Abstract

A novel detection method enabled by electro-optically tunable waveguide-coupled surface plasmon resonance sensors is demonstrated. Both the WCSPR response of sensor and the interrogation light are varied simultaneously in this hybrid scheme. Modulation and demodulation of the sensor’s response are achieved by applying a high-frequency AC electrical signal and electrically filtering the detected signal. Scanning the incident angle at a lower speed yields an angular dependent response. Theoretical analyses and experimental results show that the angular-dependent signal is closely related to the derivative of the SPR reflectivity with a sharp, linear jump near the minimum of the SPR peak. Thus, simple linear-fitting and zero-finding algorithms can be used to locate the SPR angle, and sophisticated data processing algorithms and electronic hardware can be avoided.

©2009 Optical Society of America

1. Introduction

As a highly sensitive, real-time, and label-free optical sensing method, surface plasmon resonance (SPR) has found wide applications in the areas of biomedical diagnostics, drug discovery, food safety, homeland security and environmental monitoring [1]. In most SPR sensing systems, the excitation condition of the SPR effect is monitored by measuring the reflected optical signal from the SPR sensors in the attenuated total reflection (ATR) configuration. Under a specific resonant angular and wavelength input condition, the wave vector of the incident evanescent light matches that of the surface plasmon wave (SPW). The optical power is transferred into that of the SPW, and the reflected optical power is reduced. Most of the commonly used SPR detection schemes measure the sensor’s reflectivity under varying incident angles or wavelengths, i.e. the so-called angular interrogation or wavelength interrogation scheme, respectively. The angle or wavelength corresponding to the minimal reflectance is then denoted as the SPR angle or wavelength. Since the SPR angle or wavelength is very sensitive to the changes in the optical properties of the dielectric medium such as its refractive index and thickness due to absorption adjacent to the thin metal film, tracking the tiny changes in this angle or wavelength can be exploited to monitor the bio-chemical interactions with very high sensitivity.

How to accurately determine the value (or the variations) of the SPR condition (i.e. the SPR angle or wavelength) from the interrogation data is, therefore, a critically important task directly affecting the accuracy of the SPR sensing system. The SPR curve is asymmetric, and directly identifying the minimum in the SPR response curve with a high enough accuracy from the noisy experimental results is often impossible. In general, one has to resort to rather complicated data post-processing techniques, such as the centroid method [2], polynomial curve fitting method [3], locally weighted parametric regression method [4], optimal linear method [5], asymmetric SPR sensor response curve fitting method [6], model parameterization and linear projection method [7] and dynamic baseline algorithm method [8]. The application of these data processing methods can greatly improve the accuracy in localizing and tracking the minimum in the SPR reflectivity curve, but at the cost of significantly increased system complexity, especially for the high throughput or multi-channel real-time systems.

Here we propose and experimentally demonstrate a novel SPR detection method that can generate output signals proportional to the derivative of the traditional SPR scanning curve from electrical temporal modulation, and combined with the traditional angular scanning scheme, the data from this hybrid interrogation scheme have a very simple linear angular dependence around the SPR angle. Thus, very simple linear fitting and zero-crossing algorithm can be used to locate the SPR angle with no need of more complicated data processing algorithms and the associated electronic hardware.

Recently, it has been proposed that, by quasi-statically tuning the response of a single-layer SPR sensor with DC bias, analyte concentrations can be derived from the linear regression slope of the relation between the measurand (wavelength and intensity) obtained through the conventional interrogation scheme and different applied voltage biases [9]. Here, in contrast to the previous scheme that uses DC tuning and still requires multiple traditional wavelength scans to derive the SPR wavelength, our scheme is based on relatively high-speed AC modulation of a tunable SPR sensor and demodulation of the detected signal through filtering while the angle is simultaneously tuned at a lower speed. The SPR angle is immediately available through one angular scan. The tunable SPR sensor used in our experimental demonstration is a tunable multi-layer waveguide-coupled SPR (WCSPR) sensor. WCSPR sensors have been recently studied as a potential alternative to the traditional SPR sensors for their high sensitivity and high signal-to-noise (SNR) ratio [10]. An electro-optically (EO) active WCSPR structure has been proposed to realize high-efficiency light modulators [11]. Here we demonstrate that our proposed scheme can make sensitive SPR measurements with minimal data processing efforts by using an EO tunable WCSPR sensor.

2. Principle of the operation

The electrically tunable WCSPR sensor we report here consists of three layers of metal and dielectric material, i.e., the upper gold layer U, the dielectric waveguide layer W, and the lower gold layer L, on a high-index glass substrate S, as shown in Fig. 1. The lower gold layer is in contact with the analyte, and the waveguide-coupled surface plasmon wave at the interface of the lower gold layer and the analyte can be excited by a transverse magnetic (TM) polarized wave coupled through the above layers. Similar to the traditional single-layer SPR effect, the WCSPR effect can be experimentally observed by detecting the optical reflectivity variation from the top dielectric/metal interface. The power reflectivity R of the TM wave for the five-layer WCSPR sensor can be calculated from the Fresnel equation as:

R=r1,52ri,5=ri,i+1+ri+1,5e2jdi+1kz,i+11+ri,i+1ri+1,5e2jdi+1kz,i+1(i=3,2,1;j=1)ri,i+1=ni+12kz,i+1ni2kz,ini+12kz,i+1+ni2kz,i(i=1,2,3,4)kzi=(2πλ)2ni2k0x2(i=1,2,3,4,5)k0x=2πλn1sinθ}

Where r i,i+1 is the reflection amplitude, kzi represents the wave number vector perpendicular to the interface of the transmitted light in the sequenced optical media, ni is the refractive index of the sequenced mediums, di is the thickness of the sequenced layers, k 0x is the wave number vector parallel to the interface in the first media-prism, λ is the incident wavelength, while θ is the incident angle. The lower indices 1 to 5 represent the substrate, the upper gold layer, the waveguide layer, the lower gold layer and the analyte, respectively. The SPR curve is typically characterized by the minimum of the dip, and its depth, which are affected by the optical excitation condition and the sensor parameters. Most previous interrogation schemes rely on scanning the optical excitation condition, while our proposed scheme utilizes the tunability of our SPR sensor.

