In this paper 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 shape after some propagation distance, while the ordinary chirped gaussian-pulses can recover their longitudinal shape only (since gaussian pulses suffer a progressive 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 the pulse propagation.
In this letter we present a new technique for pulse shaping. The desired pulse is shaped by two apodized chirped fiber Bragg gratings which dispersions are adjusted to be cancelled. This technique exploits the well-known property of linearly-chirped gratings, in which the apodization (amplitude) grating profile maps its spectral response. This technique presents inherent advantages of chirped fiber Bragg gratings and direct design in frequency domain.
We propose an efficient method for spatial filtering of light beams by propagating them through 2D (also 3D) longitudinally chirped photonic crystals, i.e. through the photonic structures with fixed transverse lattice period and with the longitudinal lattice period varying along the direction of the beam propagation. We prove the proposed idea by numerically solving the paraxial propagation equation in refraction index-modulated media, and we evaluate the efficiency of the process by plane-wave-expansion analysis. The technique can be applied to filter (to clean) the packages of atomic waves (…
We address soliton formation at the edge of chirped optical lattices imprinted in Kerr-type nonlinear media. We find families of power thresholdless surface waves that do not exist at other types of lattice interfaces. Such solitons form due to combined action of internal reflection at the interface, distributed Bragg-type reflection, and focusing nonlinearity. Remarkably, we discover that surfaces of chirped lattices are soliton attractors: Below an energy threshold, solitons launched well within the lattice self-bend toward the interface, and then stick to it.
We observe that focusing a femtosecond laser beam simultaneously chirped in time and space domains in glass can efficiently suppress the optical aberration caused by the refractive index mismatch at the interface of air and the glass sample. We then demonstrate three dimensional microprocessing in glass with a nearly invariant spatial resolution for a large range of penetration depth between 0.25 mm and 9 mm without any aberration correction.
The deployment of plasmonic nanostructures to enhance nonlinear signal generation requires effective far-to-near field coupling and phase matching for frequency conversion. While the latter can be easily achieved at plasmonic hotspots, the former is an antenna problem that requires dedicated structural design and optimization. Plasmonic gratings are a simple but effective platform for nonlinear signal generation since they provide a well-defined momentum for photon-plasmon coupling and local hotspots for frequency conversion. In this work, a plasmonic azimuthally chirped grating (ACG), which p…
We report and propose a simple scheme to achieve efficient and fast coherent population transfer (CPT) by utilizing either a nonlinearly chirped Gaussian shaped few-cycle laser pulse or an unchirped sinc-shaped few-cycle laser pulse. The proposed scheme is shown to be fairly robust against the variation of the laser parameters such as temporal pulse width, chirp rates, carrier envelope phases and Rabi frequencies. We find that compared to the so-called stimulated Raman adiabatic passage (STIRAP) technique, our scheme for complete population transfer with few-cycle Gaussian shaped laser pulses …
The first step in the coherent control of a photoinduced binary reaction is bond making or photoassociation. We have recently demonstrated coherent control of bond making in multi-photon femtosecond photoassociation of hot magnesium atoms, using linearly chirped pulses [Levin et al., arXiv:1411.1542]. The detected yield of photoassociated magnesium dimers was enhanced by positively chirped pulses which is explained theoretically by a combination of purification and chirp-dependent Raman transitions. The yield could be further enhanced by pulse optimization resulting in pulses with an effective…
We present a method to control photodissociation by manipulating the bond softening mechanism occurring in strong shaped laser fields, by varying the chirp sign and magnitude of an ultra-short laser pulse. Manipulation of bond-softening is experimentally demonstrated for strong field (795 nm, 10^12 - 10^13 W/cm^2) photodissociation of H2+, exhibiting substantial increase of dissociation by positively chirped pulses with respect to both negatively chirped and transform limited pulses. The measured kinetic energy release and angular distributions are used to quantify the degree of control of dis…
Advances in the amplification and manipulation of ultrashort laser pulses has led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques, pulse shaping via modulation of spatially-dispersed laser pulses, and efficient frequency-mixing in quasi-phase-matched nonlinear crystals to access new spectral regions. In this work, we introduce and demonstrate a new platform for nonlinear optics which has the potential to combine all of these separate functionalities (pulse amplification, frequency trans…
We describe a system for generating frequency-chirped and amplitude-shaped pulses on time scales from sub-nanosecond to ten nanoseconds. The system starts with cw diode-laser light at 780 nm and utilizes fiber-based electro-optical phase and intensity modulators, driven by an arbitrary waveform generator, to generate the shaped pulses. These pulses are subsequently amplified to several hundred mW with a tapered amplifier in a delayed double-pass configuration. Frequency chirps up to 5 GHz in 2 ns and pulse widths as short as 0.15 ns have been realized.
