High-quality lithium niobate photonic crystal nanocavities

Lithium niobate (LN) exhibits unique material characteristics that have found many important applications. Scaling LN devices down to a nanoscopic scale can dramatically enhance light-matter interaction that would enable nonlinear and quantum photonic functionalities beyond the reach of conventional means. However, developing LN-based nanophotonic devices turns out to be nontrivial. Although significant efforts have been devoted in recent years, LN photonic crystal structures developed to date exhibit fairly low quality. Here we demonstrate LN photonic crystal nanobeam resonators with optical Q as high as 10^5, more than two orders of magnitude higher than other LN nanocavities reported to date. The high optical quality together with tight mode confinement leads to extremely strong nonlinear photorefractive effect, with a resonance tuning rate of 0.64 GHz/aJ, or equivalently 84 MHz/photon, three orders of magnitude greater than other LN resonators. In particular, we observed intriguing quenching of photorefraction that has never been reported before. The devices also exhibit strong optomechanical coupling with gigahertz nanomechanical mode with a significant f*Q product of 1.47*10^12 Hz. The demonstration of high-Q LN photonic crystal nanoresonators paves a crucial step towards LN nanophotonics that could integrate the outstanding material properties with versatile nanoscale device engineering for diverse intriguing functionalities.

Lithium niobate (LN) exhibits outstanding electro-optic, nonlinear optical, acoustooptic, piezoelectric, photorefractive, pyroelectric, and photoconductive properties 1 that have found very broad applications in telecommunication 2 , nonlinear/quantum photonics 3,4 , microelectromechanics 5,6 , information storage 7,8 , sensing 9 , among many others 10 . Recently, significant interest has been attracted to develop LN photonic devices on chip-scale platforms 11-30 , which have shown significant advantage in device engineering compared with conventional approaches. Miniaturization of device dimensions dramatically enhances optical field in the devices which enables a variety of nonlinear optical, quantum optical, and optomechanical functionalities.
An alternative approach to get around the fabrication challenge is to fabricate waveguide structures on a different material deposited on top of a LN substrate to provide wave guidance while using LN as a cladding material [14][15][16][21][22][23][25][26][27]30 . This approach, however, limits the extent of optical mode overlap with the LN layer as well as the design flexibility of waveguide structure, due to the limitation of index contrast required between the waveguide material and the LN substrate.
In this paper, we demonstrate LN photonic crystal nanobeam resonators with optical Q up to 1.09 × 10 5 , more than two orders of magnitude higher than any other LN photonic crystal nanocavities reported to date [35][36][37][38][39][40][41][42][43][44][45] . The high optical Q together with the tiny effective mode volume (∼ 1.03(λ /n) 3 ) leads to extremely strong nonlinear photorefractive effect, with a resonance tuning rate of ∼0.64 GHz/aJ, corresponding to ∼84 MHz/photon, three orders of magnitude greater than other LN resonators 46,47 . In particular, it enables us to observe the intriguing quenching of photorefraction that has never been reported before. It also results in strong coupling between the optical cavity mode and the mechanical motion of the device structure, which allows us to sensitively probe the rich nanomechanical properties of the LN photonic crystal nanobeams up to ∼1 GHz. The demonstration of high-Q LN photonic crystal nanocavities paves the foundation towards LN nanophotonics that would combine elegantly the unique material properties of lithium niobate and versatile nanophotonic device design/fabrication, for broad nonlinear photonic, quantum photonic, optoelectronic, and optomechanical applications. as a function of position, which is optimized for high radiation-limited optical Q. e and f. The optical mode field profiles of the fundamental (TE0) and second-order (TE1) transverse-electric-like (TE-like) cavity modes, with electric field dominantly lying in the device plane. The mode field profiles are simulated by the finite element method. Note that the horizontal axes of (e) and (f) have a different scale from that of (d).

