Focus Wave Modes Research Articles

Information propagation of focus wave mode localized waves in anisotropic turbulent seawater

The evolution of the information transfer capability of an optical system for underwater focused wave mode localized wave (FWMLW) in anisotropic weakly turbulent absorbing seawater is studied. By developing the probability distribution function as well as the detection probability of the vortex modes carried by the FWMLW and the average bit error rate of the FWMLW underwater system, the information capacity of the FWMLW system with a pointing error is modeled. Through a numerical analysis of the effects of turbulent seawater and optical system parameters on the built light intensity, the detection probability, and the information capacity models, we find that the FWMLW system has an optimal delay time determined by the spectrum bandwidth when the spectrum bandwidth is greater than 1. The information capacity of the FWMLW system is higher than that of the X localized wave system under the same turbulent seawater channel condition, and FWMLW is a better optical signal source for vortex mode division multiplexing underwater systems than a Bessel–Gaussian beam.

Localized waves carrying orbital angular momentum in optical fibers

We consider the effect of orbital angular momentum (OAM) on localized waves in optical fibers using theory and numerical simulations, focusing on splash pulses and focus wave modes. For splash pulses, our results show that they may carry OAM only up to a certain maximal value. We also examine how one can optically excite these OAM-carrying modes, and discuss potential applications in communications, sensing, and signal filtering.

Vector Focus Wave Modes with Elliptic Cross-Section

Vector Focus Wave Modes with Elliptic Cross-Section

Propagation of vector nondiffracting and nondispersive pulsed beams through an air-dielectric planar interface

Here we introduce nondiffracting vector focus wave modes (FWM) pulsed beams and analyze their transmittance through an air-dielectric interface. Dispersionless propagation of FWM pulsed beams in air is caused by specific angular dispersion of individual components. However, while localized in the air, those FWMs experience upon transmission distortions due to different refractive index of dielectric material. We systematically analyze distortions in reflected and transmitted FWM’s. Next, we correct the angular dispersion in the air in order to enable the condition of dispersionless propagation of the vector pulses in dielectric medium. Lastly we discuss applications of FWM’s for laser microprocessing of transparent dielectric materials.

Spectrally partially coherent propagation-invariant fields

Polychromatic propagation-invariant fields (localized waves) with variable spectral coherence properties are considered. A bridge is provided between coherent propagation-invariant pulses, including Bessel pulses, X-waves and focus wave modes, and stationary polychromatic propagation-invariant fields using a difference-frequency spectral-correlation model. In the space-time domain, this assumption leads to a representation of a partially coherent field as a continuum of spectrally fully coherent, mutually independent pulses originating at different instants of time. The influence of partial spectral coherence on temporal coherence and pulse shape as well as intensity distribution and transverse spatial coherence is illustrated by considering fields with propagation-invariant Bessel-mode monochromatic components.

Nondispersive Acoustic Wave Reflection on Time Reversal Mirrors

Using an integral equation approach, we investigate the reflection of focus wave modes on conventional and time reversal mirrors when the total field, incident plus reflected, satisfies on these mirrors the Neumann boundary condition. It is also shown that the form of the incident pulse as a function of time has a strong effect on the behavior of time reversal mirrors.

Lommel pulses: An analytic form for localized waves of the focus wave mode type with bandlimited spectrum

A criticism of the focus wave mode (FWM) solution for localized pulses is that it contains backward propagating components that are difficult to generate in many practical situations. We describe a form of FWM where the strength of the backward propagating components is identically zero and derive special cases where the field can be written in an analytic form. In particular, a free-space version of "backward light" pulse is considered, which moves in the opposite direction with respect to all its spectral constituents.

(2+1)-dimensional X-shaped localized waves

A hybrid spectral superposition method is presented that allows a smooth transition between two seemingly distinct classes of localized wave solutions to the homogeneous scalar wave equation in free space; specifically, luminal or focus wave modes, and superluminal or X waves. This representation, which is based on superpositions of products of forward plane waves moving at a fixed speed v>c and backward plane waves moving at the speed c, is used to construct a large class of finite-energy superluminal-type X-shaped localized waves. The latter are characterized by arbitrarily high-frequency bands and are suitable for applications in the microwave and optical regime. In the limiting case v-->c, one recaptures the well-known focus wave mode-type localized wave solutions. A modified hybrid spectral representation, based on superpositions of products of forward plane waves moving at a fixed speed c and backward plane waves moving at the speed v>c, allows in the limit v-->c a smooth transition from superluminal localized waves to paraxial luminal pulsed beams. Although the proposed methods are applicable to a (n+1)-dimensional, n> or =2, scalar wave equation, the discussion will be limited to the case n=2 for simplicity; also, so that comparisons can be made to related recent results in the literature.

Photon localization barrier can be overcome

In contradistinction to a widespread belief that the spatial localization of photons is restricted by a power-law falloff of the photon energy density, Bialynicki-Birula [Phys. Rev. Lett. 80 (1998) 5247] has proved that any stronger – up to an almost exponential – falloff is allowed. We are showing that for certain specifically designed cylindrical one-photon states the localization is even better in lateral directions. If the photon state is built from the so-called focus wave mode, the falloff in the waist cross-section plane turns out to be quadratically exponential (Gaussian) and such strong localization persists in the course of propagation.

Localized and stationary light wave modes in dispersive media.

