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 to this in recent years, the LN photonic crystal structures developed to date exhibit fairly low quality (). Here we demonstrate LN photonic crystal nanobeam resonators with optical as high as , more than two orders of magnitude higher than other LN photonic crystal nanocavities reported to date. The high optical , together with tight mode confinement, leads to an extremely strong nonlinear photorefractive effect, with a resonance tuning rate of , or equivalently , three orders of magnitude greater than other LN resonators. In particular, we observed an intriguing quenching of photorefraction that has never been reported before. The devices also exhibit strong optomechanical coupling with a gigahertz nanomechanical mode with a significant product of . The demonstration of high- LN photonic crystal nanoresonators paves a crucial step toward LN nanophotonics that could integrate the outstanding material properties with versatile nanoscale device engineering for diverse and intriguing functionalities.
© 2017 Optical Society of America
Lithium niobate (LN) exhibits outstanding electro-optic, nonlinear optical, acousto-optic, piezoelectric, photorefractive, pyroelectric, and photoconductive properties  that have found very broad applications in telecommunication , nonlinear/quantum photonics [3,4], microelectromechanics [5,6], information storage [7,8], sensing , and many other areas . Recently, there has been significant interest in developing LN photonic devices on chip-scale platforms [11–30], which have shown a significant advantage in device engineering compared with conventional approaches. Miniaturization of device dimensions dramatically enhances the optical field in the devices, which enables a variety of nonlinear optical, quantum optical, and optomechanical functionalities. Among various approaches developed to date, the photonic crystal is probably one of the most efficient ones for light confinement , which has been demonstrated on a variety of material platforms [31–34]. For LN, however, it remains an open challenge to achieve high optical quality (), primarily due to significant challenges in device fabrication [35–45]. The LN photonic crystal nanocavities demonstrated to date generally exhibit low optical on the order of [42–44], which seriously limits their potential applications.
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 [14–16,21–23,25–27,30]. This approach, however, limits the extent of optical mode overlap with the LN layer as well as the design flexibility of the 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 up to , more than two orders of magnitude higher than any other LN photonic crystal nanocavities reported to date, to the best of our knowledge [35–45]. The high optical , together with the tiny effective mode volume , leads to an extremely strong nonlinear photorefractive effect, with a resonance tuning rate of , corresponding to , three orders of magnitude greater than other LN resonators [46,47]. In particular, it enables us to observe the intriguing quenching of photorefraction, which 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 . The demonstration of high- LN photonic crystal nanocavities paves a foundation toward LN nanophotonics that would elegantly combine the unique material properties of LN and versatile nanophotonic device design/fabrication, for broad nonlinear photonic, quantum photonic, optoelectronic, and optomechanical applications.
2. DEVICE DESIGN AND FABRICATION
Current plasma etching approaches for fabricating high-quality LN photonic devices generally produce a slant angle on the device sidewall [17,24]. Although it might help improve the optical of LN microresonators, it seriously impacts LN photonic crystals, which have a stringent requirement regarding the precision of device fine structures. To achieve high optical , we tailored our design to incorporate this slant angle into the structure of photonic crystals. Figure 1(a) shows the rectangular-shaped unit cell of the designed photonic crystal nanobeam [Fig. 1(c), inset], where the angles of the inside and outside sidewalls [Fig. 1(b)], and , respectively, are determined by the plasma etching process. The width of the nanobeam, the layer thickness , and the lattice constant are the free parameters that we optimized to produce an optimal bandgap. Figure 1(c) shows the band diagram simulated by the finite element method, where a LN photonic crystal nanobeam with dimensions of and and a lattice constant of exhibits a bandgap of 28 THz, covering an optical frequency from 203 to 231 THz, for the transverse-electric-like (TE-like) polarization with the electric field dominantly lying in the device plane.