To make the sensor electrically tunable, the dielectric layer is made of EO material whose refractive index n 3 can be changed by the electrical field applied to the layer. When a voltage modulation signal V is applied across the waveguide layer through the upper and lower gold layer that act as electrodes, n 3 is modulated by the electro-optical effect, and the variation of n 3 is Δn 3= - n 3 3 r 33 V/2d 3, where r 33 is the EO coefficient perpendicular to the interface of the EO waveguide layer [12]. Then the WCSPR response, i.e., the reflectivity R, is also modulated, and is a function of the incident angle of the optical beam θ and the modulation voltage V:

R=R(θ,V)

For a sinusoidal modulation signal V:

V=V0sin(ω0t)

Where V 0 represents the amplitude of the modulation signal, ω 0 is the angular frequency ° Elementary trigonometric and algebraic methods allow one to conclude that an analytic function g(V) of an independent sinusoidal variable V=V 0sin(ω 0t), possessing a Taylor series expansion in V, may be expressed in the Fourier series:

g(V0sinω0t)=n=0V02ng(2n)(0)4n(n!)2
+k=1n(1)kcos(2kω0t)2n=kV02ng(2n)(0)4n(n+k)!(nk)!
+k=0n(1)ksin((2k+1)ω0t)2n=kV02n+1g(2n+1)(0)4n(n+1+k)!(nk)!

Then

R(θ,V0sinω0t)=n=0V02nR(2n)(θ,0)4n(n!)2
+k=1n(1)kcos(2kω0t)2n=kV02nR(2n)(θ,0)4n(n+k)!(nk)!
+k=0n(1)ksin((2k+1)ω0t)2n=kV02n+1R(2n+1)(θ,0)4n(n+1+k)!(nk)!

The modulated reflectivity for a fixed incident angle θ also can be described in the frequency domain as:

F(θ,V0,ω0)=[R(θ,0)+V0242RV2V=0+V04644RV4V=0+]
+[V01!RVV=0+V0383RV3V=0+V051925RV5V=0+]×πi2δ(ωω0)
+j=2Ajδ(ωjω0)+

If the modulated reflectivity, i.e., the corresponding detected optical signal, is passed through a narrow band electrical filter centered at the frequency ω 0, only the second term on the right hand side of Eq. (6) remains. The filtering can be realized by passing the signal through a lock-in amplifier with a reference input at the frequency ω 0. Thus, the output I from the lock-in amplifier will be given by:

I=n=0V02n+14nn!(n+1)!2n+1RV2n+1V=0=V0RVV=0+V0383RV3V=0+

where the constant gain of the amplifier is ignored for simplicity.

If the ratio of the third order derivative d 3 R/dV 3 to the first order derivative dR/dV is r, then f, the ratio of the cubic term in V 0 to the term first order in V 0, is

f=V028r

This quantity f represents the relative error in neglecting the higher order cubic term in Eq. 7. The voltage associated with a particular relative error f can be found by inverting this equation, so that:

V0=8fr

In these experiments, the ratio r is approximately 3.8×10-5 while θ = 34.474°, so that the voltage associated with a particular relative error is

V0=458.83f

For a relative error of f= 0.05%, then V 0 = 10.26 V, larger than the greatest modulation voltage 10V used in these experiments. So the error in neglecting the third - order term is less than 0.05 % for the range of voltages used in these experiments. Thus the first term on the right hand side of Eq. 7 dominates the output, we can see that the signal obtained under such a simple ‘modulation-filtering’ scheme is directly proportional to the first derivative of the SPR response towards the voltage ∂R/∂V|θ=θ0V=0 at any fixed angle θ 0.

Traditionally the SPR angle is defined as the minimum of R as a function of θ, i.e. where ∂R/∂θ|θ=θ0V=0 equals 0. Here we show that ∂R/∂V is closely related to ∂R/∂θ. The tuning of the refractive index of the EO layer results in a shift in the SPR peak. When it can be assumed that the depth and shape of the SPR peak remain unchanged and only the SPR angle is changed by δθ, the SPR response under the applied voltage δV can be described as:

R'(θ,δV)=R(θδθ,0)=R(θβδV,0)

where β is the ratio of the change in the SPR angle to the applied voltage ∂θ 0/∂V. So:

R'(θ0,V)VV=0=βR(θ,0)θθ=θ0

Equation (12) describes the relationship between the AC modulated reflectivity I and R, and I is proportional to the deviation of R with respect to θ. Therefore, it is expected that the angle corresponding to I = 0 is closely related to the commonly defined SPR angle.

3. SPR Sensor Fabrication and Experimental Setup

The electrically tunable sensor chip used in our experiments is fabricated on a slide of ZF7 substrate glass, whose refractive index n 1 = 1.7761 at the wavelength of 980 nm. The upper gold layer is deposited by an ion-source-assisted evaporating deposition system. The thickness of the film is controlled at 30nm by a Quartz oscillator with an accuracy of 1 nm. A guest-host EO polymer for the dielectric waveguide layer was made by co-dissolving a nonlinear electro-optic chromophore [4-(2-{5-[2-(5-Diisocyanom ethylene-4-isocyano-2, 2-dimethyl-tetrahydro-furan-3-yl)-vinyl]-3, 4-bis-penthloxy-thiophen-2-yl}-vinyl)-phenyl]-diethyl-amine and commercially available polycarbonate with 10 wt%. The solution filtered through a 0.2-μm filter is spin-coated on top of the upper gold layer at 1800 RPM for 90s. The sensor chip is first baked in a hot stage at 100°C for half an hour and then placed in a vacuum baking oven at 120°C and 10-3Pa for 24 h to remove the residual solvent. The thickness of the dielectric layer is controlled to be around 2.5 μm, measured by a stylus profiler (Veeco Dektak 150). The refractive index of the waveguide layer is 1.6038. Finally, the lower 35 nm-thick gold film is vapor deposited on top of the EO film.

