Dual-angle technique for simultaneous measurement of refractive index and temperature based on a surface plasmon resonance sensor

Wei Luo; Sheng Chen; Lei Chen; Hualong Li; Pengcheng Miao; Huiyi Gao; Zelin Hu; Miao Li

doi:10.1364/OE.25.012733

1. Introduction

Surface plasmon resonance (SPR), as a surface-oriented phenomenon, is a high sensitivity method for detecting tiny changes in the refractive index (RI) of the sample contacted to the metal surface. With the advantage of a thick molecular layer at the metal surface, SPR sensors have been applied in a wide range of contexts [1, 2], including chemical and biological sciences, and SPR sensing has become a leading technology in the field of direct real-time observation of bio-molecular interactions.

The various applications of SPR sensors focus on the detection of tiny changes in RI, or other quantities converted into an equivalent change in RI. Although SPR sensing is currently a mature technology, typically the sample temperature needs to be carefully considered and controlled because temperature interference can be converted into a change in RI. The SPR signal also varies with temperature [3, 4], making one unable to determine whether the SPR signal is caused by a change in RI or temperature. In actual applications like environmental monitoring, the SPR sensor often has to be exposed to different temperatures. Even in the laboratory experiment, fluctuations in ambient temperatures can also occur in real-time [5, 6]. As a result, it is not practical to control the temperature passively.

Xiao et al. [7] described a dual-wavelength method for simultaneous measurement of the RI and temperature. Their experiment used an intensity interrogation scheme with two laser wavelengths and a photodetector incorporated to measure the intensity. In this case, a specific SPR sensor is needed to carry out their technique. A double-incident angle technique was also proposed by Xinyu Zhang to improve SPR sensitivity [8]. This technique is as simple and robust as conventional sensor detection schemes, providing simultaneous illumination of the sample with a range of incident angles and measuring the SPR angular spectrum.

In the present study, we present a new double-incident angle technique to simultaneously measure the RI and temperature, experimentally. The technique is based on the proven fact that the dependences of the SPR data shift on RI and temperature are quite linear and independent from each other. By monitoring the intensities of the reflected optical signal at two fixed incident angles with a conventional SPR scheme, without needing a special design or changing the traditional sensor structure, RI variation can be obtained without the need for a temperature control or calibration process.

2. Temperature effect on SPR

Figure 1 shows the schematic diagram of the most commonly used angle interrogation Kretschmann SPR, which consists of a prism, a thin metal film, and the analyte. P-polarized light illuminates the prism and undergoes attenuated total internal reflection at the metal/prism interface. The evanescent wave penetrates the thin metal layer and resonates with propagating metal-dielectric surface plasmons [9], causing the absorption of the reflected light beam. Therefore, the temperature effect on an SPR sensor can be transformed into the physical parameters of these constituent units. By incorporating the phenomena of thermo-optic effect on dispersion in the prism, and the phonon-electron scattering and electron-electron scattering in the metal layer [10], a comprehensive temperature-dependent theoretical model can be established to study the effect of temperature on SPR sensors.

Fig. 1 Schematic diagram of an SPR sensor in the Kretschmann configuration.

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2.1 Temperature effect on metal layer

Because thermal changes affect the metal film parameters significantly, the effect of temperature on the metal layer must be analyzed in detail. According to the Drude model, the frequency dependent dielectric permittivity $ε (ω)$ of the gold film can be represented as:

ε (ω) = {(n_{r} + j n_{i})}^{2} = 1 - \frac{ω_{p}^{2}}{ω (ω + i ω_{c})}

where

n_{r}

,

n_{i}

are the real and imaginary parts of the metal RI.

ω_{c}

,

ω_{p}

and

ω

represent the collision frequency, plasma frequency, and angular frequency of the electromagnetic wave, respectively. Due to the volumetric effect, with the negligible temperature dependence of effective mass of the electrons, the temperature dependence of

ω_{p}

can be calculated as [11]:

ω_{p} (T) = ω_{p 0} {[1 + γ_{e} (T - T {}_{0})]}^{- 1 / 2}

_{$ω_{p 0}$} is the plasma frequency at a reference temperature

T_{0}

, and

γ_{e}

is the expansion coefficient of the metal film.

Temperature changes affect the collision frequency in two ways, namely phonon-electron scattering ( $ω_{c p}$ ) and electron-electron scattering ( $ω_{c e}$ ) [12, 13]. By combining these effects, the temperature dependence of the collision frequency can be given as:

ω_{c} = ω_{c p} (T) + ω_{c e} (T)

The phonon-electron scattering

ω_{c p}

can be simulated by the Hubbard-Holstein model as [14]:

ω_{c p} (T) = ω_{0} [\frac{2}{5} + 4 {(\frac{T}{T_{D}})}^{5} \int_{0}^{T_{D} / T} \frac{z^{4} d z}{e^{z} - 1}]

_{$T_{D}$} and

ω_{0}

are the Debye temperature of the metal and the constant related to the electric conductivity of metal.

