How Lasers Work - A Complete Guide

everyone has seen them and have probably teased many cats with them maybe some of you have had unwanted hair removed or maybe you have built one and popped some balloons with it bottom line lasers are ubiquitous not only in scientific research but also in Industry just how do these little devices manage to put out that nice powerful cated beam of light all this and more coming up as some may or may not know laser is actually an acronym it stands for light amplification by stimulated emission of radiation however nowadays it is so common that people don't bother to capitalize it and simply write laser a very brief history of the laser starts in 1917 when Einstein introduced the concept of stimulated emission which will be explained shortly then in 195 before the first Mesa was demonstrated by Charles towns the M standing for microwave the ammonia Mesa was the first device based on Einstein's predictions and obtained the first amplification and generation of electromagnetic waves with a wavelength of about 1 cm which is in the microwave range this is recognized as the precursor to the laser it wasn't until 1960 when Theodor mayam developed the first working laser at Hughes research lab mayon's early laser used a powerful energy source to excite atoms in a synthetic Ruby to higher energy levels the development of the laser was a collaborative effort by scientists and Engineers who were leaders in Optics and photonics okay so why are lasers useful why are they ubiquitous the answer can be broken down to three unique properties the laser holds the first being line width the purity of a laser referred to as the line width can can be quite narrow more so than any other light source in layman's terms this is a measure of what frequencies are contained in the emitted light the narrower the line withd the closer the emitted light is to a single frequency single color if you will thus a laser is said to be monochromatic in reality it does output a small range of frequencies the smaller this range the better the line width and quality of the laser in contrast an incandescent bulb has a very large line width and emits the broad spectrum which is why the emitted light is white white light is a superposition of all the colors in the visible spectrum having a narrow line width is useful because many scientific experiments want to analyze stuff with certain energies different wavelengths of light corresponds to different energies hence having a source with one energy is helpful the second is coherence the light emitted by a laser is coherent light this means it is all polarized in the same direction as well as being in Phase the laser is said to Output highly coherent monochromatic light and led on the other hand is also monochromatic one color but it emits incoherent light an analogy with synchronization and Harmony can be made imagine an orchestra playing if the orchestra is in sync and everyone is playing the parts correctly it will be pleasing to the ear the laser if some players are playing out of sync but still playing the parts correctly it won't sound as good the D coherence is important because all the photons add their energies together and we can then focus them on a small spot over some distance lastly power lasers make it possible to deliver High intense light to a small area of course militaries are particularly interested in this aspect of the laser as well as medical applications laser ey surgery for example now let's take a look at how a laser works the workings of a laser are quite complex as it requires an understanding of quantum mechanics there are some commonalities behind every laser the first part can be broken down to three key pieces stimulated absorption spontaneous emission and stimulated emission which is what the SE part of laser stands for let's take a look at the first concept stimulated absorption we will need a nucleus that is made up of protons and neutrons that has an overall positive charge and an electron that has a negative charge hey there little guy most textbooks show electrons existing in discrete energy states of a material but actually electrons exist in probability density clouds around the nucleus as they have wave likee Behavior and the orbitals represent the average distance one is likely to find it let's use this average distance to define the orbital and ignore the probability distribution for Simplicity mostly always electrons are found in the lowest energy state or ground state everything in nature wants to be in a low energy State as it is easier for it to exist at this level in other words it minimizes energy think of a ball on a hill and how easy it is for it to roll down it wants to roll down because the energy state is lower closer to the Earth's core than further away in this case potential energy however it is possible to excite electrons by some kind of external means just like we can exert a force on the ball that has rolled down and push it back up light can be this push to excite electrons if a photon of Light which is one unit of light comes across an electron in a low energy state it can sacrifice itself and push the electron to a higher energy State the photon is annihilated but the energy of it is now part of the excited electron it should be noted that each material has different levels of energy in other words if the ground state is one unit and the next energy level is 5 units then the photon of light must have exactly four units of energy to excise the electron to that energy level anything lower will not suffice and anything higher would not as well as there is nowhere for that extra energy to go unless a higher energy State exists if the incident photon is very high in energy the electron would be ionized to continue our analogy it would be like trying to push the ball up the hill with not enough Force the ball would just roll back down too much force and it would roll down the other side go to another Plateau or be launched into space an exact amount of energy is required to elevate it to a particular energy State again this process is called stimulated absorption as we are stimulating the electron and it absorbs the photon's energy the next mechanism we will look at is spontaneous emission we now have an excited electron what happens now well again this higher energy level is quite unstable and after a very very short time about 100 nond of being there the electron will eventually fall for some perspective light travels about 29 m in 100 NS when it falls back down it will release a photon with energy equal to the difference in energy levels the higher the fall the higher the energy of the photon will be should the energy value of the photon that is released be in the visible range we would perceive it as color you may be thinking if the electron reaches the higher energy level through the previously mentioned stimulated absorption mechanism why exactly does it fall back down well referring back to the ball example imagine the ball on a hill but now with the top having zero friction and a sharp point the ball can remain there only if it is perfectly balanced but any tiny little force in either direction will cause it to start rolling the electron in this higher energy state is in a similar situation the forces that push it are small perturbations in vacuum energy this is a quantum mechanical effect space or vacuum is not as empty as we think things are popping into and out of existence constantly it is these vacuum events that perturb the electron this is also responsible for why things are ferromagnetic that's a different story though again this process is called spontaneous emission as the process that the electron falls back down to the lower energy state is more or less spontaneous the last Quantum process we will talk about and the most important for lasers is stimulated emission this occurs when a photon interacts with an electron that is already excited this Photon can act as a type of pertubation and force the electron to fall back down