The internet, mobile backhaul, the national power-grid communication network and the submarine cables that connect Bangladesh to the world all run on optical fiber. Fiber fundamentals — numerical aperture, acceptance angle, single-mode vs multimode, attenuation windows and dispersion — are common in BCS (Telecom/EEE), BTCL, Teletalk, BTRC, PGCB (SCADA/telecom) and university exams. This post explains everything with an animation, worked numericals and MCQs.
- An optical fiber guides light by total internal reflection in a core (higher index n₁) surrounded by cladding (lower index n₂).
- Numerical aperture NA = √(n₁² − n₂²) = sin θa (in air); θa = acceptance angle.
- Single-mode fiber (core ≈ 8–10 µm) for long distance; multimode (core 50/62.5 µm) for short links; graded-index reduces modal dispersion.
- Low-loss windows: 850 nm, 1310 nm (zero dispersion in standard SMF), 1550 nm (lowest loss ≈ 0.2 dB/km).
- Single-mode condition: V-number V = (2πa/λ)·NA < 2.405.
1. Structure of an Optical Fiber
| Layer | Material / size | Function |
|---|---|---|
| Core | Doped silica glass; 8–10 µm (SMF), 50 or 62.5 µm (MMF); n₁ ≈ 1.46–1.48 | Carries the light |
| Cladding | Pure silica; 125 µm outer diameter; n₂ slightly less than n₁ | Confines light in the core by total internal reflection |
| Coating / buffer | Acrylate polymer; 250 µm (or 900 µm tight buffer) | Protects against moisture, micro-bending and abrasion |
| Strength member & jacket | Aramid yarn, PVC/PE sheath | Mechanical strength and environmental protection |
2. Principle: Total Internal Reflection
When light travels from a denser medium (n₁) to a rarer one (n₂ < n₁) and hits the boundary at an angle greater than the critical angle θc = sin⁻¹(n₂/n₁), it is totally reflected back with practically no loss. Rays entering the fiber within the acceptance cone keep reflecting along the core. A detailed visual explanation is in How Light Travels Through Fiber Optic Cables.
3. Numerical Aperture and Acceptance Angle
NA = n₀ sin θa = √(n₁² − n₂²) ≈ n₁√(2Δ), Δ = (n₁ − n₂)/n₁- Acceptance angle θa — maximum angle to the fiber axis at which light can enter and still be guided. Rays inside this cone (acceptance cone) propagate; others leak into the cladding.
- Larger NA → easier to couple light (LEDs), but more modes and more modal dispersion.
- Typical NA: SMF ≈ 0.12–0.14; MMF ≈ 0.2–0.3.
4. Types of Fibers (Animation)
| Feature | Step-index multimode | Graded-index multimode | Single-mode (SMF) |
|---|---|---|---|
| Core diameter | 50–200 µm (and larger) | 50 / 62.5 µm | 8–10 µm |
| Index profile | Uniform core, abrupt step | Parabolic: highest at centre | Step (small core) |
| Modes | Many | Many | One |
| Modal dispersion | High | Low | None |
| Bandwidth × distance | Lowest | Medium | Highest |
| Source | LED | LED / VCSEL | Laser diode |
| Typical use | Short links, sensors | LANs, data centres (up to a few hundred metres at 10 Gb/s) | Long-haul, metro, FTTH, submarine cables |
5. V-Number and Modes
V = (2π a / λ) · NA (a = core radius)- If V < 2.405, only the fundamental mode propagates → single-mode operation. The wavelength at which V = 2.405 is the cut-off wavelength.
- Approximate number of modes: step-index M ≈ V²/2; graded-index (parabolic) M ≈ V²/4.
6. Attenuation (Losses)
Attenuation α (dB/km) = (10/L) log10(Pin/Pout). Causes:
- Absorption — intrinsic (UV and IR absorption of silica) and extrinsic (impurities, especially OH⁻ water peak near 1383 nm; low-water-peak fibers remove it).
- Rayleigh scattering — from microscopic density fluctuations; proportional to 1/λ⁴, so it dominates at short wavelengths.
- Bending losses — macro-bends (tight curves) and micro-bends (tiny deformations from poor cabling).
- Splice and connector losses — typically 0.05–0.1 dB per fusion splice and 0.3–0.5 dB per connector.
| Window | Wavelength | Typical loss | Notes |
|---|---|---|---|
| 1st | 850 nm | ≈ 2–3 dB/km | Multimode, cheap sources |
| 2nd (O-band) | 1310 nm | ≈ 0.33–0.35 dB/km | Zero chromatic dispersion in standard SMF (G.652) |
| 3rd (C-band) | 1550 nm | ≈ 0.2 dB/km | Lowest loss; EDFA optical amplifiers and DWDM |
7. Dispersion
Dispersion spreads light pulses in time, so neighbouring bits overlap (inter-symbol interference), limiting bit rate × distance.
- Modal (intermodal) dispersion — different modes travel different path lengths (multimode only; reduced by graded-index).
- Chromatic (intramodal) dispersion = material dispersion (refractive index varies with λ) + waveguide dispersion. Measured in ps/(nm·km); ≈ 17 ps/(nm·km) at 1550 nm for standard SMF. Dispersion-shifted fiber (G.653) moves zero dispersion to 1550 nm.
- Polarisation-mode dispersion (PMD) — two polarisations travel at slightly different speeds; important above 10 Gb/s.
