THEORY EXAMINATION (SEM–IV) 2016-17 LASER SYSTEMS AND APPLICATIONS

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.

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

Derivation: Expression for threshold pumping power using rate equations.

(d) Laser Classification by Medium

(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−8mL2h2​dx2d2ψ​=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: