Gires-Tournois Interferometer
Dispersion control via a GTI — constant reflectivity with tunable group delay dispersion.
δ = 4πnL / λ (round-trip phase)
φ(δ) = 2 arctan[(1−√R)/(1+√R) · tan(δ/2)]
τ = dφ/dω = (2nL/c)·(1−R) / (1+R+2√R·cos δ)
GDD = dτ/dω = 8n²L²√R(1−R)·sin δ / [c²·(1+R+2√R·cos δ)²]
Key: a lossless GTI reflects all the power (|r|² = 1) at every δ; R₁ sets how sharply the phase varies
Model: lossless GTI with a front reflector of reflectance R₁ and a 100 % back mirror; the thickness is an effective optical thickness (a different mirror phase shifts the whole pattern).
Group Delay at Center λ
65.27 fs
Round-trip Phase δ₀
3.040 rad
GDD at Center λ
2403.6 fs²
Phase & GDD vs Wavelength
Group Delay
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
Lossless GTI: a layer of index n between a front reflector of reflectance R₁ and a 100 % back mirror, normal incidence, constant n and mirror phase. Real mirrors add loss, dispersion and a finite bandwidth.
- Gires F., Tournois P. (1964). C. R. Acad. Sci. Paris 258, 6112. The lossless GTI phase.
- Kuhl J., Heppner J. (1986). Compression of femtosecond optical pulses with dielectric multilayer interferometers. IEEE J. Quantum Electron. 22, 182–185. doi:10.1109/jqe.1986.1072855