I understand that when a photon of specific properties (phase, wavelength..) comes near an excited atom with sufficient energy, the atom will most probably release a photon that has the same properties as the first photon and will fall to a lower energy state. I understand this is how light is amplified in a laser device after population inversion is achieved. I just don't understand one thing. Where does the photon that causes stimulated emission in the device come from in the first place? I tried to think of an explanation taking spontaneous emissions as a factor and using brewster's window for polarization but that seemed really unintuitve for some reason. Is there an external entity that increases the probability of the spontaneously emitted photons to be in a specific phase? It would be a great help if someone could explain this. Thanks!
Every laser medium as far as I know supports not just stimulated emission, but also spontaneous emission. When you start pumping the gain medium to its inverted state, spontaneous emission will happen naturally. Photons generated by spontaneous emission will then begin to trigger stimulated emission.
These photons don't have to be in any particular phase to produce stimulated emission. The stimulated emission photons produced will naturally match phase with whichever photon triggers the emission.
They do typically have to be at some particular frequency/wavelength in order to match the resonant frequency of the laser cavity. Simply put, the number of spontaneous emission photons will typically be enough to produce what appears as a continuous emission spectrum, and so some of them will be at a frequency close enough to the cavity resonance, and trigger stimulated emission at that frequency, so that a self-sustaining oscillation can begin.