# "Anti-collimators" for laser beams

I'm a student currently working on a science fair project which will measure the response of plants to coherent vs incoherent light of varying wavelengths. However, the only tunable and narrowband light source that I have access to is a tunable visible laser, which can obviously only produce coherent light. Is there a device which can destroy the temporal and spatial coherence of a laser beam so that it resembles the light emitted from a blackbody or something like that, but still leaves it monochromatic (i.e. the reverse of a collimator)?

A collimator does not change the coherence properties of your light source (i.e. the statistical phase correlation), but the propagation direction of the light. In wave optics terms, the wavefronts are made planar and orientated in the same direction, such that the beam is neither converging nor diverging. In ray optics terms, all rays are made parallel instead of converging or diverging. This results in beams of almost constant diameter, like a typical laser beam. (Note that this is an idealization: In reality, since plane waves cannot exist, all free-space beams will diverge noticeably after a certain propagation distance due to diffraction of its constituents - although this distance can be made very large.)

The coherence properties of your beam are defined by the statistical relationship between the phases of its constituents. In a coherent beam, two wavefronts starting out with a certain phase shift at the source will have the same phase shift when measured at any distance away. Such constant phase relation is the basis for visible interference patterns that don't fluctuate.

• The coherence of a source is reduced if the source has a large spatial extent, such that wavefronts are coming from many different locations and therefore many different distances to your measurement point (e.g. a screen). This makes it difficult for a clear, spatially extended interference pattern to form. Such source has a low spatial coherence. Note: Spatial extent means angular size as viewed from the measurement point, not absolute size! So the spatial coherence of a large-diameter source can be improved by simply moving it farther away, reducing its angular diameter.)

• The coherence of a source can also be reduced if the source has small size, but a large spectral extent (i.e. bandwidth), such that the propagating waves have a large variance in wavelengths. This also makes it difficult for a clear, temporally stable interference pattern to form, since the relative phases of waves with different wavelengths are constantly changing. Such source has a low temporal coherence. The mean time over which phase correlation is lost is the coherence time and, equivalently, the mean distance over which correlation is lost is the coherence length.

Note that all waves interfere, i.e. create interference patterns by constructive and destructive superposition, irrespective of the degree of coherence. So with a sufficiently fast and highly resolved camera, one could always get snapshots of distinct field patterns. The distinction is that patterns created by incoherent sources will rapidly fluctuate and/or propagate through space, such that all snapshots will look different and, in the realistic case of finite exposure times, get averaged out. The condition for coherence is therefore static interference, i.e. patterns that are stable in both time and space and, therefore, can be observed or measured at fixed positions from the source. And this is only possible if the phases of all constituent waves are strongly correlated.

A black body radiator would be an example for a broadband and therefore low-temporal coherence source. By confining its emission to originate from a very small orifice, one could create a source of low temporal, but high spatial coherence.

To finally answer your question: One way to reduce the spatial coherence of an otherwise narrowband, high-temporal coherence light source (e.g. in order to avoid speckle or fringe formation), is using a rotating ground glass diffuser to scramble the phase. See for instance here:

https://arxiv.org/abs/1703.05311

• As a sidenote: Interestingly, there is a lower bound for the spatial coherence of a monochromatic lightsource, i.e. you cannot decrease its spatial coherence below a certain value. This value, expressed in terms of the smallest possible spatial extent of an interference pattern, is achieved precisely in the case of spherical wavefronts converging to a point, such that the observed angular size of the source covers the full solid angle. The result is a so-called 4π point spread function (4π indicating the solid angle), a spherical volume with a size determined solely by the wavelength. Feb 3, 2023 at 13:11

Speckle patterns form when laser light hits small diffracting objects (~point scatterers). If the diffracting objects are moving slowly, this causes the speckle patterns to also vary slowly. You can see this with (eg) a green laser pointer aimed at your hand - the speckle pattern varies because of blood flow (essentially scattering by the red blood cells). Fun video https://www.youtube.com/watch?v=qzRUduby3mw

The scattered light you see in a speckle pattern is the closest to "resembles the light emitted from a blackbody ... but still leaves it monochromatic". In this case, the phases vary slowly enough (in both time and space) that you can see the variation with the naked eye. But what if you wanted a faster variation? Simple: have more point scatterers (decoheres in space) and have the scatterers move faster (decoheres in time). The tricky part comes in from doppler shift of the scattered light when the scatterers move fast. I think this is inevitable, essentially a signal which has a sinewave with rapidly shifting phase inherently has some spectral broadening as well: if you do a Fourier transform on it, you'll find it is not truly monochromatic, and this is independent of how the phase shift is produced.

The "rotating ground glass diffuser" suggested by @sarahslvmn is an example of a device with moving point scatterers; probably the simplest practical construction, and it would do the job. I think the time scale up to which it decoheres the light is roughly ~the time for a point on the diffuser to move across the beam.

• +1 for right answer, no grandstanding.
– uhoh
Feb 3, 2023 at 3:30
• What about a liquid or gas with a continuously variable index of refraction that fluctuates throughout? I'm not sure exactly how one would produce such a liquid, but it seems to me that it would change the degree of coherence if a laser was passed through it. Feb 3, 2023 at 16:28
• For instance, water with 10um oil droplets dissolved in which are bouncing around randomly. Feb 3, 2023 at 16:31
• @slithy_tove Yes, that would also work! One could even use something like glass microbeads/-sphere suspended in a very dense organic liquid (to slow down settling) and vibrate or agitate the mixture. Of course, a rotating ground glass diffuser is simpler to construct and you can precisely adjust the coherence by setting the focus spot size, whereas with a liquid, things might be a bit trickier Feb 4, 2023 at 17:19