Abstract

We experimentally demonstrate continuous-wave ultraviolet emission through forth-harmonic generation in a millimeter-scale lithium niobate whispering-gallery resonator pumped with a telecommunication-compatible infrared source. The whispering-gallery resonator provides four spectral lines at ultraviolet, visible, near-infrared and infrared, which are equally spaced in frequency via the cascaded-harmonic process and span a 2-octave frequency band. Our technique relies on a variable crystal poling and high transverse order of the modes for phase-matching and a resonator quality factor of over 107 to allow cascaded-harmonic generation up to the fourth-harmonic at input pump powers as low as 200mW. The compact size of the whispering gallery resonator pumped at telecommunication-compatible infrared wavelengths and the low pump power requirement make our device a promising ultraviolet light source for information storage, microscopy, and chemical analysis.

©2011 Optical Society of America

1. Introduction

Basic physics imposes the condition that the required energy for a conventional laser scales as 1/λ5, where λ is the laser wavelength [1]. On the other hand, high-harmonic generation is not subject to this limit and therefore allows extending the emission wavelength of a pump laser to produce coherent ultraviolet light, unrestricted by the 1/λ5 relation. However, to date such short-wavelength sources have required very high pump power levels that could generally be achieved only by ultra-short pump pulses [26]. Instead of using ultra-short pump pulses, whispering-gallery resonators can be used to provide the high field intensities required for various nonlinear phenomena. This is because high quality factor whispering-gallery resonators enhance the intensity of light continuously in time via multiple recirculations, resulting in large light-matter interaction distances [79]. This intensity enhancement mechanism has enabled various nonlinear phenomena, including optomechanical vibrations [1014], parametric oscillations [1518], Raman-lasers [1921], Erbium-lasers [22], Brillouin-lasers [1013], and continuous-wave second- and third-harmonic generation [2329].

In this work, we experimentally demonstrate continuous-wave harmonic generation up to the fourth-harmonic, enabled by multiple-recirculation intensity enhancement in a lithium niobate whispering-gallery resonator. This could potentially transform high-harmonic studies from pulsed to continuous-wave. Specifically, we generate continuous-wave near-infrared, visible, and ultraviolet light from a telecommunication-compatible infrared pump through cascaded-harmonic generation in a whispering-gallery resonator at a record-low pump power of 200 mW [26]. Further, our millimeter-scale emitter is simple, as the polished lithium niobate resonator comprises both the nonlinear medium and the mode-confining resonator. Finally, a non-uniform poling of lithium niobate [30] and existence of higher order transverse modes [24] provides the required quasi phase-matching between the infrared pump and the corresponding near-infrared, visible, and ultraviolet harmonics.

2. Whispering-gallery resonator design

Resonance calculation for the pump and its corresponding harmonics in a 3mm lithium niobate whispering-gallery resonator is done using finite element method simulation in COMSOL [31] and is shown in Fig. 1 (TM modes are considered for this analysis). The electric field profiles indicate that the infrared pump and the corresponding 2nd (near-infrared), 3rd (visible), and 4th (ultraviolet) harmonic modes are confined inside the nonlinear lithium niobate medium with a considerable mode overlap. The modes are expected to resonate at integer multiples of the pump frequency, in order to conserve energy as required by coupled-mode theory [32]. However, structural and material dispersion cause the modes’ propagation constants to be scaled differently as a function of frequency. This implies that momentum is not a priori conserved for the high-harmonic processes in the bare resonator. We compensate for the deviation from momentum conservation by quasi phase-matching, as shown below.

 figure: Fig. 1

Fig. 1 Radial electric field profiles for a 1550 nm pump and the corresponding 2nd, 3rd, and 4th harmonics, which are numerically calculated for the 3mm lithium niobate whispering-gallery resonator (TM modes).

Download Full Size | PPT Slide | PDF

Quasi phase-matching to conserve momentum for the harmonics and pump is achieved by periodic poling of lithium niobate [30,33] and facilitated by a combination of high order transverse resonance modes [24]. For momentum conservation, the optimum poling period for each three-photon interaction harmonic generation process is given byΛ=(n1/λ1+n2/λ2n3/λ3)1, where λ1 and λ2 are the wavelengths of the input photons, λ3 is the wavelength of the generated photon, n1 and n2 are the mode index of the input photons and n3 is the mode index of generated photon. A major challenge in quasi phase-matching is that different poling periods are required to compensate for the momentum mismatch of different harmonics. For example, the optimal poling periods for 2nd, 3rd, and 4th harmonic generation for a 1550nm pump are 19 µm, 7 µm, and 2.13µm, respectively. This problem has previously been solved by using a non-uniform effective poling-period [33]. The lithium niobate is poled in a striped configuration, as in Fig. 1(a) (left inset), such that the azimuthally propagating light sees a spectrum of effective poling periods as it circulates around the resonator circumference. Plotting the envelope function of the Fourier coefficients for the poling pattern seen by the azimuthally propagating mode provides information about the relative efficiency of phase matching for different processes. The efficiency of a nonlinear process is directly proportional to amplitude of the Fourier coefficient at the optimum poling period for that process.

