Abstract

Optical microresonators with high quality factors are key in photonic circuits requiring fine spectral filtering or resonant storage of optical power. Silicon (Si) photonics provides high-performance optoelectronic circuits but yields planar Si microresonators with rather low quality factors (${\rm Q}\; \lt \;{{10}^5}$). On the other hand, bulk resonators achieve exceptionally high quality factors, ${\rm Q}\; \gt \;{{10}^7}$. Si photonic waveguides and bulk resonators have very different sizes and refractive indices that preclude efficient coupling. Here, we show an efficient method to couple bulk resonators and Si waveguides based on subwavelength metamaterial engineering. We demonstrate up to 99% light coupling efficiency for microspheres and microdisks made of silica, lithium niobate, and calcium fluoride, with ${0.3}-{3.6}\;{\rm mm}$ diameter. This achievement could enable the heterogeneous integration of bulk resonators and silicon photonic circuits, with potential applications in sensing, communications, and quantum information.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Optical microresonators provide key functionalities like ultra-fine spectral filtering, lasers with high spectral purity, high-efficiency frequency comb generation, and high optomechanical coupling [1]. The performance of the resonators is typically assessed by their quality factor, ${\rm Q}$, defined as the energy stored in the resonator divided by the energy dissipated per radian. Since ${\rm Q}$ is inversely proportional to the fractional power loss per optical cycle, key performance metrics improve with increasing ${\rm Q}$. For example, power consumption and phase and intensity noise in resonator-based optical sources scale inversely with the square of ${\rm Q}$. At the same time, high ${\rm Q}$ improves precision in resolving the resonance wavelength, which is important for applications in sensing [2] and frequency stabilization [3].

Silicon (SI) photonics provides a unique potential for large volume production of optoelectronic circuits [4] and is considered a key technology for the development of emerging applications in sensing and communications. However, the performance of Si photonic circuits is often limited by the comparatively low quality factors of Si-based ring resonators, typically in the ${{10}^{4}} - {{10}^6}$ range. In addition, Si has some intrinsic physical limits that hamper the implementation of advanced nonlinear and optoelectronic functionalities. Strong two-photon absorption in the near-infrared compromises nonlinear applications, and the centro-symmetry of the Si lattice compromises the efficiency of optoelectronic circuits exploiting the Pockels effect. On the other hand, bulk whispering gallery mode (WGM) optical resonators like spheres and disks in different materials provide a wide range of remarkable optical properties and ultra-high ${\rm Q}$-factors of up to ${{10}^{11}}$, especially in fluoride crystals [5]. Si bulk WGM resonators have been recently shown with ${\rm Q} = {{10}^9}$ [6]. WGM microresonators have been exploited for both fundamental studies and practical applications [1] because of their unique properties of long cavity lifetime and small mode volumes. The strongly enhanced light–matter interaction allows the implementation of important functionalities and applications, including nonlinear and quantum sources [7], frequency combs [8], high-purity radiofrequency signal generation [9], optomechanical oscillations [10], stimulated inelastic scattering [11], laser stabilization [12], and biosensing [13].

A critical point to exploit the remarkable optical properties of WGM resonators is the implementation of an efficient, controllable, and robust approach to excite the resonator modes [14]. The common approach relies on phase-matched evanescent field coupling [15]. The state-of-the-art demonstrations rely on thin fiber tapers with a diameter of a few microns [16]; hence, they are inherently fragile and suitable only for lab demonstrations. More robust approaches are based on angle cleaved fibers [17] and integrated waveguides [18]. Prism-coupling [19] is a particularly versatile technique but relies on free space optics and requires the beam to spatially match the resonator mode, which is a critical factor in several circumstances.

Robust coupling between planar Si waveguides and low-index bulk resonators, e.g., silica, is not possible because of index mismatch [20,21]. The only way to reduce the effective index in a conventional Si waveguide is to reduce its width. This results in large mode delocalization toward the buried oxide (BOX) and the substrate. Low-index tapered fibers can be coupled to high-index resonators through excitation of higher order modes [22]. There are only a couple of examples in the literature where Si photonic waveguides are coupled to high-index bulk resonators, namely to chalcogenide spheres [20] and lithium niobate disks [21]. Efficient and robust coupling of Si waveguides and alkaline Earth fluorides remains an open challenge. Coupling of a silica microtoroid and Si waveguide has been reported based on a suspended Si photonic crystal membrane [23]. Yet, such a membrane structure has a limited mechanical robustness. In addition, the bandwidth of such photonic crystals is limited by the bandgap-based guiding mechanism. Low refractive index ultra-high ${\rm Q}$ WGM resonators made from alkaline Earth fluorides were only recently successfully coupled to a low refractive index suspended silica waveguide [24]. Coupling of an on-chip silica microtoroid and integrated Si nitride waveguides has also been demonstrated [25]. However, these strategies require rather complex fabrication processes and yield coupling only to one specific type of microresonator.

