Title of Invention

A METHOD OF CARRYING OUT A SURFACE PLASMON RESONANCE (SPR) MEASUREMENT USING A SURFACE PLASMON RESONANCE DEVICE

Abstract

This invention relates to an optical phenomena that concerns with the resonant excitation iif of "Surface Charge Density" wave (also referred to as surface plasmon wave), at the I interface of highly conducting metal and insulating sample materials, using a 'total I internally reflecting p type polarized' light wave.In this invention the authors claims of a new SPR parameter that can be of fundamental importance for the study and analysis of the SPR phenomena as well as the devices that work based on the SPR effect. For convenience, it is designated as '4 K'. it is shown that the angle of incidence and the reflectance values of every point on the SPR spectrum when mapped into corresponding new state parameters ,~8, and 'L' respectively the new SPR parameter '4K' provides a simple link between them and the resulting explicit expression ~8 2 =.1/ L K R (~8) is proposed as a new formalism for the Plasmon Resonance Curve. The advantage of the proposed new parameter is that it provides a simple connection between the real and the imaginary parts of the metal dielectric function and can be estimated from the spectrum without the need for a curve fitting procedure as well as actual thickness of the metal film. Its knowledge can be of immense use in study of optical properties of ultra thin metal films as well as in the study of absorption properties of the ultra thin absorbed overlayers of samples on the metal surface. It also facilitates, inversion of device reflectance into its corresponding angular detune with utmost ease and lifts the need for expensive angle measuring gadgets or persona D1Puters in displacement measunng applications.

Full Text

This invention relates to a method of carrying out a surface plasmon resonance (SPR) measurement using a surface plasmon resonance device and also to a method for determining the dielectric function (Sa) of a material or the thin films of metals from the said surface plasmon resonance (SPR) measurement. This invention relies on a new "SPR" Parameter which is of fundamental importance for the study & analysis of the Phenomena of Surface Plasmon Resonance and the application of the devices that work on this principle. For convenience it is designated as *4K". It provides a simple link between the angle of detune A© and a state parameter of the device L, in the New Formalism for the Plasmon Resonance Curve of a Surface Plasmon Resonance Device, proposed by the investigators. The proposed formalism is an explicit expression for A0 given by A0 = 4 L.K.R (A0); It facilitates inversion of device-reflectance, into the corresponding angular detune with utmost ease and lifts the need for either an angle measuring gadget or a personal computer for this purpose. This formalism can pave way for a new technology for the SPR based systems for variety of conventional and unconventional applications. In addition, the new SPR parameter "K" also facilitates study of the dielectric function of the metal films using the phenomena of SPR. "Surface Plasmon Resonance (SPR)" is an angularly selective mode-coupling phenomenon, which leads to the excitation of "Surface Plasmon (SP) Waves" at Metal-Dielectric interfaces, when the experimental conditions become favourable. Devices based on these phenomena are becoming increasingly popular as sensitive diagnostic tools for the study of the materials and their interfaces. A three-layer stack comprising of a thin layer of a suitable metal sandwiched between a pair of dielectric materials is often utilized for their operation. A coherent light beam undergoing "total internal reflection" at one of the interfaces of such a stack excites SP Waves at the other at a characteristic angle of incidence known as "Plasnmon angle or SPR angle - (0j) In presence of the SP Waves, the internal reflectance of such a stack varies sharply in response to changes in any of the parameters such as the dielectric property of the materials used for the stack or the wavelength of the incident light or its angle of incidence, in a narrow band of angles "AOmax" in the neighborhood of this plasmon angle. Exploiting this behavior, the SPR devices have been widely used in the past, to sense and study the micro-perturbations in the physical, chemical and biological state of various materials under a variety of experimental conditions with high resolution and high sensitivity. SPR Sensor and its Key parameters: The "Surface Plasmon Waves" are in-homogeneous, transverse magnetic type surface waves, which upon excitation propagate along planar metal-dielectric interfaces and remain confined to a very thin cross-section about such interfaces. A three-layer-two-interface system of "Dielectric-Metal-Dielectric" stack in a Kretschmann"s configuration (as shown in Fig.l of the drawings accompanying the Provisional Specification) is often used in practice to excite such waves using a coherent electromagnetic radiation. The SP waves propagate with a wave vector "Ksp" which is controlled by the dielectric functions of the materials that form the "SP Wave supporting interface" (active interface) and is given by the following equation: Where Em and the e, are the dielectric functions of the metal and dielectric regions of the active interface. As depicted in the Fig. 1, such waves grow at the Sm - Ss interface of the stack when the component of the propagation vector of the incident light beam (Kd = Ed". Ko= Bd. [ffl/c] ) resolved parallel to the - ea - Ss interface (Kev) is tailored to phase match the Ksp. The phase match is usually controlled by adjusting the angle of incidence for total internal reflection and a perfect phase match leading to near-zero reflectance (minimum reflectance) at an angle of incidence. I t where "sa" is the dielectric fiinction of the medium through which the exciting light beam reaches the internal reflection interface. The Kgp and ©sp together constitute the key parameters for the SPR sensor and remain constant for a specific choice of the parameters used for the device design. The SPR curve for a typical dielectric-silver-air stack is plotted using 8d = 2.31,8s = 1, 8m = (-18.3) + i (0.4), d = 56 nm, and A = 633 nm, (from now on referred to as reference data) and is shown as trace (a) in the shifts to a new location with a different characteristic plasmon angle as 0* shown by the trace (b). Hitherto, the SPR devices are most widely used for the measurement of the changes in the phase of the refractive index of materials that are mostly in liquid or gaseous state. The sensing mechanism necessarily involves a physical change in the plasmon angle of the device " " during such measurements. The changes in the material properties are inferred from the corresponding changes in the plasmon angle, which are either experimentally measured or estimated from the reflectance of the device using the analytical formalisms that describe the "SPR Curves". The ease with which the measurements from the SPR sensor can be interpreted depends to a large extent upon the formalism that relates the AR to the A0. The reflectance function of the SPR device available from either of the well-established theories namely "Theory of Thin films" and the "Theory of Resonance" can be conveniently utilised for this purpose. The formaUsm for the reflectance function of the device using a three-layer Dielectric-Metal-Dielectric stack, from the former theory, is given by the following equation: Where the Yn and "23 are the Fresnel reflection coefficients of the Dielectric (Ed) - Metal (8m) and Metal (8m)-Dielectric (8s) interfaces respectively, "k" is the component of the exciting light wave vector resolved parallel to the reference axis of the device and "d" the thickness of the metal layer. The values of Yn, Y23 and k in the above expression vary independently with the angle of incidence of the exciting light beam and the dielectric fiinctions for each of the materials in the three-layer stack. The formalism for the corresponding fUnction from the "Theory of Resonance" which makes use of the resonant coupling between bulk and surface modes of wave propagation is given by the following equation: decay behaviour of the surface waves during their propagation. The former arises fi-om the Ohmic losses in the metal layer while the latter represents the additional loss due to finite thickness of the metal layer through re-radiation of the plasmon field back into the dielectric (1) of