Analytical method for the description of important obstructed optical beams and the Poisson-Arago spot.

In this work, we describe analytically the diffraction of some important beams due to a circular obstacle. In order to obtain the desired results, we deal with the wave equation in paraxial approximation together with the diffraction Fresnel integral and apply the analytical method proposed by Zamboni-Rached et al. [Appl. Opt.51, 3370-3379 (2012)APOPAI0003-693510.1364/AO.51.003370]. As a byproduct of our method, we notice the formation of the Poisson-Arago spot for ordinary beams (plane wave and Gaussian beam) and a reconstruction of the beam for nondiffracting beams (Bessel beam). Then, we pass to a vectorial analysis for better describing the electromagnetic beams.

Production of dynamic frozen waves: controlling shape, location (and speed) of diffraction-resistant beams.

In recent times, we experimentally realized quite an efficient modeling of the shape of diffraction-resistant optical beams, thus generating for the first time the so-called frozen waves (FW), whose longitudinal intensity pattern can be arbitrarily chosen within a prefixed space interval of the propagation axis. In this Letter, we extend our theory of FWs, which led to beams endowed with a static envelope, through a dynamic modeling of the FWs whose shape is now allowed to evolve in time in a predetermined way. Further, we experimentally create such dynamic FWs (DFWs) in optics via a computational holographic technique and a spatial light modulator. Experimental results are presented here for two cases of DFWs, one of zeroth order and the other of higher order, the latter being the most interesting exhibiting a cylindrical surface of light whose geometry changes in space and time.

Producing acoustic 'Frozen Waves': simulated experiments with diffraction/attenuation resistant beams in lossy media.

The so-called Localized Waves (LW), and the "Frozen Waves" (FW), have raised significant attention in the areas of Optics and Ultrasound, because of their surprising energy localization properties. The LWs resist the effects of diffraction for large distances, and possess an interesting self-reconstruction -self-healing- property (after obstacles with size smaller than the antenna's); while the FWs, a sub-class of LWs, offer the possibility of arbitrarily modeling the longitudinal field intensity pattern inside a prefixed interval, for instance 0⩽z⩽L, of the wave propagation axis. More specifically, the FWs are localized fields "at rest", that is, with a static envelope (within which only the carrier wave propagates), and can be endowed moreover with a high transverse localization. In this paper we investigate, by simulated experiments, various cases of generation of ultrasonic FW fields, with the frequency of f0=1 MHz in a water-like medium, taking account of the effects of attenuation. We present results of FWs for distances up to L=80 mm, in attenuating media with absorption coefficient α in the range 70⩽α⩽170 dB/m. Such simulated FW fields are constructed by using a procedure developed by us, via appropriate finite superpositions of monochromatic ultrasonic Bessel beams. We pay due attention to the selection of the FW parameters, constrained by the rather tight restrictions imposed by experimental Acoustics, as well as to some practical implications of the transducer design. The energy localization properties of the Frozen Waves can find application even in many medical apparatus, such as bistouries or acoustic tweezers, as well as for treatment of diseased tissues (in particular, for the destruction of tumor cells, without affecting the surrounding tissues; also for kidney stone shuttering, etc.).

Producing acoustic frozen waves: simulated experiments.

In this paper, we show how appropriate superpositions of Bessel beams can be successfully used to obtain arbitrary longitudinal intensity patterns of nondiffracting ultrasonic wave fields with very high transverse localization. More precisely, the method here described allows generation of longitudinal acoustic pressure fields whose longitudinal intensity patterns can assume, in principle, any desired shape within a freely chosen interval 0 ≤ z ≤ L of the propagation axis, and that can be endowed in particular with a static envelope (within which only the carrier wave propagates). Indeed, it is here demonstrated by computer evaluations that these very special beams of nonattenuated ultrasonic field can be generated in water-like media by means of annular transducers. Such fields at rest have been called by us acoustic frozen waves (FWs). The paper presents various cases of FWs in water, and investigates their aperture characteristics, such as minimum required size and ring dimensioning, as well as the influence they have on the proper generation of the desired FW patterns. The FWs are particular localized solutions to the wave equation that can be used in many applications, such as new kinds of devices, e.g., acoustic tweezers or scalpels, and especially in various ultrasound medical apparatus.

Simple and effective method for the analytic description of important optical beams when truncated by finite apertures.

In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the three-dimensional evolution of important waves as Bessel beams, plane waves, gaussian beams, and Bessel-Gauss beams when truncated by finite apertures. One of the by-products of our mathematical method is that one can get in a few seconds, or minutes, high-precision results, which normally require quite lengthy numerical simulations. The method works in electromagnetism (optics, microwaves) as well as in acoustics.

