# Is there a way to take randomly-directed photons and deliver them in a parallel manner?

What I'm asking about is a sort of filter that adjusts the direction of propagation of photons hitting the filter so when they pass through they all have the same vector. This is a simple sketch to illustrate the idea. Is it physically possible? Is there perhaps such a technology already?

• Are you specifically asking about a passive optical element? Otherwise, the most straightforward solution would just be to absorb the photon entirely, track its direction of travel and energy, and create a new one in the right direction. Feb 24 '20 at 18:17
• @David White I want to use available light rather than generating new one.
– TLSO
Feb 24 '20 at 18:21
– rob
Feb 24 '20 at 18:37

This configuration is forbidden even in classical geometric optics; you don't even have to think about photons at all, it's impossible for light rays in general to behave in the way that you describe.

The reason is summarized in the following question: What happens if you run your apparatus in reverse? With a normal passive optical device, like a lens, there is a one-to-one correspondence between the direction of the output ray and the direction of the input ray. This means that, for every possible input ray there exists a unique output ray, and conversely it means that you can always reconstruct the input ray that created a particular output ray. This means that, for a valid passive optical device, you can always run it in reverse with no problems.

But for your device, all of the output rays come out in the same direction. How do you know which direction the input rays came from? You can't actually invert the function that takes an input ray to an output ray, so it can't be a valid passive optical device.

This rule of thumb is derived from a property of passive optical systems called the conservation of etendue. The light coming into, and going out of, a passive optical device is distributed over both a particular area and a particular range of (solid) angles. Conservation of etendue states that the area of the input multiplied by the solid angle spread of the input is the same as the area of the output multiplied by the solid angle spread of the output.

For your device, the input has both a finite area and a finite solid angle spread (since rays come in from random directions). However, the output has a finite area and zero solid angle spread (since output rays are all in the same direction). This means that your device can't be passive - optical power is not conserved, so there has to be something supplying power to manipulate light in this way.

You can also see this qualitatively from a thermodynamic standpoint. Assuming that the energy distributions of the input and output photons are the same, and you only change their direction, it's clear that the output photons have a lower entropy than the input photons (since they aren't random in direction anymore). By the Second Law of Thermodynamics, you can't have a process that decreases the entropy of the universe, so your device has to increase the entropy of its environment, which usually involves waste heat or something similar.

So it's clear that you can't build a passive filter that does this. What you can do, however, is approximate this filter: you can certainly build a device that collects light from random directions and redirects it into a cone of directions close to a particular vector. Precisely how close you can get is limited by conservation of etendue: if your input has an area $$A_{in}$$ and each point on it can accept light from a solid angle $$\Omega_{in}$$, then the solid angle around your chosen vector $$\Omega_{out}$$ is only limited by the area of your output:

$$\Omega_{out}=\frac{A_{in}\Omega_{in}}{A_{out}}$$

In other words, the bigger the area of your output, the more uniform the direction of your output light can be.

• Basically the final process I'm looking to create is having the original scattered influx of photons focused to an almost singular point. From my simple understanding for a lens to do that the input should be parallel all through its diameter, and that's why I was thinking whether there's a way to coherently "prepare" the photons like this before meeting with the lens. But it doesn't need to be perfect, so how close is a possible approximation? Perhaps collimating and then using a lens is not the only solution, and something else could be put together for this purpose?
– TLSO
Feb 24 '20 at 19:48
• @TLSO Careful with phrasing - if you actually do want coherent light, as opposed to simply collimated light, then there's definitely no way to do that passively (since the random incoming light is probably incoherent and has a random phase). How close you can get is dictated by conservation of etendue - see the last paragraph of my answer. Feb 24 '20 at 20:16
• @TLSO Conservation of etendue tells you what's physically possible for a given area-solid angle combination; it doesn't tell you precisely how to construct such a device, though, and the details of such a construction are likely beyond my expertise. As my answer says, though, it should be possible to approximate the behavior you want, as long as you don't mind this device either being pretty big or pretty dim. Feb 24 '20 at 20:18
• Yeah, I was only referring to the vector of the waves being identical, but not to their phase or frequency. But if by "dim" you're referring to photons being "lost" in the process, that's counterproductive for what I'm looking to achieve. How does a collimator work? By not allowing the photons that aren't parallel to pass through, rather than causing non-parallel photons to propagate in a parallel manner?
– TLSO
Feb 24 '20 at 22:03
• @TLSO Oh, no, by "dim" I simply mean low photon count per unit area (i.e. same number of photons as input, but distributed over a bigger area). A collimator blocks photons that aren't traveling in the right direction. Feb 24 '20 at 22:16

Such technology exists for X-rays used for imaging purposes. X-rays are a good demonstration of photons getting collimated into a beam, for example here

For visible light putting the source at the focus of a lens will give parallel rays going out. Photons will be bound by the topology of the classical beam.

The suggestion made in a deleted comment of using a laser if a parallel beam is needed, is efficient in energy use, and simple.

• Note: this doesn't adjust the direction of propagation of light. It simply absorbs light that isn't traveling in the right direction. Feb 24 '20 at 18:59
• @probably_someone The Xrays yes, the using the focus as the location of the source ir works. I am trying to think if one could make a plane of small lenses whether , it would work the way the OP wants Feb 24 '20 at 19:03
• As you can see from my answer, a plane of lenses can't do this, because it would violate conservation of etendue. You can only approximate the behavior the OP wants with passive optical elements. Feb 24 '20 at 19:04

How about a reflective cone that collects the randomly oriented rays onto a small diffuse object which you place at the focal length of a lens? Maybe not very light efficient.