Optical bandpass filter at focal point of lens

Question

Optical bandpass filters are designed for a particular angle of incidence (AOI), e.g. see Fig 4 here.

However that is for the ray picture of light. Imagine I have a thin bandpass filter positioned exactly at the focal point of a lens, and a gaussian beam coming in. Right there at the filter, the beam has some beam waist and the phase fronts are parallel. Since the phase fronts are parallel, does that mean that the light will pass through the bandpass filter as if it were all normally incident? Or, will the extreme-angle rays not be filtered in the same way (the filtering function smoothed and blue-shifted, as described at the link I pasted above) as the axial rays?

Answer 1

This depends completely on how broad the angular spectrum of the gaussian beam is $-$ i.e., basically, on where it sits in the spectrum between tightly-focused and completely collimated.

• If the angular spectrum is tight (i.e. if the beam is loosely focused), then you can essentially consider the action of the bandpass on the full spectrum to be the same as on the central angle, which basically means that you work as in the ray approximation.

• However, if the beam is tightly focused, which in practice means that the angular spectrum of your beam encompasses significant variation in the optical response of your bandpass, then this will no longer be the case, and each of the plane-wave components of your beam will have a different optical response, probably leading to some pretty ugly spatio-spectral coupling in your beam.

Unless you have very good reasons for doing so, and you're fully up to the resulting complexity, it is a much better idea to use a loose-focusing geometry with that type of device.