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). Figures 1(e) and 1(f) show the optical mode field profiles of the fundamental (TE0) and second-order (TE1) TE-like cavity modes, simulated by the finite element method. The simulations show that the two modes exhibit radiation-limited optical s of and , respectively, with effective mode volumes as small as and (where is the optical resonance wavelength and is the refractive index).
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 Figs. 2(b)–2(d). During the beginning stage of etching, the 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 reduced the thickness of the LN layer to , eventually forming a triangular 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)].
3. LINEAR OPTICAL PROPERTIES
Figures 3(a) and 3(b) show a fabricated device, which clearly shows smooth and well-defined fine features of the device structure. To characterize the optical property of the device, we launched a continuous-wave tunable laser into the device via evanescent coupling with a tapered optical fiber. Figure 3(c) shows the schematic of the experimental testing setup, where the optical wave transmitted out from the device is detected by a high-speed detector with a 3 dB bandwidth of 1.3 GHz, 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.
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). Figure 4(a) shows that the device exhibits two high- optical resonances at 1452 and 1511 nm, which correspond to the fundamental and second-order cavity modes, respectively [Figs. 1(e) and 1(f)]. Detailed characterization of these two modes [Figs. 4(b) and 4(c)] shows that the TE0 and TE1 modes exhibit intrinsic optical as high as and , respectively. These values are more than two orders of magnitude higher than other LN photonic crystal nanocavities that have been reported to date [35–45]. As discussed in the previous section, the TE0 mode has a radiation-limited optical about one order of magnitude higher than the TE1 mode. Therefore, the similarity of optical s for these two modes in our devices infers that the optical of the devices is 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 without degrading the optical , 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 and 20 nm in steps 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 steps 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 for the cavity resonance can be obtained by simultaneously varying the width and the thickness of the photonic crystal nanobeam while keeping the ratio of constant.
4. 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 , which does not affect the overall position of the cavity resonance. The overall blueshift is a typical feature of the photorefractive effect, which originates from the electro-optic effect introduced by the space-charge electric field produced via photovoltaic drift current . The slow relaxation of space charge distribution leads to a net decrease in the refractive index, which results in an overall blueshift 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 that the average optical power coupled into the cavity is , which corresponds to an averaged energy of and an averaged photon number of only inside the cavity. This results in a blue tuning rate of , corresponding to or , which is three orders of magnitude larger than those observed in millimeter-size LN resonators [46,47], clearly showing the dramatically enhanced nonlinear optical effect in the LN photonic crystal nanobeam. Such an energy-efficient resonance tuning has great potential for applications such as all-optical wavelength routing and photonic circuit reconfiguration, which are essential for photonic interconnect and optical data communication. Further characterization of the time response of photorefraction in the devices would help specify the application potential.
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 the same wavelength location, as indicated by the red dashed line in Fig. 5(a). This indicates 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 maintain 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 the 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 whether we decrease or increase the optical power, the phenomena remain the same as in Fig. 5(b), with the overall resonance wavelength nearly intact, except that the extent of the thermo-optic bistability varies with the 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 an optical wave, it will recover to its original state and all the phenomena shown in Fig. 5, such as resonance blueshifting, saturation, and quenching of photorefraction, will reappear. The physical nature underlying the observed quenching phenomena is not clear at this moment, and 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].
5. NANO-OPTOMECHANICAL PROPERTIES
The high quality of 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 , which would enable us to probe the optomechanical properties of the device. To do so, we locked the laser wavelength halfway 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.
