The Fresnel Coefficient of Thin Film Multilayer Using Transfer Matrix Method TMM

Mohammed, Zahraa H.

doi:10.1088/1757-899x/518/3/032026

Cited by 23 publications

(13 citation statements)

References 9 publications

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“…This method also consists of a form of self-interferometry, in where there are several internal reflections between the coating and substrate interfaces. These coating and substrate interfaces are often modelled using the Fresnel reflection coefficients to determine the reflected intensity present at the optical detector, however, for several layers these calculations become complex, and researchers tend to model these interfaces using Transfer Matrix Methodologies (TMM) [ 80 ]. The main operating principle for this method relies on reflection intensity, which is calculated by the ratio of the reflected intensity at the detector to the incident intensity.…”

Section: Potential In-line Coating Thickness Test Methodsmentioning

confidence: 99%

Continuous In-Line Chromium Coating Thickness Measurement Methodologies: An Investigation of Current and Potential Technology

Jones

Uggalla

et al. 2021

Sensors

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Coatings or films are applied to a substrate for several applications, such as waterproofing, corrosion resistance, adhesion performance, cosmetic effects, and optical coatings. When applying a coating to a substrate, it is vital to monitor the coating thickness during the coating process to achieve a product to the desired specification via real time production control. There are several different coating thickness measurement methods that can be used, either in-line or off-line, which can determine the coating thickness relative to the material of the coating and the substrate. In-line coating thickness measurement methods are often very difficult to design and implement due to the nature of the harsh environmental conditions of typical production processes and the speed at which the process is run. This paper addresses the current and novel coating thickness methodologies for application to chromium coatings on a ferro-magnetic steel substrate with their advantages and limitations regarding in-line measurement. The most common in-line coating thickness measurement method utilized within the steel packaging industry is the X-ray Fluorescence (XRF) method, but these systems can become costly when implemented for a wide packaging product and pose health and safety concerns due to its ionizing radiation. As technology advances, nanometer-scale coatings are becoming more common, and here three methods are highlighted, which have been used extensively in other industries (with several variants in their design) which can potentially measure coatings of nanometer thickness in a production line, precisely, safely, and do so in a non-contact and non-destructive manner. These methods are optical reflectometry, ellipsometry and interferometry.

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Section: Potential In-line Coating Thickness Test Methodsmentioning

confidence: 99%

Continuous In-Line Chromium Coating Thickness Measurement Methodologies: An Investigation of Current and Potential Technology

Jones

Uggalla

et al. 2021

Sensors

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“…The optical reflectance response of the proposed PDMS grating was calculated using rigorous coupled-wave analysisrcwa (RCWA) [ 22 ], and the uniform PDMS layer was calculated using Fresnel equations and the transfer matrix approach [ 23 ], which are in-house developed under MATLAB R2018a utilizing parallel computing.…”

Section: Methodsmentioning

confidence: 99%

Analysis of Embedded Optical Interferometry in Transparent Elastic Grating for Optical Detection of Ultrasonic Waves

Sukkasem

Sasivimolkul

Suvarnaphaet

et al. 2021

Sensors

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In this paper, we propose a theoretical framework to explain how the transparent elastic grating structure can be employed to enhance the mechanical and optical properties for ultrasonic detection. Incident ultrasonic waves can compress the flexible material, where the change in thickness of the elastic film can be measured through an optical interferometer. Herein, the polydimethylsiloxane (PDMS) was employed in the design of a thin film grating pattern. The PDMS grating with the grating period shorter than the ultrasound wavelength allowed the ultrasound to be coupled into surface acoustic wave (SAW) mode. The grating gaps provided spaces for the PDMS grating to be compressed when the ultrasound illuminated on it. This grating pattern can provide an embedded thin film based optical interferometer through Fabry–Perot resonant modes. Several optical thin film-based technologies for ultrasonic detection were compared. The proposed elastic grating gave rise to higher sensitivity to ultrasonic detection than a surface plasmon resonance-based sensor, a uniform PDMS thin film, a PDMS sensor with shearing interference, and a conventional Fabry–Perot-based sensor. The PDMS grating achieved the enhancement of sensitivity up to 1.3 × 10−5 Pa−1 and figure of merit of 1.4 × 10−5 Pa−1 which were higher than those of conventional Fabry–Perot structure by 7 times and 4 times, respectively.

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“…To more clearly explain the asymmetric coloration characteristic of our electrochromic devices, the Fresnel coefficient transfer matrix method is used to determine the reflectance on each side of the Janus devices, as well as the transmittance through the devices. [28,30,31] For a simple case with normally incident light, the transmission and reflection of electromagnetic fields in the five-layer Janus-structured devices can be described by two characteristic matrices, namely, the refractive matrix A ij , which describes the transfer of the electric vector matrix when the light passes across the interface from the i layer to the j layer, and the phase matrix U i , which denotes the propagation through the i layer at thickness d i . A ij, and U i can be expressed by the following equation (Equation (1))…”

Section: Doi: 101002/adma202007314mentioning

confidence: 99%

Mimicking Nature's Butterflies: Electrochromic Devices with Dual‐Sided Differential Colorations

et al. 2021

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Some butterfly species such as the orange oakleaf (Kallima inachus) have strikingly different colors on the dorsal (front) sides of their wings compared to those on the ventral (back) sides of their wings, which helps camouflage the butterflies from predators and attract potential mates. However, few human‐made materials, devices, and technologies can mimic such differential coloring for a long time. Here, a new type of Janus‐structured two‐sided electrochromic device is developed that, upon application of different voltages, exhibits a coloration state on one side that is distinctly different from that on the other side. This is achieved by inserting an optically thin (4–8 nm) metallic layer with a complex refractive index, such as a layer composed of tungsten, titanium, copper or silver, into typical electrochromic structures.

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The Fresnel Coefficient of Thin Film Multilayer Using Transfer Matrix Method TMM

Cited by 23 publications

References 9 publications

Continuous In-Line Chromium Coating Thickness Measurement Methodologies: An Investigation of Current and Potential Technology

Continuous In-Line Chromium Coating Thickness Measurement Methodologies: An Investigation of Current and Potential Technology

Analysis of Embedded Optical Interferometry in Transparent Elastic Grating for Optical Detection of Ultrasonic Waves

Mimicking Nature's Butterflies: Electrochromic Devices with Dual‐Sided Differential Colorations

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