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Change of a lens' focal point with wavelength. Refractive index wavelength independent

Posted Jul 13, 2019, 11:33 a.m. EDT 1 Reply

Nemanja Niketic
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Hello Everyone,

I was using a Comsol example for the focusing lens:

https://www.comsol.com/model/focusing-lens-57621

I made no changes to the model. The focal length of the lens is set to be 1000 um.

Initially, I was scanning the wavelength of the incident EM wave. The scan was done from 1 um to 9 um, see the attached pictures - there is also the equation solved by Comsol included in these pictures.

From the pictures, it is clear that the focal point of the lens is changing with the wavelength, even though the refractive index in the lens is wavelength independent - it is just artificially set to a some specific value.

I wish to ask you for a clarification of this effect, as I was not expecting it and was surprised to see it. My only explanation is that the usual "lens maker formula" (which states that if there is not wavelength dependent index of refraction, the focus should remain constant) is derived from the geometrical optics - eikonal equation, which in turn is an approximation for the wave equation for cases when the wavelength tends to zero.

In this case we are working in the MIR/NIR region, and maybe the eikonal equation is not valid anymore.

Could you please help me in understanding this issue?

Best Nemanja

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1 Reply Last Post Jul 13, 2019, 1:24 p.m. EDT
Robert Koslover Certified Consultant
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Posted: 5 years ago Jul 13, 2019, 1:24 p.m. EDT
Updated: 5 years ago Jul 13, 2019, 1:16 p.m. EDT

Caveats: I'm more of an antenna guy than an optics guy, and I haven't analyzed this particular model in any real detail, but here goes: I'm guessing that at the longer wavelengths, your lens diameter / wavelength ratio is simply becoming too small for the GO approximation to work well. I suspect that if you run your model parameters in the other direction, i.e., to shorter wavelengths than 1 um, that you will find that the apparent focal point will be ~independent of wavelength. (Just be sure you make the mesh fine enough, if you do that.) Alternatively, I suspect that if you enlarge your lens & beam diameter enough, you will see that independence. Just my 2 cents.

-------------------
Scientific Applications & Research Associates (SARA) Inc.
www.comsol.com/partners-consultants/certified-consultants/sara
Caveats: I'm more of an antenna guy than an optics guy, and I haven't analyzed this particular model in any real detail, but here goes: I'm guessing that at the longer wavelengths, your lens diameter / wavelength ratio is simply becoming too small for the GO approximation to work well. I suspect that if you run your model parameters in the other direction, i.e., to shorter wavelengths than 1 um, that you will find that the apparent focal point will be ~independent of wavelength. (Just be sure you make the mesh fine enough, if you do that.) Alternatively, I suspect that if you enlarge your lens & beam diameter enough, you will see that independence. Just my 2 cents.

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