Detailed Notes on Lasers

Laser Principles

• Lasers operate based on the principles described by Orazio Svelto, involving quantum mechanics and electromagnetism to explain light amplification.

• Detailed explanations and mathematical formulations can be found in "University Physics with Modern Physics" by H. D. Young and R. A. Freedman, covering topics from wave optics to quantum electronics.

Laser Characteristics

• Lasers possess unique spatial characteristics such as low divergence and high coherence, and temporal characteristics like short pulse duration.

• Einstein coefficients (A and B) are fundamental in describing the probabilities of spontaneous and stimulated emission, crucial for understanding laser operation.

• Population inversion, where a higher energy state has more atoms than a lower one, is essential for achieving light amplification; it's a non-equilibrium condition.

• Laser systems are categorized into two, three, and four-level systems based on the energy levels involved in the laser process, each with specific pumping requirements and efficiencies.

• Pumping schemes, including optical, electrical, and chemical methods, are used to excite atoms to higher energy levels, creating population inversion.

• The threshold gain coefficient is the minimum gain required to overcome losses in the laser cavity and achieve sustained laser oscillation.

• Laser components include active gain mediums, pumping sources, and optical resonators, each playing a critical role in laser operation.

• Common types of lasers include He-Ne, CO2, and Nd:YAG, each with distinct wavelengths, power outputs, and applications.

• Laser engineering applications span various fields, including materials processing, medical treatments, telecommunications, and metrology.

What is a Laser?

• LASER stands for Light Amplification by Stimulated Emission of Radiation, a process that produces coherent, monochromatic light.

Normal Light vs. Laser Light

Normal Light

• Polychromatic: Consisting of multiple colors, spanning a broad spectrum.

• Highly divergent: Spreading out widely from the source, resulting in low directionality.

• Low intensity: Weak brightness due to the dispersion of light.

• Not coherent: Light waves are out of phase, resulting in random interference.

• Caused by spontaneous emission, where photons are emitted randomly.

• Examples: Sun, bulb, fluorescent light.

Laser Light

• Monochromatic: Consisting of a single color or a very narrow range of wavelengths.

• Low divergence: Emitting a narrow, collimated beam that remains focused over long distances.

• High intensity: Strong brightness concentrated in a small area.

• Highly coherent: Light waves are in phase, resulting in constructive interference.

• Caused by stimulated emission, where photons are emitted in phase with the stimulating photons.

• Examples: Solid-state lasers, gas lasers, semiconductor lasers.

Applications of Lasers

• Surgery: Precise cutting, ablation, and coagulation of tissues.

• Defense and security: Range finding, target designation, and directed energy weapons.

• Laser cutting and welding: High-precision material processing in manufacturing.

• Digital services, barcode readers: Fast and accurate data capture in retail and logistics.

• Entertainment (laser shows): Visual displays using laser beams for artistic and entertainment purposes.

• Laser pointers: Simple devices for highlighting or pointing at objects.

Laser Properties (Characteristics)

• Monochromatism: Emitting light of a single color or very narrow bandwidth.

• Coherence: Maintaining a constant phase relationship in space and time.

• Directivity: Emitting light in a highly collimated, narrow beam.

• The reasons behind these properties/characteristics are interconnected, stemming from the process of stimulated emission.

Monochromatism

• A light source is monochromatic if it emits light of only one color or a very narrow range of wavelengths.

• Lasers have much smaller frequency/wavelength bandwidths compared to conventional light sources, making them highly monochromatic.

• Lasers have a high degree of monochromaticity due to the amplification of light generated by stimulated emission, which selects and amplifies specific wavelengths.

Measurement of Monochromaticity

• Monochromaticity is defined as: $\frac{ν<em>0}{Δν} = \frac{λ</em>0}{Δλ}$

• Where:

  • $\nu_0$ is the central frequency, representing the average frequency of the emitted light.

  • $\Delta\nu$ is the line width (Full Width at Half Maximum) in frequency, indicating the range of frequencies present in the laser output.

  • $\\lambda_0$ is the central wavelength, representing the average wavelength of the emitted light.

  • $\Delta\lambda$ is the line width (Full Width at Half Maximum) in wavelength, indicating the range of wavelengths present in the laser output.

