In many countries around the world, ultra-intense laser facilities are being built. These state-of-the-art lasers are
intended for innovative medical and technological applications, as well as for basic experiments at the frontiers
of fundamental science. Laser particle acceleration is a promising new endeavor. Recently developed schemes using radially polarized beams could help in reaching unprecedentedly short electron pulse durations, well in the attosecond range and potentially in the subattosecond range.
Vectorial laser beams propagating beyond the paraxial limit exhibit an intensity profile at focus that depends
upon their field structure and the width of their plane wave spectrum. Under tight focussing conditions, the
longitudinal component of the lowest order transverse magnetic laser beam has a field amplitude that becomes
comparable to that of the transverse components of the beam; the global intensity profile is then narrower
than that produced by a Gaussian beam, thus enabling hyperresolution. With a general polarization eigenmode
approach for all propagating directions in anisotropic media, we can show that privileged propagating directions
exist, allowing preservation of the transverse magnetic polarization state despite birefringence. Using wave
functions satisfying the non-paraxial wave equation, we can also find exact expressions for the field components.
During propagation of tightly focussed beams along those privileged directions inside an appropriate anisotropic
nonlinear crystal, the longitudinal electric field component may then be used to take advantage of nonlinear tensor
terms otherwise ineffective with a paraxial beam. In this work, spectral conversion rate and power conversion
efficiency of second-harmonic generation are characterized as a function of effective and undepleted nonlinear
pumping in the case of propagation along the anisotropic axis of an uniaxial nonlinear crystal. Even if the phase
matching condition is not fully satisfied for propagation along this privileged direction, we show to which extent
the nonlinear properties are preserved for a restricted interaction volume.
We first recall that Bessel beams (or `diffraction-free beams') can be produced by a Fourier optics setup where a mask with concentric transmission rings is placed at the focus of a lens. We then describe how the coherent superposition of Bessel beams with proper spatial frequencies leads to a self-imaging phenomenon. Such a behavior can be exploited to measure the curvature of the wavefront incident on the mask used to generate the Bessel beams. It is shown, theoretically and experimentally, that a parabolic phase variation along the radial coordinate for the beam incident on the mask translates into an image shift along the propagation axis. That result can be exploited for the measurement of surface deformation and for the characterization of the optical nonlinearities of materials. We also report on a procedure to optimize the sensitivity of the method.
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