LASER

The following response addresses your queries based exclusively on the provided source materials.

1. Full Form of LASER and the Main Three Processes

The full form of LASER is Light Amplification by Stimulated Emission of Radiation.

The underlying principle of laser operation involves three main quantum processes that take place when material interacts with radiation:

1. Absorption (Induced Absorption)

In this process, an atom residing in a lower energy state, $E_{1}$ (such as the ground state), absorbs an incident photon with energy $h ν$ . This absorption causes the atom to transition to a higher energy state, $E_{2}$ , which is an excited state.

The transition can be written as: $A + h ν = A^{*}$ .
Diagram: This is characterized by an upward transition from $E_{1}$ to $E_{2}$ initiated by an incident photon.

2. Spontaneous Emission (Natural Emission)

An atom in an excited state ( $E_{2}$ ) is inherently unstable and will eventually decay or return naturally to a lower energy state ( $E_{1}$ ). This downward transition occurs without the aid of any external influence or incident photon, and the excess energy is released as a photon ( $h ν$ ).

The process is controllable from outside and is known as a natural process.
The transition is written as: $A^{*} \to A + h ν$ .
Diagram: This is characterized by a downward transition from $E_{2}$ to $E_{1}$ , spontaneously emitting a photon.

3. Stimulated Emission (Induced Emission)

This phenomenon is essential for LASER operation. If an atom is in an excited state ( $E_{2}$ ) and is struck by an incident photon ( $h ν$ ) whose energy matches the energy difference between $E_{2}$ and $E_{1}$ ( $E_{2} - E_{1}$ ), the incident photon forces the excited atom to transition downward to $E_{1}$ . This transition releases the stored energy as a photon.

The resulting two photons—the incident photon and the emitted photon—are identical in terms of frequency, phase, and direction.
This process leads to the multiplication of photons and amplification of light.
The transition is written as: $A^{*} + h ν \to A + 2h ν$ .
Diagram: This is characterized by an incident photon hitting an excited atom at $E_{2}$ , causing a downward transition to $E_{1}$ and resulting in two emitted photons traveling in the same direction.

(Note: While the source refers to specific figures (Fig. 4.2.1, 4.2.2, 4.2.3) illustrating these processes, the diagrams themselves cannot be reproduced here based on the text extracts.)

2. Difference between Stimulated and Spontaneous Emission Process

The differences between spontaneous emission and stimulated emission are summarized in Table 4.2.1:

Spontaneous Emission	Stimulated Emission
Natural process	Artificial, induced process
Phase cannot be controlled	Two photons are exactly similar (identical in phase and direction)
No multiplication of photons takes place	Multiplication of photons takes place
Not useful for LASER	Essential for LASER

3. What is pumping in LASER? What are the types of pumping?

Pumping Definition

Pumping is defined as the process of raising a large number of atoms from a lower energy level to a higher energy level.

Types of Pumping

The primary types of pumping are:

Optical pumping: Uses strong light sources for excitation.
Electrical pumping (or Electrical discharge): Uses electron impact for excitation.
Chemical pumping: Uses chemical reactions for excitation.
Direct pumping: Uses direct conversion of electric energy into light.

4. Explain the terms: Population inversion, Metastable state

Population Inversion

Population inversion is defined as the state of a system at which the population of a particular energy state ( $N_{2}$ ) is more than that of a designated lower energy state ( $N_{1}$ ). That is, $N_{2} > N_{1}$ . Under conditions of thermal equilibrium, population inversion does not occur because the population of any higher energy state is always less than that of a lower state.

Metastable State

When an atom is excited, it typically returns to a lower energy state very rapidly, usually within about $1 0^{- 8}$ seconds. A metastable state is a special excited state where atoms remain for an unusually long time, typically on the order of $1 0^{- 3}$ to $1 0^{- 2}$ seconds. Metastable states are necessary because they allow the population to build up in the upper laser level, facilitating the achievement of population inversion.

5. What is population inversion? Explain its significance in the operation of LASER.

Population Inversion Definition

Population inversion is the condition where the number of atoms in the upper energy state ( $N_{2}$ ) is greater than the number of atoms in the lower energy state ( $N_{1}$ ) ( $N_{2} > N_{1}$ ).

