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 Optical Society of America

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]. 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 [215]) promising a spectacular improvement of SPR biosensor technology [16,17]. 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 [24,812]. 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 [6,7,13,14]. Both approaches enable one to achieve the detection limit of down to 10−8 Refractive Index Units (RIU) [15] that can be further improved using nanoscale designs of sensor-oriented plasmonics metamaterials, including nanorod arrays [18] and diffraction-coupled nanodot resonators [19]. Profiting from a much superior sensitivity, some promising designs of phase-sensitive SPR polarimetry are now successfully commercialized [20].

Despite ultra-high sensitivity granted by extreme sharpness of phase characteristics under SPR [24,15], practical detection limit is conditioned by thermal drifts of RI and the level of noises in the measurement system. The thermal RI drifts can be minimized by proper thermo stabilization of the measurement cell, while instrumental noise issues require an improvement of measurement setup. As we recently showed in [15], main instrumental noises are related to the instability of light source characteristics. Since for common light sources phase noises are normally much lower compared to amplitude ones (Δφ/φ≈10−6 compared to ΔI/I ≈10−2) [15], the stabilization of source amplitude characteristics becomes one of key factors, conditioning the detection limit of phase-sensitive schemes. The situation is complicated by the fact that amplitude noises can further be amplified by the instability of optical setup elements under their interaction with environment. In practice, the achievement of ultra-low detection limits requires the employment of highly stabilized laser sources and the development of amplitude reference channels that considerably complicates the design of devices.

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], 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 . 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]. 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]:

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:

 figure: Fig. 1

Fig. 1 Schematics of the experimental arrangement

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  • 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.

The amplitude noise reduction effect is achieved due to different behavior of the phase and the amplitude characteristics at point R. A phase change in the signal beam leads to responses of the F1 and F2 components of opposite polarity as a result of ascending and descending trends at the point R (Fig. 2b ). However, any amplitude change caused by a slight variation of the pumping laser power or a drift in responses of the optical elements leads to responses of the F1 and F2 components of the same polarity. Therefore, in the differential signal (F1 – F2), one can amplify the resulting phase signal by adding phase responses of the same polarity and subtract amplitude drifts. To estimate the effect, let us consider signal changes of the two harmonics (F1 and F2) under a slight change of signal amplitude ΔA. If we assume that the Bessel functions from the two harmonics are equal J1(M)=J2(M)=J (2nd Condition), the amplitudes of the harmonics after such a change will be:

F1'=F1+ΔF1=(A+ΔA)·J·cos(φ)=F1+ΔA·J·cos(φ)ΔF1=ΔA·J·cos(φ)
F2'=F2+ΔF2=(A+ΔA)·J·sin(φ)=F2+ΔA·J·sin(φ), ΔF2=ΔA·J·sin(φ)
Thus, for the differential signal we have: F1'F2'=(F1F2)+(ΔF1ΔF2) Now we can compare responses of the harmonics alone with the response of the differential signal to a variation of the amplitude ΔA. For the ratio of these responses we have:

 figure: Fig. 2

Fig. 2 (a) Dependence of Bessel functions J1, J2 and J3 on the PEM modulation amplitude M; (b) Responses of F1, F2 harmonics and differential F1– F2 signal to initial phase relation Δφ0 under the modulation amplitude of 150.7° deg.

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ΔF2ΔF1ΔF2=sinφcosφsinφ, ΔF1ΔF1ΔF2=cosφcosφsinφ

Figure 3a 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.

 figure: Fig. 3

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

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To illustrate the noise reduction effect, we simulated small phase changes in the system by a Soleil-Babinet compensator. First, we compensated phase retardations, introduced by the optical elements in the set-up to the point with equal amplitude of the first and the second harmonics (Fig. 1). Then, we finely varied the retardation around this value, which simulated changes of the phase in the signal block, as shown in Fig. 3b. It is visible from the graphs for F1 and F2 that step-like phase retardation changes cause responses of signals from the 1st and the 2nd harmonics of opposite polarity, while random noise-related amplitude fluctuations lead to the same polarity of harmonic responses. In the differential signal F1-F2, the response appears to be the sum of responses from the two harmonics, while amplitude noises are subtracted. As a result, in the differential harmonics channel, one can see a 2-times amplified signal with a drastically noise level reduction. The phase resolution of the system was experimentally estimated as Δϕ = 5⋅10−3 Deg. It should be noted that the residual noise level is determined by the precision of optical and electronics elements and their alignment.

3. Self-noise-filtering test

To test the proposed methodology, we adapted the PEM-based system for SPR sensing measurements, as shown in the inset to Fig. 1. Although the SPR block was thermally isolated by a protecting cover, the measurement system was opened and could be subjected to environmental thermal or inertial drifts. To examine the methodology, we used a well-established gas methodology for small refractive index variations Δn [3,7,24]. This method involves comparing the system response, while different inert gases with known refractive indices are brought in contact with the gold film. In our experiments, Ar and N2 were used, for which the refractive indices differ by Δn ≅1.5⋅10−5 RIU under the normal conditions [25,26]. The gases were passed through the cell through a long spiral copper tube to equalize their temperatures with the room temperature and then mixed in a mixer to provide a controlled ratio of gases in the flow cell. The mixture of gases was then brought in contact with the SPR-supporting gold film. Figure 4 demonstrates typical signals from 1st and 2nd harmonics, as well as the differential signal F1-F2 under the replacement of pure N2 by a 10% Ar/90% N2 mixture, corresponding to a 1.5⋅10−6 RIU change. One can see that the signals from the first and the second harmonics alone are so noisy that it is really difficult to resolve the refractive index change associated with the replacement of gases without applying a reference channel strategy. Our analysis identified intensity drifts of the laser diode and the optical setup as main reasons of these noises. However, the noises mostly disappear in the differential F1-F2 signal, confirming the efficiency of the proposed methodology (Fig. 4). Taking into account the level of residual noises, we can determine that the detection limit of our system is better than 10−7 RIU, which is significantly lower compared to conventional amplitude-sensitive SPR devices. It is important that such a low detection limit was achieved with a relatively inexpensive and noisy light source and open optical setup. Further improvement of the detection limit can be achieved by eliminating thermal and other noises related to the sensing block. This can be done by a better thermoisolation or active thermostating.

