Chirped Mirror Group Delay Dispersion Calculator
Ultrafast Laser Optics: Calculate Group Delay ($GD$), negative Group Delay Dispersion ($GDD$), and temporal pulse compression for chirped dielectric mirrors.
Laser Pulse & Chirped Mirror Parameters
Dispersion Compensation & Compressed Pulse
Chirped Mirrors & Ultrafast Pulse Compression
Invented in 1994 by Robert Szipocs and Ferenc Krausz, chirped dielectric mirrors revolutionized femtosecond science and attosecond pulse generation.
1. Mathematical Formulations
GD(ω) = -dφ/dω [Group Delay in fs] GDD(ω) = d(GD)/dω = -d²φ/dω² [Group Delay Dispersion in fs²] TOD(ω) = d(GDD)/dω [Third-Order Dispersion in fs³] τ_out = τ_TL · √[ 1 + (4·ln 2 · GDD_net / τ_TL²)² ]
2. Key Advantages over Prism / Grating Compressors
- Zero Spatial Chirp: Unlike prism pairs, chirped mirrors do not introduce angular dispersion or spatial pulse distension.
- Compact Footprint: Compresses pulses inside laser cavities without requiring extended meter-long beam paths.
Frequently Asked Questions
What is a chirped dielectric mirror in ultrafast optics?
A chirped mirror is an optical dielectric mirror where the layer thicknesses vary continuously (are "chirped") from thin layers near the surface to thicker layers deeper inside the coating. Because longer wavelengths penetrate deeper before meeting the Bragg resonance condition, they travel further and accumulate group delay relative to shorter wavelengths, generating negative Group Delay Dispersion (GDD) to compress laser pulses.
Why are chirped mirrors essential for Ti:Sapphire and femtosecond lasers?
When an ultra-short pulse passes through laser gain media, lenses, or air, material dispersion (positive GVD) stretches the pulse in time (positive chirp, where red frequencies lead and blue frequencies lag). Chirped dielectric mirrors provide controlled negative dispersion (e.g. $-50\,\text{fs}^2$ per bounce) with high reflectivity ($> 99.8\%$) across broad octaves, compressing the pulses down to few-cycle durations ($< 10\,\text{fs}$).
What are GDD oscillations in chirped mirrors?
Spurious reflections between the front surface and the deeper Bragg turning points create internal Gires-Tournois etalon interference, which causes severe oscillations in the group delay dispersion curve. Double-chirped mirrors (DCMs) and matched Brewster-angle pairs are engineered with impedance-matching anti-reflection sections to smooth out these GDD ripples.