Laser Module 5 Notes
Laser Module 5 Notes
Module - 5
3. What are three quantum processes when light interacts with matter?
3
Introduction
• LASER: Light Amplification through Stimulated Emission of Radiation
1. Highly directionality
2. Highly monochromatic
3. Highly intense
4. Highly coherence
5
Highly Directionality
• Where 2 and 1 are the diameters of laser spots at distances of 2 and 1 respectively
from laser source
• For laser light divergence = 10−3
• The divergence of light is very low and therefore laser light is highly directional 6
Highly Monochromatic
• In laser radiation, all the photons emitted
between discrete energy levels will have
same wavelength
• As a result the radiation is monochromatic in
nature
• Due to the stimulated characteristic of laser,
it is more monochromatic than that of a
convectional light
• laser radiation -the wavelength spread =
0.001 nm
Typical Applications of narrow spectral width
Communication Spectroscopy
Holography Interferometry
Sensors 7
Highly Intense
• Laser light is highly intense and can give very high power (>1015 W)
• 1 mill watt He-Ne laser is highly intense than the sun intensity
• when two photons each of amplitude are in phase with other; the resultant amplitude of
two photons is 2a and the intensity is 4a2
• in laser much number of photons are in phase with each other, the amplitude of the
resulting wave becomes na and hence the intensity of laser is proportional to n2a2
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Typical applications of high colimitation
• Alignment
• Bar code readers
• Communication
• Radar
• If a photon of energy 𝟐 𝟏 is incident on an atom, it imparts its energy to the atom and
disappears
• The absorbed energy make the atom to excite at energy E2, called as absorption transition
• The probability of absorption transition is proportional to photon density ρ
P12 ρ
P12 = B12 ρ
Where B12 is a Einstein coefficient for induced absorption
• The number of atoms excited during time Δt is
Nab = B12 N1 ρ Δt 13
2. Spontaneous Emission
• An atom can not stay in the excited state for a longer time (10-8 sec) and reverts to the lower energy
state by releasing a photon of energy 2 1
• The emission of photon by an atom without any external impetus is called as spontaneous emission
• The probability that a spontaneous transition occurs depends only on properties of energy levels
and not on the photon density.
(P21)Spont. = A21
• Where A21 is constant known as Einstein coefficient for spontaneous emission
• 1/A21 is a measure of the lifetime of the upper state
• The number of spontaneous transitions taking place during time Δt is
Nsp = A21 N2 Δt 14
Characteristics of spontaneous emitted radiation
• poly-monochromatic
• Incoherent
• less intense
• less directionality
• Example: light from sodium or mercury lamp
15
3. Stimulated Emission
• Since atoms in the medium is very large, coherent emission leads to an enormously high intense
light and we say that incident light is amplified
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Spontaneous vs. Stimulated Emission
Spontaneous Emission Stimulated Emission
The spontaneous emission was postulated by The stimulated emission was postulated by
Bohr Einstein
Additional photons are not required in Additional photons are required in stimulated
spontaneous emission emission
One photon is emitted in spontaneous emission Two photons are emitted in stimulated
emission
The emitted radiation is poly-monochromatic The emitted radiation is monochromatic
The emitted radiation is Incoherent The emitted radiation is Coherent
No amplification of light: less intense light Amplification of light: high intense light
𝑰𝒕𝒐𝒕𝒂𝒍 = 𝑵 𝑰 𝑰𝒕𝒐𝒕𝒂𝒍 = 𝑵𝟐 𝑰
Emitted light is non-directional Emitted light is highly directional
Unpolarized light Polarized light
Eg. Sodium and Mercury lamp Eg. Laser light
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Steady State
Under steady state condition the absorption and emission balance each other
But = 𝑒 ( )/
or = 𝑒 /
𝐴21 1
∴ 𝜌 𝜈 = /
3
𝐵12 𝑒 − 𝐵21/𝐵12
According to Plank’s law
8𝜋ℎ𝜈 𝜇 1
𝜌 𝜈 = / 4
𝑐 𝑒 −1
Energy density 𝜌 𝜈 given by eq (3) will be consistent with Plank’s law eq (4), only if
𝑨𝟐𝟏 𝟖𝝅𝒉𝝂𝟑 𝝁𝟑
= 5
𝑩𝟏𝟐 𝒄𝟑
Known as
𝑩𝟐𝟏 Einstein relations
= 𝟏 𝒐𝒓 𝑩𝟏𝟐 = 𝑩𝟐𝟏 6
𝑩𝟏𝟐 21
𝐴 8𝜋ℎ𝜈 𝜇
= 5
𝐵 𝑐
𝐵
= 1 𝑜𝑟 𝐵 =𝐵 6
𝐵
𝒄𝟑
𝑩𝟏𝟐 = 𝑩𝟐𝟏 = 𝑨 7
𝟖𝝅𝒉𝝂𝟑 𝝁𝟑 𝟐𝟏
Eq (6) shows that the coefficients for both absorption and stimulated emission are
numerically equal.
i.e. when an atom with two energy levels placed in the radiation field, the probability of
upward transition is equal to the probability for a downward transition.
