Recently, the use of Bessel beams in evaluating the possibility of using them for a new generation of GPR (ground penetrating radar) systems has been considered. Therefore, an analysis of the propagation of Bessel beam in conducting media is worthwhile. We present here an analysis of this type. Specifically, for normal incidence we analyze the propagation of a Bessel beam coming from a perfect dielectric and impinging on a conducting medium, i.e. the propagation of a Bessel beam generated by refracted inhomogeneous waves. The remarkable and unexpected result is that the incident Bessel beam does not change its shape even when propagating in the conducting medium.
Recently, the use of Bessel beams in evaluating the possibility of using them for a new generation of GPR (ground penetrating radar) systems has been considered. Therefore, an analysis of the propagation of Bessel beam in conducting media is worthwhile. We present here an analysis of this type. Specifically, for normal incidence we analyze the propagation of a Bessel beam coming from a perfect dielectric and impinging on a conducting medium, i.e. the propagation of a Bessel beam generated by refracted inhomogeneous waves. The remarkable and unexpected result is that the incident Bessel beam do…
The aim of this paper is the study of the propagation of a Bessel beam through two absorbing layers, limited by two different half-spaces. Our approach will be based on the scalar analysis, since this analysis was proved to be an excellent approximation of the vectorial field which describes a Bessel beam.
Collapse of a Gaussian beam in self-focusing Kerr media arrested by nonlinear losses may lead to the spontaneous formation of a quasi-stationary nonlinear unbalanced Bessel beam with finite energy, which can propagate without significant distortion over tens of diffraction lengths, and without peak intensity attenuation while the beam power is drastically diminishing.
Nonlinear Bessel beams in self-defocusing media are found to be the natural, non-diffracting background where vortex solitons can be nested, interact and survive for propagation distances that are one order of magnitude larger than in the usual Gaussian or super-Gaussian backgrounds. The dynamics of the vortex solitons approaches that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form…
In recent experiments, localized and stationary pulses have been generated in second-order nonlinear processes with femtosecond pulses, whose asymptotic features relate with those of nondiffracting and nondispersing polychromatic Bessel beams in linear dispersive media. We investigate on the nature of these linear waves, and show that they can be identified with the X-shaped (O-shaped) modes of the hyperbolic (elliptic) wave equation in media with normal (anomalous) dispersion. Depending on the relative strengths of mode phase mismatch, group velocity mismatch with respect to a plane pulse, an…
We report the existence of persistently rotating azimuthons in media with self-focusing Kerr and absorption nonlinearities. The nonlinear loss is balanced by power influx from the peripheral reservoir stored in slowly decaying tails of the azimuthons. These modes are excited by a superposition of two Bessel beams with opposite vorticities, $\pm s$, and slightly different conicities. The excited azimuthon exhibits opposite vorticity in its center to that of the input Bessel-beam superposition due to spontaneous inversion of the topological charge in the course of the azimuthon formation. Unlike…
Pulsed Bessel beams of light propagating in free-space experience diffraction effects that resemble those of anomalous dispersion on pulse propagation. It is then shown that a pulsed Bessel beam in a normally dispersive material can remain diffraction- and dispersion-free due to mutual cancellation of diffraction and group velocity dispersion. The size of the Bessel transversal profile for localized transmission is determined by the dispersive properties of the material at the pulse carrier frequency.
In nonlinear Kerr media at intensities such that multiphoton absorption is significant, a vortex of topological charge m in the center of a high-order nonlinear Bessel beam (NBB) can be stable and subsist endlessly. We show that the m-charged NBB is not only stable but is formed spontaneously from any other n-charged NBB and N "foreign" vortices of total charge s randomly nested in the beam cross section if n + s = m. All nested vortices merge in the center of the original NBB, which undergoes a mode conversion to the NBB that preserves the topological charge and the inward-directed power curr…
Assuming a non-paraxial propagation operator, we study the propagation of an electromagnetic field with an arbitrary initial condition in a quadratic GRIN medium. We show that at certain specific periodic distances, the propagated field is given by the fractional Fourier transform of a superposition of the initial field and of a reflected version of it. We also prove that for particular wavelengths, there is a revival and a splitting of the initial field. We apply this results, first to an initial field given by a Bessel function and show that it splits into two generalized Bessel functions, a…
We describe nonlinear Bessel vortex beams as localized and stationary solutions with embedded vorticity to the nonlinear Schrödinger equation with a dissipative term that accounts for the multi-photon absorption processes taking place at high enough powers in common optical media. In these beams, power and orbital angular momentum are permanently transferred to matter in the inner, nonlinear rings, at the same time that they are refueled by spiral inward currents of energy and angular momentum coming from the outer linear rings, acting as an intrinsic reservoir. Unlike vortex solitons and diss…
Nonlinear losses accompanying Kerr self-focusing substantially impacts the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D+1 nonlinear Schrodinger equation which are stable against radial collapse. These are featured by linear conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as strong attractor for the self-focusing dynamics in Kerr media.