The waveguide layer needs to be poled to possess the desired electro-optical characteristics. This is realized by a parallel contact method with the upper and lower gold layers serving as the electrodes. The poling process is performed at the condition of 60-V/μm with the temperature set at 130°C for 30minutes, as the transition temperature (Ttr) is estimated as 140°C. The poled film is naturally cooled to room temperature while maintaining the poling voltage. The EO coefficient r 33 of the polymer layer after poling is measured to be 22 pm/V by the simple reflection method [13].

The experimental setup to demonstrate the hybrid interrogation scheme is shown in Fig. 1. Collimated light from a 980nm semiconductor laser is passed through a p-polarized polarizer and then incident on a 45°-45°-90° triangular ZF7 prism. The tunable sensor chip is attached to the prism with index-matching fluid (its refractive index~1.70) to avoid reflection. A micro-fluidic sample channel made of polydimethylsiloxane (PDMS) is attached onto the lower gold surface of the sensor chip. The prism and the sensor are mounted on a motorized rotational stage, and the incident angle of the optical beam onto the sensor is scanned by rotating the computer-controlled stage. The reflected output light is detected by a Si photodetector, whose output is sent to a lock-in amplifier (Stanford research SR830).

 

Fig. 1. Experimental setup?D, photo detector; P, ZF7 prism; S, ZF7 substrate glass; U, upper gold layer; L, lower gold layer; W, EO waveguide layer)

Download Full Size | PPT Slide | PDF

The samples used in our experiments were glucose solutions of different concentrations, 1%, 2%, 3%, 4%, and 5% by weight, respectively. The relationship between the refractive index and the concentration of the solutions is almost linear when the concentration is low. The refractive index is assumed to increase by 1.4×10-3 with a 1 wt% increase in the glucose concentration [14].

First, the SPR responses of the sensor are measured using the traditional angular interrogation method, in which an optical chopper is used to facilitate the lock-in amplifier detection to suppress noises. The chopper is removed when the measurements are made using the novel hybrid interrogation scheme.

To realize electrical modulation of the sensor chip, a 1000 Hz, 10 V peak-to-peak amplitude sinusoidal output from the lock-in amplifier is used as the modulation source of the chip, which also acts as the reference to the lock-in amplifier. In our experiments, the initial phase between the detected signal and the reference on the lock-in amplifier is set to near 0 to maximize the X component output from it, which is recorded as the final data.

4. Result and discussion

The reflectivity of the sensor under the ATR configuration is first measured by the conventional angular interrogation scheme over a wide range of incident angles. De-ionized water is used as the analyte. Fig. 2 shows the normalized reflective intensity versus the incident angle. As shown in Fig. 2, four modes are present between the angle of 33.5° and 53.5°. Among them, three are waveguide coupled resonance (WCR) modes with relatively wider resonant dip, and the one with a resonance angle near 49.4° and a narrower dip is the WCSPR mode [15].

 

Fig. 2. Angular dependent response of the WCSPR sensor for water.

Download Full Size | PPT Slide | PDF

 

Fig. 3. Reflectivity measurements under different glucose solutions using the conventional angular interrogation method

Download Full Size | PPT Slide | PDF

The SPR response of the sensor to the solutions of different glucose concentrations are further measured based on the conventional angular interrogation. As shown in Fig. 3, it can be seen that the angular position of the SPR reflectivity dip moves towards the larger incident angle side as the glucose concentration increases. The changes in the minimum appear quite linear, while the depth of the dip also increases.

 

Fig. 4. (a) Angle shift based conventional angular interrogation for different voltages ; (b) SPR Angle shift with voltage variation

Download Full Size | PPT Slide | PDF

To demonstrate the electrical tunability of the SPR sensor, its WCSPR response is first measured under different DC bias voltages using the same system configuration when air is in the channel. It can be seen from Fig. 4 (a) that the resonant angle shifts as the DC bias varies, and the depth of the dip slightly varies as well. The SPR angle is calculated using the centroid algorithm [2]. In our current setup, the fluctuation of the detected centroid WCSPR angle has a standard deviation of 4×10-4 degree. Fig. 4 (b) shows a very linear relationship of the positions of the SPR reflectivity minimum and the bias voltage, suggesting that the differential ∂θ 0/∂V is a constant.

 

Fig. 5. The voltage modulation curve at the fixed angle 34.478°

Download Full Size | PPT Slide | PDF

As Eq. (7) shows, the lock-in amplifier’s output is dominated by the term proportional to ∂R/∂V. Thus, further measurement of the dependence of the reflectivity on the bias voltage is carried out, when the incident angle of the optical beam is fixed. Figure 5 shows the dependence of SPR response on the bias voltage under the incident angle θ 0 of 34.478°. This angle is chosen so that the curve in Eq. (12) has its minimum at zero bias, i.e. ∂R(θ 0’,V)/∂V|V=0=0 at that angle. However, this angle is different from the minimal angular position θ 0 for the angular interrogation under zero bias, i.e. where ∂R(θ, 0)/∂θ|θ=θ0=0. This is due to the fact that the depth of the SPR reflectivity dip can also be affected by the applied bias as seen in Fig. 4. Therefore, the position where ∂R/∂θ equals to 0 deviates slightly from that where ∂R/∂V equals 0, which traditionally has been labeled as the SPR angle. However, as we will show later, these two positions closely track each other, so that the measurement of the previous one provides accurate results on the later one as well.

The hybrid interrogation scheme that combines voltage modulation and angular scanning is demonstrated by applying the sinusoidal modulation voltage across the sensor chip and recording the demodulated signal I from the lock-in while the input angle is tuned by rotating the stage. The solid line in Fig. 6 shows the experimental result when 1% glucose solution is used as the analyte. Also shown in the figure are the result from the traditional angular interrogation and its derivative ∂R/∂θ versus the incident angle. We note that the shape of the signal I is highly correlated to that of ∂R/∂θ, and I is negative on the left hand side and positive on the right. Its zero-crossing point is very close to the minimum of R, and in that region, which is significantly narrower than the width of the dip in R, I changes quite linearly with the angle. Higher detection resolution could be achieved due to the much steeper slope in this region [16]. In our new detection scheme, linearly fitting the curve near the SPR angle can easily determine the zero-crossing point with much reduced computational complexity. Our experimental results are directly acquired through experimental methods by leveraging the tunability of the sensor chip, and good signal to noise ratio is demonstrated. In contrast, the derivative of R obtained by post-detection data processing from the traditional angular interrogation scheme using the same setup is much noisier.

 

Fig. 6. Experimental results of R and the modulated power I and the differential from R to θ versus incident angle for 1% solution

Download Full Size | PPT Slide | PDF

 

Fig. 7. The angle shift versus the refractive index of the analytes

Download Full Size | PPT Slide | PDF

We note that, though the shape of I curve matches very well with that of ∂R/∂θ, the I curve shifts slightly to the right compared to the ∂R/∂θ curve. This is caused by the slight difference in their shapes and minimal positions between ∂R/∂V and ∂R/∂θ, as discussed earlier in Fig. 5. To demonstrate that the results from our scheme can yield very good estimates of SPR angle shifts and to show the ability of our scheme to make sensing measurement, buffer-switching experiments are carried out. As shown in the subplot of Fig. 7, the I curves shift to the right when the concentration of glucose in the solution increases. The difference between the minimal and maximal points in the I curve also increases, and this is consistent with the results in Fig. 3 where the SPR dip gets deeper, i.e., the magnitude of derivative increases. It is also shown in Fig. 6 that the zero-crossing points from the new detection scheme increase linearly with the increase in the glucose concentration, i.e., the refractive index. Also plotted are the positions of the SPR dip using the traditional angular interrogation scheme (from data shown in Fig. 3). The positions are calculated using the widely used curve fitting and centroid algorithm [2]. We can see that the results from our method and the centroid results are in parallel to each other. Since the variation instead of the exact value of the SPR dip position is of importance to most SPR sensing applications, the zero-crossing point can be used, just like the centroid of the dip, for sensing applications.

For further system performance measurements, the WCSPR signal has been acquired for air over a long period of time using the proposed hybrid detection method, and the WCSPR angle is determined by the linear fitting and zero-crossing algorithm. For comparison, sequentially, using mostly the same setup with an optical chopper and the lock-in amplifier as described earlier, the angular interrogation results are obtained. The traditional minimum finding algorithm and the centroid algorithm are using to calculate the SPR angle, respectively. Fig. 8 shows the typical results from these measurements using different interrogation scheme and data processing algorithms. It is found that the standard deviations of the measured SPR angle θsd are 3.3×10-4, 4.0×10-4, and 7.8×10-4 degree for the hybrid interrogation /zero-finding algorithm, angular interrogation/centroid, and angular interrogation /minimum finding algorithm, respectively. Since the sensitivity of the sensor remains the same for either interrogation scheme, the reduction of the noise level will lead to an improvement in the detection limit, approximately 20% in this example, by using the proposed scheme with a very simple algorithm.

 

Fig. 8. Measurement of the WCSPR angle based on different interrogation schemes and data processing algorithms.

Download Full Size | PPT Slide | PDF

5. Conclusions

We present a novel hybrid interrogation scheme enabled by electrically tunable SPR sensors to temporally dither the SPR signal while scanning its angular dependence. In contrast to most of the previous SPR detection schemes that rely on the modifications and improvements in optical excitation and detection methods, our scheme leverages the potential of dynamically modulating the SPR sensor’s response instead. Our scheme can yield output signal directly correlated to the derivative of the SPR reflectivity response, and this new AC-modulation detection method could make determination of the SPR resonance angles simpler, faster and more accurate. In our experimental demonstration, EO-tunable SPR sensors based on the waveguide coupled surface plasmon resonance structure are fabricated and tested. The results are in good agreement with the theoretical prediction, as well as with the results from the traditional scheme.

Eliminating the relatively complicated algorithms can help the design of low-cost, compact SPR equipments by removing the need of significant computing power from an external computer or on-board high-speed digital signal processors. We also note that the lock-in amplifier used in our experiments can be replaced with a simple passive electrical filter with a passband centered at the modulation frequency. Our proposed hybrid scheme could also be applicable to other tunable SPR sensors [9] and with other interrogation schemes, such as wavelength interrogation.

Acknowledgments

This work was supported by 973 Program (2009CB930700), and the work at Beihang University was also partially supported by NSFC (60877054), NCET and PCSIRT, SEM. The authors also wish to acknowledge the helpful discussion on the mathematical representations with Prof. Jim Diamond from Lincroft College.

