JP2003014623A - Method of deciding surface plasmon resonance curve for sensing utilizing surface plasmon resonance phenomenon based on asymmetric surface plasmon resonance curve equation - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method by which an asymmetric SPR curve usable for measuring the SPR of gold more appropriately than the equation of the Kretchmann's SPR curve can be decided. SOLUTION: This method is constituted to accurately decide a surface plasmon resonance angle based on the fitting equation of an asymmetric surface plasmon resonance curve derived from the three-layer Fresnel equation for P-polarization at the time of measuring the state of a material, by utilizing a surface plasmon resonance phenomenon by using a surface plasmon resonance sensor system composed of three layers of a prism, a thin metallic film, and a sensing layer.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a method for determining a surface plasmon resonance curve in sensing using the surface plasmon resonance phenomenon by an asymmetric surface plasmon resonance curve equation.

[0002]

BACKGROUND ART As is generally known, a surface plasmon resonance (SPR) sensor is a refractive index generated by specific adsorption or a complex of a host licand formed on a gold thin film and a guest target detection substance. It is a useful analytical tool based on measuring changes. The most well-known SPR sensors are those used to detect macromolecules with specific interactions such as proteins associated with antigen-antibody interactions. In SPR measurement, the SPR curve showing the relationship between the reflectance and the incident angle is a basic concept for analyzing a signal caused by a change in the refractive index. Theoretical SP
Kretschmann was the first to lead the R curve formula,
The curve has what is commonly called the resonance angle at its minimum reflectance. According to the Kretschmann theoretical formula, the SPR signal is obtained by observing the change in the resonance angle. However, Kretschmann's theoretical formula can be applied only to the symmetric SPR curve normally obtained by SPR using silver, and cannot be applied to the asymmetric SPR curve of SPR using gold. To the best knowledge of the inventors, gold SPR is actually more widely used than silver SPR because gold has more favorable chemistry in oxidation than silver, despite the fact that gold SPR is widely used. The optimal theory and concept for SPR has not been fully examined yet.

Conventionally, when actually analyzing data of a gold SPR curve, as a simple method for finding a resonance angle (RA),
The fitting by a quadratic function, the fitting by a higher-order function, the method by the center of gravity, the method by smoothing, and the method by which the point which becomes zero in the first derivative is obtained are applied. Further advanced methods have been proposed, such as a method of partially fitting specific gravity and an optimal linear method.

[0004]

However, unfortunately, none of the conventional methods described above is based on the theory of SPR, and is merely a method for obtaining the minimum value. Valid and accurate SPR data away from the minimum are not used. Therefore, the inventors found an appropriate fitting function based on the SPR theory and found that the gold SPR
We were able to make sensing more sensitive. It is therefore an object of the present invention to provide a method for determining an asymmetric SPR curve that can be used for gold SPR measurement, which is more suitable than the Kretschmann SPR curve equation.

[0005]

In order to achieve the above object, according to the present invention, a surface plasmon resonance sensor system comprising three layers of a prism, a thin metal film and a sensing layer is used, and the surface plasmon resonance phenomenon is utilized. In the method of determining the surface plasmon resonance curve by the asymmetric surface plasmon resonance curve equation in
At least one of the five real numbers B, C, D, and E is a real parameter, s is a characteristic factor of the asymmetric surface plasmon resonance curve, R is the reflectance of light in the surface plasmon resonance sensor system, and r _pms is The amplitude reflectance at the boundary between the prism, the metal thin film, and the sensing layer is represented by k _x
Is the wave vector of the incident light parallel to the boundary surface, k _o is the complex wave number of the surface plasmon theoretically generated at the interface between the metal thin film and the sensing layer when there is no prism, and k _R is the existence of the prism. When the correction term for k _{o is set} , the formula derived from the P-polarized three-layer Fresnel formula It is characterized in that the surface plasmon resonance angle is determined based on the fitting equation of the asymmetric surface plasmon resonance curve represented by. In the fitting of the surface plasmon resonance curve obtained from the experiment, when the reflectance data is R and the incident angle data is X, the above fitting equation is The surface plasmon resonance angle can be determined based on this fitting equation. Also, the angle for the minimum reflectance is And the parameter D, which can be the surface plasmon resonance angle, can be defined as the modified resonance angle.
Further, the observed surface plasmon resonance curve can be processed by software on a computer to determine the resonance angle.

