Quantum Physics Tutorial 8 - How the LASER works

For students studying the Welsh Board  and CEA syllabus

Contents

Optical Pumping

Stimulated Emission

Population Inversion

The Need for More than Two Levels

Different Types of LASER
Uses of the LASER
Safety

 

LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.  Trips off the tongue, doesn't it?  But good for a pub quiz.

 

The invention of LASER is credited to Theodore Maiman (1927 - 2007) or to Gordon Gould (1920 - 2005).  (There was a lot of legal action as a result.)  Both were American Physicists who developed the work of two American theoretical physicists, Charles Townes (1915 - 2015) and Arthur Schawlow (1921 - 1999). 

 

The properties of LASER light are that:

These make the LASER particularly useful for optics experiments in school and college labs.  There are many other uses, which we will look at later.

 

Question 1

What is meant by the terms monochromatic and coherent?

Answer

 

Optical Pumping

The LASER itself is quite simple, with no moving parts.  Here is a diagram:

 

 

The optical resonator consists of a crystal of material such as sapphire (Al2O3) which is doped with ions of rare earth metals.  The crystal is called the host crystal, and the ions are of transition elements like titanium, ytterbium, and chromium.

 

The discharge tube is a larger version of a photographic flash bulb, which gives off an intense white light.  The intense light passes into the space between the two mirrors, which is referred to as the optical resonance cavity, or laser cavity.  The resonating light between the two mirrors becomes weaker as some of the energy is lost on reflection.  The lost energy is supplemented by the photon emission from the LASER crystal. 

 

This extra energy is referred to as optical pumping.  

 

The crystal emits LASER light when it is exposed to the intense light, by stimulated emission, i.e. photons being emitted by interaction of atoms with other photons.

 

 

Stimulated Emission

There needs to be sufficient energy for stimulated emission to occur.  If not, the crystal will not produce LASER light.  The optical pumping power needs to be above the LASER threshold.  Then the stimulated emission rapidly rises until the crystal is saturated.  Let's look at the mechanism.

 

Incident photons of exactly the right energy excite the atom so that an electron is raised to a higher energy level.  In normal (spontaneous) electron excitation, the photon is absorbed.  The electron is raised to the high energy level.  Then as the electron falls back to the ground state, it emits a photon of the same energy. However, in this case, the phase and direction are random.  Light will be given off, but this will not result in stimulated emission.

 

In LASER light, it's a rather different.  The electron is excited by external photon at exactly the right frequency (hence energy).  As the electron makes its transition between the ground and excited states (neither of which have any magnetic properties), it gains a magnetic dipole that makes it act like a tiny magnet. This oscillates at the photon frequency, and makes it more likely that the electron will achieve the excited state.  Therefore more electrons are raised to the excited state than would happen in spontaneous excitation.  The oscillations of the dipole are responsible for the optical resonance.   Almost immediately the electron falls back to the ground state, emitting another photon.  This is shown below:

 

 

Rather than just one emitted photon, we get a second emitted photon by stimulated emission.  This has the same phase relationship with the first photon.  Here we see it as being in phase.  We can calculate the photon energy using this equation:

 

 

Question 2

A LASER emits light of wavelength 620 nm. 

(a)  Calculate the energy difference that gives rise to photons of this wavelength.  Give your answer in joules and electron-volts.

(b) Work out the energy level E2 if E1 is -15.6 eV.

(Planck's Constant = 6.63 10-34 J s)

Answer

 

After emission, we have two photons that are in phase.  Stimulated emission of itself will not cause LASER action.  We need another step, population inversion

 

 

Population Inversion

In spontaneous excitation of atoms, the vast majority of the atoms are in the ground state, with just a small proportion of the atoms excited. 

 

This is the case when the process of light amplification is started by the process of optical pumping.  The photons are moving in random directions with no constant phase relationship.  So the light given off is not coherent.  However many of these photons are trapped in the optical resonator, the space between the highly reflective mirror and the half-silvered mirror.  Some are lost to the process by absorption to release a single photon in a spontaneous event.  Others, however, cause stimulated emission in excited atoms, releasing a second photon that goes off in the same direction and has the same phase relationship.  So we start to get optical amplification, resulting in coherence.

 

The number of coherent photons produced by stimulated emission increases.  The optical amplification has a factor that is greater than 1.