to a lower energy State and emit a photon we then will have two photons photons actually like to be together so if one comes near a situation where another one could be present such as the the electron falling back to a lower energy State the situation usually will play out the important part is that the emitted Photon will be identical to the one that stimulated it meaning same frequency phase and polarization they will be coherent with each other so if we could somehow Avalanche this process we would have a laser after all that is basically what a laser is a zip tillan identical coherent photons being emitted in contrast if two electrons undergo spontaneous emission the emitted photons will unlikely be traveling in the same direction nor be in Phase but in order for electrons in the excited energy level to be able to undergo stimulated emission and not spontaneous emission enough time has to be available the lifetime of an electron in the excited level is just too short however some materials have so-called meta stable States these are excited states with slightly lower energy than the excited States States these states allow the electron to remain there for much longer lifetimes milliseconds instead of Nan seconds enough time that a passing Photon can cause it to undergo stimulated emission of course an initial spontaneous emission from the metastable state to the ground state must occur in order to have the initial Photon that can stimulate other excited electrons in the metastable states to sum up if a ground state electron is hit with a photon it will absorb it and move from the ground state to the excited state the photon must have the energy equal to the difference between these levels this electron will then transition to the metast stable state if one exists this transition does not emit a photon and is said to be a radiationless transition the energy difference is dissipated in other ways heat or phons now this electron if a photon stimulates it will emit a photon with equal energy phase and Direction these are the ones that make up the laser beam it should be apparent that the photon which pumps the electron from the ground state to the excited state has a different energy than the photons that are being lazed this is because the energy difference between the ground state and the excited state is different than the difference between the meta stable State and the ground state the pumping photons are always higher in energy than the photons being lazed we obviously want lots of electrons in this meta stable State more so than the ground state in order for them to be in a situation where stimulated emission can occur something known as creating a population inversion is required if we only had a two levels we would reach a point of saturation where 50% of the electrons are excited and 50% are not the excited electrons simply spontaneously emit to fast essentially our medium becomes transparent to photons by introducing the metas stable State we force the pumping photons to excite the ground state electrons that then transition to the metastable state so the photons that are emitted by the transition from the metastable state to the ground state are primarily used to stimulate other electrons in the metastable state enough time exists for this to happen yes some of these photons will excite ground state electrons directly into the metastable state but the pumping photons should take care of the majority and create a situation where there are more excited electrons in the metast stable State than ground state electrons a population inversion by the way the above is describing a three-level laser four level lasers exist and are more efficient again we want to create an avalanche effect where the spontaneously emitted Photon that was created when an electron transitioned from the metastable state to the ground state get Amplified through the means of stimulated emission we don't want just a single puny Photon we want lots all working together it is not practical to create a laser that is extremely long so the solution is to put the laser medium in a cavity let's take a closer look at how a cavity will influence the light waves and how exactly this will create the amplification we desire since light is a wave it will be subject to constructive and destructive interference we want constructive interference in our cavity to take place in order to have a high intensity beam a laser cavity has a mirror on one side and a partial mirror on the other it is partial because we want some of the beam to escape that's the beam we see now when light waves are created through spontaneous emission they will initially travel in random directions but the ones traveling perpendicular to the mirrors will reflect back and forth let's take a look at one of these light waves it is first emitted via spontaneous emission and quickly becomes large in amplitude through stimulated emission it travels towards the mirror and is reflected back because we continue to stimulate atoms in the left and right directions we get two waves in the cavity again one moving to the left and one moving to the right waves will add their amplitudes when interfering with each other in this case we will get a standing wave meaning instead of a wave noticeably moving to the left or right the combin wave will appear to be going up and down rest sure this is just an illusion this is the effect of two waves hitting each other head on and their left and right components cancel out but their up and down components add together so when the wave looks flat this is a moment when the two waves are destructively interfering with each other and at the maximum they are in a constructive interference Point here are a few examples of some standing waves in a cavity that are resonating resonance is just a fancy word for having these waves being in a state where standing waves are being produced a mode being just what n you have Nal 1 is a mode Nal 2 is another one n equal 3 Etc is there an equation that will tell us what modes can exist in the cavity sure there is the left part is the frequency that exists in the cavity n is the mode which is always an integer V is the velocity of the wave and L is the distance between the two sides of the cavity the Velocity in our equation is the speed of light C which is 300,000 km/s the L is just the distance between the mirrors light traveling from the left of the cavity will now interfere with light traveling from the right so again we have these possible modes where the light can produce standing waves and be in resonance not all frequencies are able to exist in a cavity but a lot are also let's be clear that the standing waves produces are a collection of trillions and trillions of light waves all working together they are produced by stimulated emission and the cavity allows them to keep amplifying each other they are coherent with each other recall this was one of the big reasons why we care about lasers if we didn't have this Synergy between light waves we would just have an ugly LED I bet you can't make your cat go crazy with a red LED well maybe but you get my point question what frequencies are allowed to exist in a red Las a point of cavity answer a cheap red laser pointer has a cavity length of about 1 mm and the speed of light is c 300 million m/s plugging in these values to our equation we would get a difference between allowed frequencies of about 10050 GHz Now red light has a frequency of about 400. 0 5 terz which corresponds to an N value of 2,667 recall n must be an integer so if 400. 0 5 terz is an allowed frequency then the next one would be when n equal 2,668 which is a frequency of 400.

2 terz we can plot all allowed frequencies as we know 150 GHz will separate them the plot will look like this here we have an equal to 2,667 and the corresponding frequency of 400. 0 five terz here is 2,668 2,669 and so on these are the frequencies that are allowed to resonate in this laser cavity so if you wanted your laser to have a frequency of 400.