Integrating Second-Order Susceptibility χ (2) for Nonlinear Optics simulation in THz region

Posted Apr 17, 2024, 7:49 a.m. EDT Electromagnetics, RF & Microwave Engineering, Wave Optics 1 Reply

Ahmad Shafiei Aporvari

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I want to explore the nonlinear optic phenomena for some matamaterial such as LiNO3(LNO) and ZnTe, with second-order susceptibility. Our challenge is to incorporate a 3 by 6 matrix susceptibility to the optical properties of a material. More explicitly, the polarization elements; Px^{(2)}, Py^{(2)} and Pz^{(2)} are equal to the multiplication of susceptibility χ (2) as 3 by 6 matrix to convolution 6 by 1 matrix that its elements are: {Ex ⋅Ex}, {Ey * Ey}, {Ez * Ez}, 2{Ey * Ez}, 2{Ex * Ez} and 2{Ex * Ey}. my problem is that I dont know how to do this simulation. As one solution, I am thinking to obtain polarization using an approperiate PDE or ODE module in COMSOL. Alternatively. using Add User-Defined Variables I might be able to define separate expressions or function for each element of the χ(2) matrix if the elements have different frequency dependencies. I have attached relevant screenshots for reference. Any insights or experiences similar to mine would be greatly appreciated.

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1 Reply Last Post Jul 10, 2024, 12:31 a.m. EDT

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Hello Ahmad Shafiei Aporvari

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Miguel Bacaoco

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Posted: 1 day ago

Hi Ahmad,

I'm working on similar topic. 1. You can analytically define the explicit expression of individual component of your polarizability (or external current density) in terms of the frequency domain solution of your input wave (ewfd.Ex, ewfd.Ey, ewfd.Ez). Eg. Px = chi2xxx(lda)ewfd.Exewfd.Exewfd.Ex + chi2xxy(lda)ewfd.Exewfd.Exewfd.Ey + ...

Here, the frequency dependence of your chi2 per matrix component is defined by separate function that takes the wavelength/frequency as argument. For simple comsol model, I think it is best to keep it non-dispersive. 2. Define two frequency domain solvers (pump, nonlinear response) 3. Add physics of Polarization (External Current Density) on your metamaterial and put your defined polarizaibility (or external density) in the definition. This way, the pump solver provides input for the nonlinear solver. 4. Run the two solvers and you get both linear the nonlinear response.

Attached are screenshots from our model to help you. Cheers!

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comsol nonlinear wave mixing.png

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