The above fitting equation is R (x) = 1-
α / {(X-β) ² + γ ² } (where R is the reflectance of the incident light, α,
β and γ are real parameters or incident angles. ) Can be used as a more appropriate SPR curve equation than the Kretschmann equation given in. The above equation in the present invention is extremely effective as a function for fitting the SPR curve of SPR using gold.

[0007]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the accompanying drawings. FIG. 1 shows a simple example of a SPR sensor system consisting of three layers of prism-metal-sensing layer structure of Kretschmann Attenuated Total Reflection (ATR) type, which includes a glass prism p, a metal thin film m and a sensing layer s. Suppose that In FIG. 1, θ is the incident angle and d is the thickness of the metal thin film m. When P-polarized light is incident at an incident angle θ (unit radian), the reflectance R of the light is given by the P-polarized three-layer Fresnel equation as follows. In the above equation, γ _pm is the amplitude reflectance at the boundary of the glass prism p-metal thin film m, and γ _pm and γ _pm
ms is given by the P-polarized Fresnel equation. ε _j is the permittivity of medium j. k _jz is the wave number vector of medium j that has a component perpendicular to the boundary surface. k _x is a wave vector component of incident light parallel to the boundary surface, and is given as a real number. d is the thickness of the metal thin film m. ω is the angular frequency of the incident light,
λ is the wavelength and c is the speed of light.

The complex wave number k _o of the surface plasmon generated at the boundary between the metal thin film m and the sensing layer s without the prism p is derived from the following equation with k _x as an unknown variable.

As the simplest approximation, it can be assumed that the SPR phenomenon occurs strongly when the variable k _x equals k _o . k
_{When x} = k _o , the value of γ _{ms in} the equation (3) becomes peculiar (becomes infinite), so the equation (2) can be modified as follows.

The equation (10) can be simply expressed as follows by the four equations (13) to (16). Here, k _R is a correction term of k ₀ when the glass prism p exists. The surface plasmon in the Kretschmann configuration has a complex wave number k _SP given by the following equation. k _sp = k ₀ + k _R (21) Expression (17) is a basic expression when discussing the SPR curve. Two conditions are assumed in the approximation by Kretschmann to derive the symmetric SPR curve equation. That is, Here, φ is a real number. 2 of Expression (22) and Expression (23)
Under one condition, the term ρσ ⁻¹ can be expressed as Here, the mathematical description of χ ′ and χ ″ indicates the real and imaginary parts of the complex number χ, respectively. The SPR curve of equation (25) is (k
It is symmetric about the axis of k _x = k ' _SP because it contains only the second-order term of _x -k' _SP ).

In the present invention, the expression (17) is strictly modified as follows using the five parameters A, B, C, D and E without imposing any condition on the expression (17). it can. Here, the value s is defined as a characteristic factor of the asymmetric SPR curve. The meanings of the parameters in equation (29) for the SPR curve are as follows. A gives the maximum of the SPR curve. B and C contribute to the symmetry and asymmetry of the SPR curve, respectively. D is the modified resonance angle, which is the most suitable variable for observing the refractive index change, as will be explained later. E
Is the imaginary part of the complex wave number of the surface plasmon in the Kretschmann arrangement, and is related to the depth and width of the SPR curve. When compared with the Kretschmann's equation of Equation (25), Equation (29) in the present invention includes a first-order term of k _x -k ' _SP , and is therefore not symmetric about the k _x = k' _SP axis. The expression (29) is more general and appropriate than the Kretschmann's expression because it does not impose any condition on the basic expression (17). As a result, it is more suitable as a fitting function.

In the equation (29), the reflectance is represented by the following equation as the conventional resonance angle θ _min and the minimum reflectance R _min . The approximation shown by is obtained under the condition of B >> CE (> 0).