• For semiconducting lasers, $\Delta\nu$ is approximately 1 MHz.

• For solid-state lasers, $\Delta\nu$ is approximately 1 kHz.

• The smallest $\Delta\nu$ is around 1 Hz, achievable in highly stabilized lasers.

• Also given is the relationship $\nu = \frac{c}{\lambda}$

• And $\Delta\nu = -\frac{c}{\lambda^2} \Delta\lambda$

• The negative sign is ignored as only magnitudes are considered.

Coherence

Sources are coherent if they emit light waves with the same phase or constant phase difference, same frequency, and wavelength, allowing for predictable interference patterns.

• Coherence requires a well-defined correlation between amplitude and phase of light at one point to the amplitude and phase at another point, ensuring stable and predictable light behavior.

• Two types of coherence:

  • Temporal (longitudinal) coherence: The correlation of phase at different points along the direction of propagation.

  • Spatial (transverse) coherence: The correlation of phase at points perpendicular to the direction of propagation.

Temporal Coherence

• If the phase at two different longitudinal positions (along the direction of propagation) are correlated, the wave is temporally coherent, meaning it maintains a consistent phase over time at a given point.

• Expressed as the first-order correlation function: $\frac{\langle E(t) E(t+\tau) \rangle}{\langle |E(t)|^2 \rangle} = e^{i\omega\tau}e^{-\frac{\tau}{\tau_c}}$

• Where $\tau_c$ is the coherence time, representing the duration over which the phase of the wave remains predictable.

• Coherence Length: The maximum separation between two points along the direction of propagation of waves which maintain a constant phase difference, given by $L<em>c = c \tau</em>c$

• $L<em>c = c \tau</em>c$ (Coherence Length = speed of light * Coherence Time)

• The delay over which the phase or amplitude wanders by a significant amount is defined as the coherence time ($\tau_c$).

• Coherence time $\tau_c = \frac{1}{Δν}$

• For ordinary light source: $\tau<em>c = 10^{-10} s$ and $L</em>c = 3 cm$

• For LASER source: $\tau<em>c = 10^{-3} s$ and $L</em>c = 300 km$

• For monochromatic light $\tau<em>c \rightarrow \infty$ and $L</em>c = c \Delta\nu = \frac{\lambda_0^2}{Δ\lambda}$

• Also, $\Delta\nu = - \frac{c}{\lambda^2} \Delta\lambda$ (ignoring the negative sign, only magnitudes are considered).

Spatial Coherence

• Measures the phase relationship (correlation) among waves traveling side-by-side, indicating the uniformity of the phase front.

• Consider two points P1 and P2 with electric fields E1(t) and E2(t) respectively.

• If the phase difference between the two fields at time t = 0 is zero and remains zero at any time t > 0, there is perfect coherence between these two points, enabling clean interference patterns.

• Spatial coherence describes the ability for two points in space to interfere when averaged over time, crucial for applications like holography.

Directionality

• Measures how much the light diverges, indicating the collimation of the beam.

• Angle beam divergence is given by $\theta = \frac{d}{z}$

• Where d is the beam diameter and z is the distance.

• $\theta = \frac{d<em>2 - d</em>1}{z<em>2 - z</em>1}$

• A normal flashlight has a divergence of 20-30 degrees, resulting in a wide beam.

• A searchlight has a divergence angle of 8-10 degrees, providing a more focused beam.

• For LASER beams, the divergence angle is on the order of milliradians ($10^{-3}$ rad), allowing for highly focused beams over long distances.

• $\theta = 1.22 \frac{\lambda}{D}$, where D is the diameter of the laser aperture, describing the diffraction-limited divergence.

Absorption & Emission

Absorption

• If the incident photon energy matches the energy-level difference ($h\nu = E<em>2 - E</em>1$), the electron in the lower state absorbs the photon and occupies the higher energy state, reducing the intensity of the incident light.

Spontaneous Emission (Radiative Emission)

• Spontaneous process in which an electron at a higher energy level ($E<em>2$) emits one photon of energy ($h\nu = E</em>2 - E<em>1$) and reaches a lower energy level ($E</em>1$) on its own, without any external trigger.

