JP2010044155A - Method for designing plasmonic crystal - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for designing a plasmonic crystal which causes a plasmonic band gap in optional energy. <P>SOLUTION: In the method for designing a plasmonic crystal, the arrangement cycle Λ of a plasmon crystal formed on the surface of a metal 100 in the interface between a dielectric material and the metal 100 is determined according to a dispersion relation in the interface of a surface plasmon polariton and the Bragg reflection conditions of the surface plasmon polariton which are represented by equation (1), wherein kspp represents the wave number of the surface plasmon polariton (SPP), and A represents an arrangement cycle. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for designing a plasmonic crystal. More specifically, the present invention relates to a plasmonic crystal design method capable of generating a plasmonic band gap at an arbitrary energy by determining an arrangement period of plasmon crystals under a predetermined condition.

  “Surface Plasmon Polariton (SPP)” is a close-packed wave of electrons existing at the interface between metal and dielectric, and is a surface electromagnetic wave propagating through the metal-dielectric interface. When there is a periodic “grating structure” on the metal surface at the metal-dielectric interface, the SPP is black reflected by the grating at a certain wavelength and propagates in the opposite direction to produce a standing wave. This lattice structure is also referred to as “uneven structure” or “relief structure”.

  In an SPP that has become a standing wave, the electric field is localized in the antinode. The SPP that has become a standing wave generates two different energy states depending on the relative phase with the lattice. As a result, an energy gap called “plasmonic band gap” appears in the dispersion curve of SPP.

  A periodic relief structure of a metal surface that causes a plasmonic band gap to appear is called a “plasmonic crystal”. Since plasmonic crystals can be expected to control the radiation field and to enhance the electric field, a wide range of research is being conducted from basics to applications. Non-Patent Document 1 reports an attempt to enhance the emission intensity of a dye by depositing a dye thin film on a plasmonic crystal. Such a technique for enhancing dye emission utilizing the localization and enhancement of the electric field at the plasmonic band gap edge (hereinafter also simply referred to as “gap edge”) is called a plasmonic band gap laser. Plasmonic bandgap lasers are expected to lead to the development of organic EL devices that can achieve high luminous efficiency.

  On the other hand, in recent years, sensors using SPP have been used to detect interactions between various substances. This sensor is called a “Surface plasmon resonance (SPR) sensor”.

  When the deflected light is incident on the metal-dielectric interface under total reflection conditions to excite the SPP, a leaching component called an evanescent wave is generated at the interface. Under the total reflection condition, normally, the energy of the incident light becomes the energy of the reflected light with almost no loss. However, under wave number matching conditions where the wave numbers of the evanescent wave and the SPP match, the energy of the incident light is used for excitation of the SPP, SPR occurs, and the energy of the reflected light decreases. This energy change of the reflected light can be detected as a change in the wave number of the reflected light with respect to the incident light.

  Since the wave number matching condition depends on the incident angle θ of the incident light, if the wave number of the reflected light is detected while changing the incident angle θ, SPR occurs at a certain angle, and the change in the wave number is maximized. This angle is called “resonance angle θsp”, and the wave number of reflected light at the resonance angle θsp is called “peak wave number (or absorption peak)”.

  Since the resonance angle θsp depends on the dielectric constant of the dielectric, the change in the resonance angle θsp and the peak wave number (hereinafter referred to as “shift”) corresponds to the change in the dielectric constant of the dielectric. Therefore, the change in the dielectric constant of the sample caused by the interaction between the substances can be detected by detecting the shift of the peak wave number using the sample containing various substances as the dielectric.

  Since an SPR sensor detects an interaction between substances in a sample by a change in dielectric constant, it does not require labeling of substances with radioactive substances or fluorescent substances, and can perform sensitive detection. For this reason, the SPR sensor is particularly suitably used as a biosensor for evaluating the interaction of in vivo substances such as proteins and nucleic acids. Patent Document 1 discloses an SPR sensor as an optical biosensor device.

Japanese Patent No. 3294605 Applied Physics Letters, 2004, Vol.85, p.3968-3970

  In the SPR sensor, the change in the dielectric constant of the sample, that is, the interaction between substances in the sample is detected by detecting the shift of the peak wave number. However, when trying to detect interactions between substances with extremely low molecular weights or ultra-trace quantities, the change in the dielectric constant is so small that the peak wave number shift is below the detection limit, and sufficient measurement sensitivity is achieved. In some cases, it could not be obtained.