The principle of SPR analysis is based on the law of conservation of momentum in the real part of evanescent and surface plasmons, and is expressed by the following equation. Here, k _x is the wave number of the evanescent wave generated by the incident light, and k ′ _SP is the real part of the complex wave number of the surface plasmon wave. Equation (39) is a special angle θ given by
Have an _SPR . Therefore, the change in the refractive index of the sensing layer s can be measured based on the following effective formula, which is an approximate formula of the formula (40). In the above equation, n _S is the refractive index of the sensing layer s.
In the Kretschmann approximation formula (25), the angle θ
_{The SPR} is the conventional resonance angle because the reflectance is minimized by the equation (25). However, in the asymmetric equation of equation (29), the conventional resonance angle showing the minimum reflectance is given by equation (36), and therefore the angle θ _SPR is not the conventional resonance angle. Therefore, in this specification, θ _SPR will be referred to as a corrected resonance angle in distinction from the conventional resonance angle that gives the minimum reflectance. In a physical phenomenon, θ _SPR and θ _min are determined by the realization of the momentum conservation law of the evanescent wave and the surface plasmon and the complex number, respectively. The modified resonance angle, θ _SPR, is superior to conventional resonance angles in determining the refractive index change linearly. The reason is that the effective equation given by equation (41) is a better approximation of θ _SPR than θ _min . This is a new concept because it has long been considered that the resonance angle that gives the minimum reflectance is the most suitable for observing the refractive index change of the sensing layer s. The theory of the present invention shows that there is a theoretical limit to accurately determining the linear change in the refractive index by the conventional resonance angle.

Numerical Consideration of Asymmetric SPR Curve Equation in the Present Invention Numerical calculation was carried out using two softwares, Mathematica 4 (manufactured by Wolf resonance angle m Research) and Igor Pull (manufactured by WaveMetrics). Numerical data of theoretical SPR curve obtained by calculation using Mathematica
Igor Pro's curve fitting routine was used to fit the asymmetric SPR curve equation in the present invention. The curve fitting using Igorpur is designed so that the user can set the fitting function, the weight of each point, and the epsilon value for calculating the partial derivative of each coefficient. Igor Pro uses the Levenberg-Marquardt method, which is the standard solution for the problem of finding coefficient values by the nonlinear least-squares method. Weights and epsilon values were automatically selected for all fittings performed in the present invention. According to Igor Pro's instructions weights be to all raw data, epsilon values for each coefficient K, 10 ^{- 10} ×
K.

[0015]

EXAMPLES Hereinafter, experimental examples in which the refractive index of 0, 1, 4, 10, 20% sucrose aqueous solution was measured will be described. Sucrose was purchased from Wako Pure Chemical Industries. The experiment was conducted using a commercially available SPR device (D
KK). In this device, optical elements such as prisms and light sources can be freely changed, and the optical system is a typical Kretschmann ATR arrangement. The prism is
It is a semi-cylindrical prism made of SFL6 glass (manufactured by OHA Resonance Co.) having a high refractive index of 1.80 at 587 nm. As the light source, a light emitting diode (LED) having a half width of 20 nm and a center wavelength of 630 nm and a light emitting diode having a half width of 40 nm and a center wavelength of 88 nm were used. The light is focused through a cylindrical lens into a focused beam, which makes it possible to simultaneously observe a range of angles of incidence on the sensor surface. Charge Coupled Device (CCD) (XC made by SONY
-77) was used to measure the reflected light intensity as a function of incident angle. A linear polarizer was inserted between the prism and CCD to selectively observe the reflected light with p or s polarization. The SPR curve was obtained by dividing the reflected light intensity of p-polarized light by the reflected light intensity of s-polarized light in order to eliminate the uneven distribution of light intensity. SPR
The gold substrate used in the experiment was 51 × 20 mm, 1 mm thick SFL6.
A gold thin film having a thickness of 45 nm is formed on a glass substrate within a range of 20 × 20 mm. In order to improve the adhesion between gold and glass, a chromium layer having a thickness of 5 nm was provided between the gold thin film and the glass substrate. Matching oil was used to reduce the reflectance of the glass surface when fixing the gold substrate to the semi-cylindrical prism.

