The University of Alabama in Huntsville Physics Department,
137 Madison Hall Huntsville, Al 35899, US
In this study, a novel design of a Fabry-Perot band pass filter using as low and high index coating materials silicon dioxide (SiO2) and titanium dioxide (TiO2) is presented. Two high reflectance dielectric materials separated by a half wavelength “cavity” which is made up of SiO2 that allows light surrounding the central wavelength (550 nm) to be transmitted partially while the remaining spectrum range outside the bandwidth to be almost totally reflected. The matrix approach is the physical tool utilized to get the complex expressions that explains this behavior. The maximum transmittance peak achieved was 95.72 %, bandwidth at -3dB : 2.98 nm and bandwidth at -20 dB : 10.40 nm. A further analysis is done by increasing the number of cavities or spacers from a single to a double one and letting them have the same thickness as the first configuration. A simulation using C++ programming shows that a better and steeper slope is gotten letting the energy spectrum range within the bandwidth to be transmitted more efficiently.
Key words: multilayer antireflection coatings, band pass filter, narrow band pass filter, Fabry-Perot filter, multi-cavity Fabry-Perot filter.
An optical band pass filter (BPF) is a device that allows a certain range of electromagnetic frequencies to be transmitted and the other ones to be rejected. This range varies according to our needs and what the filter will be used for. They’re a key component for optical communications devices, laser- line cleaning and medical imaging apparatus. Currently, were facing an era where technology and high quality devices work together in such a way that the more advanced and accurate technology we work with the better the performance of the apparatus with can can build. In the field of optical band pass filters we might be interested in designing and building either narrow or wide band pass filters. In order to do so, we must have an idea of the optical behavior our BPF. That is, its reflectance and transmittance properties for different wavelengths.
A band pass Fabry-Perot filter was designed using titanium dioxide (TiO2) and silicon dioxide (SiO2) as the high and low refractive coating materials, respectively, piled over a glass substrate of index of refraction of 1.52 and whose transmission window is centered at 550 nm. A further analysis about how to enhance the sharpness of the transmission peak has been developed and eventually numerical data is presented to back it up. Finally, a program written in C++ language was used to compute the optical parameters mentioned above.
2. Theoretical Development
If we consider light s-polarized that shines a thin dielectric film between other two transparent materials (air and glass, for example) and applying the boundary conditions of the electromagnetic theory that states that the tangential components of both the electric and magnetic fields must be continuous across the boundary, then we have the following expressions 
Where [pic] are the total electric and magnetic fields on each boundary I and II, respectively. The other parameters such as [pic] corresponds to the phase shift that a wave undergoes after passing through the film once. For normal incidence, which is the easiest condition to work with and which we are going to develop all our further analysis the previous parameters may be written as 
d is a fixed physical thickness and is a key point when designing antireflection coatings. A better further analysis will be given in the next sections.
In matrix notation, expressions (1) and (2) may be written in this form ...