## Intrinsic quality factor determination in whispering gallery mode microcavities using a single Stokes parameters measurement |

Optics Express, Vol. 19, Issue 23, pp. 23544-23553 (2011)

http://dx.doi.org/10.1364/OE.19.023544

Acrobat PDF (1245 KB)

### Abstract

Determination of the intrinsic quality factor of a loaded whispering gallery mode microcavity can be important for many applications where the coupling conditions cannot be tuned. We propose a single-scan technique based on a Stokes parameters analysis to extract the intrinsic quality factor and therefore determine the coupling regime. We propose a simple model for this analysis and present experimental measurements, which are in very good agreement with the model.

© 2011 OSA

## 1. Introduction

1. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods **5**, 591–596 (2008). [CrossRef] [PubMed]

2. J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics **4**, 46–49 (2009). [CrossRef]

3. A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A **70**, 051804(R) (2004). [CrossRef]

4. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. **60**, 289–291 (1992). [CrossRef]

5. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. **95**, 033901 (2005). [CrossRef] [PubMed]

6. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature **431**, 1081–1084 (2004). [CrossRef] [PubMed]

_{2}, fluoride materials, III–V and II–VI semiconductors, polymers, chalcogenide glass, etc. WGM microcavities exist mostly in the form of microspheres [7

7. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. **21**, 453–455 (1996). [CrossRef] [PubMed]

4. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. **60**, 289–291 (1992). [CrossRef]

8. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature **421**, 925–928 (2003). [CrossRef] [PubMed]

9. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO_{2} microring resonator optical channel dropping filters,” IEEE Photonics Technol. Lett. **10**, 549–551 (1998). [CrossRef]

*Q*

_{0}), their compactness and for some, their ease for on-chip integration.

*Q*

_{0}and

*Q*is done by using

_{c}*Q*and the normalized transmission value at the resonance wavelength

_{T}*λ*[12

_{r}12. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. **91**, 043902 (2003). [CrossRef] [PubMed]

*Q*, the coupling regime has to be known to distinguish between the

_{T}*Q*

_{0}and

*Q*contributions, except when critically coupled where the normalized transmission is zero. The coupling regime can be identified by varying the gap between the waveguide and the cavity. Since sensors or telecommuncations devices are mainly designed to be on-chip with fixed waveguide configuration, a correct determination can be difficult. Most Fabry-Perot characterization techniques cannot be used since a modulated signal in the frequency range of the free spectral range (FSR) is needed [13

_{c}13. B. J. J. Slagmolen, M. B. Gray, K. G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl. Opt. **39**, 3638–3643 (2000). [CrossRef]

14. C. R. Locke, D. Stuart, E. N. Ivanov, and A. N. Luiten, “A simple technique for accurate and complete characterisation of a Fabry-Perot cavity,” Opt. Express **17**, 21935–21943 (2009). [CrossRef] [PubMed]

*et al.*[15

15. Y. Dumeige, S. Trebaol, L. Ghişa, T. K. N. Nguyên, H. Tavernier, and P. Féron, “Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers,” J. Opt. Soc. Am. B **25**, 2073–2080 (2008). [CrossRef]

*Q*

_{0}and

*Q*extraction is possible if a laser line is swept fast enough across the resonance, because the resulting ringing phenomenom does not depend on

_{c}*Q*

_{0}and

*Q*in the same way. Unfortunately, this technique requires a high speed sweep and thus, cannot be applied to

_{c}*Q*below 107. Finally, Ito

_{T}*et al.*[16

16. T. Ito and Y. Kokubun, “Nondestructive measurement of propagation loss and coupling efficiency in microring resonator filters using filter responses,” Jpn. J. Appl. Phys. **43**, 1002–1005 (2004). [CrossRef]

*Q*

_{0}and

*Q*and therefore the coupling regime of WGM and ring-type cavities. Based on a Stokes parameters analysis near the resonance wavelength, this single scan technique can be used to determine

_{c}*Q*

_{0}and

*Q*when

_{c}*Q*is above 1 × 10

_{T}^{5}with < 1% estimation error. Also, the method does not depend on the coupling regime nor on the input polarisation states. First, the theoretical model used to describe the Stokes parameters analysis is explained for different coupling regimes. The estimation of both quality factors is described with simple relations and the minimum

*Q*where the technique is valid is determined based on the estimation errors. Then, we present the experimental setup and the measurements for different coupling gaps. The very good agreement of the experimental Stokes parameters curves supports the reliability of the proposed technique.