ω_{c e}

can be presented by the Lawrence model as [15]:

ω_{c e} (T) = \frac{1}{6} π^{4} \frac{Γ Δ}{ℏ E_{F}} [{(k_{B} T)}^{2} + {(\frac{ℏ ω}{4 π^{2}})}^{2}]

where

Γ

and

Δ

are the Fermi-surface average of scattering probability and the fractional Umklapp scattering of the metal, respectively.

The metal layer thickness $d$ is also an important parameter of the SPR sensor. Since thickness changes only correspond to expansion in the normal direction, by means of a corrected thermal-expansion coefficient [16], the thickness can be expressed as

d (T) = d_{0} [1 + (T - T_{0}) γ \frac{1 + μ}{1 - μ}]

where

d_{0}

is the thickness at the reference temperature

T_{0}

and

μ

is Poisson’s number of the film material.

2.2 Temperature effect on the prism

We use a thermo-optic coefficient $d n / d T$ to express the temperature effect on RI of the prism.

n (T) = n (T_{0}) + (T - T_{0}) \frac{d n}{d T}

Considering the most commonly used prism in SPR sensors, e.g., BK9, the dispersion of glass must be seriously considered [17]. It can be observed from Eqs. (8)–(10) that RI and the thermal-optic coefficient are both functions of wavelength.

R = \frac{λ^{2}}{(λ^{2} - λ_{i g}^{2})}

2 n (λ) \frac{d n}{d T} (λ) = G R + H R^{2}

n (λ) = {(1 + \frac{A_{1} λ^{2}}{λ^{2} - B_{1}^{2}} + \frac{A_{2} λ^{2}}{λ^{2} - B_{2}^{2}} + \frac{A_{3} λ^{2}}{λ^{2} - B_{3}^{2}})}^{1 / 2}

where

A_{1}

,

A_{2}

,

A_{3}

,

B_{1}

,

B_{2}

and

B_{3}

are material-dependent values, and

λ

,

λ_{i g}

represent the incident wavelength and the band gap wavelength in units of µm.

2.3 Reflectance of SPR sensor

For the SPR geometry shown in Fig. 1, and according to the Fresnel equations, the reflectance R of the SPR sensor can be expressed as

R = {| \frac{r_{01} + r_{12} \exp (2 i d_{1} k_{z 1})}{1 + r_{01} r_{12} \exp (2 i d_{1} k_{z 1})} |}^{2}

_{$r_{i j}$} is the reflective coefficient of p-polarized light at the boundary between media $i$ and $j$ , and it can be calculated as

r_{i j} = \frac{k_{z i} / ε_{i} - k_{z j} / ε_{j}}{k_{z i} / ε_{i} + k_{z j} / ε_{j}}

k_{z i} = \frac{2 π}{λ} \sqrt{ε_{i} - ε_{0} {(\sin θ)}^{2}}

where

θ

is the incidence angle and

k_{z i}

is the component of the wave vector in medium

i

along the z-direction.

3. Principle of double-incident angle SPR detection

Combining the typical Kretschmann SPR device with the multi-layer Fresnel equation, an asymmetric SPR reflectance curve can be obtained, as shown in Fig. 2 (solid line). Once the analyte RI or the temperature is changed, the coupling of the evanescent wave becomes different, and the SPR reflectance curve shifts to the dotted line. The conventional method to obtain this variation is to detect the resonance angle variation, or to exploit the light intensity data obtained at one fixed incident angle (usually set as θ₁). Similar with θ₁, another angle θ₂ can be found in the opposite side of the resonance curve, where a linear correlation is established between the change of reflection intensity and the analyte RI. Then, the signals at two incident angles can be used to characterize the resonance shifts caused by both the RI change and temperature variation. By measuring the intensities of reflected light at two proper incident angles and defining these two signals as the sensor output, a double-incident angle method can be constructed.

Fig. 2 Double incident angle signals manifest as shifting of the resonance curve.

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Compared with the commonly used SPR method exploiting only data obtained at one fixed incident angle, or by measuring the resonance angle shift, the double-incident angle measurement scheme takes full advantage of the data detected at angles θ₁ and θ₂, and offers two output signals to indicate the temperature and RI change.

4. Temperature effect on SPR with double-incident angle technique

In order to expand the measurement range and keep the appropriate sensitivity, the thickness of the gold film was set to be 40 nm at the reference temperature of 280 K [18]. We carried out numerical simulations with the corresponding original refractive index of the analyte being 1.3336 RIU, and the two incident angles fixed at the 30% value of the resonance curve, to simultaneously investigate the dependence of double-incident angle technique output signal on RI and temperature.