the three-layer-stack shown in the Fig.l. The expressions (3) and (4) are formulated primarily with an emphasis to explain clearly "how" the SPR based signal is produced and encapsulate different sets of the key parameters of the SPR device to explain in a transparent way their role in signal generation. SPR device operation for measurements (Notation): The salient features of measurement exercise using an S! device can be explained using the notation and the curves shown in the Fig.2. The sensor is initially pre-set to operate at an angle of incidence *P (often referred to as the "phase and impedance matched" condition [9,5]) where its reflectance is minimum (R,mip) XHiring a typical measurement cycle, the quiescent point of operation (defined by ®*P , |l win) shifts to a new location and the sensor indicates the same to the observer through a prpportionate change " R b" in its reflectance. The latter can be interpreted as due to a transformation in the dynamic state of the sensing device which can occur in two ways" the first as due to a shift in the defined on the same resonance curve - trace (a). If the design of the experiment is such that the parameter under study (for example the change in the refi-active index of a material) effects an alteration in any of the device parameters (1 , Sd/ Ss, Sm) the "plasmon angle" of the device shifts from "ep" to a new value "©!" (equation (2)). The dynamic state of the device in such cases alters through a shift of the quiescent operating point fi-om one trace to another. Barring a couple of reports (11,12), the sensing mechanism in all the conventional SPR measurements are invariably based on the approach. If the parameter under study instead ahers the reflectance of the SPR device without effecting any of the device parameters ( 1 , 8d/ 8s, Sm) the plasmon angle of such a device remains "invariant" during measurement. The quiescent point of operation in such measurement remains confined to the same resonance curve and the change in the device Reflectance (R res) in Lorentzian sh>e and resembles an narrow inverted S -fimction, centred around th plaQKxn aie. In majority of the applications for the SPR jAeflOmena, the foessis invaiily on a single isolated point on the plasmon resonance cursre namely the?-"Ptaaawift Angle". In typical SPR measurements, identifying and movBimg it»loe€n» constituted the principal exercise. Hitherto the SPR based experimental measurements carried out at angles away from the "plasmon angle" have not been known for bearing or revealing Scientific information of Fundamental/technical importance and hence have not received significant attention. The present communication highlights the importance of such measurements. For example, the value of the new SPR parameter "K" can be directly estimated from such measurements. According to the prior art, after defining a layerstructure, by specifying dielectric permittivity and thickness of each layer, a SPR reflection curve can easily be calculated from Fresnel equation, the inverse problem, i.e. if the SPR reflection curve is given, the values such as the dielectric fiinction, thickness of the film, etc is much more difficult to solve. Further, without a reasonably accurate estimate of either d or E(O), there is an inherent ambiguity in determining both of these parameters from a single reflectivity measurement. By using the new formalism proposed herein, it is possible to generate the SPR curve from the parameters of the formalism and as well as calculate the dielectric function of the materials and thin films of metals from the SPR curve obtained. Further, no more the thickness of the material plays an important role in the SPR resonance device. Accordingly, it is an object of the present invention to provide a method of carrying out a surface plasmon resonance (SPR) measurement using a surface plasmon resonance device and also to a method for determining the dielectric ftmction (Sm) of a material or the thin films of metals from the said surface plasmon resonance (SPR) measurement. This invention will now be described with reference to the accompanying drawings, wherein: Fig. 1. is a schematic diagram of the three layer stack used for excitation of the Surface Plasmon Waves and Fig. 2 is the Plasmon Resonance curve of an SPR device - Reflectance variation with angle of incidence. By treating the reflectance (R res) and the absorptance ( 1 - R s) of the SPR device as a pair of inseparably coupled state parameters and using their ratio "L" =R res/ (1- R res) as a new index to the equilibrium optical state of the SPR device, the investigators propose a new formalism for the Plasmon Resonance Curve. The details of the derivation are presented below. The proposed formalism brings into light for the first time, a new SPR parameter designated for convenience as "K". This new parameter apart fi-om providing a simple link between the angle of detune " and the optical state "L" is also of fundamental importance as it establishes a new connection between the principal device constants K, Ka and Tj. Its value can be experimentally estimated easily using measurements carried out at angles away fiom the Plasmon Angle. A modified mathematical model for the SPR Curves, is obtained by transforming the expression (4) into an expression for (Fr / Fi ) and simplifying the same by taking advantage of the restrictive plasmon angle condition as detailed below. Kev and Ksp are connected to the constants of the materials used for the device and the angle of incidence of the exciting light beam as given by [11,5] Where (-)■ is such that A0 =|©sp - 0|. For well designed SPR devices, the effective range of angles of incidence "0Amax" over which the device absorptance A= 1 -Rres due to SP waves is operative, can be as small as a few milliradians such Where "K The Fr and Fj in the above expression are positive, real valued, rate constants and are nearly equal in a few milliradians active range of in the neighborhood of 0sp The first term on the right hand side of the above expression is always > 1. The second term is always less than the first term. From earlier work, it is known that for €K0q„ the value of (Fr/ Fi) is always less than T. For the SPR device restricted to operate in the region marked "A-B" in the left branch of the curve shown in the Fig.2 (as those left with the Provisional Specification), the above ratio is expected to increase gradually towards "1" as the operating point moves from "B" to "A". The appropriate solution for the (Ff/ Fi) thus corresponds to the arithmetic difference between the two terms on the right hand (in generating / sustaining the SP waves) compares with the device reflectance at various operating points and is the principal parameter