I've been using effective medium theories to represent an array of nanomaterials in a layer of glass as an approximate, homogenous medium. This actually works quite well for our intents and purposes, but it got me thinking that if pressed, I wouldn't know how to ascertain the optical properties (reflectance, transmittance etc...) from a multilayer structure if I couldn't homogenize each layer with an effective medium theory.
My first thought is that one could use a brute force calculation (FDTD, BEM, DDA) to approximate all of the nanomaterials, and this would probably be a huge endeavor. Furthermore, since the nanomaterials in the layer (for me anyway) are arranged in a predictable, periodic fashion, it would be excessive to compute the simulation for a big layer of nanoparticles, because the layers are symmetric and the nanomaterials are patterenened. Therefore, the light transmission through even a small region of the multilayer should be the same at any small region, therefore, could be calculated on a smaller scale.
Anyway, I am interested in learning this process; who is doing these calculations, what techinques do they employ, etc..? Can anyone direct me to relevant terminology and resources?
Thanks!
Multilayer systems are normally modelled using a transfer matrix approach. Each layer is modelled using a matrix and calculating the system's transmission and reflection is a relatively cheap calculation. Transfer matrix theory is covered in many places and most optical text books [1] and there are many pieces of software for performing the calculations [2,3,4,5]. There are two or three slightly different formulisms of transfer matrix theory and there are extensions for modelling thick layers (layers much thicker than the wavelength of the light) and for modelling anisotropic layers [6,5].
However, it seems that you also have structure within your layers. In this case you might want to look at "multi-layer modal methods" and rigorous coupled-wave analysis. These model multilayered structures with additional structures within each layer. Lifeng Li has written many papers in this area and so should be a useful starting point for searching the literature. I have found software for RCWA modelling but I don't have any experience with it [7].
ps. I often find that the wikipedia page on the relevant topic has links to useful software packages.
[1] my own maths notes: https://www.researchgate.net/publication/236491437_Transfer_Matrix_Theory_for_a_Type_of_Uniaxial_Layers_from_Basic_Electromagnetism_to_Quantum_Well_Intersubband_Transitions
[2] http://larfis.polymtl.ca/index.php/en/links/openfilters
[3] http://people.csail.mit.edu/jaffer/FreeSnell/
[4] http://sourceforge.net/projects/pyluminous/ (mine)
[5] countless others
[6] P. Yeh "Electromagnetic propagation in birefringent layered media" 1979
[7] http://mrcwa.sourceforge.net/
Data Transfer Matrix Theory for a Type of Uniaxial Layers: from B...
Multilayer systems are normally modelled using a transfer matrix approach. Each layer is modelled using a matrix and calculating the system's transmission and reflection is a relatively cheap calculation. Transfer matrix theory is covered in many places and most optical text books [1] and there are many pieces of software for performing the calculations [2,3,4,5]. There are two or three slightly different formulisms of transfer matrix theory and there are extensions for modelling thick layers (layers much thicker than the wavelength of the light) and for modelling anisotropic layers [6,5].
However, it seems that you also have structure within your layers. In this case you might want to look at "multi-layer modal methods" and rigorous coupled-wave analysis. These model multilayered structures with additional structures within each layer. Lifeng Li has written many papers in this area and so should be a useful starting point for searching the literature. I have found software for RCWA modelling but I don't have any experience with it [7].
ps. I often find that the wikipedia page on the relevant topic has links to useful software packages.
[1] my own maths notes: https://www.researchgate.net/publication/236491437_Transfer_Matrix_Theory_for_a_Type_of_Uniaxial_Layers_from_Basic_Electromagnetism_to_Quantum_Well_Intersubband_Transitions
[2] http://larfis.polymtl.ca/index.php/en/links/openfilters
[3] http://people.csail.mit.edu/jaffer/FreeSnell/
[4] http://sourceforge.net/projects/pyluminous/ (mine)
[5] countless others
[6] P. Yeh "Electromagnetic propagation in birefringent layered media" 1979
[7] http://mrcwa.sourceforge.net/
Data Transfer Matrix Theory for a Type of Uniaxial Layers: from B...
Thanks! Yes, we are quite familiar with TMM for solving multilayers, and this is what led me to this inquiry. Namely, TMM subsumes a homogenous dielectric function for each layer. I will look into some of these links, thanks!
You can also do something like fdtd on a very small scale (the smallest common multiple of the periods in all your layers) and use periodic (Floquet) boundary conditions.
I will ask my friend about optical properties calculations for nano-layered samples.
What about another question: “How do you calculate multilayer structures with nanomaterials?” If you mean the thickness of every layer, it is simply. Two methods we use. First – we directly see the cross section of a film with EM. Second – we calculate the number of laser pulses. Before that we deposit thick film of every substances and measure it thickness and laser pulses number which are need for that.
Depending on the thickness you can use combination of a plasma etching with XPS.
Using an ellipsometry also gives a possibility to evaluate multilayer systems if your layers are enough transparent. There are several theories how to calculate properties of multilayer films.
All about it you can easily find in Scopus or even in Google.
Thanks Mikhail but I'm actually more interested in computing it from a theoretical or modeling standpoint rather than measuring
Hi all, I am looking a software to calculate the transmittance through a layer of water between two layers of glass . Regards
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