  Therefore, a main object of the present invention is to provide a plasmonic crystal design method that can be a basic technology for increasing the sensitivity of an SPR sensor.

In order to solve the above problems, the present invention relates to the disposition relationship of plasmon crystals formed on the metal surface at the interface between the dielectric and the metal, the dispersion relationship of the surface plasmon polariton at the interface, and the surface represented by the following formula (1): Provided is a plasmonic polariton Bragg reflection condition and a plasmonic crystal design method that is determined according to the Bragg reflection condition.
In this design method, by determining the arrangement period according to the dispersion relation and the Bragg reflection condition under an arbitrary incident light frequency condition and dielectric permittivity condition, a plasmonic band is obtained at a frequency matching the incident light frequency. A plasmonic crystal having a gap end can be obtained. At this time, it is preferable to employ a surface plasmon resonance Kretschmann arrangement composed of a dielectric, a metal, and a prism.
This design method can be applied to increase the sensitivity of the surface plasmon resonance sensor by forming the obtained plasmonic crystal on the metal surface at the interface between the sample and the metal of the surface plasmon resonance sensor. This design method can also be applied to enhance the emission intensity of the dye by depositing a dye thin film on the resulting plasmonic crystal.

  In the present invention, the “plasmonic band gap” refers to an energy gap that appears in the dispersion curve of SPP at the dielectric / metal interface where the plasmon crystal is arranged, and the “plasmonic band gap end” refers to the plasmonic band gap. It means the high energy side end (upper end) and / or the low energy side end (lower end).

  By determining the arrangement period of the plasmon crystal under a predetermined condition, a plasmonic crystal design method capable of generating a plasmonic band gap at an arbitrary energy is provided.

  In the SPR sensor, the change in the dielectric constant of the sample is detected by detecting the shift of the peak wave number. Accordingly, when detecting a constant dielectric constant change, the greater the peak wave number shift due to the dielectric constant change, the higher the sensitivity of detecting the dielectric constant change.

  Therefore, this time, the present inventors pay attention to the above-mentioned plasmonic band gap, and enhance the shift of the peak wave number with respect to a constant dielectric constant change by using the change in the slope at the gap end of the dispersion curve of SPP. I thought.

FIG. 1 is a diagram for explaining the concept of increasing the sensitivity of an SPR sensor using a plasmonic band gap. The figure shows the peak wave number shift when the dielectric constant of the dielectric changes from ε _s1 to ε _s2 in the SPR sensor. In the figure, symbol G indicates a plasmonic band gap.

When the dielectric constant of the dielectric is ε _s1 , the peak wave number when the plasmonic crystal is arranged on the metal surface at the interface with the dielectric is a solid line, and the peak wave number when there is no plasmonic crystal is the dotted line Show. When the frequency of the incident light is matched with the angular frequency ω + at the gap end (the upper end on the high energy side), the peak wave number k ' ₁ when the plasmonic crystal is arranged is the peak wave number when there is no plasmonic crystal compared to the k _1, it appears in the low-frequency side. That is, “k ′ ₁ <k ₁ ”.

When the dielectric constant of the dielectric changes to ε _s2 and the peak wave number in the incident light of the same frequency is k ₂ , the peak wave number shift S ′ when the plasmonic crystal is arranged is “k ₂ -k ′ ₁ ” It becomes. In addition, shift S of the peak wave number of the case where there is no plasmonic crystal is "k ₂ -k _1".

Here, since “k ′ ₁ <k ₁ ”, “k ₂ −k ′ ₁ > k ₂ −k ₁ ” is obtained, and the peak wave number shift S ′ (k ₂ −k ₁ when a plasmonic crystal is arranged) _'1) and the peak wave number of the case where there is no plasmonic crystal shift S (k ₂ -k ₁₎ is, "S'a>S". That is, by arranging the plasmonic crystal at the interface with the dielectric, it is possible to amplify the shift of the peak wave number accompanying the change in the dielectric constant from ε _s1 to ε _s2 of the dielectric.