Stimulated Emission

• When the radiative emission of a photon of energy ($h\nu = E<em>2 - E</em>1$) occurs in the presence of another photon of the same energy, resulting in two identical photons.

• Note that radiative emission is just one of the two possible ways for the atom to decay. The decay can also occur non-radiatively, releasing heat instead of a photon.

Stimulated Emission vs. Spontaneous Emission

Principle of Laser Action

• Consider a box of atoms in which a larger number of atoms are in the higher energy state ($E<em>2$), and a photon of energy $h\nu = E</em>2 - E_1$ is hitting the box. This incoming photon can stimulate the excited atoms to emit identical photons, amplifying the light.

Population Inversion

• When the majority of the atoms are in an excited state or higher energy state, defying the thermal equilibrium.

Population Density

• $N \propto exp[-\frac{E}{kT}]$, where N is the population density, E is the energy level, k is Boltzmann's constant, and T is the temperature.

• At thermal equilibrium at temperature T: N3 < N2 < N_1, meaning more atoms are in lower energy states.

• Population inversion after pumping: N2 > N1, essential for laser operation.

Einstein Coefficients

Processes

• Absorption: The process by which an atom absorbs a photon and transitions to a higher energy state.

• Stimulated Emission: The process by which an incoming photon causes an excited atom to emit an identical photon, amplifying the light.

• Spontaneous Emission: The process by which an atom in an excited state randomly emits a photon and transitions to a lower energy state.

Equations

• $\frac{dN<em>1}{dt}</em>{absorption} = - B<em>{12} u(\nu) N</em>1$, describing the rate of change of atoms in the ground state due to absorption.

• $\frac{dN<em>1}{dt}</em>{spont \ emm} = A<em>{21} N</em>2$, describing the rate of change of atoms in the ground state due to spontaneous emission.

• $\frac{dN<em>1}{dt}</em>{stimul \ emm} = B<em>{21} u(\nu) N</em>2$, describing the rate of change of atoms in the ground state due to stimulated emission.

Variables

• $A_{21}$: Probability of spontaneous emission per unit time, a constant for a given atomic transition.

• $B_{12} u(\nu)$: Probability of stimulated absorption per unit time, dependent on the radiation density.

• $B_{21} u(\nu)$: Probability of stimulated emission per unit time, also dependent on the radiation density.

• $u(\nu)$: Radiation density, the energy per unit volume per unit frequency.

• $N<em>1$: Number of atoms in $E</em>1$ state, the ground state population.

• $N<em>2$: Number of atoms in $E</em>2$ state, the excited state population.

Overview

• All three processes (Absorption, Spontaneous Emission, Stimulated Emission) happen simultaneously, so the net rate of change of particles in energy state E1 will be,

• $\frac{dN<em>1}{dt} = - B</em>{12} u(\nu) N<em>1 + B</em>{21} u(\nu) N<em>2 + A</em>{21} N_2$, the rate equation for the population of the ground state.

• In thermal equilibrium, $\frac{dN_1}{dt} = 0$ (no net flux), indicating a stable population distribution.

• (Maxwell-Boltzmann distribution):
  $\qquad N<em>1 \propto exp[-\frac{E</em>1}{kT}]$
  $\qquad N<em>2 \propto exp[-\frac{E</em>2}{kT}]$

• Therefore,

• $u(\nu) = \frac{A<em>{21}}{B</em>{21}} \frac{1}{(\frac{B<em>{12}}{B</em>{21}} e^{\frac{h\nu}{kT}} - 1)}$, describing the radiation density in terms of Einstein coefficients.

Einstein Coefficient Relations

• Comparing with Planck’s radiation density:

• $u(\nu) = \frac{A<em>{21}}{B</em>{21}} \frac{1}{(\frac{B<em>{12}}{B</em>{21}} e^{\frac{h\nu}{kT}} - 1)}$

• $u(\nu) = \frac{8\pi h\nu^3}{c^3} \frac{1}{(e^{\frac{h\nu}{kT}} - 1)}$

• Therefore:

• $\frac{A<em>{21}}{B</em>{21}} = \frac{8\pi h\nu^3}{c^3}$, relating spontaneous and stimulated emission probabilities.

• $B<em>{12} = B</em>{21}$, indicating equal probabilities for stimulated absorption and emission.