Figure 2 shows the amplitude of the Fourier coefficients as a function of inverse grating period for our 3mm diameter resonator with 79 µm striped poling, confirming that the energy-momentum condition can be satisfied for all three harmonic-generation processes simultaneously. Additionally, the existence of high-order modes facilitates quasi phase-matching over a broad pump wavelength range [34,35]. It should be noted that poling configurations with shorter periods will have a much better phase-matching performances than the PPLN wafer available for this experiment. We anticipate that shortening the grating period will greatly improve efficiency in the next-generation devices.

 figure: Fig. 2

Fig. 2 The amplitude of the Fourier coefficients for the poling pattern seen by the azimuthally propagating mode, for our 3mm diameter resonator with Λ0 = 79 µm striped poling, confirming that the energy-momentum condition can be satisfied for all three harmonic-generation processes simultaneously.

Download Full Size | PPT Slide | PDF

3. Experimental results and discussion

The experimental setup (Fig. 3(a) ) is based on a crystalline whispering-gallery resonator that is polished to reduce optical losses introduced by scattering. Lithium niobate was chosen for our whispering-gallery resonator nonlinear medium for its second-order optical nonlinearity and its transparency from infrared to ultraviolet wavelengths. Additionally, due to its ferroelectric properties, lithium niobate crystal domains can be engineered by electrical poling to achieve quasi-phase matching of diverse optical modes. The whispering-gallery resonator was fabricated from a commercial periodically-poled, z-cut lithium niobate substrate. A 3-mm disk was cut from the wafer and the edge was mechanically polished to a spherical profile.

 figure: Fig. 3

Fig. 3 (a) Experimental setup for demonstrating cascaded-harmonic generation in the periodically poled lithium niobate resonator. (b) Measured whispering-gallery resonator resonance, implying a quality factor of 2×107 at 1540nm.

Download Full Size | PPT Slide | PDF

The pump beam, tunable from 1535 to 1545nm, is evanescently coupled to the cavity modes via a diamond prism [36]. A quality factor on the order of 107 was measured by monitoring transmission through the prism while scanning the IR pump frequency through the optical resonances (Fig. 3(b)). Measuring the quality factor in the UV is challenging because of the lack of narrow linewidth tunable lasers for the UV band, as well as the lack of spectrum analyzers with resolution in the order of 10MHz. Compared to the IR pump, absorption losses for the UV 4th harmonic will be higher in lithium niobate. However, loss via tunneling [37] decreases at shorter wavelengths. Additionally and by definition, quality factor is inversely proportional to wavelength, assuming that other losses are held constant. We therefore estimate that Q for the 4th harmonic is of the same order as for the IR pump. Also, the power used in this experiment is not high enough to distort the Lorentzian shape of the absorption line, indicating a lack of thermal bistability in this experiment [38]. Emitted light is collected by a CCD camera as well as a multimode optical fiber for analysis. In the first case, light is directly detected from the prism coupler, and in the second case the signal is collected from the residual Rayleigh scattering to the sides of the resonator.

Experimental visualization of the cascaded-harmonic generation process is achieved by photographing spatially resolved spots on a color and IR CCD camera, with spot separations corresponding to the infrared pump and its 2nd, 3rd, and 4th harmonics (Fig. 4 ). Spectral filters are employed to prevent saturation of the camera by the 2nd and 3rd harmonics, and the 4th harmonic is observed by coating the CCD with a fluorescent ink that is sensitive to ultraviolet. The noncircular shape of the spots suggests that high order transverse modes are involved in this process. We emphasize that this picture describes a continuous-wave emission for all of the generated harmonics.

 figure: Fig. 4

Fig. 4 Visual verification of cascaded-harmonic generation: The pump beam is recorded with an infrared CCD camera, and the harmonics are observed on a color CCD coated with ultraviolet fluorescent ink. The photograph is taken at a pump wavelength of 1538 nm and a pump power of 200mW.

