Lecture 4.102- Working of Lasers

Einstein’s Theory – Interaction of Radiation with Matter

The interaction of matter and radiation are of different type, here we are focused on the emission and absorption phenomena but majorly on emission mechanism. According to Einstein,

“When a system in equilibrium, the number of particles leaving a certain energy state in a particular path is equal to the number of particle entering the state in the same path”

Here the path is the transitions between two fixed energy states say E₂ and E₁ levels.

Now since we have already discussed the model of multiple reflection and emission of light wave, let’s see how we construct the system. There are two type of emission

• Spontaneous Emission – This is the process of emission and absorption that we studied from the earlier standards, the all possible emission from excited state to the ground state.
• Stimulated Emission – This is a special case and this is the process responsible for the laser, we know that we need coherent source of light and no two natural sources are but after using the equilibrium principle given by  Einstein we have a way of producing them, same direction, phase , energy, wavelength everything. The process is based on the very simple face that every state can have a fix number of atoms in equilibrium and like any equilibrium it tries to maintain it.

Say I insert a photon of energy (E2 – E1), it will make a atom excited to the E2 level but then E2 will try to give that extra energy back and to maintain equilibrium that most probable transition is E2 — >E1.

And within no time, the atom we excited will come back, coherent with the one emitted on the excitation. So the one photon triggered the stimulation of a coherent photon. This process happen repeatedly and thus amplifies the Intensity and power, all the characters of the Laser.

Stimulated Emission is used to produce more coherent photons in short.

There are few more things like one needs to take care of choosing the correct state. On average the time an electron can move or say stay in an excited state for around 10^-9s. Although there are a certain state called as a meta-stable state which tends to have a longer lifetime and thus we prefer to have them as the excited energy state for the stimulated emission process.

 Einstein didn’t just got away with a theory but he also derived some formula for the calculations of energy requirements for the energy radiation input and ratio’s of possible processes taking place,

We know that there are three possible processes

• Spontaneous Emission
• Stimulated Emission
• Stimulated Absorption

Population Inversion as a Necessary Condition for Laser Action

The normal case scenario of distribution in a system is as shown in the figure below, the lower states hold more of the atoms and the number decrease as we go up the energy level, and this type of distribution is called as normal population.

While the inverted case as shown, i.e. higher atom density is on higher level.

Condition a system in which N2 numbers of atoms are there in the ground state and N1 be the number of atoms in the excited state. Now the rate of absorption depends on the density of atom in ground state and so the rate of emission depends on N1. Both the absorption and Emission processes are taking place simultaneously and therefore for the Laser action(amplification) process we need the emission process to be faster so,

N1/N2 > 1     is a must situation and assuming that system is in equilibrium extending the Boltzmann Equation, we have

 N1/N2     = Exp {-(E1-E2)/K_bT}

On applying the condition on the two we have a requirement since E2,E1,K_b all are positive quantities a must condition that the term T(temperature) as negative, which isn’t possible as the 0K is an absolute minimum temperature.

Now the only assumption we took was that the system was in equilibrium to apply the Boltzmann Equation, so from there it can be concluded that the system is therefore not in equilibrium state. This is called Negative temperature condition (as shown in figure).

Now since we saw what a laser is and how does it work Let’s take a view on some particular in your syllabus only, to get to know about some specific designs and mechanism of things like the oscillator and the pumps.

(Physics at Utkarshini)

Abhishek kumar jha