Measuring sub-Planck structural analogues in chronocyclic phase space

TL;DR

This paper demonstrates how spectral shearing interferometry can measure sub-Planck scale structures in the phase space of ultrashort optical pulses, revealing detailed quantum-like features in classical light fields.

Contribution

It introduces a method to directly measure sub-Planck structures in optical pulses using multiple-shear spectral interferometry, extending previous approaches.

Findings

Successfully characterized a two-sub-pulse structure without phase ambiguity.

Revealed that sub-Planck scale features can be detected regardless of their orientation.

Computed the Wigner distribution showing tilted fringes indicating sub-Planck structures.

Abstract

The phase space structure of certain quantum states reveals structure on a scale that is small compared to the Planck area. Using an analog between the wavefunction of a single photon and the electric field of a classical ultrashort optical pulse we show that spectral shearing interferometry enables measurement of such structures directly. Thereby extending the idea of Praxmeyer et al. In particular, we use multiple-shear spectral interferometry to fully characterize a pulse consisting of two sub-pulses which are temporally and spectrally disjoint, without a relative-phase ambiguity. This enables us to compute the Wigner distribution of the pulse. This spectrographic representation of the pulse field features fringes that are tilted with respect to both the time- and frequency axes, showing that in general the shortest sub-Planck distances may not be in the directions of the canonical (and easily experimentally accessible) directions. Further, independent of this orientation, evidence of the sub-Planck scale of the structure maybe extracted directly from the measured signal.