Download Full Size | PPT Slide | PDF

Measuring the harmonics wavelengths is done by three spectrum analyzers which cover the infrared to ultraviolet band. The nth harmonic is expected to be at the (pump wavelength)/n. The experimentally measured 2nd, 3rd, and 4th harmonic lines for the pump wavelength of 1546nm are at 773 nm, 515 nm, and 387 nm, respectively (Fig. 5 ). These measured wavelengths lay within the 2nm error margin of our spectrum analyzers.

 figure: Fig. 5

Fig. 5 Measured emission spectrum at 1546nm pump wavelength, indicating generation of the 2nd, 3rd, and 4th harmonics. Harmonics are measured using three different spectrum analyzers and are plotted at different intensity scales.

Download Full Size | PPT Slide | PDF

Tuning the harmonics wavelengths is possible in our experimental setup by sweeping the pump wavelength through the very dense infrared resonance modes of the whispering-gallery resonator to reveal a nearly continuous tuning capacity. We experimentally demonstrate continuous tuning of the 2nd, 3rd, and 4th harmonics wavelengths while sweeping the pump wavelength between 1535nm and 1545nm (Fig. 6 ). All three harmonics wavelengths are observed to track the expected values as the pump wave length is varied.

 figure: Fig. 6

Fig. 6 Measured spectrograms of the generated 2nd, 3rd, and 4th harmonics at a pump wavelength range of 1535-1545nm are illustrated in a, b, and c. Colors stand for intensity. All three harmonics display wide tunability within this wavelength range.

Download Full Size | PPT Slide | PDF

Measuring the harmonics’ power as a function of the input pump power is performed to confirm the cascaded-harmonic generation process. Inherently, the nth harmonics power should scale as (pump power)n, which is verified via a logarithmic fit of the 2nd, 3rd, and 4th harmonic power as a function of the pump power level (Fig. 7 ). This measurement was done by scanning the pump wavelength through several whispering-gallery resonances to record an average output power for each harmonic at a given pump power. As it is evident from the measured harmonics power, the cascaded-harmonic process improves its efficiency as pump power increases. This is expected from the (pump power)n scaling of the nth harmonic power. This efficiency will, of course, stop increasing when limiting effects such as pump depletion become evident.

 figure: Fig. 7

Fig. 7 Measured power of the generated 2nd, 3rd, and 4th harmonics at a pump wavelength of 1550nm, as a function of the pump power are illustrated in d, e, and f, revealing nearly quadratic, cubic and power-of-4 dependency for the 2nd, 3rd, and 4th order processes

Download Full Size | PPT Slide | PDF

We have experimentally confirmed that the mechanism responsible for the observed harmonic generation is cascaded-harmonic generation via χ(2) processes. This is because the 3rd harmonic is only observed simultaneously with the 2nd harmonic. Similarly, the 4th harmonic is only observed simultaneously with both the 2nd and 3rd harmonics. This suggests that the 3rd and 4th harmonics arise from cascaded χ(2) processes, as opposed to χ(3) and χ(4) effects. This observation is further supported by the fact that third and fourth order nonlinear coefficients are many orders of magnitude smaller than the second order coefficient for lithium niobate [39]. In order to further validate the effectiveness of the employed quasi-phase matching technique, a second lithium niobate whispering-gallery resonator with no crystal poling was fabricated and tested using the same experimental setups. Harmonic generation was not observed in the similar experimental conditions, confirming the significant role of the employed non-uniform poling in providing quasi-phase matching for 2nd, 3rd, and 4th harmonic generation processes.

In conclusion, we experimentally demonstrate continuous-wave cascaded harmonic generation up to the fourth harmonic in a millimeter-scale whispering gallery resonator, allowing four spectral lines which are equally spaced in frequency and span a 2-octave frequency band. Many challenges exist, but we believe this work can be extended toward continuous-in-time extreme nonlinear optics where the electron is repeatedly torn from and recombines with the atom. These challenges include phase matching and concentration of light in the gaseous region near the evanescent tail of the modes discussed here. Still, the first steps in this journey, demonstrated here, can be followed toward the extreme by adding structures such as in [40] as suggested in [41].

Acknowledgments

The authors would like to thank Dr. Harald Schwefel, Prof. Mani Hossein-Zadeh at the University of New Mexico, and Prof. Bahram Jalali’s group at UCLA for advice and assistance with the experiment, and Opticology, Inc. for assistance with fabrication. Matthew Tomes is supported by a Graduate Research Fellowship from the National Science Foundation. This work is supported by National Science Foundation ENG-ECCS-065614, and by the Air Force Office of Scientific Research Young Investigator Award under contract number FA9550-10-1-0078.

