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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 17 — Aug. 18, 2008
  • pp: 13158–13167
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Loss determination in microsphere resonators by phase-shift cavity ring-down measurements

J. Barnes, B. Carver, J. M. Fraser, G. Gagliardi, H.-P. Loock, Z. Tian, M.W.B. Wilson, S. Yam, and O. Yastrubshak  »View Author Affiliations


Optics Express, Vol. 16, Issue 17, pp. 13158-13167 (2008)
http://dx.doi.org/10.1364/OE.16.013158


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Abstract

The optical loss of whispering gallery modes of resonantly excited microresonator spheres is determined by optical lifetime measurements. The phase-shift cavity ring-down technique is used to extract ring-down times and optical loss from the difference in amplitude modulation phase between the light entering the microresonator and light scattered from the microresonator. In addition, the phase lag of the light exiting the waveguide, which was used to couple light into the resonator, was measured. The intensity and phase measurements were fully described by a model that assumed interference of the cavity modes with the light propagating in the waveguide.

© 2008 Optical Society of America

1. Introduction

The interaction of a chemical analyte with a microresonator occurs through the modification of the optical environment of the resonator. An analyte may have two effects on the cavity mode spectrum of the microresonator. If the effective refractive index of the WGM is increased due to the presence of the analyte, as is frequently the case, the mode field volume increases and the cavity spectrum shifts to longer wavelength. [11

11. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272 (2003). [CrossRef] [PubMed]

] In addition, the analyte may also absorb light, which reduces the quality factor of the cavity and broadens the cavity resonance lines. [13

13. A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-Q microcavities,” Opt. Lett. 31, 1896 (2006). [CrossRef] [PubMed]

,14

14. A. T. Rosenberger, “Analysis of whispering-gallery microcavity-enhanced chemical absorption sensors,” Opt. Express 15, 12959 (2007). [CrossRef] [PubMed]

] Both effects have been used to implement microresonators as chemical sensors. For chemical sensing the measurement of optical absorption is of particular interest, because it is more specific and less influenced by temperature compared to a refractive index measurement. In the past the reduction in the Q-factor has usually been observed by measuring the linewidth of the cavity resonances, but may also be observed in the time domain using cavity-ring-down spectroscopy (CRD) [15

15. K. J. Vahala, “Optical microcavities,” Nature 424, 839 (2003). [CrossRef] [PubMed]

].

Time-domain measurements have been routinely used to measure optical lifetimes in mirror optical cavities [16

16. G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565 (2000). [CrossRef]

], as well as in monolithic devices [17

17. A. C. R. Pipino, “Ultrasensitive surface spectroscopy with a miniature optical resonator,” Phys. Rev. Lett. 83, 3093 (1999). [CrossRef]

], fiber-optic loops [18

18. R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, “Fiber-loop ring-down spectroscopy,” J. Chem. Phys. 117, 10444 (2002). [CrossRef]

] and microresonators [8

8. T. J. Kippenberg, S.M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29, 1224 (2004). [CrossRef] [PubMed]

,19

19. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 42, 925 (2003). [CrossRef]

]. The intensity of a short optical pulse injected into the cavity decays exponentially with time as the circulating power is dissipated. The time-constant for the decay reflects the optical lifetime of the cavity. While this method is practical for macroscopic cavities, the photon lifetime of microcavities is frequently on the order of nanoseconds requiring picosecond laser pulses and fast data acquisition systems. This will not only increase the cost but also result in a low duty cycle.

2. Experimental

The microresonator used is this work consists of a silica microsphere formed by fusing the end of a single-mode optical fiber in the arc of a fusion splicer. Surface tension draws the molten silica into a sphere with a nominal diameter of 300 µm. The residual fiber supporting the sphere is placed in a fiber chuck that is held in an X-Y-Z stage to allow positioning of the sphere. A tapered single-mode optical fiber, with a waist diameter of 3–4 µm, is used to evanescently couple to the WGMs of the microsphere. The taper is formed by clamping a stripped and cleaned length of single-mode fiber between two motorized translational stages that move in opposition. The fiber is softened in a propane/air flame while the stages separate by a distance of approximately 2 cm. After tapering, the fiber is too fragile for further manipulation. To allow removal of the fiber from the tapering fixture, drops of wax are used to secure the stretched fiber to a microscope slide. An optical microscope is used to measure the taper diameter. The mounted taper is secured to a stage adjacent to the microsphere X-Y-Z stage and the microsphere is carefully brought into contact with the tapered region of the fiber. Optical contact can be easily determined by shining a visible diode laser through the delivery fiber. The microsphere scatters brightly when contact is made with the fiber taper.