Significance in LASER Operation

Population inversion is a fundamental precondition of LASER operation.

Achieving Amplification: For LASER action (Light Amplification by Stimulated Emission of Radiation) to occur, the rate of stimulated emission must be greater than the rate of absorption.
Overcoming Equilibrium: In thermal equilibrium, the population of the upper state is always less than the lower state. Pumping must be used to move atoms up, but only when population inversion is achieved ( $N_{2} > N_{1}$ ) does the system favor stimulated emission over absorption, leading to light amplification.
Utilizing Metastable States: Population inversion is usually achieved with the crucial help of a metastable state, which allows atoms to reside long enough in the upper level to build up the necessary population density.

6. Derive the relation between Einstein coefficients.

The Einstein coefficients ( $A_{21}, B_{12}, B_{21}$ ) relate the probabilities of spontaneous emission, stimulated absorption, and stimulated emission, respectively.

Consider two energy levels, $E_{1}$ (lower) and $E_{2}$ (upper), with populations $N_{1}$ and $N_{2}$ , and assume the system is in thermal equilibrium with radiation density $ρ (ν)$ .

Rates of Transition:
- Upward transition rate (Absorption): $N_{1} B_{12} ρ (ν)$
- Downward transition rate (Spontaneous + Stimulated Emission): $N_{2} A_{21} + N_{2} B_{21} ρ (ν)$ .
Thermal Equilibrium Condition: Under thermal equilibrium, the total rate of upward transitions equals the total rate of downward transitions per unit volume per second: $N_{1} B_{12} ρ (ν) = N_{2} [A_{21} + B_{21} ρ (ν)] ...(4.9.1)$
Solving for Radiation Density ( $ρ (ν)$ ): Rearranging equation (4.9.1) gives the expression for radiation density $ρ (ν)$ : $ρ (ν) = \frac{A _{21} N _{2}}{B _{12} N _{1} - B _{21} N _{2}}$ Dividing the numerator and denominator by $B_{21} N_{2}$ : $ρ (ν) = \frac{A _{21} / B _{21}}{( B _{12} / B _{21} ) ( N _{1} / N _{2} ) - 1} ...(4.9.2)$
Applying Boltzmann Statistics: The ratio of populations in thermal equilibrium is governed by the Boltzmann factor, where $E_{2} - E_{1} = h ν$ : $\frac{N _{1}}{N _{2}} = exp (\frac{E _{2} - E _{1}}{k T}) = exp (\frac{h ν}{k T}) ...(4.9.3)$
Comparison with Planck’s Law: Substituting $N_{1} / N_{2}$ into equation (4.9.2) gives: $ρ (ν) = \frac{A _{21} / B _{21}}{( B _{12} / B _{21} ) e x p ( h ν / k T ) - 1} ...(4.9.4)$ For this equation to agree with Planck’s energy distribution formula, which is: $ρ (ν) = \frac{8 πh ν ^{3}}{c ^{3}} \frac{1}{e x p ( h ν / k T ) - 1}$ The following relations between Einstein coefficients must hold:

Relation 1: Equality of Stimulated Coefficients $(B_{12} / B_{21}) = 1$ $B_{12} = B_{21} ...(4.9.5)$ (The probability of stimulated absorption equals the probability of stimulated emission.)

Relation 2: Ratio of Spontaneous to Stimulated Emission $A_{21} / B_{21} = \frac{8 πh ν ^{3}}{c ^{3}}$ $\frac{A _{21}}{B _{21}} = \frac{8 π h ν ^{3}}{c ^{3}} ...(4.9.6)$

7. Explain three and four level LASER system. Why two level LASER system is not acceptable for LASER action. Explain why four level laser is more efficient that three-level laser.

Two-Level LASER System

A two-level pumping scheme is not suitable for population inversion. In such a system, continuous pumping from the ground state ( $E_{1}$ ) to the excited state ( $E_{2}$ ) eventually leads to the populations $N_{1}$ and $N_{2}$ becoming nearly equal ( $N_{1} \approx N_{2}$ ). Since the rate of stimulated emission is proportional to $N_{2}$ and the rate of absorption is proportional to $N_{1}$ (given $B_{12} = B_{21}$ ), as $N_{2}$ approaches $N_{1}$ , the rates balance out, and true population inversion ( $N_{2} > N_{1}$ ) cannot be sustained.

