Spontaneous symmetry breaking in plasmon lattice lasers

Spontaneous symmetry breaking (SSB) is key for our understanding of phase transitions and the spontaneous emergence of order. In this work, we report that, for a two-dimensional (2D) periodic metasurface with gain, SSB occurs in the lasing transition. We study diffractive hexagonal plasmon nanoparticle lattices, where the K-points in momentum space provide two modes that are degenerate in frequency and identically distributed in space. Using femtosecond pulses to energize the gain medium, we simultaneously capture single-shot real-space and Fourier-space images of laser emission. By combining Fourier and real space, we resolve the two order parameters for which symmetry breaking simultaneously occurs: spatial parity and U(1) (rotational) symmetry breaking, evident respectively as random relative mode amplitude and phase. The methodology reported in this work is generally applicable to 2D plasmonic and dielectric metasurfaces and opens numerous opportunities for the study of SSB and the emergence of spatial coherence in metaphotonics.