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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 14 — Jul. 5, 2010
  • pp: 14353–14358
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Self-noise-filtering phase-sensitive surface plasmon resonance biosensing

Sergiy Patskovsky, Michel Meunier, Paras N. Prasad, and Andrei V. Kabashin  »View Author Affiliations


Optics Express, Vol. 18, Issue 14, pp. 14353-14358 (2010)
http://dx.doi.org/10.1364/OE.18.014353


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Abstract

Emerged as an upgrade of currently available Surface Plasmon Resonance (SPR) biosensing in terms of sensitivity, phase-sensitive SPR technology still requires the minimization of instrumental noises to profit from its projected ultra-low detection limit (10−8 refractive index units and lower). We present a polarimetry-based methodology for the efficient reduction of main instrumental noises in phase-sensitive measurements. The proposed approach employs a sinusoidal phase modulation of pumping light and is based on selection of proper modulation amplitude and initial phase relation for the first two modulation harmonics (F1 and F2), which enables to subtract amplitude drifts in the difference (F1 - F2) signal while doubling the phase response. The resulting effect can be called self-noise-filtering, since it implies an inherent noise subtraction in every phase sensing measurement. This methodology allows one to tackle drifts related to instabilities of light sources and optical elements and thus drastically lower the detection limit of phase-sensitive SPR sensing even in relatively simple and noisy experimental implementations.

© 2010 OSA

1. Introduction

Phase of light reflected from a solid/solid, solid/liquid, or solid/gas interface provides a powerful tool for the characterization of media and interfaces, as well as can serve as a very sensitive parameter in sensing [1

1. M. Born, and E. Wolf, “Principles of Optics,” (Cambridge University Press, Cambridge, UK), (2002).

]. In particular, the employment of phase characteristics in conditions of Surface Plasmon Resonance (SPR) can provide about two-order of magnitude improvement of sensitivity in refractive index (RI) monitoring compared to conventional amplitude-sensitive SPR (see, e.g., Refs [2

2. A. V. Kabashin and P. I. Nikitin, “Surface plasmon resonance interferometer for bio- and chemical-sensors,” Opt. Commun. 150(1-6), 5–8 (1998). [CrossRef]

15

15. A. V. Kabashin, S. Patskovsky, and A. N. Grigorenko, “Phase and amplitude sensitivities in surface plasmon resonance bio and chemical sensing,” Opt. Express 17(23), 21191–21204 (2009). [CrossRef] [PubMed]

]) promising a spectacular improvement of SPR biosensor technology [16

16. B. Liedberg, C. Nylander, and I. Lundstrom, “Biosensing with surface plasmon resonance - how it all started,” Biosens. Bioelectron. 10(8), 1–9 (1995). [CrossRef]

,17

17. R. B. M. Schasfoort, and A. J. Tudos, eds., Handbook of SPR, (Royal Society of Chemistry, 2008).

]. Information on phase of light reflected under SPR is normally obtained by interferometry or polarimetry methods. The interferometric approach is based on extraction of phase information from an optical interference pattern formed by interfering the signal beam and a reference one, which is unaffected by the sensing event [2

2. A. V. Kabashin and P. I. Nikitin, “Surface plasmon resonance interferometer for bio- and chemical-sensors,” Opt. Commun. 150(1-6), 5–8 (1998). [CrossRef]

4

4. A. V. Kabashin, V. E. Kochergin, and P. I. Nikitin, “Surface plasmon resonance bio- and chemical sensors with phase-polarisation contrast,” Sens. Actuators B Chem. 54(1-2), 51–56 (1999). [CrossRef]

,8

8. A. K. Sheridan, R. D. Harris, P. N. Bartlett, and J. S. Wilkinson, “Phase interrogation of an integrated optical SPR sensor,” Sens. Actuators B Chem. 97(1), 114–121 (2004). [CrossRef]

12

12. H. P. Ho, W. Yuan, C. L. Wong, S. Y. Wu, Y. K. Suen, S. K. Kong, and C. Lin, “Sensitivity enhancement based on application of multi-pass interferometry in phase-sensitive surface plasmon resonance biosensor,” Opt. Commun. 275(2), 491–496 (2007). [CrossRef]

