Module I - Lasers | Applied Physics

1. Introduction to LASER

LASER

Light Amplification by Stimulated Emission of Radiation

A laser is a device that produces an intense, highly directional beam of light by amplifying electromagnetic radiation through the process of stimulated emission. Unlike ordinary light sources (bulbs, sun) that emit light in all directions with various wavelengths, laser light has unique properties that make it useful in various applications.

Key Properties of Laser Light

Monochromatic: Single wavelength (single color)
Coherent: All waves are in phase with each other
Collimated: Light travels in a parallel beam with very little divergence
High Intensity: Concentrated energy in a narrow beam

2. Spontaneous Emission

When an atom is in an excited state (higher energy level E₂), it is unstable and naturally tends to return to its ground state (lower energy level E₁). During this transition, the atom releases the excess energy in the form of a photon. This process occurs randomly and without any external trigger.

Spontaneous Emission Process

An excited electron spontaneously drops to a lower energy level, emitting a photon

Characteristics of Spontaneous Emission

Occurs randomly without any external influence
Emitted photons travel in random directions
Photons have random phases (incoherent)
Energy of emitted photon: E = hν = E₂ - E₁
This is the process in ordinary light sources like bulbs

E = hν = E₂ - E₁

Energy of emitted photon in spontaneous emission

Where: h = Planck's constant (6.626 × 10⁻³⁴ J·s), ν = frequency of light

Example: Spontaneous Emission Energy

An electron in a hydrogen atom transitions from an excited state at energy -1.51 eV to the ground state at -13.6 eV. Calculate the wavelength of the emitted photon.

Step 1: Calculate energy difference

ΔE = E₂ - E₁ = -1.51 - (-13.6) = 12.09 eV

Step 2: Convert to Joules

ΔE = 12.09 × 1.6 × 10⁻¹⁹ = 1.934 × 10⁻¹⁸ J

Step 3: Use E = hc/λ to find wavelength

λ = hc/ΔE = (6.626 × 10⁻³⁴ × 3 × 10⁸) / (1.934 × 10⁻¹⁸)

λ = 1.028 × 10⁻⁷ m = 102.8 nm

Wavelength of emitted photon = 102.8 nm (Ultraviolet region)

3. Stimulated Emission

When an atom in an excited state is struck by an incoming photon whose energy exactly matches the energy gap between the excited and ground states, the atom is stimulated (forced) to emit a photon and transition to the lower energy level. This process is called stimulated emission and is the fundamental principle behind laser operation.

Stimulated Emission Process

An incoming photon stimulates the excited atom to emit an identical photon

Characteristics of Stimulated Emission

Requires an external photon to trigger the emission
Emitted photon is identical to the incident photon
Both photons have the same frequency, phase, direction, and polarization
Results in amplification (1 photon in → 2 photons out)
This is the basis of LASER operation

Important Note

The key difference between spontaneous and stimulated emission is that spontaneous emission produces random, incoherent light, while stimulated emission produces coherent light where all photons are in phase. This coherence is what makes laser light special.

Property	Spontaneous Emission	Stimulated Emission
Trigger	No external trigger needed	Requires incident photon
Direction	Random directions	Same as incident photon
Phase	Random (incoherent)	Same as incident photon (coherent)
Result	1 photon emitted	2 identical photons (amplification)
Application	Ordinary light sources	LASER

4. Population Inversion

Under normal thermal equilibrium conditions, most atoms exist in the ground state (lower energy level), and only a few are in excited states. This is described by the Boltzmann distribution. For laser action to occur, we need more atoms in the excited state than in the ground state – a condition called population inversion.

Population Inversion

A non-equilibrium condition where the number of atoms in a higher energy state (N₂) exceeds the number of atoms in a lower energy state (N₁), i.e., N₂ > N₁

Normal Condition (N₁ > N₂)

Most atoms in ground state

Absorption dominates over stimulated emission

Net result: Light is absorbed

Population Inversion (N₂ > N₁)

Most atoms in excited state

Stimulated emission dominates

Net result: Light is amplified

Normal vs Population Inversion

N₂/N₁ = exp[-(E₂ - E₁)/kT]

Boltzmann Distribution (Normal equilibrium)

Where: k = Boltzmann constant (1.38 × 10⁻²³ J/K), T = Temperature in Kelvin

Why is Population Inversion Necessary?

