-diffraction” and the “self healing” properties are generated, in fact, by a continuum of sideways contributions to the field. The uniform ray representation provides a systematic framework to synthesize aperture sources for other beam solutions with similar properties in uniform or in non-uniform media.

Spectral analysis of the Airy pulsed beam

The Airy beam (AiB) has attracted a lot of attention recently because of its intriguing features such as propagation along curved trajectories in free-space and the weak difraction. Here we derive a class of ultra wide band (UWB) Airy pulsed beams (AiPB) which are the extension of the AiB into the time domain. We introduce a frequency scaling that renders the ray skeleton of the feld frequency independent, thus insuring that the resulting AiPB is non-dispersive and preserves the intriguing features of the time-harmonic AiB. An exact closed form solution for the AiPB is derived using the spectral theory of transients (STT).

Pulsed beam propagation in plane stratified media: Asymptotically exact solutions

Closed form solutions for pulsed beam (PB) propagation in general inhomogeneous media can be obtained via paraxial wave tracking along the curved propagation trajectories. As a test bed to validate these solutions, we derive here an asymptotically exact solution for a PB in a general plane stratified medium. Such a solution can be derived via the complex source (CS) approach, but this requires an extension of the inhomogeneous wave-speed to the complex coordinates space. To circumvent this difficulty, we use a generalized plane-wave representation in which the CS field is used as the initial condition in the aperture plane. The spectral integral for the 3D PB field is then evaluated via the spectral theory of transients (STT) which expresses the field as a spectral integral of transient plane-waves that can be contracted to a simple and compact 1D integral.

Airy Pulsed Beams

The Airy beams (AiBs) have attracted a lot of attention recently because of their intriguing features, the most distinctive one is the propagation along curved trajectories in free-space. These beams are also weakly diffractive along their trajectories, i.e., they retain their structure and remain essentially diffraction-free for distances that are much longer than Gaussian beams with the same width. We have previously shown that the AiB is in fact a caustic of rays that radiate from the periphery of the aperture. In the present paper we derive ultra wideband (UWB) Airy Pulsed Beams (AiPBs), which are the extension of the AiBs into the time domain. We introduce a frequency scaling of the initial aperture field that renders the ray skeleton of the field, including the caustic, frequency independent, thus ensuring that all the frequency components propagate along the same curved trajectory, so that the AiPB does not disperse due to the wide frequency band. The resulting AiPBs preserve the intriguing features of the time-harmonic AiBs discussed above. Closed form solutions for the AiPBs are derived using the Spectral Theory of Transients (STT). The STT solution also explains how the strong pulsed field is formed in regions near the caustic, including its shadow side.

Analysis of radiation from a line source in a grounded dielectric slab covered by a metal strip grating

A metal strip grating over a grounded dielectric slab (MSG-GDS) is a well studied canonical structure with many applications to antennas. Although many studies on the dispersion characteristics of the MSG-GDS can be found in the literature, not much work can be found on the excitation of this structure by a localized source. It is therefore our aim to investigate the later. To this end we solve the 2D problem with a line source excitation.

Error analysis of the Gaussian beam summation method for ultra wide-band radiation in inhomogeneous medium

We address issues related to the accuracy of the beam summation method (BSM) for ultra wideband (UWB) radiation in inhomogeneous medium. In the BSM, the field is expanded using a lattice of beam propagators that are tracked locally in the medium. As a test bed for the accuracy of the BSM, we derive a solution for a beam in a general plane stratified medium which is valid beyond the paraxial regime. We then use it to derive bounds on the error away from the beam axis, and to obtain rules for optimizing the choice of the parameters in the BSM.