References and links

1. H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science 317(5839), 775–778 (2007). [CrossRef]   [PubMed]  

2. I. A. Bufetov, M. V. Grekov, K. M. Golant, E. M. Dianov, and R. R. Khrapko, “Ultraviolet-light generation in nitrogen-doped silica fiber,” Opt. Lett. 22(18), 1394–1396 (1997). [CrossRef]   [PubMed]  

3. R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002). [PubMed]  

4. A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003). [CrossRef]   [PubMed]  

5. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004). [CrossRef]   [PubMed]  

6. X. Zhang, Z. Wang, G. Wang, Y. Zhu, Z. Xu, and C. Chen, “Widely tunable and high-average-power fourth-harmonic generation of a Ti:sapphire laser with a KBe2BO3F2 prism-coupled device,” Opt. Lett. 34(9), 1342–1344 (2009). [CrossRef]   [PubMed]  

7. K. Vahala, Optical Microcavities (World Scientific Publishing Co. Pte. Ltd., 2004).

8. A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006). [CrossRef]  

9. V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006). [CrossRef]  

10. I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009). [CrossRef]   [PubMed]  

11. M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009). [CrossRef]   [PubMed]  

12. G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011), doi:. [CrossRef]   [PubMed]  

13. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Surface acoustic wave frequency comb,” arXiv:1106.1477v1 (2011).

14. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005). [CrossRef]   [PubMed]  

15. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004). [CrossRef]   [PubMed]  

16. A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007). [CrossRef]   [PubMed]  

17. T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011). [CrossRef]   [PubMed]  

18. J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010). [CrossRef]   [PubMed]  

19. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002). [CrossRef]   [PubMed]  

20. S. X. Qian and R. K. Chang, “Multiorder stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56(9), 926–929 (1986). [CrossRef]   [PubMed]  

21. H.-B. Lin, A. L. Huston, J. D. Eversole, and A. J. Campillo, “Double-resonance stimulated Raman scattering in micrometer-sized droplets,” J. Opt. Soc. Am. B 7(10), 2079–2089 (1990). [CrossRef]  

22. L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process,” Appl. Phys. Lett. 86(9), 091114 (2005). [CrossRef]  

23. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004). [CrossRef]   [PubMed]  

24. T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007). [CrossRef]  

25. K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO: LiNbO3 disk resonator,” Appl. Phys. Express 2(12), 122401 (2009). [CrossRef]  

26. D. H. Leach, R. K. Chang, W. P. Acker, and S. C. Hill, “Third-order sum-frequency generation in droplets—experimental results,” J. Opt. Soc. Am. B 10(1), 34–45 (1993). [CrossRef]  

27. W. P. Acker, D. H. Leach, and R. K. Chang, “Third-order optical sum-frequency generation in micrometer-sized liquid droplets,” Opt. Lett. 14(8), 402–404 (1989). [CrossRef]   [PubMed]  

28. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010). [CrossRef]   [PubMed]  

29. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010). [CrossRef]   [PubMed]  

30. T. Haertle, “Domain patterns for quasi-phase matching in whispering-gallery modes,” J. Opt. 12(3), 035202 (2010). [CrossRef]  

31. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007). [CrossRef]  

32. H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991). [CrossRef]  

33. V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. 20(6), 1304–1308 (2003). [CrossRef]  

34. T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008). [CrossRef]   [PubMed]  

35. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007). [CrossRef]  

36. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16(1), 147–154 (1999). [CrossRef]  

37. M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express 17(21), 19160–19165 (2009). [CrossRef]   [PubMed]  

38. T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004). [CrossRef]   [PubMed]  

39. R. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).

40. S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008). [CrossRef]   [PubMed]  

41. M. Kozlov, O. Kfir, A. Fleischer, T. Carmon, H. G. Schwefel, and O. Cohen, “High-order harmonics of a continuous-wave driving laser,” Frontiers in Optics, OSA Technical Digest (CD), paper FWE2 (2010).