We report on the stationary and robust propagation of light beams with rather arbitrary and controllable intensity and dissipation transverse patterns in self-focusing Kerr media with nonlinear absorption. When nonlinear absorption is due to multi-photon ionization at high beam powers in transparent media such as glasses or air, these beams can generate multiple plasma channels with tailored geometries. Their nature and spatial characteristics are discussed in detail, as well as the laws determining their spontaneous formation from coherent superpositions of Bessel beams of different amplitude…
General properties of linear propagation of discretized light in homogeneous and curved waveguide arrays are comprehensively investigated and compared to those of paraxial diffraction in continuous media. In particular, general laws describing beam spreading, beam decay and discrete far-field patterns in homogeneous arrays are derived using the method of moments and the steepest descend method. In curved arrays, the method of moments is extended to describe evolution of global beam parameters. A family of beams which propagate in curved arrays maintaining their functional shape -referred to as…
In this work, in terms of suitable superpositions of equal-frequency Bessel beams, we develop a theoretical method to obtain nondiffractive beams in absorbing media (weakly conductive) capable to resist the loss effects for long distances.
An integrated super resolution THz 3D imaging system based on a linear nonlocal achromatic freeform Bessel beam lens and high power oscillator radiator array
City University of Hong Kong（香港城市大学）；Southeast University（东南大学）
We investigate the reflection properties of electromagnetic/optical waves in isotropic chiral media. When the chiral parameter is strong enough, we show that an unusual \emph{negative reflection} occurs at the interface of the chiral medium and a perfectly conducting plane, where the incident wave and one of reflected eigenwaves lie in the same side of the boundary normal. Using such a property, we further demonstrate that such a conducting plane can be used for focusing in the strong chiral medium. The related equations under paraxial optics approximation are deduced. In a special case of chi…
We show that a high-order Bessel beam propagating in a medium with nonlinear absorption is not completely absorbed, but survives in the form of a new propagation invariant vortex beam in which the beam energy and orbital angular momentum are permanently transferred to matter and at the same time refueled by spiral inward currents of energy and angular momentum. Unlike vortex solitons and dissipative vortex solitons, these vortex beams are not supported by specific dispersive nonlinearities (self-focusing or self-defocusing) and do not require gain. Propagation invariance in presence of multipl…
We present a detailed experimental investigation, which uncovers the nature of light bullets generated from self-focusing in a bulk dielectric medium with Kerr nonlinearity in the anomalous group velocity dispersion regime. By high dynamic range measurements of three-dimensional intensity profiles, we demonstrate that the light bullets consist of a sharply localized high-intensity core, which carries the self-compressed pulse and contains approximately 25% of the total energy, and a ring-shaped spatiotemporal periphery. Sub-diffractive propagation along with dispersive broadening of the light …
We consider the paraxial propagation of nondiffracting singular beams inside natural biaxial and biaxially-induced birefringent media in vicinity of one of the optical axes in terms of eigenmode vortex-beams, whose angular momentum does not change upon propagation. We have predicted a series of new optical effects in the natural biaxial crystals such as the stable propagation of vector singular beams bearing the coupled optical vortices with fractional topological charges, the conversion of the zero-order Bessel beam with a uniformly distributed linear polarization into the radially-, azimutha…
We report a method to design at will the spatial profile of transmitted coherent light after propagation through a scattering sample. We compute an operator based on the experimentally measured transmission matrix, obtained by numerically adding an arbitrary mask in the Fourier domain prior to focusing. We demonstrate the strength of the technique through several examples: propagating Bessel beams, thus generating foci smaller than the diffraction limited speckle grain, donut beams, and helical beams. We characterize the 3D profile of the achieved foci and analyze the fundamental limitations o…
We perform micromagnetic simulations to investigate the propagation of spin-wave beams through spin-wave optical elements. Despite spin-wave propagation in magnetic media being strongly anisotropic, we use axicons to excite spinwave Bessel-Gaussian beams and gradient-index lenses to focus spin waves in analogy to conventional optics with light in isotropic media. Moreover, we demonstrate spin-wave Fourier optics using gradient-index lenses. These results contribute to the growing field of spin-wave optics.
Optical activity, the power of a medium to rotate the polarization of a light beam, has contributed significantly to molecular structure assessments in stereochemistry, biomolecular science and crystallography. Thus far, it is commonly believed that optical activity is manifested only in the chiral media which can give rise to circular birefringence of light. Here, we experimentally demonstrate that free space can also support the implementation of non-reciprocal optical activity with Bessel beams by spin-orbital interaction. Specifically, non-diffractive optically active beams are realized, w…
Recently, a method for obtaining diffraction-attenuation resistant beams in absorbing media was developed through suitable superposition of ideal zero-order Bessel beams. In this work, we will show that such beams maintain their resistance to diffraction and absorption even when generated by finite apertures. Also, we shall extend the original method to allow a higher control over the transverse intensity profile of the beams. Although the method has been developed for scalar fields, it can be applied to paraxial vector wave fields as well. These new beams can possess potential applications, s…
In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in terms of the ordinary, so-called "X-shaped waves". Moeover, by the present formalism we obtain the first analytical localized Superluminal approximate solutions which represent beams propagating in dispersive media. Our solutions may find application in different fields, like optics, microwaves, radio waves, and so on. [PACS nos.: 03.50.De ; 41.20.Jb ; 83.50.…