None of the above coupling techniques allows efficient coupling to different kinds of resonators, leaving untapped the wide range of materials and optical properties provided by different types of bulk WGM resonators. Here, we propose and demonstrate a new type of highly versatile coupling approach, which enables coupling between integrated Si waveguides and a wide range of bulk WGM resonators with largely disparate sizes (300 µm–3.6 mm diameter) and refractive indices (1.42–2.21). The proposed coupler is monolithically integrated on a silicon-on-insulator (SOI) wafer (350 µm thickness), being mechanically more robust than solutions based on tapered fibers. This universal coupling approach leverages the subwavelength grating (SWG) metamaterial waveguides to shape the optical field distribution and wave vector of guided modes [26]. Specifically, we use a tapered coupler geometry, schematically shown in Fig. 1(a), where the SWG metamaterial index is continuously varied to allow efficient coupling to different types of resonators. Our SWG waveguides allow the utilization of a wider waveguide width by changing the duty cycle, which in turn reduces the effective index by delocalizing the mode in the horizontal direction, at the same time also reducing the substrate leakage.

 figure: Fig. 1.

Fig. 1. (a) Schematic diagram of the SWG metamaterial tapered waveguide designed for coupling light to bulk WGM resonators. (b) Scanning electron microscope image of SWG metamaterial coupler.

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SWG metamaterials, since their first demonstration in Si waveguides [2730], have been advantageously used as a powerful tool for overcoming performance limitations of conventional Si-based integrated photonic devices [26,31]. SWG waveguides use metamaterial index confinement to guide the light avoiding photonic bandgap regime, hence achieving ultra-wideband operation (exceeding 200 nm), and they have been used to demonstrate a plethora of integrated photonic devices with unprecedented performance [26]. However, they have not been exploited yet as WGM microresonator couplers.

SWG coupler design, schematically shown in Fig. 1(a), leverages the mode transformation principle reported in [32]. The coupler is designed for Si thickness ${t} = {220}\;{\rm nm}$. At both ends, the coupler is connected to conventional strip waveguides of width ${{\rm W}_{\rm wg}} = {500}\;{\rm nm}$ (effective index ${{n}_{\rm eff}} = {2.4}$), using graded transitions of length ${{\rm L}_{\rm A}} = {17}\;{\unicode{x00B5}{\rm m}}$, designed to yield an adiabatic variation of the effective waveguide index along the transition, as described in [32]. The SWG taper has a length of ${{\rm L}_{\rm B}}$, which varies between 75 µm and 450 µm. The period (${\Lambda}$) and gap length (${{\rm L}_{\rm g}}$) are varied linearly. This ensures negligible excitation of higher order modes for transverse-electric (TE) polarized mode near 1550 nm wavelength. At the beginning of the taper, the SWG waveguide has a width of ${{\rm W}_{\rm S}} = {400}\;{\rm nm}$, a period of ${\Lambda = 270\,\,\rm nm}$, and a gap length of ${{\rm L}_{\rm g}} = {100}\;{\rm nm}$. At the end of the taper, the SWG waveguide has a period of ${\Lambda = 400\,\,\rm nm}$ and a gap of ${{\rm L}_{\rm g}} = {200}\;{\rm nm}$. The waveguide width at the end of the taper, ${{\rm W}_{\rm C}}$, is varied between 200 nm and 450 nm to implement different effective index profiles. The effective index at each section of the taper is calculated with second-order Rytov’s equivalent index approximation and three-dimensional simulations, as discussed in [26].

We fabricated 24 different SWG couplers. The final taper width, ${{\rm W}_{\rm C}}$, has been varied between 200 nm and 450 nm with a step of 50 nm. For each value of ${{\rm W}_{\rm c}}$, four different taper lengths, of ${{\rm L}_{\rm B}} = {75}\;{\unicode{x00B5}{\rm m}}$, 150 µm, 300 µm, and 450 µm, have been used. The devices were fabricated by electron-beam lithography and reactive ion etching using a 220-nm-thick single crystal Si layer of a SOI wafer, with a 3-µm-thick BOX layer. The samples were then spin coated with a 300-nm-thick PMMA upper cladding, with a refractive index of 1.5. Figure 1(b) shows scanning electron microscope (SEM) images of the coupler with ${{\rm W}_{\rm C}} = {200}\;{\rm nm}$ and ${{\rm L}_{\rm B}} = {75}\;{\unicode{x00B5}{\rm m}}$.

In order to test our SWG couplers, different WGM resonators made from ${{\rm CaF}_2}$ (${{\rm n}_{\rm CaF2}} = {1.42}$), ${{\rm MgF}_2}$ (${{\rm n}_{\rm MgF2}} = {1.37}$), silica (${{\rm n}_{\rm SiO2}} = {1.44}$), and ${{\rm LiNbO}_3}$ (${{\rm n}_{\rm LiNbO3}} = {2.21}$) were fabricated. We have employed an arc-discharge melting technique for manufacturing silica microspheres, with a diameter ranging from 20 µm to 400 µm [33]. A polishing technique with diamond suspensions has been used for ${{\rm CaF}_2}$, ${{\rm MgF}_2}$, silica, and ${{\rm LiNbO}_3}$ disks, with diameters between 2 and 5 mm and a thickness of 0.5 mm [18].