]. In contrast, the polarimetric approach implies the analysis of the polarization state of light of a mixed polarization, while one of polarization components is unaffected and used as the reference one. A prominent example of polarimetry design is based on temporal phase modulation and the extraction of phase information on various harmonics of the modulation frequency [6

6. H. P. Ho, W. W. Lam, and S. Y. Wu, “Surface plasmon resonance sensor based on the measurement of differential phase,” Rev. Sci. Instrum. 73(10), 3534–3539 (2002). [CrossRef]

,7

7. I. R. Hooper and J. R. Sambles, “Differential ellipsometric surface plasmon resonance sensors with liquid crystal polarization modulators,” Appl. Phys. Lett. 85(15), 3017–3019 (2004). [CrossRef]

,13

13. P. P. Markowicz, W. C. Law, A. Baev, P. Prasad, S. Patskovsky, and A. V. Kabashin, “Phase-sensitive time-modulated SPR polarimetry for wide dynamic range biosensing,” Opt. Express 15, 1745 (2007). [CrossRef] [PubMed]

,14

14. S. Patskovsky, M. Maisonneuve, M. Meunier, and A. V. Kabashin, “Mechanical modulation method for ultrasensitive phase measurements in photonics biosensing,” Opt. Express 16(26), 21305–21314 (2008). [CrossRef] [PubMed]

]. Both approaches enable one to achieve the detection limit of down to 10−8 Refractive Index Units (RIU) [15

15. A. V. Kabashin, S. Patskovsky, and A. N. Grigorenko, “Phase and amplitude sensitivities in surface plasmon resonance bio and chemical sensing,” Opt. Express 17(23), 21191–21204 (2009). [CrossRef] [PubMed]

] that can be further improved using nanoscale designs of sensor-oriented plasmonics metamaterials, including nanorod arrays [18

18. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. J. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]

] and diffraction-coupled nanodot resonators [19

19. V. G. Kravets, F. Schedin, A. V. Kabashin, and A. N. Grigorenko, “Sensitivity of collective plasmon modes of gold nanoresonators to local environment,” Opt. Lett. 35(7), 956–958 (2010). [CrossRef] [PubMed]

]. Profiting from a much superior sensitivity, some promising designs of phase-sensitive SPR polarimetry are now successfully commercialized [20].

In this paper, we present a methodology to efficiently remove amplitude noises in phase-sensitive SPR sensing and develop a self-noise-filtering channel on its basis. Based on principles of temporally modulated polarimetry [21

21. R. M. A. Azzam, and N. M. Bashara, Ellipsometry and polarized light, (Elsevier Science Pub Co, North-Holland), (1987)

], our approach makes possible the noise subtraction in properly conditioned differential signal from different modulation harmonics.

2. Measurement methodology

Light from a laser source is passed through a polarizer to provide a 45 deg. linearly polarized beam, as shown in Fig. 1
Fig. 1 Schematics of the experimental arrangement
. In our study, we used a relatively noisy laser diode from Hitachi operating at 635 nm. After passing through a Soleil-Babinet compensator, which serves to optimize the initial phase retardation, the phase- modulated light is directed to a Photoelastic Modulator (PEM), which is used to sinusoidally modulate the p-component at the frequency ν = 50 kHz. The beam is then directed through a BK7 prism to be reflected from a gold covered glass facet in contact with the sample medium. The angle of light incidence on the gold surface is selected to provide SPR coupling and excite surface plasmons over the gold/liquid interface. The SPR effect is accompanied by a drastic decrease in the intensity of the p-polarized component and a sharp jump of its phase, changing the total polarization state of light. The thickness of the SPR-supporting gold film (50 nm) is selected to provide the minimal intensity inside the dip and the sharpest phase jump [22

22. S. Patskovsky, M. Vallieres, M. Maisonneuve, I.-H. Song, M. Meunier, and A. V. Kabashin, “Designing efficient zero calibration point for phase-sensitive surface plasmon resonance biosensing,” Opt. Express 17(4), 2255–2263 (2009). [CrossRef] [PubMed]

