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Atoms

What is the structure of the atom?

The atom is the smallest part of the matter which has chemical properties. In 1 gram of Hydrogen there are 6,022⋅10^23 atoms. It contains the three type of elementary particles which constitutes the matter. The protons (positively electrically charged particles) and the neutrons (neutral positively electrically charged particles) are packed in the nucleus while the smaller electrons (negatively charged partices). The mass of the atom is the sum of the masses of these particles but because the eletrons are lighter only the 0,06% of the mass of the atom is electronic. 
However the electrons gives the atom all its chemical properties. The number of electrons is the Atomic Number of the element. The Quantum Mechanics tells us that the electrons in the atom may have only some energies in a discrete way.
The energy of the n-th level is given by the formula 

where h is the Planck constant, c is the speed of light, R_∞ is the Rydberg formula and Z is the Atomic Number of the atom.

When an electron goes from a higher level of energy to a lower level it emits a quantum of electromagnetic energy (a foton). The energy is the difference of the energies of the levels involved and it is emitted with a frequency f given by the formula

being E₂ the energy of the higher level (i.e. the starting level of the electron) and E₁ the energy of the lower level (i.e. the destination level). 

This kind of emission is called spontaneous or radiative emission. 

In order to fully understand the of the dynamics of this kind of emission is important to recall some characteristics of the constitution of the atom.

The electrons obey to the laws of Quantum Mechanics that tell us that 

• we can’t find the position and the momentum of the particles with an infinite precision (Heisenberg Uncertainty Principle) 
• we can only know the probability of finding a particle in a certain position in space through the use of the Schroedinger equation. The solutions of the this equation give us the probability as function of the space coordinates. As a result we can visualize the zone of the space where the probability of interaction with a partice is non negligible.

In the case of the electrons in the atom the solutions of the Schroedinger equation are called orbitals. 

The Pauli Exclusion Principle allows only two electrons (one for each direction of the electronic property called spin) to occupy one orbital i.e. to satisfy the conditions of the Schroedinger equation. 

The energy level structure of the atom and the transitions between them are depending on these rules.

The laser effect

The word laser is the acronym of Light Amplification by Stimulated Emission of Radiation. 

The reason of this name comes from the fact that when we have some electrons in a higher level than the level of minimum energy an electromagnetic wave of the right frequency may stimulate the decay of the electrons onto a lower level. The amazing thing in this situation is that the emitted electromagnetic wave has the same frequency and phase and direction of the incident stimulating wave.
 

This means that the incident light is highly reinforced because

• the same direction of emitted light leads to a very low spreading of the light ray (collimation)
• the same phase implies that there is no interference between the photons (coherence)

In order to achieve a high powerful stimulated emission we have to pump a large number of electrons in the same level and let them decay on to the lower level together at the same time. 

The problem in this situation is that if we pump some electrons in a higher energy level by stimulated absorption of energy the atoms emit with the same rate as the pumping occurs. We have to “lock” the electrons in a level that doesn’t decay at the same rate as the pumping.

The laser emission

The laws of the Quantum Mechanics applied to the the electronic levels tell us that the rate of the decay is not the same for each couple of levels. Each transition has a characterisc decay time. Some transitions have aI very short decay time (i.e. the electron stays in the upper level for a minimal time) while other transitions may not occur for long time. 

A system with a lot of identical atoms in a certain time N₂ (in a volume unit) atoms have at least one electron in the level 2 which, has a higher energy than the corresponding level 1 (lower energy) where the electron can go. 

The number of atoms ΔN₂  which do this transition  ( 2 to 1 ) in a certain amount of time Δt is given by the formula

where the number A is called Einstein coefficent and is the inverse of the mean lifetime by spontaneous emission  of the electron in the level 2. 

After the lifetime the mean number of atoms in the level 2 is where  is the Napier number.

When the atom is hit by an electromagnetic wave whose frequency is the same of that of the atomic transition the photons of the wave force the atom to undergo the transition. 

The fundamental difference of the stimulated emission as compared to the spontaneous emission is that the emitted photon has the same phase and direction of the incident wave.

Obviously we obtain an enhancement of the radiation if the number of the electrons (population) in the level 2 is higher than the population of the level 1.

The three level atom

An effective configuration in order to achieve a laser device is to use not only two levels (the level of the laser transition) of an atom but a three level configuration in order to achieve the so called population inversion in the high level from which the stimulus of the incident wave let the atoms emit at the same time.

In order to achive the population inversion we have to pump the electron in the level 1 on to the level 2 via an electromagnetic wave of the right frequency that gives to the atoms the energy to jump on the higher level.
If we have only two levels the electrognetic wave pumps the electrons in the lower level on the higher level with the same rate the wave stimulates the emission from the level 2 to the level 1. We need to “trap” the electron in the higher level.

Using three levels of an atom we can pum the electron in a high level (level 3 ). The electron decays rapidly in an intermediate level (level 2) and stays there until a wave of the right frequency stimulates the decay on level 1.

This procedure needs two different stimulating waves with different frequencies. The first (pumping radiation) has the frequency while the second one (stimulating radiation) has the frequency .

The device will be set in a “ready” state by the inversion of population caused by the pumping wave. When we need the laser emission we let the stimulating wave go through the material and the electrons in the second level decay all at once giving a strong emission of radiation.
In order to fully use the stimulating incident wave in the laser device the active material is located inside mirrors.

These mirrors make a resonant cavity that enhance the radiation emission.

Out of the active material like ruby in modern technology are used also diode lasers.