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Light Amplification
• Absorption and spontaneous emission always occur together with stimulated emission
• Light amplification requires that stimulated emission occur almost exclusively
Condition for stimulated emission to dominate spontaneous emission:
𝑆𝑡𝑖𝑚𝑢𝑙𝑎𝑡𝑒𝑑 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 B21 N2 ρ(𝜈) 𝐵
= = 𝜌(𝜈)
𝑆𝑝𝑜𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 A21 N2 𝐴
• This indicate that stimulated transitions will dominate the spontaneous transitions if the
radiation density is very large
• Thus, the presence of a large number of photons in the active medium is required
• However, it will lead to more absorption transitions and therefore large photon density
alone is not sufficient and need the ratio B21/A21 to be a large
• So to increase the probability of stimulated emission, the lifetime of atoms at the excited
state should be larger
• It means that there is a requirement of states of larger lifetime 23
Condition for stimulated emission to dominate absorption transitions:
• Taking the ratio of these two transitions yields,
B21 N2 ρ
12N1 ρ
• It indicates that the stimulated emission will be larger than absorption process if
N2 > N1
• A medium amplifies light only when following three conditions are fulfilled:
i) High photon density in the active medium
ii) Larger lifetime excited states
iii) N2 > N1
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Population Inversion
• If material is in thermal equilibrium, the population ratio is given by Boltzmann factor,
𝟐 𝑬𝟐 𝑬𝟏 /𝒌𝑻
𝟏
• It means that population N2 at the excited level E2 is far smaller than the population N1 at
the level E1 at normal or equilibrium condition (N1>>N2)
• Population inversion is a non-equilibrium state in which population of the upper energy
level N2 far exceeds the population of the lower level N1 (N1<<N2)
• Population inversion can be obtained by employing pumping techniques
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Metastable States
• Metastable state is an excited state of atoms where atoms remains excited for an
appreciable time (10-6 to 10-3 sec) which allows accumulation of a large number of excited
atoms at this level
• Metastable state can be obtained by incorporating impurity atoms in the crystal system.
These levels lie in the forbidden band gap
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Components of Laser
The essential components of laser are
i) Active medium
ii) Pumping agent
iii) Optical resonator
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Active medium
• Active medium is the material in which the laser action takes place
• Most important requirement of laser medium is that population inversion should be possible
• The atoms, which cause laser action, are called as active centres. The rest of the medium acts as
host and supports active centres
• This medium after excitation reaches to population inversion and promotes stimulated emissions
leading to the light amplification
• Depending upon the active medium the lasers are classified as solid state, liquid state, gaseous
state and semiconductor lasers
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The Pump (Energy Source)
The pump is an external source that supplies energy needed to transfer the laser medium into the
state of population inversion
Pumping techniques:
1. Optical pumping
• A light source such as a flash discharge tube is used to illuminate the laser medium
• Optical pumping is used in solid laser. The solid materials have very broad absorption band, so
sufficient amount of energy is absorbed from the emission band of flash lamp to create
population inversion
• Xenon or Krypton flash tubes are used for optical pumping
• Examples: - Ruby laser, Nd:YAG Laser (Neodymium: Yttrium Aluminum Garnet), Nd: Glass Laser
2. Electrical Pumping
• This pumping is used only in laser materials that can conduct electricity. This method is limited to
gases medium
• A high voltage pulse ionizes the gas so that it conducts electricity. An electric current flowing
through the gas excites atoms to excited level
• Examples:- He-Ne laser, CO2 laser, Argon-ion laser, etc. 29
3. Injection current pumping
• This pumping mechanism is used in semiconductor lasers
• In semiconductor lasers, by passing high currents across the junction, the population
inversion will create
• In semiconductors lasers the population inversion always creates among majority and
minority charge carriers
• Examples:- InP and GaAs lasers
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Pumping Schemes
1. Three-Level pumping scheme
• The pumping leads to a large number of atoms at E3 which further rapidly undergo
downward transition to metastable state E2 through non-radiative transitions
• The population inversion is achieved only when more than half of the ground state atoms
are pumped to upper state
• Thus, require very high pump power for population inversion
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• Three level pumping scheme produces light only in pulses
