Revered Members,
An electron in ground state makes its way to an excited state upon absorption of photon of energy, equivalent to energy difference between ground state and excited state, and after some time, it decays by emitting the photon and returns to the ground state. This is called spontaneous decay.
For Laser action, population inversion and stimulated emission should occur.
Now let me explain the scenario
1) An atom(electron) in the energy level E1 absorbs a photon and goes to a state of higher energy say E3
2) While decaying from E3 to E1, it reaches a metastable state E2. Now, due to longevity of the stay in E2 than in E3, we can achieve population inversion in E2
My question is ,
1) Do we supply a photon to the electron which stays in the meta stable state E2, so as to trigger stimulated emission?
2) If yes, what is the energy of the supplied photon. Is it E3 - E1 or E2 - E1?

 

The excited state can be achieved several ways. With a laser diode it is the electrical current, and the pumping occurs much the same way as with an LED (they are very similar in several respects)

Older lasers, the kind that used YAG or ruby rods, used high intensity white light, IE, photons, to pump the crystal lattice. I remember an engineer telling me it is possible to pump too much energy into a crystalline rod (like ruby), and cause the crystalline structure to randomize. At this point it is ruined. I used to service high intensity lasers like this, it was a Xenon tube continuously fired at 300VDC in a DI water bath to keep it cool. The DI water was kept that way by a epoxy resin filter, and recirculated to a heat exchanger.

Nowdays the photon pump source is LEDs. They are much more efficient, do not require the high voltages, or DI water. The crystal rods and mirrors have changed very little.

Yet another laser is our old friend the HeNe laser. It uses electricity to create plasma, which is definitely an excited gas. Same principle as a neon sign, but with mirrors to create the optical oscillation.

Quick side note, people assume all LASERs produce light. This is like saying all amplifiers produce sound. They can, but we are using light amplifiers as oscillators. In light wave communications we have true amplifiers, the light goes in the input, and comes out 30db greater (that is X1000), sometimes to dangerous levels, but the circuits do not produce the light, they amplify it (and the modulated information on the light wave carrier).

 

Thanks for the reply Bill.
Atoms come to meta stable state. Now, for stimulated emission, do we supply photon to the atoms in the meta stable state. I infer, that if we supply a photon which then will interact with the atom in the metastable state, which already has an absorbed photon will give rise to two photons in phase. If i inference is right?

 

You are correct, but that is only one of several ways to do it. Plasma is created through heating or ionization, and it is in a very excited state.

As I understand it, one photon in, one photon out. You are just saturating the environment with photons.

 

I think that the "stimulated emission" part of the name is because the passing electromagnetic wave somehow stimulates the excited electron not only to drop to the lower energy state end emit its photon, but its photon is emitted in phase with the passing wave, resulting in a greater peak energy of the wave.

Lasers use a reflective cavity of some kind to reflect one (ideally but not always) wavelength back and forth, which eventually results in that wavelength building to an extremely strong amplitude. One end of the reflective cavity is only partially reflective to allow some of that wavelength to escape as the output beam of light.

I'm not sure whether it makes sense to talk about photons stimulating the electron to emit, or if it is more the overall electromagnetic wave in its entirety that does the stimulation. I'm guessing that once photons add their energy to the wave, they lose their individual identity, similar to raindrops that fall into a river and lose their individual identity as drops.

My guess is that the stimulation that results in the electron emitting its photon does not pull energy from the passing wave. It may temporarily borrow energy to get the electron over the edge of its trapped state and allow it to fall to its lower state, but that energy is probably returned almost immediately along with the additional energy of the emitted photon.

Sorry, I can't answer your question about the E1, E2, E3 levels of energy.

 

In many ways it is a chain reaction, very similar to fission. When an excited electron (which has already absorbed a photon) absorbs a second photon it emits two photons (two in and two out) that are the same phase and same frequency as the incoming second photon. This is the key to the LASERs operation.

In the example I gave earlier it would been better to say this is like saying all amplifiers are oscillators, which is obviously not correct. The mirrors in a laser is the positive feedback mechanism for the oscillator portion. Modern YAG lasers, which are used a lot for microelectronics, things like trimming resistors to precise values, precision cut the yag rod to give the ends a mirror finish and simplify the end product.