References and links

1. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008). [CrossRef]   [PubMed]  

2. K. Kukanskis, J. Elkind, J. Melendez, T. Murphy, and G. Miller, “Detection of DNA hybridization using the TISPR-1 surface plsmon resonance biosensor,” Anal. Biochem. 274, 7–17 (1999). [CrossRef]   [PubMed]  

3. A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, “Sensitivity and detection limit of concentration and adsorption measurements by laser-induced surface plasmon resonance,” Appl. Opt. 36, 6539–6547 (1997). [CrossRef]  

4. K. S. Johnson, S. S. Yee, and K. S. Boolsh, “Calibration of surface plasmon resonance refractometers using locally weighted parametric regression,” Anal. Chem. 69, 1844–1851 (1997). [CrossRef]  

5. T. M. Chinowsky, L. S. Jung, and S. S. Yee, “Optimal linear data analysis for surface plasmon resonance biosensors,” Sens. Actuators. B. 54, 89–97 (1999). [CrossRef]  

6. K. Kurihara, K. Nakamura, and K. Suzuki, “Asymmetric SPR sensor response curve-fitting equation for the accurate determination of SPR resonance angle,” Sens. Actuators. B. 86, 49–57 (2002). [CrossRef]  

7. P. Tobiška and J. Homola, “Advanced data processing for SPR biosensors,” Sens. Actuators. B. 107, 162–169 (2005). [CrossRef]  

8. C. Thirstrup and W. Zong, “Data analysis for surface plasmon resonance sensors using dynamic baseline algorithm,” Sens. Actuators. B. 106, 796–802 (2005). [CrossRef]  

9. T. J. Wang, W. S. Lin, and F. K. Liu, “Integrated-optic biosensor by electro-optically modulated surface plasmon resonance,” Bios. Bioelectron. 22, 1441–1446 (2007). [CrossRef]  

10. J. N. Yih, F. C. Chien, C. Y. Lin, H. F. Yau, and S. J. Chen, “Angular-interrogation attenuated total reflection metrology system for plasmonic sensors,” Appl. Opt. 44, 6155–6162 (2005). [CrossRef]   [PubMed]  

11. J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003). [CrossRef]  

12. Y. Jiang, Z. Q. Cao, Q. S. Shen, X. M. Dou, and Y. L. Chen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am.B 17, 805–808 (2000). [CrossRef]  

13. C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990). [CrossRef]  

14. D. R. Lide, “Concentrative properties of aqueous solutions: density, refractive index, freezing point depression, and viscosity” in Handbook of chemistry and physics, (CRC press, Boca Raton, FL, 2005) pp.8–65.

15. J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005). [CrossRef]  

16. T. G. Wang and C. W. Hsieh, “Surface Plasmon resonance biosensor based on electro-optically modulated phase detection,” Opt. Lett. 32, 2834–2836 (2007). [CrossRef]   [PubMed]  

References

  • View by:
  • |
  • |
  • |

  1. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008).
    [Crossref] [PubMed]
  2. K. Kukanskis, J. Elkind, J. Melendez, T. Murphy, and G. Miller, “Detection of DNA hybridization using the TISPR-1 surface plsmon resonance biosensor,” Anal. Biochem. 274, 7–17 (1999).
    [Crossref] [PubMed]
  3. A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, “Sensitivity and detection limit of concentration and adsorption measurements by laser-induced surface plasmon resonance,” Appl. Opt. 36, 6539–6547 (1997).
    [Crossref]
  4. K. S. Johnson, S. S. Yee, and K. S. Boolsh, “Calibration of surface plasmon resonance refractometers using locally weighted parametric regression,” Anal. Chem. 69, 1844–1851 (1997).
    [Crossref]
  5. T. M. Chinowsky, L. S. Jung, and S. S. Yee, “Optimal linear data analysis for surface plasmon resonance biosensors,” Sens. Actuators. B. 54, 89–97 (1999).
    [Crossref]
  6. K. Kurihara, K. Nakamura, and K. Suzuki, “Asymmetric SPR sensor response curve-fitting equation for the accurate determination of SPR resonance angle,” Sens. Actuators. B. 86, 49–57 (2002).
    [Crossref]
  7. P. Tobiška and J. Homola, “Advanced data processing for SPR biosensors,” Sens. Actuators. B. 107, 162–169 (2005).
    [Crossref]
  8. C. Thirstrup and W. Zong, “Data analysis for surface plasmon resonance sensors using dynamic baseline algorithm,” Sens. Actuators. B. 106, 796–802 (2005).
    [Crossref]
  9. T. J. Wang, W. S. Lin, and F. K. Liu, “Integrated-optic biosensor by electro-optically modulated surface plasmon resonance,” Bios. Bioelectron. 22, 1441–1446 (2007).
    [Crossref]
  10. J. N. Yih, F. C. Chien, C. Y. Lin, H. F. Yau, and S. J. Chen, “Angular-interrogation attenuated total reflection metrology system for plasmonic sensors,” Appl. Opt. 44, 6155–6162 (2005).
    [Crossref] [PubMed]
  11. J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
    [Crossref]
  12. Y. Jiang, Z. Q. Cao, Q. S. Shen, X. M. Dou, and Y. L. Chen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am.B 17, 805–808 (2000).
    [Crossref]
  13. C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
    [Crossref]
  14. D. R. Lide, “Concentrative properties of aqueous solutions: density, refractive index, freezing point depression, and viscosity” in Handbook of chemistry and physics, (CRC press, Boca Raton, FL, 2005) pp.8–65.
  15. J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005).
    [Crossref]
  16. T. G. Wang and C. W. Hsieh, “Surface Plasmon resonance biosensor based on electro-optically modulated phase detection,” Opt. Lett. 32, 2834–2836 (2007).
    [Crossref] [PubMed]

2008 (1)

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008).
[Crossref] [PubMed]

2007 (2)

T. J. Wang, W. S. Lin, and F. K. Liu, “Integrated-optic biosensor by electro-optically modulated surface plasmon resonance,” Bios. Bioelectron. 22, 1441–1446 (2007).
[Crossref]

