Hello all,
I'm currently researching metalenses and facing an intriguing challenge.
In my simulations using Lumerical FDTD, based on methods from DOI: 10.1038/ncomms8069, I'm trying to calculate the focus efficiency of metalenses. My process involves placing an aperture at the incident with PML boundaries and measuring the total intensity at the focal point. Initially, I conducted this with only the glass substrate, then repeated with both glass and nanopillars, measuring over an area about three times the FWHM at the focal point.
Here's where it gets puzzling: The intensity with just the glass substrate is consistently lower than with both glass and nanopillars. Interestingly, I also tried the process without any glass substrate at the incident, yet the focal point intensity remained significantly higher than expected.
Could you offer any insights or thoughts on why this might be happening? Your advice or any pointers towards relevant resources would be invaluable.
Thank you for your time and consideration.
Best regards,
It‘s hard to say without more information. My only thought is probably ridiculous, and not at all what you are actually doing. However, one way to see what you describe is if the aperture is very small. It is easy to run up against the diffraction limit. If D^2 < 2*lambda*focal length you can’t make a spot smaller than D. Anything you put in the aperture to modify the phase and try and concentrate the light can only make the spot worse.
For example, let’s say your screen is 5 cm from your aperture and you are trying to design a lens to focus the aperture into a tight spot on the screen. If your aperture was only 0.2 mm in diameter (I know, I’m sure that’s not what you’re doing. I’m just saying this would match the described behavior. And this is just the sort of thing people might do in Lumerical). Then the diffraction limited spot on the screen through the bare aperture is also 0.2 mm in diameter. The minimum spot size is already as big as the source, and diffraction guarantees you have no chance of focusing it down. When you add a 5 cm focal length lens to concentrate the light, it can only spoil the spot and make it more diffuse. That’s why it’s called the diffraction limit. It is the limiting best case. Now, a faster lens with a shorter focal length could make a spot smaller than the aperture on a screen much closer to the aperture. Conversely, a 5 cm lens could make a spot on a screen at 5 cm that is smaller than some larger diameter aperture. But no lens or metalens or fresnel lens is going to make the spot from a 0.2 mm aperture smaller than that at a screen 5 cm away.
Because Lumerical does an incredibly large complete simulation at the wavelength scale people sometimes make very small dimensions to keep the calculation time down. That’s why I’m mentioning the diffraction limit. However, like I said, I’m sure that isn’t what you are doing. I’m just noting that’s one way to get the symptoms you describe.
Hi Mike,
Big thanks for getting back to me about my metalens research woes. Your thoughts, especially on the diffraction limit and aperture size, really opened my eyes – much appreciated!
So, I've been digging back into my data, and I think I found where I might have goofed up. I was measuring light intensity (Abs²) all this time, not the power of light (the real part). This little mix-up probably threw my numbers all out of whack.
Thanks a ton for your help and for sharing your wisdom.
Cheers,
I believe abs^2 is what you want. The instantaneous electric field is not generally a measurable quantity (due to the impossibly high frequency). What you see on a screen or what any detector measures is the abs^2 intensity.
Thank you so much for your input; you're absolutely right! Your insights have led me to reconsider the integration of Poynting vectors in my simulation.
Also, I used to set up the mesh as non-uniform, which I now believe was the main source of the problem. I've since switched to using a uniform mesh type.
Your advice has been incredibly valuable in guiding my work. Thanks again for your help!
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