Next, the asymmetric SPR given by equation (29)
Regarding the curve equation, the effectiveness as an approximate expression and the usefulness as a fitting function will be described. In the computational simulation of the SPR experiment, it was assumed that the refractive index of the aqueous solution was measured using a gold SPR sensor with a high index prism with n _p = 1.80. The typical refractive index n _w of water is n _w = 1.3330 at a wavelength of 589.3 nm and a temperature of 20 ° C.
The effect of dispersion was taken into account for gold, but not for prisms and aqueous solutions. As an optical parameter indicating the dispersion of gold, a Drude model was assumed for the dielectric constant ε _{m of the} metal layer represented by the following equation.

2 and 3, the asymmetric SP of equation (29) is shown.
The result of having investigated the R curve equation about wavelength 600nm and 800nm is shown. FIG. 2 illustrates the numerical calculation of the asymmetric SPR curve equation at an excitation wavelength of 600 nm, and assumes that water with a refractive index of 1.3330 is used to measure the SPR of gold with a prism of high refractive index of 1.80. The graph of FIG. 2A shows the asymmetric SPR curve formula (broken line) given by formula (29) and the complete p-polarization three-layer Fresnel formula (solid line) for the thicknesses of the gold thin films 30, 40. ,
It is a comparison of 5 SPR curves at 50, 60 and 70 nm. The graph in (b) was obtained with a complete formula
An example of fitting the SPR curve (solid line) with the asymmetric SPR curve equation of the equation (29) having unknown variables A, B, C, D and E is shown. The graph in (c) has five parameters
For A, B, C, D, and E, the ratios obtained by fitting are divided by those obtained by equations (30) to (35) of the asymmetric equation.

FIG. 3 shows an asymmetric SPR at an excitation wavelength of 800 nm.
The numerical calculation of the curve equation is illustrated, and the same numerical values as those used in FIG. 2 are used in the calculation except the excitation wavelength. 2 and 3, the solid line shows the prototype SPR curve obtained from the p-polarized three-layer Fresnel equation, and the broken line shows the equation (2
9) is an SPR curve obtained by approximating an asymmetric SPR curve equation using Equations (35) to (35). 30, 40, 50, 60, 70nm
We examined the SPR curve with different gold film thickness. Dashed S
The PR curve and the solid prototype SPR curve are in good agreement when the film thickness is 50, 60, 70 nm in FIG. 2 and when the film thickness is 40, 50, 60, 70 nm in FIG. Is. Approximation
The SPR curve is close to the original SPR curve, but not exactly.

The prototype SPR curves shown by the solid lines in FIGS. 2 and 3 (b) were fitted with an asymmetric SPR curve of Equation 29 having unknown deformations A, B, C, D and E. The fitting is performed in the range of 10 ° of 52-62 ° in FIG.
In FIG. 3 (b), it was performed in the range of 48 ° to 58 °, 10 °. The fitting curve shown by the broken line is not visible because the fitting curve and the prototype SPR curve are in good agreement. This means that the asymmetric SPR curve equation is extremely effective as a fitting function for the SPR curve.

2 and 3 (c), the five parameters A to E obtained by fitting and the asymmetric SPR are shown.
A to E given by equations (30) to (34) of the curve equation
The ratios of the five parameters are shown. Of the five parameters, only parameter D is 1 within 0.2%. The parameter D is particularly important because it gives correct information due to the linear variation of the refractive index of the sensing layer. The exact agreement of the parameter D between theory and fitting is very effective in the approximation, and the asymmetric SP of equation (29)
It shows that the R-curve equation is useful as a fitting function.

In the actual SPR curve for observing the real-time change of the reflection valley of the SPR curve, not the absolute measurement of the angle but the
Relative measurements are usually made. In that case, the asymmetric SPR curve equation given by the equation (29) requires information on the absolute value of the incident angle θ, and is not suitable for numerical calculation in data processing. This problem is a function k _x (θ)
Can be solved by applying the Taylor expansion up to the first order in θ = θ _SPR . Here, X is the incident angle, and a description of replacement is omitted here. This is a fitting function of the Kretschmann SPR equation suitable for actual experiments.

