Bend-Insensitive Fiber Design
Compare the macrobend loss of standard single-mode fibre with a reduced-MFD step-index design and check the design against the ITU-T G.657 limits.
Standard SMF at 7.5 mm
3.10 dB/turn
Meets the G.657.A1 macrobend limits
Design at 7.5 mm
0.0213 dB/turn
Meets the G.657.A2 macrobend limits, but its MFD is below 8.2 µm
Design MFD
7.39 µm at 1310 nm
8.37 µm at 1550 nm (SMF 10.08 µm); below the 8.2 µm that G.657 allows
Design LP11 cutoff
1332 nm
V = 2.067 at 1550 nm (SMF λc 1335 nm)
Bend Loss vs Radius (1550 nm)
Design vs ITU-T G.657 Macrobend Limits
| Category | Radius | Turns | Limit 1550 / 1625 nm | Design 1550 / 1625 nm | Meets |
|---|---|---|---|---|---|
| B3 | 10 mm | 1 | 0.03 / 0.1 dB | 4.66e-4 / 3.94e-3 dB | yes |
| B3 | 7.5 mm | 1 | 0.08 / 0.25 dB | 0.0213 / 0.102 dB | yes |
| B3 | 5 mm | 1 | 0.15 / 0.45 dB | 0.920 / 2.48 dB | no |
| A2 | 15 mm | 10 | 0.03 / 0.1 dB | 2.04e-6 / 5.41e-5 dB | yes |
| A2 | 10 mm | 1 | 0.1 / 0.2 dB | 4.66e-4 / 3.94e-3 dB | yes |
| A2 | 7.5 mm | 1 | 0.5 / 1 dB | 0.0213 / 0.102 dB | yes |
| A1 | 15 mm | 10 | 0.25 / 1 dB | 2.04e-6 / 5.41e-5 dB | yes |
| A1 | 10 mm | 1 | 0.75 / 1.5 dB | 4.66e-4 / 3.94e-3 dB | yes |
Macrobend limits only. G.657 also limits the cable cutoff (≤ 1260 nm) and the MFD at 1310 nm. Commercial A2 and B3 fibres keep an MFD of about 8.5–9 µm at 1310 nm, which a plain step profile cannot combine with B3 bend loss.
Model
α = √π κ² exp(−2γ³R / 3β²) / (2 γ^(3/2) V² √R K₁²(W)), loss/turn = 4.343 α · 2πR
Marcuse's curvature loss of the LP01 mode (J. Opt. Soc. Am. 66, 216, 1976) for two step-index fibres: an SMF-28-like G.652 equivalent (a = 4.1 µm, NA 0.1246) and your design. Raising NA and shrinking the core at the same cutoff confines the mode (smaller MFD), which is how G.657.A1 fibres cut bend loss. A2 and B3 fibres use a depressed trench around the core instead, which keeps the MFD near 9 µm; trench profiles need a numerical mode solver and are not modelled.
The elasto-optic correction (Nagano et al. 1978; Schermer & Cole 2007) is on by default: bending stretches the outer side, lowering its index, and compresses the inner side, partly undoing the bend's tilt of the index profile, so silica loses as if the radius were R/(1 − p_e), about 1.25× larger (the turn length stays 2πR). Untick it for the plain Marcuse formula. Coating reflections and transition loss are left out, so treat the category as indicative.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Marcuse curvature loss of LP01 for two step-index fibres, checked against the G.657 (08/2024) macrobend limits, with an optional elasto-optic correction R_eff = R/(1 − p_e) ≈ 1.25R. Not modelled: trench profiles, coating, transitions.
- Nagano K., Kawakami S., Nishida S. (1978). Change of the refractive index in an optical fiber due to external forces. Appl. Opt. 17, 2080. Elasto-optic equivalent bend radius. doi:10.1364/ao.17.002080
- Schermer R. T., Cole J. H. (2007). Improved bend loss formula verified for optical fiber by simulation and experiment. IEEE J. Quantum Electron. 43, 899. R_eff ≈ 1.28R for silica. doi:10.1109/jqe.2007.903364
- Marcuse D. (1976). Curvature loss formula for optical fibers. J. Opt. Soc. Am. 66, 216. Bend loss of LP01. doi:10.1364/josa.66.000216
- ITU-T G.657 (08/2024). Characteristics of a bending-loss insensitive single-mode optical fibre and cable. Tables 1 and 2: macrobend loss limits of A1, A2 and B3, MFD 8.6–9.2 µm ± 0.4 µm at 1310 nm. itu.int
- Gloge D. (1971). Weakly Guiding Fibers. Appl. Opt. 10, 2252. LP modes, eigenvalue equation and core power fraction. doi:10.1364/ao.10.002252