I'm searching for an optical element that converts a parallel bundle of individually collimated beamlets into a converging or diverging bundle of still collimated beamlets (or vice versa). So basically the blackbox in the following ray diagram, but with beamlets (red, green, blue) going from right to left:

Ray diagram 1

(Image: Modified from original)

The diagram is actually a good representation of the problem as, after passing through the optical element in question, the beamlets are supposed to be focused by a telecentric lens system (here: "Lens, f = 100 mm"), with the aperture stop representing the rear entrance pupil of the telecentric system.

  • The big challenge here is that the angle of the individual beamlets passing through an aperture stop needs to stay variable or, in other words, the spacing of the parallel input bundle. Therefore, e.g. a lens/fiber array or segmented prism would not work as the distance between the individual beams isn't fixed.
  • Also, a potentially large number of beamlets would quickly drive up material costs and alignment complexity. Consider e.g. a confocal array of 100 fibers, requiring 100 output collimators, 100 fiber launchers for 1000-1500 EUR apiece (or some crazy 1-to-100-port fiber multiplexer), and 200 individual alignments. Clearly, a monolithic solution would be extremely beneficial!

Obviously, a simple/economic solution is desired, as one surely can - somehow - design a super-complex system with dozens of elements that does the job. This also precludes any fancy control loops with adaptive optics, wavefront sensors etc. In other words, the system should be scalable and lend itself e.g. to miniaturization.

I've been thinking about this for a while now and was hoping that maybe there is something blatantly obvious that I'm missing...

UPDATE 1: Let me further relax the problem constraints by allowing

  • approximate solutions, i.e. both the size and position of the aperture stop may vary within reasonable bounds and therefore also the focus plane ("Object" in the diagram), since one can always readjust the focus with a simple zoom system. Condition: All beamlets must be focused into the same focal plane by the telecentric system.
  • static solutions, i.e. a fixed beamlet spacing at the input/fixed angles at the aperture stop. Condition: The required optics are cheap, can be bought off the shelf, and do not require custom manufacturing (such as segmented/multifaceted prisms).
  • loss of optical power as my sources are cheap and can easily be scaled up in power (LEDs, laser diodes).

I should also mention that, differing from the diagram, the individual beamlets do not actually overlap, which could potentially simplify the problem. Imagine a bundle of expanded and collimated laser beams that all need to pass through a small aperture while retaining collimation (or at least have identical wavefront curvatures, so all beamlets are focused into the same focal plane by the telecentric system). For clarity, here is a second sketch showing only the optical element in question (please ignore the non-uniform output beam diameters):

Ray diagram 2

Also, if not already obvious, the diameter of the beamlets are free to change uniformly across all beamlets.

UPDATE 2: This problem might fall under the category of non-imaging and/or transformation optics.

After some more brainstorming, I'm currently thinking about

  • meniscus lenses
  • gradient index lenses

but I don't have the experience or tools to find a working solution, e.g. by ray tracing simulations.

  • 1
    $\begingroup$ Because such a device reduces the entropy of the light, it would have to be active rather than passive, and thus would take energy from either the light, itself, or from an external power source. BTW, I'm not aware of any such device. $\endgroup$
    – Digiproc
    Feb 16, 2023 at 0:59
  • $\begingroup$ Hi @Digiproc, could you explain in a bit more detail what you mean by entropy of light? Also, loss of power would be totally fine as I'm working with cheap, scalable sources that provides much more power than required (LEDs, laser diodes) $\endgroup$
    – srhslvmn
    Feb 16, 2023 at 1:22
  • 1
    $\begingroup$ Consider that thermodynamics forbids one to create a passive device that focuses light such that the absorber gets hotter than the surface temperature of the emitter. The device you are looking for would have to do just that, and therefore it would have to be an active device (i.e., you have to add extra energy to it so it would work) $\endgroup$
    – Digiproc
    Feb 16, 2023 at 20:17
  • $\begingroup$ ...actually, I don't think this problem does not violate any thermodynamic laws as it's clearly possible to realize such device, although I cannot think of a simplistic solution (hence, the question). $\endgroup$
    – srhslvmn
    Feb 17, 2023 at 7:31
  • 2
    $\begingroup$ I've explained why a similar scenario is impossible in Is it possible to construct a lens which focuses all the light rays from an extended object in one point?. Have a look at the third picture from the top in my answer there. This is the situation you describe in your question. $\endgroup$
    – A. P.
    Feb 19, 2023 at 17:51


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