4 and 5 show an evaluation of the usefulness of the asymmetric SPR curve equation of equation (45) as a fitting function for the SPR curve. Figure 4 shows the original SPR with excitation wavelength 6
When calculated using the p-polarized three-layer Fresnel equation at 00 nm,
The curve fitting by the asymmetric SPR curve equation is shown. A 50 nm gold thin film of an aqueous solution with a refractive index of 0.005 intervals from 1.333 to 1.368 is used for the SPR of gold with a 1.80 refractive index prism.
Suppose you measure at. The graph of (a) shows an example of fitting the SPR curve obtained by the calculation indicated by the solid line with the asymmetric SPR curve equation, and the fitted SP
The R-curves are shown by broken lines, but they are almost invisible because they overlap. The graph in (b) shows the fitting parameters.
A, B, C, D, E showing the dependence of the refractive index of the sensing layer,
The fitting parameters are standardized by the parameters shown in Table 1 obtained when the refractive index of the sensing layer is 1.333. The graph in (c) shows the parameters
The modified resonance angle defined as D and the response to the change in refractive index of the conventional resonance angle which gives the minimum value in reflection are shown in equation (47).

FIG. 5 shows the curve fitting by the asymmetric SPR curve equation when the original SPR was calculated using the p-polarization three-layer Fresnel equation at the excitation wavelength of 800 nm, and the numerical calculation was performed except for the excitation wavelength. The same as that used in.

As the SPR curve which is the basis for fitting the asymmetric SPR curve equation, the SPR curve calculated by the p-polarization Fresnel equation at the wavelengths of 600 nm and 800 nm as shown in FIGS. 4 and 5 was used. Calculations show that a gold film with a thickness of 50 nm and a prism with a refractive index of 1.80 is used.
It was assumed that an aqueous solution having a refractive index of 0.005 intervals from 1.333 to 1.368 was measured using SPR. (A) of FIG. 4 and FIG.
In, the original SPR curve is shown by a solid line, and the fitting SPR curve is shown by a broken line. The fitting was also carried out in the range of 52 ° to 62 ° in FIG. 4A and in the range of 10 ° to 48 ° in FIG. 5A. The fitting curve is almost invisible because the original curve and the fitting curve almost overlap. 4 and 5B show the dependence of the fitting parameters A to E on the refractive index of the sensing layer. As shown in Table 1, these five fitting parameters A to E are standardized by the fitting parameters obtained when the refractive index is 1.333.

[0025]

Parameters having a linear correlation coefficient γ such that 1− | γ | <10 ⁻³ are A, D and E in FIG. 4B and D in FIG. 5B. A used in FIGS. 4 and 5B,
Table 2 shows the linear correlation coefficients of B, C, D and E.

[0027]

In both cases, only the parameter D satisfies the condition 1- | γ | <10 ^-4 . That is, the parameter D
Means that it has a linear relationship with respect to the refractive index than other parameters.

The parameter D is shown in FIGS. 4 and 5C.
The modified resonance angle exactly equal to is compared with the conventional resonance angle given by the mathematical expression (47). The two lines of the conventional resonance angle and the corrected resonance angle have a parallel relationship with each other. 4 in (c) of FIGS. 4 and 5
All three straight lines have a linear correlation coefficient γ that satisfies the condition 1− | γ | <10 ⁻⁴ . The results in FIGS. 4 and 5 mean that the asymmetric SPR curve equation of equation (45) is extremely useful as a fitting function for the SPR curve.

On the other hand, the theory of the present invention predicts that the modified resonance angle has better linearity than the conventional resonance angle. FIG. 4C shows that the corrected resonance angle is better than the conventional resonance angle by linear correlation coefficient of 1.9 × 10 ⁻⁵ . In FIG. 5C, the linearity is the same between the modified resonance angle and the conventional resonance angle. This result supports the theory of the present invention.

Further, the effect of the instrumental function on the original SPR curve will be described for an actual SPR experiment. 6 and 7, the device function is included as a convolution of a box-shaped function given by a quadratic expression.

FIG. 6 shows the device function as the original S at an excitation wavelength of 600 nm.
When included in the PR curve, the one fitted to the asymmetric SPR curve equation is shown. An aqueous solution having a refractive index of 0.005 intervals from 1.333 to 1.368 is formed with a gold thin film of 50 nm and a prism refractive index.
It is assumed to measure with a gold SPR of 1.80. FIG. 6A
In the graph of, the SPR curve shown by the solid line is the original SPR curve including the device function, and the SPR curve shown by the broken line is the one fitted by the asymmetric SPR curve equation given by equation (45), The SPR shown is almost invisible because it overlaps with the original SPR curve. The graph in (b) shows the response of the modified resonance angle and the conventional resonance angle to the refractive index.