In recent experiments, localized and stationary optical wave packets have been generated in second-order nonlinear processes with femtosecond pulses, whose asymptotic features relate to those of nondiffracting and nondispersing polychromatic Bessel beams in linear dispersive media. We investigate 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, and the defeated group velocity dispersion, these modes can adopt the form of pulsed Bessel beams, focus wave modes, and X waves (O waves), respectively.

Electromagnetic field propagation in neutral isotropic plasmas

Interested in electromagnetic waves inside plasmas with known dielectric properties, we prove that Courant-Hilbert fields of the focus wave mode type can propagate in a steady-state, isotropic, neutral plasma which is in fact a dielectric with the refractive index $n^{2}(\omega) = 1-\omega^{2}_{p}/\omega^{2}$ where $\omega_{p}$ is the plasma frequency. We also prove that neutral, isotropic plasmas with memory behave for harmonic plane waves as a time reversal mirror when the memory function is a decreasing exponential.

BATEMAN CONFORMAL TRANSFORMATIONS WITHIN THE FRAMEWORK OF THE BIDIRECTIONAL SPECTRAL REPRESENTATION

Four-dimensional conformal transformations due originally to Bateman have been used in the past by Hillion as alternative approaches to focus wave mode solutions to the 3D scalar wave equation. More recently, more extended families of focus wave mode solutions to the 3D scalar wave equation have been derived by Borisov and Utkin, as well as Kiselev, based on Bateman transformations together with a dimension-reduction approach, whereby the wave function is separated incompletely into a product of two functions. One particular goal in this exposition is to comment on and extend the work of Borisov and Utkin and simplify and extend the method used by Kiselev. More generally, however, the aim is to show that an already existing method, known as the bidirectional spectral representation, when examined in conjunction with Bateman conformal transformations, encompasses the Borisov-Utkin-Kiselev theories as special cases and allows a systematic derivation of extended families of FWM-type localized waves beyond the ranges of their applicability. † Dedicated to the memory of Frederick D. Tappert 202 Besieris, Shaarawi, and Attiya

Localized Wave Propagation in Nonhomogeneous Media

The wave equation has in free space many classes of localized solutions with finite energy propagating without distortion which would make these pulses useful in many domains as soon as one is able to launch them. Among these localized waves, the so-called focus wave modes are the most serious candidates and could be constituents of the cosmic gamma rays recently observed. So the analysis of their propagation in nonhomogeneous media, a problem of interest in itself, could be used to deal with their behavior in the interstellar space. We assume here a medium with a refractive index varying slightly with the altitude, a bit like in troposphere. We get approximate expressions for plane waves and focus wave modes propagating in this medium.

Localized optical subcycle pulses in dispersive media

The conditions for creation of broadband localized optical fields (Bessel X pulses and focus wave modes) in dispersive media are analyzed. It is shown that transmission of focus wave modes with subcycle pulse durations through fused silica is possible.

Superluminal electromagnetic focus wave modes

A particular transformation of coordinates, associated with superluminal X-pulses, leaves the wave equation invariant and changes focus wave modes into superluminal focus wave pulses. Rather simple and manageable expressions for TM electromagnetic waves allow the investigation of these new localized solutions of Maxwell's equations.

Focus wave modes in optical parametric generators

It is shown that in the paraxial approximation the conditions for noncollinear phase matching for three-wave parametric interaction in a nonlinear crystal coincide with the conditions for generation of focus wave modes. As a result, the creation of broadband localized optical fields (pulsed beams without diffraction and dispersion spreading) inside the crystals of parametric generators is feasible.

Experimental demonstration of realizability of optical focus wave modes.

The homogeneous scalar wave equation has a number of so-called localized wave (LW) solutions, instantaneous, Gaussian pulselike intensity distribution of which propagates without any spread or distortions in free space. Despite the undoubtedly intriguing properties and considerable effort that has been made to implement such wave fields, in the optical domain only their limiting case-the so-called Bessel-X pulses-has been experimentally launched so far. In this paper we report on experimental evidence of the optical realizability of the "fundamental" special case of the LW's-the focus wave modes.

Spatial frequency content of focused ultrashort pulsed beams*

The generalized pupil concept has proved useful for representation of focused monochromatic fields. The generalized pupil can also be used to describe, and give insight into, the focusing of different types of ultrashort pulses, including Gaussian beams and focus wave modes.

Self-imaging of three-dimensional images by pulsed wave fields

Recently, the classical Talbot effect (self-imaging of optical wave fields) has attracted a renewed interest, as the concept has been generalized to the domain of pulsed wave fields by several authors. In this paper we discuss the self-imaging of three-dimensional images. We construct pulsed wave fields that can be used as self-imaging "pixels" of a three-dimensional image and show that their superpositions reproduce the spatial separated copies of its initial three-dimensional intensity distribution at specific time intervals. The derived wave fields will be shown to be directly related to the fundamental localized wave solutions of the homogeneous scalar wave equation - focus wave modes. Our discussion is illustrated by some spectacular numerical simulations. We also propose a general idea for the optical generation of the derived wave fields. The results will be compared to the work, published so far on the subject.

Optically realizable localized wave solutions of the homogeneous scalar wave equation.

One of the most frequently discussed problems in construction of localized wave (LW) solutions of the homogeneous scalar wave equation has been their energy content--the LW's generally have infinite energy content and special methods have to be used to obtain physically realizable wave fields. So far the problem has mainly been addressed as a pure mathematical one and the proposed LW's can hardly be implemented in optics. In this paper we propose an approach for constructing physically realizable LW's that have a transparent interpretation in terms of optical setups. It will be shown that such LW's can be derived as finite aperture approximations of fundamental LW's, the focus wave modes.