Dual Galilean invariance in a temporally dispersive medium.

The bidispersive equation, accounting for second-order temporal dispersion in a lossless medium, is examined under a Galilei-like transformation, as well as a conditional ordinary Galilei transformation. In the former case, the roles of space and time are reversed by comparison to the application of the same transformation to the quantum mechanical Schrödinger equation. Such an invariance can result in envelope speeds that can assume values above or below the group speed of the medium; also, they can be negative.

Autofocusing luminal and superluminal spatiotemporally localized waves.

Highly focused space-time wavepackets in free space have already been achieved by means of suitable superpositions of nondiffracting and almost undistorted spatiotemporally localized pulses. Here, we present analytically individual autofocusing luminal and superluminal localized waves that can attain high-intensity peaks and spatiotemporal localization at prespecified positions along the path of their propagation.

Realization of laterally nondispersing ultrabroadband Airy pulses.

We present the measurements of the spatiotemporal impulse response of a system creating nondispersing Airy pulses, i.e., ultrabroadband Airy beams whose main lobe size remains constant over propagation.

Spatiotemporal characterization of ultrabroadband Airy pulses.

We present experimental results of a full spatiotemporal characterization of an optical system for ultrabroadband Airy pulse generation with a liquid-crystal-on-silicon spatial light modulator. Measurements with a few micrometer spatial and almost one-wave-cycle temporal resolution were performed using a white light spatial spectral interferometry setup based on the SEA TADPOLE ultrashort pulse characterization technique. The results were compared with the theoretical model for Airy pulse propagation.

Basic diffraction phenomena in time domain.

Using a recently developed technique (SEA TADPOLE) for easily measuring the complete spatiotemporal electric field of light pulses with micrometer spatial and femtosecond temporal resolution, we directly demonstrate the formation of theo-called boundary diffraction wave and Arago's spot after an aperture, as well as the superluminal propagation of the spot. Our spatiotemporally resolved measurements beautifully confirm the time-domain treatment of diffraction. Also they prove very useful for modern physical optics, especially in micro- and meso-optics, and also significantly aid in the understanding of diffraction phenomena in general.

Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets.

We measure the spatiotemporal field of ultrashort pulses with complex spatiotemporal profiles using the linear-optical, interferometric pulse-measurement technique SEA TADPOLE. Accelerating and decelerating ultrashort, localized, nonspreading Bessel-X wavepackets were generated from a approximately 27 fs duration Ti:Sapphire oscillator pulse using a combination of an axicon and a convex or concave lens. The wavefields are measured with approximately 5 microm spatial and approximately 15 fs temporal resolutions.

Measuring the spatiotemporal field of ultrashort Bessel-X pulses.

We present direct measurements of the spatiotemporal electric field of an ultrashort Bessel-X pulse generated using a conical lens (axicon). These measurements were made using the linear-optical interferometric technique SEA TADPOLE, which has micrometer spatial resolution and femtosecond temporal resolution. From our measurements, both the superluminal velocity of the Bessel pulse and the propagation invariance of the central spot are apparent.

Laterally accelerating airy pulses.

By making use of the recently found expression for finite-energy 2D paraxial Airy beam, three types of ultrashort Airy pulses have been derived and numerically simulated. They differ in frequency dependences of their parameters and exhibit different spatial profiles and propagation features.

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.

Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves.

We show that the field of the optically feasible luminal localized wave solutions of the scalar homogeneous wave equation can be modeled by means of Bessel-Gauss pulses. As the Bessel-Gauss pulses have a closed-form expression, this fact may be of great value in numerical simulations of various experimental situations.

Generation and classification of localized waves by Lorentz transformations in Fourier space.

The Lorentz transformations of propagation-invariant localized waves (also known as nondispersive or nondiffracting or undistorted progressive waves) are studied in the frequency-momentum space. For supports of wave functions in this space rules of transformation are derived which allow one to group all localized waves into distinct classes: subluminal, luminal, and superluminal localized waves. It is shown that for each class there is an inertial frame in which any given localized wave takes a particularly simple form.

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.

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.