To
explain the process of light amplification in a laser requires an understanding
of the energy transition phenomena in the atoms of its active medium. They
include: spontaneous emission,
stimulated emission/absorption and non-radiative decay.
The
theory of quantum mechanics states that the electrons of atoms can take
different energy states, E1, E2, E3, for example, with E1<E2<E3.
By
quantum mechanics the lower energy level is more stable than higher energy
levels, so electrons tend to occupy the lower level. Those electrons in higher
energy levels decay into lower levels, with the emission of EM radiation. This
process is called spontaneous emission.
The radiation emitted is equal to the energy difference between the two levels.
E2
- E1 = hn0
Where
E2 is the upper energy level
E1
is the lower energy level
h
is Plank’s constant
n0
is frequency of the radiated EM wave.
This
is crucial if lasing is to occur. Suppose the atoms of the active medium are
initially in E2. If external EM waves with frequency n0
that
is near the transition frequency between E2 and E1 is incident on the medium,
then there is a finite probability that the incident waves will force the atoms
to undergo a transition E2 to E1. Every E2-E1 transition gives out an EM wave in
the form of a photon. We call this stimulated
emission since the process is caused by an external excitation. The emitted
photon is in phase with the incident photon, has the same wavelength as it and
travels in the same direction as the incident photon.
If
the atom is initially in the ground level E1, the atom will remain in this level
until it gets excited. When an EM wave of frequency n0
is incident on the material, there is a finite probability that the atom will
absorb the incident energy and jump to energy level E2. This process is called
Stimulated Absorption.
Note
that the energy difference between the two levels can decay by non-radiative decay. The energy difference can change into kinetic
energy or internal energy through collisions with surrounding atoms, molecules
or walls.
Normally
the population of the lower energy levels is larger than that of the higher
levels. The processes of stimulated radiation/absorption and spontaneous
emission are going on in the same time, yet even if we ignore the decay factors,
stimulated absorption still dominates over stimulated radiation. This means that
the incident EM wave cannot be amplified in this case.
Amplification of incident wave is only
possible when the population of the upper level is greater than that of the
lower level. This case is called Population
Inversion. This is a mechanism by which we can add more atoms to the
metastable level and hold them there long enough for them to store energy,
thereby allowing the production of great numbers of stimulated photons.
To do this, we pump atoms into the metastable level at a rate that exceeds the rate at which they leave. A large number of atoms are therefore excited to and held in this level, leaving an almost empty level below it. The atoms stay in this metastable level without de-exciting while the population builds up, giving rise to a population inversion.
In practise laser action cannot be achieved for only two levels, as described above. Three and four level systems work however. An analysis of these systems follows, followed by a description of the pumping schemes for each system.
(Note: A metastable level is one that has a long lifetime and the for which the probability of spontaneous emission is low. This favours conditions for stimulated emission. If an atom is excited to a metastable state it can remain there long enough for a photon of the correct frequency to arrive. This photon will then stimulate the emission of a second photon.)
If population inversion exists, N2>N1, the incident signal will be amplified. The incident signal has energy equal to the number of photons times the photon energy we have
U(x) = nhn. The increase in the signal is given by
Where K is a proportionality constant. The solution is
This means that the signal will increase exponentially when there is population inversion. The exponential increase continues until the population inversion reaches a certain point, then the signal saturates, and reaches the steady state.