]. A polarizer (analyzer) is placed just after the SPR sensing block and oriented 45 deg. in front of the detector. Using a lock-in amplifier, the final periodic signal is decomposed into harmonics. Since our time domain signal is periodic and continuous, we can use the Fourier transform method to model the harmonics of a frequency spectrum. Thus, for the first two harmonics, we have [23

23. M. Abramowitz, and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, (Dover, New York, 1965), Chap 9.

]:
F1=A·J1(M)·cos(φ),F2=A·J2(M)·sin(φ),F3=A·J3(M)·cos(φ)
where A and M are harmonics and modulation amplitudes, Jn are Bessel functions. The proposed methodology implies the implementation of the following three conditions:

  • 1. The use of differential signal as the sensing parameter;
  • 2. Properly selected phase modulation amplitude M, which conditions identical responses for the harmonics. It is clear that despite almost similar dependences for the harmonics, their response will be different due to dependences of the Bessel functions on the PEM modulation amplitude. The response optimization can be performed by using the dependence of the Bessel functions on the modulation amplitude as shown in Fig. 2(a). Here, the responses of signals from the 1st and 2nd harmonics become identical at M = 150.7° deg (J1 = J2 = 0.462), whereas the responses of the 2nd and 3rd harmonics are equal at M = 216° deg (J1 = J2 = 0.41). Although 2nd and 3rd harmonics can be applied for the formation of sensing response, in our experimental conditions it is preferable to choose the 1st and 2nd harmonics due to a higher signal amplitude in the point of intersection (contributing to lower noises) and a lower modulation amplitude (making possible operation in optimal regimes of the lock-in).
  • 3. Properly selected initial phase retardation, conditioned by the waveplate-based retarder. Figure 2(b) presents signals of the two harmonics and their difference F1-F2 as a function of the phase retardation φ for modulation amplitudes M = 150.7° deg. One can clearly see the point of intersection (R) for signals of the F1 and F2 harmonics. At this point, signals from the two harmonics have opposite trends (ascending and descending, respectively), as the retardation increases. As an example, in the schematics of Fig. 1, the point R is produced under initial phase retardation of 45 deg. It is seen that the F1-F2 signal is two times more sensitive to variations of φ due to the opposite trends of the 1st and 2nd harmonics.

ΔF2ΔF1ΔF2=sinφcosφsinφ, ΔF1ΔF1ΔF2=cosφcosφsinφ

Figure 3a
Fig. 3 (a) Noise ratio of F1 and F2 signals to the harmonic difference (F1 – F2) as a function of initial phase relation Δφ0 (M = 150.7° deg); (b) Real time phase measurements using F1, F2 and F1– F2. Data are shown for lock-in integration times of 300ms, 3s and 10 s
shows the ratios of responses to a slight variation in the amplitude ΔA. Here, the point R is characterized by a drastic increase in the ratio associated with the minimization of the system response in the differential F1-F2 signal. In other words, it means that in the differential signal, the system subtracted all noises associated with amplitude drifts. Notice that theoretically the increase of the ratio is infinite, as illustrated by the curve of Fig. 3a, but in practice this ratio is limited by non-idealities in the system. In our experimental arrangement, we managed to achieve a noise reduction ratio of the factor of 1000.

3. Self-noise-filtering test

Conclusions

Acknowledgements

The authors acknowledge the financial contribution from the Natural Science and Engineering Research Council of Canada and Agence Nationale de Recherche, France. Partial support at Buffalo from the John P Oshei Foundation is also acknowledged.

References and links

1.

M. Born, and E. Wolf, “Principles of Optics,” (Cambridge University Press, Cambridge, UK), (2002).

2.

A. V. Kabashin and P. I. Nikitin, “Surface plasmon resonance interferometer for bio- and chemical-sensors,” Opt. Commun. 150(1-6), 5–8 (1998). [CrossRef]

3.

A. N. Grigorenko, P. I. Nikitin, and A. V. Kabashin, “Phase Jumps and Interferometric Surface Plasmon Resonance Imaging,” Appl. Phys. Lett. 75(25), 3917–3919 (1999). [CrossRef]

4.

