Curve fitting Fresnel equation

Hi, my friend and I are trying to obtain metal film thickness and dielectric constant through Fresnel equation based on surface plasmon resonance (SPR) experiment. The parameters that we got from experiment are the incident angle and reflectance. We used the curve fitting apps on MatLab. For the first approachment we got the result “Complex value computed by model function, fitting cannot continue. Try using or tightening upper and lower bounds on coefficients”. Then, we change the lower bounds and we got “NaN computed by model function, fitting cannot continue. Try using or tightening upper and lower bounds on coefficients”. Anyone in here has any suggestions about our problem? Thank you.

[Torsten]

Anyone in here has any suggestions about our problem?

My guess is that you use mathematical operations that lead to complex numbers in your model equation (e.g. the power or the logarithm of a negative number).

If this is not the case, please show your code.

Answer 1

[Shashwat Bajpai]

Following is a set of equations which calculates the reflectance for a S(Rs) and p(Rp) polarised incident wave.

According to my understanding you are getting complex values of reflectance because of the nature of these equations. Please take look at the values you receive for reflectance and try removing the complex part to use the curve fitting apps.

Hope this helps!