Understanding Laser Initiation: The Role of Spontaneous Emission Explained

[kelly0303]

Hello! I read a bit about how lasers work and I am confused about the initiation process. From what I read, the amplification process (i.e. oscillations in the cavity at the right frequency, once the population inversion is created) is started by spontaneous emission.

A photon that happens to be along the cavity axis will be able to produce stimulated emission and amplify (as it has constructive interference), while the photons emitted at random direction will leave the cavity after a few round trips. However, even if the photons emitted through stimulated emission will have the same phase, photons created by spontaneous emission will not have the same phase among themselves.

So if several photons will be emitted (spontaneously) along the cavity axis, each photon will all create coherent radiation with itself, but not necessary with the others. So if 2 spontaneously emitted photons are out of phase by half a wavelength, they would cancel each other (basically the photon they create through amplification will interfere destructively), even if they are along the cavity axis. What am I missing here? Thank you!

 

[.Scott]

In the unlikely event that the first two spontaneous emissions exactly cancel each other out, there will still be a lot of stimulated emissions waiting to happen. So a third spontaneous emission will do it.

 

[kelly0303]

In the unlikely event that the first two spontaneous emissions exactly cancel each other out, there will still be a lot of stimulated emissions waiting to happen. So a third spontaneous emission will do it.

Thank you for your reply! My example with exact cancelation was a bit extreme. What I meant was that you can have lots of photons spontaneously emitted along the axis of the cavity, which interfere randomly. They might not cancel each other, but they will interfere in a random way. Is the amplitude of the laser field some sort of average over all the possible phases? And what is the phases of the field leaving the cavity?

 

[.Scott]

Is the amplitude of the laser field some sort of average over all the possible phases?

Once a photon is emitted - either spontaneously or stimulated, it can stimulate further emission. So you quickly get most opportunities for stimulation than you need. So, the amplitude is ultimately limited by how much power is being pumped in.

And what is the phases of the field leaving the cavity?

The phase relative to what?

 

[kelly0303]

Once a photon is emitted - either spontaneously or stimulated, it can stimulate further emission. So you quickly get most opportunities for stimulation than you need. So, the amplitude is ultimately limited by how much power is being pumped in.The phase relative to what?

What I mean is, assume you get 2 spontaneously emitted photons, along the cavity axis, such that they differ in phases by some very small amount (they don't cancel each other, but they don't add up perfectly, I assume they create some sort of beats). Each of them will create amplification (as they both have the right frequency and direction), but the amplified beams will have different phase, right? So does the amplitude of the beam leaving the laser will be a superposition of these 2 types of oscillations? Will it look like a beat?

 

[.Scott]

You would only get a "beat" if there was more than one frequency. Combining two oscillators at the same frequency will not generate a beat.

Also, allowing for wear, when you turn a CW laser on, you get the same steady beam every time.

 

[DrDu]

Single photons don't have a phase.

 

[kelly0303]

Single photons don't have a phase.

I am not sure about naming... in the books I looked over they say something along the line: during stimulated emission a new photon is emitted in phase and direction with the incident one.

 

[DrDu]

There is an uncertainty relation between the number of photons and the phase. For a state with definite number of photons, the phase is undefined.

 

[DrDu]

Thinking about this question, I would say that this is a continuous process where the initial state with e.g. all atoms in the excited state evolves into one where the atoms are in a superposition of being excited or in the ground state and this state is entangled with a coherent laser field whose mean intensity grows in time.

 

[Henryk]

Hello! I read a bit about how lasers work and I am confused about the initiation process. From what I read, the amplification process (i.e. oscillations in the cavity at the right frequency, once the population inversion is created) is started by spontaneous emission.

That is correct.

So if several photons will be emitted (spontaneously) along the cavity axis, each photon will all create coherent radiation with itself, but not necessary with the others.

That is correct too.
Moreover, the photons need not have to have exactly the same frequency. In fact, most lasers produce light at several longitudinal and transverse modes. All modes are possible as long as there is a resonator gain at that particular mode. It takes special care (extra filters) to ensure a true single mode, single frequency operation.