• Probability rate of stimulated absorption = Probability rate of stimulated emission

• $A<em>{21} B</em>{21}u(\nu) = exp(\frac{h\nu}{kT}) - 1$

• $A<em>{21}(1-e^{-\beta h \nu}) + \frac{8 \pi h\nu^3}{c^3} e^{-\beta h \nu} B</em>{21} - \frac{8 \pi h \nu^3}{c^3} B_{12} = 0$

• In the limit $T \rightarrow \infty$, $e^{-\beta h\nu} \rightarrow 1$, therefore, from equation (1), we get

  • $B<em>{21} = B</em>{12}$ (1)

  • This equation must be satisfied for all the temperatures including and limits.

• In the limit $T \rightarrow 0$, $e^{-\beta h\nu} \rightarrow 0$, therefore, from equation (1), we get

  • $\frac{A<em>{21}}{B</em>{12}} = \frac{8\pi h\nu^3}{c^3}$ (2)

• These equations (2) and (3) are the relation between Einstein’s coefficients. Although we derived these relations in the and limits, (because they are constants) the relation must be correct for other temperatures as well.

• Significance: this relation means that,

  • rate of stimulated emission is equal to the rate of absorption. This is one of the reasons why a two-level system cannot have population inversion.

  • $\frac{A<em>{21}}{B</em>{12}}$ is inversely proportional to $c^3$ and directly proportional to $\nu^3$, that is “higher the frequency lower is the rate of absorption and higher is the rate of spontaneous emission”.

Einstein Coefficient at Higher Temperature

• At higher temperature, satisfying the condition kT ≥ hν, the stimulation emission rates are always higher than the spontaneous emission rates.

• $\frac{A<em>{21}}{B</em>{21}u(\nu)} = \frac{exp(\frac{h\nu}{kT})}{ - 1}$

• Probability rate of spontaneous emission $\frac{A<em>{21}}{B</em>{21}u(\nu)} = \frac{h\nu}{kT}$

• Probability rate of stimulated emission

• At higher frequencies, the ratio of spontaneous to stimulated emission rates increases, which means that it is difficult to make higher rates of stimulated emission at higher frequency.

• Since stimulated emissions are must for LASER, it is difficult to make LASER with higher frequency as compare to the LASER with lower frequency.

Population Inversion Conditions

• In population inversion, the number of atoms in an excited state ($N<em>2$) is greater than the number of atoms in the lower energy state ($N</em>1$).

• To achieve population inversion, we need to pump, by providing energy, to move atoms to a higher state.

• The number of atoms in higher energy levels cannot be larger than the number of atoms in the lower energy level (this condition is also called two-level saturation).

• Reasons for this include:

  • Under thermodynamic equilibrium [Temperature T], the number of atoms (N) in energy E is an exponentially decaying function of energy called the Maxwell-Boltzmann distribution: $N \propto exp[-\frac{E}{kT}]$

  • Einstein proved that the rate of stimulated emission is equal to the rate of absorption. Therefore, at best, the number of atoms in energy levels E1 and E2 are equal.

Population Inversion In a Two-Level System Is Not Possible

• $\frac{dN<em>1}{dt} = - B</em>{12} u(\nu) N<em>1 + B</em>{21} u(\nu) N<em>2 + A</em>{21} N_2$

• In thermal equilibrium $\frac{dN_1}{dt} = 0$

• $B<em>{12} = B</em>{21} = B$

• $A_{21} = A$

• \frac{N2}{N1} = \frac{B u(\nu)}{A + B u(\nu)} < 1

• At thermal equilibrium, population inversion is not possible in two-level systems

• A system with only two discrete energy levels is called a two-level system

Metastable States

• Atoms can be excited to a higher level by supplying energy.

• Normally, excited atoms have short lifetimes and release their energy in nanoseconds through spontaneous emission.

• Atoms do not stay long enough at the excited state to be stimulated.

• Even though the pumping agent continuously raises the atoms to the excited level, they undergo spontaneous transitions and rapidly return to the lower energy level.

• In order to establish population inversion, the excited atoms are required to 'wait' at the upper energy level until a large number of atoms accumulate at that level. The excited state should have a longer lifetime.

• A metastable state is such a state, where atoms remain excited for an appreciable time, of the order of $10^{-6}$ to $10^{-3}$ seconds.

