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    Walk-off-free second-harmonic generation by dispersion engineering

    E. Aleksandravicius1, V. Jarutis1, D. Gailevicius1, and K. Staliunas1,2,3

    • 1Vilnius University, Faculty of Physics, Laser Research Center, Sauletekio Avenue 10, Vilnius, Lithuania
    • 2UPC, Departamento de Fisica, Rambla Sant Nebridi 22, 08222 Terrassa (Barcelona), Spain
    • 3ICREA, Passeig Lluís Companys 23, 08010 Barcelona, Spain

    Phys. Rev. A 114, 033524 – Published 22 September, 2026

    DOI: https://doi.org/10.1103/tnn6-zz66

    Abstract

    Spatial walk-off limits second-harmonic generation in birefringent crystals by separating the fundamental and second-harmonic beams, particularly for tightly focused fields. We show that wavelength-scale periodic modulation of the refractive index can suppress this limitation by reshaping the angular dispersion near an existing birefringent phase-matching point. The modulation couples two second-harmonic propagation directions so that their transverse energy flows cancel, eliminating the leading walk-off contribution while phase matching is recovered on the modified dispersion branch. We derive simple design conditions for this regime and confirm the mechanism with spatially resolved simulations that include pump depletion and grating-induced modification of both frequencies. For representative type-I second-harmonic generation in beta barium borate, the modulated structure can maintain spatial overlap and enhance the interaction at a millimeter scale. The approach is therefore most relevant to compact, walk-off-limited frequency converters and tightly focused beams.

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