FIG. 7 shows the instrumental function as the original S at an excitation wavelength of 800 nm.
When included in the PR curve, the one fitted by the asymmetric SPR curve equation is shown, and the numerical values used for the calculation are the same as those used in FIG. 6 except the excitation wavelength. The SPR curve shown by the solid line in FIG. 7A is the original SPR including the device function.
The curve, while the SPR curve shown by the dashed line, shows the fitted asymmetric SPR curve equation. Further, FIG. 7B shows the responses of the modified resonance angle and the conventional resonance angle to the refractive index.

In practice, IgorPro's box-type smoothing algorithm of the software was used. The original SPR curve shown by the solid line in FIG. 6 was obtained from the one in FIG. 4 (a) using the box smoothing algorithm. on the other hand,
The SPR curve which is the basis of (a) of FIG. 7 was obtained from that of (a) of FIG. In FIG. 6A, the fitting curve exactly matches the original SPR curve. On the other hand, in FIG. 7A, the original curve and the fitting curve are only slightly overlapped. Due to the effect of the device function, the difference between the original curve and the fitting function is generated in FIG. 7A, but it is not generated in FIG. 6A. This difference becomes large when the width of the SPR curve is smaller than the width of the device function. That is, the asymmetric SPR curve equation is valid for an SPR curve including a device function when the width of the SPR curve is much larger than the device function. In FIG. 7, the original curve and the fitting curve are only slightly overlapped,
FIG. 7 (b) shows that the asymmetric SPR curve equation is still valid in determining the resonance angle. This means that some difference between the original curve and the fitting curve is acceptable for determining the resonance angle in the fitting function. In (b) of FIG. 6 and (b) of FIG. 7, the corrected resonance angle was better than the conventional resonance angle by linearity of 2.8 × 10 ⁻⁵ and 3 × 10 ⁻⁶ , respectively. This result shows that the modified resonance angle is more suitable for determining the refractive index change more accurately than the conventional resonance angle.

Finally, referring to FIGS. 8 and 9, the asymmetric SP
The R-curve equation will be described based on actual experiments using five concentrations of sucrose aqueous solutions of 0, 1, 4, 10, and 20% by weight. FIG. 8 shows the experimental consideration of the asymmetric SPR curve equation by fitting the SPR curve obtained at the excitation wavelength of 630 nm at concentrations of 0, 1, 4, 10, 20% by weight.
In the graph of (a), the SPR curve of the experiment is shown by the solid line, and the broken line is shown by the formula (4).
5) SP fitted with asymmetric SPR curve equation
The R curve is shown. The graph of (b) shows the refractive index response of the modified resonance angle and the conventional resonance angle, and the modified resonance angle is given as the parameter D in the fitting of the asymmetric SPR equation. The conventional resonance angle is

FIG. 9 shows an experimental consideration of the asymmetric SPR curve equation by fitting the SPR curve obtained at the excitation wavelength of 880 nm, and the concentrations of 0, 1, 4, 1 were measured.
An aqueous sucrose solution of 0 or 20% by weight was used.

The solid line in FIGS. 8 and 9 (a) is 63.
It was obtained in the experiment of 0 and 880 nm excitation wavelength, and the broken line is the fitting curve by the asymmetric SPR curve equation. Table 3 shows that sucrose 0 in FIG.
The five parameters obtained when fitting the wt% SPR curve are shown.

[0038]

It should be noted that, although the theoretical SPR curve and the experimental SPR curve are greatly different due to the optical distortion due to the semi-cylindrical prism or the cylindrical lens and the spectral spread of the light source, the fitting curve is It is in good agreement with the experimental curve. Experimental results show that the asymmetric SPR fitting curve equation in the present invention is most suitable for fitting the gold SPR curve. In other words, it is impossible to exactly fit the experimental SPR curve with fitting of less than 5 parameters, and fitting with more than 5 parameters gives meaningless information on the SPR curve. That is.

