The cause of stimulated emission

[hobz]

I am currently examing this phenomenon but I have not found a single text describing the cause of the emission.

 

What governs the need for the excited electron to emit a coherent photon when stimulated by an incident photon?

Why must it have same phase, direction and wavelength?

 

(I guess these may vary due to the uncertainty, so that the wavelength might be slightly different and the direction as well?)

[swansont]

It has the same wavelength because the energy difference of the states dictates this. If it wasn't in phase, the states would be interfering, meaning less energy, and that violates conservation of energy.

[hobz]

Interesting. What's the math like?

And what about the Heisenberg uncertainty stuff?

[Bob_for_short]

... the cause of the emission.

 

What governs the need for the excited electron to emit a coherent photon when stimulated by an incident photon? Why must it have same phase, direction and wavelength?

 

(I guess these may vary due to the uncertainty, so that the wavelength might be slightly different and the direction as well?)

 

An external field makes any bound electron oscillate according to this field, OK? When the field is resonance for a given transition, the transition happens most likely in phase.

 

There are other transitions - with different directions but they are suppressed. In absence of an external field the atomic radiation is spontaneous - in all directions.

 

Mathematically you can consider a population of photons in a given state N(k,t): with time it grows to finally describe a radiated photon. In an external resonance field there is an additional "pumping" term that increases the rate of population of the coherent states and suppresses the non coherent ones.

Edited September 20, 2009 by Bob_for_short

[hobz]

An external field makes any bound electron oscillate according to this field, OK? When the field is resonance for a given transition, the transition happens most likely in phase.

 

There are other transitions - with different directions but they are suppressed. In absence of an external field the atomic radiation is spontaneous - in all directions.

 

Mathematically you can consider a population of photons in a given state N(k,t): with time it grows to finally describe a radiated photon. In an external resonance field there is an additional "pumping" term that increases the rate of population of the coherent states and suppresses the non coherent ones.

 

Most likely in phase? I was under the impression that if emission occured due to an incident photon, the emitted photon would ALWAYS be in phase.

 

 

Supressed by what?

[Bob_for_short]

Most likely in phase? I was under the impression that if emission occured due to an incident photon, the emitted photon would ALWAYS be in phase.

Were not it you who spoke about uncertainties?

 

Suppressed by what?

 

If the coherent states are "enriched" (pumped), non coherent ones are suppressed, the total number of photons being conserved (equal in stimulated and spontaneous emission scenarios).

Edited September 20, 2009 by Bob_for_short

[froarty]

Most likely in phase? I was under the impression that if emission occured due to an incident photon, the emitted photon would ALWAYS be in phase.

also

Why must it have same phase, direction and wavelength?

The Phase and wavelength are easy, the Balmer series defines the wavelength of emission for a particular atom and the phase control is due to the same principal as a "slaved multivibrators" like those which keep your picture horizontally and vertically synchronized on a TV. the free running frequency is just a little slower than transmitted synch pulses such that if a sync pulse is received and fed capacitavely to the feedback circuit that is nearing the threshold trip point anyway -it swamps it over the gate treshold and keeps all the pixels properly alligned.

That said, I must admit that I also do not understand how this controls the direction... any help?

[Bob_for_short]

...I must admit that I also do not understand how this controls the direction... any help?

 

The quantum oscillator of a given frequency ω is characterized with polarization e, direction k, and the number of its exited state n. So the photon population of a given mode is N(k, e, t). The equations for N(t) contain the external wave with its own direction, say, k' and polarization e'. The resonance conditions occur for k = k', e = e'. This mode gets enriched due to forced or stimulated conditions, the other modes (k ≠ k', e ≠ e') get depleted (with respect to the spontaneus radiation regime populations).

[froarty]

Thanks, I followed your math and I think I can see it from a resonance - decaying side bands kind of model -I was hoping for a simple billiard ball sort of model but that doesn't really work. I take it the direction k and k' remain fixed because the moving atom is considered a perfect sphere and the energy transmission direction using a coherent source will always trigger the oscillator at the same point in the orbit regardless of the atoms orientation.

Regards

Fran