Tutorial · 10 min read

Chirped Mirrors: A Beginner's Guide

A plain-English introduction to the most elegant tool in ultrafast optics. Learn how a stack of dielectric layers can compress a 1-picosecond pulse back to 25 femtoseconds — without lenses, prisms, or moving parts.

📖 Audience: students, new ultrafast users, sales engineers 🎯 Prereqs: high-school physics 🔗 See also: Double-Angle CM (advanced)
Section 1

What is a chirped mirror?

A chirped mirror is a flat dielectric mirror that does two jobs at once: it reflects light with very high efficiency (typically >99 %), and it gives a controlled, color-dependent time delay to the reflected pulse.

The trick lives inside the coating. A normal high-reflector is a stack of alternating high- and low-index layers, each one quarter-wavelength thick — a so-called Bragg stack. A chirped mirror uses the same idea, but the layer thicknesses vary smoothly with depth: thin layers near the surface, thicker layers deeper in. The depth at which a given color reflects becomes a function of wavelength, so different colors travel different optical path lengths and pick up different group delays.

Race-track analogy. Picture a marathon where the inside lane is short (red light, deeper layers, longer round-trip) and the outside lane is long (blue light, shallow layers, shorter round-trip). On a normal mirror everyone runs the same distance. A chirped mirror lets a slow runner (red) take a shortcut so it finishes alongside the fast runner (blue) — the pulse gets resynchronized.
Substrate (UVFS) Anti-reflection Pulse in blue (shallow) red (deep) — longer path → larger delay → catches up Compressed out
Fig. 1 — Layer thickness grows with depth. Long wavelengths (red) penetrate deeper before reflecting, picking up extra group delay. The result is negative GDD — a built-in pulse compressor.
Section 2

Why we need them — the pulse-broadening problem

Every transparent material in your lab is a low-pass filter for short pulses. The refractive index n(λ) depends on wavelength, so the colors that make up a femtosecond pulse don't travel at the same group velocity. The pulse stretches in time as it propagates. This is chromatic dispersion, and it is unavoidable for any pulse shorter than ~100 fs.

Δtout2 = Δtin2 + (4 ln 2 · GDD / Δtin)2 Output pulse duration after passing through medium with group-delay dispersion GDD (Gaussian envelope, transform-limited input).

A few real-world examples for a 25 fs pulse at 800 nm:

Optic in beam pathGDD addedPulse out
5 mm UVFS window+180 fs²~32 fs
1 mm BBO crystal+80 fs²~28 fs
10 mm sapphire (Ti:Sa rod)+580 fs²~70 fs
100 mm air at 1 atm+2 fs²25 fs (negligible)
20 m SMF-28 fiber+360 000 fs²~12 ps (!)
The fix. Add the same magnitude of GDD with the opposite sign somewhere else in the beam path. Chirped mirrors deliver negative GDD per bounce (typically −40 fs² to −1 000 fs²), so a few well-placed bounces cancel hundreds of fs² of accumulated material dispersion. No alignment-sensitive prism pair, no lossy grating compressor — just bounce and go.

Try it: the pulse-stretching simulator

Drag the slider to add material into your beam and watch a 25 fs pulse stretch. Then add chirped-mirror bounces to put it back together.

Live Demo

Pulse Stretching & Compression Simulator

Watch how a 25 fs pulse stretches when you push it through glass — and how a few chirped-mirror bounces put it back together. Every number is computed live from the Gaussian-pulse formula.

Beam path (schematic)
LASER 25 fs in UVFS 5.0 mm CM × 0 OUT 28 fs SOURCE MATERIAL (+GDD) CHIRPED MIRRORS (−GDD) DETECTOR
Pulse intensity vs. time
Material GDD +180 fs² CM GDD 0 fs² Net GDD +180 fs² Output Δt 28.0 fs Stretch factor 1.12×

For a precise calculation with arbitrary material, repetition rate, and pulse shape, use our full Pulse Stretching Calculator.

Section 3

How they work — the physics in three steps

Step 1 · Bragg reflection

A periodic stack of two materials (high-index H, low-index L) reflects light at a center wavelength λB = 2(nH dH + nL dL), where d is the physical layer thickness. With ~30 quarter-wave layer pairs you reach R > 99.5 %. So far, no dispersion control yet.

Step 2 · Vary the period with depth — "chirp"

Let the layer thickness change linearly with depth: thin near the surface (which reflects blue), thick deep in the stack (which reflects red). The local Bragg wavelength now varies through the coating. Each color has its own preferred reflection plane — its turning point.