Three-Level LASER System

This system utilizes three energy levels: $E_{1}$ (Ground state), $E_{3}$ (Pumping level), and $E_{2}$ (Metastable state).

Pumping: Atoms are pumped from the ground state $E_{1}$ to $E_{3}$ .
Decay to Metastable State: Atoms rapidly decay from $E_{3}$ to the metastable state $E_{2}$ .
Laser Action: Population inversion is achieved between the upper level $E_{2}$ and the ground state $E_{1}$ ( $N_{2} > N_{1}$ ). The laser transition occurs from $E_{2}$ to $E_{1}$ .
Efficiency Constraint: Since the lower laser level is the heavily populated ground state ( $E_{1}$ ), a very high pumping power is required to raise the population $N_{2}$ above $N_{1}$ .

Four-Level LASER System

This system utilizes four energy levels: $E_{1}$ (Ground state), $E_{4}$ (Pumping level), $E_{3}$ (Metastable/Upper Laser Level), and $E_{2}$ (Lower Laser Level).

Pumping: Atoms are pumped from $E_{1}$ to $E_{4}$ .
Decay to Upper Laser Level: Atoms rapidly decay from $E_{4}$ to the metastable state $E_{3}$ , accumulating population $N_{3}$ .
Laser Action: The laser transition occurs between $E_{3}$ and $E_{2}$ .
Rapid Decay of Lower Level: Atoms in $E_{2}$ rapidly decay to the ground state $E_{1}$ via non-radiative transition. This means $E_{2}$ is kept virtually empty ( $N_{2}$ is very small).

Efficiency Comparison

The four-level laser is more efficient than the three-level laser.

In a three-level system, inversion requires overcoming the high population of the ground state ( $E_{1}$ ), demanding high pumping power.
In a four-level system, the laser transition ends at $E_{2}$ , which is constantly depopulated because atoms quickly transition from $E_{2}$ to $E_{1}$ . Since $N_{2}$ remains very small, population inversion ( $N_{3} > N_{2}$ ) can be achieved with a much lower pumping power.

8. In He-Ne laser, what is the function of He atoms? Describe the construction and working of He-Ne laser. Also draw the energy level diagram.

Function of He atoms

The He-Ne laser utilizes a mixture of Helium (He) and Neon (Ne) gases. The Neon atoms act as the active centers where the stimulated emission occurs. The primary function of the Helium atoms is to absorb energy from the electrical discharge and then transfer this energy efficiently to the Neon atoms through collisions. This specific energy transfer is known as resonance transfer of energy.

Construction

The He-Ne laser consists of:

A long and narrow discharge tube filled with a mixture of He and Ne gases (typically in a 10:1 ratio).
Electrodes placed in the tube to apply a high voltage (around $1 kV$ ).
An Optical Resonator formed by two mirrors placed at the ends of the tube. One mirror is fully silvered (100% reflecting), and the other is partially silvered (allowing approximately 1% of the incident light to be transmitted).
Brewster windows sealed to the tube ends to minimize reflection losses and ensure the output is polarized.

Working

The He-Ne laser operates through an electrical discharge, which creates laser action via resonance energy transfer:

Excitation of He: Applying a voltage (e.g., $1 kV$ ) causes electrons to accelerate and collide with He atoms, exciting them to their metastable states, primarily $F_{2}$ ( $20.61 eV$ ) and $F_{3}$ ( $20.66 eV$ ).
Resonance Transfer: These metastable states of He have energies nearly matching the $E_{4}$ ( $20.61 eV$ ) and $E_{5}$ ( $20.66 eV$ ) metastable states of Ne. He atoms collide with Ne atoms, transferring their energy to Ne and raising Ne atoms to $E_{4}$ and $E_{5}$ . The He atoms return to their ground state.
Population Inversion: $E_{4}$ and $E_{5}$ serve as the upper laser levels for Ne, where population builds up due to their metastable nature. $E_{2}$ and $E_{3}$ act as the lower laser levels. Population inversion is achieved between ( $E_{5}, E_{4}$ ) and ( $E_{3}, E_{2}$ ).
Laser Transition: The main visible laser action occurs from $E_{4} \to E_{2}$ , resulting in the emission of red light at $6328 \overset{˚}{A}$ . Other transitions include $E_{5} \to E_{3}$ ( $3.39 μ m$ ) and $E_{5} \to E_{2}$ ( $1.15 μ m$ ).
Ground State Return: Atoms in the lower laser levels $E_{2}$ and $E_{3}$ quickly decay to the ground state $E_{1}$ through spontaneous emission or collision with the tube walls.