Figure 3 shows the output signal shifts of reflected light intensity versus simultaneous variations in temperature and RI at θ₁ and θ₂, respectively. It is obvious that the output signal varies quite linearly with both RI and temperature. For θ₁, the reflected signal rises with an increase of RI and a decrease of temperature. For θ₂, the signal decreases with increases in either RI or temperature. The absolute values of these curve slopes show that the SPR signal changes much faster with RI than with temperature, which reveals that the SPR signal shift is mainly dependent on the RI variation and is less sensitive to temperature variation. Furthermore, it can be seen that the slope of the reflected intensity change versus RI at θ₁ is larger than that at θ₂, which means that the reflected output signal is more sensitive to changes in RI at the left fixed incident angle. Therefore, the relationships governing the output signal change versus RI or temperature are approximately linear, with the slopes being dependent upon the incident angles used in the measurement.

Fig. 3 The SPR reflected intensity signal shifts versus temperature and RI for the two incident angles.

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More detail scenarios are shown in Figs. 4 and 5. As the variation of SPR reflectance intensity versus the sample RI sensed at different temperatures and incident angles, shown in Fig. 4, we observe that when θ = θ₁ (and θ = θ₂), the dependence of the output signal on RI is nearly the same for T = 280 K and T = 300 K. The difference in the slope of the reflectivity versus RI is negligible compared to either of the two slopes, revealing that, for the two fixed incident angles, the dependence of the output signal on RI can be considered independent of temperature. Furthermore, the spacing between pairs of curves at different temperatures at θ₁ is larger than that at θ₂, indicating that the sensor is more sensitive to the temperature change at the left fixed incident angle. From Fig. 5, which shows the reflectance signal change versus the temperature for different RIs and incident angles, it is obvious that, for the two incident angles, the slopes of the reflectance signal versus temperature for n_s = 1.3336 and n_s = 1.3346 are nearly equal. This means that, for a certain incident angle, the dependence of the double-incident angle technique output on temperature is approximately unchanged at different RIs.

Fig. 4 SPR reflected signal shifts versus RI for 280K and 300K.

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Fig. 5 SPR reflected signal shifts versus temperature for 1.3336 RIU and 1.33346 RIU.

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Due to the fact that the dependence of double-incident angle output on the RI and temperature is quite linear and independent of each other, both variations in temperature and RI can be resolved through measurement of the output signal at the two incident angles. Therefore, the total shifts of the output signal at the two incident angles can be expressed as:

(\begin{matrix} Δ S_{1} \\ Δ S_{2} \end{matrix}) = (\begin{matrix} m_{n 1} & m_{T 1} \\ m_{n 2} & m_{T 2} \end{matrix}) (\begin{matrix} Δ n \\ Δ T \end{matrix}) = M (\begin{matrix} Δ n \\ Δ T \end{matrix})

where ∆S₁, ∆S₂, ∆n and ∆T represent the output signals at angle θ₁ and θ₂, RI variation and temperature variation, respectively. M is called the sensitivity matrix, which takes into account the cross-sensitivity between the variation of RI and temperature at the two incident angles. The elements of sensitivity matrix are the sensitivity coefficients obtained from the linear fitting coefficients of the double-incident angle signal shift versus the variation of the RI and temperature shown in Fig. 4 and 5. Therefore, by detecting the signals at double incident angles and calculating the inverse matrix of M, both variations in RI and temperature can be measured as follows:

(\begin{matrix} Δ n \\ Δ T \end{matrix}) = M^{- 1} (\begin{matrix} Δ S_{1} \\ Δ S_{2} \end{matrix}) = (\begin{matrix} 0.0087 & - 0.0172 \\ - 604.2918 & - 781.26 \end{matrix}) (\begin{matrix} Δ S_{1} \\ Δ S_{2} \end{matrix})

Then, with the reference RI and temperature chosen arbitrarily, both the RI and temperature can be detected. Further calculation also reveals that defining the difference of these two outputs as one of the signals, a similar expression can be obtained as:

(\begin{matrix} Δ S_{1} \\ Δ S_{1} - Δ S_{2} \end{matrix}) = (\begin{matrix} m_{n 1} & m_{T 1} \\ m_{n (1 - 2)} & m_{T (1 - 2)} \end{matrix}) (\begin{matrix} Δ n \\ Δ T \end{matrix})

It is worth noting that this double-incident angle technique is very accurate when the two incident angles are properly chosen to be on opposite sides of the resonance curve, where the dependence of the output signal on both temperature and RI is linear and independent.

