---
title: "Microscopic and macroscopic bending losses"
subject: "Propagation and Antenna"
chapter: 6
key: "semester_6/propagation_and_antenna:microbend-macrobend-losses"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/microbend-macrobend-losses
site: BCT Engineering
---

# Microscopic and macroscopic bending losses

Propagation and Antenna · Chapter 6: Optical Fibres

- Asked in: 2077 Chaitra, 7 marks
- Video: [Bending Losses in Optical Fiber - Macrobending Loss - Microbending Losses](https://www.youtube.com/watch?v=g1EOLhvxvPw) — Padmasri Naban
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/microbend-macrobend-losses
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-6

## Question

Explain the contribution of microscopic and macroscopic fiber bends towards the bending losses in optical fiber.

## Short answer

Macrobends (large-radius curves) cause radiation loss when outer modal fields cannot satisfy total internal reflection; loss rises exponentially with decreasing radius. Microbends are micron-scale random axis deviations from coating/thermal stress, coupling guided modes to radiation modes. Control: observe minimum bend radius and use proper cable design.

## Answer

**Bending loss** (radiation loss) occurs when a fibre is bent, so some light no longer meets the condition for total internal reflection and leaks out into the cladding and jacket. It has two contributions: **macroscopic bends** and **microscopic bends**.

#### Macroscopic bending (macrobending)

Macrobends are bends whose radius is large compared with the fibre diameter, e.g. when a cable goes round a corner or is coiled in a tray.

```text
          outer side: wave must travel faster
            ____________
          /  ___________ \   <- light radiates out
         /  /           \ \
   =====/  /             \ \=====
   =======/   bend R      \======
```

- In a bend, the part of the modal field on the outer side would have to travel faster than light in the cladding to keep up with the wavefront. It cannot, so this energy **radiates away**.
- In ray terms, the angle of incidence at the outer boundary drops below the critical angle, so rays refract out.
- The loss is small for large radius but rises **exponentially** as the radius falls below a critical radius. For multimode fibre:

```text
Rc ≈ 3·n1²·λ / ( 4π·(n1² − n2²)^(3/2) )
```

- Higher-order modes (near cut-off) are lost first. Loss is larger at longer wavelengths and for small Δ or small NA. Single-mode fibre at 1550 nm is especially sensitive.
- **Control:** respect the minimum bend radius (typically 10–20 times the cable diameter), use bend-insensitive fibre (ITU-T G.657) in FTTH.

#### Microscopic bending (microbending)

Microbends are small, repetitive, random bends of the fibre axis with amplitudes of a few µm and periods of about a millimetre.

```text
   core axis:  ~^~v~^~~v~^~v~~^~   (exaggerated)
```

- Causes: uneven pressure from the cable jacket or a rough surface, cabling and winding stress, and differential thermal contraction of the coating and glass at low temperature.
- Each microbend couples power from guided modes into higher-order and radiating (cladding) modes, which are then lost. The loss is spread along the whole length.
- Microbending loss is greater for fibres with small NA and for multimode fibres with many near cut-off modes.
- **Control:** a soft primary coating and a harder secondary coating (dual coating), loose-tube cable design so the fibre is not stressed, and fibres with higher Δ.

#### Comparison

| Feature | Macrobend | Microbend |
|---|---|---|
| Radius / size | mm to cm curvature | µm-scale axis deviations |
| Cause | Cable routing, coiling | Jacket pressure, thermal stress |
| Location | At the bend | Distributed along the fibre |
| Remedy | Keep R above minimum | Good coating and cable design |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why does light leak out at a macroscopic bend?
   A. The core index rises at the bend
   B. The cladding absorbs light at the bend
   C. The glass melts under bending
   D. The angle of incidence at the outer boundary falls below the critical angle
   Answer: D. At a sharp bend the ray strikes the outer wall below phi_c, so it refracts out instead of being totally reflected. (Key point: Macrobend cause)

2. How does macrobending loss vary with bend radius?
   A. It is small for large radius but rises exponentially below a critical radius
   B. It rises linearly as radius increases
   C. It is constant at all radii
   D. It is zero below the critical radius
   Answer: A. Loss is negligible for gentle bends but increases exponentially once the radius falls below Rc. (Key point: Macrobend radius dependence)

3. What are microbends?
   A. Large curves when a cable goes round a corner
   B. Small, random, repetitive deviations of the fibre axis of a few micrometres amplitude
   C. Cracks in the cladding
   D. Changes in core diameter
   Answer: B. Microbends are tiny axis bends caused by uneven pressure or thermal stress; they couple guided modes to radiating modes. (Key point: Microbend definition)

4. Which measure reduces microbending loss?
   A. Keeping the cable above its minimum bend radius
   B. Using a smaller NA
   C. Soft primary plus harder secondary coating and loose-tube cable design
   D. Using a longer wavelength
   Answer: C. Dual coating and loose-tube design isolate the fibre from stress; keeping minimum radius is the remedy for macrobends. (Key point: Microbend remedy)

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