Figures 6(a) and 6(b) show the recorded power spectra of a device, revealing 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 . Detailed characterization [Fig. 6(c)] shows that this mode exhibits an intrinsic mechanical of 1465, corresponding to an product of , 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 the environment. Numerical simulations show that this mechanical mode corresponds to a highly localized mode, as shown in the inset of Fig. 6(a), with an effective motion mass of and a theoretical frequency of 1.099 GHz. A detailed comparison of the experimental spectrum with theory shows that this mode exhibits an optomechanical coupling coefficient of , which corresponds to a single-photon/single-phonon optomechanical coupling rate of . This value is similar to those observed in most other optomechanical crystals [54–58], although our devices are not specifically designed for optomechanical applications. It is lower than those in the optimized optomechanical crystals reported in Refs. [59,60] that were optimized to enhance the photoelastic contribution. As LN exhibits outstanding acousto-optic properties , 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 values on the order of , which is primarily due to air damping, since low-frequency mechanical modes exhibit large amplitudes of thermal mechanical motion, sensitive to air damping. Two examples are given in Figs. 6(d) and 6(e), where the modes at 1.71 MHz and 4.68 MHz exhibit mechanical s . Numerical simulations show that these two modes correspond to the first-order and second-order flexural modes [Fig. 6(b), insets II and III], 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 and 0.45 GHz/nm, respectively, corresponding to and 6.8 kHz. The small values of optomechanical coupling are primarily due to the nature of the mechanical modes [Fig. 6(b), inset II and III], 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 of 6142, which is likely to be a high-order flexural mode [Fig. 6(b), inset IV] that is not as sensitive to air damping as other modes.
6. CONCLUSION AND DISCUSSION
In summary, we have demonstrated LN photonic crystal nanobeam resonators with an optical up to , which, to the best of our knowledge, is more than two orders of magnitude higher than other LN photonic crystal nanocavities reported to date [35–45]. The devices exhibit an effective mode volume as small as . The high optical , 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 , corresponding to , 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. The conventional approach to mitigate photorefraction is to dope the LN crystal with certain ions to increase the photorefraction threshold . 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 modes 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 frequencies up to 1.003 GHz with an product of , which is comparable to state-of-the-art LN micromechanical devices [5,6,24,53]. The devices exhibit a single-photon/single-phonon optomechanical coupling rate of that is similar to most other optomechanical crystals [54–58], although our devices are not specifically designed for optomechanical applications. LN exhibits strong piezoelectric effect, electro-optic effect, and electromechanical coupling, significantly greater 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 coupling between electrical, optical, and mechanical degrees of freedom for various optoelectronic, optomechanical, and electromechanical applications.
National Science Foundation (NSF) (EFRI-1641099, ECCS-1509749, CCF-1533842); Defense Advanced Research Projects Agency (DARPA) SCOUT program (W31P4Q-15-1-0007); State Key Laboratory of Advanced Optical Communication Systems and Networks at Shanghai Jiao Tong University, China, Open Program (2016GZKF0JT001).
