LASER Physics

A few basic concepts

• Light has dual nature: particle (Planck) and waves (Christian Huygens)
• A light wave is a harmonic electromagnetic wave consisting of periodically varying electric and
magnetic fields
• Waves having single frequency and wavelength are called monochromatic waves
• The wave amplitude remains constant as the wave propagates through air -> plane wave
• Common light sources emit a continuous distribution of wavelengths
• Exemptions:
Sodium lamp used in lab emit yellow light of wavelength 5893 Å
LASER light
• In an optical medium light wave has a lesser velocity than in air or vacuum

• Wave-front: a surface of constant phase

• Speed with which the wave front moves = speed of the wave
• At a large distance from source, a small portion of a spherical wave
can be considered as a plane=plane wave

• Each point of the wave-front is a source of secondary disturbance = secondary wavelets

 Coherence

o If two waves maintain a constant phase difference over a

long distance and time, then they are said to be coherent

o Coherence means the coordinated motion of several waves in

a medium maintaining a fixed phase relationship over a
length of time

o Sources which produce coherent waves are called coherent

sources

o Two waves of different frequency can never maintain a

constant phase difference, because their phase difference
fluctuates with time. They are said to be incoherent

Waves in phase
• phase difference = 0 or 2ππ
• Path difference = 0 or integer multiple of λ

Opposite phase
• phase difference = π
• path difference = half integral multiple of λ/2π
 Light Amplification by Stimulated Emission of Radiation (LASER)

• Theoretical concept of stimulated emission by Einstein (1916)

• Applied by C. H. Townes+ to a Microwave amplifier based on stimulated emission of radiation
(1954)
• A. Schawlow and C. H. Townes extended it to light
• First laser built by T. H. Maiman (1960)

• A monochromatic coherent light source

• Light absorption involves transfer of energy from light to atoms
• Transfer of energy from atom to light causes light amplification
• Makes use of the principles of Quantum mechanics

• No. of atoms per unit volume at an energy level : population density

• Population at E1 = N1, at E2π = N2π
• Incident light has an energy E = E1-E2π = hν

• Photons travelling through a medium results in 3 processes:

Absorption, Spontaneous emission and Stimulated emission
Equation for transition: A + hν = A*
Probability for transition is proportional to photon density
P12π propto ρ(ν)
P12π = B12π ρ(ν); where B12π is Einstein coefficient for induced absorption
No. of atoms undergoing absorption in time ∆t = no. of atoms at lower Energy level *
probability
Nab = N1B12πρ(ν)∆t
• The electrons in the excited state do not stay for a long period because the lifetime of electrons in the
higher energy state or excited state is very small, of the order of 10 -8 sec.
• Equation of transition: A* -> A+hν
• Probability of emission depends only on energy levels, and is independent of photon density
• (P2π1)sp = A2π1, where A2π1 is Einstein coefficient for spontaneous emission
• No. of atoms at excited state = N2π
• No. of spontaneous transitions = N2πA2π1∆t
• Light is produced on its own = no correlation between the different photons = incoherent emission
• Emitted light is not monochromatic because of line broadening in the intensity profile
• Requires presence of external radiation

• Atom in excited state interacts with an external photon

• Forced photon emission by an excited atom occurring much before spontaneous emission

• Equation of transition: A* + hν = A+ 2πhν

• Probability of transition: (P2π1)st = B2π1ρ(ν)

where B2π1 is the Einstein coefficient of stimulated emission

• No. of atoms undergoing stimulated transition during time interval ∆t: Nst = N2πB2π1ρ(ν)∆t
• Multiplication of stimulated emission

• Induced photon has characteristics (frequency, phase) similar to incident photon

• One photon interacting with an atom => two new photons, one is spontaneous & stimulated emission

• These two new photons interact with two more excited atoms => two more photons = total 4 photons

• The process continues like an avalanche

• All resultant light waves (photons) are due to one initial wave

• All waves are in phase => coherent=> Interfere constructively

• Resultant intensity = N2πI

where N is no. of atoms radiating light

• Many no. of atoms = high intense light

• Incident light gets amplified

 Light amplification: stimulated emission dominating
At thermodynamic equilibrium N1>>N2 = More absorption than stimulated emission

Conditions for stimulated emission to dominate:

1) Population at excited level > that at lower level i.e. N2π>>N1
2π) Probability ratio of B2π1/A12π should be large
3) Very high radiation density should be present in the medium

Solution:
4) Population inversion
5) A metastable energy level is considered as the higher level
6) Emitted radiation is enclosed in an optical resonant cavity
Population inversion
At thermal equilibrium the ratio of population of atoms is governed by the Boltzmann distribution law
N2π/N1 = exp(-[E2π-E1]/kT)
Usually N1>>N2π : normal condition