A schematic of the experimental setup is shown in Fig. 2(a). We use a continuous-wave tunable external-cavity laser with a linewidth of 300 kHz. The wavelength is finely tuned around 1550 nm by an external voltage control. Light is coupled to the chip via a lensed single mode fiber with 2 µm Gaussian beam waist. We use 3-µm-wide input Si waveguides, yielding a coupling loss of $\sim {10}\;{\rm dB}$. The output is collected through a $10 \times$ objective and a photodiode and analyzed using an oscilloscope. The SWG coupler was experimentally characterized, showing a measured taper loss in the 1–3 dB range, depending on the final waveguide width and taper length. The bulk resonators are placed on top of the SWG coupler using nano-positioner with an accuracy of 10 nm. Figure 2(b) shows the relative position between a WGM microsphere resonator and a set of SWG waveguides.

 figure: Fig. 2.

Fig. 2. (a) Simplified schematic of the experimental setup. TL, tunable laser; PC, polarization controller; LF, lensed fiber; SWG, subwavelength grating waveguide; OBJ, ${10} \times$ micro-objective; PD, photodetector; OSC, oscilloscope. (b) Optical microscope image of a WGM microsphere resonator placed above the silicon chip with a set of SWG waveguides. The resonator is centered above and in the middle of a SWG tapered waveguide coupler.

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We start with the study of the silica microsphere. As shown in the transmission spectrum of Fig. 3, silica microspheres can be critically coupled to tapered SWGs with ${{\rm W}_{\rm C}} = {400}\;{\rm nm}$. The measured coupling efficiency is CE ${\sim}99\%$, and the maximum quality factor is ${\rm Q}\sim 2 \times 10^{7}$. Decreasing the width ${\rm W}_{\rm C}$ results in a reduction of the resonance contrast, down to 40% for ${{\rm W}_{\rm C}} = {200}\;{\rm nm}$. No significant difference in coupling efficiency has been observed changing the SWG coupler lengths (${{\rm L}_{\rm B}} = {300}$, 150, and 75 µm). The coupling performance has been evaluated for the microsphere being directly in contact with the chip surface, as well as for a small separation gap (${\lt}{50}\;{\rm nm}$). In contact, the ${\rm Q}$-factor decreases to $\sim 5 \times 10^{6}$, with no variation of coupling efficiency.

 figure: Fig. 3.

Fig. 3. Transmission spectrum of a SWG waveguide coupled to a silica microsphere. The red line represents the Lorentzian fit of a resonance.

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Then, we study the coupling with disks made of different materials (${{\rm LiNbO}_3}$, ${{\rm SiO}_2}$, ${{\rm CaF}_2}$, and ${{\rm MgF}_2}$) with millimeter-scale radius. ${Z}$-cut lithium niobate disk, with a high refractive index of ${{\rm n}_{\rm LiNbO3}} = {2.21}$, is critically coupled (CE of 98%) to a SWG taper with ${{\rm W}_{\rm C}} = {450}\;{\rm nm}$, reaching a ${\rm Q}$-factor of $\sim 8 \times 10^{6}$, as shown in Fig. 4(a). This coupling efficiency is higher than the one achieved with ${{\rm LiNbO}_3}$ waveguides [18]. Coupling to different WGMs results in uneven resonance spacing and depth. No differences in coupling efficiency have been observed when changing the SWG coupler length ${{\rm L}_{\rm C}}$ between 450 µm and 75 µm. For tapered SWG with ${{\rm W}_{\rm C}} = {400}$ and 350 nm, the coupling efficiency is reduced to ${\rm CE} = {40}\% - {50}\%$. For ${{\rm W}_{\rm C}} = {300}$, 250, and 200 nm, coupling efficiency drops below 5%.

 figure: Fig. 4.

Fig. 4. Transmission spectrum of a SWG waveguide coupled to (a) ${{\rm LiNbO}_3}$ disk, (b) a silica disk, and (c) a ${{\rm CaF}_2}$ disk.

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A silica disk, with a lower refractive index of ${{\rm n}_{\rm SiO2}} = {1.44}$, is critically coupled to tapered SWGs with a central width of ${{\rm W}_{\rm C}} = {350}$, 300, 250, and 200 nm. As shown in Fig. 4(b), the measured ${\rm Q}$-factor reaches up to ${\rm Q}\sim{1.7}{\times}{{10}^7}$. No critical coupling has been obtained for ${{\rm W}_{\rm C}} = {400}\;{\rm nm}$ (coupling efficiency up to 60%). No differences have been observed changing the SWG coupler length, i.e., for ${{\rm L}_{\rm C}} = {450}$, 300, 150, and 75 µm). Compared with the coupling efficiency obtained for ${{\rm SiO}_2}$ microspheres, these results indicate that larger resonators achieve higher coupling efficiency to a wider range of SWG geometries.

A calcium fluoride disk, with a refractive index of ${{\rm n}_{\rm CaF2}} = {1.42}$, yields high coupling efficiency CE = 77 %, with a ${\rm Q}$-factor of $\sim {4.7}\;{\times}\;{{10}^6}$, for ${{\rm W}_{\rm C}} = {250}\;{\rm nm}$ and ${{\rm L}_{\rm B}} = {150}\;{\unicode{x00B5}{\rm m}}$. However, critical coupling is not achieved with any of the SWG couplers. Magnesium fluoride disk, with the lowest refractive index considered here (${{\rm n}_{\rm MgF2}} = {1.37}$), yields a comparatively low coupling efficiency, ${\rm CE}\; \lt \;{5}\%$, achieved for ${{\rm W}_{\rm C}} = {250}\;{\rm nm}$ and 200 nm and a taper length of 75 µm. Measured ${\rm Q}$-factors do not exceed $\sim {{10}^5}$. These results suggest that coupling to resonators with very low refractive index may require narrower taper widths or shorter taper lengths.