8. A Fiber-Optic Link
Transmitter (LED or laser diode, modulated by data) → connectors/splices → fiber → (optical amplifiers/repeaters for long distances) → receiver (PIN or APD photodiode) → electrical signal. Bangladesh connects to the global internet through submarine fiber systems such as SEA-ME-WE 4 (landing at Cox’s Bazar) and SEA-ME-WE 5 (landing at Kuakata), operated by BSCCL, plus terrestrial cross-border links. Advantages and limitations are discussed in Advantages of Optical Fiber Communication.
9. Solved Problems
Problem 1. A fiber has n₁ = 1.48 and n₂ = 1.46. Find NA, acceptance angle and critical angle.
- NA = √(1.48² − 1.46²) = √(2.1904 − 2.1316) = √0.0588 ≈ 0.242
- θa = sin⁻¹(0.242) ≈ 14.0° (full acceptance cone ≈ 28°)
- θc = sin⁻¹(1.46/1.48) = sin⁻¹(0.9865) ≈ 80.6°
Problem 2. A fiber has core radius 4.1 µm and NA 0.12. Is it single-mode at 1310 nm?
V = (2π × 4.1/1.31) × 0.12 ≈ 19.67 × 0.12 ≈ 2.36 < 2.405 ⇒ single-mode ✔
Problem 3 (power budget). A 60 km link at 1550 nm uses fiber with 0.25 dB/km, 12 splices (0.1 dB each) and 2 connectors (0.5 dB each). Transmitter power is 0 dBm and receiver sensitivity −28 dBm. Is the link feasible?
- Fiber loss = 60 × 0.25 = 15 dB; splices = 1.2 dB; connectors = 1.0 dB ⇒ total = 17.2 dB
- Received power = 0 − 17.2 = −17.2 dBm ⇒ margin = −17.2 − (−28) = 10.8 dB ✔ (well above the usual 3–6 dB safety margin)
10. Practice MCQs (click to see answer)
1. Light is guided in an optical fiber by: (a) Refraction (b) Total internal reflection (c) Diffraction (d) Scattering
2. For guiding to occur, the refractive index of the core must be: (a) Less than cladding (b) Equal to cladding (c) Greater than cladding (d) Zero
3. Numerical aperture is given by: (a) n₁ − n₂ (b) √(n₁² − n₂²) (c) n₂/n₁ (d) √(n₁ + n₂)
4. Lowest attenuation in silica fiber occurs at about: (a) 850 nm (b) 1310 nm (c) 1550 nm (d) 650 nm
5. Core diameter of single-mode fiber is about: (a) 8–10 µm (b) 50 µm (c) 62.5 µm (d) 125 µm
6. Modal dispersion is absent in: (a) Step-index multimode (b) Graded-index multimode (c) Single-mode fiber (d) Plastic fiber
7. Rayleigh scattering loss varies as: (a) λ (b) λ² (c) 1/λ⁴ (d) 1/λ
8. A fiber is single-mode when V-number is less than: (a) 1 (b) 2.405 (c) 3.14 (d) 10
9. Zero chromatic dispersion of standard single-mode fiber is near: (a) 850 nm (b) 1310 nm (c) 1550 nm (d) 1625 nm
10. The photodetector with internal gain is: (a) PIN photodiode (b) Avalanche photodiode (APD) (c) LED (d) Laser
11. Graded-index fiber reduces modal dispersion because: (a) Its core is smaller (b) Rays travelling longer paths move faster in lower-index regions (c) It uses a laser (d) It has no cladding
11. বাংলায় দ্রুত রিভিশন
- অপটিক্যাল ফাইবার পূর্ণ অভ্যন্তরীণ প্রতিফলন নীতিতে আলো বহন করে; কোরের প্রতিসরাঙ্ক (n₁) ক্ল্যাডিং (n₂)-এর চেয়ে বেশি।
- নিউমেরিক্যাল অ্যাপারচার NA = √(n₁² − n₂²) = sin θa; ক্রিটিক্যাল কোণ θc = sin⁻¹(n₂/n₁)।
- প্রকার: স্টেপ-ইনডেক্স মাল্টিমোড, গ্রেডেড-ইনডেক্স মাল্টিমোড (কম ডিসপারশন), সিঙ্গেল-মোড (কোর ৮–১০ µm, দূরপাল্লা)। V < 2.405 হলে সিঙ্গেল-মোড।
- লস উইন্ডো: ৮৫০ nm, ১৩১০ nm (শূন্য ডিসপারশন), ১৫৫০ nm (সর্বনিম্ন লস ≈ ০.২ dB/km)।
- ক্ষতির কারণ: শোষণ, রেলে বিক্ষেপণ (∝ 1/λ⁴), বাঁকানো, স্প্লাইস ও কানেক্টর। ডিসপারশন: মোডাল, ক্রোমাটিক, PMD।
- বাংলাদেশ সাবমেরিন ক্যাবল SEA-ME-WE 4 (কক্সবাজার) ও SEA-ME-WE 5 (কুয়াকাটা)-এর মাধ্যমে আন্তর্জাতিক ইন্টারনেটে যুক্ত।
Related Posts
- How Light Travels Through Fiber Optic Cables
- Advantages of Optical Fiber Communication
- Can Satellite Communication Be Hacked?
- Most Asked Communication Systems MCQs
References: Gerd Keiser, Optical Fiber Communications; John M. Senior, Optical Fiber Communications; ITU-T G.652/G.653. Images and animations: original work by Totalecer.
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