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Module I: Lasers - Question Solutions

Question 1: Metastable State and its Role in LASER

Question
What is metastable state? What is the role of metastable state in LASER?
Definition of Metastable State

A metastable state is an excited energy state of an atom or molecule that has a relatively long lifetime compared to ordinary excited states. While normal excited states have lifetimes of about 10⁻⁸ seconds, metastable states can have lifetimes ranging from 10⁻³ to 10⁻² seconds or even longer.

Key Characteristics of Metastable State:
  • It is an intermediate excited state between ground state and higher excited states
  • Direct transition to ground state is forbidden or highly improbable by selection rules
  • Atoms can accumulate in this state due to long lifetime
  • Spontaneous emission from this state is very low
Role of Metastable State in LASER
Essential Functions:
  • Population Inversion: The long lifetime allows atoms to accumulate in the metastable state, making it possible to achieve population inversion where more atoms exist in the excited state than in the ground state.
  • Stimulated Emission: Once population inversion is achieved, incoming photons can trigger stimulated emission from metastable atoms, producing coherent light.
  • Energy Storage: Acts as a reservoir for storing energy that can be released coherently when stimulated.
  • Amplification: Enables sustained light amplification as atoms remain available for stimulated emission longer.
Why is Metastable State Essential?
Without a metastable state, atoms would quickly return to the ground state through spontaneous emission before enough atoms could accumulate for population inversion. The metastable state essentially acts as a "holding area" where atoms wait until stimulated emission triggers the laser action.

Question 2: Resonant Cavity in Laser Generation

Question
What is resonant cavity? Explain its use in the generation of Laser beams.
Definition of Resonant Cavity

A resonant cavity (also called optical resonator or laser cavity) is a system of mirrors placed at both ends of the active medium that reflects light back and forth through the medium, allowing the light to be amplified with each pass.

Resonant Cavity Structure
Fully Reflecting Active Medium Partially Reflecting Laser Output
Schematic of a laser resonant cavity with active medium
Components of Resonant Cavity
  1. Fully Reflecting Mirror (M₁): Reflects 100% of the incident light back into the cavity
  2. Partially Reflecting Mirror (M₂): Reflects about 95-99% and transmits 1-5% of light as output beam
  3. Active Medium: The gain medium placed between the mirrors where stimulated emission occurs
Uses in Laser Generation
Light Amplification
Photons bounce back and forth between mirrors, passing through the active medium multiple times. Each pass causes more stimulated emission, amplifying the light intensity exponentially.
Mode Selection
Only light waves that are exact multiples of half-wavelength between mirrors (standing waves) are reinforced. This selects specific frequencies, ensuring monochromaticity.
L = n × (λ/2)
where L = cavity length, n = integer, λ = wavelength
Directionality
Only photons traveling parallel to the cavity axis remain in the cavity. Off-axis photons escape through the sides, ensuring the output beam is highly directional.
Coherence Enhancement
Multiple passes ensure all photons are in phase (temporal coherence) and traveling in the same direction (spatial coherence), resulting in a coherent laser beam.
Threshold Achievement
The cavity provides optical feedback to overcome losses. When gain exceeds losses, the laser reaches threshold and produces sustained output.

Question 3: He-Ne Laser - Construction and Working

Question
With the neat energy level diagram, explain the construction and working of He-Ne Gas laser.
Introduction

The He-Ne (Helium-Neon) laser was the first continuous-wave (CW) gas laser, developed by Ali Javan in 1960. It typically emits red light at a wavelength of 632.8 nm.

