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Laser light is monochromatic, coherent and (in many cases) collimated. Are these properties due to stimulated emission of radiation? Also, is it true that a photon emitted as a result of the stimulated emission is always emitted to the same mode as the original stimulating photon? In other words, is it true that the stimulated photon is exactly the same as the stimulating photon? What is strange to me is that spontaneous emission does not seem to have the above properties although we can think about the spontaneous emission as a result of emission stimulated by vacuum fluctuations.

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  • $\begingroup$ It can be a little tricky to make this precise, but generally the phase coherence of a laser is indeed due to the fact that the beam is made up of stimulated emission photons. In fact, you can basically figure out how long it will take for the phase to meander far away from its initial value by looking at the fraction of photons $\approx 1/n_{k}$ that were emitted spontaneously rather via stimulation. $\endgroup$
    – Buzz
    Nov 3, 2023 at 18:47
  • $\begingroup$ Yes, yes and yes. State transition in spontaneous emission is affected by all vacuum modes, while in stimulated emission,- just of resonant frequency and "in phase" photon is able to "knock out" atom from a population inversion to the ground state thereby producing sibling collimated photon. Good analogy of this collimation is the snow avalanche in the mountains, where new parcels of snow is also roughly "collimated" to the same direction. Old snow parcels generates new ones and the process repeats until high-power flow of snow is generated at the bottom. $\endgroup$ Nov 3, 2023 at 20:09

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Coherence is due to stimulated emission. But collimation and monochromaticity are more largely due to the cavity.

A typical cavity has two slightly concave mirrors. One is perhaps 99% reflective and 1% transmissive. If you solve the Maxwell's equations for that boundary condition, you get a number of modes where the phase change on a round trip back and forth between the mirrors is an integer number of wavelengths. In this case each successive reflection interferes constructively with the last.

There are many such modes. If one frequency has N wavelengths in a round trip, another slightly higher frequency has N+1. All of these can coexist. The laser medium has a band of wavelengths that it can amplify. Wavelengths near the center of the band have a higher gain. A wavelength at the center will grow at the expense of lower gain modes, and soon it will be the only mode.

The best shape of the solution is a Gaussian Beam. To a first approximation, a laser beam is cylindrical and the rays are parallel straight lines. This ignores diffraction, which is another way of saying the wave properties of light. In a Gaussian beam, rays are hyperbolic. Far from the laser, they approximate a cone with a typical divergence angle of a few milliradians.

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  • $\begingroup$ Excellent answer, but I would like to rephrase your 3rd paragraph in other words, in order to emphasize the selection the cavity does, to address OPs concern's regarding spontaneous emission not having specific rules, and why those arent present. The cavity is extremely highly selective to which modes are allowed, and which aren't: non-allowed modes are extremely lossy, which in turn makes them less likely to get amplified, while allowed modes are so much more efficient that they "eat away available gain". These two get rid of non-allowed modes from spontaneous emission and stabilize output $\endgroup$ Nov 5, 2023 at 14:22

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