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Recent experiments in the doped cuprates La$_{2-x}$Ba$_x$CuO$_4$ haverevealed the emission of anomalous terahertz radiation after impulsive opticalexcitation. Here, we theoretically investigate the nonlinear electrodynamics ofsuch striped superconductors and explore the origin of the observed radiation.We argue that photoexcitation is converted into a photocurrent by asecond-order optical nonlinearity, which is activated by the breaking ofinversion symmetry in certain stripe configurations. We point out theimportance of including Umklapp photocurrents modulated at the stripeperiodicity itself, which impulsively drive surface Josephson plasmons and leadto a resonant structure of outgoing radiation, consistent with the experiments.We speculate on the utility of the proposed mechanism in the context ofgenerating tunable terahertz radiation.

Theory for Anomalous Terahertz Emission in Striped Cuprate Superconductors