The theoretical foundations of the laser were put forward by Einstein in 1917 but it wasn’t until the 1940s that physicists found applications for his ideas. Nowadays, lasers are responsible for a multi-billion pound industry which includes correcting vision defects through laser eye surgery and sending data across the globe via optical communication. The operation of a laser relies on the principles of time-dependent quantum mechanics and thermodynamics.
What is a Laser?
Laser is an acronym for Light Amplification by Stimulated Emission of Radiation. A laser produces a beam of coherent, monochromatic light focused onto a very small area. Unlike most light sources, which spread out equally in all directions, lasers direct light in a given direction, making them a neat and concentrated source of energy.
Lasers work off of a process known as stimulated emission of radiation. Atomic electrons will occasionally transition between energy levels; moving to a higher level requires the absorption of energy whereas falling to a lower level is followed by the emission of a photon, a particle of light. It turns out, a great way to force these transitions to occur is by bombarding the collection of atoms with an external photon source. Under certain conditions, an incident photon can induce the emission of a second photon with identical frequency, phase and direction. This process converts a single photon into two, hence the phrase light amplification.
So, we know that it’s possible for photons incident on a sample of atoms to stimulate the emission of more photons. The problem is that a handful of the photons will also be absorbed, resulting in electrons jumping to higher levels. This process doesn’t amplify the amount of light and thus doesn’t contribute to the working of the laser. A process is needed to minimise the fraction of incident photons that end up being absorbed.
The desired process is known as population inversion. Electrons in thermal equilibrium assume the lowest energy state and will therefore occupy the lowest unfilled energy level. The laser is therefore kept in a non-equilibrium state, where electrons are constantly driven up to higher levels and prevented from cascading down. The population of the excited state is kept larger than the lower energy state.
Population inversion can be obtained in a number of ways. In a helium-neon laser, electrons are excited into metastable states by electrical discharges. The electrons are prohibited from returning to their initial state due to selection rules, conditions that arise from the quantum mechanical treatment of angular momentum that reduce the likelihood of certain transitions. Maintaining the population inversion allows for continuous stimulated emission and thus sustained operation of the laser.
Einstein A and B Coefficients
Stimulated emission is not the only process that must be considered when working with lasers. As well as the previously mentioned absorption of radiation, the phenomenon of spontaneous emission, the natural transition of electrons to lower states followed by the emission of radiation, must also be accounted for.
Einstein introduced three coefficients to keep track of the rate of each process within the laser. The first coefficient, A, keeps track of the rate of spontaneous emission. The second and third coefficients, denoted B1 and B2 , keep track of the rates of absorption and stimulated emission respectively.
It can be shown that, in the absence of an external influence, the values of B1 and B2 are equal, B1 = B2. This means the rate of electrons moving between two energy levels is the same for the upwards and downwards transitions and the populations of each level remain constant. This emphasises the importance of a mechanism to cause the population inversion, i.e., a mechanism to alter the Einstein absorption coefficient such that B1 > B2, increasing the population of the upper level.
Building a Laser
There are three basic components of any laser. The first is the lasing medium, a substance in which two atomic energy levels are separated by an energy much greater than the thermal energy of the surroundings. Common choices involve crystals like neodymium or gases such as helium and neon. The second component is some mechanism for repopulating the upper energy level to maintain a population inversion; a common choice is optical pumping. The third is a cavity in which the lasing medium and stimulated photons can be contained. The setup for a typical optical pumping based laser is shown below.