We need to begin with the idea of atomic energy levels. In chemistry you will probably remember doing 'Shell' diagrams of atoms. The electrons placed on circles around the atom, two in the first layer, eight in the second, etc. thus for Oxygen with eight electrons we drew:
fig. 1
The shells arise because an electron may not have just any value of its energy, but is limited to a series of fixed values. This is an example of QUANTISATION. other physical effects limit the number or electrons which may occupy a given energy level, but that is not important here.
Now, we shall consider an idealised atom with two electron energy levels and one electron. ( In fact, many real atoms can behave in this way. It is not as crazy as it sounds at first ). The electron may be in either of the two energy levels, thus:
fig. 2 
We may make the analogy of a person who is only allowed to stand on a chair or on the ground, two defined levels. If the electron is in the higher level it may fall down into the lower level. In its doing this it must give up an amount of energy equal to the energy difference between the two levels. This is the law of conservation of energy being applied. This energy is given up in the form of light.
Light is also quantised. It may be represented as groups of photons. Each photon carries one quantum of light energy. The amount of energy in a quantum depends upon the wavelength ( colour ) of the light.
fig. 3
So we see that a short wavelength such as blue light at 470 nm has a high energy, and red light at 670 nm has a low energy per photon.
All that is not an explanation to understand, but a statement to just believe. The important point is that the wavelength of light is linked to the energy of a photon in a defined way. Thus our electron in the idealised atom which has given out a photon of defined energy emits light of a defined wavelength or 'colour'.
This is seen in street lights. They contain Sodium atoms which take electrical energy to move their electrons into higher levels, these electrons then fall back down to the initial, lower, state giving light at 589 nm the characteristic orange of street lights.
This process is known as SPONTANEOUS EMISSION The atom emits light spontaneously, without external influences. If however the atom is not isolated, other effects may occur. Photons of the same energy as the energy of the upper level may use their energy to move an electron from the lower level to the upper one. This is known as ABSORBTION, as the photon is destroyed in the process. If a photon of the correct energy passes an atom with its electron in the upper level, then it may cause the electron to fall to the lower level. This STIMULATED EMISSION is very different from spontaneous emission. In the spontaneous process the photon may travel in any direction and be emitted at any time, Stimulated emission, however, causes the emitted photon to travel in the identical direction to the passing photon and at the same time.
fig. 4
Now we finally get to lasers. L.A.S.E.R. is an acronym for Light Amplification by the Stimulated Emission of Radiation. Which is why I have had to explain all about Stimulated emission. The three processes above all happen if we have a group of N atoms some of which (N2) have their electrons in the upper level and some (N1) with their electrons in the lower level. In a laser we want stimulated emission to be the biggest effect ( as indicated by the acronym ). Let us then look at the rate at which each process occurs:
This is only dependent on the electron being in the upper level. A certain proportion ( call it a ) of the upper level electrons will emit in a given time, so:
Spontaneous rate = a N2
This depends upon the electron being in the lower level and there being a photon present. Using the number of photons as n and the proportion of possible interactions which occur as b :
Absorbtion rate = b N1 n
This is the same as for absorbtion, but the electron must start in the upper level. :
Stimulated emission rate = b N2 n
We require that the last of these expressions is the largest. Now a and b are constants which depend upon the particular atom used and are thus not under our control. So for stimulated emission to be greater than spontaneous emission, we require n to be large - we need many photons in the laser. For stimulated emission to be greater than absorbtion we require N2 to be greater than N1 - more atoms have their electrons in the upper level than have their electrons in the lower level. This is known as an Inversion as it is normal for electrons to be in their lowest energy level. This may be readily seen from the fact that in the absence of external influences, ie. no photons n=0, the only process which can occur is spontaneous emission which will allow any electron which began in the upper level to fall to the lower level, but not vice-versa.
The fundamental difficulty in producing a laser is creating this necessary inversion in the populations of the two levels. It must be stressed here that we are talking about many atoms each with a single electron which may be in one of two levels. We have not got many electrons in one atom which would be restricted in their movements between levels by the rules governing how many electrons may occupy a single level of a particular atom.