Device Design and Fabrication
Current plasma etching approaches to fabricate high-quality LN photonic devices generally produce a slant angle on the device sidewall 17,24 . Although it might help improve the optical quality of LN microresonators, it impacts seriously on LN photonic crystals which have stringent requirement on the precision of device fine structures. To achieve high optical Q, we tailored our design to incorporate such slant angle into the structure of photonic crystals. The insets of Fig. 1(a) show the rectangular-shaped unit cell of the designed photonic crystal nanobeam ( Fig. 1(c where the angles of inside and outside sidewalls ( Fig. 1(b)), θ in = 45 • and θ out =75 • , are determined by the plasma etching process. The width W of the nanobeam, the layer thickness H, and the lattice constant a are the free parameters which we optimized to produce an optimal bandgap. To produce a defect cavity, we gradually decreased the lattice constant from 600 nm to 540 nm around the center of the nanobeam. We optimized the nanobeam with a pattern of lattice constants as shown in Fig. 1(d), which results in a localized defect cavity at the center of the nanobeam whose fundamental cavity mode exhibits a resonance frequency close to the center of the photonic bandgap, as indicated by the blue dot in Fig. 2(c). Figure 1 Our devices were fabricated on a 300-nm-thick x-cut congruent single-crystalline LN thin film sitting on a 2-µm-thick buried oxide layer. The structure was patterned with ZEP-520A positive resist as a mask via electron beam lithography ( Fig. 2(a)) and was etched with the Ar-ion milling process 17,24 . We developed an over-etching process to produce desired fine structures and sidewall smoothness, as schematically shown in Fig. 2  Ar-ion milling process produces slant angles on the device sidewall, leading to a trapezoid-shaped cross section ( Fig. 2(b)). Further Ar-ion milling etched the ZEP-520A mask away and thinned the thickness of the LN layer down to ∼250 nm, eventually forming a triangularly-shaped cross section ( Fig. 2(c)). Finally, the buried oxide layer was undercut by diluted hydrofluoric acid to form a suspended photonic crystal nanobeam ( Fig. 2(d)).  whose output is characterized by an oscilloscope or an electrical spectrum analyzer, depending on the measured contents. The laser wavelength is calibrated by a Mach-Zehnder interferometer.

Linear optical properties
By scanning the laser wavelength over a broad telecom band and monitoring the power transmission from the device, we obtained the transmission spectrum of the device shown in Fig. 4(a). respectively, which correspond to the fundamental and second-order cavity modes ( Fig. 1(e) and (f)). Detailed characterization of these two modes ( Fig. 4(b) and (c)) shows that the TE0 and TE1 modes exhibit optical Q as high as 1.09 × 10 5 and 1.08 × 10 5 , respectively. These values are more than two orders of magnitude higher than other LN photonic crystal nanocavities that have ever been reported to date [35][36][37][38][39][40][41][42][43][44][45] . As discussed in the previous section, the TE0 mode has a radiation-limited optical Q about one order of magnitude higher than the TE1 mode. Therefore, the similarity of optical Qs for these two modes in our devices infers that the optical quality of the devices are still limited by the scattering loss from the sidewall roughness, which can be improved by further optimization of device fabrication.
We are able to precisely control the device dimensions to tune the cavity resonance, as shown in Fig. 4(d). On one hand, the cavity resonance depends nearly linearly on the lattice constant.
By tuning the lattice constants by an amount between -20 nm and 20 nm in a step of 5 nm from the nominal values shown in Fig. 1(d), we are able to shift the cavity resonance wavelength in a linear fashion from 1480 nm to 1560 nm, by a step of about 10 nm (Fig. 4(d), black dots). On the other hand, the cavity resonance is sensitive to the width and the thickness of the photonic crystal nanobeam. As shown in Fig. 4(d), a similar broadband tuning range of cavity resonance can be obtained by varying simultaneously the width and the thickness of the photonic crystal nanobeam while keeping the ratio of W/H constant.