This study was performed in part at the Cornell NanoScale Science and Technology Facility (CNF), a member of the National Nanotechnology Infrastructure Network.
1. R. S. Weis and T. K. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A 37, 191–203 (1985). [CrossRef]
2. E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, and D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000). [CrossRef]
3. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12, 2102–2116 (1995). [CrossRef]
4. M. Halder, A. Beberatos, N. Gisin, V. Scarani, C. Simon, and H. Zbinden, “Entangling independent photons by time measurement,” Nat. Phys. 3, 692–695 (2007). [CrossRef]
5. M. Pijolat, S. Loubriat, S. Queste, D. Mercier, A. Reinhardt, E. Defay, C. Deguet, L. Clavelier, H. Moriceau, M. Aid, and S. Ballandras, “Large electromechanical coupling factor film bulk acoustic resonator with X-cut LiNbO3 layer transfer,” Appl. Phys. Lett. 95, 182106 (2009). [CrossRef]
6. S. Gong and G. Piazza, “Design and analysis of lithium-niobate-based high electromechanical coupling RF-MEMS resonators for wideband filtering,” IEEE Trans. Microw. Theory Tech. 61, 403–414 (2013). [CrossRef]
7. J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994). [CrossRef]
8. K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature 393, 665–668 (1998). [CrossRef]
9. L. M. Reindl and I. M. Shrena, “Wireless measurement of temperature using surface acoustic waves sensors,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 1457–1463 (2004). [CrossRef]
10. L. Arizmendi, “Photonic applications of lithium niobate crystals,” Phys. Stat. Sol. A 201, 253–283 (2004). [CrossRef]
11. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, “Electrio-optically tunable microring resonators in lithium niobate,” Nat. Photonics 1, 407–410 (2007). [CrossRef]
12. G. Poberaj, H. Hu, W. Sohler, and P. Günter, “Lithium niobate on insulator (LNOI) for micro-photonic devices,” Laser Photon. Rev. 6, 488–503 (2012). [CrossRef]
13. T.-J. Wang, J.-Y. He, C.-A. Lee, and H. Niu, “High-quality LiNbO3 microdisk resonators by undercut etching and surface tension reshaping,” Opt. Express 20, 28119–28124 (2012). [CrossRef]
14. P. Rabiei, J. Ma, S. Khan, J. Chiles, and S. Fathpour, “Heterogeneous lithium niobate photonics on silicon substrates,” Opt. Express 21, 25573–25581 (2013). [CrossRef]
15. L. Chen, Q. Xu, M. G. Wood, and R. M. Reano, “Hybrid silicon and lithium niobate electro-optical ring modulator,” Optica 1, 112–118 (2014). [CrossRef]
16. J. Chiles and S. Fathpour, “Mid-infrared integrated waveguide modulators based on silicon-on-lithium-niobate photonics,” Optica 1, 350–355 (2014). [CrossRef]
17. C. Wang, M. J. Burek, Z. Lin, H. A. Atikian, V. Venkataraman, I.-C. Huang, P. Stark, and M. Lončar, “Integrated high quality factor lithium niobate microdisk resonators,” Opt. Express 22, 30924–30933 (2014). [CrossRef]
18. J. Lin, Y. Xu, Z. Fang, M. Wang, J. Song, N. Wang, L. Qiao, W. Fang, and Y. Cheng, “Fabrication of high-Q lithium niobate microresonators using femtosecond laser micromachining,” Sci. Rep. 5, 8072 (2015). [CrossRef]
19. R. Geiss, S. Saravi, A. Sergeyev, S. Diziain, F. Setzpfandt, F. Schrempel, R. Grange, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Fabrication of nanoscale lithium niobate waveguides for second-harmonic generation,” Opt. Lett. 40, 2715–2718 (2015). [CrossRef]
20. J. Wang, F. Bo, S. Wan, W. Li, F. Gao, J. Li, G. Zhang, and J. Xu, “High-Q lithium niobate microdisk resonators on a chip for efficient electro-optic modulation,” Opt. Express 23, 23072–23078 (2015). [CrossRef]