Figure 5 summarizes the best experimental results for the optimized SWG taper width that were obtained within the C band, yielding critical coupling for ${{\rm LiNbO}_3}$ and ${{\rm SiO}_2}$, resonators, and maximum measured coupling efficiency for ${{\rm CaF}_2}$ and ${{\rm MgF}_2}$ resonators. The consistency of these results was confirmed by independent measurements on different resonators and different chips. The coupling mechanism presented here cannot be fully described by conventional effective index matching theory [15]. The effective index in the SWG couplers varies between 2.4 near the strip waveguide and 1.49 at the center for ${{\rm W}_{\rm C}} = {200}\;{\rm nm}$. Note that achieving a mode index of 1.48 with strip would require widths near 150 nm, resulting in strong leakage to the Si substrate. Hence, only coupling to ${{\rm LiNbO}_2}$ (${{\rm n}_{\rm LiNbO3}} = {2.21}$) could be described by index matching theory. Fully describing the coupling to low-index bulk resonators made of silica and calcium fluoride may require the development of a new theoretical framework where the phase-gradient effect [34] could play a key role. Here, coupling is demonstrated using micro-positioners to place the resonators. A low-index layer, e.g.,  Teflon, could be used to lock the position of the resonator [35], making the system mechanically stable and facilitating packaging.

 figure: Fig. 5.

Fig. 5. Optimum SWG taper width, ${{\rm W}_{\rm C}}$, yielding maximum coupling efficiency for the bulk WGM resonators studied in this work.

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In conclusion, we have shown that SWG metamaterial engineered couplers provide unique flexibility to combine a wide range of bulk WGM microresonators with Si waveguides, achieving very high coupling efficiencies close to 100%. The SWG couplers studied in this work demonstrate a proof-of-concept validation of a universal integrated photonic coupling approach that can be implemented using Si photonic technology, opening a new route to exploit a wide range of optical properties enhanced by ultra-high ${\rm Q}$ resonances. The presented approach can be readily exploited to implement robust devices combining high-performance bulk resonators and complex Si photonic circuits, with promising prospects for a wide range of applications, including sensing, nonlinear optics, microwave photonics, and quantum photonics. Indeed, the combination of bulk and integrated photonic circuits will provide a powerful platform potentially transforming how advanced photonic circuits are implemented.

Funding

Agence Nationale de la Recherche (BRIGHT ANR-18-CE24-0023-01).

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

REFERENCES

1. A. B. Matsko, Practical Applications of Microresonators in Optics and Photonics (CRC Press, 2009).

2. N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021). [CrossRef]  

3. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, J. Opt. Soc. Am. B 24, 2988 (2007). [CrossRef]  

4. F. Boeuf, S. Crémer, E. Temporiti, M. Ferè, M. Shaw, C. Baudot, N. Vulliet, T. Pinguet, A. Mekis, G. Masini, H. Petiton, P. Le Maitre, M. Traldi, and L. Maggi, J. Lightwave Technol. 34, 286 (2016). [CrossRef]  

5. A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]  

6. A. E. Shitikov, I. A. Bilenko, N. M. Kondratiev, V. E. Lobanov, A. Markosyan, and M. L. Gorodetsky, Optica 5, 1525 (2018). [CrossRef]  

7. Y. K. Chembo, Phys. Rev. A 93, 033820 (2016). [CrossRef]  

8. T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, Science 361, 567 (2018). [CrossRef]  

9. W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015). [CrossRef]  

10. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014). [CrossRef]  

11. I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009). [CrossRef]  

12. N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018). [CrossRef]  

13. Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018). [CrossRef]  

14. L. Cai, J. Pan, and S. Hu, Opt. Laser Eng. 127, 105968 (2020). [CrossRef]  

15. A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010). [CrossRef]  

16. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, Opt. Lett. 22, 1129 (1997). [CrossRef]  

17. V. S. Ilchenko, X. S. Yao, and L. Maleki, Opt. Lett. 24, 723 (1999). [CrossRef]  

18. G. N. Conti, S. Berneschi, F. Cosi, S. Pelli, S. Soria, G. C. Righini, M. Dispenza, and A. Secchi, Opt. Express 19, 3651 (2011). [CrossRef]  

19. M. L. Gorodetsky and V. S. Ilchenko, J. Opt. Soc. Am. B 16, 147 (1999). [CrossRef]  

20. D. H. Broaddus, M. A. Foster, I. H. Agha, J. T. Robinson, M. Lipson, and A. L. Gaeta, Opt. Express 17, 5998 (2009). [CrossRef]  

21. M. Soltani, V. Ilchenko, A. Matsko, A. Savchenkov, J. Schlafer, C. Ryan, and L. Maleki, Opt. Lett. 41, 4375 (2016). [CrossRef]  