In normal conditions, when light passes through a medium, absorption is more likely than stimulated emission (because more atoms are in the ground state). This results in net absorption of light. For amplification (more light out than in), we need more atoms ready to emit than absorb – hence population inversion is essential for laser action.

Example: Population Ratio

Calculate the ratio of atoms in excited state to ground state at room temperature (T = 300 K) for a He-Ne laser transition with energy gap of 1.96 eV.

Step 1: Convert energy to Joules

ΔE = 1.96 × 1.6 × 10⁻¹⁹ = 3.136 × 10⁻¹⁹ J

Step 2: Calculate kT

kT = 1.38 × 10⁻²³ × 300 = 4.14 × 10⁻²¹ J

Step 3: Apply Boltzmann distribution

N₂/N₁ = exp(-ΔE/kT) = exp(-3.136 × 10⁻¹⁹ / 4.14 × 10⁻²¹)

N₂/N₁ = exp(-75.75) ≈ 10⁻³³

N₂/N₁ ≈ 10⁻³³ (Almost no atoms in excited state under thermal equilibrium – this shows why external pumping is needed!)

5. Pumping

Pumping

The process of supplying energy to the active medium to achieve population inversion. It excites atoms from the ground state to higher energy levels.

Since population inversion does not occur naturally, we need an external energy source to excite atoms from the ground state to higher energy states. This process is called pumping. Different types of pumping methods are used depending on the type of laser.

Types of Pumping

1. Optical Pumping

High-intensity light (flash lamp or another laser) is used to excite atoms.

Used in: Ruby laser, Nd:YAG laser

Advantage: Simple and effective for solid-state lasers

2. Electrical Pumping

Electric discharge through gas excites atoms through electron collisions.

Used in: He-Ne laser, CO₂ laser, Argon laser

Advantage: Continuous operation possible

3. Chemical Pumping

Energy released from chemical reactions excites atoms.

Used in: Chemical lasers (HF, DF lasers)

Advantage: High power output

Three-Level and Four-Level Laser Systems

Three-Level System: Atoms are pumped to level E₃, quickly decay to metastable level E₂, then emit laser light transitioning to E₁. Example: Ruby laser.

Four-Level System: Has an additional lower level E₁ above ground state E₀. Atoms quickly empty from E₁ to E₀, making population inversion easier. Example: He-Ne laser, Nd:YAG laser.

Four-level systems are more efficient because population inversion is easier to achieve.

6. Active Medium and Active Center

Active Medium

The material in which population inversion is created and light amplification takes place. It can be a gas, liquid, or solid. The active medium determines the wavelength of the laser output.

Active Center

The specific atoms, ions, or molecules within the active medium that actually undergo the stimulated emission process. These are the "lasing species."

Laser Type	Active Medium	Active Center	Wavelength
He-Ne Laser	Helium-Neon gas mixture	Neon atoms (Ne)	632.8 nm (Red)
Ruby Laser	Ruby crystal (Al₂O₃)	Chromium ions (Cr³⁺)	694.3 nm (Red)
Nd:YAG Laser	YAG crystal	Neodymium ions (Nd³⁺)	1064 nm (IR)
CO₂ Laser	CO₂ gas mixture	CO₂ molecules	10.6 μm (Far IR)
Fiber Laser	Optical fiber (silica)	Rare earth ions (Yb, Er)	1030-1080 nm

7. Resonant Cavity (Optical Resonator)

Resonant Cavity

A system of mirrors that confines light within the active medium, allowing it to pass through multiple times for amplification. It consists of two mirrors placed at both ends of the active medium – one fully reflecting and one partially reflecting.

Laser Resonant Cavity

Light bounces between mirrors, getting amplified with each pass through the active medium

Functions of Resonant Cavity

Amplification: Light makes multiple passes through the active medium, getting amplified each time
Mode Selection: Only light waves that fit exactly within the cavity (standing waves) are reinforced
Directionality: Only light traveling along the axis is reinforced; other directions are lost
Output Coupling: Partially reflecting mirror allows some light to exit as the laser beam

Resonance Condition

For constructive interference (standing waves) to form in the cavity, the cavity length must be an integer multiple of half wavelengths:

L = nλ/2

Resonance condition (n = 1, 2, 3, ...)

Example: Cavity Modes

A He-Ne laser has a cavity length of 30 cm and operates at 632.8 nm. How many half wavelengths fit in the cavity?

