Modeling Multi-Layer Thin Films (Mltf) In The Visible Ranges Of Electromagnetic Spectrum Using Transfer Matrix Method (Tmm)

Abstract

Multi-layer Thin-films are the stack of layer of material ranging from fractions of a nanometer to several micrometer in thickness. Therefore the intensity of light reflected off the surface of the material and transmitted through the materials can be controlled by optical coating of multilayer thin-film. The design and optimization of such complex structure is heavy problem. At most achieving the desired optical response from a multi-layer thin-film structure over a broad range of wavelengths and angles of incidence is challenging and also there is no systematic method for the design of optical coating but trial and error. The transfer matrix method assisted by accurate computer calculation allows us to simplify the complexity of the optical function of thin film. The computer program which calculates the optical functions of multi-layer thinfilm is developed by MATLAB programming language, based on the transfer-matrix method. By the program developed, anti-reflecting and high reflecting coating was modeled and their optical functions (reflectance and transmittance) calculated as function of wavelength. The reference wavelength λ0 = 550nm. In the case of anti-reflecting coating with the thickness of quarter wavelength (λ 4 0 ) and half wavelength, (λ 2 0 ) layers are arranged in different forms (quarter-quarter and quarter-half-quarter). The double thin film layer (quarter-quarter) between the air and substrate, can achieve minimum reflectance and maximum transmittance at only single wavelength (the reference wavelength). The three layer(quarter-half-quarter) films exhibits slightly greater reflectance (minimum transmittance) at the center of the band and reflectance is reduced while transmittance is increased, over a much wider wave length range. In the case of high reflective coating the stack of two (high index and low index) thin film layer with thickness of quarter wavelength (λ 4 0 ) was used. The obtained result indicates that the reflectance of high reflective coating increases as the number of stacks (layers) added between incidence medium(air) and substrate(glass) within the stop-band (450nm-700nm) while, the transmittance decreases in this range. The addition of extra layers does not affect the width of the zone (stop-band) of high reflectance, rather increases the reflectance within it and the number of oscillations outside the zone