22. C. Grillet, S. N. Bian, E. C. Magi, and B. J. Eggleton, Appl. Phys. Lett. 92, 171109 (2008) [CrossRef]  

23. Y. Zhuang, H. Kumazaki, S. Fujii, R. Imamura, N. A. B. Daud, R. Ishida, H. Chen, and T. Tanabe, Opt. Lett. 44, 5731 (2019). [CrossRef]  

24. M. Anderson, N. G. Pavlov, J. D. Jost, G. Lihachev, J. Liu, T. Morais, M. Zervas, M. L. Gorodetsky, and T. J. Kippenberg, Opt. Lett. 43, 2106 (2018). [CrossRef]  

25. K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018). [CrossRef]  

26. P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, Nature 560, 565 (2018). [CrossRef]  

27. P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006). [CrossRef]  

28. J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D.-X. Xu, Opt. Lett. 32, 1794 (2007). [CrossRef]  

29. P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, Opt. Express 17, 19120 (2009). [CrossRef]  

30. J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011). [CrossRef]  

31. R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018). [CrossRef]  

32. P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015). [CrossRef]  

33. S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011). [CrossRef]  

34. Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017). [CrossRef]  

35. Y. Panitchob, G. S. Murugan, M. N. Zervas, P. Horak, S. Berneschi, S. Pelli, G. N. Conti, and J. S. Wilkinson, Opt. Express 16, 11066 (2008). [CrossRef]  

References

  • View by:

  1. A. B. Matsko, Practical Applications of Microresonators in Optics and Photonics (CRC Press, 2009).
  2. N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021).
    [Crossref]
  3. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, J. Opt. Soc. Am. B 24, 2988 (2007).
    [Crossref]
  4. F. Boeuf, S. Crémer, E. Temporiti, M. Ferè, M. Shaw, C. Baudot, N. Vulliet, T. Pinguet, A. Mekis, G. Masini, H. Petiton, P. Le Maitre, M. Traldi, and L. Maggi, J. Lightwave Technol. 34, 286 (2016).
    [Crossref]
  5. A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
    [Crossref]
  6. A. E. Shitikov, I. A. Bilenko, N. M. Kondratiev, V. E. Lobanov, A. Markosyan, and M. L. Gorodetsky, Optica 5, 1525 (2018).
    [Crossref]
  7. Y. K. Chembo, Phys. Rev. A 93, 033820 (2016).
    [Crossref]
  8. T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, Science 361, 567 (2018).
    [Crossref]
  9. W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
    [Crossref]
  10. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
    [Crossref]
  11. I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
    [Crossref]
  12. N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
    [Crossref]
  13. Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018).
    [Crossref]
  14. L. Cai, J. Pan, and S. Hu, Opt. Laser Eng. 127, 105968 (2020).
    [Crossref]
  15. A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
    [Crossref]
  16. J. C. Knight, G. Cheung, F. Jacques, and T. A. Birks, Opt. Lett. 22, 1129 (1997).
    [Crossref]
  17. V. S. Ilchenko, X. S. Yao, and L. Maleki, Opt. Lett. 24, 723 (1999).
    [Crossref]
  18. G. N. Conti, S. Berneschi, F. Cosi, S. Pelli, S. Soria, G. C. Righini, M. Dispenza, and A. Secchi, Opt. Express 19, 3651 (2011).
    [Crossref]
  19. M. L. Gorodetsky and V. S. Ilchenko, J. Opt. Soc. Am. B 16, 147 (1999).
    [Crossref]
  20. D. H. Broaddus, M. A. Foster, I. H. Agha, J. T. Robinson, M. Lipson, and A. L. Gaeta, Opt. Express 17, 5998 (2009).
    [Crossref]
  21. M. Soltani, V. Ilchenko, A. Matsko, A. Savchenkov, J. Schlafer, C. Ryan, and L. Maleki, Opt. Lett. 41, 4375 (2016).
    [Crossref]
  22. C. Grillet, S. N. Bian, E. C. Magi, and B. J. Eggleton, Appl. Phys. Lett. 92, 171109 (2008)
    [Crossref]
  23. Y. Zhuang, H. Kumazaki, S. Fujii, R. Imamura, N. A. B. Daud, R. Ishida, H. Chen, and T. Tanabe, Opt. Lett. 44, 5731 (2019).
    [Crossref]
  24. M. Anderson, N. G. Pavlov, J. D. Jost, G. Lihachev, J. Liu, T. Morais, M. Zervas, M. L. Gorodetsky, and T. J. Kippenberg, Opt. Lett. 43, 2106 (2018).
    [Crossref]
  25. K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
    [Crossref]
  26. P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, Nature 560, 565 (2018).
    [Crossref]
  27. P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006).
    [Crossref]
  28. J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D.-X. Xu, Opt. Lett. 32, 1794 (2007).
    [Crossref]
  29. P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, Opt. Express 17, 19120 (2009).
    [Crossref]
  30. J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
    [Crossref]
  31. R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
    [Crossref]
  32. P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
    [Crossref]
  33. S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011).
    [Crossref]
  34. Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
    [Crossref]
  35. Y. Panitchob, G. S. Murugan, M. N. Zervas, P. Horak, S. Berneschi, S. Pelli, G. N. Conti, and J. S. Wilkinson, Opt. Express 16, 11066 (2008).
    [Crossref]

2021 (1)

N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021).
[Crossref]

2020 (1)