Step 1: Convert units

L = 30 cm = 0.3 m = 3 × 10⁸ nm

λ = 632.8 nm

Step 2: Calculate n from L = nλ/2

n = 2L/λ = 2 × 3 × 10⁸ / 632.8

n = 9.48 × 10⁵ ≈ 948,000

Approximately 948,000 half wavelengths fit in the cavity

8. Coherence Length and Coherence Time

Coherence describes the degree to which light waves maintain a fixed phase relationship. Laser light is highly coherent compared to ordinary light. There are two types of coherence:

Temporal Coherence

The correlation between the phase of a wave at one time and the phase at another time at the same point in space.

Related to the monochromaticity of the source.

Measured by coherence time (τc)

Spatial Coherence

The correlation between the phase at one point in space and another point at the same time.

Related to the size and directionality of the source.

Measured by coherence area

Coherence Time (τc)

The time duration over which the wave maintains a predictable phase. It is the time interval during which the light wave can be considered coherent.

Coherence Length (Lc)

The distance over which the wave maintains a predictable phase. It is the distance traveled by light during the coherence time.

τc = 1/Δν

Coherence Time

Lc = c · τc = c/Δν = λ²/Δλ

Coherence Length

Where: Δν = spectral bandwidth (frequency spread), Δλ = wavelength spread, c = speed of light

Light Source	Spectral Width (Δλ)	Coherence Length
White light (sun)	~300 nm	~1 μm
Sodium lamp	~0.02 nm	~1.7 cm
He-Ne laser	~0.001 nm	~20-30 cm
Stabilized He-Ne laser	~10⁻⁶ nm	~100 m to km

Example: Coherence Length Calculation

A He-Ne laser operates at wavelength 632.8 nm with a linewidth of 0.002 nm. Calculate the coherence length and coherence time.

Step 1: Calculate coherence length

Lc = λ²/Δλ = (632.8 × 10⁻⁹)² / (0.002 × 10⁻⁹)

Lc = 4.004 × 10⁻¹³ / 2 × 10⁻¹² = 0.2 m = 20 cm

Step 2: Calculate coherence time

τc = Lc/c = 0.2 / (3 × 10⁸)

τc = 6.67 × 10⁻¹⁰ s ≈ 0.67 ns

Coherence Length = 20 cm, Coherence Time = 0.67 nanoseconds

9. Characteristics of Lasers

Laser light possesses several unique properties that distinguish it from ordinary light sources. These characteristics make lasers invaluable in numerous applications.

1. Monochromaticity

Laser light consists of a single wavelength (color). While ordinary light contains many wavelengths, laser light has an extremely narrow spectral width. This is because stimulated emission produces photons of exactly the same energy/frequency as the stimulating photon.

2. Coherence

All photons in a laser beam are in phase with each other (both temporally and spatially). This high coherence enables interference effects and is essential for applications like holography. Ordinary light sources produce incoherent light with random phase relationships.

3. Directionality (Collimation)

Laser beam has very small divergence angle (typically milliradians). The beam remains narrow over long distances. This is due to the optical resonator selecting only axial modes. A torch spreads its light, but a laser pointer maintains its small spot size.

4. High Intensity

The energy is concentrated in a narrow beam rather than spreading in all directions. Even low-power lasers can have high intensity (power per unit area). A 1 mW laser can be more intense at its focal point than sunlight.

Divergence angle θ ≈ λ/D

Where D is the beam diameter at the output mirror

10. He-Ne Laser: Construction and Working

The Helium-Neon (He-Ne) laser was the first continuous-wave (CW) gas laser, developed in 1960. It produces a characteristic red beam at 632.8 nm and is widely used in laboratories, barcode scanners, and alignment applications.

Construction

He-Ne Laser Construction

Key Components

Glass Tube: Contains the gas mixture, typically 25-100 cm long
Gas Mixture: Helium and Neon in ratio 10:1 at low pressure (~1 torr)
Electrodes: Anode and cathode for electrical discharge
Brewster Windows: Glass plates at Brewster angle to minimize reflection losses and produce polarized output
Mirrors: One fully reflecting (100%), one partially reflecting (99%)
Power Supply: High voltage DC (1-2 kV) to create gas discharge

Working Principle

Energy Level Diagram of He-Ne Laser

Electrical Excitation of Helium

When high voltage is applied, electrons are accelerated through the gas. These electrons collide with helium atoms, exciting them to metastable states 2¹S (20.61 eV) and 2³S (19.82 eV). Helium atoms accumulate in these states because they are metastable (long-lived).