An Ando AQ4320D tunable diode laser is used as the excitation light source. The laser is continuously tunable from 1520–1620 nm with a quoted line width of less than 1 MHz. The diode laser intensity is sinusoidally modulated externally using a JDS Uniphase Mach-Zehnder modulator. Unfortunately, the maximum modulation frequency is presently limited to 2 MHz by the function generator (Dae Shin DOA-141). The Mach-Zehnder Interferometer was biased such that the contribution of frequency modulation (FM) was minimized. FM manifests itself in the intensity spectrum through asymmetric lineshapes (see Section 3 below). When examining the WGMs in transmission mode, a D400FC InGaAs detector (Thorlabs, Inc.) is used to measure the light intensity passing through the tapered delivery fiber. A Stanford Research Systems Model SR844 lock-in amplifier processes the detector output, providing an intensity and a phase angle measurement referenced to the diode laser modulation. To examine the WGMs in scattering mode, a switchable gain PDA10CS InGaAs detector (Thorlabs, Inc.), attached to a second X-Y-Z stage, is positioned above the microsphere. To enhance light collection efficiency, an anti-reflection coated ball lens is mounted before the detector. The detector output is processed through a second SR844 lock-in to provide scatter intensity and phase data. The lock-in outputs pass through a Measurement Computing PMD-1608FS A/D before being collected on a computer.

To shield the microresonator and fiber taper from contamination, the entire optical setup is placed under a plastic enclosure that is continuously purged with a gentle flow of nitrogen gas.

3. Theory

Einc=E0eiωt(1β+i2βcosΩt)
=E01βeiωt+E0β2(ei(ω+Ω)t+π2+ei(ωΩ)t+π2)
(1)

Where β is the modulation depth, ω is the carrier frequency and Ω is the amplitudemodulation frequency of the electric field. Note that the intensity is then modulated by 2Ω. The carrier and each frequency sideband will experience their own attenuation and phase-shift (Φ, Φ+ and Φ-, respectively) through interaction with the resonator, and the output field will be

Etrans=Eω1βei(ωt+Φ)+Eω+Ωβ2ei[(ω+Ω)t+Φ++π2]+EωΩβ2ei[(ωΩ)t+Φ+π2]
(2)

The transmitted intensity is given by

Itrans=neffε0c2
[(1β)Eω2+β2(Eω+Ω2+Eω+Ω2)+EωEω+Ω2β(1β)sin(Ωt+ΦΦ+)+EωEωΩ2β(1β)sin(Ωt+ΦΦ)+βEω+ΩEωΩcos(2Ωt+Φ+Φ)]
(3)

In our case, we only record the signal modulated at 2Ω with the lock-in amplifier and the associated phase-shift of the modulation envelope is given by (Φ+-).

Rezac’s formalism can now be used to calculate the phase-shift at each sideband frequency; the difference (Φ+-) yielding the desired modulation envelope phase-shift. [23

23. J. Rezac, “Properties and applications of whispering-gallery mode resonances in fused silica microspheres,” Ph.D. (Oklahoma State University, 2002).

] In Eq. (1) we assume that the contribution of frequency modulation (FM) is negligible. This is easily verified experimentally. If FM were present, one would observe dispersive-like lineshapes with zero-crossing at the resonance peak as a consequence of the π phase difference between the sidebands. Such “derivative-type” lineshapes were indeed observed in preliminary experiments when the laser was current modulated, and FM contributions were considerable. When using the Mach-Zehnder interferometer no such effect was observed.

The ring-resonator model assumes a single frequency electric field incident upon a multimirror ring-cavity (Fig. 1). The input mirror has a field amplitude reflectivity, Γ, while the other mirrors are assumed totally reflective in our model. As the field propagates within the resonator, it experiences a fractional loss of exp(-αL/2) per pass (the intensity loss is exp(-αL) per pass), where α is the distributed loss coefficient and L is the round-trip path length. The reflected field from the ring-resonator consists of the superposition of the partially reflected incident field and the partially transmitted field inside the resonator. In our case of a fiber coupled microsphere resonator the reflected field of this model corresponds to the light transmitted through the tapered delivery fiber. The normalized amplitude of the respective field for a single frequency incident field, is given by [23

23. J. Rezac, “Properties and applications of whispering-gallery mode resonances in fused silica microspheres,” Ph.D. (Oklahoma State University, 2002).