L. Cai, J. Pan, and S. Hu, Opt. Laser Eng. 127, 105968 (2020).
[Crossref]

2019 (1)

2018 (8)

M. Anderson, N. G. Pavlov, J. D. Jost, G. Lihachev, J. Liu, T. Morais, M. Zervas, M. L. Gorodetsky, and T. J. Kippenberg, Opt. Lett. 43, 2106 (2018).
[Crossref]

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, Nature 560, 565 (2018).
[Crossref]

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

A. E. Shitikov, I. A. Bilenko, N. M. Kondratiev, V. E. Lobanov, A. Markosyan, and M. L. Gorodetsky, Optica 5, 1525 (2018).
[Crossref]

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
[Crossref]

Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018).
[Crossref]

T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, Science 361, 567 (2018).
[Crossref]

2017 (1)

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

2016 (3)

2015 (2)

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

2014 (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

2011 (3)

G. N. Conti, S. Berneschi, F. Cosi, S. Pelli, S. Soria, G. C. Righini, M. Dispenza, and A. Secchi, Opt. Express 19, 3651 (2011).
[Crossref]

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011).
[Crossref]

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

2010 (1)

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

2009 (3)

2008 (2)

2007 (2)

2006 (1)

2004 (1)

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[Crossref]

1999 (2)

1997 (1)

Agarwal, A. M.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Agha, I. H.

Anderson, M.

Aspelmeyer, M.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Atwater, H. A.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, Nature 560, 565 (2018).
[Crossref]

Baudot, C.

Benedikovic, D.

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

Berneschi, S.

Bian, S. N.

C. Grillet, S. N. Bian, E. C. Magi, and B. J. Eggleton, Appl. Phys. Lett. 92, 171109 (2008)
[Crossref]

Bilenko, I. A.

Birks, T. A.

Bock, P. J.

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, Opt. Express 17, 19120 (2009).
[Crossref]

Boeuf, F.

Brenci, M.

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011).
[Crossref]

Broaddus, D. H.

Cabello, G.

N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021).
[Crossref]

Cai, L.

L. Cai, J. Pan, and S. Hu, Opt. Laser Eng. 127, 105968 (2020).
[Crossref]

Cheben, P.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, Nature 560, 565 (2018).
[Crossref]

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, Opt. Express 17, 19120 (2009).
[Crossref]

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D.-X. Xu, Opt. Lett. 32, 1794 (2007).
[Crossref]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006).
[Crossref]

Chembo, Y. K.

Y. K. Chembo, Phys. Rev. A 93, 033820 (2016).
[Crossref]

Chen, H.

Cheung, G.

Chiasera, A.

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Conti, G. N.

G. N. Conti, S. Berneschi, F. Cosi, S. Pelli, S. Soria, G. C. Righini, M. Dispenza, and A. Secchi, Opt. Express 19, 3651 (2011).
[Crossref]

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Y. Panitchob, G. S. Murugan, M. N. Zervas, P. Horak, S. Berneschi, S. Pelli, G. N. Conti, and J. S. Wilkinson, Opt. Express 16, 11066 (2008).
[Crossref]

Cosi, F.

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011).
[Crossref]

G. N. Conti, S. Berneschi, F. Cosi, S. Pelli, S. Soria, G. C. Righini, M. Dispenza, and A. Secchi, Opt. Express 19, 3651 (2011).
[Crossref]

Crémer, S.

Daud, N. A. B.

Delage, A.

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

Delâge, A.

Densmore, A.

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, Opt. Express 14, 4695 (2006).
[Crossref]

Dispenza, M.

Dumeige, Y.

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Eggleton, B. J.

C. Grillet, S. N. Bian, E. C. Magi, and B. J. Eggleton, Appl. Phys. Lett. 92, 171109 (2008)
[Crossref]

Eliyahu, D.

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
[Crossref]

Fedeli, J.-M.

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

Ferè, M.

Féron, P.

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Ferrari, M.

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Foster, M. A.

Fujii, S.

Gaeta, A. L.

Gorodetsky, M. L.

Gorodnitskiy, A. S.

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
[Crossref]

Grillet, C.

C. Grillet, S. N. Bian, E. C. Magi, and B. J. Eggleton, Appl. Phys. Lett. 92, 171109 (2008)
[Crossref]

Grudinin, I. S.

I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

Gutta, R. R.

N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021).
[Crossref]

Halir, R.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, Nature 560, 565 (2018).
[Crossref]

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

Hall, T. J.

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, Opt. Express 17, 19120 (2009).
[Crossref]

Han, B.

Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018).
[Crossref]

Han, Z.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Horak, P.

Hu, S.

L. Cai, J. Pan, and S. Hu, Opt. Laser Eng. 127, 105968 (2020).
[Crossref]

Ilchenko, V.

Ilchenko, V. S.

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, J. Opt. Soc. Am. B 24, 2988 (2007).
[Crossref]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, J. Opt. Soc. Am. B 16, 147 (1999).
[Crossref]

V. S. Ilchenko, X. S. Yao, and L. Maleki, Opt. Lett. 24, 723 (1999).
[Crossref]

Imamura, R.

Ishida, R.

Jacques, F.

Janz, S.

Jestin, Y.

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Jost, J. D.

Kim, M.-H.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Kippenberg, T. J.

