About this previous year paper
Course: B.Tech (All Branches – Elective)
Subject Code: EOE043
Subject Title: Laser Systems and Applications
Exam Type: Theory
Duration: 3 Hours
Maximum Marks: 100
SECTION – A (10 × 2 = 20 Marks)
Short theoretical questions focusing on laser physics and quantum concepts.
| No. | Question | Concept Summary |
|---|---|---|
| (a) | de Broglie Wavelength for an Electron | λ=h2meeV\lambda = \frac{h}{\sqrt{2m_e eV}}λ=2meeVh, shows wave–particle duality of electrons. |
| (b) | Objective of Davisson–Germer Experiment | Verified electron diffraction and confirmed the wave nature of matter. |
| (c) | Unmodified Radiation in Compton Scattering | The part of scattered radiation that retains its original wavelength (no energy loss). |
| (d) | Stimulated Emission | Emission of photons in phase and direction with an incident photon — fundamental to laser operation. |
| (e) | Role of Optical Cavity | Provides feedback by reflecting photons multiple times to amplify coherent light. |
| (f) | Two-Level Pumping Scheme Inefficiency | Population inversion impossible; equal absorption and emission rates. |
| (g) | Spiking in Ruby Laser | Temporary oscillations in laser output during initial population inversion. |
| (h) | Gain Medium in Excimer Laser | Excited dimers (e.g., ArF, KrF) that exist only in excited states and emit UV radiation. |
| (i) | Q-Switching | Technique for producing high-intensity, short-duration pulses by modulating cavity quality. |
| (j) | Characteristics of a Hologram | Contains full 3D information via interference and diffraction; can reconstruct phase and amplitude. |
SECTION – B (5 × 10 = 50 Marks)
Long-answer questions on quantum mechanics, laser theory, and systems.
(a) Heisenberg’s Uncertainty Principle
ΔxΔp≥h4π\Delta x \Delta p \geq \frac{h}{4\pi}ΔxΔp≥4πh.
Explains why microscopic particles (electrons) cannot have definite position and momentum simultaneously.
Used to approximate binding energy of an electron by equating kinetic and potential energies.
(b) Principle & Components of Laser
Components: Active medium, Optical resonator, Pumping source.
Principle: Stimulated emission and population inversion.
Coherence Length:
- Lc=cΔvL_c = \frac{c}{\Delta v}Lc=Δvc
For Δv=3000 Hz\Delta v = 3000 \text{ Hz}Δv=3000 Hz, Lc=1×105 mL_c = 1 \times 10^5 \, \text{m}Lc=1×105m.
(c) Three-Level vs Four-Level Lasers
| Type | Example | Advantage |
|---|---|---|
| Three-Level | Ruby laser | Requires high pumping power for inversion |
| Four-Level | Nd:YAG, He–Ne | Easier inversion, lower threshold power |
Derivation: Expression for threshold pumping power using rate equations.
(d) Laser Classification by Medium
| Type | Example | Feature |
|---|---|---|
| Solid-State | Ruby, Nd:YAG | High power, pulsed/continuous |
| Gas | He–Ne, CO₂ | High coherence, long lifetime |
| Liquid (Dye) | Rhodamine | Tunable wavelength |
| Semiconductor | GaAs | Compact, low cost |
(e) CO₂ Laser
Construction: Mixture of CO₂, N₂, and He gases; optical resonator with mirrors.
Working: Excitation by electrical discharge; energy transfer from N₂ to CO₂.
Photon Calculation Example:
Given power P=4 mW,λ=680 nmP = 4 \text{ mW}, \lambda = 680 \text{ nm}P=4 mW,λ=680 nm:
- N=Pλhc≈1.37×1016 photons/sN = \frac{P\lambda}{hc} \approx 1.37 \times 10^{16} \, \text{photons/s}N=hcPλ≈1.37×1016photons/s
(f) Mode Locking
Combines multiple longitudinal modes in phase → ultrashort (picosecond/femtosecond) pulses.
Methods: Active (using modulator) and Passive (using saturable absorber).
(g) Dye Lasers
Use organic dyes (e.g., Rhodamine 6G) dissolved in solvent.
Tunable over wide spectral range (500–800 nm).
Pumped by other lasers or flash lamps.
(h) Lasers in LIDAR
LIDAR Principle: Measures distance by timing laser pulse reflection.
Applications: Atmospheric monitoring, topographic mapping, autonomous navigation, speed detection.
SECTION – C (2 × 15 = 30 Marks)
Comprehensive, analytical problems and system explanations.
Q3. Schrödinger’s Equation – Particle in a Box
Wave equation:
- −h28mL2d2ψdx2=Eψ-\frac{h^2}{8mL^2}\frac{d^2\psi}{dx^2} = E\psi−8mL2h2dx2d2ψ=Eψ
Eigenvalues:
- En=n2h28mL2E_n = \frac{n^2h^2}{8mL^2}En=8mL2n2h2
Example: For electron confined in L=1 A˚L = 1 \, ÅL=1A˚:
- E1=37.6 eV,E2=150.4 eVE_1 = 37.6 \, eV, \quad E_2 = 150.4 \, eVE1=37.6eV,E2=150.4eV
(Discrete energy levels confirmed.)
Q4. Solid-State Lasers – Alexandrite Laser
Medium: Cr³⁺-doped chrysoberyl (BeAl₂O₄).
Wavelength Range: 700–820 nm (tunable).
Advantages: Tunability, high repetition rate, better beam quality than Nd:YAG.
Applications: Dermatology, surgery, spectroscopy.
Q5. Laser Applications
(i) Material Processing:
Drilling & Cutting: High energy density melts/vaporizes target.
Melting/Welding: Precise energy control enables localized heating.
(ii) Laser in Metrology:
Characteristics: High coherence, monochromaticity, stability.
Length Measurement:
Interference-based technique using Michelson Interferometer.
Distance d=Nλ2d = \frac{N\lambda}{2}d=2Nλ.
Summary
This Laser Systems and Applications (EOE043) paper comprehensively covers:
| Topic | Key Concepts |
|---|---|
| Quantum Foundations | de Broglie wavelength, Heisenberg principle, Schrödinger’s equation |
| Laser Theory | Stimulated emission, population inversion, pumping, optical cavity |
| Laser Types | Solid-state, gas, dye, semiconductor, excimer |
| Advanced Techniques | Mode locking, Q-switching, holography |
| Applications | LIDAR, medicine, industry, metrology |