Resonant Energy Transfer to Neon

Excited helium atoms collide with ground-state neon atoms. The energy levels of He (2¹S and 2³S) closely match the 5s and 4s levels of neon. During collision, helium transfers its energy to neon, exciting neon to 5s or 4s levels. Helium returns to ground state.

Population Inversion in Neon

Continuous energy transfer from helium creates population inversion between neon's 5s/4s levels and 3p level. The 3p level has short lifetime and quickly decays, keeping its population low.

Stimulated Emission

When neon atoms in 5s state undergo stimulated emission to 3p state, they emit photons of wavelength 632.8 nm (red). These photons travel along the tube axis, bouncing between mirrors and stimulating more emissions.

Laser Output

A fraction of the amplified light exits through the partially reflecting mirror as the laser beam. The process is continuous, providing CW (continuous wave) output.

Why Helium is Used

Helium is easily excited by electron impact
Metastable states of He have energy very close to Ne upper laser levels (resonant transfer)
He-Ne collision efficiently transfers energy to Neon
Helium acts as a "pump" for Neon – Neon is the actual lasing medium

He-Ne Laser Specifications

Wavelength: 632.8 nm (visible red) – most common; also 543.5 nm (green), 1152 nm, 3391 nm
Power Output: 0.5 mW to 50 mW (typical)
Efficiency: ~0.1% (low but acceptable for many applications)
Beam Diameter: 0.5 to 1 mm
Coherence Length: 20-30 cm (can be > 1 km with stabilization)

11. Fiber Laser: Construction and Working

A fiber laser is a laser in which the active gain medium is an optical fiber doped with rare-earth elements such as Erbium (Er), Ytterbium (Yb), Neodymium (Nd), or Thulium (Tm). Fiber lasers have become increasingly important due to their high efficiency, excellent beam quality, and compact design.

Construction

Fiber Laser Schematic

Key Components

Pump Source: High-power laser diodes (915-976 nm for Yb-doped fibers)
Doped Optical Fiber: Silica fiber with rare-earth ions in the core – this is the active medium
Fiber Bragg Gratings (FBG): Act as mirrors – periodic variation in refractive index reflects specific wavelength
Cladding: Double-clad fiber allows pump light to propagate in inner cladding while signal propagates in core

Working Principle

Optical Pumping

Pump light from laser diodes (typically 915-976 nm) is coupled into the optical fiber. In double-clad fibers, pump light enters the inner cladding and propagates along the fiber, gradually being absorbed by the doped core.

Absorption and Excitation

Rare-earth ions (e.g., Yb³⁺) in the fiber core absorb pump photons and get excited to higher energy levels. For Ytterbium, absorption of 976 nm photon excites Yb³⁺ from ²F₇/₂ ground state to ²F₅/₂ excited state.

Population Inversion

Continuous pumping creates population inversion between the excited and ground states of the rare-earth ions. The long interaction length of the fiber ensures efficient pump absorption.

Stimulated Emission and Amplification

Spontaneously emitted photons at the lasing wavelength (~1060 nm for Yb) trigger stimulated emission. The fiber Bragg gratings form the resonant cavity – HR-FBG reflects ~100% while OC-FBG reflects 10-20% and transmits the rest as output.

Laser Output

Light bounces between the FBGs, getting amplified with each pass through the doped fiber. The output coupler FBG allows a portion of the amplified light to exit as the laser beam.

Advantages of Fiber Lasers

High Efficiency: 30-40% electrical-to-optical efficiency (vs ~0.1% for He-Ne)
Excellent Beam Quality: Single-mode fiber produces near-perfect Gaussian beam
Compact & Robust: All-fiber design, no alignment needed, vibration resistant
High Power: Can reach kilowatts to tens of kilowatts
Long Lifetime: No consumables, >100,000 hours
Flexible Delivery: Output can be easily delivered through fiber

Dopant	Pump Wavelength	Output Wavelength	Application
Ytterbium (Yb)	915-976 nm	1030-1080 nm	Industrial cutting, welding
Erbium (Er)	980, 1480 nm	1530-1620 nm	Telecom amplifiers
Thulium (Tm)	790 nm	1900-2050 nm	Medical, material processing
Neodymium (Nd)	808 nm	1060 nm	General purpose

Example: Fiber Laser Efficiency

A Ytterbium fiber laser is pumped with 100 W of optical power at 976 nm and produces 40 W of output at 1064 nm. Calculate the optical-to-optical efficiency and the quantum defect.