Photorefraction and its saturation and quenching
The high quality of the LN photonic crystal nanobeams enables us to observe intriguing nonlinear optical phenomena. Figure 5 shows an example. We scanned the laser wavelength across a cavity resonance back and forth in a periodic triangular fashion, and monitored the transmission of the device. When the input optical power increases from 330 nW to 8 µW, the transmission spectrum changes from a Lorentzian shape to a bistability-type shape while the overall resonance wavelength shifts towards blue by about 55 pm (Fig. 5(a), Region I). The bistability-type behavior is simply due to the thermo-optic nonlinearity that responds fairly rapidly to photothermal heating 48 , which does not affect the overall position of the cavity resonance. The overall blue shift is a typical feature of the photorefractive effect that originates from the electro-optic effect introduced by the space-charge electric field produced via photovoltaic drift current 49 . The slow relaxation of space charge distribution leads to a net decrease of refractive index which results in an overall blue shift of the cavity resonance 46,47,50 .
As the linewidth of the loaded cavity resonance is about 15 pm with a coupling depth of 30  % while the laser continuously scans over a tuning range of 280 pm, we estimate the average optical power coupled into the cavity is ∼133 nW, which corresponds to an averaged energy of ∼11.5 aJ and an averaged photon number of only ∼87 inside the cavity. This results in a blue tuning rate of ∼0.64 GHz/aJ, corresponding to ∼84 MHz/photon or ∼55 GHz/µW , which is 3 orders of magnitude larger than those observed in millimeter-size LN resonators 46,47 , clearly showing the dramatically enhanced nonlinear optical effect in LN photonic crystal nanobeam.
Such an energy-efficient resonance tuning is of great potential for applications such as all-optical wavelength routing and photonic circuit reconfiguration that are essential for photonic interconnect and optical data communication.
When the input power increases further from 8 µW to 41 µW (Fig. 5(a), Region II), although the thermo-optic bistability becomes more profound, as expected, the left edge of the cavity resonance stays at a same wavelength location, as indicated by the red dashed line in Fig. 5(a). This infers that the overall cavity resonance wavelength remains unchanged, implying that the photorefraction saturates completely with increased power, in contrast to the photorefraction phenomena observed in other devices 46,47,50 . The underlying mechanism is likely due to the saturation of the generation of space charges responsible for photorefraction, since the extremely tiny physical size of the LN photonic crystal nanocavity leads to a limited number of donors/acceptors that can be excited by optical absorption to produce space charge carriers.
Of particular surprise is that, when we maintained the periodic laser scanning of the cavity mode at an input power of 41 µW, the cavity resonance wavelength moves gradually by itself back to its original value of the passive cavity in the absence of optical power, as indicated by the arrows in Fig. 5. After this stage, the overall resonance remains unchanged at its passive value no matter how much optical power is launched into the device, as indicated by the blue dashed line in Fig. 5(b) showing the left edge of the cavity resonance. This indicates that the photorefraction is completely quenched by the optical wave launched into the device, which has never been observed before. At this state, no matter if we decreased or increased optical power, the phenomena remain same as Fig. 5(b), with the overall resonance wavelength nearly intact, except that the extent of thermo-optic bistability varies with optical power. Interestingly, the whole process is reversible.
For example, after the photorefraction is quenched, if the device stays at rest for a few hours in the absence of optical wave, it will recover to its original state and all the phenomena shown in Fig. 5, such as resonance blue shifting, saturation and quenching of photorefraction, re-appear. The physical nature underlying the observed quenching phenomena is not clear at this moment, which requires further exploration. The quenching of photorefraction would be of great importance for nonlinear optical applications of LN nanophotonic devices, since photorefraction has been shown to be potentially detrimental to nonlinear optical processes 49,51 .

Nano-optomechanical properties
The high quality of the LN photonic crystal nanobeams together with tight optical mode confinement results in strong coupling between the optical field inside the cavity and the mechanical motion of the device structure 52 , which would enable us to probe the optomechanical properties of the device. To do so, we locked the laser wavelength half way into the cavity resonance at the blue detuned side, and monitored the power spectrum of the cavity transmission. The device was tested in the atmospheric environment at room temperature. show recorded power spectra of a device, which shows rich mechanical mode families extending over a broad frequency range. As shown in Fig. 6(a), the device exhibits a mechanical mode with a frequency at Ω m 2π = 1.003 GHz. Detailed characterization (Fig. 6(c)) shows that this mode exhibits an intrinsic mechanical Q of 1465, corresponding to a f · Q product of 1.47 × 10 12 Hz, which is comparable to state-of-the-art LN micromechanical resonators 5,6,24,53 .
