Fiber V-Number
Normalized frequency V = 2πa·NA/λ of a step-index fiber, NA from core and cladding indices, the single-mode check (V < 2.405) and the exact guided-mode count.
V-number
2.071
V < 2.405: single-mode (LP01 only)
Numerical aperture
0.1246
Acceptance half-angle 7.16° in air
LP11 cutoff wavelength
1335 nm
λc = 2πa·NA/2.405; single-mode above it
Guided modes
2
Exact count (V²/2 ≈ 2.1); 1 LP modes
Guided LP modes: LP01.
V = 2π a NA / λ, NA = √(n₁² − n₂²)
LP_lm is guided above its cutoff: the m-th zero of J_(l−1) (LP_0m: the (m−1)-th zero of J₁; LP01 has none). Each LP_0m carries 2 modes and each LP_lm (l ≥ 1) carries 4. For large V the count tends to V²/2 (Gloge 1971).
V-Number vs Wavelength
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
V = 2πa·NA/λ and the LP mode count from Bessel-function zeros (weak guidance; V²/2 estimate above V = 40). Step-index profile only.
- Gloge D. (1971). Weakly Guiding Fibers. Appl. Opt. 10, 2252. LP modes, eigenvalue equation and core power fraction. doi:10.1364/ao.10.002252
- NIST DLMF §10.21. Zeros of Bessel functions (LP mode cutoffs). dlmf.nist.gov