A. V. Kabashin, V. E. Kochergin, and P. I. Nikitin, “Surface plasmon resonance bio- and chemical sensors with phase-polarisation contrast,” Sens. Actuators B Chem. 54(1-2), 51–56 (1999). [CrossRef]

5.

A. G. Notcovich, V. Zhuk, and S. G. Lipson, “Surface plasmon resonance phase imaging,” Appl. Phys. Lett. 76(13), 1665–1667 (2000). [CrossRef]

6.

H. P. Ho, W. W. Lam, and S. Y. Wu, “Surface plasmon resonance sensor based on the measurement of differential phase,” Rev. Sci. Instrum. 73(10), 3534–3539 (2002). [CrossRef]

7.

I. R. Hooper and J. R. Sambles, “Differential ellipsometric surface plasmon resonance sensors with liquid crystal polarization modulators,” Appl. Phys. Lett. 85(15), 3017–3019 (2004). [CrossRef]

8.

A. K. Sheridan, R. D. Harris, P. N. Bartlett, and J. S. Wilkinson, “Phase interrogation of an integrated optical SPR sensor,” Sens. Actuators B Chem. 97(1), 114–121 (2004). [CrossRef]

9.

Y.-D. Su, S.-J. Chen, and T.-L. Yeh, “Common-path phase-shift interferometry surface plasmon resonance imaging system,” Opt. Lett. 30(12), 1488–1490 (2005). [CrossRef] [PubMed]

10.

Y. Xinglong, W. Dingxin, W. Xing, D. Xiang, L. Wei, and Z. Xinsheng, “A surface plasmon resonance imaging interferometry for protein micro-array detection,” Sens. Actuators B Chem. 108(1-2), 765–771 (2005). [CrossRef]

11.

W. Yuan, H. P. Ho, C. L. Wong, S. K. Kong, and C. Lin, “Surface Plasmon Resonance Biosensor incorporated in a Michelson Interferometer with enhanced sensitivity,” IEEE Sens. J. 7(1), 70–73 (2007). [CrossRef]

12.

H. P. Ho, W. Yuan, C. L. Wong, S. Y. Wu, Y. K. Suen, S. K. Kong, and C. Lin, “Sensitivity enhancement based on application of multi-pass interferometry in phase-sensitive surface plasmon resonance biosensor,” Opt. Commun. 275(2), 491–496 (2007). [CrossRef]

13.

P. P. Markowicz, W. C. Law, A. Baev, P. Prasad, S. Patskovsky, and A. V. Kabashin, “Phase-sensitive time-modulated SPR polarimetry for wide dynamic range biosensing,” Opt. Express 15, 1745 (2007). [CrossRef] [PubMed]

14.

S. Patskovsky, M. Maisonneuve, M. Meunier, and A. V. Kabashin, “Mechanical modulation method for ultrasensitive phase measurements in photonics biosensing,” Opt. Express 16(26), 21305–21314 (2008). [CrossRef] [PubMed]

15.

A. V. Kabashin, S. Patskovsky, and A. N. Grigorenko, “Phase and amplitude sensitivities in surface plasmon resonance bio and chemical sensing,” Opt. Express 17(23), 21191–21204 (2009). [CrossRef] [PubMed]

16.

B. Liedberg, C. Nylander, and I. Lundstrom, “Biosensing with surface plasmon resonance - how it all started,” Biosens. Bioelectron. 10(8), 1–9 (1995). [CrossRef]

17.

R. B. M. Schasfoort, and A. J. Tudos, eds., Handbook of SPR, (Royal Society of Chemistry, 2008).

18.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. J. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]

19.

V. G. Kravets, F. Schedin, A. V. Kabashin, and A. N. Grigorenko, “Sensitivity of collective plasmon modes of gold nanoresonators to local environment,” Opt. Lett. 35(7), 956–958 (2010). [CrossRef] [PubMed]

20.

www.bioptix.com, www.cambridgeconsultants.com/news_pr76.html

21.

R. M. A. Azzam, and N. M. Bashara, Ellipsometry and polarized light, (Elsevier Science Pub Co, North-Holland), (1987)

22.

