Principal frequency, super-bandwidth, and low-order harmonics generated by super-oscillatory pulses

TL;DR

This paper extends the concept of principal frequency to super-oscillatory pulses, analyzing their nonlinear interactions and harmonic generation using quantum and wavelet methods, revealing new insights into ultrafast optics and wave phenomena.

Contribution

It introduces an upgraded definition of principal frequency incorporating spectral phase, enabling better characterization of super-oscillatory and sub-cycle pulses.

Findings

Spectral characteristics of harmonics are well explained by the principal frequency.

Super-oscillatory pulses have increased effective bandwidth.

Linear synthesis can generate unique frequencies.

Abstract

An alternative definition to the main frequency of an ultra-short laser pulse, named principal frequency ($\omega_P$), was recently introduced in E.G. Neyra, et al. Phys. Rev. A 103, 053124 (2021), resulting in a more transparent description of the nonlinear dynamics of a system driven by this coherent source. In this work, we extend the definition of $\omega_P$ incorporating the spectral phase of the pulse. This upgraded definition allow us to deal with super-oscillatory pulses as well as to characterize sub-cycle pulses with a complex spectral content. Simultaneously, we study the nonlinear interaction between a few-cycle super-oscillatory pulse with a gaseous system, analysing the spectral characteristics of the fundamental, third and fifth harmonics. Here, we make use of an \textit{ab-initio} quantum mechanical approach, supplemented with a wavelet analysis. We show that the spectral characteristics of the low-order harmonics are very well explained in terms of $\omega_P$, as well as the effective bandwidth of the super-oscillatory pulse. Our findings reinforce previous results that showed an increase of the effective bandwidth in the super-oscillatory region and the possibility to generate unique frequencies by a linear synthesis. We open, thus, not only new perspectives in ultrafast optics, exploring novel pathways towards the generation of fully tunable strong and short coherent sources, but also discuss possible extensions of the concepts presented here to other wave phenomena, that can be found in acoustics, signal processing or quantum mechanics.