  In this way, by arranging a plasmonic crystal at the interface with the dielectric and detecting the peak wave number shift using incident light having a frequency at the gap end, the peak wave number shift with respect to a constant permittivity change can be further increased. Large detection is possible, and the detection sensitivity of the change in dielectric constant can be increased.

  However, in order to perform such high-sensitivity detection in an ordinary SPR sensor, a plasmonic crystal whose frequency at the gap end matches the frequency of incident light provided in the sensor is prepared in advance, and the metal surface It is necessary to arrange in the.

  As a result of studies to produce a plasmonic crystal having a gap edge frequency that coincides with an arbitrary incident light frequency, the present inventors have found a predetermined condition that can provide such a plasmonic crystal, and the present invention. The design method of the plasmonic crystal related to was completed. That is, the present inventors arbitrarily determined the arrangement period of the plasmon crystal according to the dispersion relation of SPP at the interface between the dielectric and the metal and the Bragg reflection condition of SPP shown in the following formula (1). It was clarified that a plasmonic crystal having a plasmonic bandgap edge at a frequency that coincides with the incident light frequency was obtained.

  In this plasmonic crystal design method, the arrangement period is determined according to the SPP dispersion relation and the Bragg reflection condition under any incident light frequency condition and dielectric permittivity condition, so that the plasmonic crystal is plunged to a frequency that matches the incident light frequency. It is possible to obtain a plasmonic crystal having a monic band gap edge.

  Hereinafter, a preferred embodiment for carrying out the present invention will be described with reference to the drawings, taking as an example a surface plasmon resonance Kretschmann arrangement widely used for excitation of SPP. In addition, embodiment described below shows an example of typical embodiment of this invention, and, thereby, the range of this invention is not interpreted narrowly.

  FIG. 2 is a schematic diagram for explaining the arrangement period of plasmonic crystals in the design method according to the present invention. The surface plasmon resonance Kretschmann arrangement is composed of dielectric / metal / prism. In FIG. 2, reference numeral 12 denotes a prism, reference numeral 100 denotes a metal, and reference numeral 102 denotes a plasmonic crystal formed on the surface of the metal on the dielectric side.

  In FIG. 2, symbol Λ indicates the relief arrangement period in the periodic relief structure of the plasmonic crystal 102. When this arrangement period Λ satisfies a predetermined condition, the SPP generates a standing wave, and the electric field is localized at the antinode.

  The SPP that has become a standing wave can take two energy states, angular frequencies ω + and ω−, as shown in the upper and lower parts of FIG. As a result, a plasmonic band gap having angular frequencies ω + and ω− at the upper and lower ends of the gap is generated in the dispersion curve of the SPP (see FIG. 1).

  When a plasmonic band gap occurs, SPPs with frequencies in the gap are prohibited from propagating. At the gap end, the slope of the dispersion curve (dω / dk) becomes 0, the group velocity becomes 0, and a large electric field enhancement occurs due to the confinement of the SPP.

  At this time, the arrangement period Λ is formed so as to satisfy the SPP dispersion relation at the dielectric / metal 100 interface and the Bragg reflection condition of the SPP at the same time, so that the frequency of the incident light coincides with the angular frequency ω + at the upper end of the gap. It becomes possible to make it. That is, it is possible to obtain a plasmonic crystal having a gap end (upper end) at a frequency that matches the incident light frequency under any incident light frequency condition and dielectric permittivity condition.

  Next, a specific procedure of the plasmonic crystal design method according to the present invention will be described.

  First, an SPP dispersion relationship is obtained under predetermined incident light frequency conditions and dielectric permittivity conditions. The reflected light intensity in the three-layer system of dielectric / metal / prism is calculated using the Fresnel equation and the multi-wave interference equation, and the SPR curve is obtained under any incident light wavelength and dielectric constant conditions. Then, the dip angle is plotted against the incident light wavelength to obtain the dispersion relationship of SPP.

  Next, an SPP Bragg reflection condition is obtained under a predetermined incident light frequency condition. The Bragg reflection condition is expressed by the following formula (1). Here, “kspp” is the wave number of the SPP, but is the same as the wave number of the dielectric / metal interface.

  In this way, the SPP dispersion relation and the Bragg reflection condition that the arrangement period Λ should satisfy can be obtained. A plasmonic crystal having a gap edge (upper end) at a frequency matching the incident light frequency can be obtained by obtaining an arrangement period Λ that satisfies these conditions under any incident light frequency condition and dielectric permittivity condition. .