• Metastable states allow the accumulation of a large number of excited atoms at that level.

• The metastable state population can exceed the population at a lower level, establishing population inversion in the lasing medium.

• It would be impossible to create the state of population inversion without a metastable state.

• Metastable states can be readily obtained in a crystal system containing impurity atoms and lie in the forbidden band gap of the host crystal.

• There could be no population inversion and hence no laser action if metastable states do not exist.

Three-Level Energy Systems

• Atoms are excited from Level 1 to Level 3 via optical pumping.

• The atoms quickly de-excite to Level 2 (metastable state) through rapid transition (non-radiative).

• Continuous pumping and de-excitation populate Level 2 and de-populate Level 1.

• The spontaneous transition rate between Level 2 to Level 3 has to be low.

• After population inversion, stimulated emission can occur between Level 2 and Level 1, resulting in laser action.

• More than 50% of atoms need to be excited in order to achieve population inversion in a three-level laser system.

• This drawback can be avoided in a four-level laser.

Four-Level Energy Systems

• Population inversion happens between Levels 3 and 2 via optical pumping from level 1 to level 4 and a rapid non-radiative transition from level 4 to level 3.

• From Level 2, atoms quickly depopulate to Level 1 through a rapid transition.

• No need to pump 50% of atoms because the ground state population is nearly zero.

• Most lasers use four-level systems due to their higher efficiency.

Pumping

• Pumping is a process of energy transfer from an external source to atoms to achieve population inversion, essential for laser operation.

Types of Pumping

• Optical pumping: A strong light source such as gaseous discharge, flash lamp, or arc lamp is used.

  • The light emitted excites atoms.

  • Used in solid-state lasers like ruby lasers and Nd:YAG lasers. In ruby lasers, a xenon flash lamp is used.

• Electrical pumping: Electrons are accelerated to high velocities by a strong electrical field.

  • These electrons collide with gas atoms and transfer their energy, exciting the atoms to a higher energy level.

  • Used in gas lasers like argon and CO2 lasers.

• Chemical pumping: Population inversion is achieved using a suitable chemical reaction.

  • If an atom or molecule is produced through a chemical reaction and remains in an excited state, it can be used for pumping.

  • Used in Hydrogen Fluoride and Deuterium Fluoride LASERs.

Components of a Laser

• Active medium (Gain medium): The material where light amplification occurs.

• Pumping energy source: Provides energy to the active medium to create population inversion.

• Resonance cavity (optical resonators): Provides feedback of light to sustain laser oscillation.

Active Medium (Gain Medium)

• The material in which the laser action takes place, determining the laser's wavelength and power.

• Contains a collection of atoms that can be in an excited state.

• Using an external source (radiation, electrical or chemical), these atoms can be excited to a higher energy level.

• The atoms later relax to a meta-stable state, and as a result population inversion can be achieved.

• The active medium may be solid crystals (ruby or Nd:YAG), liquid dyes, gases (CO2 or Helium/Neon), or semiconductors.

Pumping Energy Source

• The energy source pumps the active centers (atoms in the gain medium) from the ground state to the excited state to achieve population inversion, requiring precise energy input.

• Three types of pumping sources: optical, electrical, and chemical, depending on the nature of the active medium.

• In solid-state LASERs, optical pumping is used, and in gas LASERs, electrical pumping is used.

Resonant Cavity (Optical Resonator)

• Consists of two parallel mirrors placed around the gain medium, providing feedback for stimulated emission.

• One mirror is highly reflective (100% reflective), and the other is partially transmissive (99% reflective), allowing a portion of the light to exit as the laser beam.

• Light generated in the medium by spontaneous emission is reflected by the mirrors back into the medium, where it may be amplified by stimulated emission.

• The light reflects from the mirrors and passes through the gain medium hundreds of times before exiting the cavity.

• The design and alignment of the mirrors with respect to the medium are crucial for determining the exact operating wavelength and other attributes of the laser system.

Optical Gain and Threshold Gain Coefficients

• Change in intensity: Describes how the intensity of light changes as it passes through the gain medium.

