# How to calculate the phase of a nanopost?

#1

Hi, I am new to the Lumerical FDTD. I am trying to quantify the phase shift that a nanopost exerts on the incoming wave as described in the paper https://arxiv.org/abs/1711.07158 Fig. 1b and in the paper https://arxiv.org/abs/1708.01972 Fig. S2 b.

I also look through this post in KX. It seems that the phase retardation is calculated for a single point. I wonder how to quantify the phase delay that the post introduces as a whole device? So much thanks!

#2

Hi @ztk18

We use a point time monitor to calculate the phase. This is because time monitor records the electromagnetic fields (both magnitude and phase) at a mesh cell (Yee cell) as a function of time. This means that we can study how the field is modified at a point in the presence of nanospot. You can obtain the information about the point where the phase is calculated from the paper.

#4

(1)where to put the point(the axial and lateral position)?
(2)and why monitoring the evolution with time rather than the stable field distribution?
Thanks again!

#5

Hi @ztk18

1. I checked the attached papers, but still not quite sure where this point is located. It is possible that the authors measured the phase in the focal point. There is also phase profile of the metalens which is related to the design of the metalens and should not be confused.

2. I am not sure what you mean here. By Fourier transforming the results of time domain monitor (i.e. E(t) and $\phi(t)$), you can obtain the phase information as a function of wavelength (i.e. E($\lambda$) and $\phi (\lambda)$). I think authors refer to $\phi (\lambda)$ here.

#6

1. Actually the phase profile of the metalens is exactly what I want to retrieve. What do you mean by the design of the metalens?

#7

Hi @ztk18

oh! If that’s the case, you can use s_param_adv analysis group to calculate the phase in the presence of a nanospot. For more details, please visit the link below:
https://kb.lumerical.com/en/index.html?metamaterials_metalens-design-example.html

and check these files which relates duty cycle to the phase profile:
metalens_2D_duty_cycle_sweep.fsp
metalens_2D_duty_cycle_sweep.lsf

Please let me know if you have any further questions.

#8

I found the related document read the script you listed. And I have a question on the script:

How is the transmission power in each grating order calculated in the function grating? The document of the function does not describe much about the details. Say, if I only have the field distribution on the monitor, how can I allocate the field to each grating order myself?

Thank you!

#9

Hi @ztk18

The grating functions automatically calculate the fraction of power in each grating order. The near field results is decomposed into plane waves with different k-vectors and then are propagated to farfield. More details can be found in the direct below:
https://kb.lumerical.com/en/solvers_grating-projections-(fdtd).html