|Surface plasmon waves are transverse magnetic electromagnetic waves propagating along a dielectric-metal interface. These waves can be excited by resonant absorption of electromagnetic radiation leading to surface plasmon resonance (SPR) at the interface. The resonance is characterised by a reduction in the intensity of the reflected light at the interface due to strong coupling of incident optical radiation to surface plasmons. This gives rise to a minimum at a sharply defined angle of incidence, referred to as SPR angle or plasmon angle. The phenomenon of SPR has been extensively used in the past to develop reflective type optical devices for sensing applications on account of the high dielectric function dependent sensitivity of the SPR angle. Basically, devices which exhibit this phenomenon have a structure consisting of a metal film sandwiched between two dielectrics. The reflectivity of such a device is theoretically modelled based on either theory of thin films (Fresnel's model) or theory of resonance (Lorentzian model). These models have very effectively predicted the behaviour of such devices based on the shift in SPR angle due to the dielectric function variations.
We have been investigating the SPR device for intensity based metrological applications utilising its high angular sensitive reflectivity, with fixed SPR angle. In these intensity based applications or measurements, direct and simple expressions connecting intensity variation to angular change are unavailable in the literature and quantitative estimation or data inversion is based on either curve fitting or iterative methods. Fresnel and Lorentzian models have commonly been used in the experiments but data inversion through the Fresnel model is computationally complex and the Lorentzian model, although less complicated, gives erroneous results due to its approximate nature. In order to obtain a simple expression between intensity variation and the angular change, we have re-looked at the two existing models in order to derive an expression which has the simplicity of the Lorentzian model and the accuracy of the Fresnel model in the experiments with fixed plasmon angles. These efforts have been particularly directed to understand the relationship between intensity variation and meteorologically important properties of such devices. This thesis is an attempt to summarize the computational results which have led us to some novel experimental methodologies which have been used to exploit these devices for inverse type, illumination specific, SPR based applications.
The work presented in this thesis is organised in six chapters. Chapter 1, gives an overview of optical sensing, theory of surface plasmons, excitation schemes for surface plasmons, development of the SPR device and its characterisation. It also includes a brief literature review in the area of surface plasmon resonance, covering both the theoretical and experimental aspects. The objectives of the work and the scope of the thesis are also presented.
Chapter 2 presents the existing models of SPR device, based on Fresnel's and the Lorentzian models. These models allow reflectance calculations from knowledge of either the optical parameters that describe the layers or the parameters of the waves that propagate through them. Using these models, the inverse problem of estimating either the angle of incidence or the optical constants of the layers of the sensors utilizing the intensity based measurements is generally difficult. In order to solve this problem where the plasmon angles are fixed, a modified formalism for the angle scanned SPR spectrum of a three-layered SPR sensor is presented in this chapter. The new formalism regroups the wave vector parameters of Lorentzian resonance theory into a set of non-dimensional parameters 1, 4K and R. The new reflectivity index (1), which is the ratio of reflectance to the absorptance, has been introduced to help explain the physical processes underlying the device operation in the high sensitivity region of the characteristics. The parameter 4Kis a constant of the device and it depends on the dielectric constants of the device. This is a new SPR index and is identified at a point where reflectance and absorptance match. Parameter R is related to the loss mechanisms in the device and will be explained in detail in Chapter 3. This simple model links the new reflectivity index (1) to the angular detune from SPR angle (ΔƟ) and it brings out a parabolic variation of ΔƟ with 1. In this chapter the mathematical derivation of the proposed model is presented and the significance of the new parameters 1, 4Kand Rare discussed.
Chapter 3 evaluates the characteristic nature of errors associated with the predictions from the proposed model and presents methods for neutralizing them. It is demonstrated with the help of the function K which is linearly dependant on 1, that the proposed model predicts the reflectance from the wave vector parameters as accurately as the Fresnel's model. This R parameter explains the slowly varying nature of the radiative loss with the angle of incidence and
this variation contributes significantly to the SPR characteristics. As a consequence, it is found that the SPR characteristics can be represented as a sum of two primary functions which are parabolic and linear, respectively, and this leads to the easy explanation of the SPR characteristics. The present chapter also discusses a new observation that the angle-scanned SPR spectrum can be accurately described using a straight line in intercept form. The intercept value depends on 4Kand the slope depends on K. In addition to this, this chapter discusses practical methods for estimation of the intercept and the slope of such a straight line which are functions of the key wave vector parameters. A detailed discussion on the proposed model highlighting its advantages for inverse type, illumination specific, SPR-based applications with fixed SPR angle is also presented.
Chapter 4 describes the applications of the proposed model for optical constant measurements. The first part highlights a new approach for the determination of the dielectric constants of the metal film used for the optimised- or nearly-optimised SPR sensors using the proposed model. In the complex dielectric constant, the real part is calculated from the SPR angle and the imaginary part from 4K. A discussion on the dielectric constant study of silver and gold metal film is presented. The advantages of the proposed approach such as its simplicity and direct methodology are then discussed. The second part of the chapter also proposes a new approach to carry out measurements on the absorbance of the medium with enhanced sensitivity utilising the parameter 4K It describes a computational study on the variation of 4K values with the dielectric function and highlights the relationship of 4K variation due to the imaginary part of the dielectric function (absorption) of the samples. The physical processes causing a change in the value of 4Kdue to absorption is also discussed along with some computational results.
Chapter 5 reports the study carried out to bring out the importance of the new index,4K in metrological applications. Based on the new model, the effect of the laser beam divergence on SPR curve is studied. This chapter first of all discusses the design of the SPR device and the new methods for the development and characterisation of such a device. Details of the experimental procedure for laser divergence evaluation are proposed along with some of the significant computational results. Furthermore, a few applications such as focal length measurement of optical lenses, micro-displacement measurement based on the divergence of the laser beam are also reported. Since the SPR characteristics can be represented easily using the new model, the angular dependent intensity variation can be utilised for some metrological applications with simple data processing. In this context, the high angular sensitivity of the SPR device is studied and some applications such as micro-displacement measurement, pressure measurement and optical wedge angle measurement are included to highlight the above advantages.
The last chapter, Chapter 6, gives a summary and conclusions of the work presented in the thesis. The scope for future investigations is also included in this chapter.