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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 1 — Jan. 4, 2012
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Continuous-wave ultraviolet emission through fourth-harmonic generation in a whispering-gallery resonator

Jeremy Moore, Matthew Tomes, Tal Carmon, and Mona Jarrahi  »View Author Affiliations


Optics Express, Vol. 19, Issue 24, pp. 24139-24146 (2011)
http://dx.doi.org/10.1364/OE.19.024139


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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 OSA

1. Introduction

2. Whispering-gallery resonator design

Quasi phase-matching to conserve momentum for the harmonics and pump is achieved by periodic poling of lithium niobate [30

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

,33

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]

] and facilitated by a combination of high order transverse resonance modes [24

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]

]. 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

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]

]. 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
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.
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

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

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]

]. 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.

3. Experimental results and discussion

The pump beam, tunable from 1535 to 1545nm, is evanescently coupled to the cavity modes via a diamond prism [36

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]

]. 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

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]

] 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

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]

]. 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
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.
). 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.

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
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.
). These measured wavelengths lay within the 2nm error margin of our spectrum analyzers.

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).

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(230.0230) Optical devices : Optical devices

ToC Category:
Nonlinear Optics

History
Original Manuscript: September 28, 2011
Revised Manuscript: October 25, 2011
Manuscript Accepted: October 26, 2011
Published: November 10, 2011

Virtual Issues
Vol. 7, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Jeremy Moore, Matthew Tomes, Tal Carmon, and Mona Jarrahi, "Continuous-wave ultraviolet emission through fourth-harmonic generation in a whispering-gallery resonator," Opt. Express 19, 24139-24146 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-24-24139


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References

  1. H. Kapteyn, O. Cohen, I. Christov, and M. Murnane, “Harnessing attosecond science in the quest for coherent X-rays,” Science317(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,” Science297(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,” Nature421(6918), 51–54 (2003). [CrossRef] [PubMed]
  5. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature432(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,” Nature415(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. B7(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. Express2(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. B10(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. IEEE79(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. A76(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. B16(1), 147–154 (1999). [CrossRef]
  37. M. Tomes, K. J. Vahala, and T. Carmon, “Direct imaging of tunneling from a potential well,” Opt. Express17(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. Express12(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,” Nature453(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).

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