M. Anderson, N. G. Pavlov, J. D. Jost, G. Lihachev, J. Liu, T. Morais, M. Zervas, M. L. Gorodetsky, and T. J. Kippenberg, Opt. Lett. 43, 2106 (2018).
[Crossref]

T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, Science 361, 567 (2018).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Knight, J. C.

Kondratiev, N. M.

Koptyaev, S.

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
[Crossref]

Kumazaki, H.

Lamontagne, B.

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

Lapointe, J.

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D.-X. Xu, Opt. Lett. 32, 1794 (2007).
[Crossref]

Le Maitre, P.

Lee, S. H.

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Li, Z.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Liang, W.

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
[Crossref]

Lihachev, G.

Lihachev, G. V.

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
[Crossref]

Lipson, M.

Liu, J.

Lobanov, V. E.

Loncar, M.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Lu, M.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Ma, R.

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

Maggi, L.

Magi, E. C.

C. Grillet, S. N. Bian, E. C. Magi, and B. J. Eggleton, Appl. Phys. Lett. 92, 171109 (2008)
[Crossref]

Maleki, L.

M. Soltani, V. Ilchenko, A. Matsko, A. Savchenkov, J. Schlafer, C. Ryan, and L. Maleki, Opt. Lett. 41, 4375 (2016).
[Crossref]

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
[Crossref]

I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, J. Opt. Soc. Am. B 24, 2988 (2007).
[Crossref]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[Crossref]

V. S. Ilchenko, X. S. Yao, and L. Maleki, Opt. Lett. 24, 723 (1999).
[Crossref]

Markosyan, A.

Marquardt, F.

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Mashanovich, G. Z.

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

Masini, G.

Matsko, A.

Matsko, A. B.

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
[Crossref]

I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, J. Opt. Soc. Am. B 24, 2988 (2007).
[Crossref]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[Crossref]

A. B. Matsko, Practical Applications of Microresonators in Optics and Photonics (CRC Press, 2009).

Mekis, A.

Molina-Fernandez, I.

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

Morais, T.

Murugan, G. S.

Oh, D. Y.

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Ortega-Monux, A.

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

Overvig, A. C.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Painchaud, Y.

Pan, J.

L. Cai, J. Pan, and S. Hu, Opt. Laser Eng. 127, 105968 (2020).
[Crossref]

Panitchob, Y.

Pavlov, N. G.

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
[Crossref]

M. Anderson, N. G. Pavlov, J. D. Jost, G. Lihachev, J. Liu, T. Morais, M. Zervas, M. L. Gorodetsky, and T. J. Kippenberg, Opt. Lett. 43, 2106 (2018).
[Crossref]

Pelli, S.

G. N. Conti, S. Berneschi, F. Cosi, S. Pelli, S. Soria, G. C. Righini, M. Dispenza, and A. Secchi, Opt. Express 19, 3651 (2011).
[Crossref]

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Y. Panitchob, G. S. Murugan, M. N. Zervas, P. Horak, S. Berneschi, S. Pelli, G. N. Conti, and J. S. Wilkinson, Opt. Express 16, 11066 (2008).
[Crossref]

Petiton, H.

Picard, M.-J.

Pinguet, T.

Polonsky, S. V.

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
[Crossref]

Post, E.

Rafti, M.

N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021).
[Crossref]

Righini, G. C.

G. N. Conti, S. Berneschi, F. Cosi, S. Pelli, S. Soria, G. C. Righini, M. Dispenza, and A. Secchi, Opt. Express 19, 3651 (2011).
[Crossref]

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Robinson, J. T.

Ryabko, M. V.

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
[Crossref]

Ryan, C.

Savchenkov, A.

Savchenkov, A. A.

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, J. Opt. Soc. Am. B 24, 2988 (2007).
[Crossref]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[Crossref]

Schlafer, J.

Schmid, J. H.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, Nature 560, 565 (2018).
[Crossref]

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

P. Cheben, J. H. Schmid, S. Wang, D.-X. Xu, M. Vachon, S. Janz, J. Lapointe, Y. Painchaud, and M.-J. Picard, Opt. Express 23, 22553 (2015).
[Crossref]

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, A. Delâge, D.-X. Xu, S. Janz, and T. J. Hall, Opt. Express 17, 19120 (2009).
[Crossref]

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D.-X. Xu, Opt. Lett. 32, 1794 (2007).
[Crossref]

Secchi, A.

Seidel, D.

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
[Crossref]

Serrano, M. P.

N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021).
[Crossref]

Shaw, M.

Shen, B.

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Shitikov, A. E.

Shrestha, S.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Smith, D. R.

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, Nature 560, 565 (2018).
[Crossref]

Soltani, M.

Soria, S.

G. N. Conti, S. Berneschi, F. Cosi, S. Pelli, S. Soria, G. C. Righini, M. Dispenza, and A. Secchi, Opt. Express 19, 3651 (2011).
[Crossref]

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011).
[Crossref]

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Stein, A.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Tanabe, T.

Temporiti, E.

Toropov, N.

N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021).
[Crossref]

Traldi, M.

Vachon, M.

Vahala, K.

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Vollmer, F.

N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021).
[Crossref]

Voloshin, A. S.

