About T-matrix and S-matrix, and how to obtain the electromagnetic field distribution of the diffraction structure under the specified amplitude ?

[xungu1]

I noticed that your program uses the enhanced T-matrix method to calculate the diffraction efficiency when calculating the multi-layer structure, and I also noticed that your program seems to provide a calculation method for the S-matrix. I currently have two doubts : The first is if I want to get the S-matrix at the interface of each interface of the multi-layer structure, how do I operate ? Can I use the calculation results of T-matrix to get the S-matrix at the interface of each interface ? If so, how should I operate ? The other is how do I operate if I want to get the effect of a specific amplitude on a certain layer of structure ? I have noticed that the S-matrix can be used as a calculation when there are inputs on both sides of the interface. I want to use this S-matrix to calculate the electromagnetic field energy distribution of the layer under different illumination on both sides at the same time, or can the same operation be achieved in another way ?

[yonghakim]

SMM option in meent was disabled. I will try to make it available again (or make it sure if it's already available) but cannot say when.

Regarding two questions,

• S matrix
  • SMM and TMM are about how the waves of in and out are connected at the interfaces. S matrix is not defined in TMM. You can utilize other information of Enhanced TMM in meent to calculate S matrix. If you need S matrix, I recommend you TORCWA which is open source python RCWA tool. This uses classical SMM.
• Both sides
  • Meent doesn't support this. If what you mean is to calculate two situations (one situation with incident light from the top and one other situation with incident light from the bottom) with single simulation, not one situation with two light sources, then I suggest to look reticolo(matlab) or TORCWA(python). They are both open source so you can take a look. TORCWA uses classical SMM.

[xungu1]

Thank you for your answer.
For the first question, I will try to calculate the S-matrix by using the correlation of the enhanced T-matrix.
On the second question, I should be unclear. I want to obtain the electromagnetic field distribution inside the diffraction structure under a given amplitude. This ' given amplitude ' contains both real and imaginary parts. In the previous question, you pointed out that the amplitude of the incident wave in the strictly coupled wave is normalized to 1. Then, in the case of normal incidence, is the electromagnetic field distribution inside the diffraction structure under the ' given amplitude ' multiplied by the current calculated electromagnetic field distribution multiplied by ' the proportion of the given amplitude to the normalized amplitude ' ?

[yonghakim]

I'm afraid it cannot be done in such a way. It probably can be done in the code to change the amplitude of the input but am not sure if it is correct in terms of RCWA steps. This is not considered in meent.

Do you have any paper or material about this input amplitude? How did other researchers simulate this?

[xungu1]

In the third chapter of ' On design strategies for binary dielectric metasurfaces based on the Fourier modal method ' in the literature I refer to, the S-matrix at each interface of the multilayer structure is calculated to calculate the electromagnetic field distribution inside the diffraction structure, and the transmission amplitude and reflection amplitude under given illumination conditions can be obtained. The proposed S matrix can achieve the effect of simultaneous illumination of two light sources as you mentioned earlier, and it is shown in the text that the S matrix is converted from the T matrix ( although I am still not clear about the details of this conversion ). In the calculation of the S matrix, the weight of the forward propagation and back propagation modes on both sides of the interface is included.
Is the internal electromagnetic field distribution of the diffraction structure under the so-called ' given amplitude ' calculated from this ? Or if I want to obtain the influence under the ' given amplitude ', I have to rely on the S matrix calculation method when two light sources can be illuminated at the same time ?

[yonghakim]

https://opg.optica.org/josaa/abstract.cfm?uri=josaa-34-10-1769

This seems what you are looking for, and doable with reasonable amount of effort. You don't need S-matrix if this can be done with ETM, right?

[xungu1]

Sincerely thanks for your help ! I think that the bidirectional incidence mentioned in this paper, and the result of the reverse incidence can be obtained by the matrix calculated by the forward incidence, which is what I am looking for. I have the following questions about RCWA and this paper : In the fourth section of this paper, I have a general understanding of the derivation process, but I do not know the expression of S1 and S2 variables given in Formula ( 14 ) and Formula ( 16 ). Taking TM polarization as an example, Formula ( 8 ) in this paper gives its normalized expression, but it seems that it still needs to be modified when it is substituted in practice. I 'm sorry, is this what I 'm thinking about now, with the formula ( 41 ) in Moharam 's article [ 1 ] as a reference, to reverse the expression of S1 in formula ( 14 ) ? At the same time, the same expression can be set when the TM polarization is also set when the reverse incidence is also set ?



[1]https://opg.optica.org/josaa/abstract.cfm?uri=josaa-12-5-1068