  Therefore, for example, by designing in advance a plasmonic crystal having a gap end frequency that matches the frequency of incident light provided in the SPR sensor and forming it on the metal surface at the interface between the sample of the sensor and the metal, It is possible to detect the shift of the peak wave number with respect to a constant dielectric constant change more greatly and increase the detection sensitivity of the dielectric constant change.

  In general, the sensitivity of the SPR sensor increases as the wavelength of incident light increases. The sensitivity of the sensor can be further improved by determining the arrangement period of the plasmonic crystal in accordance with this long wavelength incident light by the plasmonic crystal designing method according to the present invention. Note that the frequency of the gap edge of the plasmonic crystal does not need to exactly match the frequency of the incident light of the SPR sensor. If a plasmonic crystal is used in which the incident light has higher energy than the gap edge, Sensitivity can be increased.

  Furthermore, the method for designing a plasmonic crystal according to the present invention uses not only high sensitivity of the SPR sensor but also localized / enhanced energy to excite various substances with high efficiency or to react between substances. It can be applied to various applications for the purpose of promoting. That is, according to the plasmonic crystal design method according to the present invention, by determining the arrangement period of the plasmon crystal under a predetermined condition, a plasmonic band gap is generated at an arbitrary energy (frequency), and the energy Can be localized and enhanced. For this reason, this design method uses specific energy that is localized and enhanced, for example, to efficiently excite a dye thin film deposited on a plasmonic crystal and enhance the emission intensity of the dye. Applicable. Further, for example, it is possible to use a specific frequency that is localized and enhanced to promote the reaction of the photoresist on the plasmonic crystal and to improve the resist drawing accuracy.

<Example 1>
1. Prediction of arrangement period of plasmonic crystal In the Kretschmann configuration (see Journal of Applied Physics, Vol.79, p.7383-7385) where SPP is coupled using a prism, the conditions under which SPR occurs (SPP dispersion relationship) and SPP We estimated a system that satisfies both the plasmonic crystal couple condition (Bragg reflection condition).

  As the metal thin film, a plasmonic crystal in which a periodic relief structure was formed on an Au 45 nm / BK7 substrate was used. The surface dielectric layer was air (n = 1) or pure water (n = 1.33).

  The reflected light intensity in the three-layer system of surface dielectric layer / metal thin film / prism was calculated using the Fresnel equation and the multiwave interference equation, and the SPR curve was obtained at any incident light wavelength and dielectric constant conditions ( (See Kazuyoshi Kurihara et al., Bunseki, 2002, 4, p.161-167). FIG. 3 shows an SPR curve when the incident light wavelength is 770 nm and the surface refractive index is 1. The dip angle was plotted against the incident light wavelength to obtain the SPP dispersion relationship.

  On the other hand, the Bragg reflection condition of SPP in an arbitrary crystal is given by the following formula (1).

  FIG. 4 shows the SPP dispersion relation and the Bragg reflection condition when the arrangement period of the relief structure of the plasmonic crystal is 280 nm. The condition that satisfies the SPP dispersion relation and the Bragg reflection condition at the same time was assumed to be a condition for generating a plasmonic band gap. And the arrangement period of the plasmonic crystal which satisfy | fills this condition with respect to arbitrary incident light wavelengths was calculated, and the arrangement period which produces a plasmonic band gap was determined. FIG. 5 shows the arrangement period with respect to the incident light wavelength calculated in the arrangement period of 200 to 350 nm.

<Example 2>
2. Verification of Plasmonic Crystal Arrangement Period that Generates Plasmonic Band Gap for Arbitrary Incident Wavelength About Plasmonic Crystal Arrangement Period determined in Example 1, the plasmonic band gap was measured and the assumption was verified. .

(1) Measurement of band gap using white light Plasmonic crystal with a surface dielectric layer of air (n = 1) and a relief structure with an arrangement period of 180 to 340 nm under the condition of wavelength 347 to 784 nm Was used to measure the plasmonic band gap. The relief structure of the plasmonic crystal was fabricated in steps of 10 nm from 180 to 340 nm.

