Fiber Coupler Calculator
Power splitting, transfer curve and spectral response of a directional coupler of two identical single-mode cores, with the coupling coefficient computed from the core spacing and fibre parameters.
Coupling ratio
49.0 : 51.0
coupled : through, before excess loss
Coupling coefficient κ
0.554 mm⁻¹
V = 2.078; dκ/dλ ÷ κ = 0.186 % per nm
Length for 50:50
1.417 mm
full transfer at 2.835 mm
Port powers
-3.19 dBm
coupled; through -3.03 dBm
Model
P_coupled = P_in sin²(κL) 10^(−α/10), P_through = P_in cos²(κL) 10^(−α/10)
κ(λ) = (NA/(n₁a)) (U²/V³) K₀(WD/a) / K₁²(W), L₅₀:₅₀ = π/(4κ)
Two identical, parallel single-mode cores a distance D apart exchange power through their evanescent fields. κ is Snyder's coupled-mode coefficient, computed from the exact LP01 eigenvalues U and W at each wavelength. For well-separated cores a longer wavelength spreads the mode further into the cladding, so κ grows with λ and the coupler is wavelength-dependent; that is the wavelength dependence that WDM couplers exploit.
Not included: fused biconical taper couplers, where the light couples through cladding modes of the narrowed waist and κ follows a different law; dispersion of n₁ and NA; unequal cores (incomplete transfer); and polarization dependence.
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
Two identical parallel step-index cores: Snyder κ(λ) from the exact LP01 mode, transfer sin²(κL). Fused biconical tapers (cladding-mode coupling), unequal cores and dispersion are not modelled.
- Snyder A. W. (1972). Coupled-mode theory for optical fibers. J. Opt. Soc. Am. 62, 1267. Coupling coefficient of two identical step-index cores. doi:10.1364/josa.62.001267
- Snyder A. W., Love J. D. (1983). Optical Waveguide Theory. Chapman & Hall (Springer reprint 1984). Step-profile modes, perturbation theory and weakly coupled fibres. doi:10.1007/978-1-4613-2813-1