Lasers

A LASER (Light Amplification by Stimulated Emission of Radiation) is capable of producing an intense beam of photons having identical scalar and vector properties (frequency, phase, direction and polarization).  As a result, a laser beam can be bright, monochromatic, coherent, and unidirectional.

Quantum mechanics predicts that all atomic and molecular systems are characterized by discreet energy levels. (Confinement leads to quantization.)  The state corresponding to the lowest possible energy level is termed the ground state and the states corresponding to the other levels are termed excited states. 
In a dense medium, such as a solid, liquid, or high pressure gas, frequent collisions between the atoms or molecules cause transitions between energy levels.  Optically allowed transitions can also change the energy of the system.  An optically allowed transition between energy levels involves the absorption or emission of a photon with frequency f, such that hf = ∆Eif, where ∆Eif is the energy difference between the initial and final energy level and h is Planck's constant.  If the angular momentum quantum number li of the initial state and the angular momentum quantum number lf of the final state differ by 1, i.e. if ∆l = ±1, then a transition involving a photon is very likely.  If ∆l ≠ ±1, then a transition involving a photon is much less likely. 
If no lower lying state satisfying ∆l = ±1 exists, an excited state is called metastable.  ∆l = ±1 is called a selection rule.  If this selection rule is not satisfied, an optical transition is forbidden (unlikely).

The selection rule ∆l = ±1 is a consequence of the photon being a spin 1 particle.  Each photon either delivers or carries away one unit of intrinsic angular momentum.  Angular momentum conservation can be satisfied if the orbital angular momentum of the atom also changes by one unit.  Angular momentum is a vector.   Adding two vectors can yield a resultant vector with a larger or smaller magnitude, depending on the relative orientation of the two vectors. 

imageAn atom or molecule can emit a photon via spontaneous emission or stimulated emission.  Atoms and molecules in excited states randomly emit single photons in all directions according to statistical rules via spontaneous emission.  In the process of stimulated emission, a photon of energy hf perturbs an excited atom or molecule and causes it to relax to a lower level, emitting a photon of the same frequency, phase, and polarization as the perturbing photon.  Stimulated emission is the basis for photon amplification and it is the fundamental mechanism underlying all laser action.

Consider the simple case of a two-level system with lower level 1 and upper level 2.  The rate of absorption and stimulated emission depends on the number of photons present.  Quantum mechanics lets us calculate those rates. The probability that the system in level 1 absorbs a photon is equal to the probability that the system in level 2 emits a photon via stimulated emission.  The rate of spontaneous emission, however, is independent of the number of photons present.  Stimulated emission becomes much more likely than spontaneous emission if many photons are present.
The competition between absorption, stimulated emission, and spontaneous emission defines the criteria for laser action.

imageConsider the simple case of a two-level system with lower level 1 and upper level 2.  Let N1 be the number density of atoms in level 1 and N2 be the number density in level 2.
In thermal equilibrium N1 > N2.  Therefore a resonant photon is more likely to be absorbed than to stimulate emission.  But if N2 > N1 there is the possibility of average overall amplification for an array of photons passing through a volume of atoms of the two-level system.  This situation is termed population inversion, since under normal conditions N1 > N2.

Spontaneous emission depletes N2, producing unwanted photons with random phases, propagation directions, and polarizations.  Because of loss associated with spontaneous emission and other losses associated with the laser cavity, each laser is characterized by a minimum value of N2 - N1, termed the threshold inversion.  Only if N2 - N1 is greater then the threshold inversion do we see laser action.

imageThere are several ways of pumping a system to produce a population inversion.  It is, however, impossible to optically pump a two-level system, since once N2 = N1 the induced transition rate equals the absorption rate.  Three or four levels are needed to pump the system and produce the population inversion required for laser action.  Let us investigate the pumping of a four-level system.

An atom is first excited by optical, electrical, or other means through the "pump transition" from a starting level "0" to a temporary level or group of levels "3".  The atom quickly relaxes to a level "2", which may or may not be metastable.  Stimulated emission occurs from level "2" to level "1".  Level "1" quickly decays back to level "0", so that absorption from level "1" to level "2" is unlikely.  At any given time more of the atoms are at level "2" than at level "1", there is a "population inversion".  The rate of stimulated emission will exceed the absorption rate resulting in an optical amplifier.


To sustain laser action it is usually necessary to place the lasing material between the two mirrors of an optical cavity.  Some possible cavity designs are shown below.  Photons are reflected back and forth through the lasing medium, which greatly increases the probability of stimulated emission.


image

The Helium- Neon (He-Ne) Laser

imageFor many years the most common continuous wave (CW) laser was the He-Ne laser.  These low-power (mW) lasers use an electric discharge to create the population inversion.  Most He-Ne laser emit in the red at 633 nm.  They are used in interferometers, bar-code reader, and laser printers.  They also are used for many sighting and pointing applications from medical surgery to high-energy physics.  You used a He-Ne laser in the last two studio sessions.

In a helium neon laser, a low pressure mixture of helium and neon (<15%) is contained in a narrow bore glass tube.  A longitudinal, DC electrical discharge is maintained in the narrow tube.  This creates a plasma.  Collisions with free electrons in the plasma excite the helium atoms and cause a significant number of them to be trapped in the lowest-energy metastable states.  Neon is a larger, more complex atom, with 10 electrons, which are arranged in a 1s22s22p6 configuration in the ground state.  Neon has many excited states, and the ones concerned with laser action are shown in the energy level diagram on the right.

An excited state of neon occurs at excitation energies similar to that of the lowest-energy metastable state of helium.  Collisions between excited state helium atoms and ground state neon atoms cause some of the neon atoms to be excited to this state.

The 632.8 nm red laser output is produced by the 3s - 2p transition in neon. (See diagram.)  The energy level labeled 2p lies ~18.6 eV above the ground state and therefore is negligibly populated, even in the plasma.  Consequently, a population inversion between 3s and 2p is easily maintained by collisional pumping with excited helium atoms.  The states labeled 2p is populated by the laser transitions but is rapidly depopulated by spontaneous emission to lower levels.  However, the state labeled 1s is metastable and must be depopulated by collisions with the walls of the tube.  That is why He-Ne lasers all have very narrow-bore tubes.

imageThe helium neon laser is low gain device and require cavity mirrors of high reflectance in order to achieve lasing action.  Typically, one end of the cavity is defined by a total reflector (reflectance >99.9%), and the other end is defined by a mirror which permits ~ 1% of the intra cavity light to escape, forming the useful output of the laser.  It therefore follows that the intra cavity beam is up to 200 times more intense than the output beam.

Problem:

A helium-neon laser emits laser light at a wavelength of 632.8 nm and a power of 2.3 mW.  At what rate are photons emitted by this device?

Solution:

 

Module 11, Question 2

Discuss this with your fellow students in the discussion forum!