  On a 0.7 mm thick BK7 substrate, Au 45 nm was vapor-deposited with Cr 1 nm sandwiched as an adhesive layer. Using PMMA as a resist, a relief structure was drawn on the gold surface using an EB exposure apparatus ELS-7500. After development, 30 nm of Au was evaporated and PMMA was lifted off. FIG. 6 shows an electron micrograph of a plasmonic crystal in which a relief structure was produced with an arrangement period of 180 nm.

  The substrate on which the plasmonic crystal was produced was placed on the bottom surface of a semicylindrical prism made of BK7 via a refractive liquid. A tungsten lamp was used as the light source, and light coupled to the fiber was incident from the prism side, and the reflected light was guided to the CCD spectrometer using the fiber to obtain a spectrum. FIG. 7 shows an outline of the experimental apparatus.

  The SPP dispersion relation and plasmonic band gap were measured by measuring the reflected light spectrum while scanning the incident angle of incident light by 0.2 degrees from 41 degrees to 50 degrees.

  FIG. 8 shows the results of measuring the reflected light spectrum at each incident angle of the plasmonic crystal having a relief structure with an arrangement period of 280 nm. The figure shows the result of normalization using the reflected light spectrum at an incident angle of 40 °. In the figure, the dotted line indicates the wavelength of incident light predicted from the relationship between the incident wavelength determined in Example 1 and the arrangement period, and indicates the incident light wavelength that causes a plasmonic band gap in a plasmonic crystal with an arrangement period of 280 nm. .

  As shown in FIG. 8, on the low angle side, in addition to the main peak, a second peak is seen around 595 nm, and on the high angle side, a peak is seen around 610 nm. This is a peak that cannot be seen on a flat gold substrate without a relief structure, and is considered to be a split of the peak due to a plasmonic band gap. The appearance wavelength of the plasmonic band gap coincided with the wavelength of incident light predicted from the relationship between the incident wavelength determined in Example 1 and the arrangement period.

  Similarly, FIG. 9 shows the SPP dispersion relationship obtained by actually measuring the plasmonic band gap in a plasmonic crystal having a relief structure with arrangement periods of 300, 320, and 340 nm. FIGS. 9A to 9D show SPP dispersion relationships of plasmonic crystals with relief structures having arrangement periods of 280, 300, 320, and 340 nm, respectively.

  In the plasmonic crystal in which the relief structure having the arrangement period of 300 nm shown in FIG. 9A is fabricated, peak splitting due to the plasmonic band gap is confirmed from around 595 nm to around 610 nm.

  Table 1 summarizes the energy of the plasmonic band gap obtained for the plasmonic crystals of each arrangement period.

  Further, FIG. 10 shows the predicted value from the relationship between the incident wavelength and the arrangement period determined in Example 1, and the actual measurement in this example, for the energy of the plasmonic band gap obtained for the plasmonic crystal of each arrangement period. The result of comparing with the value is shown.

  FIG. 10 confirms that the predicted value of the plasmonic band gap energy and the measured value are in good agreement for the plasmonic crystals of each arrangement period. From the above results, it was confirmed that the prediction by the theoretical calculation on the band gap energy of the plasmonic crystal was effective.

(2) Actual measurement of SPR in the vicinity of the plasmonic band gap edge According to the theoretical prediction based on the relationship between the incident wavelength and the arrangement period determined in Example 1, the energy of the incident wave (single wavelength) hits the plasmonic band gap edge. Such a plasmonic crystal can be produced. In this example, the behavior of the SPR curve near the end of the plasmonic band gap was measured.

  Assuming that the dielectric constant of the surface dielectric layer is n = 1.33 (pure water), the arrangement period of the plasmonic crystal with respect to the incident wave wavelength of 770 nm was predicted to be 275 nm. SPR measurements were performed using plasmonic crystals with relief structures with arrangement periods of 250, 260, 270, 280, and 290 nm. The SPR measurement was performed by attaching a PDMS microchannel on a plasmonic crystal chip and flowing pure water over the plasmonic crystal. The measuring device used was an SPR sensor from Fluidware Technology.