We believe that the mechanical damping is dominated by clamping loss, as the device has not been engineered to isolate the mechanical mode from environment. Numerical simulations show that this mechanical mode corresponds to a breathing mode ( Fig. 6(a), inset) with an effective motion mass of m eff = 0.81 picograms and a theoretical frequency of 1.099 GHz. Detailed comparison of the experimental spectrum with theory shows that this mode exhibits an optomechanical coupling coefficient of |g OM | 2π = 22 GH/nm, which corresponds to a single-photon/single-phonon optomechanical coupling rate of |g o | 2π = |g OM | 2π h 2m eff Ω m = 71 kHz. This value is comparable to those observed in most other optomechanical crystals [54][55][56][57][58] , although our devices are not specifically designed for optomechanical applications. It is lower than those in optimized optomechanical crystals reported in 59,60 that were optimized to enhance the photoelastic contribution. As LN exhibits outstanding acousto-optic property 1 , we expect that future optimization of device design would be able to significantly improve the optomechanical properties of the LN photonic crystal nanobeams.
On the other hand, detailed characterization of low-frequency modes ( Fig. 6(b)) shows that a majority of them exhibit low mechanical qualities in the order of ∼ 100, which is primarily due to  two modes correspond to the first-order and second-order flexural modes ( Fig. 6(b), inset I and II), respectively, with effective motional masses of 7.2 and 7.9 picograms. Comparison of the experimental spectra with theory shows that these two modes exhibit |g OM | 2π = 0.35 and 0.45 GHz/nm, respectively, corresponding to |g o | 2π = 9.1 and 6.8 kHz. The small values of optomechanical cou-pling are primarily due to the nature of the mechanical modes ( Fig. 6(b), inset I and II) which do not couple well with the optical cavity mode localized at the beam center. Figure 6(f) shows that a mechanical mode at 11.18 MHz shows a high mechanical Q of 6142, which is likely to be a high-order flexural mode ( Fig. 6(b), inset III) that is not as sensitive to air damping as other modes.
The high optical Q together with tight optical mode confinement results in intriguing nonlinear optical phenomena. We have observed significant cavity resonance tuning induced by the photorefractive effect, with a tuning rate of ∼0.64 GHz/aJ, corresponding to ∼84 MHz/photon, three orders of magnitude greater than other LN resonators 46,47 . In particular, the devices exhibit strong saturation and quenching of photorefraction that has never been observed before.
Photorefraction-induced optical damage is known to be detrimental to nonlinear optical processes in LN crystals 49,51 , which has become a major obstacle to LN nonlinear photonics. Conventional approaches to mitigate photorefraction is to dope LN crystal with certain ions to increase the photorefraction threshold 51 . The strong saturation and quenching of photorefraction observed in our devices might offer an elegant solution to this problem, making LN nanophotonic devices particularly promising for nonlinear photonic applications.
On the other hand, the demonstrated devices exhibit strong coupling between the optical cavity mode and the mechanical motion of the device structures, with which we were able to characterize the rich nanomechanical motions of the device. We observed mechanical modes with frequency up to 1.003 GHz with a f · Q product of 1.47 × 10 12 Hz that is comparable to state-ofthe-art LN micromechanical devices 5,6,24,53 . The devices exhibit a single-photon/single-phonon optomechanical coupling rate of |g o | 2π = 71 kHz that is comparable to most other optomechanical crystals [54][55][56][57][58] , although our devices are not specifically designed for optomechanical applications.
LN exhibits strong piezoelectric effect, electro-optic effect, and electromechanical coupling, significantly larger than other materials such as aluminum nitride and gallium arsenide 1,6,61 . Therefore, LN photonic crystals would offer a promising device platform that could achieve mutual strong couplings between electrical, optical, and mechanical degrees of freedom for various opto-electronic, optomechanical, and electromechanical applications.