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
[Crossref]

Vulliet, N.

Wang, C.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Wang, H.

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Wang, S.

Wanguemert-Perez, J. G.

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

Wilkinson, J. S.

Xu, D.-X.

Yang, K. Y.

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Yang, Q.-F.

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Yao, X. S.

Yi, X.

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

Yu, N.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, N. Yu, and L. Maleki, J. Opt. Soc. Am. B 24, 2988 (2007).
[Crossref]

Zervas, M.

Zervas, M. N.

Zhang, A.

Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018).
[Crossref]

Zhang, Y.

Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018).
[Crossref]

Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018).
[Crossref]

Zhao, Y.

Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018).
[Crossref]

Zhou, T.

Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018).
[Crossref]

Zhuang, Y.

Appl. Phys. Lett. (1)

C. Grillet, S. N. Bian, E. C. Magi, and B. J. Eggleton, Appl. Phys. Lett. 92, 171109 (2008)
[Crossref]

IEEE Photon. J. (1)

J. H. Schmid, P. Cheben, P. J. Bock, R. Halir, J. Lapointe, S. Janz, A. Delage, A. Densmore, J.-M. Fedeli, T. J. Hall, B. Lamontagne, R. Ma, I. Molina-Fernandez, and D.-X. Xu, IEEE Photon. J. 3, 597 (2011).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (2)

Laser Photon. Rev. (1)

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. N. Conti, S. Pelli, S. Soria, and G. C. Righini, Laser Photon. Rev. 4, 457 (2010).
[Crossref]

Light Sci. Appl. (1)

N. Toropov, G. Cabello, M. P. Serrano, R. R. Gutta, M. Rafti, and F. Vollmer, Light Sci. Appl. 10, 42 (2021).
[Crossref]

Nanoscale (1)

Y. Zhang, T. Zhou, B. Han, A. Zhang, Y. Zhao, and Y. Zhang, Nanoscale 10, 13832 (2018).
[Crossref]

Nat. Commun. (1)

W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, D. Seidel, and L. Maleki, Nat. Commun. 6, 7957 (2015).
[Crossref]

Nat. Nanotechnol. (1)

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Lončar, and N. Yu, Nat. Nanotechnol. 12, 675 (2017).
[Crossref]

Nat. Photonics (2)

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, Nat. Photonics 12, 297 (2018).
[Crossref]

N. G. Pavlov, S. Koptyaev, G. V. Lihachev, A. S. Voloshin, A. S. Gorodnitskiy, M. V. Ryabko, S. V. Polonsky, and M. L. Gorodetsky, Nat. Photonics 12, 694 (2018).
[Crossref]

Nature (1)

P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, and D. R. Smith, Nature 560, 565 (2018).
[Crossref]

Opt. Express (6)

Opt. Laser Eng. (1)

L. Cai, J. Pan, and S. Hu, Opt. Laser Eng. 127, 105968 (2020).
[Crossref]

Opt. Lett. (6)

Optica (1)

Phys. Rev. A (2)

Y. K. Chembo, Phys. Rev. A 93, 033820 (2016).
[Crossref]

A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004).
[Crossref]

Phys. Rev. Lett. (1)

I. S. Grudinin, A. B. Matsko, and L. Maleki, Phys. Rev. Lett. 102, 043902 (2009).
[Crossref]

Proc. IEEE (1)

R. Halir, A. Ortega-Monux, D. Benedikovic, G. Z. Mashanovich, J. G. Wanguemert-Perez, J. H. Schmid, I. Molina-Fernandez, and P. Cheben, Proc. IEEE 106, 2144 (2018).
[Crossref]

Rev. Mod. Phys. (1)

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
[Crossref]

Science (1)

T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, Science 361, 567 (2018).
[Crossref]

Sensors (1)

S. Soria, S. Berneschi, M. Brenci, F. Cosi, G. N. Conti, S. Pelli, and G. C. Righini, Sensors 11, 785 (2011).
[Crossref]

Other (1)

A. B. Matsko, Practical Applications of Microresonators in Optics and Photonics (CRC Press, 2009).

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic diagram of the SWG metamaterial tapered waveguide designed for coupling light to bulk WGM resonators. (b) Scanning electron microscope image of SWG metamaterial coupler.
Fig. 2.
Fig. 2. (a) Simplified schematic of the experimental setup. TL, tunable laser; PC, polarization controller; LF, lensed fiber; SWG, subwavelength grating waveguide; OBJ, ${10} \times$ micro-objective; PD, photodetector; OSC, oscilloscope. (b) Optical microscope image of a WGM microsphere resonator placed above the silicon chip with a set of SWG waveguides. The resonator is centered above and in the middle of a SWG tapered waveguide coupler.
Fig. 3.
Fig. 3. Transmission spectrum of a SWG waveguide coupled to a silica microsphere. The red line represents the Lorentzian fit of a resonance.
Fig. 4.
Fig. 4. Transmission spectrum of a SWG waveguide coupled to (a) ${{\rm LiNbO}_3}$ disk, (b) a silica disk, and (c) a ${{\rm CaF}_2}$ disk.
Fig. 5.
Fig. 5. Optimum SWG taper width, ${{\rm W}_{\rm C}}$, yielding maximum coupling efficiency for the bulk WGM resonators studied in this work.