]

E=ErefEinc=ΓeαL2eiLk1ΓeαL2eiLk
(4)

where the wave vector kneff/c. Accordingly the intensity (shown in Fig. 1(a)) is calculated from the absolute square of (4) as

I=Γ22ΓeαL2cos(Lk)+eαL12ΓeαL2cos(Lk)+Γ2eαL
(5)

To calculate the phase angle associated with the field of (4) the expression is expanded by the complex conjugate of the denominator

E=Γ(Γ2+1)eαL2cos(Lk)+ΓeαL+i(Γ21)eαL2sin(Lk)12ΓeαL2cos(Lk)+Γ2eαL
(6)

With this expression the phase angle associated with the field of (4) is readily described in the complex plane as

tanϕ=Im(E)Re(E)
=(Γ21)eαL2sin(Lk)Γ(Γ2+1)eαL2cos(Lk)+ΓeαL
(7)

The phase-shifts at the two sideband frequencies Φ+ and Φ- can be calculated from Eq. (7) by using k +=(ω+Ω) neff/c and k -=(ω-Ω) neff/c respectively.

It is helpful to distinguish different coupling regimes before examining the implications of the above expressions. When -2 lnΓ>αL, the cavity is ‘overcoupled’. In this regime, coupling to the fiber is the dominant loss mechanism controlling the resonance linewidth [25

25. T. J. Kippenberg, “Nonlinear Optics in Ultra-high-Q Whispering-Gallery Optical Microcavities,” Ph.D. (California Institute of Technology, 2004).

]. When -2 lnΓ<αL, the cavity is referred to as ‘undercoupled’, and ‘critically coupled’ when -2 lnΓ=αL. At the point of critical coupling, no light is transmitted through the delivery fiber on resonance. Plots of the phase angle obtained from Eq. (7) are shown in Figure 1B for different values of α and assuming Γ=0.9995 and L=1 mm. It is apparent that for the undercoupled case the slope is negative in the vicinity of the resonance, and that the magnitude of the slope increases with decreasing loss α. The phase-shift for an intensity-modulated input is given by the difference in the phase angles associated with the sideband frequencies (Eq. (3)). In our experiments the modulation frequency is <10-8 of the carrier frequency, and we can simplify

(Φ+Φ)=2ΩneffLcΦLk
(8)

Based on Eq. (8), one would expect to observe a phase-shift that varies linearly with modulation frequency, having a slope that increases with decreasing loss in the resonator. When operating near resonance, it is possible to use small angle approximations for the trigonometric functions in Eq. (7) and obtain the result

ΔΦ=Φ+Φ2ΩneffLcx(1Γ2)Γ(1+x2)x(1+Γ2)
(9)

where x=e -αL/2. This may also be expressed as

ΔΦ=Φ+Φ2ΩneffLc2ln(Γ)(lnΓ)2(αL2)2
(10)
Fig. 1. (a) Intensity of the transmission through the waveguide near a resonance (Eq. (5)). (b) the phase near that resonance calculated from Eq. (7) (c) The corresponding phase-shift spectrum from Eq. (8). For all calculations the absorption coefficient α was varied in 10 increments between 0.1–1.9 m-1critical=1 m-1) and the following set of parameters was used: coupling parameter Γ=0.9995, neff=1.45; L=1 mm; ω=2 1014 s-1.

Equation (9) and (10) explicitly relate the phase-shift to the modulation frequency and loss within the microresonator. Equation (10) shows that the phase-shift is negative in the case of an undercoupled excitation and positive if the resonator is operated in the overcoupled regime. This is also illustrated in Fig. 1(c), where it is apparent that the phase-shift switches abruptly from positive to negative as α is increased from the undercoupled to the overcoupled case. From (10) it is apparent that the phase-shift increases linearly with increasing modulation frequency Ω, and with decreasing dB loss. As can be shown, the resonance line width decreases accordingly.