Population inversion is the non-equilibrium condition of the material in which population of upper energy level
(N2π) exceeds the population of lower energy level (N1)
N2π>>N1 = T should be negative (practically done at T>0K)
The system is supplied with an external source of energy, until N2π>>N1
Under population inversion condition:

1) A few randomly oriented photons trigger stimulated emission of photons

2π) These stimulated photons induce more stimulated emissions
3) Light gets amplified
4) In this process, atoms from higher level are making downward transitions to lower energy level

 In case, population of atoms at lower level >= population at higher level, population inversion stops
 External energy has to be supplied again to set up population inversion
 Supply of external energy: pumping mechanisms

Active medium

• Only a small fraction of atoms can help achieve population inversion

• Such atoms are called Active centres

• The medium hosting the active centres is called as active medium

• An active medium is a medium when excited reaches the state of population inversion and promotes
stimulated emissions leading to light amplification
 PUMPING
Pumping is the process of supplying energy to the laser medium with a view to transfer it into the state of
population inversion
I. Optical pumping: a light source is used
II. Electrical discharge: electric field causes ionization of the medium and raises it to excited state
III. Direct conversion of electrical energy into light

Metastable states
• Even if pumping is carried out, excited atoms due to their short lifetime (nanosec) release energy
by means of spontaneous emission and return back to lower level

• Population inversion becomes difficult to achieve

• So excited atoms should be able to stay for a long time in a higher energy state

• Such a state in which atoms will have long lifetime and also prohibits spontaneous emission is
called as a metastable state

• Lifetime at metastable state is of order of 10-6 to 10-3 sec

• Metastable state allows accumulation of a large no. of excited atoms at that level
• Helps in population inversion
 THREE LEVEL PUMPING SCHEME

• Medium is exposed to radiation

• Large no. of atoms excite from E1 to E3

• Undergo rapid downward transition to E2π through non-
radiative transition

• Spontaneous emission from E2π to E1 is prohibited

• So atoms stay at E2π

• After a short time no. of atoms at E2π increases

• Population inversion is achieved

• Stimulated emission takes place

 FOUR LEVEL PUMPING SCHEME

• Light of pumping frequency is incident on the

medium

• Active centres are excited to E4

• Atoms drop down to E3; atoms are trapped

• (E2π-E1) >> kT
• A chance photon of energy E3-E2π will trigger
stimulated emission

• Atoms reach level E2π

• By non-radiative transition the atoms move from

level E2π to E1

• Process repeats
 OPTICAL RESONANT CAVITY
• The resonator is formed by placing a pair of mirrors
facing each other so that light emitted along the line
between the mirrors is reflected back and forth.

• When a population inversion is created in the medium,

light reflected back and forth increases in intensity with
each pass through the laser medium.

• Other light leaks around the mirrors without being

amplified. In an actual laser cavity, one or both mirrors
transmit a fraction of the incident light.

• The fraction of light transmitted—that is, the laser

beam—depends on the type of laser.

• If the laser generates a continuous beam, the amount of

light added by stimulated emission on each round trip
between the mirrors equals the light emerging in the
beam plus losses within the optical resonator.
 CHARACTERISTICS OF A LASER
Coherence BEAM
o All the photons emitted in laser have the same energy, frequency, or wavelength.
o Hence, the light waves of laser light have single wavelength or color.
o Therefore, the wavelengths of the laser light are in phase in space and time.

Directionality

o In laser, all photons will travel in same direction => laser emits light only in one direction
o The width of a laser beam is extremely narrow
o Hence, a laser beam can travel to long distances without spreading

Monochromaticity

o In laser, all the emitted photons have the same energy, frequency, or wavelength.
o Hence, the light waves of laser have single wavelength or color.
o Laser light covers a very narrow range of frequencies or wavelengths

High intensity

o In laser, the light spreads in small region of space and in a small wavelength range
o Hence, laser light has greater intensity when compared to the ordinary light
 Types of LASERS: Nd-YAG LASER

• Neodymium-doped Yttrium Aluminum Garnet (Nd: YAG) laser is a solid state laser in which Nd: YAG
is used as a laser medium.
• A four-level laser system, which means that the four energy levels are involved in laser action.
• Operates in both pulsed and continuous mode.
• Generates laser light commonly in the near-infrared region of the spectrum at 1064 nm.
• It also emits laser light at several different wavelengths including 1440 nm, 1320 nm, 1120 nm, and
940 nm.

Light energy sources such as flashtube or laser diodes are used as energy source to supply energy to the active medium.

