Polarization-Selective Out-Coupling of Whispering-Gallery Modes

Whispering-gallery mode (WGM) resonators are an important platform for linear, nonlinear, and quantum optical experiments. In such experiments, independent control of in-coupling and out-coupling rates to different modes can lead to higher conversion efficiencies and greater flexibility in the generation of nonclassical states based on parametric down-conversion. In this work, we introduce a scheme that enables selective out-coupling of WGMs belonging to a specific polarization family, while the orthogonally polarized modes remain largely unperturbed. Our technique utilizes material birefringence in both the resonator and the coupler such that a negative (positive) birefringence allows for polarization-selective coupling to TE (TM) WGMs. We formulate a refined coupling condition suitable for describing the case where the refractive indices of the resonator and the coupler are almost the same, from which we derive a criterion for polarization-selective coupling. Finally, we experimentally demonstrate our proposed method using a lithium niobate disk resonator coupled to a lithium niobate prism, where we show a 22-dB suppression of coupling to TM modes relative to TE modes.

Figure 1

(left) Coordinate system and geometrical parameters considered in this work. (right) Illustration of the coupling condition within the ray-optics picture.

Figure 2

The inset schematic shows the configuration considered in this work: the optic axis of the $z$-cut WGM resonator is perpendicular to the optic axis of the prism which are both made from the same material. The main plot shows the $k_y$ spectrum of a fundamental TE and TM mode at the prism interface for the case of a LN resonator ($\lambda =1550\mathrm{nm}$, $R=2.1\mathrm{mm}$). The corresponding propagation constants and bulk wave numbers inside the LN prism ($n_{o}k$ and $n_{e}k$) are also indicated. Note that the coupling of the out-of-plane TE-polarized mode (red) is possible, whereas it is not for the in-plane TM case (blue).

Figure 3

(a) Schematic of the experimental setup. The gray intensity maps in panels (b) and (c) show the evolution of the spectra for the TE and TM modes, respectively, as the LN prism is brought closer to the resonator. The top (blue) spectra correspond to the critically coupled, almost unperturbed resonator (the distance between the LN prism and the resonator is approximately 252 nm), while the lower (red) plots show the spectra when the LN prism and resonator are in contact.

Figure 4

WGM linewidth change induced by coupling to the LN prism for two different radial-order TE and TM modes. The linewidth changes are plotted against the voltage applied to the piezoelectric stage (bottom axis) and the corresponding estimated relative displacement of the LN prism (top axis). The qualitative change of the linewidths is used to identify the mechanical contact point between the LN prism and the resonator. The linewidth of the TE modes increases by approximately 53 MHz before contact, while the linewidth of the TM modes is largely unchanged.