  FIG. 11 shows the obtained SPR curve. A decrease in peak intensity was observed for plasmonic crystals with 270 nm and 280 nm arrangement periods across the predicted value of 275 nm. This is thought to be the result of the fact that the incident wave with a wavelength of 770 nm is prohibited from propagating in the plasmonic crystal due to the presence of the plasmonic band gap, and the absorption of light energy into the gold thin film does not occur. From the above results, it can be said that the plasmonic band gap was successfully captured by angle scanning (wavelength fixing).

  As described above, in Examples 1 and 2, first, the plasmonic band gap is used under an arbitrary incident wavelength condition, so that the SPR occurs and the SPP causes the Bragg reflection, the plasmonic band gap occurs. Predicted. Then, in the SPR sensor with Kretschmann arrangement, a plasmonic crystal satisfying this condition was actually fabricated and verified. As a result, we succeeded in capturing the plasmonic band gap in an angle-scanning SPR sensor using monochromatic light by controlling the wavelength at which the band gap appears.

  The plasmonic crystal design method according to the present invention is effectively used to increase the sensitivity of an SPR sensor. In addition, the plasmonic crystal obtained by this design method is also effectively used for plasmonic band gap laser and fine drawing of a photoresist.

It is a figure for demonstrating the concept of high sensitivity of the SPR sensor using a plasmonic band gap. It is a schematic diagram for demonstrating the arrangement period of the plasmonic crystal in the design method which concerns on this invention. FIG. 6 is a diagram showing an SPR curve calculated using a Fresnel equation and a multi-wave interference equation in a three-layer system of surface dielectric layer / metal thin film / prism, and obtained with an incident light wavelength of 770 nm and a surface refractive index of 1. . It is a figure which shows the SPP dispersion | distribution relationship and Bragg reflection conditions when the arrangement period of the relief structure of a plasmonic crystal is 280 nm. It is a figure which shows the arrangement | positioning period (200-350 nm) of the plasmonic crystal which satisfy | fills SPP dispersion | distribution relation and Bragg reflection conditions with respect to arbitrary incident light wavelengths. FIG. 5 is a drawing-substituting photograph showing an electron micrograph of a plasmonic crystal having a relief structure with an arrangement period of 180 nm. FIG. 3 is a diagram showing an outline of an experimental apparatus used in Example 2. It is a figure which shows the result of having measured the reflected light spectrum in each incident angle of the plasmonic crystal which produced the relief structure of arrangement | positioning period 280 nm. The SPP dispersion relation obtained by actually measuring the plasmonic band gap is shown for a plasmonic crystal having a relief structure with arrangement periods of 280, 300, 320, and 340 nm. (A)-(D) show the SPP dispersion relationship of plasmonic crystals produced with relief structures having arrangement periods of 280, 300, 320, and 340 nm, respectively. Regarding the energy of the plasmonic band gap obtained for the plasmonic crystals with arrangement periods of 280, 300, 320, and 340 nm, the predicted value from the relationship between the incident wavelength and the arrangement period determined in Example 1 and the actual measurement in Example 2 It is a figure which shows the result of having compared with the value. It is a figure which shows the SPR curve obtained by performing SPR measurement using the plasmonic crystal which produced the relief structure of the arrangement period of 250, 260, 270, 280, 290 nm.

Explanation of symbols

100 metal
102 Plasmonic crystal
12 Prism

Claims (5)

The arrangement period of the plasmon crystal formed on the metal surface at the interface between the dielectric and the metal is determined according to the dispersion relation of the surface plasmon polariton at the interface and the Bragg reflection condition of the surface plasmon polariton represented by the following formula (1) To design plasmonic crystals.
  By determining the arrangement period according to the dispersion relation and the Bragg reflection condition under any incident light frequency condition and dielectric permittivity condition, a plasmonic having a plasmonic band gap edge at a frequency matching the incident light frequency The design method according to claim 1, wherein a crystal is obtained.   3. The design method according to claim 2, wherein, in a surface plasmon resonance Kretschmann arrangement composed of a dielectric, a metal, and a prism, the arrangement period is determined according to the dispersion relation and the Bragg reflection condition.   A method for increasing the sensitivity of a surface plasmon resonance sensor by forming a plasmonic crystal obtained by the design method according to claim 1 on a metal surface at an interface between a sample of the surface plasmon resonance sensor and a metal. A method for enhancing the emission intensity of a dye by depositing a dye thin film on a plasmonic crystal obtained by the design method according to claim 1.