In the case of scattered light, we need only concern ourselves with the field circulating within the microresonator. This case is very similar to those described in the cavity ring-down literature for an optical cavity with two or more mirrors. The intensity of resonant light circulating within the cavity will decay exponentially over time, with a lifetime given by

τ=neffLc(lnΓ2+αL)
(11)

In our experiment intensity modulated light is injected into the microresonator. From the field in Eq. (1) the intensity is [20

20. R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105 (1996). [CrossRef]

]

I(ω,t)=E02(ω)(1+βcos(2Ωt))
(12)

where 0≤β≤1is the modulation depth. The intensity, E 2 0(ω), is dictated by the WGM spectrum. The intensity of light scattered from the microresonator at time t is given by [20

20. R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105 (1996). [CrossRef]

]

I(ω,t)=1τtE02(ω)(1+βcos(2Ωt))exp[(tt)τ]dt
=E02(ω)(1+β1+4Ω2τ2cos(2Ωttan1(2Ωτ)))
(13)

From this expression we can see that the scattered light is phase-shifted with respect to the input light by an amount

ΔΦ=tan1(2Ωτ)
2Ωτ
2ΩneffLc12lnΓ+αL
(14)

for small phase-shifts. Note that the phase-shifts described by Eqs. (14) and (10) are different especially with respect to the sign of the coupling parameter Γ, i.e. only in Eq. (14) is Γ contributing to the optical loss.

As shown in (13) the depth of the modulation amplitude is also dependent on Ω and τ but since Ωτ≪1 this contribution can be neglected and the intensity I(ω) is proportional to the measured quantity βI0(ω). Similarly, in deriving Eq. (5) for the intensity of the transmitted light, we also assumed that the angular modulation period is long compared to the WGM ring-down time.

4. Results and discussion

Fig. 2. Whispering-gallery mode spectrum of a 300 micron diameter silica microsphere in contact with a 3 micron diameter tapered fiber. Spectra are recorded in transmission (top) and in scattering mode (bottom).
Fig. 3. Phase-shift spectrum and intensity spectra of a 300 µm diameter microsphere. (a) The measurement was conducted by detecting the light transmitted through the fiber taper. (b) Scattered light was collected above the microsphere. The modulation frequency is 1.6 MHz.
Fig. 4. Transmitted light (upper trace) and phase angle WGM spectrum of the microsphere. The phase-shift CRD spectra show that some of the WGMs are overcoupled (positive going peaks) whereas others are undercoupled (negative).
Fig. 5. Modulation frequency dependent phase-shift for the four peaks shown in the transmission spectrum (solid lines and symbols, see Fig. 3(a)) and the three peaks shown in the scattering spectrum (dashed, empty symbols, Fig. 3(b) From the former the slopes of the linear fits can be used to calculate the parameter 2lnΓ/[(2lnΓ)2-(αL/2)2] as 757, 829, 962, 1039, respectively (see Eq. (10)). Ring-down times of 5.6, 7.5 and 4.6 ns are obtained directly from the slope of linear fits of the modulation frequency dependent phase-shift for peaks A, B and C in the scattering spectrum.

The scattering peak amplitudes in the phase-shift and in the intensity spectra are not expected to be similar (Fig. 3(b)). In the scattering intensity spectrum the amplitude represents the power coupled into the respective mode, i.e. a quantity that depends on the square of the ring-down time, whereas in the phase-shift spectrum the peak amplitude scales linearly with the ring-down time. Also, the scattering intensity is easily influenced by a background arising e.g. from scattering off the tapered waveguide. By contrast, a large change in phase shift can only arise from a WGM with a long decay time. Since the decay time is strongly affected by the presence of analytes on the microresonator surface, the phase-shift measurement may be more robust, albeit less sensitive, compared to an intensity or linewidth measurement.

The transmission peak amplitudes in the phase shift and intensity spectra (Fig. 3(a)) are also not well correlated, since the phase-shift is much more strongly dependent on the coupling regime compared to the intensity. The most pronounced peaks in the transmission phase-shift spectrum correspond to WGM which experience near critical coupling conditions.

Figure 5 displays the modulation frequency dependence of the measured scattering phase angle for resonant excitation of three different modes corresponding to non-overlapped peaks in the respective spectra (Fig. 3). The phase angle measurements have a considerable measurement error due to the low light level emitted by the high-Q resonator, but with eq. (14) nevertheless give reasonable estimates of the ring-down times as τ=4-8 ns. For these three modes the quality (Q) factor is therefore between about 5 106 and 10 106. With an estimated sphere circumference of 1 mm and assuming a refractive index of 1.45 the loss per roundtrip is calculated to be between 0.0025 dB and 0.005 dB. The propagation loss of 2.5–5.0 dB/m for these WGMs compares poorly to losses achieved in single mode waveguides made from the same silica material (3 dB/km), but is comparable to propagation losses achieved in some microtoroidal resonators (0.5 dB/m) [19

19. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 42, 925 (2003). [CrossRef]

].

