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I am trying to establish a model inside my head of how light behaves but find it hard with all the seemingly contradicting information.

For example, electrons inside a Laser are raised to a higher energetic state and consequently emit photons of a specific wavelength when falling back to their ground state.

Am i not supposed to think of a photon created in such a process as traveling in all possible directions, with the wave function giving me the probability of finding that photon in a specific volume of space at a given time-interval?

In the above description, photons do not have any specific direction at all. So i would like to ask if we can create a single photon in a vacuum which then travels in a specific direction?

If not, then is the direction of a photon merely an "illusion" created by overlapping wave functions which result in a very low probabilities to find a photon in certain volumes of space?

When photons exit a laser, can i treat them as single photons, hence, imagine the wave-function for each photon extending in all directions in space, then overlap all wave-functions of every photon and calculate the probabilities of finding a photon in a certain volume of space at a given time-interval or is there more going on i have to account for? Because i cannot see why a laser beam would stay so focused for such long distances just by the cancellation of waves in all directions other than the direction the laser is pointing towards. Would a single photon exiting the laser have any higher probability to be found on the straight line the laser is pointing towards later than in any other direction? If yes, why?

I hope that someone can help me to create a better model inside my head of how light really works.

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You are correct in one thing: if an atom in an isotropic medium spontaneously emits a photon, it can do so in any direction at all, and the overall emission will be evenly spread over the unit sphere. However, lasers work using stimulated emission, which is slightly different: if an atom is excited, you can induce it to emit its energy by shining an initial photon at it, in which case the atom will emit its photon in the same direction as the original one, and with the same phase (so they will always interfere constructively). The way this works is by having some atoms emit spontaneously, and then by a snowball effect pile the photons of all the other atoms on top of the first photon, so they all have the same direction and phase.

Of course, there's nothing stopping the first photon from going in any old random direction, so here is where the laser cavity comes in. Except in very specific cases, you always put the gain medium in between two different mirrors facing each other. You then engineer the situation so that if a photon is spontaneously emitted, the probability of other atoms emitting on top of it is fairly small for a single pass of the gain medium. If a photon is emitted into the cavity mode, towards one of the mirrors, it will bounce around a large number of times, and it will have multiple opportunities to stimulate further emission. If it's emitted in an unwanted mode, on the other hand, it just leaves the cavity and doesn't excite much further emission, so it doesn't drain the excited atom population by much.

The photons then leave the laser via one of the mirrors, which is not perfectly reflective. The output beam is essentially the same as the cavity mode as it reaches the output mirror, which is a small spot that's been quite carefully collimated. One way to thing about this is to 'unfold' the cavity, and think of it as a chain of gain media in a line, separated by apertures the size of the mirrors. Photons emitted by the first gain medium need to pass through all the apertures to go through the final one, so you select on only a small set of directions. This set of directions does have a small spread, of course, and any laser beam will show some spreading after a while, but if you're careful (if you engineer your cavity so that any one photon will stay inside the cavity for a very long time) then this spreading can be very small.

Your final question is very interesting:

Would a single photon exiting the laser have any higher probability to be found on the straight line the laser is pointing towards later than in any other direction? If yes, why?

Photons don't really have wavefunctions of their own. More fundamentally, photons are discrete excitations of the underlying classical wave mode, and it is this classical mode which governs the spatial distribution. For a laser, the classical mode is an initial collimated mode, which then spreads due to diffraction. All of the photons are on this mode! Thus, if you have some other mode and you try to detect photons on it, you won't get anything there (unless your test mode has significant overlap with the laser mode).

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  • $\begingroup$ "...you can induce it to emit its energy by shining an initial photon at it, in which case the atom will emit its photon in the same direction as the original one..." this particular part is what makes my head spin. What would cause a "freshly created" photon to have a direction at all. Do photons have a direction or is what we experience as direction just a result of overlapping wave functions, hence not really a direction but more of a higher probability distribution along a certain path. And if this is the case, then what causes this distribution for that newly created photon? $\endgroup$ – pZombie Apr 19 '15 at 11:39
  • $\begingroup$ Yes, photons have a direction. More specifically, photons are a form of 'population' of each classical wave mode, and those have a direction given by their wave vector. Waves, in general, have a direction, and that should not be surprising. $\endgroup$ – Emilio Pisanty Apr 19 '15 at 11:53
  • $\begingroup$ If photons have a direction, given we created a single photon in space, which got some given direction randomly. Would that photon travel in a straight line along the given direction it got, indefinitely at c? Why would i need a wave function at all then? Wouldn't i be able to tell exactly where it is with certainty by calculating the time it traveled? $\endgroup$ – pZombie Apr 19 '15 at 12:04
  • $\begingroup$ OR let me put it differently. If we used a laser and managed to somehow let just a single photon escape in the direction it is pointing towards, then shut the exit. Would that photon travel indefinitely at c in that direction through a vacuum? $\endgroup$ – pZombie Apr 19 '15 at 12:22
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    $\begingroup$ When a laser is starting up, photons are spontaneously emitted in many random directions. Most go sideways and are lost. If one happens to be aligned with the mirrors, it will bounce back and forth, and stimulate many atoms to emit identical photons that are also traveling in just the right direction. Soon very few photons are emitted sideways because so many photons are traveling the right direction that excited atoms don't live very long. They are usually stimulated to emit a photon before they spontaneously decay. $\endgroup$ – mmesser314 Apr 19 '15 at 13:46

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