References

  • View by:
  • |
  • |
  • |

  1. H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science 317(5839), 775–778 (2007).
    [Crossref] [PubMed]
  2. I. A. Bufetov, M. V. Grekov, K. M. Golant, E. M. Dianov, and R. R. Khrapko, “Ultraviolet-light generation in nitrogen-doped silica fiber,” Opt. Lett. 22(18), 1394–1396 (1997).
    [Crossref] [PubMed]
  3. R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
    [PubMed]
  4. A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
    [Crossref] [PubMed]
  5. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004).
    [Crossref] [PubMed]
  6. X. Zhang, Z. Wang, G. Wang, Y. Zhu, Z. Xu, and C. Chen, “Widely tunable and high-average-power fourth-harmonic generation of a Ti:sapphire laser with a KBe2BO3F2 prism-coupled device,” Opt. Lett. 34(9), 1342–1344 (2009).
    [Crossref] [PubMed]
  7. K. Vahala, Optical Microcavities (World Scientific Publishing Co. Pte. Ltd., 2004).
  8. A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
    [Crossref]
  9. V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
    [Crossref]
  10. I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
    [Crossref] [PubMed]
  11. M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009).
    [Crossref] [PubMed]
  12. G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011), doi:.
    [Crossref] [PubMed]
  13. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Surface acoustic wave frequency comb,” arXiv:1106.1477v1 (2011).
  14. T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
    [Crossref] [PubMed]
  15. T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
    [Crossref] [PubMed]
  16. A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
    [Crossref] [PubMed]
  17. T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
    [Crossref] [PubMed]
  18. J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
    [Crossref] [PubMed]
  19. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
    [Crossref] [PubMed]
  20. S. X. Qian and R. K. Chang, “Multiorder stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56(9), 926–929 (1986).
    [Crossref] [PubMed]
  21. H.-B. Lin, A. L. Huston, J. D. Eversole, and A. J. Campillo, “Double-resonance stimulated Raman scattering in micrometer-sized droplets,” J. Opt. Soc. Am. B 7(10), 2079–2089 (1990).
    [Crossref]
  22. L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
    [Crossref]
  23. V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004).
    [Crossref] [PubMed]
  24. T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
    [Crossref]
  25. K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO: LiNbO3 disk resonator,” Appl. Phys. Express 2(12), 122401 (2009).
    [Crossref]
  26. D. H. Leach, R. K. Chang, W. P. Acker, and S. C. Hill, “Third-order sum-frequency generation in droplets—experimental results,” J. Opt. Soc. Am. B 10(1), 34–45 (1993).
    [Crossref]
  27. W. P. Acker, D. H. Leach, and R. K. Chang, “Third-order optical sum-frequency generation in micrometer-sized liquid droplets,” Opt. Lett. 14(8), 402–404 (1989).
    [Crossref] [PubMed]
  28. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
    [Crossref] [PubMed]
  29. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
    [Crossref] [PubMed]
  30. T. Haertle, “Domain patterns for quasi-phase matching in whispering-gallery modes,” J. Opt. 12(3), 035202 (2010).
    [Crossref]
  31. M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007).
    [Crossref]
  32. H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
    [Crossref]
  33. V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. 20(6), 1304–1308 (2003).
    [Crossref]
  34. T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
    [Crossref] [PubMed]
  35. A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
    [Crossref]
  36. M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16(1), 147–154 (1999).
    [Crossref]
  37. M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express 17(21), 19160–19165 (2009).
    [Crossref] [PubMed]
  38. T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
    [Crossref] [PubMed]
  39. R. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).
  40. S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
    [Crossref] [PubMed]
  41. M. Kozlov, O. Kfir, A. Fleischer, T. Carmon, H. G. Schwefel, and O. Cohen, “High-order harmonics of a continuous-wave driving laser,” Frontiers in Optics, OSA Technical Digest (CD), paper FWE2 (2010).

2011 (2)

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011), doi:.
[Crossref] [PubMed]

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
[Crossref] [PubMed]

2010 (4)

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

T. Haertle, “Domain patterns for quasi-phase matching in whispering-gallery modes,” J. Opt. 12(3), 035202 (2010).
[Crossref]

2009 (5)

K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO: LiNbO3 disk resonator,” Appl. Phys. Express 2(12), 122401 (2009).
[Crossref]

M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express 17(21), 19160–19165 (2009).
[Crossref] [PubMed]

X. Zhang, Z. Wang, G. Wang, Y. Zhu, Z. Xu, and C. Chen, “Widely tunable and high-average-power fourth-harmonic generation of a Ti:sapphire laser with a KBe2BO3F2 prism-coupled device,” Opt. Lett. 34(9), 1342–1344 (2009).
[Crossref] [PubMed]

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[Crossref] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009).
[Crossref] [PubMed]

2008 (2)

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[Crossref] [PubMed]

2007 (5)

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[Crossref]

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007).
[Crossref]

T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
[Crossref]

H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science 317(5839), 775–778 (2007).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[Crossref] [PubMed]

2006 (2)

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[Crossref]

2005 (2)

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[Crossref]

2004 (4)

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004).
[Crossref] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[Crossref] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[Crossref] [PubMed]

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004).
[Crossref] [PubMed]

2003 (2)

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. 20(6), 1304–1308 (2003).
[Crossref]

2002 (2)

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[Crossref] [PubMed]

1999 (1)

1997 (1)

1993 (1)

1991 (1)

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

1990 (1)

1989 (1)

1986 (1)

S. X. Qian and R. K. Chang, “Multiorder stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56(9), 926–929 (1986).
[Crossref] [PubMed]

Acker, W. P.