21. S. Li, L. Cai, Y. Wang, Y. Jiang, and H. Hu, “Waveguides consisting of single-crystal lithium niobate thin film and oxidized titanium stripe,” Opt. Express 23, 24212–24219 (2015). [CrossRef]
22. F. Bo, J. Wang, J. Cui, S. K. Ozdemir, Y. Kong, G. Zhang, J. Xu, and L. Yang, “Lithium-niobate-silica hybrid whispering-gallery-mode resonators,” Adv. Mater. 27, 8075–8081 (2015). [CrossRef]
23. P. O. Weigel, M. Savanier, C. T. DeRose, A. T. Pomerene, A. L. Starbuck, A. L. Lentine, V. Stenger, and S. Mookherjea, “Lightwave circuits in lithium niobate through hybrid waveguides with silicon photonics,” Sci. Rep. 6, 22301 (2016). [CrossRef]
24. W. C. Jiang and Q. Lin, “Chip-scale cavity optomechanics in lithium niobate,” Sci. Rep. 6, 36920 (2016). [CrossRef]
25. L. Chang, Y. Li, N. Volet, L. Wang, J. Peters, and J. E. Bowers, “Thin film wavelength converters for photonic integrated circuits,” Optica 3, 531–535 (2016). [CrossRef]
26. L. Chang, M. H. P. Pfeiffer, N. Volet, M. Zervas, J. D. Peters, C. L. Manganelli, E. J. Stanton, Y. Li, T. J. Kippenberg, and J. E. Bowers, “Heterogeneous integration of lithium niobate and silicon nitride waveguides for wafer-scale photonic integrated circuits on silicon,” Opt. Lett. 42, 803–806 (2017). [CrossRef]
27. A. Rao, J. Chiles, S. Khan, S. Toroghi, M. Malinowski, G. F. Camacho-González, and S. Fathpour, “Second-harmonic generation in single-mode integrated waveguides based on mode-shape modulation,” Appl. Phys. Lett. 110, 111109 (2017). [CrossRef]
28. C. Wang, X. Xiong, N. Andrade, V. Venkataraman, X.-F. Ren, G.-C. Guo, and M. Lončar, “Second harmonic generation in nanostructured thin-film lithium niobate waveguides,” Opt. Express 25, 6963–6973 (2017). [CrossRef]
29. R. Luo, H. Jiang, H. Liang, Y. Chen, and Q. Lin, “Self-referenced temperature sensing with a lithium niobate microdisk resonator,” Opt. Lett. 42, 1281–1284 (2017). [CrossRef]
30. J. D. Witmer, J. A. Valery, P. Arrangoiz-Arriola, C. J. Sarabalis, J. T. Hill, and A. H. Safavi-Naeini, “High-Q photonic resonators and electro-optic coupling using silicon-on-lithium-niobate,” Sci. Rep. 7, 46313 (2017). [CrossRef]
31. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).
32. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystal and nanocavities,” Nat. Photonics 1, 449–458 (2007). [CrossRef]
33. P. Lalanne, C. Sauvan, and J. P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photon. Rev. 2, 514–526 (2008). [CrossRef]
34. M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73, 096501 (2010). [CrossRef]
35. M. Roussey, M.-P. Bernal, N. Courjal, and F. I. Baida, “Experimental and theoretical characterization of a lithium niobate photonic crystal,” Appl. Phys. Lett. 87, 241101 (2005). [CrossRef]
36. G. Zhou and M. Gu, “Direct optical fabrication of three-dimensional photonic crystals in a high refractive index LiNbO3 crystal,” Opt. Lett. 31, 2783–2785 (2006). [CrossRef]
37. M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, F. I. Baida, and R. Salut, “Electro-optic effect exaltation on lithium niobate photonic crystals due to slow photons,” Appl. Phys. Lett. 89, 241110 (2006). [CrossRef]
38. F. Sulser, G. Poberaj, M. Koechlin, and P. Günter, “Photonic crystal structures in ion-sliced lithium niobate thin films,” Opt. Express 17, 20291–20300 (2009). [CrossRef]
39. R. Geiss, S. Diziain, R. Iliew, C. Etrich, H. Hartung, N. Janunts, F. Schrempel, F. Lederer, T. Pertsch, and E.-B. Kley, “Light propagation in a free-standing lithium niobate photonic crystal waveguide,” Appl. Phys. Lett. 97, 131109 (2010). [CrossRef]
40. N. Courjal, S. Benchabane, J. Dahdah, G. Ulliac, Y. Gruson, and V. Laude, “Acousto-optically tunable lithium niobate photonic crystal,” Appl. Phys. Lett. 96, 131103 (2010). [CrossRef]
