Hi all,
I have a rectangular UV laser beam (4*2 mm) that I want to filter in order to keep it's TEM00 mode. I am wondering if it's better to use a rectangular slit instead of a pinhole. Also should I consider the diagonal of the rectangle as beam dimension or the rectangle length (4mm) in order to calculate the pinhole's dimeter.
Thanks for the help.
One has to be careful with diffraction effects. A rectangular slit may result in a "starburst" type of pattern. The majority of the intensity will be concentrated in the central maximum (similar to Airy disk with a pinhole aperture). I think the 2 mm dimension is to be used for any calculations you need.
Im not 100% sure as to what set up you have but look into a 4f system/ spacial Fourier filtering
The most effective way, although sometimes hard to achieve depending on the equipment you have available especially given you are working in the UV domain, is spacial filtering (using a circular filter) to ensure an absolute TEM00 mode. One other possibility to attain TEM00 is to pass the light through a long single mode fiber.
By TEM00 I assume you mean a Gaussian transverse spatial profile. A rectangular slit certainly won't do (it will produce a sinc^2 type diffraction pattern). The simplest solution would be to use 2 mm diameter iris as you want to fill the iris completely. This will lead to an Airy pattern in the far field, closer to a Gaussian profile but with small modulations that show up as outer rings with reduced intensity. Of course you would then loose a large fraction of the original intensity.
If you really need something very close to a Gaussian beam you could try a mirror with a Gaussian spatial reflectivity profile, but for UV wavelengths this would probably be a custom item that you would have to order from a specialty supplier. A specialty holographic filter or a spatial light modulator that works in the UV are other possible alternatives.
Dear Salma, since you have to filter a multimode beam in both dimensions, a rectangular slit is not approriate. If you focus your beam with a spherical lens, your pinhole has to match the diagonal of your beam (d=1.22.lambda/sin(alpha)) for the best filtering. If the intensity is for you an issue, you must use two cylindrical lenses to match both convergence angles (alpha) before your pinhole. Good luck.
Dear Salma,
"TEM00" and "rectangular" are not really self-consistent. If you started with a round TEM00 beam, and then passed it through an aperture to make it the shape you describe, then there will be diffraction effects as you move downstream from the aperture. Can you describe the source of the beam and what has been done to it between the source and where it is 2mm by 4 mm?
In general, almost any beam which is not Gaussian (it can be elliptical instead of round, but it can't have sharply defined edges) will change shape as it propagates.
You cannot produce a TEM00 beam by spatial filtering. What you can do is remove fast wiggles in the beam's amplitude and phase, as described by J.M. Poyet above.
Please note that the "strong lens" mentioned by Efrain Solarte is only needed if you are using a small pinhole. If instead you use a weak lens, you simply need a wider aperture. With a lens of, say, 10 cm focal length, and assuming a UV wavelength of 400 nm, your 2mm dimension would focus down to about 20µm (full-width at half max), and the 4mm dimension would focus down to about 10µm. You could use a variable slit of those dimensions. If you go to a ten times longer lens your slit would be ten times wider.
Hi Salma Bejaoui, to answer your question, you should remember that lens focal plane, where pinhole usually is placed, is plane of angular distribution of laser beam intensity, while you are speaking about its spatial (rectangular) shape. It seems that rectangular shape was produced by kind of diaphragms or other optical elements, interaction with which will produce diffraction effects in beam intensity distribution. They will be present in focal plane and filtered or not by pinhole. Result will depends on relationships between their angular width and angular size of pinhole.
I don't know details of you layout, but if you need rectangular shape of the beam, it would be better to filter it by pinhole and only then direct beam through rectangular diaphragm, trying to minimize distance between diaphragm and place, where beam have to rectangular.
Good luck!
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