Aiello, A.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
[Crossref] [PubMed]

Andersen, U. L.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

Attwood, D.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Backus, S.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Bahl, G.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011), doi:.
[Crossref] [PubMed]

Bartels, R. A.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Beckmann, T.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
[Crossref] [PubMed]

Breunig, I.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
[Crossref] [PubMed]

Bufetov, I. A.

Buse, K.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
[Crossref] [PubMed]

Campillo, A. J.

Carmon, T.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011), doi:.
[Crossref] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009).
[Crossref] [PubMed]

M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express 17(21), 19160–19165 (2009).
[Crossref] [PubMed]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[Crossref] [PubMed]

T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
[Crossref]

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[Crossref] [PubMed]

Chang, R. K.

Chen, C.

Christov, I.

H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science 317(5839), 775–778 (2007).
[Crossref] [PubMed]

Christov, I. P.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Cohen, O.

H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science 317(5839), 775–778 (2007).
[Crossref] [PubMed]

Dianov, E. M.

Elser, D.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

Eversole, J. D.

Fürst, J. U.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
[Crossref] [PubMed]

Golant, K. M.

Gorodetsky, M. L.

Green, H.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Grekov, M. V.

Grudinin, I. S.

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[Crossref] [PubMed]

Haertle, D.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
[Crossref] [PubMed]

Haertle, T.

T. Haertle, “Domain patterns for quasi-phase matching in whispering-gallery modes,” J. Opt. 12(3), 035202 (2010).
[Crossref]

Haus, H. A.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Hill, S. C.

Huang, W.

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Huston, A. L.

Ilchenko, V. S.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[Crossref]

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[Crossref]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004).
[Crossref] [PubMed]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. 20(6), 1304–1308 (2003).
[Crossref]

M. L. Gorodetsky and V. S. Ilchenko, “Optical microsphere resonators: optimal coupling to high-Q whispering-gallery modes,” J. Opt. Soc. Am. B 16(1), 147–154 (1999).
[Crossref]

Jacobsen, C.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Jin, J.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Kanai, T.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004).
[Crossref] [PubMed]

Kapteyn, H.

H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science 317(5839), 775–778 (2007).
[Crossref] [PubMed]

Kapteyn, H. C.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Khrapko, R. R.

Kim, S.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Kim, S.-W.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Kim, Y.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Kim, Y.-J.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Kippenberg, T. J.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[Crossref] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[Crossref] [PubMed]

Kosuge, A.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004).
[Crossref] [PubMed]

Lassen, M.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

Leach, D. H.

Leuchs, G.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

Lin, H.-B.

Linnenbank, H.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
[Crossref] [PubMed]

Liu, Y.

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Maleki, L.

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[Crossref]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004).
[Crossref] [PubMed]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. 20(6), 1304–1308 (2003).
[Crossref]

Marquardt, C.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

Marquardt, Ch.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
[Crossref] [PubMed]

Matsko, A. B.

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[Crossref]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[Crossref]

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004).
[Crossref] [PubMed]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. 20(6), 1304–1308 (2003).
[Crossref]

Min, B.

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[Crossref]

Mohageg, M.

Murnane, M.

H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science 317(5839), 775–778 (2007).
[Crossref] [PubMed]

Murnane, M. M.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Oxborrow, M.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[Crossref] [PubMed]

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007).
[Crossref]

Park, I.-Y.

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Paul, A.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Qian, S. X.

S. X. Qian and R. K. Chang, “Multiorder stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56(9), 926–929 (1986).
[Crossref] [PubMed]

Rokhsari, H.

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

Sasagawa, K.

K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO: LiNbO3 disk resonator,” Appl. Phys. Express 2(12), 122401 (2009).
[Crossref]

Savchenkov, A. A.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[Crossref]

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[Crossref] [PubMed]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004).
[Crossref] [PubMed]

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. 20(6), 1304–1308 (2003).
[Crossref]

Schwefel, H. G. L.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[Crossref] [PubMed]

Sekikawa, T.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004).
[Crossref] [PubMed]

Spillane, S. M.

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[Crossref]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[Crossref] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[Crossref] [PubMed]

Steigerwald, H.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
[Crossref] [PubMed]

Stone, A. D.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[Crossref] [PubMed]

Strekalov, D.

