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Sensors and Materials, Volume 34, Number 5(1) (2022)
Copyright(C) MYU K.K.
pp. 1721-1731
S&M2923 Research Paper of Special Issue
https://doi.org/10.18494/SAM3818
Published: May 10, 2022

Using Overall Transfer Matrix to Simulate a Blue-light Bragg Reflector with Optimization Properties [PDF]

Yonghu Yang, Jin-Yu Chen, Cheng-Fu Yang, Chang Hong Lin, and Chiang-Lung Lin

(Received December 30, 2021; Accepted March 23, 2022)

Keywords: blue-light Bragg reflector, simulation, overall transfer matrix, MgF2-Nb2O5 bilayer film, different thicknesses

In this study, an e-beam evaporation method was used to deposit Nb2O5 and MgF2 single-layer films on glass substrates; then, the refractive indexes (n values) of the glass substrate and Nb2O5 and MgF2 single-layer films were measured in the range of 200–1700 nm. The equation d = λ/(4n) was used to determine the thicknesses (d) of the two films with 1/4 wavelength (λ), which were used in a distributed Bragg reflector (DBR) with the central wavelength of ~450 nm (blue light). The calculated thicknesses of the Nb2O5 and MgF2 single-layer films were 49.0 and 80.9 nm, respectively. The measured refractive indexes of the Nb2O5 and MgF2 single-layer films were incorporated into an approximate equation proposed by Sheppard to measure the maximum reflective ratios (MaxR) of the blue-light DBRs with different periods (two, four, and six were investigated in this study). Also, an overall transfer matrix (TM) was investigated to calculate the simulative reflective spectra of the blue-light DBRs with two, four, and six periods. The TM of each layer with the same thickness was obtained by changing the thicknesses of the MgF2 film from 76.9 to 84.9 nm (the thickness of the Nb2O5 film was set at 49.0 nm) and those of the Nb2O5 film from 45.0 to 53.0 nm (the thickness of the MgF2 film was set at 80.9 nm). The effects of the variations in the thicknesses of the Nb2O5 and MgF2 films on the simulated reflective spectra of the designed blue-light DBRs were well investigated. The measured MaxR values were also compared with the results calculated using the equation proposed by Sheppard, because it can only be used to calculate the MaxR value of a designed DBR.

Corresponding author: Cheng-Fu Yang, Chiang-Lung Lin


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Cite this article
Yonghu Yang, Jin-Yu Chen, Cheng-Fu Yang, Chang Hong Lin, and Chiang-Lung Lin, Using Overall Transfer Matrix to Simulate a Blue-light Bragg Reflector with Optimization Properties, Sens. Mater., Vol. 34, No. 5, 2022, p. 1721-1731.



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