Hi Rituraj,

There are two important aspects in modelling, you should always check and be aware of:

(a) What approximations have been made? (e.g. electrostatic limit, local approximation, dipolar approximation, etc.)

(b) What are the convergence criteria of the method that is used? (e.g. meshing, element size, orbital momentum number, reciprocal space vectors, time steps, adaptive methods, etc.)

To point 1)

Mathematically, Maxwell's equations in time and reciprocal (frequency) space are equivalent, and in principle, different methods should yield same results. However, approximations often have to be made in order to obtain equations that allow implementing a feasible numerical framework.

To point 2)

For analytical methods, most likely stronger approximations had to be made. In the electrostatic limit, e.g., retardation effects are neglected, and the method is not suitable for more complex, larger systems.

To point 3)

You are naming comercial software, not numerical methods. Those are - to my knowledge - based on FEM/FTDT. Under similar settings regarding, e.g., meshing and boundary conditions, they should yield similar results. These are suitable for larger and more complex structures with no symmetries, however, convergence is an issue to keep in mind for small gaps, corners/edges etc. and computational time suffers from complex meshing.

I'd recommend reading: Article Modeling the optical response of gold nanoparticles

which compares different methods and discusses in depth advantages and disadvantages of those methods for gold NPs of complex shapes.

And regarding implementing nanoscale effects beyond classical Maxwell's equations, my own work might help:

Article Microscopic Electron Dynamics in Metal Nanoparticles for Pho...

All the best,

Christin

Hi Christin,

Thanks a lot for your elaborate answer. It really helps!

Deeper insight is really needed in certain cases where the system is complex. For instance, on COMSOL I am able to converge a solution (using direct solver) for a micron size silica nanoparticle, but the scattering spectra is completely noisy. Even with adequate mesh and other parameters, these converged solutions dont seem convincing when there is not enough literature in support.

Edit: It is also a bit "discomforting" to see that even for simple gold nanospheres, the agreement is not very good (error>1%) at lower wavelengths. Generally, at LSPR, the agreement is better. This is an intriguing aspect for me as I probably do not have sufficient insight into the Maxwell's equations and the solution procedure.

I'd like to add that besides those pointed out by Christin how the electromagnetic or optical materials are modeled concerns different levels of approximation, ranging from classical, semi-classical, quantum to experimental data.

And regarding the figure you appended I believe something is wrong with the simulation or Mie results. For such a curve it should not be very difficult to make the results agree with each other.

Thank you Pu Zhang for your answer.

Yes, I believe it may be an error with the Mie code as the COMSOL results agree with some other literature.

Another uncertainty might be in the material data used. Are you sure that COMSOL and your Mie code use the same permittivity, e.g. Johnson&Christy data? The next question would be, what inter-/extrapolation technique is used to connect the permittivity for values that are not in the list (linear, cubic etc.).