## Solving for SCATTERING FIELD

According to my experience:

1) Scattering field can be used when one is interested in the solutions in the near-field zone

2) When solving case of nanoparticles in uniform media

3) When we know exact analytical description of the excitation field in the whole geometry (except PMLs)

1) If we are looking for the far-field response of nanoparticle (antennas)-angular distribution or cross sections (scattering, absorption or extinction), one can utilize Straton-Chu formula that is implemented in the Comsol. This comes very handy, cause it is near-field to far-field transformation, so our modelling volume can be shrunk pretty much into the near-field zone, depending on PML performance and meshing. That will reduce computational resources and time.

2) Straton-Chu works only for homogeneous environment, thus substrate case is not covered. Modifying it to substrate case is very tricky, and I am not sure that future versions will solve this issue. However nothing prevents you to use it, and to tune your solution, which is documented in the literature, although it is mathematically incorrect.

3)Defining excitation is very simple in homogeneous environment, namely E0i=Ai*exp(-j*k0_rfw*n*r), where Ai is corresponding x,y or z component of the field amplitude, k0_rfw is free space wave vector with amplitude defined by 2*pi/lambda0_rfw, and r is radius vector. In substrate case things become more complicated, cause introducing interface brings into play Fresnel coefficients, and it has to be solved by you analytically (old fashion way-pencil and paper). These expressions can be more than hundreds characters long for each component depending on incident angle, and so very prone to typo errors. Also, total internal reflection (TIR) case is similar. Reported 2-step procedure gives no difference according to the test I had performed in the past, so I don´t recommend playing with it.

Even if you use Straton-Chu formula in improper way, most likely that you will get resonances positions correctly, but amplitudes and radiation pattern can be wrong.

1) Scattering field can be used when one is interested in the solutions in the near-field zone

2) When solving case of nanoparticles in uniform media

3) When we know exact analytical description of the excitation field in the whole geometry (except PMLs)

1) If we are looking for the far-field response of nanoparticle (antennas)-angular distribution or cross sections (scattering, absorption or extinction), one can utilize Straton-Chu formula that is implemented in the Comsol. This comes very handy, cause it is near-field to far-field transformation, so our modelling volume can be shrunk pretty much into the near-field zone, depending on PML performance and meshing. That will reduce computational resources and time.

2) Straton-Chu works only for homogeneous environment, thus substrate case is not covered. Modifying it to substrate case is very tricky, and I am not sure that future versions will solve this issue. However nothing prevents you to use it, and to tune your solution, which is documented in the literature, although it is mathematically incorrect.

3)Defining excitation is very simple in homogeneous environment, namely E0i=Ai*exp(-j*k0_rfw*n*r), where Ai is corresponding x,y or z component of the field amplitude, k0_rfw is free space wave vector with amplitude defined by 2*pi/lambda0_rfw, and r is radius vector. In substrate case things become more complicated, cause introducing interface brings into play Fresnel coefficients, and it has to be solved by you analytically (old fashion way-pencil and paper). These expressions can be more than hundreds characters long for each component depending on incident angle, and so very prone to typo errors. Also, total internal reflection (TIR) case is similar. Reported 2-step procedure gives no difference according to the test I had performed in the past, so I don´t recommend playing with it.

Even if you use Straton-Chu formula in improper way, most likely that you will get resonances positions correctly, but amplitudes and radiation pattern can be wrong.