_{T}## 2. Theoretical model

*Q*

_{0}and

*Q*is based on a polarization analysis (Stokes parameters) where the phase change in the WGM cavity gives, along with

_{c}*Q*, an additional information about the coupling regime. In this section, we present the theoretical basis of how

_{T}*Q*

_{0}and

*Q*are determined and the conditions for which this technique is applicable.

_{c}*a⃗*+

_{x}*a⃗*=

_{y}*a*+

_{x}x⃗*a*enters the coupling region where

_{y}e^{iϕ}y⃗*a*and

_{x}*a*are the modulus of the

_{y}*x*and

*y*components, and

*ϕ*, their phase difference. Only one axis is coupled to the cavity mode, we chose

*a⃗*in this article.

_{y}*T*,

*θ*) and the system parameters (

*a*,

_{x}*a*and

_{y}*ϕ*) as follows [19

19. D. Goldstein, *Polarized Light* (Marcel Dekker, Inc., New York, 2003), 2nd ed. [CrossRef]

*δ*is the accumulated phase difference between axis. These expressions reveal that a spectral characterization of the Stokes parameters provides, along with the normalized transmission

*S*

_{0}, an additional information about the phase

*θ*considering a non-zero value of

*a*and

_{x}*a*. Since

_{y}*S*

_{0}and

*S*

_{2}are similar to

*S*

_{1}and

*S*

_{3}respectively, the following equations are developed for

*S*

_{2}but one can use

*S*

_{3}as well since it only has a

*π*/2 phase difference.

*S*

_{2}as a function of the system parameters

*t*,

*α*,

*L*,

*β*

_{0}and

*ϕ*by inserting Eq. (1) and Eq. (2) into the definition for

*S*

_{2}using trigonometric identities:

*ϕ*values. The spectra of

*S*

_{0}in blue,

*S*

_{1}in purple,

*S*

_{2}in green and

*S*

_{3}in red are shown for each case. It can be seen that the

*S*

_{1}does not provide additional information compared to

*S*

_{0}since it is only its complementary response.

*S*

_{2}and

*S*

_{3}spectra as

*Q*decreases can be understood considering that more photons are entering the cavity and are then recollected by the waveguide. Consequently, the polarization state of a higher amount of light is changed by the cavity. Since the

_{c}*S*

_{0}spectrum tends to flatten as

*Q*decreases, the

_{c}*S*

_{2}spectrum can be used to spot collapsed peaks, mainly in the overcoupled regime (Fig. 2(e) and 2(f)).

*S*

_{3}curves and the red dots show the points that define the FWHM of the

*S*

_{0}curves. For

*ϕ*= 0, the wavelength positions of the black and red dots match for any coupling regime. In the case where

*ϕ*≠ 0, the positions no longer agree and the distance between black dots increases as the coupling increases. However, it can be seen that

*ϕ*is modified but increase monotonically when the coupling increases. Their values go from 0 to 1 as the coupling regime passes from undercoupled to critically coupled and from 1 to 2 as it passes from critically coupled to overcoupled. Compared to the resonance transmission value which can give the same value in the undercoupled regime and in overcoupled regime [12

12. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. **91**, 043902 (2003). [CrossRef] [PubMed]

*S*

_{2}or Δ

*S*

_{3}can be used to determine the coupling regime.

*S*

_{3}spectrum (or

*S*

_{2}spectrum depending on

*ϕ*value) is its steep slope near the resonance, which is a consequence of its phase response dependency (Eq. (3)). This attribute can be exploited in applications where high sensitivity is required, such as biosensing or laser stabilization.