Also included in Fig. 5 is the modulation frequency dependence of the transmission phase angle given at the resonance peak of four modes (viz. Fig. 3). A linear relationship, with negative slope, is observed as predicted by Eq. (10) for the undercoupled regime. The differences in slope are due to differences in coupling efficiency and/or optical loss. For the overcoupled regime the model predicts a positive phase-shift and slope. Very close to critical coupling the model presented in Eq. (10) breaks down and it can be shown that the respective graphs then deviate from linearity. Given the total loss calculated from the scattering phase-shift one obtains Γ critical=0.9998 and α critical=0.43 m-1. As can be seen in Fig. 4 we operated very close to critical coupling conditions, since both undercoupled and overcoupled WGMs could be observed.

5. Summary and conclusion

Acknowledgments

We thank Photonics Research Ontario (Ontario Centres of Excellence) for financial support of this work. Contributions from the Canadian Institute for Photonic Innovations (CIPI), from the Natural Science and Engineering Research Council (NSERC) are acknowledged by the Canadian researchers. GG also acknowledges financial support from the Italian Ministry for Education, University and Research (PON-SIMONA) and assistance from the Consiglio Nazionale delle Ricerche by the RSTL-project and the short term-mobility program.

References and links

1.

A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, “Ultra-high-Q microcavity operation in H2O and D2O,” Appl. Phys. Lett. 87, 151118 (2005). [CrossRef]

2.

R. W. Boyd and J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40, 5742 (2001). [CrossRef]

3.

C. Chao and L. J. Guo, “Polymer microring resonators fabricated by nanoimprint technique,” J. Vac. Sci. Technol. B 20, 2862 (2002). [CrossRef]

4.

E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, “Integrated optical microcavities for enhanced evanescent-wave spectroscopy,” Opt. Lett. 27, 1504 (2002). [CrossRef]

5.

T. Ling and L. J. Guo, “A unique resonance mode observed in a prism-coupled micro-tube resonator sensor with superior index sensitivity,” Opt. Express 15, 17424 (2007). [CrossRef] [PubMed]

6.

D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, “High-Q measurements of fused-silica microspheres in the near infrared,” Opt. Lett. 23, 247 (1998). [CrossRef]

7.

I. M. White, H. Oveys, and X. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31, 1319 (2008). [CrossRef]

8.

T. J. Kippenberg, S.M. Spillane, D. K. Armani, and K. J. Vahala, “Ultralow-threshold microcavity Raman laser on a microelectronic chip,” Opt. Lett. 29, 1224 (2004). [CrossRef] [PubMed]

9.

S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. S. Wickramanayake, and N. A. Kotov, “Microsphere whispering-gallery-mode laser using HgTe quantum dots,” Appl. Phys. Lett. 85, 6101 (2004). [CrossRef]

10.

M. Cai, G. Hunziker, and K. Vahala, “Fiber-Optic Add-Drop Device Based on a Silica Microsphere Whispering Gallery Mode System,” IEEE Photon. Technol. Lett 11, 686 (1999). [CrossRef]

11.

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272 (2003). [CrossRef] [PubMed]

12.

G. Farca, S. I. Shopova, and A. T. Rosenberger, “Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes,” Opt. Express 15, 17443 (2007). [CrossRef] [PubMed]

13.

A. M. Armani and K. J. Vahala, “Heavy water detection using ultra-high-Q microcavities,” Opt. Lett. 31, 1896 (2006). [CrossRef] [PubMed]

14.

A. T. Rosenberger, “Analysis of whispering-gallery microcavity-enhanced chemical absorption sensors,” Opt. Express 15, 12959 (2007). [CrossRef] [PubMed]

15.

K. J. Vahala, “Optical microcavities,” Nature 424, 839 (2003). [CrossRef] [PubMed]

16.

G. Berden, R. Peeters, and G. Meijer, “Cavity ring-down spectroscopy: Experimental schemes and applications,” Int. Rev. Phys. Chem. 19, 565 (2000). [CrossRef]

17.

A. C. R. Pipino, “Ultrasensitive surface spectroscopy with a miniature optical resonator,” Phys. Rev. Lett. 83, 3093 (1999). [CrossRef]

18.

R. S. Brown, I. Kozin, Z. Tong, R. D. Oleschuk, and H.-P. Loock, “Fiber-loop ring-down spectroscopy,” J. Chem. Phys. 117, 10444 (2002). [CrossRef]

19.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 42, 925 (2003). [CrossRef]

20.

