Multiscale dynamical symmetries and selection rules in nonlinear optics.

Symmetries and their associated selection rules are extremely useful in many fields of science. For systems of electromagnetic (EM) fields interacting with matter, the symmetries of matter and the EM fields' time-dependent polarization determine the properties of the nonlinear responses, and they can be facilitated for controlling light emission and enabling ultrafast symmetry breaking spectroscopy of various properties. Here, we formulate a general theory that describes the macroscopic and microscopic dynamical symmetries (including quasicrystal-like symmetries) of EM vector fields, revealing many previously unidentified symmetries and selection rules in light-matter interactions. We demonstrate an example of multiscale selection rules experimentally in the framework of high harmonic generation. This work paves the way for novel spectroscopic techniques in multiscale systems and for imprinting complex structures in extreme ultraviolet-x-ray beams, attosecond pulses, or the interacting medium itself.

On-the-Fly Control of High-Harmonic Generation Using a Structured Pump Beam.

We demonstrate experimentally a relatively simple yet powerful all-optical enhancement and control technique for high harmonic generation. This is achieved by using as a pump beam two different spatial optical modes interfering together to realize tunable periodic quasi-phase matching of the interaction. With this technique, we demonstrate on-the-fly quasi-phase matching of harmonic orders 29-41 at ambient gas pressure levels of 50 and 100 Torr, where an up to 100-fold enhancement of the emission is observed. The technique is scalable to different harmonic orders and ambient pressure conditions.

Experimental realization of structured super-oscillatory pulses.

We demonstrate experimentally a generic method for the synthesis of optical femtosecond pulses based on Gaussian, Airy and Hermite-Gauss functions, which are transformed to exhibit fringes with tunable width. The width of the fringes is set in some cases to be much narrower than the inverse of the spectral bandwidth. Such pulses might be useful for ultrafast spectroscopy, coherent control and nonlinear optics.

Breaking the Temporal Resolution Limit by Superoscillating Optical Beats.

Band-limited functions can oscillate locally at an arbitrarily fast rate through an interference phenomenon known as superoscillations. Using an optical pulse with a superoscillatory envelope we experimentally break the temporal Fourier-transform focusing limit with a temporal feature that is approximately three times shorter than the duration of a transform-limited Gaussian pulse having a comparable bandwidth while maintaining 30% visibility. We experimentally demonstrate the ability of such signals to achieve temporal superresolution and show numerically in which cases such pulses can outperform transform-limited pulses.