Transfer Matrix Mathematical Method for Evaluation the DBR Mirror for Light Emitting Diode and Laser

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Abstract
Applied mathematics is one of the most widely sciences used to serve other sciences, especially physical mathematics, which is one of the most important applied mathematics topics used in physics. In this work, we used the Transfer matrix mathematical method for evaluation the Distributed Bragg Reflectors mirrors for vertical cavity and the wavelength And The method of light extraction from the martials pay attention from the researchers since the LED and Laser become the most popular devices in different applications. This study focused on the development of simulation method to design and optimization for the DBR(Distributed Bragg Reflectors) structures, which are commonly used in designing DBR mirrors for vertical cavity surface emitting GaN based LEDs and lasers. From the multi-layer simulation, the simulation results are given for the investigation of several properties. First, the wavelength(nm) vs. reflectance(%) can be calculated in the DBR structures that TiO2 and SiO2 thin films are stacked alternately. As a results, it is suggested that highly efficient DBR structures can be designed and manufactured using simulation methodology.

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