Bandwidth
650–1050 nm
Ultrafast Optics · Dispersion Control
Double-Angle Chirped
Mirrors
Sub-cycle pulse compression, without the ripple.
A single coating run. Two angles of incidence. π-phase complementary GDD oscillations that cancel where it matters — delivering ultra-broadband negative group-delay dispersion with residual ripple suppressed below ±5 fs² across the entire reflection band.
FIG. 01 Wavelength-resolved penetration depth
Longer wavelengths penetrate deeper into the chirped λ/4 stack, accumulating greater group delay — the geometric origin of negative GDD.
§ 01 The Physics
Why two angles?
A conventional chirped mirror generates negative dispersion by varying the Bragg layer thickness with depth. But the air–coating interface inevitably produces a partial Fresnel reflection, which interferes with the deep Bragg reflection in the manner of a Gires–Tournois etalon — superimposing parasitic oscillations of tens of fs² on the group-delay dispersion.
For sub-10 fs pulses, these oscillations are catastrophic. The double-angle approach exploits a simple fact: the GTI ripple phase shifts with the optical path length through the front section, which depends on incidence angle. Two carefully chosen angles produce two ripple patterns offset by exactly π radians. Used in alternation, they cancel — leaving the smooth, monotonic GDD profile the chirp was designed to produce.
A · Origin of the ripple
A weak Fresnel echo at the front interface interferes with the deep Bragg reflection.
The amplitude reflectivity r at the air–coating interface is small but nonzero. Combined with the strong reflection from the chirped Bragg section, this forms a low-finesse GTI cavity. The reflected group delay acquires a sinusoidal modulation:
τ_g(ω) = τ_chirp(ω) + 2r · sin(2ωL/c) · ∂φ/∂ω
Amplitude scales with r; period is set by the front-section optical thickness L.
B · The π-phase trick
Tilt the mirror; the optical path through the front section changes; the ripple shifts.
For an incidence angle θ, the projected path length becomes L·cos(θ′), where θ′ is the refracted angle inside the high-index layer. Choosing the second angle such that:
2ωL/c · [cos(θ₁′) − cos(θ₂′)] = π
produces a ripple precisely 180° out of phase with the first. Since both are inscribed on the same coating run, fabrication errors are correlated — the cancellation condition survives manufacturing variation. This is the engineering breakthrough of Pervak et al. (2009).
§ 02 Interactive
See the cancellation.
Adjust the two incidence angles below. The plot overlays the GDD spectrum of each individual reflection and their average — what your pulse actually accumulates after one bounce off each mirror. Watch the residual ripple collapse toward zero as the phase difference approaches π.
Switch the Mode toggle to compare a single-mirror configuration with the double-angle scheme, and observe how the time-domain pulse degrades when ripple is present.
Live GDD Compensation Simulator
WQ-LAB-01 / RT.SIM
Avg GDD
−120 fs²
Residual ripple
±6 fs²
Phase Δφ
π / 1.00
Pulse fidelity
98.4%
§ 03 Geometry
How the bounces actually fit on a table.
The math says you need 8–14 bounces. The table says you have ~30 cm. The trick — used in every commercial DACM compressor since Pervak's 2009 paper — is the multi-bounce zigzag: place the α-pair as two parallel mirrors a few centimeters apart, and let the pulse zigzag between them, picking up one bounce per crossing. Bounce count N ≈ L · cos(α) / sep · 2, set entirely by mirror length L and inter-mirror separation.
Drag the sliders below to see it. Reduce the α-pair separation and watch the bounce count automatically grow. The β-pair downstream does the same trick with its own angle — the ratio of α-bounces to β-bounces is what tunes the GDD-ripple cancellation to perfection.
FIG. Pervak-style multi-bounce zigzag · animated
Parameters
α (incidence)20°
β (incidence)5°
α-pair separation90 px
β-pair separation160 px
Mirror length280 px
Pulse speed1.0×
Presets
Animation
Reflection Stats
α-group bounces
8
β-group bounces
6
Total reflections
14
Reflection law
θ_in = θ_out ✓
Geometry rule
N ≈ L cos(α) / sep · 2
Pervak-style multi-bounce reflection geometry. The pulse enters from the lower edge of the α-pair, zigzags between the two parallel α-mirrors with strict θ_in = θ_out at every encounter (specular reflection only — no transmission), and exits at the upper edge to fly diagonally toward the β-pair, where the same process repeats. Tightening the α-pair separation automatically increases the bounce count, since N ≈ L cos(α) / sep × 2. The α/β bounce ratio is what makes Pervak's design work: pick separations such that the two groups' GDD-ripple oscillations land exactly π out of phase, and the residual modulation cancels. Try the Dense preset to see what a sub-10 fs Ti:Sapphire compressor actually looks like in steel.