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[Crossref]

Strekalov, D. V.

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
[Crossref] [PubMed]

A. A. Savchenkov, A. B. Matsko, M. Mohageg, D. V. Strekalov, and L. Maleki, “Parametric oscillations in a whispering gallery resonator,” Opt. Lett. 32(2), 157–159 (2007).
[Crossref] [PubMed]

Sturman, B.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
[Crossref] [PubMed]

Tobey, R.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

Tomes, M.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011), doi:.
[Crossref] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009).
[Crossref] [PubMed]

M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express 17(21), 19160–19165 (2009).
[Crossref] [PubMed]

Tsuchiya, M.

K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO: LiNbO3 disk resonator,” Appl. Phys. Express 2(12), 122401 (2009).
[Crossref]

Vahala, K. J.

M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express 17(21), 19160–19165 (2009).
[Crossref] [PubMed]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[Crossref] [PubMed]

T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
[Crossref]

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[Crossref] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[Crossref] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[Crossref] [PubMed]

Wang, G.

Wang, Z.

Watanabe, S.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004).
[Crossref] [PubMed]

Weiman, S.

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

Xu, Z.

Yang, L.

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[Crossref] [PubMed]

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[Crossref]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermal behavior and thermal self-stability of microcavities,” Opt. Express 12(20), 4742–4750 (2004).
[Crossref] [PubMed]

Zehnpfennig, J.

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011), doi:.
[Crossref] [PubMed]

Zhang, X.

Zhu, Y.

Appl. Phys. Express (1)

K. Sasagawa and M. Tsuchiya, “Highly efficient third harmonic generation in a periodically poled MgO: LiNbO3 disk resonator,” Appl. Phys. Express 2(12), 122401 (2009).
[Crossref]

Appl. Phys. Lett. (1)

L. Yang, T. Carmon, B. Min, S. M. Spillane, and K. J. Vahala, “Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process,” Appl. Phys. Lett. 86(9), 091114 (2005).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

A. B. Matsko and V. S. Ilchenko, “Optical resonators with whispering-gallery modes—Part I: Basics,” IEEE J. Sel. Top. Quantum Electron. 12(1), 3–14 (2006).
[Crossref]

V. S. Ilchenko and A. B. Matsko, “Optical resonators with whispering-gallery modes—Part II: Applications,” IEEE J. Sel. Top. Quantum Electron. 12(1), 15–32 (2006).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

M. Oxborrow, “Traceable 2-D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators,” IEEE Trans. Microw. Theory Tech. 55(6), 1209–1218 (2007).
[Crossref]

J. Opt. (1)

T. Haertle, “Domain patterns for quasi-phase matching in whispering-gallery modes,” J. Opt. 12(3), 035202 (2010).
[Crossref]

J. Opt. Soc. Am. (1)

V. S. Ilchenko, A. B. Matsko, A. A. Savchenkov, and L. Maleki, “Low-threshold parametric nonlinear optics with quasi-phase-matched whispering-gallery modes,” J. Opt. Soc. Am. 20(6), 1304–1308 (2003).
[Crossref]

J. Opt. Soc. Am. B (3)

Nat. Commun. (1)

G. Bahl, J. Zehnpfennig, M. Tomes, and T. Carmon, “Stimulated optomechanical excitation of surface acoustic waves in a microdevice,” Nat. Commun. 2, 403 (2011), doi:.
[Crossref] [PubMed]

Nat. Phys. (1)

T. Carmon and K. J. Vahala, “Visible continuous emission from a silica microphotonic device by third-harmonic generation,” Nat. Phys. 3(6), 430–435 (2007).
[Crossref]

Nature (4)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using a spherical dielectric microcavity,” Nature 415(6872), 621–623 (2002).
[Crossref] [PubMed]

A. Paul, R. A. Bartels, R. Tobey, H. Green, S. Weiman, I. P. Christov, M. M. Murnane, H. C. Kapteyn, and S. Backus, “Quasi-phase-matched generation of coherent extreme-ultraviolet light,” Nature 421(6918), 51–54 (2003).
[Crossref] [PubMed]

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432(7017), 605–608 (2004).
[Crossref] [PubMed]

S. Kim, J. Jin, Y.-J. Kim, I.-Y. Park, Y. Kim, and S.-W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (1)

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Strekalov, and L. Maleki, “Direct observation of stopped light in a whispering-gallery-mode microresonator,” Phys. Rev. A 76(2), 023816 (2007).
[Crossref]

Phys. Rev. Lett. (11)

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. 104(15), 153901 (2010).
[Crossref] [PubMed]

