Selective Coupling Enhances Harmonic Generation of Whispering-Gallery Modes

We demonstrate second-harmonic generation (SHG) in an $x$-cut congruent lithium niobate (LN) whispering-gallery mode (WGM) resonator. First, we show theoretically that independent control of the coupling of the pump and signal modes is optimal for high conversion rates. A coupling scheme based on our earlier work [F. Sedlmeir et al., Phys. Rev. Applied 7, 024029 (2017)] is then implemented experimentally to verify this improvement. Thereby, we are able to improve on the efficiency of SHG by more than an order of magnitude by selectively outcoupling using a LN prism, utilizing the birefringence of it and the resonator in kind. This method is also applicable to other nonlinear processes in WGM resonators.

Figure 1

SHG as a function of the coupler distance. In (a), the pump mode’s contrast and linewidth are plotted as the prism is moved closer to the resonator till the two are on contact. At about 150 nm away, the contrast is maximum and the resonance is critically coupled. The behavior of the coupling linewidth changes from exponential at some point. We believe this change is due to contact between the prism and the resonator. Further change on the distance axis is then depression of the resonator by the prism by an unknown amount. Meanwhile, in (b), we measure the second harmonic both scattered from the resonator and coupled out via the prism. The scattered second harmonic gives an indication of the intracavity power. The scattered second-harmonic power reaches a maximum when the prism is critically coupled to the pump, but the outcoupled power follows much later when the signal is better coupled at a closer distance. This is the case even when we believe the prism is depressing the resonator. The method for this experiment is described in detail in Sec. 3a.

Figure 2

Selective coupling in a negative uniaxial, $x$-cut WGM resonator. (a) Refractive indices for TE (orange) and TM (purple) modes at different angles, $\gamma$, from the resonator’s optic axis, as well as inside a prism for selective coupling made from the same material. This prism is illustrated in (b). It is placed at the resonator’s optic axis and has its optic axis perpendicular to that of the resonator. Modes can evanescently couple to a prism if their refractive index inside the prism is greater than or equal to that in the resonator. Therefore, only TM modes can couple to this prism. In a positive crystal, TE modes would couple at this prism.

Figure 3

The experimental setup. Red indicates pump (approximately 1550 nm) light. Green shows the path of the second harmonic when one is generated. Pump light is coupled to an $x$-cut congruent LN WGM resonator using a diamond prism, which can be moved with a piezoelectric linear stage, at the resonator’s optic axis. Its reflected spectrum is measured with an (In,Ga)As detector. When second-harmonic light is generated, it can be outcoupled at the diamond prism and measured with a Si detector. In addition, there is a $z$-cut LN prism located opposite to the diamond prism controlled by another piezoelectric linear stage. Second-harmonic (TM-polarized) light can couple out through this prism, but pump (TE-polarized) light cannot.

Figure 4

Second-harmonic (at 777.7 nm) power as a function of pump power. The green markers are measurements where we maximize power selectively outcoupled by the LN prism. The blue markers have power outcoupled by the diamond prism maximized (when no LN prism is present). The LN prism is represented by circles, the diamond prism by diamonds. The linear data for each curve is fitted to a quadratic, and their intercept at 1 mW is labeled. When selective coupling is used, some—but much less—power couples out of the diamond prism. These data are truncated at low SHG power, as their errors approach the noise level.