In this work, we show the light that propagate along a frequency synthetic dimension through EO modulation, can be reflected by a frequency domain mirror, which leads to interference and trapped state in frequency domain! 

We create a frequency domain crystal using EO modulation on a thin-film lithium niobate (TFLN) resonator (see our previous work on forming high-dimensional frequency crystals in a single TFLN resonator: https://doi.org/10.1364/OPTICA.395114).
The frequency domain mirror is then formed by mode-splitting which breaks the periodic translation symmetry of the crystal. 

We first theoretically model this phenomenon and investigate the mirror properties. We then experimentally provide two different approaches to demonstrate such a frequency domain mirror: polarization crossing and coupled-resonators. 

Enabled by the strong EO, low optical loss, and scalablity of TFLN coupled-resonator platform, we are able to create light propagation along the frequency dimension with a low propagation loss of ~0.1 dB/lattice point and a strong mirror reflectivity (>0.9999) therefore we can observe the interference and trapped state in frequency domain. This mirror-induced reflection can be interesting for control the optical energy distribution in the frequency domain as well as tailoring the shape of frequency comb. For example, we show that the frequency mirror changed the normal dynamics of EO comb and lead to a completely flat-slope frequency comb at every other comb line, due to the interference of forward and backward propagation of light in frequency domain.

Check our paper here!