*S*

_{2}definition,

*Q*

_{0}and

*Q*. This can be done with

_{c}*S*

_{2}extrema are found by inserting their respective

*β*

_{0}

*L*values,

*β*

_{0}

*L*

^{(1)}and

*β*

_{0}

*L*

^{(2)}, in Eq. (4). Using trigonometric identities, the resulting extrema,

*ϕ*dependence. Thus, the difference

*Q*

_{0}and

*Q*definitions and exp(−

_{c}*αL*) ≈ 1 –

*αL*. This approximation represents a 0.5% deviation from the equality for

*Q*

_{0}> 10

^{4},

*λ*∼ 1550 nm,

*n*∼ 1.45 and

_{m}*L*∼ 100

*πμ*m.

*Q*quantifies the intrinsic and coupling optical losses as: Finally, both

_{T}*Q*

_{0}and

*Q*can be estimated from Eq. (5) and Eq. (6) as: when

_{c}*β*

_{0}

*L*can be neglected compared to

*Q*

_{0}and

*Q*. Thus, knowing

_{c}*a*and

_{x}*a*, both

_{y}*λ*and Δ

*S*

_{2}. In order to be precise, these estimations require that the real

*Q*

_{0}and

*Q*be high enough. This condition is usually achieved for WGM and ring-type resonators. Also, since both are independent of

_{c}*ϕ*, phase fluctuations do not change the results.

*Q*value needed in order to estimate

_{T}*Q*

_{0}and

*Q*within an acceptable error range. The relative errors of

_{c}*Q*and

_{c}*Q*

_{0}, Δ

*Q*/

_{c}*Q*and Δ

_{c}*Q*

_{0}/

*Q*

_{0}, are calculated from Δ

*S*

_{2}and

*Q*for each (

_{T}*Q*

_{0},

*Q*) combination, for

_{c}*Q*

_{0}and

*Q*above 10

_{c}^{4}. We limit the analysis to 104 since previous assumptions (

*t*,

*κ*,

*α*and

*ϕ*constant) are not guaranteed below this limit. This lower value of

*Q*implies a power coupling coefficient

_{c}*κ*

^{2}up to 0.18 which includes realistic values below 0.05 or

*Q*> 3.7 × 10

_{c}^{4}for a WGM cavity-to-waveguide evanescent coupling [20

20. M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. **271**, 124–131 (2007). [CrossRef]

*S*

_{2}amplitude is maximized.

*Q*

_{0}and

*Q*can be expressed as: For a relative error smaller than 1%, in the case of

_{c}*Q*

_{0}≥ 10

^{4}and a

*Q*≥ 10

_{c}^{5}. For

*Q*

_{0},

*Q*) must be higher than (1 × 10

_{c}^{4},7.5 × 10

^{4}) or (9 × 10

^{4},1 × 10

^{4}). From Eq. (6), for a given

*Q*value,

_{T}*Q*

_{0}and

*Q*are higher than

_{c}*Q*. Consequently, the measured

_{T}*Q*has to be above 10

_{T}^{5}in order to be within the 1% error limit of

*Q*≥ 2 × 10

_{T}^{4}is required.

## 3. Measurements and discussion

*S*

_{2}is easier to measure than

*S*

_{3}since it does not need a quarter wave plate.

*S*

_{0}and

*S*

_{2}can be obtained by measuring the total power,

*I*(0°, 0°) +

*I*(90°,0°), and the intensity after the polarizer rotated by 45° with respect to the chosen reference axis,

*I*(45°,0°). The experimental setup used to simultaneously determine

*S*

_{0}and

*S*

_{2}is shown in Fig. 3. A tunable laser source (TLS) sweeps across the resonance wavelength while an oscilloscope (OSC) records the signal from the detectors D1 and D2. Both are synchronized via a trigger signal (TRIG). The first half wave plate HWP1 is used to rotate the linearly polarized output of the source and therefore, to control the input power ratio

*x*and

*y*axis are turned 45° compared to the horizontal and vertical reference axis. This allows to write the detector intensities as a function of the cavity parameters in a simple form (Eq. (7)). Finally, the polarizer axis is set along the horizontal axis or 45° compared to

*a*. Both signals are focused on the detectors. This simple configuration can be used to mesure the transmission spectrum via D1 without any modification. Since both signals are recorded simultaneously, any fluctuation in the resonance wavelength due to external parameters such as temperature does not affect the result.

