Module 5: Fibre Optics and Lasers
Module 5: Fibre Optics and Lasers
Complete Notes with All Important Formulas and Clear Explanation
Part A: Fibre Optics
1. Basic Structure and Principle
Optical fibre: Thin transparent fibre made of glass/plastic with core (refractive index n₁) surrounded by cladding (n₂ < n₁). Light travels by Total Internal Reflection (TIR).
2. Acceptance Angle and Numerical Aperture (NA)
Critical angle at core-cladding: θc = sin−1(n₂ / n₁)
Maximum acceptance angle in air (imax):
sin imax = n₁ sin(90° − θc) = √(n₁² − n₂²)
sin imax = n₁ sin(90° − θc) = √(n₁² − n₂²)
Numerical Aperture (NA):
NA = sin imax = √(n₁² − n₂²)
NA = sin imax = √(n₁² − n₂²)
NA measures light-gathering capacity. Typical value: 0.15 – 0.5
3. Normalized Frequency (V-Number)
V = 2π a⁄λ ⋅ NA (a = core radius, λ = wavelength in vacuum)
| V-value | Type of Fibre | Number of Modes |
|---|---|---|
| V < 2.405 | Single-mode fibre | Only 1 mode (HE₁₁ |
| V > 2.405 | Multi-mode fibre | Hundreds/thousands of modes |
4. Classification of Optical Fibres
| Type | Core size | Refractive index profile | Use |
|---|---|---|---|
| Single-mode step-index | 8–10 μm | Sharp step | Long-distance telecom |
| Multi-mode step-index | 50–200 μm | Sharp step | Short distance, high power |
| Graded-index multi-mode | 50–62.5 μm | Parabolic decrease | LANs, less modal dispersion |
5. Attenuation (Loss) in Fibre
α (dB/km) = 10 log10 (Pin/Pout)
Lowest attenuation windows: 1310 nm (≈0.35 dB/km) and 1550 nm (≈0.2 dB/km)
6. Dispersion (Pulse Broadening)
| Type | Cause | Effect |
|---|---|---|
| Modal dispersion | Different paths in multi-mode | Dominant in multi-mode fibres |
| Chromatic dispersion | Different λ travel at different speeds | Present in all fibres |
| Waveguide dispersion | Dependence on core size | Used to make zero-dispersion fibre |
Part B: Lasers
7. Interaction of Radiation with Matter
| Process | Description | Einstein Coefficient |
|---|---|---|
| Absorption | Atom in ground state absorbs photon → excited | B12 |
| Spontaneous emission | Excited atom emits photon randomly | A21 |
| Stimulated emission | Incident photon triggers identical photon | B21 |
Important relation: A21 / B21 = 8π h ν³ / c³
8. Population Inversion and Pumping
Population Inversion: More atoms in upper energy level than lower → essential for laser action.
Achieved by Optical pumping, Electrical discharge, Chemical reaction, etc.
9. Three-Level and Four-Level Laser Systems
- Three-level (e.g., Ruby): Pumping to level 3 → fast decay to metastable level 2 → lasing between 2→1
- Four-level (e.g., He-Ne, Nd:YAG): Lasing between 3→2, level 2 empties fast → easier inversion
10. Ruby Laser (First laser, 1960)
- Active medium: Ruby crystal (Al₂O₃ + 0.05% Cr³⁺)
- Three-level system
- λ = 694.3 nm (deep red)
- Pumping: Xenon flash lamp
- Output: Pulsed
11. Helium-Neon (He-Ne) Laser
- Active medium: Mixture of He and Ne gas
- Four-level system
- Common wavelengths: 632.8 nm (red), 1152 nm, 3390 nm
- Pumping: Electrical discharge
- Output: Continuous wave (CW), highly coherent
12. Characteristics and Applications of Lasers
- Highly monochromatic, coherent, directional, intense
- Applications: Communication, surgery, cutting/welding, holography, barcode reading, LIDAR, nuclear fusion, defence, scientific research
Summary of Most Important Formulas
| Quantity | Formula | Remarks |
|---|---|---|
| Numerical Aperture | NA = √(n₁² − n₂²) | Most important |
| Acceptance angle | sin imax = NA | |
| V-number | V = (2πa/λ) NA | Decides single/multi-mode |
| Attenuation | α (dB/km) = 10 log(Pin/Pout) | |
| Einstein relation | A21/B21 = 8π h ν³ / c³ |
Exam Tips: Remember NA = √(n₁² − n₂²) and V-number criterion for single-mode fibre.
Also know difference between three-level and four-level lasers and working of Ruby & He-Ne lasers.