Cherenkov radiation versus X-shaped localized waves.

Localized waves (LW) are nondiffracting ("soliton-like") solutions to the wave equations and are known to exist with subluminal, luminal, and superluminal peak velocities V. For mathematical and experimental reasons, those that have attracted more attention are the "X-shaped" superluminal waves. Such waves are associated with a cone, so that one may be tempted-let us confine ourselves to electromagnetism-to look [Phys. Rev. Lett.99, 244802 (2007)] for links between them and the Cherenkov radiation. However, the X-shaped waves belong to a very different realm: For instance, they can be shown to exist, independently of any media, even in vacuum, as localized non-diffracting pulses propagating rigidly with a peak-velocity V>c [Hernández et al., eds., Localized Waves (Wiley, 2008)]. We dissect the whole question on the basis of a rigorous formalism and clear physical considerations.

Theory of "frozen waves": modeling the shape of stationary wave fields.

In this work, starting by suitable superpositions of equal-frequency Bessel beams, we develop a theoretical and experimental methodology to obtain localized stationary wave fields (with high transverse localization) whose longitudinal intensity pattern can approximately assume any desired shape within a chosen interval 0 < or = z < or = L of the propagation axis z. Their intensity envelope remains static, i.e., with velocity v = 0, so we have named "frozen waves" (FWs) these new solutions to the wave equations (and, in particular, to the Maxwell equation). Inside the envelope of a FW, only the carrier wave propagates. The longitudinal shape, within the interval 0 < or = z < or = L, can be chosen in such a way that no nonnegligible field exists outside the predetermined region (consisting, e.g., in one or more high-intensity peaks). Our solutions are notable also for the different and interesting applications they can have--especially in electromagnetism and acoustics--such as optical tweezers, atom guides, optical or acoustic bistouries, and various important medical apparatuses.

Chirped optical X-shaped pulses in material media.

We analyze the properties of chirped optical X-shaped pulses propagating in material media without boundaries. We show that such ("superluminal") pulses may recover their transverse and longitudinal shapes after some propagation distance, whereas the ordinary chirped Gaussian pulses can recover their longitudinal width only (since Gaussian pulses suffer a progressive transverse spreading during their propagation). We therefore propose the use of chirped optical X-type pulses to overcome the problems of both dispersion and diffraction during pulse propagation.

Focused X-shaped pulses.

The space-time focusing of a (continuous) succession of localized X-shaped pulses is obtained by suitably integrating over their speed, i.e., over their axicon angle, thus generalizing a previous (discrete) approach. New superluminal wave pulses are first constructed and then tailored so that they become temporally focused at a chosen spatial point, where the wave field can reach very high intensities for a short time. Results of this kind may find applications in many fields, besides electromagnetism and optics, including acoustics, gravitation, and elementary particle physics.

Localized X-shaped field generated by a superluminal electric charge.

It is now well known that Maxwell equations admit of wavelet-type solutions endowed with arbitrary group velocities (0< v(g)< infinity). Some of them, which are rigidly moving and have been called localized solutions, attracted large attention. In particular, much work has been done with regard to the superluminal localized solutions (SLSs), the most interesting of which are the "X-shaped" ones. The SLSs have been actually produced in a number of experiments, always by suitable interference of ordinary-speed waves. In this paper we show, by contrast, that even a superluminal charge creates an electromagnetic X-shaped wave: namely, on the basis of Maxwell equations, we are able to evaluate the field associated with a superluminal charge (under the approximation of pointlikeness): it results in constituting a very simple example of a true X wave.

Superluminal localized solutions to Maxwell equations propagating along a waveguide: the finite-energy case.

In a previous paper we have shown localized (nonevanescent) solutions to Maxwell equations to exist, which propagate without distortion with superluminal speed along normal-sized waveguides, and consist in trains of "X-shaped" beams. Those solutions possessed infinite energy. In this paper we show how to obtain, by contrast, finite-energy solutions, with the same localization and superluminality properties.

Superluminal X-shaped beams propagating without distortion along a coaxial guide.

In a previous paper we showed that localized superluminal solutions to the Maxwell equations exist, which propagate down (nonevanescence) regions of a metallic cylindrical waveguide. In this paper we construct analogous nondispersive waves propagating along coaxial cables. Such new solutions, in general, consist in trains of (undistorted) superluminal "X-shaped" pulses. Particular attention is paid to the construction of finite total energy solutions. Any results of this kind may find application in the other fields in which an essential role is played by a wave equation (like acoustics, geophysics, etc.).