 

At a certain point, we find that more atoms are in the excited state than in the ground state.  We have achieved the LASER threshold.  Suppose we have N1 atoms in the ground energy state E1, and N2 atoms in the excited energy state E2, the photon absorption is the main process and the light level falls.

 

If N1 = N2, the absorption balances the emission.  The material is said to be optically transparent.

 

If N2 > N1, then the LASER threshold is passed.  We say that there is population inversion, meaning that the number of excited atoms is greater than the number of atoms at the ground state.

 

As the process continues, the more atoms are excited, until eventually all atoms are excited.  We say that the crystal is saturated.  The LASER is in steady state.

 

Half the light is reflected at the half-silvered mirror called the output coupler, while half the photons pass through the output coupler.

 

Question 3

What is meant by population inversion?

Answer

 

 

The Need for More than Two Levels

In the discussion above, we modelled a LASER system that was based on two energy levels, the excited level, and the ground level.  However this does not work in practice. If the energy from the pump is the same as the difference between the ground and the excited state, we would get a combination of:

Surprisingly, it is possible for an atom to be de-excited by interaction with a photon.

 

With a two level system, the highest proportion of atoms excited by stimulated emission can only be 50 %, with the rest being at the ground state or undergoing spontaneous emission of photons.  Therefore, at best, we would get optical transparency.  We do NOT get stimulated emission.  We need to have three or even four levels.  The atoms need to be pumped up to a third (or even fourth) level to maintain the population inversion.  We will look at just three levels.

 

 

The pumping occurs at a photon energy of E3 - E1, to excite the atom to energy level E3.  Level E3 is sometimes called the pump band.

 

Then the electron drops from E3 to E2.  It could be a spontaneous emission, but more often it's a rapid drop without giving off a photon.  The energy is simply transferred as vibrational kinetic energy to heat up the surrounding material.  The lifetime of this transition is short.

 

When the electron falls from E2 to the ground state, the lifetime is very much longer than the transition lifetime from E3 to E2.  Since the population at E3 is much lower than that at E2, we can say that most of the atoms are in the E2 state.  There are many more atoms at E2 than are at E1, so a population inversion occurs, leading to stimulated emission.

 

The pumping of the electrons has to be done strongly to get over half the atoms to level 3 and thence to level 2.  This makes the laser rather inefficient.  So a more efficient laser can be achieved with a four level system.  The idea is shown in the diagram:

 

 

The transition that gives the stimulated emission is E3 to E2.  Because the transition is very rapid from E4 to E3, the number of electrons at E4 is very low.  The number at E3 is high.  At E2, the number of electrons is very low, since they have fallen rapidly to the ground state.  Therefore the population inversion is more easily achieved.  Most LASER sources are of this type.

 

Question 4

Explain why a LASER needs to have at least 3 energy levels.  What are the features of the energy levels?

Answer

 

 

Different Types of LASER

We have looked at the crystal LASER to explain how lasing works.  They are often called solid state LASER.  They can give a range of wavelengths.  We tend to associate them with red light, as the red light LASER is most often used in schools and colleges.  The wavelength, which gives rise to the colour, is determined by the material in the LASER crystal.

 

There are other types:

 

 

Uses of the LASER

There are many uses of the LASER, other than teaching in school and college optics.  Other uses include:

 

 

Safety

The concentrated nature of LASER light makes it potentially very dangerous.  You must never stare into a LASER beam, even a very low-powered one.  It will blind you.  The intensity will burn the retina, and scar tissue will replace the cones.  When working with a LASER, you must work under the supervision of your tutor, and wear goggles that will protect you against LASER light.

 

LASER pens are available at very low prices.  They are NOT toys.  Some moronic people think that shining LASER pointers at the pilots of aeroplanes coming in to land is some kind of joke.  The consequences of such behaviour need no explanation, and the punishments meted out to offenders are severe.

 

Question 5

A school LASER has a power of 1.5 mW.  The wavelength emitted is 620 nm.  The LASER beam passes through a hole that is 2.0 mm in diameter.  It is being used in an optics demonstration in the physics lab.

(a)  Which data item in the question is irrelevant?  Explain your answer.

(b)  Calculate the intensity.

(c)  Hence calculate the the radiation pressure exerted on the screen at the front of the physics lab.

Answer