Mode Field Diameter
Mode-field diameter (Petermann II and Gaussian fit), effective area, V, b and core confinement of a step-index single-mode fiber, with its bend loss.
MFD (Petermann II)
9.89 µm
Exact LP01; ITU-T G.650.1 definition
MFD (Gaussian fit)
10.08 µm
Marcuse 1977: w/a = 0.65 + 1.619/V^1.5 + 2.879/V^6
Effective area
79.9 µm²
π w² of the Gaussian fit
V-number
2.071
LP11 cutoff λc = 1335 nm
Relative index Δ
0.370 %
n₂ = √(n₁² − NA²) = 1.4440
Normalized b
0.4386
n_eff = 1.44639
Power in core Γ
75.9 %
Mode Intensity Profile
MFD vs Wavelength
Bend Loss per Turn vs Radius (1550 nm)
Marcuse 1976 curvature loss of LP01, as on the macrobending-loss page. The elasto-optic correction R_eff = R/(1 − p_e) ≈ 1.26 R is on (Schermer & Cole 2007 fit 1.28 R to measured SMF-28). At 10 mm: 0.367 dB/turn.
Model
V = 2π a NA / λ, U J₁(U)/J₀(U) = W K₁(W)/K₀(W), U² + W² = V²
w_PII = √2 a K₁(W) / (U K₀(W)), MFD = 2w
Γ = (W²/V²)(1 + J₀²(U)/J₁²(U)), b = W²/V²
Weakly guiding step-index fibre (Gloge 1971). Petermann II is the far-field MFD that ITU-T G.650.1 specifies; for the step profile it follows in closed form from the exact LP01 field. Marcuse's fit is the best Gaussian to the near field, about 2 % larger near V = 2. Graded or trench profiles (real G.652 and G.657 fibres) need a numerical mode solver.
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
Exact LP01 of a weakly guiding step-index fibre: Petermann II MFD in closed form, Marcuse's Gaussian-fit MFD and πw² area, Marcuse bend loss with the elasto-optic R_eff ≈ 1.25R (on by default). Graded and trench profiles need a mode solver.
- Gloge D. (1971). Weakly Guiding Fibers. Appl. Opt. 10, 2252. LP modes, eigenvalue equation and core power fraction. doi:10.1364/ao.10.002252
- Petermann K. (1983). Constraints for fundamental-mode spot size for broadband dispersion-compensated single-mode fibres. Electron. Lett. 19, 712–714. Petermann II spot size. doi:10.1049/el:19830485
- Marcuse D. (1977). Loss Analysis of Single-Mode Fiber Splices. Bell Syst. Tech. J. 56, 703–718. Gaussian fit of the mode-field radius. doi:10.1002/j.1538-7305.1977.tb00534.x
- 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
- 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