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.
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.