We demonstrate that, with the help of a Gaussian potential barrier, dark modes in the form of a local depression ("bubbles") can be supported by the repulsive Kerr nonlinearity in combination with fractional dimension. Similarly, W-shaped modes are supported by a double potential barrier. Families of the modes are constructed in a numerical form, and also by means of the Thomas-Fermi and variational approximations. All these modes are stable, which is predicted by computation of eigenvalues for small perturbations and confirmed by direct numerical simulations.
We show that the spatial distribution of the energy density of optimally shaped waves inside a scattering medium can be described by considering only a few of the lowest eigenfunctions of the diffusion equation. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtained the energy density inside a quasi-1D disordered waveguide by numerical calculation of the joined scatte…
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…
Using a combination of the variation approximation (VA) and direct simulations, we consider the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provide for the hitherto elusive stabilization of vortex solitons in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, i…
In the FIRST PART we present simple introductions to gaussian and Bessel waves, and to the Localized Waves (LW), pulses or beams, showing the important properties of the latter, and their applications whenever a role is played by a wave-equation (electromagnetism, optics, acoustics, seismology, geophysics, gravitation, elementary particle physics,...). The First Part ends with a historical APPENDIX, recalling how the geometrical methods of Special Relativity (SR) had predicted the most interesting LWs, i.e., the X-shaped pulses; and presenting a bird's-eye view of the experiments performed wit…
In media with strong spatial dispersion the electric displacement vector and the electric field are typically linked by a partial differential equation in the bulk region. The objective of this work is to highlight that in the vicinity of an interface the relation between the macroscopic fields cannot be univocally determined from the bulk response of the involved materials, but requires instead the knowledge of internal degrees of freedom of the materials. We derive such relation for the particular case of "wire media", and describe a numerical formalism that enables characterizing the electr…
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.…
We present a new method for building sequences of solvable profiles of the electromagnetic (EM) admittance in lossless isotropic materials with 1D graded permittivity and permeability (in particular profiles of the optical refractive-index). These solvable profiles lead to analytical closed-form expressions of the EM fields, for both TE and TM modes. The Property-and-Field Darboux Transformations method, initially developed for heat diffusion modelling, is here transposed to the Maxwell equations in the optical-depth space. Several examples are provided, all stemming from a constant seed-poten…
A quantum theory of 3D X-shaped optical bullets in Kerr media is presented. The existence of progressive undistorted squeezed vacuum is predicted. Applications to quantum non-demolition experiments, entanglement and interferometers for gravitational waves detection are envisaged.
Since the early works[1-4] on the so-called nondiffracting waves (called also Localized Waves), a great deal of results has been published on this important subject, from both the theoretical and the experimental point of view. Initially, the theory was developed taking into account only free space; however, in recent years, it has been extended for more complex media exhibiting effects such as dispersion[5-7], nonlinearity[8], anisotropy[9] and losses[10]. Such extensions have been carried out along with the development of efficient methods for obtaining nondiffracting beams and pulses in the…
Laser Pulse Diagnostics of Ultrafast <8 fs Pulses Through Two-Photon Absorption Fluorescence In Liquid Media -- The Role of GVD and Third-Order Dispersion
We analytically study the linear propagation of arbitrarily shaped light-pulses through an absorbing medium with a narrow transparency-window or through a resonant amplifying medium. We point out that, under certain general conditions, the pulse acquires a nearly Gaussian shape, irrespective of its initial shape and of the spectral profile of the line. We explicitly derive in this case the pulse parameters, including its skewness responsible for a deviation of the delay of the pulse maximum from the group delay. We illustrate our general results by analysing the slow-light experiments having d…
We address ring-shaped surface waves supported by defocusing thermal media with circular cross-section. Such waves exist because of the balance between repulsion from the interface and deflection of light from the bulk medium due to defocusing nonlocal nonlinearity. The properties of such surface waves are determined by the geometry of the sample. Nodeless ring surface waves are stable for all values of their winding number, while surface waves with a small number of azimuthal nodes can be metastable.
In this paper, we study the propagation of the Frozen Wave type beams through non-absorbing stratified media and develop a theoretical method capable to provide the desired spatially shaped diffraction resistant beam in the last material medium. In this context, we also develop a matrix method to deal with stratified media with large number of layers. Additionally, we undertake some discussion about minimizing reflection of the incident FW beam on the first material interface by using thin films. Our results show that it is indeed possible to obtain the control, on demand, of the longitudinal …
The applications of vortex beam in biomedical field are always hindered by light scattering of biological tissues. Recently wavefront shaping technology has shown the potential in focusing a structured light field through scattering media. Herein we have proposed a novel theory to describe the field transformation property of the opaque lens. This theory makes it possible to generate foci with specified amplitude and phase profiles by well-designing the incident field. We verify the validity of this theory by experimentally generating doughnut-shaped foci with various topological charges, and …
Nonlinear optical media that are normally dispersive, support a new type of localized (nondiffractive and nondispersive) wavepackets that are X-shaped in space and time and have slower than exponential decay. High-intensity X-waves, unlike linear ones, can be formed spontaneously through a trigger mechanism of conical emission, thus playing an important role in experiments.