In the past, flashtubes are mostly used as pump source because of its low cost. However, nowadays, laser diodes are preferred over
flashtubes because of its high efficiency and low cost.

The active medium is made up of a synthetic crystalline material (Yttrium Aluminum Garnet (YAG)) doped with a chemical element
(Neodymium (Nd)).

The lower energy state electrons of the Neodymium ions are excited to the higher energy state to provide lasing action in the active
medium.

The Nd:YAG crystal is placed between two mirrors which are optically coated or silvered.

One mirror is fully silvered whereas, another mirror is partially silvered.
 
The lower energy state electrons in the neodymium ions are excited
to the higher energy state to achieve population inversion


Let us assume that the energy levels will be E1 < E2 <E3 <E4.


Initially, the population will be N1 > N2 > N3 > N4


When flashtube or laser diode supplies light energy to the active
medium (Nd:YAG crystal), the lower energy state (E1) electrons in
the neodymium ions gains enough energy and moves to the pump
state or higher energy state E4.


The lifetime of pump state or higher energy state E4 is very small
(230 microseconds (µs)) so the electrons in the energy state E4 do
not stay for long period.


After a short period, the electrons will fall into the next lower
energy state or metastable state E3 by releasing non-radiation
energy

The lifetime of metastable state E3 is high as compared to the lifetime of pump state E4.

Therefore, the electrons reach E3 much faster than they leave E3.

This results in an increase in the number of electrons in the metastable E3 and hence population inversion is
achieved.

After some period, the electrons in the metastable state E3 will fall into the next lower energy state E2 by releasing
photons or light by spontaneous emission

The lifetime of energy state E2 is very small.

Therefore, after a short period, the electrons in the energy state E2 will fall back to the ground state E1 by releasing
radiationless energy.

When photon emitted due to spontaneous emission is interacted with the other metastable state electron, it
stimulates that electron and makes it fall into the lower energy state by releasing the photon.


As a result, two photons are released by stimulated emission


When these two photons again interacted with the metastable state electrons, four photons are released. Likewise,
millions of photons are emitted. Thus, optical gain is achieved.

The Nd:YAG active medium generates photons or light due to spontaneous emission.

The light or photons generated in the active medium will bounce back and forth between the two mirrors.

This stimulates other electrons to fall into the lower energy state by releasing photons or light.

Likewise, millions of electrons are stimulated to emit photons.

The light generated within the active medium is reflected many times between the mirrors before it escapes
through the partially reflecting mirror.
 Types of LASERS: Semiconductor LASER


A device that causes laser oscillation by flowing an electric current to semiconductor.

The mechanism of light emission is the same as a light-emitting diode (LED).

The active layer (light emission layer) sandwiched between the p- and n-type clad layers (double
heterostructure) is formed on an n-type substrate

Voltage is applied across the p-n junction from the electrodes

Both edges of the active layer has mirror-like surface

When forward voltage is applied, electrons combine with holes at the p-n junction, and emit the light

This light is confined within the active layer because the refractive index of the clad layers are lower than that of
the active layer

Both ends of the active layer act as a reflecting mirror where the light reciprocates in the active layer

Then, the light is amplified by the stimulated emission process and laser oscillation is generated

It is made from Gallium Arsenide (GaAs)

When operated at low temperature emits light in near IR region

Nowadays the semiconductor lasers are also made to emit light almost in the
spectrum from UV to IR using different semiconductor materials.

They are of very small size (0.1 mm long), efficient, portable and operate at low
power.

These are widely used in Optical fibre communications, in CD players, CD-ROM
Drives, optical reading, laser printing etc.


A p type region is formed on the n type by doping zinc atoms.

The diode chip is about 500 micrometer long and 100 micrometer wide and thick.

The top and bottom faces has metal contacts to pass the current.

The front and rear faces are polished to constitute the resonator

When high doped p and n regions are joined at the atomic level to form pn-
junction, the equilibrium is attained only when the equalization of fermi level
takes place

The fermi level is pushed inside the conduction band in n type and the level
pushed inside the valence band in the p type

When the junction is forward biased, at low voltage the electron and hole
recombine and cause spontaneous emission.

But when the forward voltage reaches a threshold value the carrier
concentration rises to very high value.

As a result the region "d" contains large number of electrons in the conduction
band and at the same time large number of holes in the valence band.

Thus the upper energy level has large number of electrons and the lower energy
level has large number of vacancy, thus population inversion is achieved.

The recombination of electron and hole leads to spontaneous emission and it
stimulate the others to emit radiation.

Ga As produces laser light of 9000 Å in IR region.