S. X. Qian and R. K. Chang, “Multiorder stokes emission from micrometer-size droplets,” Phys. Rev. Lett. 56(9), 926–929 (1986).
[Crossref] [PubMed]

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004).
[Crossref] [PubMed]

T. Carmon, H. G. L. Schwefel, L. Yang, M. Oxborrow, A. D. Stone, and K. J. Vahala, “Static envelope patterns in composite resonances generated by level crossing in optical toroidal microcavities,” Phys. Rev. Lett. 100(10), 103905 (2008).
[Crossref] [PubMed]

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, “Highly tunable low-threshold optical parametric oscillation in radially poled whispering gallery resonators,” Phys. Rev. Lett. 106(14), 143903 (2011).
[Crossref] [PubMed]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, “Low-threshold optical parametric oscillations in a whispering gallery mode resonator,” Phys. Rev. Lett. 105(26), 263904 (2010).
[Crossref] [PubMed]

T. Carmon, H. Rokhsari, L. Yang, T. J. Kippenberg, and K. J. Vahala, “Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode,” Phys. Rev. Lett. 94(22), 223902 (2005).
[Crossref] [PubMed]

T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Kerr-nonlinearity optical parametric oscillation in an ultrahigh-Q toroid microcavity,” Phys. Rev. Lett. 93(8), 083904 (2004).
[Crossref] [PubMed]

I. S. Grudinin, A. B. Matsko, and L. Maleki, “Brillouin lasing with a CaF2 whispering gallery mode resonator,” Phys. Rev. Lett. 102(4), 043902 (2009).
[Crossref] [PubMed]

M. Tomes and T. Carmon, “Photonic micro-electromechanical systems vibrating at X-band (11-GHz) rates,” Phys. Rev. Lett. 102(11), 113601 (2009).
[Crossref] [PubMed]

Proc. IEEE (1)

H. A. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Science (2)

H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science 317(5839), 775–778 (2007).
[Crossref] [PubMed]

R. A. Bartels, A. Paul, H. Green, H. C. Kapteyn, M. M. Murnane, S. Backus, I. P. Christov, Y. Liu, D. Attwood, and C. Jacobsen, “Generation of spatially coherent light at extreme ultraviolet wavelengths,” Science 297(5580), 376–378 (2002).
[PubMed]

Other (4)

A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Surface acoustic wave frequency comb,” arXiv:1106.1477v1 (2011).

K. Vahala, Optical Microcavities (World Scientific Publishing Co. Pte. Ltd., 2004).

M. Kozlov, O. Kfir, A. Fleischer, T. Carmon, H. G. Schwefel, and O. Cohen, “High-order harmonics of a continuous-wave driving laser,” Frontiers in Optics, OSA Technical Digest (CD), paper FWE2 (2010).

R. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1 Radial electric field profiles for a 1550 nm pump and the corresponding 2nd, 3rd, and 4th harmonics, which are numerically calculated for the 3mm lithium niobate whispering-gallery resonator (TM modes).
Fig. 2
Fig. 2 The amplitude of the Fourier coefficients for the poling pattern seen by the azimuthally propagating mode, for our 3mm diameter resonator with Λ0 = 79 µm striped poling, confirming that the energy-momentum condition can be satisfied for all three harmonic-generation processes simultaneously.
Fig. 3
Fig. 3 (a) Experimental setup for demonstrating cascaded-harmonic generation in the periodically poled lithium niobate resonator. (b) Measured whispering-gallery resonator resonance, implying a quality factor of 2×107 at 1540nm.
Fig. 4
Fig. 4 Visual verification of cascaded-harmonic generation: The pump beam is recorded with an infrared CCD camera, and the harmonics are observed on a color CCD coated with ultraviolet fluorescent ink. The photograph is taken at a pump wavelength of 1538 nm and a pump power of 200mW.
Fig. 5
Fig. 5 Measured emission spectrum at 1546nm pump wavelength, indicating generation of the 2nd, 3rd, and 4th harmonics. Harmonics are measured using three different spectrum analyzers and are plotted at different intensity scales.
Fig. 6
Fig. 6 Measured spectrograms of the generated 2nd, 3rd, and 4th harmonics at a pump wavelength range of 1535-1545nm are illustrated in a, b, and c. Colors stand for intensity. All three harmonics display wide tunability within this wavelength range.
Fig. 7
Fig. 7 Measured power of the generated 2nd, 3rd, and 4th harmonics at a pump wavelength of 1550nm, as a function of the pump power are illustrated in d, e, and f, revealing nearly quadratic, cubic and power-of-4 dependency for the 2nd, 3rd, and 4th order processes

Metrics