Microwave whispering-gallery resonator for efficient optical up-conversion

Conversion of microwave radiation into the optical range has been predicted to reach unity quantum efficiency in whispering-gallery resonators made from an optically nonlinear crystal and supporting microwave and optical modes simultaneously. In this work, we theoretically explore and experimentally demonstrate a resonator geometry that can provide the required phase matching for such a conversion at any desired frequency in the sub-THz range. We show that such a ring-shaped resonator not only allows for the phase matching but also maximizes the overlap of the interacting fields. As a result, unity-efficient conversion is expected in a resonator with feasible parameters.

Figure 1

(Color online) A phase-matching solution for lithium niobate, type-I up-conversion, is achieved at ${\omega }_c=2\pi \times 100\text{GHz}$, $L_c=13$. Curve (A) is the phase-matching curve resulting from Eq. (5); curve (B) is the microwave dispersion curve calculated numerically.

Figure 2

(Color online) Absolute value of the $E_z$ component of a microwave WGM mode in a lithium niobate resonator with ${\omega }_c=2\pi \times 100\text{GHz}$, $L_c=13$. The plot is on a log scale with color map given on the right. A sketch of the geometry is shown in the inset, where the red box represents the calculation window.

Figure 3

(Color online) Phase-matching solutions for lithium tantalate, type-II up-conversion, can be achieved at $L_c=76,77,78$ with the dc bias voltages shown on the plot. Curve (A) is the phase-matching curve resulting from Eq. (5); curve (B) is the microwave dispersion curve calculated numerically.

Figure 4

(Color online) Absolute value of the $E_r$ component of a microwave WGM mode in a lithium tantalate resonator with ${\omega }_c=2\pi \times 231\text{GHz}$, $L_c=77$. The plot is on a log scale with color map given on the right. A sketch of the geometry is shown in the inset, where the red box represents the calculation window.

Figure 5

(Color online) A lithium niobate WGM ring resonator mounted on a fused silica post (photo) coupled with a tapered dielectric waveguide (drawing). The ring height is 0.29 mm; the outer radius is 2.9 mm.

Figure 6

(Color online) Dependence of the microwave spectrum on the resonators’ outer radius. The experimental data and theoretical calculations done by finite element method show very good agreement for the effective inner ring radius determined to be $R_{in}=2.61\text{mm}$.

Figure 7

(Color online) Microwave spectrum of the ring resonator shown in Fig. 5. The modes are labeled by the orbital number $L_c$.