| MadSci Network: Physics |
Hi Dave,
Interesting question you have there. Let's first take a look at the laser system you use. LPSS means, if I'm not mistaking, Lamp-Pumped Solid State. This is a laser in which the lasing medium is pumped by flash lamps. The lasing medium is a solid-state crystal, just like the original laser as invented by Maiman [1]. TEM00 means that the laser is blasting light out in the first harmonic. This is important, as other laser modes tend to have larger light patterns; the first harmonic is basically a single spot on the axis of the beam, and is generally the smallest pattern you can get with a laser [2]. Q-switching is essentially a technique in which the laser power is "saved up" for very short, very intense bursts, typically in the nanosecond range [3]. This leads to enormous peak power, which is very nice for cutting things.
Having explained the jargon, we'll take a look at your question: What is the relation between the wavelength and the beam diameter? Well, the total theory is extremely complex, and I won't go into that. The specs of your lasers should give you those details. Instead, I'll take a look at the general physics that's behind it, and give an approximate relation.
The absolute minimum of the beam width of a laser is determined by diffraction. This case occurs when the laser is focused by a very good positive lens in something resembling a point source, with size dmin The wave-like nature of light causes the focus size to be finite, however. The formula is[2,4]:
dmin=2.44 f &lambda / D
where D is the size of the laser beam as it is produced by the laser and f the focal length of the lens that is used, and &lambda is the wavelength. As you can see, the bigger the beam is, the smaller you can focus it-quite a surprising result. More importantly, the spot size gets bigger for larger laser wavelengths. This is intuitively correct: diffraction is caused by the finite size of the wavelength of the used light, so bigger waves should make it worse.
Without going too deeply into the subject of diffraction, the basic cause of it is Huygens' principle. In this method, each point of a wavefront is seen as a source of secondary spherical wavefronts [4]. When the spot size becomes comparable to the laser wavelength, the "blooming" caused by the spherical wavelets at the edge of the beam limits further reduction of the beam size.
I hope this explanation clarifies things a bit. Essentially, larger wavelengths mean a larger focus. If the physics behind it are not quite clear, I recommend you pick up a basic university text on optics, such as [4], where the theory behind diffraction is explained.
Good luck cutting your diamonds,
Bart
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