SPR sensor system mainly consists of light source, CCD sensor, parallel light path structure and a rotation system. The light source and CCD module are used to realize the output of polarized light and its intensity sensing. The optical path structure uses a silicon reflex mirror being placed parallelly with the bevel surface of the prism. Therefore, the output light is parallel to the incident. The entire parallel light path structure is set on the holey round platform rotating with a stepping motor. The whole system is controlled with Labview software showing in Figure 2.

Fig.2

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	Fig.2 Parallel optical path surface plasmon resonance system

Polarized light source (Hangzhou SPL Photonics Co., Ltd, wavelength 632.8 nm, partial ratio 500∶ 1, output power ≥ 4 mW, power stability ≤ 3%, beam divergence≤ 1.3 mrad); polarizer GCL-05003; Light intensity is detected by CCD sensor with TCD1208 (Toshiba, Japan, pixel spacing 14um, spectral response range of 300~1 000 nm), which has an effective sensing length of 28.672mm. With a USB interface to supply energy and transfer data, it simplifies the optical design. However, although TCD1208 has high accuracy, it is easily saturated. A polarizer is added in the light path to adjust the light intensity as well as to ensure thatthe reflected light intensity is in the linear detecting range.

With the parallel light path design, the incident angle is changed under the condition that the output/incident lights are parallel to each other. A silicon reflex mirror is used to change the optical path. With the coated reflex film on the surface of the mirror, little light energy is lost during the reflection. The prism is made of K9 glass (Spectral analysis optics: Refractive index: 1.516 8, Abbe number: 63.96, Poisson ratio: 0.21).

In order to ensure the parallelism of the output light and the incident, the optical path should pass through the geometric center of the mirror and sensing metal film. With a holey platform to place the whole structure, it is suitable for the preliminary adjustment of the optical pathwhich is adjusted precisely with the screws of the columns (figure 3). With a stepping motor, the incident angle shifts with the accuracy of one-tenth thousandth degree.

Fig.3

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	Fig.3 Adjustable parallel light path system

To study the temperature property, the temperature is controlled with a semiconductor TEC chip. With an APT platinum resistance temperature sensor, a closed-loop temperature control system is constructed.

First, the bevel surface of K9 prism is cleaned with ultrapure water and dry with nitrogen. Then, the gold sensor film is coupled to the surface with cedar oil (RI, 1.515 2~1.517 1). PDMS flow cell and TEC are pressed to the surface of gold film, a sealed liquid detecting channel is formed. Analytes can be injected into the flow cell with a pump. When changing the incident angle and monitoring the reflectance intensity with CCD sensor, resonance curves can be obtained.

2.2.1 Measurement of glucose mass concentration

SPR resonance curves are measured with different mass concentrations from 5% to 40%. Each sample is separated with air. And the temperature is controlled at 20 ℃, as is shown in Fig.4.

Fig.4

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	Fig.4 Resonance curves with different mass concentrations

It can be seen that, the resonance curves shift to the right with the increase of concentration, and the resonance angles increase. Detail analysis shows that there is a linear relationship between the resonance angle and the mass, and the fitting equation can be obtained from Fig.5 as:

y=0.1402x+67.3141

x represents the mass percentage in units of %.

Fig.5

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	Fig.5 Fitting curve between the resonance and mass concentration

2.2.2 The analysis of temperature dependence RI

Temperature change affects the SPR system, and the resonance angle. With the 40% glucose solution being injected, the temperature is changed and the resonance curve is detected to measure the resonance angle, as is shown in Fig.6. A linear temperature dependence resonance can be obtained:

y=-0.0125x+73.0944

y is the resonance angle, x represents the temperature in units of ℃.

Fig.6

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	Fig.6 Fitting curve between the resonance and temperature

The temperature influence on the SPR sensor system is complex. According to the Drude model, the frequency-dependent dielectric function of the sensor film can be represented as:

ε(ω)=(nr+jni)2=1-ωp2ω(ω+iωc)

ε is the metal dielectric permittivity. n_r and n_i are the real and imaginary parts, respectively. As a result of the volumetric effects, plasma frequency ω _p can be calculated as

ωp=ωp0[1+γ(T-T0)]-12

Where γ , T₀ and ω _p0 are the metal expansion coefficient, reference temperature, and the plasma frequency at the reference temperature.

ω _c is called the collision frequency and can be affected by temperature variation in two aspects: phonon-electron scattering (ω _cp) and electro-electron scattering (ω _ce)^{[9, 10]}.

ωcp(T)=ω025+4T5TD5∫0TD/Tz4dzez-1

Here T_D is Debye temperature, and ω ₀ is a constant related to the electric conductivity.

ωce(T)=π4ΓΔ6ћEF(kBT)2+ћω4π22

Where Γ , Δ , ћ , E_F and k_B are all constants, representing the average over the Fermi surface of scattering probability, the fractional umklapp scattering, the Planck’ s constant, the Fermi energy and the Boltzmann constant, respectively.

The metal layer thickness d is also affected by temperature^[11].

d=d01+(T-T0)γ1+μ1-μ

Here μ is Poisson’ s number of the film material. d₀ is the thickness at the reference temperature T₀, taking 50 nm at 300 K in our calculation.

According to the Fresnel equations and Maxwell theory, the reflectance R of the prism-based SPR sensor can be expressed as:

R=rpm+rmaexp(2idkmz)1+rpmrmaexp(2idkmz)2rij=kzi/εi-kzj/εjkzi/εi+kzj/εjkzi=2πλεi-ε0(sinθ)2

r_ij is the reflective coefficient of p-polarized light at the boundary between media i and j.

Detail scenarios for the dependence of SPR resonance shift on the simultaneous variation of RI and temperature are shown in Fig.7.

Fig.7

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	Fig.7 SPR resonance shift versus the RI and temperature

It can be seen that, the line surface of the relationships governing the resonance angle changes versus RI vasiation and temperature change is almost an inclined plane, which reveals that the resonance angle changes linearly with both the temperature and the RI. Fitting lines for resonance angle versus RI at different temperatures and its linear coefficients are calculated theoretically, as is shown in Fig.8 and Fig.9, respectively.

Fig.8

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	Fig.8 Fitting lines for the resonance angle versus RI at different temperatures (RI range: 1.33~1.346)

Fig.9

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	Fig.9 The variation of SPR resonance sensitivity with RI at different temperatures (RI range: 1.33~1.346)

From the figures, it is observed that, with the temperature shift from 270 to 380 K, the little change of linear coefficient between the resonance and RI is 0.75/130.875. Further calculation reveals the resonance angle changes linearly with temperature at different RIs, and the linear coefficients also change very small. Then, when ignoring the tiny changes of the line-fitting sensitivities in a detecting range, the dependences of SPR resonance shift on RI and temperature are quite linear

and independent from each other. Therefore, a sensitivity matrix M can be constructed to measure the resonance shift versus the simultaneous changes of RI and temperature^{[12, 13]}.

ΔA=MΔnΔT=[mn mT]ΔnΔT

Where Δ A, Δ n and Δ T represent resonance shift, RI change and temperature variation. Note that glucose mass concentration corresponds linearly with its RI. Therefore, when ignoring the tiny changes in the linear coefficients, the resonance angle shift can be expressed as^[14]:

ΔA=[0.1402 -0.0125]ΔZΔT

Δ Z and Δ T represent the mass concentration and temperature variation in units of % and ℃, respectively. This approach is very accurate when the dependences of SPR resonance on both temperature and RI are linear and the changes of linear coefficients are small.