Microscopic and macroscopic bending losses

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.

          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:

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.

   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