T. G. Wang and C. W. Hsieh, “Surface Plasmon resonance biosensor based on electro-optically modulated phase detection,” Opt. Lett. 32, 2834–2836 (2007).
[Crossref] [PubMed]

2005 (4)

J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005).
[Crossref]

J. N. Yih, F. C. Chien, C. Y. Lin, H. F. Yau, and S. J. Chen, “Angular-interrogation attenuated total reflection metrology system for plasmonic sensors,” Appl. Opt. 44, 6155–6162 (2005).
[Crossref] [PubMed]

P. Tobiška and J. Homola, “Advanced data processing for SPR biosensors,” Sens. Actuators. B. 107, 162–169 (2005).
[Crossref]

C. Thirstrup and W. Zong, “Data analysis for surface plasmon resonance sensors using dynamic baseline algorithm,” Sens. Actuators. B. 106, 796–802 (2005).
[Crossref]

2003 (1)

J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
[Crossref]

2002 (1)

K. Kurihara, K. Nakamura, and K. Suzuki, “Asymmetric SPR sensor response curve-fitting equation for the accurate determination of SPR resonance angle,” Sens. Actuators. B. 86, 49–57 (2002).
[Crossref]

2000 (1)

Y. Jiang, Z. Q. Cao, Q. S. Shen, X. M. Dou, and Y. L. Chen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am.B 17, 805–808 (2000).
[Crossref]

1999 (2)

T. M. Chinowsky, L. S. Jung, and S. S. Yee, “Optimal linear data analysis for surface plasmon resonance biosensors,” Sens. Actuators. B. 54, 89–97 (1999).
[Crossref]

K. Kukanskis, J. Elkind, J. Melendez, T. Murphy, and G. Miller, “Detection of DNA hybridization using the TISPR-1 surface plsmon resonance biosensor,” Anal. Biochem. 274, 7–17 (1999).
[Crossref] [PubMed]

1997 (2)

A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, “Sensitivity and detection limit of concentration and adsorption measurements by laser-induced surface plasmon resonance,” Appl. Opt. 36, 6539–6547 (1997).
[Crossref]

K. S. Johnson, S. S. Yee, and K. S. Boolsh, “Calibration of surface plasmon resonance refractometers using locally weighted parametric regression,” Anal. Chem. 69, 1844–1851 (1997).
[Crossref]

1990 (1)

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[Crossref]

Boolsh, K. S.

K. S. Johnson, S. S. Yee, and K. S. Boolsh, “Calibration of surface plasmon resonance refractometers using locally weighted parametric regression,” Anal. Chem. 69, 1844–1851 (1997).
[Crossref]

Cao, Z. Q.

Y. Jiang, Z. Q. Cao, Q. S. Shen, X. M. Dou, and Y. L. Chen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am.B 17, 805–808 (2000).
[Crossref]

Chen, S. J.

J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005).
[Crossref]

J. N. Yih, F. C. Chien, C. Y. Lin, H. F. Yau, and S. J. Chen, “Angular-interrogation attenuated total reflection metrology system for plasmonic sensors,” Appl. Opt. 44, 6155–6162 (2005).
[Crossref] [PubMed]

J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
[Crossref]

Chen, Y. L.

Y. Jiang, Z. Q. Cao, Q. S. Shen, X. M. Dou, and Y. L. Chen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am.B 17, 805–808 (2000).
[Crossref]

Chien, F. C.

Chinowsky, T. M.

T. M. Chinowsky, L. S. Jung, and S. S. Yee, “Optimal linear data analysis for surface plasmon resonance biosensors,” Sens. Actuators. B. 54, 89–97 (1999).
[Crossref]

Chu, C.-S.

J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005).
[Crossref]

Chua, C. S.

J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
[Crossref]

Chyou, J. J.

J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005).
[Crossref]

J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
[Crossref]

Dou, X. M.

Y. Jiang, Z. Q. Cao, Q. S. Shen, X. M. Dou, and Y. L. Chen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am.B 17, 805–808 (2000).
[Crossref]

Elkind, J.

K. Kukanskis, J. Elkind, J. Melendez, T. Murphy, and G. Miller, “Detection of DNA hybridization using the TISPR-1 surface plsmon resonance biosensor,” Anal. Biochem. 274, 7–17 (1999).
[Crossref] [PubMed]

Gershon, P. D.

Homola, J.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008).
[Crossref] [PubMed]

P. Tobiška and J. Homola, “Advanced data processing for SPR biosensors,” Sens. Actuators. B. 107, 162–169 (2005).
[Crossref]

Hsieh, C. W.

Huang, K. T.

J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
[Crossref]

Jiang, Y.

Y. Jiang, Z. Q. Cao, Q. S. Shen, X. M. Dou, and Y. L. Chen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am.B 17, 805–808 (2000).
[Crossref]

Johnson, K. S.

K. S. Johnson, S. S. Yee, and K. S. Boolsh, “Calibration of surface plasmon resonance refractometers using locally weighted parametric regression,” Anal. Chem. 69, 1844–1851 (1997).
[Crossref]

Jung, L. S.

T. M. Chinowsky, L. S. Jung, and S. S. Yee, “Optimal linear data analysis for surface plasmon resonance biosensors,” Sens. Actuators. B. 54, 89–97 (1999).
[Crossref]

Kolomenskii, A. A.

Kukanskis, K.

K. Kukanskis, J. Elkind, J. Melendez, T. Murphy, and G. Miller, “Detection of DNA hybridization using the TISPR-1 surface plsmon resonance biosensor,” Anal. Biochem. 274, 7–17 (1999).
[Crossref] [PubMed]

Kurihara, K.