_{x}*μ*m diameter tapered optical fiber is used to couple the light to a silica toroidal micro-cavity. The microcavities are formed from a 0.8

*μ*m thick thermal SiO

_{2}layer. Using a standard photolithographic process, the disk shapes are transfered to the silica layer. An SF

_{6}isotropic etch of the subjacent silicon follows. The toroidal shapes are obtained using laser reflow process [8

8. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature **421**, 925–928 (2003). [CrossRef] [PubMed]

*μ*m minor diameter and are formed out of a 100

*μ*m diameter disk. A micrography of the coupling region is shown in Fig. 4. The gap between the tapered fiber and the cavity is controlled using a piezoelectric stage.

*I*

_{1}and

*I*

_{2}, can be written as: where the |

*T*

_{45}|

^{2}and |

*T*

_{−45}|

^{2}cube beamsplitter transmission coefficients are considered equal for a 45° and a −45° linear input polarization with respect to the horizontal axis. The reflection coefficients, |

*R*

_{45}|

^{2}and |

*R*

_{−45}|

^{2}, are also considered equal.

*f*is the power fraction on the

*a*axis. The total power,

_{y}*P*, is written as:

_{tot}*T*|

^{2}= 1).

*Q*and their corresponding

_{T}*Q*values were obtained by fitting a lorentzian curve to

_{T}*S*

_{0}and the transmission |

*T*|

^{2}. As it can be seen from the increasing amplitude of

*S*

_{0}(black curve) and

*S*

_{2}(blue curve) are drawn using

*f*-parameters equal to 0.4, 0.435 and 0.445 for the first, second and third coupling condition respectively. These changes show the rotation of the polarization between different measurements. The

*ϕ*parameter is extracted using the off resonance value of

*θ*+

*ϕ*) → cos(

*ϕ*). There is a very good agreement between the experimental and the calculated curves, which shows that the proposed model, despite its simplicity, represents well the polarization changes inside the cavity.

*Q*≈

_{T}*Q*

_{0}gave a

*Q*= (2.26 ± 0.05) × 10

_{T}^{6}which fits well with the presented data. This anticipated behavior shows that only the coupling losses are changed if the coupling conditions change. Thus, the intrinsic losses are only slightly changed by the fiber presence.

## 4. Conclusion

*Q*

_{0}and the coupling Q-factor

*Q*of a WGM or ring-type microcavity, regardless of the coupling regime. This technique is based on a simple Stokes parameters measurement. The theoretical model has been detailed and experimentally verified with a very good agreement. The determination of

_{c}*Q*

_{0}and

*Q*is accurate within 1 percent if

_{c}*Q*is higher than 1 × 10

_{T}^{5}. Compared to the laser sweeping technique [15

15. Y. Dumeige, S. Trebaol, L. Ghişa, T. K. N. Nguyên, H. Tavernier, and P. Féron, “Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers,” J. Opt. Soc. Am. B **25**, 2073–2080 (2008). [CrossRef]

*Q*∼ 10

_{T}^{7}, our method can be used for lower

*Q*resonators such as integrated microrings. The detection setup requires only simple optical components excluding usually needed fast electronics [13

_{T}13. B. J. J. Slagmolen, M. B. Gray, K. G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl. Opt. **39**, 3638–3643 (2000). [CrossRef]

14. C. R. Locke, D. Stuart, E. N. Ivanov, and A. N. Luiten, “A simple technique for accurate and complete characterisation of a Fabry-Perot cavity,” Opt. Express **17**, 21935–21943 (2009). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods |

2. | J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics |

3. | A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A |

4. | S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. |

5. | T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. |

6. | V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature |

7. | M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. |

8. | D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature |

9. | B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO |

10. | M. Sumetsky, “Optimization of optical ring resonator devices for sensing applications,” Opt. Lett. |

11. | M. Hossein-Zadeh and K. J. Vahala, “Importance of intrinsic-Q in microring-based optical filters and dispersion-compensation devices,” IEEE Photonics Technol. Lett. |

12. | S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. |

13. | B. J. J. Slagmolen, M. B. Gray, K. G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl. Opt. |

14. | C. R. Locke, D. Stuart, E. N. Ivanov, and A. N. Luiten, “A simple technique for accurate and complete characterisation of a Fabry-Perot cavity,” Opt. Express |