Energy Level Diagram

(Note: The diagram itself, Figure 4.11.2, cannot be fully reproduced here, but the description identifies key levels in Ne and He atoms:)

He States: Ground state $F_{1}$ . Metastable states $F_{2}$ ( $20.61 eV$ ) and $F_{3}$ ( $20.66 eV$ ).
Ne States: Ground state $E_{1}$ . Lower laser levels $E_{2}$ ( $18.70 eV$ ) and $E_{3}$ ( $19.78 eV$ ). Upper metastable laser levels $E_{4}$ ( $20.61 eV$ ) and $E_{5}$ ( $20.66 eV$ ). Energy is transferred from He ( $F_{2} \to F_{1}$ ) to Ne ( $E_{1} \to E_{4}$ ) and He ( $F_{3} \to F_{1}$ ) to Ne ( $E_{1} \to E_{5}$ ).

9. Describe the construction and working of fibre laser. Also draw the energy level diagram.

The provided sources discuss several types of lasers (He-Ne, Nd:YAG, Semiconductor), but they do not contain information regarding the construction, working, or energy level diagram of a fiber laser.

10. Describe the applications of LASER in different fields.

LASERs have wide-ranging applications due to their unique properties. Major fields of application include:

Industrial Applications (Material Processing): Used extensively in manufacturing for processes like cutting, welding, and drilling. Laser cutting uses high energy density to melt or vaporize materials.
Medical Applications: Lasers are widely used in medicine. Examples include using Nd:YAG lasers for treating gastrointestinal diseases, surgical applications (often described as bloodless surgery), and repairing detached retinas.
Holography: Lasers are crucial for holography, the technique used for the recording and reconstruction of three-dimensional images.
Information Storage and Reading: Semiconductor lasers are used in various optical data handling equipment, such as laser printers, copiers, CD players, optical communication, and memory reading/writing systems like CD-ROM, WORM, and Erasable Optical Disks.
Military Applications: High power YAG lasers are used as range finders. Lasers are also used in guidance systems for missiles/tanks and for targeting.

11. Discuss the components of LASER.

A typical laser system requires three essential components: the active medium, the pumping system, and the resonant cavity.

Active Medium: This is the material—which may be solid (like Ruby, Nd:YAG), liquid, or gas (like He-Ne, $CO_{2}$ )—in which light is amplified. The active medium must be capable of supporting population inversion.
Pumping System (Excitation Source): This is the external energy source required to excite the atoms in the active medium from lower energy levels to higher energy levels to achieve population inversion. Examples include optical pumping (flash lamps), electrical pumping (discharge), or direct chemical/electrical conversion.
Resonant Cavity / Optical Resonator: This consists of the active medium bounded by two mirrors or highly reflecting surfaces. The mirrors are aligned parallel to each other. One mirror is fully reflecting (100% reflectance), and the other is partially reflecting (slightly less than 100% reflectance) to allow the laser beam output. The cavity ensures that emitted photons travel back and forth, stimulating further emission and forming a standing wave pattern, thus sustaining oscillation and amplification.

12. What do you mean by active medium, active center, resonant cavity/optical resonator, coherence length and coherence time?

