Femtosecond filamentation in transparent media

Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications

Diffraction-free optical beams propagate freely without change in shape and scale. Monochromatic beams that avoid diffractive spreading require two-dimensional transverse profiles and there are no corresponding solutions for profiles restricted to one transverse dimension. Here, we demonstrate that the temporal degree of freedom can be exploited to efficiently synthesize one-dimensional pulsed light sheets that propagate self-similarly in free space, with no need for nonlinearity or dispersion. By introducing programmable conical (hyperbolic, parabolic or elliptical) spectral correlations between the beam’s spatiotemporal degrees of freedom, a continuum of families of propagation-invariant light sheets is generated. The spectral loci of such beams are the reduced-dimensionality trajectories at the intersection of the light-cone with spatiotemporal spectral planes. Far from being exceptional, self-similar axial-propagation in free space is a generic feature of fields whose spatial and temporal degrees of freedom are tightly correlated. These ‘space–time’ light sheets can be useful in microscopy, nonlinear spectroscopy, and non-contact measurements. One-dimensional non-diffracting sheets of light are achieved without exploiting nonlinearity. Such light sheets may be exploited in microscopy and sensing applications.

Diffraction-free space–time light sheets

Nonlinear optical media that are normally dispersive support a new type of localized (nondiffractive and nondispersive) wave packets 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.

Nonlinear electromagnetic X waves.

Implementations for exciting two or more modes via modal decomposition of a pulse by a wave launcher are generally disclosed.

Localized Wave Generation Via Model Decomposition of a Pulse by a Wave Launcher

The peculiar spatiotemporal profile of an optical realization of the nonspreading axisymmetric $X$ wave has been recorded. For treatment of the experiment a simple representation of $X$-type waves and their correlation with plane waves has been introduced, which covers also a broader class of incoherent wave fields.

Evidence of X -Shaped Propagation-Invariant Localized Light Waves

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 In other words, any localized wave is nothing but a relativistically aberrated and Doppler shifted version of a simple ``seed'' wave Also discussed are the relations of the physical (subluminal) Lorentz tranformation to other mathematical tranformations used in the literature on localized waves, as well as physical interpretation of the substantial changes that localized waves undergo if observed and generated in different inertial frames

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

Localized wave solutions of free-space wave equation can be used in numerous applications where the localized transmission of electromagnetic energy is of major importance. However, an optical implementation of localized wave fields has not been accomplished yet, except for an ultrashort version of the Bessel beams or the so called Bessel-X pulses. We propose an approach to constructing realizable optical schemes for generation of localized wave fields. We show that wavelength dispersion of the cone angle of axicons and circular diffraction gratings can be used to generate good approximation to focus wave modes.

Optical generation of 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.

Kaido Reivelt

Papers

Evidence of X -Shaped Propagation-Invariant Localized Light Waves

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

Optical generation of focus wave modes.

Experimental demonstration of realizability of optical focus wave modes.

Methods for generating wideband localized waves of superluminal group velocity