2. Four-Level pumping scheme
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Threshold Condition for Lasing
• Let laser medium fills the space between the mirrors 1 and 2 which have reflectivity r1
and r2 respectively
• Let the intensity of light beam be 0 at mirror 1
• In traveling from mirror 1 to 2, the beam intensity increases from 0 to , given by
Where is the gain coefficient and the loss coefficient of the active medium
34
After reflection at M2, the intensity will be 𝑟2𝐼 𝑒
After complete round trip the final intensity will be
𝐼 2𝐿 = 𝑟1𝑟2𝐼 𝑒
The amplification obtained during the round trip is
𝐼(2𝐿)
𝐺= = 𝑟1𝑟2𝑒
𝐼
𝑟1𝑟2 represents the losses at the mirrors
𝛼 s represents losses due to scattering, diffraction and absorption occurring at the medium
The losses are balanced by gain, when G ≥ 1 ⟹ 𝑰(𝟐𝑳) = 𝑰𝟎
⟹ 𝑟1𝑟2𝑒 ≥1
𝑒 ≥
Taking log on both sides,
2𝐿 𝛾 − 𝛼 ≥ − ln 𝑟 𝑟
1
𝛾−𝛼 ≥− ln 𝑟 𝑟
2𝐿
1
𝛾≥𝛼 + ln 𝑟 𝑟
2𝐿
𝟏 𝟏
𝜸 ≥ 𝜶𝒔 + 𝒍𝒏 Condition for lasing 35
𝟐𝑳 𝒓𝟏 𝒓𝟐
• It shows that that the initial gain must exceed the sum of the losses in the cavity
• This condition is used to determine the threshold value of pumping energy for lasing
action
• depends on how hard the laser medium is pumped. At particular pump power, the
threshold value ( th) will be reached and the laser will starts oscillating
𝒔
𝟏 𝟐
This is a threshold condition for lasing
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Modes of the Laser Beam
• The light waves oscillating at some modes that match the oscillation modes of the cavity
are sustained
• There are two types of resonant modes
1. Longitudinal modes: governed by the axial dimensions of the resonant cavity
2. Transverse modes: determined by the cross-sectional dimensions of the laser cavity
37
Longitudinal Modes
• The two waves of the same frequency and amplitude moving in opposite directions creates a
standing wave in the cavity
• To create standing wave, a phase must be same at the mirror
• Therefore, the optical path from one mirror to other and back must be an integer multiplication of
wavelength
Thus
Or
Light waves are amplified strongly if, and only if, they satisfy the above condition in the cavity38
• The resonator may support several standing waves called as longitudinal modes
• These are the allowed frequencies inside the laser cavity of length L
• The frequency difference between two adjacent modes ( is
• Only those frequencies (modes) that have the amplification above the lasing threshold will be
emitted out of the laser
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Types of Laser
Based on the material used, some of the important lasers are
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Nd:YAG laser
• Nd:YAG laser stands for Neodymium: Yttrium
Aluminium Garnet (Y3Al5O12)
• One of the most popular solid state laser with
four-level laser system
• The system consist of an elliptically cylindrical
reflector having laser rod along one focus line and
a flash lamp along the other focus line
• Doping concentration of Nd is typically of the
order of 0.725% by weight, where Y3+ ions are
replaced by Nd3+ ions
• The crystal atoms do not participate in the lasing
action serve as a host lattice in which the active
centres Nd3+ ions resides
• The YAG crystal rods are typically of 10 cm in
length and 12 mm in diameter
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Working:
• The Krypton flash lamp pump the Nd3+ ions to excited state E4. These ions make non-radiative transition to
metastable state E3 leading to accumulation of Nd3+ ions at this energy level
• Therefore population inversion is readily achieved between the E3 level and E2 level and hence stimulated
emission initiated triggering many excited atoms to emit photons
• The laser emission occurs in infra red (IR) region at a wavelength of about 1.06 µm 43
Silent features of Nd:YAG laser
• Uses four-level pumping scheme
• The active centres are Nd3+ ions
• Krypton or Xenon flash lamp is used for pumping
• Low efficiency (1%) and moderate power output
• Operate in CW/pulsed mode
44
Helium-Neon Laser
• He-Ne laser is the first gas laser invented in 1961 by Ali Javan and co-workers
• It is made of a long discharge tube filled with mixture of helium and neon gases in the ratio 10:1
• Neon atoms are the active centres and have energy levels suitable for laser transitions while
helium atoms help in exciting neon atoms
45
Role of Helium in He-Ne laser
• The Helium atoms are lighter. So more
Energy Transfer readily excitable than neon atoms
E3 E6 (20.61 eV) • Helium atoms in excited energy levels E2
E5 and E3 collide with Neon atoms in the
E2 ground level. Neon atoms are excited to
E4 (19.81 eV)
energy levels E4 and E6 and Helium atoms
come back to the ground state (Resonant
E3 energy transfer)
E2 • The Neon atoms are much heavier and
could not be pumped efficiently without
E1 E1 Helium atoms
• The role of Helium atoms is to excite Neon
He Ne atoms and cause population inversion
Levels Levels
46
Why the population of He : Ne is 10:1 ?