5. Experimental results and discussion

We carried out a proof-of-concept experiment to demonstrate the ability of the proposed double-incident angle technique. The schematic diagram of the optical arrangement is shown in Fig. 6. The setup consisted of a fixed-wavelength light emitting diode (LED), a ‘stop’ (iris), three spherical lens, two polarizers, a prism, and a CCD detector array (TCD1208, Toshiba). The first part of the optical system (LED to lens C) functions as a beam expander, through which light is focused onto the SPR chip, which consists of a 40 nm gold thin film attached onto the prism using the radio frequency magnetron sputtering method. The incident light generated by the LED has a center wavelength of 630 nm. The first polarizer (left) is used to adjust the intensity of incident light beam, to ensure that the intensity of reflected light beam falls in the linear range of the photodetector array sensitivity, and the transverse magnetic (TM) is kept by the second polarizer (right). The CCD detector array is incorporated in the reflected side of the optical arrangement.

Fig. 6 Experimental arrangement.

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This arrangement provides simultaneous illumination of the sample with a range of incident angles, and the entire SPR angular spectrum can be monitored. The reflectance beam image shows a dark line on the detector array, and the intensity profile exhibits a dip or minimal intensity at the resonance angle. Then, each sensor element position of the CCD detector can be used to characterize a unique incident angle. As a result, the SPR experiment to measure the reflection light intensity at double incident angles can be transferred to monitor the light intensity variation at two CCD elements. Due to the divergence of the reflected beam, we adjusted the distance between the prism and detector to make the angular resolution meet the demand of experiment, and fixed the two positions at the 30% value of the resonance curve. Therefore, we measured the RI varied by different concentrations of aqueous NaCl solution and confirmed with an Abel refractive index measuring instrument. The temperature was changed with a hot plate, and the output signal at the double-incident angles could be measured in real time.

Figure 7 shows the reflectance intensity versus analyte RI for the two fixed CCD detector elements at 15 °C. From these discrete points, it is obvious that a linear reflected optical intensity versus the RI response, and the linear fitted lines for both incident angles are also displayed in the figure. With the RI of analyte varying between 1.3375 and 1.3386 RIU, the reflectance intensity changes from 51.5 to 85.6 mV at the left sensor element of the detector, and changes from 50.5 to 25.9 mV at the other one, resulting in slopes of 3.3842 mV/10⁴ RIU and −2.4824 mV/10⁴ RIU, respectively. Figure 8 depicts the reflected optical intensity versus temperature with an RI of 1.3381 RIU. For the two sensor elements of the detector, the intensities all decrease with the temperature, resulting in measured slopes of −0.7592 mV/°C and −0.4786 mV/°C, respectively.

Fig. 7 Light reflectance signal versus RI and the corresponding linear fit lines.

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Fig. 8 Light reflectance signal versus temperature and the corresponding linear fit lines.

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With the linear fitting coefficients obtained in the sensor calibration and the proposed double-incident technique, both the RI and temperature variation can be detected simultaneously and in real time.

(\begin{matrix} Δ n \\ Δ T \end{matrix}) = M^{- 1} (\begin{matrix} Δ S_{1} \\ Δ S_{2} \end{matrix}) = (\begin{matrix} 0.1366 & - 0.2166 \\ - 0.7084 & - 0.9657 \end{matrix}) (\begin{matrix} Δ S_{1} \\ Δ S_{2} \end{matrix})

Here the ∆n and ∆T are the RI variation and temperature change of the analyte in units of 10⁴ RIU and °C. ∆S₁ and ∆S₂ are the reflected optical intensity changes at the two fixed sensor elements of the CCD detector.

6. Conclusion

In conclusion, we have proposed a practical double-incident angle technique for simultaneous measurement of changes in refractive index and temperature of the analyte. The method is based on the observation that the output signals obtained from two different incident angles each have a linear dependence on RI and temperature, and are independent. A proof-of-principle of the technique has been demonstrated through theoretical simulation and experiment. This method can be directly applied with the conventional SPR detection measuring the reflected intensities using a convergent light beam, making the method practical and convenient. Because the double-incident angle technique makes full use of the data measured at two fixed angles, the RI variation can be distinguished from the temperature change. This approach will further extend the potential of SPR-sensing technology and allow SPR sensors to suppress temperature interference.

Funding

Program 863 (SS2013AA102302); National Key Research and Development Program (2016YFD0800901-03); National Key Technology Research and Development Program of the Ministry of Science and Technology of China (2014BAD08B11); National Natural Science Foundation of China (31601268).

Acknowledgments

Thanks to Guangyan Hui for her assistance.

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Dual-angle technique for simultaneous measurement of refractive index and temperature based on a surface plasmon resonance sensor

Abstract

1. Introduction

2. Temperature effect on SPR

2.1 Temperature effect on metal layer

2.2 Temperature effect on the prism

2.3 Reflectance of SPR sensor

3. Principle of double-incident angle SPR detection

4. Temperature effect on SPR with double-incident angle technique

5. Experimental results and discussion

6. Conclusion

Funding

Acknowledgments

References and links

Cited By

Figures (8)

Equations (17)

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