Spatiotemporal toroidal waves from the transverse second-harmonic generation
We study the second-harmonic generation via transversely matched interaction of two counterpropagating ultrashort pulses in X⁽²⁾ photonic structures. We show that the emitted second-harmonic wave attains the form of spatially expanding toroid with the initial thickness given by the cross correlation of the pulses. We demonstrate the formation of such toroidal waves in crystals with random ferroelectric domains as well as in annularly poled nonlinear photonic structures.
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