FIG. 8 and FIG. 9 (b) are plots of the modified resonance angle equal to the parameter D and the conventional resonance angle as a function of the refractive index of the sucrose aqueous solution at 20 ° C. and 589 nm wavelength. Although the actual measurement conditions in the present invention are clearly different from the wavelength of the reference data, the relative change in the refractive index of the sucrose aqueous solution with respect to pure water is almost the same regardless of the wavelength, and therefore the consideration in the present invention regarding the linear response is correct. Is recognized. In FIGS. 8 and 9B, the corrected resonance angle has a linear correlation coefficient of 2.0 × 10 ⁻⁴ and 1.4 × 10 ⁻⁴ better than the conventional resonance angle. This result shows that the theory of the present invention is more effective in actual experiments than in the case of numerical calculation.

The numerical simulations of FIGS. 2 to 7 and the experimental analyzes of FIGS. 8 and 9 show that the asymmetric SPR curve equation is extremely useful as a fitting function in the SPR curve. Also, to observe that the refractive index of the sensing layer changes linearly, an asymmetric SPR
It is shown that the modified resonance angle obtained by fitting the curve equation as the parameter D is superior to the conventional resonance angle. The fitting function in the present invention is also effective for the SPR curve of the light absorption type SPR.

[0042]

As described above, according to the present invention, the surface plasmon resonance sensor system comprising three layers of prism-metal thin film-sensing layer is used to measure the substance state by utilizing the surface plasmon resonance phenomenon. Equation derived from the P-polarized three-layer Fresnel equation Since it is configured to accurately determine the surface plasmon resonance angle based on the fitting equation of the asymmetric surface plasmon resonance curve represented by, it can be used as a more appropriate SPR curve equation than the expression by Kletschmann, and especially SPR using gold. It is extremely effective as a function for fitting the SPR curve of, and the linear change of the refractive index can be determined from the SPR curve.
It is effective for the asymmetric SPR curve obtained by the SPR sensor, and naturally effective for the deep peak symmetrical SPR curve obtained by the silver SPR. That is, the modified resonance angle, defined as the parameter D in the fitting equation, can be used as an optimal variable for observing linear changes in the refractive index, and thus the method according to the present invention accurately determines the analyte.
Very useful in data processing of SPR equipment.

[Brief description of drawings]

FIG. 1 is a schematic cross-sectional view showing a Kretschmann arrangement composed of a prism-metal-sensing layer interface.

FIG. 2 shows an example of numerical calculation of an asymmetric SPR curve equation at an excitation wavelength of 600 nm, (a) shows an SPR curve comparison between the asymmetric SPR curve equation (dashed line) and the complete p-polarization three-layer Fresnel equation (solid line). (B) is a graph showing the SPR curve (solid line) obtained by a complete equation with unknown variables A, B, C,
A graph exemplifying the case of fitting with an asymmetric SPR curve equation having D and E, and (c) is the one obtained by the fitting with respect to the five parameters A, B, C, D and E. Graph showing the ratio divided by.

FIG. 3 shows a numerical calculation example of an asymmetric SPR curve equation at an excitation wavelength of 800 nm, (a) shows an SPR curve comparison between an asymmetric SPR curve equation (dashed line) and a complete p-polarization three-layer Fresnel equation (solid line). (B) is a graph showing the SPR curve (solid line) obtained by a complete equation with unknown variables A, B, C,
A graph exemplifying the case of fitting with an asymmetric SPR curve equation having D and E, and (c) is the one obtained by the fitting with respect to the five parameters A, B, C, D and E. Graph showing the ratio divided by.

FIG. 4 shows curve fitting by an asymmetric SPR curve equation when the original SPR was calculated using a p-polarized three-layer Fresnel equation at an excitation wavelength of 600 nm, and (a) is calculated by a solid line. A graph showing an example of fitting the obtained SPR curve with an asymmetric SPR curve equation, (b)
Is a graph showing the dependency of the fitting parameters A, B, C, D, and E on the refractive index of the sensing layer, and (c) is the conventional resonance that gives the minimum value at the modified resonance angle and reflection defined as the parameter D. It is a graph which shows the response with respect to the refractive index change of a corner.