• $dI = [N<em>2B</em>{21}u(\nu) − N<em>1B</em>{12}u(\nu)]h\nu dz$

• $dI = [N<em>2B</em>{21} − N<em>1B</em>{12}] \frac{I}{c} h\nu dz$

• Optical gain: $\gamma = [N<em>2B</em>{21} − N<em>1B</em>{12}] \frac{h\nu}{c}$

• $\frac{dI}{I} = \gamma dz$

• $I = I_0e^{\gamma z}$

• In reality, there is always some loss (α)

• $I = I_0e^{(\gamma−\alpha)z}$

Threshold Gain Coefficients

• $I<em>1 = I</em>0e^{(\gamma−\alpha)L}$

• $I<em>2 = R</em>2I_0e^{(\gamma−\alpha)L}$

• $I<em>4 = R</em>1R<em>2I</em>0e^{2(\gamma−\alpha)L}$

• In LASER, light moves back and forth between mirrors, experiencing gain and losses.

• R1 and R2 are the reflection coefficients of the mirrors, determining the amount of light reflected back into the gain medium.

• Incident intensity = I0

• Intensity after one cycle = I4

• For threshold gain ($\gamma_{th}$), the gain should at least compensate for losses in reflection and medium loss, ensuring sustained laser oscillation.

• $I<em>4 = R</em>1R<em>2I</em>0e^{2(\gamma_{th}−\alpha)L}$

• $\gamma<em>{th} = \alpha - \frac{1}{2L}ln(R*1R</em>2)$, the minimum gain required for laser operation.

He-Ne Laser

• The Helium-Neon laser was the first continuous gas laser, demonstrating continuous wave operation.

• A gas laser is a type of laser in which a mixture of gas is used as the active medium or laser medium. Gas lasers are the most widely used lasers.

• It is an atomic laser that employs a four-level pumping scheme, utilizing energy transfer from Helium to excite Neon atoms.

• Its usual operation wavelength is 632.8 nm, in the red portion of the visible spectrum, although other wavelengths are possible.

• The active medium is a mixture of 10 parts of Helium and one part of Neon, optimized for efficient energy transfer.

• Ne atoms are active centers and have energy levels suitable for laser transitions, while He atoms help in efficient excitation of Ne atoms.

• The optical cavity typically consists of a plane, highly reflecting mirror at one end of the laser tube and a concave output coupler mirror of approximately 1% transmission at the other end, forming a stable resonant cavity.

• Since the cavity window is outside the tube, Brewster's windows may be used at the ends of the tube to minimize reflection loss, ensuring high beam quality.

• HeNe lasers are normally small, with cavity lengths of around 15 cm up to 0.5 m, and optical output powers ranging from 1 mW to 100 mW, suitable for various applications.

Brewster Window

• A Brewster window is an uncoated substrate that is positioned at Brewster's angle within a laser instead of external mirrors.

• This substrate acts as a polarizer, such that the p-polarized light enters and exits the window without reflection losses, while the s-polarized light is reflected, resulting in polarized output.

He-Ne Laser Energy Function

• Energy is transferred via collision from Helium to Neon, exciting Neon atoms to higher energy levels.

• Wavelengths of emitted Photons: 632.8 nm (red), 1.15 μm (infrared), and 3.39 μm (infrared), depending on the specific energy level transitions.

Advantages of He-Ne Lasers

• Emits laser light in the visible portion of the spectrum, making it ideal for visual applications.

• High stability, providing consistent output over long periods.

• Low cost, making it accessible for educational and commercial applications.

• Operates without damage at higher temperatures, ensuring reliable performance.

Disadvantages of He-Ne Lasers

• Low efficiency, converting only a small percentage of input power into laser output.

• Low gain, requiring long cavity lengths for sufficient amplification.

• Limited to low-power tasks, unsuitable for high-power applications.

Applications of He-Ne Lasers

• Supermarkets use the narrow red beam to read barcodes, enabling quick and accurate scanning.

• Holography for producing 3D images of objects, utilizing the coherence of the laser light.

• Many industrial and scientific uses and laboratory demonstrations of optics, serving as a versatile tool for experiments.

CO2 Laser

• The CO2 laser was one of the earliest gas lasers, developed in BELL Labs in 1964 by Indian-born CKN Patel, marking a significant advancement in laser technology.