 

[sophiecentaur]

So if 2 spontaneously emitted photons are out of phase by half a wavelength, they would cancel each other (basically the photon they create through amplification will interfere destructively), even if they are along the cavity axis. What am I missing here?

Photons can't cancel each other out. Where would the energy go? The interference of waves along the axis takes a while to build up and two photons, emitted before all that happens, could be looked upon as producing a wave that has a minimum is 'some direction' but not in others. Laser action will only start when there is some energy flow (some photons) along the axis. Other energy flow will just dissipate against the walls. The stimulated photons will, of course, be in the 'right phase' for laser action appropriate to where their source atoms were.
Laser action (as with all resonances) has a certain bandwidth so stimulated emission will not be at precisely the same frequency (whatever that means) for all atoms.

 

[kelly0303]

That is correct.

That is correct too.
Moreover, the photons need not have to have exactly the same frequency. In fact, most lasers produce light at several longitudinal and transverse modes. All modes are possible as long as there is a resonator gain at that particular mode. It takes special care (extra filters) to ensure a true single mode, single frequency operation.

Thank you for this! So if we have multiple frequencies, the output will not be coherent and we need some filters to get only one frequency for example. However, assume that we have just one frequency inside the cavity (for example a small enough cavity and small enough linewidth of the active medium). Now all the photons that build up in the cavity will have the same frequency, but they still might not be in phase. Just to make it clear, the photons that build up from one spontaneously emitted photon will be in phase with each other, but not necessarily with the ones coming from a different spontaneously emitted photon. So we will have relatively big electric fields inside, all with the same frequencies, but will random relative phase. Is this right? And if so, how does one solve this problem? In the books I looked over they seem to imply that if you have just one frequency, you have perfect coherence (ignoring the cavity losses maybe, which are not an issue for my question).

 

[sophiecentaur]

What I mean is, assume you get 2 spontaneously emitted photons,

I think your original problem was that you were discussing it only in terms of QM. There is no identifiable 'pair' of photons involved.

Starting off laser action is much the same as starting off any electronic oscillator. Random noise causes one cycle to start when a high enough noise frequency peak turns up and the positive feedback process takes off. Stimulation is constantly occurring but the probability is very small. Two photons resulting from a single photon will not initiate 'lasing' unless you give them the right conditions. Most will plough into the sides of the cavity.

The action of the Resonator is essential and that's a strictly macroscopic mechanism. If you look at the stimulated emission of a photon as a microscopic resonance , the passing field oscillations will take a bound, excited electron 'just over the edge' and it will release one quantum of energy that's at the same (or very near) frequency and with a small fixed phase with that field. Then the wave amplitude in that direction will be greater and there is the possibility of laser action.

There is no 'exact frequency' involved. There will be many different waves (sets of photons) but the resonator will select more and more at its central resonance frequency during the startup. The width of resonator (and the quality of the reflectors) imposes a bandwidth on the generated beam.

 

[Marisa5]

A photon that happens to be along the cavity axis will be able to produce stimulated emission and amplify (as it has constructive interference), while the photons emitted at random direction will leave the cavity after a few round trips.

All of the photons are emitted in a random direction, the only ones that get amplified are the ones along the longitudinal axis of the laser due to stimulated emission creating coherent photons. The rest are absorbed by the walls outside the cavity because they miss the mirrors on each end. A small fraction might hit more than one mirror before being absorbed by the casing but that's irrelevant next to the fact that the mirrors impose conditions favoring photons emitted along the longitudinal axis.

 

[tech99]

The laser seems to be just an oscillator like any other - in other words, an amplifier with sufficient positive feedback to sustain oscillation. Actually, was it not developed from the MASER?
Oscillators rely on a small signal, maybe noise, to start them. It is like the beat of a butterflies wing in Siberia, as they say. One is reminded of the sudden crystallisation of super cooled solutions in Chemistry. The phase of oscillation must depend on the phase of the initiating signal, but the frequency is determined only by the requirement that the phase shift around the loop is exactly 360 degrees, so does not depend on the starting pulse. The time for oscillation to grow to maximum must depend on the size of the initiating pulse.