FIG. 5 shows curve fitting by an asymmetric SPR curve equation when the original SPR is calculated using a p-polarized three-layer Fresnel equation at an excitation wavelength of 800 nm, and (a) shows the calculation by the solid line. It is a graph showing an example of fitting the obtained SPR curve with an asymmetric SPR curve equation,
(B) is a graph showing the dependence of the fitting parameters A, B, C, D, and E on the refractive index of the sensing layer, and (c) is the modified resonance angle defined as the parameter D and the minimum value at reflection. 5 is a graph showing a response to a change in the refractive index of the conventional resonance angle that gives

FIG. 6 shows the fitting to an asymmetric SPR curve equation when the instrument function was included in the original SPR curve with an excitation wavelength of 600 nm, and (a) is the original SPR curve including the instrument function, which is shown by a solid line. 2B is a graph showing the SPR curve shown by a broken line fitted with the SPR curve and the asymmetric SPR curve equation, and (b) is a graph showing the response to the refractive index of the modified resonance angle and the conventional resonance angle.

FIG. 7 shows the fitting by an asymmetric SPR curve equation when the instrument function was included in the original SPR curve with the excitation wavelength of 800 nm, and (a) is shown by the solid line which is the original SPR curve including the instrument function. 2B is a graph showing the SPR curve shown by a broken line fitted with the SPR curve and the asymmetric SPR curve equation, and (b) is a graph showing the response to the refractive index of the modified resonance angle and the conventional resonance angle.

FIG. 8 shows an asymmetric SPR curve equation obtained by fitting an SPR curve obtained at an excitation wavelength of 630 nm, and experimental consideration by measurement of a sucrose aqueous solution having a concentration of 0, 1, 4, 10, or 20% by weight, (a). Is a graph showing the experimental SPR curve (solid line) and the fitted SPR curve (dashed line) in the asymmetric SPR curve equation, and (b)
6 is a graph showing the refractive index response of a modified resonance angle and a conventional resonance angle.

FIG. 9 shows experimentally an asymmetric SPR curve equation by fitting an SPR curve obtained at an excitation wavelength of 880 nm, (a) shows an experimental SPR curve (solid line) and an asymmetric S
FIG. 6 is a graph showing a fitted SPR curve (dashed line) in the PR curve equation, and FIG. 6B is a graph showing the refractive index response of the modified resonance angle and the conventional resonance angle.

[Explanation of symbols]

p prism m Metal layer s Sensing layer θ incident angle d Metal film thickness

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Kazuyoshi Kurihara             4-1 Idasugiyama-cho, Nakahara-ku, Kawasaki-shi, Kanagawa             305 Claire Maison Oseto F term (reference) 2G059 AA05 BB12 CC16 EE02 EE04                       EE05 GG02 GG04 HH01 HH02                       HH06 JJ11 JJ12 JJ19 KK04                       MM01

Claims (5)

[Claims] 1. A surface plasmon resonance sensor system comprising three layers of a prism, a metal thin film and a sensing layer is used.
A, B, C, D, E in the method of determining the surface plasmon resonance curve in the sensing using the surface plasmon resonance phenomenon by the asymmetric surface plasmon resonance curve equation
Of at least one of the five real numbers of ## EQU1 ## as a real number parameter, s as a characteristic factor of the asymmetric surface plasmon resonance curve, R as the light reflectance in the surface plasmon resonance sensor system, and r _pms as the prism-metal thin film-sensing layer. of the amplitude reflectance at the boundary, the k _x and wave vector parallel incident light on the boundary surface, k _o the theoretically generated surface plasmons at the interface between the metal thin film and the sensing layer in the absence of the prism An equation derived from the P-polarized three-layer Fresnel equation, where complex wave number and k _R are the correction terms for k _o when a prism is present. A method of determining a surface plasmon resonance angle based on a fitting equation of an asymmetric surface plasmon resonance curve represented by. 2. In the fitting of a surface plasmon resonance curve obtained from an experiment, when the reflectance data is R and the incident angle data is X, the fitting equation is The method according to claim 1, wherein the surface plasmon resonance angle is determined based on this fitting equation. 3. The angle for minimum reflectance The surface plasmon resonance angle is defined as
Or the method described in 2. 4. The method according to claim 1, wherein the parameter D is defined as a modified resonance angle. 5. The method according to claim 1, wherein the observed surface plasmon resonance curve is processed by software on a computer to obtain a resonance angle.