Learning Forum

[Shangxuan Yu]

As a continuation of another post called "How to accurately measure propagation loss for a wave-guide with surface roughness?", I checked the example provided at the page of "Tips for adding surface roughness to structures". I am quite confused about the algorithm used in creating the geometry in the case of Advanced surface roughness. I wonder how does the correlation equation work? Why is it a more "advanced" method, any advantage conpare to the simple model? Is there any literature reference that help understanding the algorithm would be appreciated. Thanks! 

[Afroditi Petropoulou]

Hello and thank you for contacting us!

The difference between the simple and advanced models, is that in the case of the simple model the roughness is created by just adding slices of different heights using the rand command (in the example of the ridge waveguide), while in the advanced model the user can define the RMS and the correlation length of the rough surface.

The correlation length and RMS are important roughness parameters and have a significant impact when you want to accurately simulate a rough surface, especially for industrial applications where these values might have been measured and hence are available as inputs for the simulation. The difference between rough surfaces with different correlation length l but the same RMS height δ and rough surfaces with different RMS height δ but the same correlation length l can be seen in the link images.

As explained in the Tips for adding surface roughness to structures article, the set up script initially fills the surface matrix in K-space with uniform random numbers. A filter is applied to remove all high frequency components. The matrix is transformed back into real space, where the amplitude is corrected using the RMS value. The steps are the following:

• Create x and y vectors using linspace command.

• Create kx and ky vectors by applying fftk to the x and y vectors. Create Kx and Ky grids.

• Create the random Zk matrix. Each element of the matrix is Zk=rand*exp(2πi*rand)

• Subtract the average value: Zk=Zk-sum(Zk)/length(Zk)

• Apply correlation length (Lx and Ly) and gaussian shape in k space: 

Zk = Zk*exp(-(1/8)*( (Kx*Lx)^2+(Ky*Ly)^2 ))

• Convert to real space (Zrand matrix) using the czt command.

• Apply the sigma RMS: Zrand = Zrand * sigma_rms

Best Regards,

Afroditi