Active Medium: A medium in which light gets amplified. Examples include solid crystals (Ruby, Nd:YAG), liquids, or gases (He-Ne, $CO_{2}$ ).
Active Center: In the context of the He-Ne laser, the Neon atoms are described as the active centers, while Helium atoms are used only for energy transfer. Generally, this refers to the atoms/ions within the active medium responsible for the actual laser transition.
Resonant Cavity / Optical Resonator: A structure comprising an active medium bounded between two mirrors or highly reflecting surfaces. The cavity length ( $L$ ) must support a standing wave pattern, meaning $L = m \frac{λ}{2}$ , where $m$ is an integer and $λ$ is the wavelength of the laser light. This component provides the feedback necessary to sustain oscillation.
Coherence Length ( $Δ L$ ): This concept is related to temporal coherence. Temporal coherence refers to the wave propagation correlation observed at the same place at different times. Coherence length is the maximum path difference between two waves at which constructive interference can take place.
Coherence Time: Coherence time is directly associated with temporal coherence, which describes the correlation of the wave propagation system observed at the same place but not along the line of wave propagation. (A precise, standalone definition for ‘coherence time’ as a numerical value is not detailed in the source, but it is intrinsically linked to the length $Δ L$ and the frequency width $Δ ν$ of the laser light).

13. Write the characteristics of spontaneous emission and stimulated emission.

Characteristics of Spontaneous Emission

It is a natural process.
It occurs without the aid of an external photon.
The phase of the emitted photon cannot be controlled.
There is no multiplication of photons.
It is not useful for LASER action.

Characteristics of Stimulated Emission

It is an artificial, induced process.
The emitted photon is identical to the incident photon in all respects, including frequency, phase, and polarization.
Both the incident and emitted photons travel in the same direction.
It leads to the multiplication of photons (amplification).
It is essential for LASER action.

14. What are the properties of laser and what is Einstein A, B coefficient?

Properties of LASER

Laser light possesses several important characteristics that distinguish it from ordinary light:

High Directionality: Laser light is highly collimated, meaning the beam diverges very little, even over long distances.
Highly Monochromatic: Laser light generally consists of only one wavelength, or a very narrow bandwidth.
Highly Coherent: Laser light possesses a high degree of coherence (both temporal and spatial coherence), meaning the waves are highly correlated in phase.
High Intensity/Brightness: Due to low divergence and high coherence, laser energy is concentrated, making it highly intense.

Einstein A, B Coefficients

The Einstein coefficients relate the probabilities of atomic transitions involving photons:

A coefficient ( $A_{21}$ ): Represents the probability of spontaneous emission from an upper energy state ( $E_{2}$ ) to a lower energy state ( $E_{1}$ ).
B coefficient ( $B_{12}$ and $B_{21}$ ): Represents the probability of stimulated absorption ( $B_{12}$ ) from $E_{1}$ to $E_{2}$ or the probability of stimulated emission ( $B_{21}$ ) from $E_{2}$ to $E_{1}$ . In the derived relation, $B_{12} = B_{21}$ .

15. What do you mean by LiDAR? Write any five application.

The terms LiDAR and its applications are not mentioned in the provided source materials.

16. What is barcode reader? Explain its working.

Barcode readers are mentioned as an application field for semiconductor lasers, alongside laser printers and CD players. However, the provided sources do not define what a barcode reader is or explain its working principle.

17. Calculate the relative population of Na atoms in a Na lamp in the first excited state and in the ground state at a temperature of 250 C

The relative population ratio ( $\frac{N _{e x c i t e d}}{N _{g ro u n d}}$ or $\frac{N _{2}}{N _{1}}$ ) between two energy states in thermal equilibrium is determined by the Boltzmann factor:

$\frac{N _{2}}{N _{1}} = exp (- \frac{E _{2} - E _{1}}{k T}) = exp (- \frac{Δ E}{k T})$

Where:

$T$ is the temperature in Kelvin.
$k$ is the Boltzmann constant.
$Δ E = E_{2} - E_{1}$ is the energy difference between the first excited state and the ground state.

The query provides the temperature ( $T = 25 0^{\circ} C$ ). Converting to Kelvin is necessary ( $T = 250 + 273.15 K = 523.15 K$ ).

However, the specific energy difference ( $Δ E$ ) between the first excited state and the ground state for Sodium (Na) atoms is not provided anywhere within the given source materials.

Therefore, this calculation cannot be completed using only the information available in the sources.

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