Step 3 · The longer wavelengths take a longer round trip

Light entering the coating doesn't reflect from the front face; it propagates inward until it reaches its turning point, then comes back out. Since red light goes deeper, it accumulates more optical path and therefore more group delay. The frequency-dependent delay τ(ω) is the group delay, and its derivative is the group-delay dispersion (GDD):

GDD(ω) = dτ(ω)/dω  =  d²φ(ω)/dω² GDD is the second derivative of the spectral phase. Negative GDD ⇒ red is delayed ⇒ a positively chirped pulse gets compressed.
Catch. A simple chirp produces strong oscillations in the GDD vs. wavelength curve, caused by an impedance mismatch at the air–coating interface. Half the bounces "ring" instead of compressing. Real designs fix this with a matching section on top of the chirp, with one of three flavors:
  • Double-Chirped Mirror (DCM) — both layer thickness and refractive-index contrast are chirped.
  • Backside-Coated (BASIC) — coating on the rear face plus a matched front-AR.
  • Double-Angle (DACM) — pair two complementary designs, used at slightly different AOI; their oscillations cancel coherently. Read more →
Section 4

Key parameters — what to read on the datasheet

GDD per bounce (fs²)

Negative for compression. Typical: −40 fs² (low) to −1 000 fs² (high). Larger |GDD| ⇒ fewer bounces but narrower bandwidth.

Bandwidth (Δλ)

Wavelength range over which |R|>99 % and GDD stays within spec. Must fully cover your pulse spectrum, or the wings get clipped.

Angle of incidence (AOI)

Coatings are designed for one specific AOI (commonly 0°, 5°, 19°, or 45°). Off-design AOI shifts the spectrum and GDD curve.

Reflectance (R)

Usually >99 % across the bandwidth. Below 99 %, every bounce becomes a power tax — important when you cascade 8–20 mirrors.

Damage threshold (LIDT)

For fs lasers, >0.2 J/cm² @ 100 fs is industry standard. High-power amplifier output may need IBS-coated mirrors at >0.5 J/cm².

Polarization

Most CMs are designed for s- or p-polarization. Performance degrades quickly for the wrong state. Mark your beam orientation before installing.

Section 5

How to choose — the 4-step decision flow

Picking the right chirped mirror

1
Calculate the total GDD you need to compensate. Sum the GDD of every transmissive optic in the beam path (windows, lenses, crystals, AOMs). Use our Material Dispersion Calculator if datasheets only quote thickness.
2
Decide on bounce count vs. GDD per bounce. More bounces with low |GDD| (e.g., −40 fs² × 20 = −800 fs²) gives smoother compression but uses more table real estate. High |GDD| (e.g., −1 000 fs² × 1) is compact but bandwidth-limited.
3
Match the bandwidth to your laser spectrum. Octave-spanning Ti:Sapphire (600–1100 nm)? You need a UV-VIS-NIR design. Yb fiber at 1030 nm? A narrow 1015–1045 nm CM gives you 5–10× more |GDD|.
4
Verify AOI, polarization, and LIDT. Pick mounting that lets you set AOI within ±1° of design. If your peak fluence is >0.15 J/cm², request the IBS-coated variant. Use the LIDT Calculator to convert pulse energy + spot size to fluence.
WaveQuanta recommendation. If you don't know your total GDD yet, start with a −40 fs² UV-VIS-NIR pair (PC1332 family). 4–8 bounces handle most Ti:Sapphire setups, and the wide bandwidth tolerates spectrum drift while you learn your system.
Section 6

Featured WaveQuanta chirped mirrors

A starter shortlist by application. Every product page links the full reflectance + GDD curves and the original measurement data.

Section 7

Try it yourself — interactive calculators

Every formula in this guide has a click-and-drag implementation in our calculator suite. No registration, no login, runs entirely in your browser.

Pulse Stretching

How much does N mm of glass stretch your pulse?

Chirp ↔ GDD

Convert between linear chirp rate and GDD.

Chirped-Mirror Spacing

Plan a 4–20 bounce compressor on a 12″ × 24″ table.

Material Dispersion

GDD & TOD of UVFS, sapphire, BBO, BK7, ZnSe, and more.

Time–Bandwidth Product

How short can your pulse be, given its spectrum?

Fourier-Limited Pulse

Δλ → Δt for sech², Gaussian, square envelopes.

Grating Pair (Compare)

The CM alternative for very large GDD (> 10 000 fs²).

Prism Pair (Compare)

The classic tunable compressor — see why CMs replaced it.

LIDT / Damage Threshold

Convert pulse energy + spot size → fluence in J/cm².
Section 8

Further reading

  1. R. Szipöcs et al., "Chirped multilayer coatings for broadband dispersion control in femtosecond lasers," Opt. Lett. 19, 201 (1994). The original 1994 paper.
  2. F. X. Kärtner et al., "Design and fabrication of double-chirped mirrors," Opt. Lett. 22, 831 (1997). DCM concept.
  3. V. Pervak et al., "Dispersion control over the ultraviolet, visible, and near-infrared spectral range with HfO₂/SiO₂-chirped dielectric mirrors," Opt. Lett. 32, 2925 (2007). Modern UV-VIS-NIR DACM.
  4. RP Photonics Encyclopedia, "Chirped Mirrors" — encyclopedic overview.
  5. Wikipedia, "Dielectric mirror" — Bragg stack background.

Ready for the deep dive?

Once you've internalised the basics, jump to the technical follow-up — Double-Angle Chirped Mirrors: design, performance, and selection.

Read DACM Tutorial →