• It is a molecular gas laser working in the infrared frequency range (IR LASER), with high power output.

• In CO2 laser, the transitions occurring between different vibrational states are responsible for the laser effect, leading to the emission of infrared light.

• The CO2 molecule has a central carbon and two Oxygen atoms at either end. These atoms vibrate in distinct modes that determine the laser's output wavelength.

• Such a molecule can vibrate in three different modes of vibration, and in each mode of vibration, the center of gravity remains fixed:

  1. Symmetric Stretching mode ($\nu_1$): Both oxygen atoms move in and out symmetrically with respect to the carbon atom.

  2. Bending mode ($\nu_2$): The molecule bends, changing the angle between the oxygen atoms and the carbon atom.

  3. Asymmetric Stretching mode ($\nu_3$): One oxygen atom moves towards the carbon atom while the other moves away.

CO2 Vibrational Modes

• Symmetry stretching vibrational modes ($\nu_1$): Both oxygen atoms move in and out symmetrically with respect to the carbon atom influencing energy level transitions.

• Asymmetric stretching vibrational mode ($\nu_3$): One oxygen atom moves towards the carbon atom while the other moves away, playing an important role in population inversion.

• Bending vibrational mode ($\nu_2$): The molecule bends, changing the angle between the oxygen atoms and the carbon atom affecting energy transitions.

CO2 Laser Energy

• CO2 lasers work in the infrared frequency range (IR), emitting radiation at wavelengths around 9.6μm and 10.6μm.

CO2 Laser Construction

• Consists of a discharge tube made of fused Quartz, typically 2.5 cm in diameter and 5 m long, containing the gas mixture.

• A special feature of the CO2 laser is that the output is dependent on the diameter of the discharge tube, with larger diameters enabling higher power outputs.

• The active medium consists of He, N2, and CO2, with Brewster's windows at the ends, optimizing the gas mixture for efficient laser operation.

• A near-confocal silicon mirror coated with Aluminum forms the resonant cavity, providing high reflectivity in the infrared region.

• In CO2 lasers, N2 plays a similar role to He in He-Ne lasers. N2 goes to the excited state by collision with electrons.

• The excited N2 transfers energy to CO2, and CO2 gets excited, facilitating population inversion.

• The lowest vibrational level of N2 has nearly as much energy as the asymmetric stretching mode of the CO2 molecule, so the excited N2 readily transfers energy to CO2 in resonant collisions.

Advantages of the CO2 Laser

• CO2 laser emits radiation in the far-infrared region, useful for many industrial applications.

• Output power depends on the diameter of the tube, allowing for scalability.

• Emits radiation with power up to 100kW at 9.6μm and 10.6μm, making it suitable for high-power applications.

• Efficiency is high, around 30%, due to the efficient energy transfer between the gases.

• Output power can be controlled, enabling precise material processing.

• High intensity makes it effective for cutting and welding.

Disadvantages of the CO2 Laser

• Due to higher intensity, the laser tube is heated, requiring effective cooling mechanisms.

• Requires a cooling setup to dissipate heat and maintain stable operation.

• It is difficult to control and maintain the precise mixing of the gases in the desired ratio, needing sophisticated gas handling systems.

• For proper operation, contaminated gases have to be removed, and a fresh mixture introduced, requiring regular maintenance.

Applications of the CO2 Laser

• Used in open-air communication, although atmospheric absorption can limit range.

• Used in the military for spying, due to their high power and infrared emission.

• Due to high power, it is used in industries for cutting, drilling, welding, and other heavy applications, providing precision and speed.

• They are used as LIDAR, the operation of which is similar to RADAR, enabling remote sensing and mapping.

• In medicine, they are used for bloodless surgery, offering precise tissue ablation.

Nd-YAG Laser (Neodymium: Yttrium Aluminum Garnet)

• $Y<em>3Al</em>5O_{12}$

Nd-YAG Function

• Laser Wavelength: 1.064 μm, emitting in the near-infrared region.

Energy

• Ground State: The lowest energy level of the Nd atoms.

• Metastable State: A long-lived excited state critical for population inversion.

• Excited states: Higher energy levels to which Nd atoms are initially pumped.

• Non-radiative /Spontaneous transitions: Mechanisms by which atoms lose