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.

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.

In this tutorial we discuss the macroscopic aspects of the extreme nonlinear frequency conversion process of high-order harmonic generation. For most, this entails describing the phase mismatch of the process and the means to mitigate it by tuning global parameters or by modulations perturbing the process. Additionally, we consider applications of phase matching in general for probing and for controlling different parameters of the emitted radiation.

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.

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 limit having a temporal feature which is approximately three times shorter than the duration of a transform-limited Gaussian pulse having a comparable bandwidth while maintaining 29.5% visibility. Numerical simulations demonstrate the ability of such signals to achieve temporal super-resolution.