41. N. Courjal, J. Dahdah, G. Ulliac, P. Sevillano, B. Guichardaz, and F. Baida, “Optimization of LiNbO3 photonic crystals: toward 3D LiNbO3 micro-components,” Opt. Express 19, 23008–23016 (2011). [CrossRef]
42. H. Lu, F. I. Baida, G. Ulliac, N. Courjal, M. Collet, and M.-P. Bernal, “Lithium niobate photonic crystal wire cavity: realization of a compact electro-optically tunable filter,” Appl. Phys. Lett. 101, 151117 (2012). [CrossRef]
43. S. Diziain, R. Geiss, M. Zilk, F. Schrempel, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Second harmonic generation in free-standing lithium niobate photonic crystal L3 cavity,” Appl. Phys. Lett. 103, 051117 (2013). [CrossRef]
44. R. Geiss, S. Diziain, M. Steinert, F. Schrempel, E.-B. Kley, A. Tünnermann, and T. Pertsch, “Photonic crystals in lithium niobate by combining focussed ion beam writing and ion-beam enhanced etching,” Phys. Stat. Sol. A 211, 2421–2425 (2014). [CrossRef]
45. L. Cai, H. Han, S. Zhang, H. Hu, and K. Wang, “Photonic crystal slab fabricated on the platform of lithium niobate-on-insulator,” Opt. Lett. 39, 2094–2096 (2014). [CrossRef]
46. A. A. Savchenkov, A. B. Matsko, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Enhancement of photorefraction in whispering gallery mode resonators,” Phys. Rev. B 74, 245119 (2006). [CrossRef]
47. M. Leidinger, C. S. Werner, W. Yoshiki, K. Buse, and I. Breunig, “Impact of the photorefractive and pyroelectric-electro-optic effect in lithium niobate on whispering-gallery modes,” Opt. Lett. 41, 5474–5477 (2016). [CrossRef]
48. T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12, 4742–4750 (2004). [CrossRef]
49. P. Günter and J.-P. Huignard, eds., Photorefractive Materials and Their Applications (Springer, 2006).
50. X. Sun, H. Liang, R. Luo, W. C. Jiang, X.-C. Zhang, and Q. Lin, “Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators,” Opt. Express 25, 13504–13516 (2017). [CrossRef]
51. Y. Kong, S. Liu, and J. Xu, “Recent advances in the photorefraction of doped lithium niobate crystals,” Materials 5, 1954–1971 (2012). [CrossRef]
52. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014). [CrossRef]
53. R. Wang, S. A. Bhave, and K. Bhattacharjee, “Design and fabrication of S0 Lamb-wave thin-film lithium niobate micromechanical resonators,” J. Microelectromech. Sys. 24, 300–308 (2015). [CrossRef]
54. M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009). [CrossRef]
55. M. Davanco, S. Ates, Y. Liu, and K. Srinivasan, “Si3N4 optomechanical crystals in the resolved-sideband regime,” Appl. Phys. Lett. 104, 041101 (2014). [CrossRef]
56. L. Fan, X. Sun, C. Xiong, C. Schuck, and H. X. Tang, “Aluminum nitride piezo-acousto-photonic crystal nanocavity with high quality factors,” Appl. Phys. Lett. 102, 153507 (2013). [CrossRef]
57. A. Vainsencher, K. J. Satzinger, G. A. Peairs, and A. N. Cleland, “Bi-directional conversion between microwave and optical frequencies in a piezoelectric optomechanical device,” Appl. Phys. Lett. 109, 033107 (2016). [CrossRef]
58. M. J. Burek, J. D. Cohen, S. M. Meenehan, N. El-Sawah, C. Chia, T. Ruelle, S. Meesala, J. Rochman, H. A. Atikian, M. Markham, D. J. Twitchen, M. D. Lukin, O. Painter, and M. Lončar, “Diamond optomechanical crystals,” Optica 3, 1404–1412 (2016). [CrossRef]
59. J. Chan, A. H. Safavi-Naeini, J. T. Hill, S. Meenehan, and O. Painter, “Optimized optomechanical crystal with acoustic radiation shield,” Appl. Phys. Lett. 101, 081115 (2012). [CrossRef]
60. K. C. Balram, M. I. Davanco, J. D. Song, and K. Srinivasan, “Coherent coupling between radio frequency, optical and acoustic waves in piezo-optomechanical circuits,” Nat. Photonics 10, 346–352 (2016). [CrossRef]
61. S. Tadigadapa and K. Mateti, “Piezoelectric MEMS sensors: state-of-the-art and perspectives,” Meas. Sci. Technol. 20, 092001 (2009). [CrossRef]