• Many He atoms excited to
Energy Transfer higher energy levels E2 andE3
E3 E6 will fall down due to
E5 spontaneous emission and
won’t be able to transfer their
E2 E4 energy to Ne atoms
47
Working of He-Ne Laser
48
Silent features of He-Ne Laser
• The laser is simple, practical and less expensive
• Uses four-level pumping scheme and hence emits continuous laser beam
• The laser beam is highly collimated, coherent and monochromatic compared to solid
state laser
• Widely used in interferometer, laser printing, bar code reader, etc.
• He-Ne laser is highly stable and require no external cooling
• The overall gain of He-Ne laser is very low and is typically about 0.010 % to 0.1 %
• The output power of He-Ne laser is very low ranging from 0.5 to 50 mW in the red
portion of the visible spectrum
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Carbon Dioxide Laser: Definition, Principle
Definition
In carbon dioxide laser, CO2 gas molecules are used as the active medium
and population inversion is achieved by the electrical pumping method.
Principle
The active medium is a gas mixture of CO2, N2 and He. The laser transition
takes place between the vibrational states of CO2 molecules.
Energy states of CO2 molecules Carbon dioxide (Co2) is a symmetric
molecule (O=C=O) and it has three modes of vibration:
•Symmetric stretching.
•Bending.
•Antisymmetric stretching is shown in the figure
0.163 eV
0.078 eV
0.276 eV
Discharge tube : 2.5 cm dia; 5 m in
Length
E5 to E4 : 10.6um (IR)
E5 to E3 : 9.6 um (IR)
Components of Co2 Laser
Active medium ( or Carbon dioxide laser gain medium )
The main component of a Carbon dioxide laser is a medium in the form of CO2 gas molecules called
an active medium. The main characteristics of the active medium are as follows:
•It must have a pair of energy levels separated by a certain amount of energy. The energy level
having energy is known as an upper energy level or higher excited energy level and the energy level
having low energy is known as low energy or ground state.
When an electric discharge is passed through the tube, the number of electrons is emitted, which pumps
nitrogen molecules to V = 1 state.
In CO2 laser, the energy difference between the vibrational energy levels of Nitrogen and carbon dioxide is
very small ( i.e. about 0.3 eV ) and hence there are a large number of electrons in the gas discharge tube
having the energy of more than 0.3 eV.
Application of CO2 laser
•Due to the high power of CO2 laser, it has frequently used in industrial areas such as for cutting and
welding.
•used in skincare problems to treat different non-cancerous (benign) and cancerous (malignant).
While current optical disc technologies such as DVD, DVD±R, DVD±RW, and
DVD-RAM rely on a red laser to read and write data, the new format uses a blue-
violet laser instead, hence the name Blu-ray.
The benefit of using a blue-violet laser (405nm) is that it has a shorter wavelength
than a red laser (650nm), which makes it possible to focus the laser spot with
even greater precision. This allows data to be packed more tightly and stored in
less space, so it's possible to fit more data on the disc even though it's the same
size as a CD/DVD. This together with the change of numerical aperture to 0.85 is
what enables Blu-ray Discs to hold 25GB/50GB. Storage capacity to 500GB (20
layers) is also achieved.
HOW CAN 50GB BE STORED ON ONE DISC?
The structure of a Blu-ray (BD) disc fundamentally differs from the structure
of a DVD/CD. Because the data layer on a Blu-ray disc is placed much
“closer” to the laser lens than on a DVD/CD, the laser beam provides more
precision. (fig. A)
The Blu-ray Drive uses a blue-violet laser and improved lens specifications
(wavelength, NA-numerical aperture) allowing for a laser beam focus that’s
approximately one-fifth smaller than the red laser used to burn DVDs.
This combination enables recording much smaller and higher density pits onto
BD discs.