Exact analysis of cascaded second-order nonlinearity in rotated Ti:LiNbO₃ Couplers

Abstract

The effects of anisotropic coupling on the nonlinear behavior of different LiNbO₃ waveguides and couplers employing cascaded second-order nonlinearity are analyzed and the importance of leaky mode effect is shown. A set of practical coupling structures made of both symmetric and asymmetric waveguides is investigated and their performance is compared. The home-made computer-code, based on coupled wave theory and anisotropic mode propagation in the complex domain, allows an exact electromagnetic investigation of devices, taking into account both guided and leaky propagation in structures which exhibit losses, the generated second harmonic wave having leaky nature. As an example, for the well-investigated slab three layer waveguide, by taking into account the leaky nature of the generated second harmonic, the modal mismatch Δβ = 333 m⁻¹ is obtained at the azimuthal angle θ_m ≅ 61.9^∘ (between the crystal optical c-axis and the propagation direction) while the angle found via the conventional approach is θ_m ≅ 63.5^∘. Moreover, the calculated second harmonic wave exhibits an attenuation equal to 7.44 × 10⁻¹dB/cm that strongly influences the whole cascaded second-order phenomenon. The simulation results, for those structures in which it is possible to neglect the hybrid and leaky nature of the propagation modes, are compared with the literature data and an excellent agreement is found.