Photonic Nambu-Goldstone bosons

TL;DR

This paper investigates the spatial dynamics of light in nonlinear photonic lattices, revealing phase patterns dependent on nonlinearity type and identifying phase excitations as Nambu-Goldstone bosons, with potential applications in tunable optical waveguides.

Contribution

It demonstrates that phase excitations in nonlinear photonic lattices are Nambu-Goldstone bosons resulting from spontaneous symmetry breaking, providing a new theoretical framework for understanding these systems.

Findings

Defocusing nonlinearity leads to uniform phase patterns.

Focusing nonlinearity results in a chessboard phase pattern.

Finite structures can serve as tunable metawaveguides for phase excitations.

Abstract

We study numerically the spatial dynamics of light in periodic square lattices in the presence of a Kerr term, emphasizing the peculiarities stemming from the nonlinearity. We find that, under rather general circumstances, the phase pattern of the stable ground state depends on the character of the nonlinearity: the phase is spatially uniform if it is defocusing whereas in the focusing case, it presents a chess board pattern, with a difference of $\pi$ between neighboring sites. We show that the lowest lying perturbative excitations can be described as perturbations of the phase and that finite-sized structures can act as tunable metawaveguides for them. The tuning is made by varying the intensity of the light that, because of the nonlinearity, affects the dynamics of the phase fluctuations. We interpret the results using methods of condensed matter physics, based on an effective description of the optical system. This interpretation sheds new light on the phenomena, facilitating the understanding of individual systems and leading to a framework for relating different problems with the same symmetry. In this context, we show that the perturbative excitations of the phase are Nambu-Goldstone bosons of a spontaneously broken $U(1)$ symmetry.