BTW, before lasers were available to adjust resistors they probed the build in resistor on the substrate and used chemicals (acids and neutralizers) to adjust the resistor to tolerance. Lasers brought this process from ±10% and ±20% to ±0.1%. Of course, with all the heating/cooling and other processes the value drifts, but I thought it was interesting.

It does make me wonder if you were to shine a HeNe laser through a neon sign tube if you couldn't get the same amplification.

The fiber optic communication laser amplifiers were a major break through in the field. They use power laser diodes to pump a erbium doped fiber optic cable, and the operation is extremely simple. FO signal in, FO signal out with 30db added. For the first time laser safety glasses had to be worn dealing with a communications signal.

Previous to this every 65KM a full receiver rack has to be inserted into the FO line, the recovered signals feed into another full transmit rack (50 A power supply, 8 feet tall, 19" wide). This very expensive setup was replaced by a 19" wide 4" tall shelf that plugged into the wall. I've often wondered if the rapid decrease in equipment prices along with the radical increase in bandwidth allowed in the same cable didn't contribute to the telecom crash. At the start it was an LED with 50Mb bandwidth, when I left the field over 10 years ago it was 40 channels 40GB each on the same FO cable. Each channel was a laser that was a slightly different color.

I looked this up, might as well post the link.

http://en.wikipedia.org/wiki/Optical_amplifier

 

In the original question note that the state E3 is also meta stable ( proved by the fact that it decays ) You really need only E1 and E3.

I am less sure if you need an inverted population to get laser action, although it is clear that the more electrons in the higher state the more stimulated emission you can get ( all other things being equal ) you can only stimulate an excited electron to make a downward transition.

 

In the original question note that the state E3 is also meta stable ( proved by the fact that it decays ) You really need only E1 and E3.

E3 does not have to be a metastable state. Three level lasers are characterized by having a ground state E1, a metastable state E2 and an upper excited state E3 used to absorb energy for pumping. The E3 lifetime needs to be short compared to the E2 lifetime to allow for population inversion between the ground state and the E2 level. Often the energy difference between E2 and E3 is small enough to allow thermal decay (heat, or phonon emission). So, it is typically not a metastable level.

A four level laser is a little different because the laser action occurs from E2 down to another level (call it E1.5) which is between E1 and E2. It is much easier to get population inversion between E2 and E1.5 because E1.5 typically has a short lifetime and decays thermally to E1 quickly. In the case of a 4 level laser, you might have E3 as another metastable state which competes with the E2 state.

I am less sure if you need an inverted population to get laser action, although it is clear that the more electrons in the higher state the more stimulated emission you can get ( all other things being equal ) you can only stimulate an excited electron to make a downward transition.

Laser action does require population inversion. LASER stands for Light Amplification which can only occur if there are more stimulated emissions than stimulated absorptions. Population inversion between two levels, is what allows this.

However, you are correct in the sense that a stimulated emission can occur, even without population inversion. A stimulated emission can occur locally without laser action (or light amplification), in the medium at large.

 

steveb -- you have convinced me -- sloppy thinking on my part, and confused meta stable with unstable.

 

Thanks everyone. I came across a term chance photon which initiates stimulated emission.
What is meant by chance photon? Where does it come from?
Also one more question
A photon induces excitation of atom from E1 to E3(my example). When it reaches metastable state E2, it encounters another photon which is responsible for stimulated emission. Now my doubt is, why the atom does not get excited again to higher energy level when it absorbs this photon, rather initiating laser action?

 

Also one more question
A photon induces excitation of atom from E1 to E3(my example). When it reaches metastable state E2, it encounters another photon which is responsible for stimulated emission. Now my doubt is, why the atom does not get excited again to higher energy level when it absorbs this photon, rather initiating laser action?

That can, in fact, happen in some laser systems, and is referred to excited state absorption. Excited state absorption can happen to either the pumping photons (those with energy E3-E1) or to the signal photons (those with energy E2-E1). In the former case, there needs to be another energy level (call it E4) where E4-E3=E3-E1. In the latter case there needs to be an energy level where E4-E2=E2-E1. In either case, the level E4 needs to be in the right spot so that the absorption can occur from E3 to E4, or from E2 to E4, as the case may be.