R. Engeln, G. von Helden, G. Berden, and G. Meijer, “Phase shift cavity ring down absorption spectroscopy,” Chem. Phys. Lett. 262, 105 (1996). [CrossRef]

21.

Z. Tong, A. Wright, T. McCormick, R. Li, R. D. Oleschuk, and H.-P. Loock, “Phase-Shift Fiber-Loop Ring-Down Spectroscopy,” Anal. Chem. 76, 6594 (2004). [CrossRef] [PubMed]

22.

M. C. Chan and S. H. Yeung, “High-resolution cavity enhanced absorption spectroscopy using phase-sensitive detection,” Chem. Phys. Lett. 373, 100 (2003). [CrossRef]

23.

J. Rezac, “Properties and applications of whispering-gallery mode resonances in fused silica microspheres,” Ph.D. (Oklahoma State University, 2002).

24.

A. C. R. Pipino, J. W. Hudgens, and R. E. Huie, “Evanescent wave cavity ring-down spectroscopy with a total-internal-reflection minicavity,” Rev Sci Instrum 68, 2978 (1997). [CrossRef]

25.

T. J. Kippenberg, “Nonlinear Optics in Ultra-high-Q Whispering-Gallery Optical Microcavities,” Ph.D. (California Institute of Technology, 2004).

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators

ToC Category:
Optical Devices

History
Original Manuscript: April 30, 2008
Revised Manuscript: August 8, 2008
Manuscript Accepted: August 11, 2008
Published: August 13, 2008

Citation
J. Barnes, B. Carver, J. M. Fraser, G. Gagliardi, H.-P. Loock, Z. Tian, M.W.B. Wilson, S. Yam, and O. Yastrubshak, "Loss determination in microsphere resonators by phase-shift cavity ring-down measurements," Opt. Express 16, 13158-13167 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13158


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References

  1. A. M. Armani, D. K. Armani, B. Min, K. J. Vahala, and S. M. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Appl. Phys. Lett. 87, 151118 (2005). [CrossRef]
  2. R. W. Boyd and J. E. Heebner, "Sensitive disk resonator photonic biosensor," Appl. Opt. 40, 5742 (2001). [CrossRef]
  3. C. Chao and L. J. Guo, "Polymer microring resonators fabricated by nanoimprint technique," J. Vac. Sci. Technol. B 20, 2862 (2002). [CrossRef]
  4. E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, "Integrated optical microcavities for enhanced evanescent-wave spectroscopy," Opt. Lett. 27, 1504 (2002). [CrossRef]
  5. T. Ling and L. J. Guo, "A unique resonance mode observed in a prism-coupled micro-tube resonator sensor with superior index sensitivity," Opt. Express 15, 17424 (2007). [CrossRef] [PubMed]
  6. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, "High-Q measurements of fused-silica microspheres in the near infrared," Opt. Lett. 23, 247 (1998). [CrossRef]
  7. I. M. White, H. Oveys, and X. Fan, "Liquid-core optical ring-resonator sensors," Opt. Lett. 31, 1319 (2008). [CrossRef]
  8. T. J. Kippenberg, S. M. Spillane, D. K. Armani, and K. J. Vahala, "Ultralow-threshold microcavity Raman laser on a microelectronic chip," Opt. Lett. 29, 1224 (2004). [CrossRef] [PubMed]
  9. S. I. Shopova, G. Farca, A. T. Rosenberger, W. M. S. Wickramanayake, and N. A. Kotov, "Microsphere whispering-gallery-mode laser using HgTe quantum dots," Appl. Phys. Lett. 85, 6101 (2004). [CrossRef]
  10. M. Cai, G. Hunziker, and K. Vahala, "Fiber-Optic Add-Drop Device Based on a Silica Microsphere Whispering Gallery Mode System," IEEE Photon. Technol. Lett 11, 686 (1999). [CrossRef]
  11. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, "Shift of whispering-gallery modes in microspheres by protein adsorption," Opt. Lett. 28, 272 (2003). [CrossRef] [PubMed]
  12. G. Farca, S. I. Shopova, and A. T. Rosenberger, "Cavity-enhanced laser absorption spectroscopy using microresonator whispering-gallery modes," Opt. Express 15, 17443 (2007). [CrossRef] [PubMed]
  13. A. M. Armani and K. J. Vahala, "Heavy water detection using ultra-high-Q microcavities," Opt. Lett. 31, 1896 (2006). [CrossRef] [PubMed]
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