Fiber Bragg Grating Calculator
Calculate the reflection spectrum, peak reflectance, FWHM and first-zero bandwidth of uniform, Gaussian-apodized and linearly chirped fiber Bragg gratings.
≈ 0.8 × the core index change for SMF
Results
Formulas (Erdogan 1997)
λ_B = 2·n_eff·Λ, κ = π·Δn/λ
σ̂ = 2π·n_eff·(1/λ − 1/λ_B), γ² = κ² − σ̂²
R = sinh²(γL) / (cosh²(γL) − σ̂²/κ²), R_max = tanh²(κL)
Δλ₀ = (λ·Δn/n_eff)·√(1 + (λ/(Δn·L))²)
Uniform: closed form. FWHM found numerically.
Reflection spectrum: peak 93.3 % at 1550 nm, FWHM 0.1499 nm.
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
Lossless coupled-mode theory, closed form for uniform gratings. Gaussian (FWHM L/2, ac only) and linear chirp (|chirp|·L ≤ 0.1λ_B) by transfer matrices. Phase n_eff for detuning and delay: no waveguide dispersion.
- Erdogan T. (1997). Fiber grating spectra. J. Lightwave Technol. 15, 1277. Coupled-mode reflectance (eq. 20), bandwidth, transfer matrices. doi:10.1109/50.618322
- Yamada M., Sakuda K. (1987). Analysis of almost-periodic distributed feedback slab waveguides via a fundamental matrix approach. Appl. Opt. 26, 3474. Transfer-matrix method. doi:10.1364/AO.26.003474
- Ouellette F. (1987). Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides. Opt. Lett. 12, 847. Chirped-grating dispersion. doi:10.1364/OL.12.000847