 figure: Fig. 4

Fig. 4 Signals from the first F1 and second F2 harmonics, as well as the differential signal F1-F2, under the replacement of pure N2 by 10%Ar/90%N2 mixture. The plots were obtained under optimal modulation amplitude and phase retardation.

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Conclusions

We proposed a polarimetry-based methodology to eliminate amplitude-related noises in phase-sensitive bio- and chemical sensing. The proposed method enables one to obtain low noise signals in a single control measurement (self-noise-filtering), with an anticipated resolution better than Δϕ = 5⋅10−3 Deg. Such self-noise-filtering makes possible the achievement of a relatively low detection limit even with relatively simple and noisy experimental setups and is expected to provide substantial advantages in the development of low-cost, portable gas- or biological sensor devices. We illustrated the efficiency of the method in SPR sensing, but it can be generalized to other phenomena employing phase-sensitive sensing tests such as, e.g. Si-based Total internal Reflection [27,28].

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]  

References

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  • |

  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]

2010 (1)

2009 (4)

2008 (1)

2007 (4)

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]

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]

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]

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]

2005 (2)

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]

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]

2004 (2)

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]

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]

2002 (1)

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]

2000 (1)

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

1999 (2)

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]

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]

1998 (1)

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]

1995 (1)

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

1994 (1)

1966 (1)

1949 (1)

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]

Atkinson, R.

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]

Baev, A.

Bartlett, P. N.

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]

Botzen, A.

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]

Chen, S.-J.

Dingxin, W.

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]

Evans, P.

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]

Gass, P. A.

Grigorenko, A. N.

Harris, R. D.

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]

Hendren, W.

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]

Ho, H. P.

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]

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]

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]

Hooper, I. R.

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]

Kabashin, A. V.

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Khanna, B. N.

Kochergin, V. E.

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]

Kong, S. K.

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]

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]

Kravets, V. G.

Lam, W. W.

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]

Law, W. C.

Liedberg, B.

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

Lin, C.

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]

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]

Lipson, S. G.

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

Lundstrom, I.

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

Maisonneuve, M.

Markowicz, P. P.

Meunier, M.

Michels, A.

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]

Nikitin, P. I.

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]

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]

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]

Notcovich, A. G.

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

Nylander, C.

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

Pastkovsky, S.

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]

Patskovsky, S.

Peck, E. D.

Podolskiy, V. A.

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]

Pollard, R. J.

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]

Prasad, P.

Sambles, J. R.

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]

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]

Schalk, S.

Schedin, F.

Sheridan, A. K.

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]

Song, I.-H.

Su, Y.-D.

Suen, Y. K.

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]

Vallieres, M.

Wei, L.

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]

Wilkinson, J. S.

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]

Wong, C. L.

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]

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]

Wu, S. Y.

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]

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]

Wurtz, G. A.

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]

Xiang, D.

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]

Xing, W.

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]

Xinglong, Y.

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]

Xinsheng, Z.

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]

Yeh, T.-L.

Yuan, W.

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]

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]

Zayats, A. V.

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]

Zhuk, V.

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

Appl. Opt. (1)

Appl. Phys. Lett. (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]

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

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]

Biosens. Bioelectron. (1)

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

IEEE Sens. J. (1)

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]

J. Opt. Soc. Am. (1)

Nat. Mater. (1)

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]

Opt. Commun. (2)

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]

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]

Opt. Express (6)

Opt. Lett. (2)

Physica (1)

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]

Rev. Sci. Instrum. (1)

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]

Sens. Actuators B Chem. (3)

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]

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]

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]

Other (5)

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

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

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

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

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

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Figures (4)

Fig. 1
Fig. 1 Schematics of the experimental arrangement
Fig. 2
Fig. 2 (a) Dependence of Bessel functions J1 , J2 and J3 on the PEM modulation amplitude M; (b) Responses of F1, F2 harmonics and differential F1– F2 signal to initial phase relation Δφ0 under the modulation amplitude of 150.7° deg.
Fig. 3
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
Fig. 4
Fig. 4 Signals from the first F1 and second F2 harmonics, as well as the differential signal F1-F2, under the replacement of pure N2 by 10%Ar/90%N2 mixture. The plots were obtained under optimal modulation amplitude and phase retardation.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

F 1 = A · J 1 ( M ) · cos ( φ ) , F 2 = A · J 2 ( M ) · sin ( φ ) , F 3 = A · J 3 ( M ) · cos ( φ )
F 1 ' = F 1 + Δ F 1 = ( A + Δ A ) · J · cos ( φ ) = F 1 + Δ A · J · cos ( φ )
Δ F 1 = Δ A · J · cos ( φ )
F 2 ' = F 2 + Δ F 2 = ( A + Δ A ) · J · sin ( φ ) = F 2 + Δ A · J · sin ( φ )
Δ F 2 = Δ A · J · sin ( φ )
Δ F 2 Δ F 1 Δ F 2 = sin φ cos φ sin φ
Δ F 1 Δ F 1 Δ F 2 = cos φ cos φ sin φ

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