Now assuming that we have an inversion, N2 greater than N1 , then we can get the SE part of laSEr. Now how do we amplify light using this? consider a single photon entering a region with the atoms in. This photon will pass by an atom with its electron in the upper level and cause it to emit a second photon travelling in the same direction, by the process of stimulated emission. There are now two photons, each of which can cause stimulated emission in two more atoms to give four photons , and so on.
fig. 5
Thus we have amplification, which is also known as gain. The region containing the atoms is known as the gain medium. The final stage in a laser is to get this first photon to amplify. This is done by placing the gain medium between two mirrors. This forms what is known as a laser CAVITY.
fig. 6
Initially there is no light in the cavity. The only possible process for the atoms to undergo is therefore spontaneous emission, and this duly occurs. As stated earlier, this may travel in any direction out of the gain medium, and most is lost from the cavity. However out of the millions of photons emitted by the millions of atoms in any real medium, there is bound to be at least one which travels directly to one of the mirrors and is reflected back to the gain medium. This is now our first photon. As it passes through the gain medium, it causes stimulated emission as described above and by the end of the gain medium there are, say, ten photons. Now the important part is that these are all travelling int the SAME DIRECTION as the first photon, so will be reflected back to the gain region by the other mirror.These ten photons now each cause stimulated emission, and when they get out of the medium to the first mirror again there are one hundred which are reflected back to the gain medium again and are amplified to 1000 etc...
fig. 7
Thus we very rapidly get very many photons travelling back and forward in the cavity. Obviously in this idealised case where no photons are lost from the steadily amplified beam, the photon number just goes on increasing. In any real laser some photons are lost, for many various reasons. One of these is quite deliberate. One of the mirrors is made to reflect only part of the light, and to allow the rest through. This is then the output beam of the laser and the 'leaky' mirror is referred to as the output coupler. A steady state may then be reached where the gain exactly replaces the photons lost from the cavity by the output coupler. There is then a constant number of photons in the cavity at any time. For example a laser with a gain of 1.12 ( much more realistic than the gain of ten used earlier as the illustration ) and an output coupler which reflects just 80% of the light we have:
fig. 8
The output beam thus has photons which are travelling in a fixed direction and also have a fixed wavelength (colour) defined by the energy levels of the electrons in the atoms of the gain medium.
So there you have it. Pretty wacky eh?
Small low power cheap lasers which use Neon as the gain medium ( The Helium plays a role in the creation of the inversion ). these are the red lasers that you probably saw at school. One of the earliest lasers developed.
My lasers are:
This literally has vapourised copper inside at 1500oC. An electrical discharge is run through the copper vapour, and this excites the electrons in the copper to the upper laser level, creating the inversion. There are two different upper levels from which laser action can occur and so the output beam has photons of two wavelengths - Green at 511nm and yellow at 578nm.
Here the atoms giving the gain are Titanium (Ti). These are introduced in small quantities to sapphire (Al2O3). This is not blue like the gemstone sapphire. Sapphire itself, pure Al2O3, is a colourless crystal. When it occurs naturally it has impurities which make it blue (mainly iron). Our artificially grown titanium doped sapphire is red. The inversion is created by absorbtion of the light from the CVL, a process known as PUMPING. This is possible because these are not our idealised two-level atoms. There are four active levels. The atoms are excited to the highest level by the pump light from the CVL. They then fall to the middle level, and are able to lase ( verb: to lase- what a laser does ) when they undergo stimulated emission to the lowest level:
fig. 9
Clearly the energy available for the stimulated photon is less than the energy of the absorbed pump photon, so it will have a longer wavelength. My Ti:Sapphire runs at 780nm. The point to pumping one laser with another is that the titanium atoms in the Sapphire do not behave in quite the same way as free atoms. Their electron energy levels are disturbed by the other atoms in the crystal, making them wide in energy, more like bands than discrete levels. This means that a range of wavelengths across the band are possible, rather than a single wavelength. We can then select the exact wavelength which we want. Exactly how is a very complicated matter.
These are very new and trendy lasers which use the techniques of making computer chips to make tiny lasers out of silicon and other semiconductors. I am not exactly sure how they work, but it is the same properties of silicon which make it work in computer chips that make it also work as a laser. They are used in CD players, supermarket barcode readers, laser guided missiles, my lab. etc. The huge advantages are that they are very small and very efficient in the conversion of their electrical power input into light output. Typical efficiencies are 70-80%, whereas a CVL, one of the most efficient lasers of the other types, is typically 1% efficient. The only reason that they have not completely taken over the world of lasers is that they are very suceptable to damage and are still only relatively low power ( the biggest are about 5 Watts, whereas my CVL is 40W, and the biggest CVLs are several hundred watts. ). These problems are being steadily overcome, and I see the day when I shall have to adapt my Ti:Sapphire laser to be pumped by a diode laser rather than a CVL.
By William Wadsworth 1994
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