Construction
He-Ne Laser Construction
He + Ne Gas Mixture (10:1) Brewster Window Brewster Window M₁ (100%) M₂ (99%) Anode (+) Cathode (-) DC Supply Laser
Schematic diagram of He-Ne laser construction
Construction Components:
  • Discharge Tube: A narrow glass tube (typically 10-100 cm long, 2-8 mm diameter) containing the gas mixture
  • Gas Mixture: Helium and Neon in the ratio 10:1 at low pressure (~1 torr)
  • Electrodes: Anode and cathode for electrical discharge
  • Brewster Windows: Inclined at Brewster's angle to minimize reflection losses and produce polarized output
  • Mirrors: One fully reflecting (M₁) and one partially reflecting (M₂, ~99% reflective)
  • Power Supply: DC power supply providing 1000-2000V for gas discharge
Energy Level Diagram
Energy Level Diagram of He-Ne Laser
Energy (eV) Helium Neon 1¹S₀ (Ground) 2¹S₀ (20.61 eV) 2³S₁ (19.82 eV) Ground State 3s₂ (20.66 eV) Metastable 2s₂ (19.78 eV) 2p₄ (18.70 eV) 3p₄ 1s (Intermediate) Electron Impact Resonance Transfer 632.8 nm (Red) 1152 nm (IR) Spontaneous Collision with walls
Energy level diagram showing laser transitions in He-Ne laser
Working Principle
Electrical Discharge
When high voltage DC is applied, electrons are released from the cathode and accelerated towards the anode, creating a discharge in the gas mixture.
Helium Excitation
Fast-moving electrons collide with helium atoms, exciting them to metastable states (2¹S₀ at 20.61 eV and 2³S₁ at 19.82 eV). These states have long lifetimes (~10⁻⁴ s).
Resonance Energy Transfer
Excited helium atoms collide with ground state neon atoms. Due to nearly equal energy levels (energy matching), helium transfers its energy to neon, exciting Ne atoms to 3s₂ and 2s₂ states. Helium returns to ground state.
He* + Ne → He + Ne*
Resonance energy transfer process
Population Inversion
The upper laser levels (3s₂ and 2s₂) of neon get populated faster than they deplete. Since lower levels (2p₄ and 3p₄) have shorter lifetimes, population inversion is achieved between upper and lower laser levels.
Laser Transition
Stimulated emission occurs when neon atoms transition from upper to lower levels:
  • 3s₂ → 2p₄: Produces 632.8 nm (Red) laser light
  • 3s₂ → 3p₄: Produces 3391 nm (IR)
  • 2s₂ → 2p₄: Produces 1152 nm (IR)
De-excitation
Neon atoms in lower laser levels (2p₄) quickly decay to 1s level through spontaneous emission, then return to ground state by collisions with tube walls. The narrow tube diameter ensures efficient wall collisions.
Characteristics of He-Ne Laser:
  • Type: Four-level laser system
  • Wavelength: 632.8 nm (red), also 1152 nm, 3391 nm (IR)
  • Output Power: 0.5 mW to 50 mW (typical)
  • Efficiency: ~0.1% (low)
  • Mode of Operation: Continuous Wave (CW)
  • Applications: Barcode readers, laser pointers, holography, alignment

Question 4: LiDAR Technology

Question
What is Lidar technology and how does it work?
Definition

LiDAR (Light Detection and Ranging) is a remote sensing technology that uses laser light pulses to measure distances and create precise three-dimensional representations of the target and its surroundings.

LiDAR Acronym:
Light Detection And Ranging - Similar to RADAR but uses light waves instead of radio waves.
Working Principle
LiDAR Working Mechanism
LiDAR Scanner Emitted Laser Pulse Target Reflected Pulse Distance = (c × t) / 2 Laser + Detector
Basic Working Steps
Pulse Emission
The LiDAR system emits rapid pulses of laser light (typically infrared at 905 nm or 1550 nm) towards the target area. A single LiDAR system can emit 150,000+ pulses per second.
Light Interaction
The laser pulse travels through the atmosphere and hits objects (ground, buildings, trees, etc.). Part of the light is reflected back towards the sensor.
Detection
The photodetector in the LiDAR system receives the reflected light pulse and measures the exact time of arrival.
Distance Calculation
Using the time-of-flight principle, the distance to the object is calculated:
Distance = (c × t) / 2
where c = speed of light (3×10⁸ m/s), t = time for round trip
3D Point Cloud Generation
By scanning in multiple directions and combining with GPS and IMU data, the system creates a dense "point cloud" - millions of data points forming a 3D representation of the environment.
Components of a LiDAR System
Component Function
Laser Source Generates coherent light pulses (typically solid-state or fiber lasers)
Scanner/Optics Directs laser beams across the target area using rotating mirrors
Photodetector Detects returning light pulses (avalanche photodiodes or PMTs)
GPS Receiver Provides precise position of the LiDAR system
IMU (Inertial Measurement Unit) Measures orientation and movement of the system
Processing Unit Computes distances and generates point cloud data
Applications of LiDAR
  • Autonomous Vehicles: Navigation and obstacle detection
  • Topographic Mapping: Terrain and elevation surveys
  • Forestry: Tree height and canopy analysis
  • Archaeology: Discovering hidden structures under vegetation
  • Urban Planning: 3D city modeling
  • Flood Modeling: Terrain analysis for water flow
  • Mining: Volume calculations and surveying
  • Atmospheric Science: Measuring aerosols and clouds
Types of LiDAR
  • Airborne LiDAR: Mounted on aircraft/drones for large-area mapping
  • Terrestrial LiDAR: Ground-based scanning for buildings, infrastructure
  • Mobile LiDAR: Mounted on vehicles for road surveying
  • Bathymetric LiDAR: Uses green light to penetrate water for underwater mapping
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