Lithium niobate (LN) is the workhorse for modern optoelectronics industry and nonlinear optics. High quality (Q) factor LN microresonators are promising candidates for applications in optical communications, quantum photonics, and sensing. However, the phase-matching requirement of traditional evanescent coupling methods poses significant challenges to achieve high coupling efficiencies of the pump and signal light simultaneously, ultimately limiting the practical usefulness of these high Q

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... or LN resonators. Here, for the first time, to the best of our knowledge, we demonstrate deformed chaotic LN microcavities that feature directional emission patterns and high Q factors simultaneously. The chaotic LN microdisks are created using conventional semiconductor fabrication processes, with measured Q factors exceeding 10 6 in the telecommunication band. We show that our devices can be free-space-coupled with high efficiency by leveraging directional emission from the asymmetric cavity. Using this broadband approach, we demonstrate a 58-fold enhancement of free-space collection efficiency of a second harmonic generation signal, compared with a circular microdisk. Single-crystal lithium niobate (LiNbO 3 , LN) [1] is an important material for optical communications and various linear and nonlinear optical applications, thanks to its high second-order susceptibilities [χ 2 ], wide transmission window, and relatively high ordinary and extraordinary refractive indices (n o 2.21, n e 2.14). Its nonlinear coefficients for second-harmonic generation (SHG, d 33 41.7 pm∕V) and electro-optic modulation (r 33 30.9 pm∕V) are high, compared with other commonly used χ 2 materials. Microresonators, which manifest excellent light confinement in a small volume for a long time via total internal reflection, can greatly enhance the interaction between light and matter [2] [3] [4] . Combining the excellent physical properties of LN and the tremendous light field enhancement in microresonators, many demonstrations on high-Q LN microresonators have recently been reported, showing great promise for efficient nonlinear optical processes on chip [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] . However, such systems typically suffer from a small coupling bandwidth due to the momentum mismatch between the resonator and the coupling fiber or prism [17] [18] [19] , while the pump and signal wavelength in nonlinear processes are often dramatically different [20] . This key obstacle has become a major limitation for these high-Q factor LN resonators. In this Letter, we design a chaotic LN microcavity that supports high-Q factor and directional emission at the same time, allowing for significantly more efficient coupling of pump and signal light in SHG process simultaneously. The deformed microdisk is fabricated by standard semiconductor fabrication process, which features Q factors exceeding 10 6 and supports efficient free-space coupling. The property of directional emission is verified by measuring the free-space coupling efficiency with different coupling angles. Using the deformed LN microcavity, we show nearly two orders of magnitude enhancement in SHG collection efficiency, compared with a circular LN cavity. The geometric profile of the deformed microcavities is defined by an angle-dependent radius, Rϕ R 0 P n 1 a n cos ϕ n , where ϕ represents the polar angle, R 0 is a size parameter, and a n are shape parameters with fixed numbers (a 2 −0.0045, a 3 −0.0305, a 4 −0.0273, a 5 0.0314, and a 6 −0.0381). The deformed microdisk resonators are fabricated on an LN-silica-silicon wafer prepared using ion slicing and wafer bonding techniques (NANOLN). The thicknesses of the LN device layer (z-cut), the sacrificial silica layer, and the silicon substrate are 0.5, 2, and 500 μm, respectively. The fabrication processes [21] are schematically illustrated in Fig. 1(a) , which involves six major steps: UV-lithography, Ar plasma etching, first HF etching, XeF 2 etching, and second HF etching. First, Vol. 43, No. 12 / Letter