Generally you won't see this in practical systems, simply because if the effect happens significantly in a particular laser system, then that is probably not a good practical laser system, or is at least not the most efficient system. Above I mentioned 4-level lasers and these lasers are much more tolerant to excited state absorption because population inversion is easier to achieve, even with inefficiencies.

EDIT: By the way, I don't know what a "chance photon" is.

 

I came across a term chance photon which initiates stimulated emission.
What is meant by chance photon? Where does it come from?

So, I'm not familiar with this term "chance photon", so I tried to do a google search. This did not give me much information, but reading a couple of articles that mention this term in passing makes me think that a chance photon might be a spontaneously emitted photon. Typically, metastable states will not stay excited forever, and if a stimulated emission does not occur, the state will eventually emit a photon randomly with an average lifetime. The photon will have a energy over a broad band in the region of E2-E1, and the direction, polarization and phase of the emitted photon will be random. This spontaneous emission is different than a stimulated emission which has frequency, phase, polarization and direction exactly the same as the stimulating photon.

 

Thanks a lot steveb.

 

Steveb,
In Ruby laser, Xenon flash lamp emits photon of wavelength 550nm and on absorption of this photon, Cr^3+ atoms goes from level E1 to E3. Later it undergoes non radiant transition from E2 to E1. Here E1 is metastable state. Now more and more accumulate in metastable state due to longer stay. Now a chance photon of energy difference E2-E1 triggers stimulated emission. I discussed the term chance photon with my friend who said that chance photon is nothing but a spontaneously emitted photon. Among many atoms residing in metastable state ,one among them will spontaneously emit a photon which triggers stimulated emission. What he said about chance photon is exactly same as told by you.
My doubt is, atoms undergoing excitation has energy difference E3 - E1 and when it comes to E2, it does not emit radiation which means it does not lost its energy. Then how this chance photon has an energy difference E2 - E1?

 

My doubt is, atoms undergoing excitation has energy difference E3 - E1 and when it comes to E2, it does not emit radiation which means it does not lost its energy. Then how this chance photon has an energy difference E2 - E1?

The fact that E3 decays to E2 without a photon emission does not mean there is not an energy loss. The energy is lost as mechanical energy. People often talk about phonons, which are analogous to photons in that they are quanta of vibrational energy which can be thought of as heat, sound or vibrational energy. However, it's easiest to just think of heat energy loss when you have a non-radiative transition. Conservation of energy requires that the energy has to go somewhere.

 

Thanks steveb.
Induced absorption takes place with 550nm light from Xenon flash tube. Now, when the atoms come to metastable state , what about the wavelength? Will the wavelength of light be same or increased? Because as Energy difference(E2-E1) is less, i think wavelength will be more according to formula E = hc/λ?

 

Thanks steveb.
Induced absorption takes place with 550nm light from Xenon flash tube. Now, when the atoms come to metastable state , what about the wavelength? Will the wavelength of light be same or increased? Because as Energy difference(E2-E1) is less, i think wavelength will be more according to formula E = hc/λ?

Yes, it will. The emitted wavelength is greater than the absorbed wavelength in a 3-level laser. So, in the case of the ruby laser, the higher energy 550 nm green pump wavelength is absorbed, and the 694 nm deep red wavelength is emitted.

Recent decades has seen the invention of another interesting 3-level LASER system. Erbium-doped silica optical fiber happens to have an E2-E1 emission wavelength right in the 1550 nm lowest loss communication wavelength band. For 3-level operation of an erbium laser, a 980 nm pump wavelength is used.

There is an interesting thing about 3-level lasers, in comparison to 4-level lasers. The difficulty of getting population inversion (because the ground state is the terminating level for the transition) means that special techniques are needed to get the high intensity pumping wavelength without melting the system. For ruby lasers, the high intensity is obtained by pulse pumping. This confines the energy in time so that peak intensity is high, but average power is low. With the erbium laser, the peak intensity is high because the single-model optical fiber is a waveguide that confines the light to a very small area. For this reason, the erbium laser was the first example of a practical continuous wave 3-level operation.

 

Thanks again. So, the stimulating photon 's wavelength is equal to output photon(694 nm, in the case of ruby laser).
You have used the word pulse pumping. What does it mean?
Also, what is the role played by reflecting mirrors? In what way, photon reflected by the mirror increases the intensity of the output?