Slow-light enhanced collinear second-harmonic generation in two-dimensional photonic crystals

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Abstract
We predict an enhanced efficiency of collinear second-harmonic generation in photonic crystals. This can be achieved by taking advantage of the complexity of the dispersion relation in periodic lattices. Thus, two essential conditions for increasing the nonlinear interaction, namely, phase matching and small group velocity (slow light), can be met simultaneously. The analytical results based on a modal approach are verified with rigorous simulations by means of the finite-difference time-domain method. The influence of material dispersion on optimal phase match is discussed.