15. | Y. Dumeige, S. Trebaol, L. Ghişa, T. K. N. Nguyên, H. Tavernier, and P. Féron, “Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers,” J. Opt. Soc. Am. B |

16. | T. Ito and Y. Kokubun, “Nondestructive measurement of propagation loss and coupling efficiency in microring resonator filters using filter responses,” Jpn. J. Appl. Phys. |

17. | G. Griffel, S. Arnold, D. Taskent, A. Serpengüzel, J. Connolly, and N. Morris, “Morphology-dependent resonances of a microsphere-optical fiber system,” Opt. Lett. |

18. | P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Whispering gallery mode microresonators as polarization converters,” Opt. Lett. |

19. | D. Goldstein, |

20. | M. J. Humphrey, E. Dale, A. T. Rosenberger, and D. K. Bandy, “Calculation of optimal fiber radius and whispering-gallery mode spectra for a fiber-coupled microsphere,” Opt. Commun. |

**OCIS Codes**

(260.5430) Physical optics : Polarization

(140.3945) Lasers and laser optics : Microcavities

(130.5440) Integrated optics : Polarization-selective devices

**ToC Category:**

Lasers and Laser Optics

**Virtual Issues**

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

**Citation**

Francis Vanier, Cecilia La Mela, Ahmad Hayat, and Yves-Alain Peter, "Intrinsic quality factor determination in whispering gallery mode microcavities using a single Stokes parameters measurement," Opt. Express **19**, 23544-23553 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-23-23544

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### References

- F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008). [CrossRef] [PubMed]
- J. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009). [CrossRef]
- A. A. Savchenkov, V. S. Ilchenko, A. B. Matsko, and L. Maleki, “Kilohertz optical resonances in dielectric crystal cavities,” Phys. Rev. A 70, 051804(R) (2004). [CrossRef]
- S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60, 289–291 (1992). [CrossRef]
- T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, “Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity,” Phys. Rev. Lett. 95, 033901 (2005). [CrossRef] [PubMed]
- V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]
- M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996). [CrossRef] [PubMed]
- D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003). [CrossRef] [PubMed]
- B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photonics Technol. Lett. 10, 549–551 (1998). [CrossRef]
- M. Sumetsky, “Optimization of optical ring resonator devices for sensing applications,” Opt. Lett. 32, 2577–2579 (2007). [CrossRef] [PubMed]
- M. Hossein-Zadeh and K. J. Vahala, “Importance of intrinsic-Q in microring-based optical filters and dispersion-compensation devices,” IEEE Photonics Technol. Lett. 19, 1045–1047 (2007). [CrossRef]
- S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003). [CrossRef] [PubMed]
- B. J. J. Slagmolen, M. B. Gray, K. G. Baigent, and D. E. McClelland, “Phase-sensitive reflection technique for characterization of a Fabry-Perot interferometer,” Appl. Opt. 39, 3638–3643 (2000). [CrossRef]
- C. R. Locke, D. Stuart, E. N. Ivanov, and A. N. Luiten, “A simple technique for accurate and complete characterisation of a Fabry-Perot cavity,” Opt. Express 17, 21935–21943 (2009). [CrossRef] [PubMed]
- Y. Dumeige, S. Trebaol, L. Ghişa, T. K. N. Nguyên, H. Tavernier, and P. Féron, “Determination of coupling regime of high-Q resonators and optical gain of highly selective amplifiers,” J. Opt. Soc. Am. B 25, 2073–2080 (2008). [CrossRef]
- T. Ito and Y. Kokubun, “Nondestructive measurement of propagation loss and coupling efficiency in microring resonator filters using filter responses,” Jpn. J. Appl. Phys. 43, 1002–1005 (2004). [CrossRef]
- G. Griffel, S. Arnold, D. Taskent, A. Serpengüzel, J. Connolly, and N. Morris, “Morphology-dependent resonances of a microsphere-optical fiber system,” Opt. Lett. 21, 695–697 (1996). [CrossRef] [PubMed]
- P. Bianucci, C. R. Fietz, J. W. Robertson, G. Shvets, and C.-K. Shih, “Whispering gallery mode microresonators as polarization converters,” Opt. Lett. 32, 2224–2226 (2007). [CrossRef] [PubMed]
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