Learning Forum

[akhalili]

Hello Lumerical Community,

I hope this message finds you well. I am currently working on a project that involves designing an achromatic metalens, and I need to simulate and plot the phase of the transmitted electric field as a function of frequency using Lumerical FDTD. Just like the examples in Fig. 2 of this paper: https://www.nature.com/articles/s41565-017-0034-6

Setup Details:

• I have designed my unit cell and set up the simulation region with periodic boundary conditions.
• I am using a plane wave source covering a wavelength range from 400 nm to 700 nm (circular polarized).
• I have placed frequency-domain monitors to capture the transmitted fields.

Challenge: I need to perform a frequency sweep to collect phase information of the transmitted field and then plot the phase as a function of frequency. I am specifically looking for guidance on:

The exact parameter to select in the sweep settings to capture the phase angle (phase shift) of the transmitted electric field.

Current setting in sweep window:

Current Attempt:

• I have set up a parameter sweep for the wavelength range with multiple points.
• I am unsure if selecting the "angle" parameter in the monitor results is correct for capturing phase information.
• So far, I simulated the red square (right) unit cell and the purple one (left), but the results are not similar to the paper (the range of the phase etc.) (attached photo)!
• 

I would greatly appreciate any detailed instructions or examples from those who have performed similar simulations. Your expertise and suggestions will be invaluable to my research.

Thank you in advance for your help!

Best regards,

 

 

 

[Greg Baethge]

Hi Alireza, thank you for posting your question. The main issue here is, I think, the phase cannot be directly extracted from the electric field stored by a monitor, as this phase will depend on the position. To avoid this, the typical approach is to use the S parameters, complex transmission and reflection coefficients, of the nano-structure. This is the approach we use for our metalens example. This calculation can be done in FDTD using the S parameter analysis group from the object library, or it can be obtained from the RCWA solver directly (this is our current approach). Also, note that, you don't necessarily have to sweep over the wavelength as you can run a broadband simulation (although this can get tricky with FDTD at non normal incidence).