S. Patskovsky, M. Vallieres, M. Maisonneuve, I.-H. Song, M. Meunier, and A. V. Kabashin, “Designing efficient zero calibration point for phase-sensitive surface plasmon resonance biosensing,” Opt. Express 17(4), 2255–2263 (2009). [CrossRef] [PubMed]

23.

M. Abramowitz, and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, (Dover, New York, 1965), Chap 9.

24.

P. A. Gass, S. Schalk, and J. R. Sambles, “Highly sensitive optical measurement techniques based on acousto-optic devices,” Appl. Opt. 33(31), 7501–7510 (1994). [CrossRef] [PubMed]

25.

A. Michels and A. Botzen, “Refractive index and Lorentz-Lorenz function of argon up to 2300 atmospheres at 25°C,” Physica 15(8-9), 769–773 (1949). [CrossRef]

26.

E. D. Peck and B. N. Khanna, “Dispersion of Nitrogen,” J. Opt. Soc. Am. 56(8), 1059–1063 (1966). [CrossRef]

27.

S. Patskovsky, M. Meunier, and A. V. Kabashin, “Phase-sensitive silicon-based total internal reflection sensor,” Opt. Express 15(19), 12523–12528 (2007). [CrossRef] [PubMed]

28.

S. Patskovsky, I.-H. Song, M. Meunier, and A. V. Kabashin, “Silicon based total internal reflection bio and chemical sensing with spectral phase detection,” Opt. Express 17(23), 20847–20852 (2009). [CrossRef] [PubMed]

OCIS Codes
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Sensors

History
Original Manuscript: April 29, 2010
Revised Manuscript: June 6, 2010
Manuscript Accepted: June 7, 2010
Published: June 21, 2010

Virtual Issues
Vol. 5, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Sergiy Patskovsky, Michel Meunier, Paras N. Prasad, and Andrei V. Kabashin, "Self-noise-filtering phase-sensitive surface plasmon resonance biosensing," Opt. Express 18, 14353-14358 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-14-14353


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References

  1. M. Born, and E. Wolf, “Principles of Optics,” (Cambridge University Press, Cambridge, UK), (2002).
  2. A. V. Kabashin and P. I. Nikitin, “Surface plasmon resonance interferometer for bio- and chemical-sensors,” Opt. Commun. 150(1-6), 5–8 (1998). [CrossRef]
  3. A. N. Grigorenko, P. I. Nikitin, and A. V. Kabashin, “Phase Jumps and Interferometric Surface Plasmon Resonance Imaging,” Appl. Phys. Lett. 75(25), 3917–3919 (1999). [CrossRef]
  4. A. V. Kabashin, V. E. Kochergin, and P. I. Nikitin, “Surface plasmon resonance bio- and chemical sensors with phase-polarisation contrast,” Sens. Actuators B Chem. 54(1-2), 51–56 (1999). [CrossRef]
  5. A. G. Notcovich, V. Zhuk, and S. G. Lipson, “Surface plasmon resonance phase imaging,” Appl. Phys. Lett. 76(13), 1665–1667 (2000). [CrossRef]
  6. H. P. Ho, W. W. Lam, and S. Y. Wu, “Surface plasmon resonance sensor based on the measurement of differential phase,” Rev. Sci. Instrum. 73(10), 3534–3539 (2002). [CrossRef]
  7. I. R. Hooper and J. R. Sambles, “Differential ellipsometric surface plasmon resonance sensors with liquid crystal polarization modulators,” Appl. Phys. Lett. 85(15), 3017–3019 (2004). [CrossRef]
  8. A. K. Sheridan, R. D. Harris, P. N. Bartlett, and J. S. Wilkinson, “Phase interrogation of an integrated optical SPR sensor,” Sens. Actuators B Chem. 97(1), 114–121 (2004). [CrossRef]
  9. Y.-D. Su, S.-J. Chen, and T.-L. Yeh, “Common-path phase-shift interferometry surface plasmon resonance imaging system,” Opt. Lett. 30(12), 1488–1490 (2005). [CrossRef] [PubMed]
  10. Y. Xinglong, W. Dingxin, W. Xing, D. Xiang, L. Wei, and Z. Xinsheng, “A surface plasmon resonance imaging interferometry for protein micro-array detection,” Sens. Actuators B Chem. 108(1-2), 765–771 (2005). [CrossRef]
  11. W. Yuan, H. P. Ho, C. L. Wong, S. K. Kong, and C. Lin, “Surface Plasmon Resonance Biosensor incorporated in a Michelson Interferometer with enhanced sensitivity,” IEEE Sens. J. 7(1), 70–73 (2007). [CrossRef]
  12. H. P. Ho, W. Yuan, C. L. Wong, S. Y. Wu, Y. K. Suen, S. K. Kong, and C. Lin, “Sensitivity enhancement based on application of multi-pass interferometry in phase-sensitive surface plasmon resonance biosensor,” Opt. Commun. 275(2), 491–496 (2007). [CrossRef]
  13. P. P. Markowicz, W. C. Law, A. Baev, P. Prasad, S. Patskovsky, and A. V. Kabashin, “Phase-sensitive time-modulated SPR polarimetry for wide dynamic range biosensing,” Opt. Express 15, 1745 (2007). [CrossRef] [PubMed]
  14. S. Patskovsky, M. Maisonneuve, M. Meunier, and A. V. Kabashin, “Mechanical modulation method for ultrasensitive phase measurements in photonics biosensing,” Opt. Express 16(26), 21305–21314 (2008). [CrossRef] [PubMed]
  15. A. V. Kabashin, S. Patskovsky, and A. N. Grigorenko, “Phase and amplitude sensitivities in surface plasmon resonance bio and chemical sensing,” Opt. Express 17(23), 21191–21204 (2009). [CrossRef] [PubMed]
  16. B. Liedberg, C. Nylander, and I. Lundstrom, “Biosensing with surface plasmon resonance - how it all started,” Biosens. Bioelectron. 10(8), 1–9 (1995). [CrossRef]
  17. R. B. M. Schasfoort, and A. J. Tudos, eds., Handbook of SPR, (Royal Society of Chemistry, 2008).
  18. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. J. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]
  19. V. G. Kravets, F. Schedin, A. V. Kabashin, and A. N. Grigorenko, “Sensitivity of collective plasmon modes of gold nanoresonators to local environment,” Opt. Lett. 35(7), 956–958 (2010). [CrossRef] [PubMed]
  20. www.bioptix.com, www.cambridgeconsultants.com/news_pr76.html
  21. R. M. A. Azzam, and N. M. Bashara, Ellipsometry and polarized light, (Elsevier Science Pub Co, North-Holland), (1987)
  22. S. Patskovsky, M. Vallieres, M. Maisonneuve, I.-H. Song, M. Meunier, and A. V. Kabashin, “Designing efficient zero calibration point for phase-sensitive surface plasmon resonance biosensing,” Opt. Express 17(4), 2255–2263 (2009). [CrossRef] [PubMed]
  23. M. Abramowitz, and I. A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, (Dover, New York, 1965), Chap 9.
  24. P. A. Gass, S. Schalk, and J. R. Sambles, “Highly sensitive optical measurement techniques based on acousto-optic devices,” Appl. Opt. 33(31), 7501–7510 (1994). [CrossRef] [PubMed]
  25. A. Michels and A. Botzen, “Refractive index and Lorentz-Lorenz function of argon up to 2300 atmospheres at 25°C,” Physica 15(8-9), 769–773 (1949). [CrossRef]
  26. E. D. Peck and B. N. Khanna, “Dispersion of Nitrogen,” J. Opt. Soc. Am. 56(8), 1059–1063 (1966). [CrossRef]
  27. S. Patskovsky, M. Meunier, and A. V. Kabashin, “Phase-sensitive silicon-based total internal reflection sensor,” Opt. Express 15(19), 12523–12528 (2007). [CrossRef] [PubMed]
  28. S. Patskovsky, I.-H. Song, M. Meunier, and A. V. Kabashin, “Silicon based total internal reflection bio and chemical sensing with spectral phase detection,” Opt. Express 17(23), 20847–20852 (2009). [CrossRef] [PubMed]

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