There is some porous dielectric membrane with strictly vertical cylindrical pores. I would like to find theoreticaly optical transmission spectra of this membrane, depending on the bulk material optical dispersion, radius and height of cylindrical pores and the distance between their centers.
In result I want to find a formula for optical transmission spectra depends on wavelength (to compare with experiments). The material is dielectric, so it's only about complex diffraction and Beer–Lambert–Bouguer law, but I don't know how to start with porous system.
Depends on the size of these pores. If they are really big (orders of magnitude larger than wavelength) and no diffraction-related, photonic-crystalline or metametrial-like effects are involved, then simply combine the bulk material optical transmission with air transmission in relevant proportions. If the pores are small, then I would suggest using a specialised software (i.e. COMSOL, CST etc), where you just draw the unit cell of the structure, define the bulk dispersion, and it quickly gives you the answer for the transmission spectra.
Thank you very much, Alexander! There's a lot of interesting things these packages can do. But generally I want to have some formula, not simulation of the problem. Pores are small ( diameter from 10 to 200 nm for different techniques).
Lev,
What wavelengths are you using? Based off the information above, it appears that you might be able to use the cylindrical solution for Mie scattering to determine the scattering coefficient of the medium (If you can assume the pores are spherical, you can use this: http://omlc.org/calc/mie_calc.html). Then you may use that in either Beer--Lambert (for a very thin slice of tissue) or the diffusion equation to find the transmission for each wavelength.
Thank you, Joseph! Mie instrument is very interesting for my other work about scattering in colloids.
Wavelengths are 190-3000 nm (UV-near infrared). Pores are not spheres, length of cilinder more than 100 times higher then pore diameter.
Why do you want these properties? How will very precise measurements help you?
If you decide to go forward with this you will probably want to use dual integrating spheres to resolve the optical properties. Try pulling the following article:
J. Pickering, S. Prahl, N. van Wieringen, J. Beek, H. Sterenborg, and M. van Gemert, "Double-integrating-sphere system for measuring the optical properties of tissue," Appl. Opt. 32, 399-410 (1993).
- Badges
- Science topic
- Similar topics
- Agricultural Science
- Horticulture