Comparison of Measurement and Electromagnetic Overall Transfer Matrix Simulation Results of MgF 2 -Nb 2 O 5 Distributed Bragg Reflectors with Different Layers

Abstract

In this study, glasses were used as substrates and an e-beam was used the method to deposit MgF2 and Nb2O5 single-layer films, and the optical properties, including extinction coefficients (k values) and refractive indices (n values), were measured by using the light wavelength as variable. The equation d = λ/(4n) was used to calculate the thickness (d) of 1/4 wavelength (λ) for each layer of the MgF2-Nb2O5 bilayer films in distributed Bragg reflectors (DBRs) with a designed reflective wavelength at blue light (~450nm). Each MgF2-Nb2O5 bilayer film was called a period, and the glass substrates were used to deposit the films with two, four, and six periods for fabricating the DBRs. The field emission scanning electron microscope equipped with a focused ion beam was used to measure the thickness of each MgF2-Nb2O5 layer in the DBRs with different periods. The measured maximum reflective ratios were compared with Sheppard’s approximate equation, which calculates only the maximum reflective ratio at a specific wavelength. An overall transfer matrix was investigated to calculate the reflective spectra by incorporating the variable n values and thicknesses of the MgF2-Nb2O5 films in each layer. We show that the measured results of the fabricated DBRs matched the results simulated using Sheppard’s approximate equation and the overall transfer matrix.