Population Inversion: 7 Important Factors Related To It

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Contents : Population inversion

What is population inversion?

Population inversion refers to the state where the amount of atoms or subatomic particles residing in a higher excited energy level is more than the number of atoms or subatomic particles residing in a lower excited energy level or ground level. This state is termed population inversion because, in normal conditions, the population in the lower energy states are higher than the excited states. The concept of population inversion is the guiding principle in making lasers and masers.

population inversion
Energy level diagram of population inversion.
Image source: Bob Mellish CC BY-SA 3.0 File:Population-inversion-3level.png

What is absorption?

Planck stated that

“The energy of electromagnetic radiation is confined to indivisible packets of energy called quanta, each of this quanta or packets has energy same as to the product of the Planck’s constant and the freqn of the radiation.”

The electrons in the lower energy states absorb external energy in the form of heat (phonons) or light (photons) for reaching a higher energy state, can happen only when energy-diff inbetween the high and lower states is same. In the case of photons, this translates as, particles can absorb a specific wavelength of light only for undergoing a transition. This concept of light energy in terms of quanta was proposed by Max Planck.

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h is Planck’s constant.
v frequency.
c is the speed of light.
λ is the wavelength.

What is stimulated emission?

The photon emitted when an electron transits from a higher energy state to a lower energy state after the photon absorption occurs matches the original photons in terms of phase, direction, and wavelength and this known as stimulated emission, and is the main phenomenon behind the working of lasers. Lasers have a gain medium which is a material (solid, liquid, or gas) that obtains energy from an external source and provides it to the atoms for exciting them to their higher states. The optical gain medium is analyzed in terms of shape, size, concentration, and purity.

What is spontaneous emission?

The electron surrounding nucleus in not capable for staying in the higher excited state forever and these electrons lose energy or decay to fall back into a lower energy state. This high to low level transition of electron happens at separate time interval and the energy is emitted in the form of photon and process of electron transition without any application of external energy. The electrons emitted via this process have a random phase and direction. This type of emission is not capable of producing high intensity coherent light output.

What is the relation between stimulated emission and population inversion?

Lasers have an optical gain medium in the form of a material (solid, liquid or gas) that amplifies the emitted photon beam. The optical gain medium is analyzed in terms of shape, size, concentration, and purity. Population inversion will occur if the no of particles in the excited energy level has become more than the no of particles existed in the lower energy level after the stimulated emission process and for the case of lasers, the rate of stimulated emission exceeds the rate of absorption by the electron and this is how the emitted light or photon beam is amplified. The process of amplitude gain in a photon beam is termed as optical amplification.

1920px Stimulated Emission.svg
Stimulated emission energy diagram.
Image source: http://V1adis1av contribs) (https://commons.wikimedia.org/wiki/File:Stimulated Emission.svg), https://creativecommons.org/licenses/by-sa/4.0/legalcode (laser physics)

Why is population inversion necessary for lasing action?

Lasing action occurs when a large number of atoms or subatomic particles i.e. electrons (a material- solid, liquid, or gas) simultaneously release energy in the form of photons while transitioning from a higher excited state to a lower ground state by the process of stimulated emission. For this action to occur, the atoms or subatomic particles need to be excited to a higher energy state first for stimulated emission to follow. This state is achieved by population inversion. In case of lasers, the rate of stimulated emission exceeds the rate of absorption by the electrons. This is how the emitted light or photon beam is amplified. Without population inversion, lasing action can not occur.

What is Boltzmann distribution?

If there are N number of atoms, and two energy states (ground state E1 and excited state E2). Then N can be given by

N1 + N2 = N (N1 is the number of atoms in ground state E1 & N2 is the number of atoms in excited state E2)

The energy difference between the two excited states is given by

ΔE = E2 – E1 = hv12 (v12 is the frequency of the wave emitted during transition from E2 to E1 & h is Planck’s constant)

According to Maxwell–Boltzmann statistics, during the group of atoms are in thermal equilibrium, then ratio of the no. of atoms in each state is expressed by the following equation.

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 Here, T is the thermodynamic temp of the group of atoms.
 k is Boltzmann’s constant.

Population inversion will happen if the no of atom in excited state N2 is higher than the no of atom in ground state i.e. N1. From the equation we can say that the ratio of N2/N1 is greater than 1 only when the thermodynamic temperature T is negative as E2 – E1 will always be positive.

Other ways of creating a population inversion

Coherent microwave electromagnetic emission is produced by the process of amplification through stimulated emission in an instrument known as MASER “Microwave amplification by stimulated emission of radiation” and This is obtained by the removal of specific type of atoms from the system based on certain property differences.

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