K. Kurihara, K. Nakamura, and K. Suzuki, “Asymmetric SPR sensor response curve-fitting equation for the accurate determination of SPR resonance angle,” Sens. Actuators. B. 86, 49–57 (2002).
[Crossref]

Lide, D. R.

D. R. Lide, “Concentrative properties of aqueous solutions: density, refractive index, freezing point depression, and viscosity” in Handbook of chemistry and physics, (CRC press, Boca Raton, FL, 2005) pp.8–65.

Lin, C. Y.

J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005).
[Crossref]

J. N. Yih, F. C. Chien, C. Y. Lin, H. F. Yau, and S. J. Chen, “Angular-interrogation attenuated total reflection metrology system for plasmonic sensors,” Appl. Opt. 44, 6155–6162 (2005).
[Crossref] [PubMed]

J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
[Crossref]

Lin, W. S.

T. J. Wang, W. S. Lin, and F. K. Liu, “Integrated-optic biosensor by electro-optically modulated surface plasmon resonance,” Bios. Bioelectron. 22, 1441–1446 (2007).
[Crossref]

Liu, F. K.

T. J. Wang, W. S. Lin, and F. K. Liu, “Integrated-optic biosensor by electro-optically modulated surface plasmon resonance,” Bios. Bioelectron. 22, 1441–1446 (2007).
[Crossref]

Man, H. T.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[Crossref]

Melendez, J.

K. Kukanskis, J. Elkind, J. Melendez, T. Murphy, and G. Miller, “Detection of DNA hybridization using the TISPR-1 surface plsmon resonance biosensor,” Anal. Biochem. 274, 7–17 (1999).
[Crossref] [PubMed]

Miller, G.

K. Kukanskis, J. Elkind, J. Melendez, T. Murphy, and G. Miller, “Detection of DNA hybridization using the TISPR-1 surface plsmon resonance biosensor,” Anal. Biochem. 274, 7–17 (1999).
[Crossref] [PubMed]

Murphy, T.

K. Kukanskis, J. Elkind, J. Melendez, T. Murphy, and G. Miller, “Detection of DNA hybridization using the TISPR-1 surface plsmon resonance biosensor,” Anal. Biochem. 274, 7–17 (1999).
[Crossref] [PubMed]

Nakamura, K.

K. Kurihara, K. Nakamura, and K. Suzuki, “Asymmetric SPR sensor response curve-fitting equation for the accurate determination of SPR resonance angle,” Sens. Actuators. B. 86, 49–57 (2002).
[Crossref]

Schuessler, H. A.

Shen, Q. S.

Y. Jiang, Z. Q. Cao, Q. S. Shen, X. M. Dou, and Y. L. Chen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am.B 17, 805–808 (2000).
[Crossref]

Shih, Z. H.

J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005).
[Crossref]

J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
[Crossref]

Shu, C. F.

J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005).
[Crossref]

Shu, S. F.

J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
[Crossref]

Suzuki, K.

K. Kurihara, K. Nakamura, and K. Suzuki, “Asymmetric SPR sensor response curve-fitting equation for the accurate determination of SPR resonance angle,” Sens. Actuators. B. 86, 49–57 (2002).
[Crossref]

Teng, C. C.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[Crossref]

Thirstrup, C.

C. Thirstrup and W. Zong, “Data analysis for surface plasmon resonance sensors using dynamic baseline algorithm,” Sens. Actuators. B. 106, 796–802 (2005).
[Crossref]

Tobiška, P.

P. Tobiška and J. Homola, “Advanced data processing for SPR biosensors,” Sens. Actuators. B. 107, 162–169 (2005).
[Crossref]

Wang, T. G.

Wang, T. J.

T. J. Wang, W. S. Lin, and F. K. Liu, “Integrated-optic biosensor by electro-optically modulated surface plasmon resonance,” Bios. Bioelectron. 22, 1441–1446 (2007).
[Crossref]

Yau, H. F.

Yee, S. S.

T. M. Chinowsky, L. S. Jung, and S. S. Yee, “Optimal linear data analysis for surface plasmon resonance biosensors,” Sens. Actuators. B. 54, 89–97 (1999).
[Crossref]

K. S. Johnson, S. S. Yee, and K. S. Boolsh, “Calibration of surface plasmon resonance refractometers using locally weighted parametric regression,” Anal. Chem. 69, 1844–1851 (1997).
[Crossref]

Yih, J. N.

Zong, W.

C. Thirstrup and W. Zong, “Data analysis for surface plasmon resonance sensors using dynamic baseline algorithm,” Sens. Actuators. B. 106, 796–802 (2005).
[Crossref]

Anal. Biochem. (1)

K. Kukanskis, J. Elkind, J. Melendez, T. Murphy, and G. Miller, “Detection of DNA hybridization using the TISPR-1 surface plsmon resonance biosensor,” Anal. Biochem. 274, 7–17 (1999).
[Crossref] [PubMed]

Anal. Chem. (1)

K. S. Johnson, S. S. Yee, and K. S. Boolsh, “Calibration of surface plasmon resonance refractometers using locally weighted parametric regression,” Anal. Chem. 69, 1844–1851 (1997).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[Crossref]

Bios. Bioelectron. (1)

T. J. Wang, W. S. Lin, and F. K. Liu, “Integrated-optic biosensor by electro-optically modulated surface plasmon resonance,” Bios. Bioelectron. 22, 1441–1446 (2007).
[Crossref]

Chem. Rev. (1)

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108, 462–493 (2008).
[Crossref] [PubMed]

J. Opt. Soc. Am.B (1)

Y. Jiang, Z. Q. Cao, Q. S. Shen, X. M. Dou, and Y. L. Chen, “Improved attenuated-total-reflection technique for measuring the electro-optic coefficients of nonlinear optical polymers,” J. Opt. Soc. Am.B 17, 805–808 (2000).
[Crossref]