Step 1: Calculate optical-to-optical efficiency

η = P_out / P_pump = 40 W / 100 W = 0.4 = 40%

Step 2: Calculate quantum defect

Quantum defect is the energy lost per photon conversion:

Quantum Defect = 1 - (λ_pump / λ_laser) = 1 - (976/1064)

= 1 - 0.917 = 0.083 = 8.3%

Optical-to-optical efficiency = 40%, Quantum defect = 8.3%

12. Applications of Lasers

12.1 LiDAR (Light Detection and Ranging)

LiDAR

A remote sensing technology that uses laser pulses to measure distances and create precise 3D maps of objects and environments. The name is a combination of "light" and "radar."

Basic LiDAR Operation

Working Principle

Laser emits short pulses of light toward the target
Light reflects off the target surface
Sensor detects the reflected light
Distance is calculated from the time delay: d = ct/2
Scanning mechanism creates millions of distance measurements (point cloud)

Applications of LiDAR

Autonomous Vehicles: 3D mapping for navigation and obstacle detection
Topographic Mapping: Creating detailed terrain maps for surveying
Forestry: Measuring tree height and forest density
Archaeology: Discovering hidden structures under vegetation
Atmospheric Studies: Measuring pollution, aerosols, and cloud properties

12.2 Barcode Reader

Barcode Reader

A device that uses a laser beam to scan and decode information stored in barcode patterns. The laser provides a focused, bright light source for precise reading.

Barcode Scanner Working

Working Principle

Laser Source: Low-power He-Ne or diode laser produces focused beam
Scanning: Rotating mirror sweeps laser beam across the barcode
Reflection: White bars reflect light, black bars absorb light
Detection: Photodetector converts reflected light into electrical signal
Decoding: Pattern of high/low signals is decoded into numbers/letters

Why Laser is Used

Highly focused beam provides precise illumination
Monochromatic light simplifies detector design
Coherent light maintains intensity over distance
Can read barcodes from greater distances than LED scanners

12.3 Laser in Metal Work

High-power lasers (especially fiber lasers and CO₂ lasers) are extensively used in industrial metalworking for cutting, welding, drilling, and surface treatment.

Laser Cutting

High-intensity laser beam melts, burns, or vaporizes material along a defined path.

Clean, precise cuts
Minimal heat-affected zone
No tool wear
CNC controlled for complex shapes

Laser Welding

Focused laser beam creates deep, narrow welds by melting and fusing materials.

Deep penetration welding
High speed welding
Minimal distortion
Suitable for dissimilar metals

Laser Drilling

Pulsed lasers create precise holes by ablating material.

Micro-holes possible
High aspect ratio holes
No drill bit wear
Used in aerospace, electronics

Additional Metalworking Applications

Laser Marking/Engraving: Permanent marking on metals for identification, branding
Surface Hardening: Laser heats surface rapidly, quenching creates hard layer
Cladding: Adding material layer to surfaces for wear/corrosion resistance
Additive Manufacturing: 3D printing metals layer by layer (SLM, DMLS)

Laser Type	Power Range	Primary Use in Metalworking
CO₂ Laser	1-20 kW	Cutting thick mild steel, non-metals
Fiber Laser	0.5-100 kW	Cutting reflective metals, welding, marking
Nd:YAG Laser	0.1-6 kW	Precision welding, drilling
Disk Laser	1-16 kW	High-quality cutting and welding

Summary: Key Formulas

E = hν = E₂ - E₁

Photon Energy

N₂/N₁ = e^(-(E₂-E₁)/kT)

Boltzmann Distribution

L = nλ/2

Cavity Resonance

Lc = c/Δν = λ²/Δλ

Coherence Length

τc = 1/Δν

Coherence Time

d = ct/2

LiDAR Distance

Module I: Lasers

1. Introduction to LASER

2. Spontaneous Emission

3. Stimulated Emission

4. Population Inversion

5. Pumping

Types of Pumping

6. Active Medium and Active Center

7. Resonant Cavity (Optical Resonator)

8. Coherence Length and Coherence Time

9. Characteristics of Lasers

10. He-Ne Laser: Construction and Working

Construction

Working Principle

11. Fiber Laser: Construction and Working

Construction

Working Principle

12. Applications of Lasers

12.1 LiDAR (Light Detection and Ranging)

12.2 Barcode Reader

12.3 Laser in Metal Work

Summary: Key Formulas