Other than wave optics, is there any methods such as simulation software that I could use to analyse the resonance of em waves in the crystal structure of TiO2?
How can the tetragonal crystal system affect the emf?
Can thickness affect resonance?
The main properties are the optical properties of thin films that depends on the crystal structure related to the deposition mode, annealing... Film of nanometric thickness are influenced by the substrate properties.
Another critical parameter is the surface roughness.
You have to characterize the surface roughness and try to recover the optical properties if possible by ellipsometry.
If the surface is flat, you could apply an inverse problem method (Measurement of thicknesses and optical properties of thin films from Surface Plasmon Resonance (SPR)
J Salvi, D Barchiesi, Applied Physics A 115 (1), 245-255 - Numerical retrieval of thin aluminium layer properties from SPR experimental data D Barchiesi Optics express 20 (8), 9064-9078)
I think the main factors will be thickness, dielectric constant (permittivity), density and surface geometry (flat / rough/ periodic hillocks etc.).
Trying to interpret your question, you seem to be interested in building up the electric field inside the thin film. One way to think about this is as a fabry perot cavity where the air film interface is one mirror and if on a substrate the film substrate would act as another mirror. As Dominique and Thomas mention above the the material properties and the morphology of the film will be important. Without having to go to a full blown electromagnetic simulation the fabry-perot cavity can provide a back of the envelop answer. There are some nice paper by Swanepoel including "Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films" R Swanepoel 1984 J. Phys. E: Sci. Instrum. 17 896. doi:10.1088/0022-3735/17/10/023 that if I remember correctly show how to modify a simple fabry perot formula to take into account absorption, having the thickness be a wedge, and account for surface roughness. When I took his formula's and put them into a simple mathcad program I got very good matches with experimental results for thin films using transmission and reflection measurments. Of course there are a lot of commercial products that will now fit the spectrum and try to give you the refractive index and thickness of a thin film. Most commercial ellipsometers will have this type of software. Modern spectrophometers may also have some software, both are usually using the data to find the index and thickness of the film.
So does the crystal structure affect the resonance. The short answer is yes, but the practical answer is that often the difference of the index of refraction may not be that different. To correct your calculations you would need to consider the index of refraction to be anisentropic. this gets substantially more complicated mathematically if considering guided waves. Depending on the orientation of your film, you could be aligned along one axis and with the light beam perpendicular to the film you will see effectively one index. If the crystal is tilted, the light beam might have one polarization delayed with respect to the other as it goes through the film, so the details matter. One way to think of this is as a quarter or half wave plate, but not at the correct thickness to be a commercial optical element.
Yes the thickness will matter. In the fabry-perot equation, n*d are always together. So if you change the thickness the optical path length will change. So you will see a shift in the optical resonance as the film thickness is changed.
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