Abstract

Creating materials with time-variant properties is critical for breaking reciprocity that imposes fundamental limitations on wave propagation. However, it is challenging to realize efficient and ultrafast temporal modulation in a photonic system. Here, leveraging both spatial and temporal phase manipulation offered by an ultrathin nonlinear metasurface, we experimentally demonstrated nonreciprocal light reflection at wavelengths around 860 nm. The metasurface, with travelling-wave modulation upon nonlinear Kerr building blocks, creates spatial phase gradient and multi-terahertz temporal phase wobbling, which leads to unidirectional photonic transitions in both the momentum and energy spaces. We observed completely asymmetric reflections in forward and backward light propagations over a large bandwidth around 5.77 THz within a sub-wavelength interaction length of 150 nm. Our approach highlights a potential means for creating miniaturized and integratable nonreciprocal optical components.

Highlights

  • Reciprocity is a fundamental principle rooted in linear physical systems with time-reversal symmetry, requiring that the received–transmitted field ratios are the same when the source and detector are interchanged[1]

  • Note that only the zeroth- and first-order Bessel functions are retained since the phase modulation depth Δφ is small, which leads to negligible contributions from higher-order functions

  • The heterodyne interference created by frequency-shifted pump beams provides robust and controllable spatiotemporal modulation, of which Δω and kM can be readily tuned as desired

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Summary

Introduction

Reciprocity is a fundamental principle rooted in linear physical systems with time-reversal symmetry, requiring that the received–transmitted field ratios are the same when the source and detector are interchanged[1]. To date, based on the strong electro-optic[9,10], acousto-optic[11,12,13,14], or optomechanical effects[15,16] of different materials, proof-of-concept temporal modulation has been demonstrated at frequencies ranging from kilohertz to gigahertz, which are much lower than the optical frequency as a result of the slow carrier injection of electrooptic modulation and low-frequency acoustic or mechanical modes in acousto-optic or optomechanical modulation These dynamic systems suffer from limited bandwidth either due to the group velocity mismatch among photonic modes or the intrinsic narrow linewidths of acoustic and mechanical modes. Nonreciprocity with a sub-wavelength interaction length and an ultrafast modulation frequency over the THz bandwidth is technically challenging and has not been realized to date

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