Figure 1

A simple model describing the proposed theory. (a) Second-harmonic generation in a bulk crystal or a single waveguide. (b) Second-harmonic generation in a directional coupler. White and black circles represent the 0-phase SHG waves and the $\pi$-phase SHG waves. In (a), as the white circles propagate to the positions of the black circles, destructive interference occurs. In (b), the white circles “escape” to the lower waveguide at the positions that the black circles are generated and thus destructive interference is avoided. It is to be noted that the circles become larger along the interaction length since the new generated waves at a particular position constructively add to the waves generated ahead.Reuse & Permissions

Figure 2

(a) Refractive-index distribution of the proposed directional coupler for the fundamental wave (solid line) and the SHG wave (dashed line). (b) Phase mismatching $\Delta k$ (solid line) and the coupling coefficient ${\kappa }_{2\omega }$ (dashed line) versus the waveguide separation. (c) Simulation of mode intensity versus the propagation distance by the beam-propagation method. This figure is for the wavelength at $1.55/2\mu \mathrm{m}$. The solid line and the dashed line represent mode intensities in waveguides 1 and 2, respectively.Reuse & Permissions