Performance of a surface plasmon resonance (SPR) sensor based on Kretchmann configuration for silver (Ag) film is evaluated via theoretical simulation. The film thickness and incident angle are varied to obtain the SPR wavelength in the range of 500-550 nm. Shift of SPR wavelength with refractive index of the dielectric defines the sensitivity whereas the resolution is obtained from the ratio of the instrumental resolution to the sensitivity. The SPR sensor shows increasing sensitivity for thicker film however the absorption magnitudes of such films are high and unfavourable for data acquisition. Film thickness of 45 nm and 50 nm which has good sensitivity and resolution with high absorbance magnitude of the SPR wavelength is the best thickness to be employed for sensing purpose.

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Nowadays, to develop new generation of nanodevices, most researchers such as chemists, physicists, biologists, even the engineers are focusing their studies towards the uniqueness as well as the chemical properties of metal nanoparticles. Even, the mathematician also has governed the appropriate mathematical modelling regarding of properties of nanoparticles such as gold nanoparticles. In this paper, some experiment regarding the photochemical and photocatalytic processes for predicting the growth of gold nanoparticles from previous studies has been reviewed. Besides that, in observing the growth rate of gold nanoparticles, a mathematical modelling has been governed. Where, ultraviolet, UV radiation with wavelength of 366 nm and 253.7 nm has been fixed as the constant parameters. The governing equation is then solved numerically using some iterative method known as Jacobi and Gauss Seidel. The convergence of both methods is discussed in detail and the numerical analysis is presented in table form to justify and validate the convergence as well as the performance of the proposed iterative methods.