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I'm working a lot with lasers the last few years, and trying to understand the basics. So some of what I say next may be wrong or partially correct - if I find that out, that will be valuable.

As I understand it, a laser is a light source (these days it might well be a diode) where the frequency and phase of the light is coherent. If you use suitable optics, you can then make a parallel beam which can then be focused onto a spot. If the spot is small enough and the power high enough, that beam can then be used for applications such as cutting, basically because it heats the surface it falls on to very high temperatures.

My question is this : couldn't you do the same thing with (for instance) a high power LED? You can certainly have a fairly narrow band of frequencies from a non-laser, if that makes optics design easier. So why, then, do we favour lasers for this kind of application? Why do we prefer the light to also be phase-coherent?

danmcb
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Laser light has an important property: it's initially (in the cavity) very well collimated. If the exit aperture of the cavity is large enough, then the beam remains collimated, which makes it easy to focus it to a very small spot (on the order of wavelength). If the aperture is so small that beam diverges considerably, this means that the aperture has the size on the order of wavelength, which makes the light source basically point-like. Such a beam can be collimated easily, and the resulting collimated beam can be focused* to a spot with size similar to that of the aperture.

An incoherent light source, OTOH, is usually much larger than wavelength of light it emits. The result is that, due to conservation of étendue, such light can't be focused to a spot smaller than the size of the light source, and thus its power density can't compete with that of a laser of similar power output.

*Of course you don't have to first collimate and then focus, this can be done in one step by correct placement of the lens.

Ruslan
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    is this so? actually it's contrary to what I learned on the project I worked on, where we use laser diodes and then a collimating lens. I understood that the light coming out of the diode, while coherent, was scattering in all kinds of directions. – danmcb Jan 24 '20 at 23:01
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    @danmcb it wasn't "scattering", it was expanding due to diffraction. But in any case, since the emitting aperture is very small, this beam can be refocused back to almost the same size (or collimated to an almost non-divergent beam). This is addressed in the first paragraph of my answer. – Ruslan Jan 24 '20 at 23:15
  • @danmcb Correct. Lasers are always coherent but do not always need to be collimated. But being coherenct does make collimation a lot easier – DKNguyen Mar 27 '22 at 00:18
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The acronym LASER is short for "light amplification by stimulated emission of radiation". The stimulation part is important, because this way we are able to obtain high energy densities. In contrast to a light bulb or a LED, the laser beam is also rather directional. This enables us to focus the beam onto "small" spot sizes. Thereby the energy density increases further.

As Jon Custer already pointed out, the coherence is not really that important. A $CO_2$ laser is not particular coherent. However, it efficiently uses the available power and transfers it into the laser modes -- all high power lasers must by multi-mode, because the population inversion factor can't be larger than $1/2$.

Semoi
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    "Rather directional"? Have you ever tried to disassemble a laser pointer or a CD/DVD/BluRay head, removing the lens and then turning on the diode laser in there? Its divergence angle can easily reach 40°, which is quite comparable with that of a LED. See Why does a laser beam diverge? for details. – Ruslan Jan 24 '20 at 21:39
  • I have set-up several "low power" diode lasers and tapered amplifiers, but also "high power" solid state lasers. We didn't aim to cut materials, unfortunately, sometimes we still managed to do so. As I see it, the divergence of the laser beam at the output is the wrong characteristic to look at. Take for example a fibre laser. The light travels/is generated along the fibre. Thus, I would say that it is "rather directional". Nevertheless, at it's output the laser beam is diverging. However, this is such, that we are able to refocus the beam. – Semoi Jan 24 '20 at 22:06
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    Well yes, in a fiber laser you can say that light is "directional". But what about the diode lasers? They have a cavity a fraction of millimeter long, on exit from which the beam diverges quite much. I wouldn't say anything about "directionality" (in the layman meaning) of such a laser. "we are able to refocus the beam" — this is what saves us, and what makes lasers different from e.g. LEDs and even such small light emitters as xenon arc lamps, which are still incomparably larger than laser diode apertures. – Ruslan Jan 24 '20 at 22:12
  • it seems to me that there is probably not a single correct answer to this question - it depends on the use-case. On my project we are not cutting but exposing a photo-resist - laser diode is of the order of 100's of mW. But when the beam is well focussed, it is powerful enough to leave a burn make on the surface, although not to cut. And this beam is quite coherent, and single mode - we could not focus accurately enough otherwise. – danmcb Jan 24 '20 at 23:06
  • I don't believe that this question is about lasers which produce "just a few watts". Usually, if one speaks about laser cutting, one is referring to lasers which are used in industry. These beasts are to my knowledge not made of diodes. But since I left that field many years ago, things might have changed. – Semoi Jan 25 '20 at 00:05
  • I’m gonna concur that saying lasers are “directional” is nonsensical at best. Lasers in industry are not directional until the beam goes through a lens. The lens is not part of the laser and has nothing to do with "light amplification by stimulated emission of radiation". – Navin Apr 02 '22 at 05:37