Opt. Eng. (1)

J. J. Chyou, S. J. Chen, C.-S. Chu, Z. H. Shih, C. Y. Lin, and C. F. Shu, “Fabrication and metrology of E-O polymer light modulator based on waveguide-coupled surface plasmon resonance,” Opt. Eng. 44, 034001–034007 (2005).
[Crossref]

Opt. Lett. (1)

Proc. SPIE (1)

J. J. Chyou, C. S. Chua, Z. H. Shih, C. Y. Lin, K. T. Huang, S. J. Chen, and S. F. Shu, “High efficiency electro-optic polymer light modulator based on waveguide-coupled surface plasmon resonance,” Proc. SPIE 5211, 197–206 (2003).
[Crossref]

Sens. Actuators. B. (4)

T. M. Chinowsky, L. S. Jung, and S. S. Yee, “Optimal linear data analysis for surface plasmon resonance biosensors,” Sens. Actuators. B. 54, 89–97 (1999).
[Crossref]

K. Kurihara, K. Nakamura, and K. Suzuki, “Asymmetric SPR sensor response curve-fitting equation for the accurate determination of SPR resonance angle,” Sens. Actuators. B. 86, 49–57 (2002).
[Crossref]

P. Tobiška and J. Homola, “Advanced data processing for SPR biosensors,” Sens. Actuators. B. 107, 162–169 (2005).
[Crossref]

C. Thirstrup and W. Zong, “Data analysis for surface plasmon resonance sensors using dynamic baseline algorithm,” Sens. Actuators. B. 106, 796–802 (2005).
[Crossref]

Other (1)

D. R. Lide, “Concentrative properties of aqueous solutions: density, refractive index, freezing point depression, and viscosity” in Handbook of chemistry and physics, (CRC press, Boca Raton, FL, 2005) pp.8–65.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1. Experimental setup?D, photo detector; P, ZF7 prism; S, ZF7 substrate glass; U, upper gold layer; L, lower gold layer; W, EO waveguide layer)
Fig. 2.
Fig. 2. Angular dependent response of the WCSPR sensor for water.
Fig. 3.
Fig. 3. Reflectivity measurements under different glucose solutions using the conventional angular interrogation method
Fig. 4.
Fig. 4. (a) Angle shift based conventional angular interrogation for different voltages ; (b) SPR Angle shift with voltage variation
Fig. 5.
Fig. 5. The voltage modulation curve at the fixed angle 34.478°
Fig. 6.
Fig. 6. Experimental results of R and the modulated power I and the differential from R to θ versus incident angle for 1% solution
Fig. 7.
Fig. 7. The angle shift versus the refractive index of the analytes
Fig. 8.
Fig. 8. Measurement of the WCSPR angle based on different interrogation schemes and data processing algorithms.

Equations (18)

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

R = r 1,5 2 r i , 5 = r i , i + 1 + r i + 1,5 e 2 j d i + 1 k z , i + 1 1 + r i , i + 1 r i + 1,5 e 2 j d i + 1 k z , i + 1 ( i = 3,2,1 ; j = 1 ) r i , i + 1 = n i + 1 2 k z , i + 1 n i 2 k z , i n i + 1 2 k z , i + 1 + n i 2 k z , i ( i = 1,2,3,4 ) k zi = ( 2 π λ ) 2 n i 2 k 0 x 2 ( i = 1,2,3,4,5 ) k 0 x = 2 π λ n 1 sin θ }
R = R ( θ , V )
V = V 0 sin ( ω 0 t )
g ( V 0 sin ω 0 t ) = n = 0 V 0 2 n g ( 2 n ) ( 0 ) 4 n ( n ! ) 2
+ k = 1 n ( 1 ) k cos ( 2 k ω 0 t ) 2 n = k V 0 2 n g ( 2 n ) ( 0 ) 4 n ( n + k ) ! ( n k ) !
+ k = 0 n ( 1 ) k sin ( ( 2 k + 1 ) ω 0 t ) 2 n = k V 0 2 n + 1 g ( 2 n + 1 ) ( 0 ) 4 n ( n + 1 + k ) ! ( n k ) !
R ( θ , V 0 sin ω 0 t ) = n = 0 V 0 2 n R ( 2 n ) ( θ , 0 ) 4 n ( n ! ) 2
+ k = 1 n ( 1 ) k cos ( 2 k ω 0 t ) 2 n = k V 0 2 n R ( 2 n ) ( θ , 0 ) 4 n ( n + k ) ! ( n k ) !
+ k = 0 n ( 1 ) k sin ( ( 2 k + 1 ) ω 0 t ) 2 n = k V 0 2 n + 1 R ( 2 n + 1 ) ( θ , 0 ) 4 n ( n + 1 + k ) ! ( n k ) !
F ( θ , V 0 , ω 0 ) = [ R ( θ , 0 ) + V 0 2 4 2 R V 2 V = 0 + V 0 4 64 4 R V 4 V = 0 + ]
+ [ V 0 1 ! R V V = 0 + V 0 3 8 3 R V 3 V = 0 + V 0 5 192 5 R V 5 V = 0 + ] × πi 2 δ ( ω ω 0 )
+ j = 2 A j δ ( ω j ω 0 ) +
I = n = 0 V 0 2 n + 1 4 n n ! ( n + 1 ) ! 2 n + 1 R V 2 n + 1 V = 0 = V 0 R V V = 0 + V 0 3 8 3 R V 3 V = 0 +
f = V 0 2 8 r
V 0 = 8 f r
V 0 = 458.83 f
R ' ( θ , δV ) = R ( θ δθ , 0 ) = R ( θ βδV , 0 )
R ' ( θ 0 , V ) V V = 0 = β R ( θ , 0 ) θ θ = θ 0

Metrics