How much is possible to concentrate a laser beam on a plane? For example is it possible to concentrate 4 laser beams on 4 close spots on a surface equal to 1 mm^2 without interference?
A laser beam can be focused to an astonishingly small spot size. For example that is how they make the tiny features on your computer chips (at least down to the 50nm node anyway). The size of the focal spot depends on the wavelength and the cone angle. For a near diffraction limited beam you will get an Airy pattern. The radius from the center of the spot to the first Airy null is 1.22 x (wavelength) x NA where NA is numerical aperture and is the sine of the half cone angle.
Many lasers are nearly diffraction limited and can achieve something very close to the diffraction limited spot size. However others are not. Choices in how the beam is formed or aberrations in optics spoil the beam. This is called the beam quality. It is compared to the perfect diffraction limited beam by a parameter “M”. You would say that the beam is “M times diffraction limited”. Then the smallest spot size is M^2 the diffraction limit.
In your case the trick is the NA. How close together can you squeeze 4 lenses? And it’s not just the lens size, it’s the size of the beam going into the lens that determines NA. To avoid working with tiny lenses and short focal lengths you might want to expand the beam beam so it nearly fills a reasonable sized lens. The beams can be tilted towards each other to put the spots close together as you show, but that gets harder and harder as the NA gets larger.
So, for example, suppose we have 2 HeNe lasers (almost always very nearly diffraction limited) We expand the beams so the 1/e^2 diameter is 10 mm and put them into good aspheric lenses with diameter = 12.5 mm and focal length = 10 mm. That gives an NA of about 0.45 and a long enough focal length that the beams can be tilted together to put the spots next to each other as you show. In that case the Airy radius is about 1/3 of a micron. As I said, astonishingly small.
Theoretically the laser beams with different wavelengths or polarizations can get very close to each other without interference.
It rather depends on what you meant by "without interference". As someone say earlier, you can focus a laser beam to a very tight spot. The amplitude distribution is given by J1(r)/x, which is the so called Jinc function, with J1 the first order Bessel function of the first kind and r is the normalised radial coordinate. The main-lobe of the Jinc function has a diameter given by 1.22*Lamda/NA. In theory, with reasonable optics, you can get the diameter of the main-lobe down to micron level. Whether you can place another focused spot a few microns next to the first one requires more consideration. Apart from the main-lobe the Jinc function will have light amplitude spreading from the centre, and in theory the spreading has an infinite extent. Therefore no matter how far away you put the second light spot relative to the first one, there will always be fields from the two spots which would overlap, and interfere with one another. The amplitudes of those fields are small as you go away from the centre. So the question really is: how small an interference can you stand. With this question answered, one should be able to come up with an optical arrangement for your application. Hope the above is of use.
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