§ 04 Where it goes
Three missions, one technology.
Every modern femtosecond architecture relies on GDD compensation somewhere in the chain. Below are the three deployments where double-angle chirped mirrors outperform every alternative — gratings, prisms, single-mirror compressors, and Gires–Tournois interferometers alike.
01 / 03
Few-cycle Ti:Sa oscillators
Sub-6 fs pulse generation requires intracavity dispersion control across more than an octave. Single-mirror designs introduce pre/post-pulse satellites that mode-locking cannot suppress. Double-angle pairs deliver the smoothness needed to reach the Fourier limit.
Pulse 3–8 fs
Bandwidth 600–1100 nm
Bounces / pass 4 to 12
Bandwidth 600–1100 nm
Bounces / pass 4 to 12
02 / 03
CPA compressor stages
Hybrid grating + chirped-mirror compressors clean residual third- and fourth-order phase from chirped-pulse-amplifier outputs. Yb-based industrial systems running at hundreds of watts benefit from the low absorption and high LIDT of dielectric multilayers.
Power handling > 200 W avg
LIDT > 0.3 J/cm² @ 100 fs
GDD per bounce −500 to −1000 fs²
LIDT > 0.3 J/cm² @ 100 fs
GDD per bounce −500 to −1000 fs²
03 / 03
Hollow-fiber post-compression
Spectral broadening in noble-gas-filled hollow-core fibers requires precise compensation of the broadened spectrum's quadratic and cubic phase. Octave-spanning DACM sets routinely reach 3 fs at 800 nm — the canonical route to attosecond pulse generation.
Output pulse < 4 fs
Spectral coverage > 1.5 octaves
Use case HHG / attosecond
Spectral coverage > 1.5 octaves
Use case HHG / attosecond
"Inherent fluctuations of the group-delay dispersion are suppressed by using the mirrors at two different angles of incidence... the resultant GDD is substantially free from spectral oscillations."
Pervak, Pronin, Razskazovskaya, Trubetskov, Naumov, Krausz, Apolonski · Optics Express · Vol. 17, p. 7943 · 2009
§ 05 Specifications
Featured DACM products.
Three representative double-angle chirped mirrors from our active catalog, covering Ti:Sapphire (800 nm), octave-spanning broadband, and Yb-band / SWIR operation. Each is supplied as a matched pair from a single deposition run, pre-aligned to its specified angle pair, with measured group-delay data on request.
| Parameter | PC70-25.4-6.35 | PC1332-25.4-6.35 | PC1816-25.4-6.35 |
|---|---|---|---|
| Wavelength range | 500 – 1050 nm | 450 – 1000 nm | 1000 – 1800 nm |
| Angle pair (single / double) | 5° / 19° | 5° / 19° | 5° / 19° |
| GDD per bounce | −40 fs² | −40 fs² | −70 fs² |
| Reflectivity (p-pol, avg) | > 99.0% | > 99.0% | > 99.2% |
| LIDT (fs pulses) | > 0.2 J/cm² | > 0.2 J/cm² | > 0.2 J/cm² |
| Substrate | UVFS, λ/10 @ 633 nm | UVFS, λ/10 @ 633 nm | UVFS, λ/10 @ 633 nm |
| Standard size | Ø 25.4 mm × 6.35 mm | Ø 25.4 mm × 6.35 mm | Ø 25.4 mm × 6.35 mm |
| Subtype | BBDM | BBDM (octave) | BBDM (NIR/SWIR) |
| Recommended platform | Ti:Sapphire oscillators & amplifiers (Mira, Tsunami, Legend) | Octave-spanning Ti:Sa & supercontinuum | Yb / Cr:Forsterite / OPA SWIR signal & idler |
Browse the full catalog of 126 chirped mirrors → All Chirped Mirrors · Request Custom Spec
References
- N. Matuschek, F. X. Kärtner, U. Keller, "Theory of double-chirped mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
- V. Pervak, I. Ahmad, S. A. Trushin, et al., "Double-angle multilayer mirrors with smooth dispersion characteristics," Opt. Express 17, 7943–7951 (2009).
- F. X. Kärtner et al., "Double-chirped mirror systems and methods," US Patent 6,590,925 B1 (2003).
- P. Baum, M. Breuer, E. Riedle, G. Steinmeyer, "Brewster-angled chirped mirrors for broadband pulse compression without dispersion oscillations," Opt. Lett. 31, 2220–2222 (2006).
- R. Paschotta, "Chirped Mirrors," RP Photonics Encyclopedia, rp-photonics.com.