Spectral self-imaging of optical orbital angular momentum modes

Zhongzheng Lin,Siyuan Yu,Yujie Chen,Camille-Sophie Brès,Jianqi Hu

doi:10.1063/5.0067668

Abstract

The Talbot self-imaging effect is mostly present in the forms of space or time, or in the frequency domain by the Fourier duality. Here, we disclose a new spectral Talbot effect arising in optical orbital angular momentum (OAM) modes. The effect occurs in the context of petal-like beams, which are typically constructed from a number of in-phase equidistant OAM modes with at least one void mode in between. When illuminating such beams on phase masks that are azimuthally modulated with Talbot phases, the initial OAM modes are self-imaged to create new OAM modes, meanwhile preserving the initial OAM spectral profile. Such a phenomenon is theoretically predicted, and a close analogy is drawn with the spectral Talbot effect of frequency combs. The prediction is also experimentally confirmed by observing versatile spectral self-imaging on various optical petal-like beams.

Highlights

As a consequence of spatial diffraction, a spatially periodic wave revives its pattern along the propagation direction in near field, known as the Talbot effect.1 Such a self-imaging phenomenon can be generalized and explained through quadratic Gauss sums2,3 and was observed in diverse types of waves including light waves.4 Given the space–time duality, the Talbot effect arises in the time domain
Once these phases satisfy the specific Talbot condition, the output pulse train could remain identical to the input, or with multiplied repetition rates, while the comb free spectral range (FSR) and intensity profile are maintained
We extend the concept of spectral Talbot effect into orbital angular momentum (OAM) modes

Summary

INTRODUCTION

As a consequence of spatial diffraction, a spatially periodic wave revives its pattern along the propagation direction in near field, known as the Talbot effect. Such a self-imaging phenomenon can be generalized and explained through quadratic Gauss sums and was observed in diverse types of waves including light waves. Given the space–time duality, the Talbot effect arises in the time domain. These petals are initially in-phase or follow linear phase relation, being repetitive around the 2π azimuth, spaced by multiple OAM orders in the spectrum If such a petal-like field illuminates on phase masks that are azimuthally modulated with Talbot phases, the energy within the initial OAM modes will be redistributed and self-imaged to generate new OAM modes, preserving the initial OAM spectral profile. This is exactly the OAM counterpart of the well-known spectral Talbot effect extensively explored in frequency combs, and a close analogy is drawn between them. We foresee that the effect can be interesting for OAM-based classical and quantum information processing and multicasting in mode-division-multiplexed optical communications.

Theoretical considerations

Analogy between spectral self-imaging of frequency combs

EXPERIMENTAL SETUP

Demonstration of OAM spectral self-imaging

Versatile OAM spectrum manipulation

CONCLUSION