that gets largely effected during the measurement. In typical SPR based measurements, the experimentally measured reflectance change"a"is used to estimate"L"which changes from 0 to (ARa/(1-/ARa)) as the device reflectance changes from Rnun to Rmin /ARa. For the device reflectance restricted to the range of 0 to 75% (the region where the resonance curve exhibits sharp and sensitive variation as shown in the Fig.2) the "L" value will be correspondingly bounded numerically between 0 to 3. The factor "K" characterizes to a large extent, the collective role of the materials and waves used for the operation of the SPR device, in establishing the equilibrium between the reflectance and the absorptance at any operating point defined by the angle of incidence. Its value is decided by "K" vectors of the exciting light wave ("Ka"), the excited surface waves ("K,") and the decay rate of the latter due to internal damping characterized by a rate constant T,. The parameter K can also be expressed in an alternative functional form. The T, can be estimated from the constants of the materials used for the device using [14). Since the choice of the materials used for the device completely decide its value, the parameter "4K" can be treated as an "universal constant" for the SPR sensor, when the plasmon angle " ©,p" of the device is held invariant during measurement. The expression (16) when rewritten as also suggests that during the measurement under invariant plasmon angle condition, the transformations in each of the experimental parameters "L", "A0" and "R(A0)" are such that they always satisfy expression (20). The third factor "R(A0)" encapsulates the SPR device parameters that characterize the decaying processes of the SP waves and if the approximation R(A0)" 1 is valid in the active range of the sensor, the expression (16) can be simplified into Designating the estimated from the equations (21) and (16) as AGapprox" and ABtrue" respectively, the latter can be rewritten more conveniently as The expression (16), (21) and (22) comprehensively describe the new formalism for the plasmon resonance curves due to the proposed model. The expression (21) implies that for every SPR device there exists an equivalent geometrical parabola. The experimental variables "A0" and "L" constitute the co-ordinates of every point of such curve. The "focal distance" and the "latusrectum" of such an equivalent parabola are given by the parameters "K" and "4K" respectively. As the numerical value of the latter can be known a priori for a given choice of the device constants, the change in the angle of incidence A0 can be estimated almost instantaneously from the experimentally measured change in the ARres (or "L") using the expression (21). If the errors in the computation from this expression are tdale, a comparison of the same with the expressions (3) and (4) at this stage clearly brings out the ease and simplicity of the present formalism in inverting the ARres into its corresponding "A©". The user friendly character of the present formalism can be appreciated from the fact that the functional role of many standard parameters of the SPR device namely Sd, Sm, Sm, es, A, Ksp, K«v and ©sp are now completely specified in an integrated fashion by "K". Experimental method for estimation of "K" Since the rate constants are already used by the earlier researches, their ratio at every A© can be utilized in (22) to remove the errors that arise due to its omission. The value of "K" can be experimentally estimated by physically measuring the angle of detune required for setting the device at L=l (or R,ss = 0.5), which is (like SPR angle) thus a new critical point on the plasmon resonance curve but away from plasmon angle. Fundamental nature of the information from "K* The expression (10) and (15) clearly bring out the fundamental importance of the "K". It may be noted here that while the individual influence of each of the device parameters BCsp, K The advantages of the method of the present invention can be summarized as follows: > In this invention, the thickness of the metal film is immaterial to measure the surface plasmon resonance. The surface plasmon resonance (SPR) measurement is simplified to such an extend that the requirement of accurately estimating either d or e((o) from a single reflectivity measurement is done away with. By keeping the initial reflectance at zero, it is possible to measure the angle of detune, estimate the angle of detune and invert this through the corresponding Fresnel"s reflection equation and determine the dielectric of any material or thin films of metals. We Claim 1. A method for carrying out a surface plasmon resonance (SPR) measurement comprising passing a coherent light beam undergoing "total internal reflection" at one of the interfaces of a stack in a surface plasmon device, in which the initial reflectance of the device is kept at zero, the said reflection excites SP waves at the free surface of metal in the region where resonance occurs, measuring the reflectance (Rres) and the absorptance (1-Rres) of the surface plasmon resonance device; and estimating the angle of detune. 2. A method for carrying out a surface plasmon resonance (SPR) measurement as claimed in claim 1, wherein the angle of detune being estimated by the following equation: in which L is the ratio of reflectance (Rres) and absorptance (1-Rres); K is the new universal constant of the SPR sensor and R(A0) being defined as Fr/Pi; Fr and Fi being the positive, real valued rate constants. 3. A method for determining the dielectric function of a material or thin films of metals using the surface plasmon resonance measurement obtained by the method as claimed in claims 1 and 2. 4. A method for determining the dielectric function of a material as claimed in claim 3, wherein the initial reflectance of the surface plasmon resonance device is kept at zero and the material to be tested is placed on the free surface of the metal in contact with air. 5. A method for determining the dielectric function of thin metal films as claimed in claim 3, wherein the ratio of the imaginary part to the real part of a metal film is connected to the angle of detune for changing reflectance from R = 0 to R = 0.5 which is in effect equal to L = 0 to L == 1.

Documents:

501-mas-1999 abstract dublicate.pdf

501-mas-1999 claims dublicate.pdf

501-mas-1999 claims.pdf

501-mas-1999 correspondence others.pdf

501-mas-1999 correspondence po.pdf

501-mas-1999 description (complete) dublicate.pdf

501-mas-1999 description (complete).pdf

501-mas-1999 drawings (provisional).pdf

501-mas-1999 drawings.pdf

501-mas-1999 form-1.pdf

501-mas-1999 form-13.pdf

501-mas-1999 form-19.pdf

501-mas-1999 form-26.pdf

501-mas-1999 form-5.pdf