 

[DaveE]

I think that maybe you're missing the point that the laser (normally) has very high gain in the combination of the resonator cavity plus the gain media. Once some photons, perhaps from spontaneous emission, start to stimulate additional coherent photons to be emitted this will quickly dominate the statistics of the photon population. Yes, there are still other non-coherent photons that may be emitted, but most will not be amplified (i.e. noise); others may create different oscillating modes that also lase provided those modes have the required gain.

 

[kelly0303]

I think your original problem was that you were discussing it only in terms of QM. There is no identifiable 'pair' of photons involved.

Starting off laser action is much the same as starting off any electronic oscillator. Random noise causes one cycle to start when a high enough noise frequency peak turns up and the positive feedback process takes off. Stimulation is constantly occurring but the probability is very small. Two photons resulting from a single photon will not initiate 'lasing' unless you give them the right conditions. Most will plough into the sides of the cavity.

The action of the Resonator is essential and that's a strictly macroscopic mechanism. If you look at the stimulated emission of a photon as a microscopic resonance , the passing field oscillations will take a bound, excited electron 'just over the edge' and it will release one quantum of energy that's at the same (or very near) frequency and with a small fixed phase with that field. Then the wave amplitude in that direction will be greater and there is the possibility of laser action.

There is no 'exact frequency' involved. There will be many different waves (sets of photons) but the resonator will select more and more at its central resonance frequency during the startup. The width of resonator (and the quality of the reflectors) imposes a bandwidth on the generated beam.

Thank you for your reply! I just started reading about this, so my understanding could be flawed.

However in all the books/articles/videos I read/watched (including textbook used in places like MIT) the laser in presented at a particle level, not a wave level i.e. they show a single photon, from a single spontaneously emitting atom (that happened to be emitted parallel to the cavity axis) hitting another atom and thus creating another photon (with the same phase and amplitude),

then these 2 photons create 4 then 8 and so on (of course it is not exactly a doubling all the time, but this is the main idea they show). So the way I imagine the laser is that for (almost) every spontaneously emitted photon, that is along the cavity axis (and thus it can get positive feedback), after a few round trips you get a huge number of photons that are like a bunch oh photons traveling together.

So the laser would be lots of these bunches (each coming from a different spontaneously emitted photon). The photons in a bunch are all in phase and have the same frequency, but different bunches have different frequencies and different phases. Is this right? If not, how should I think about the laser?

 

[Swamp Thing]

Looking at the classical picture for a moment, let's think of a weak noise source coupled to a resonator with very high Q. The resonator is bound to accumulate energy steadily until an equilibrium is reached between the power flows in the two directions. If the energy in the resonator can somehow trigger an increase in the noise magnitude, then the equilibrium will shift towards more and more power in the resonator (until some new limiting factor kicks in, such as total power flow available from the outside).

The initial noise source could either be thermal noise or "shot noise" from spontaneous emissions. To decide which one is at play, maybe we need to compare the magnitudes of $kTB$ and $N\hbar\omega$

 

[sophiecentaur]

a single photon, from a single spontaneously emitting atom (that happened to be emitted parallel to the cavity axis) hitting another atom and thus creating another photon (with the same phase and amplitude),

E= hf is always the photon energy.
The expression "hitting an atom" is problematic. "Hitting" implies a collision between two objects of finite dimension. Now, if you don't think too hard about this, it is possible to go along with the 'two particles' but how close does the photon have to get in order to 'hit' that atom?
I think that the models that you have read can't deal with that. Surely it's much more consistent with the rest of what we 'know' to think of the interaction between a field that has a probability function that's centred somewhere near that atom. This field can tip the balance in the energy state of the atom and that will involve energy release. The difference here, though, is that the 'location' of the source of stimulated photon is actually known. Only when that photon again interacts with something is its position known.
I wouldn't say that they are 'wrong' but 'they' will be able to look at things from multiple angles at once and particle - particle is a convenient shorthand - as long as you don't insist that the particles are both points (in which case there would never be any collisions).