9 Pulse Measurement

ETH Zurich Ultrafast Laser Physics

Ursula Keller / Lukas Gallmann

ETH Zurich, Physics Department, Switzerland www.ulp.ethz.ch

Chapter 9: Pulse measurement

Ultrafast Laser Physics

Ultrashort optical pulse

E(t ) = A(t)eiϕ ( t)e−iω 0t E(ω) = A(ω )eiϕ (ω )Time-domain! Frequency-domain!

Fourier transforms!

-1.0

-0.5

0.0

0.5

1.0

-30 -20 -10 0 10 20 30Time (fs)

1.0

0.8

0.6

0.4

0.2

0.0

-30 -20 -10 0 10 20 30Time (fs)

τp

I( t) = E(t)2 I(ω ) = E(ω )2

τ p ∝1Δω

Δω ∝ 1τ p

1.0

0.8

0.6

0.4

0.2

0.0

3.02.82.62.42.22.01.8Frequency (fs-1)

Δω

Cables and connectors

Connector type Frequency region Compatibility

BNC (Bayonet Navy Connector) DC – 2 GHz

SMC (Sub-Miniature C) DC – 7 GHz

APC-7 (Amphenol Precision Connector) DC – 18 GHz

Type N (Navy) 50 DC – 18 GHz

SMA (Sub-Miniature A) DC – 24 GHz 3.5 mm, 2.92 mm, Wiltron K

3.5 mm DC – 34 GHz SMA, 2.92 mm, Wiltron K

2.92 mm or Wiltron K DC – 40 GHz SMA, 3.5 mm

2.4 mm DC – 50 GHz 1.85 mm, Wiltron V

1.85 mm or Wiltron V DC – 65 GHz 2.4 mm

BNC

Type N

K connector trademarked by Wiltron Corporation (1983), now part of Anritsu Corporation

SMA connector

coaxial RF connector

SMA: DC to 18 GHz

When turning the nut, it is very important that the remainder of the connector does not rotate, otherwise premature wear of the connector will result.

The connector should be carefully inspected before each use, and any debris cleaned with compressed air.

3.5 mm or APC-3.5 (HP) - SMA compatible

SMA male on left, 3.5 mm male on right 3.5 mm female on left (air) 3.5 mm male on right (black dielectric)

2.4 mm connectors - not SMA compatible

Male and female 2.4 mm connectors

The 2.4 mm geometries designed to go beyond the SMA interface constraints are not SMA compatible

Developed by HP for 50 GHz bandwidth Inside of the outer conductor is 2.4 mm in diameter, and outside is 4.7 mm

Fast photodiode

Rs

J Cp

Equivalent circuit of an ideal photodiode: Ideal current source with a series resistor and a capacitor in parallel

Electrical current generated in photodiode

J =qηPopthν

Fast photodiode connected to microwave instrument

Kirchhoff’s law at a nodal point:

Jii∑ = 0

J RL

V

C J RJ C

J

JC = C dVdt

−J + C dVdt

+ VRL

= 0

dVdt

+ VRLC

= JC

dynamics of a first-order linear system

C = CL + Cp

Fast photodiode connected to microwave instrument

dVdt

+ VRLC

= JC

dynamics of a first-order linear system general form in the time domain frequency domain

with the transfer function of the linear system:

τ y + y = xy t( ) = V t( )x t( ) = RLJ t( )τ = RLC = const. τ iω y + y = x

h ω( ) = y

x= 11+ iωτ

C = CL + Cp

Impulse response of microwave test system

3dB bandwidth of measurement system: impulse response (Fourier transform of the transfer function):

h ω( ) = y

x= 11+ iωτ

H ω( ) = h ω( ) 2 = 11+ ωτ( )2

H ω 3dB( ) = 1

2Max H ω( ) ⇒ ω 3dB = 1

τ

h t( ) = 1τe− t /τ ∝ e− t /RLC τ = RLC , f3dB = ω 3dB

2π= 12πRLC

Impulse response of microwave test system

impulse response:

h t( ) = 1τe− t /τ ∝ e− t /RLC

Popt t( )

J t( ) = qηPopt t( )hν

V t( ) = h t( )∗ J t( ) = h t '( ) J t − t '( )∫ dt ' = 1Ce− t '/RLC J t − t '( )∫ dt '

τ = RLC , f3dB = ω 3dB

2π= 12πRLC

Step response of microwave test system

Step response Popt t( )



2π= 12πRLC

V t( ) ∝ 1− e−t τ⎡⎣ ⎤⎦

10% to 90% of the maximum value rise time:

Example: 60 GHz photo detector has a step response of 5.8 ps (i.e. 10%-90% rise time)

Δt ps[ ] = ln9 × τ ps[ ] = 2.2 × τ ps[ ] = 2.2 × 12π f3dB

ps[ ] ≈ 350 GHzf3dB[GHz]

ps[ ]

Gaussian impulse response approximation

impulse response Popt t( )



2π= 12πRLC

h t( ) = exp −t 2 τ 2( )

htot ω( ) = exp − ω2τ1

2

4⎛⎝⎜

⎞⎠⎟exp − ω

2τ 22

4⎛⎝⎜

⎞⎠⎟... = exp −

ω 2 τ12 + τ 2

2 + ...( )4

⎛

⎝⎜

⎞

⎠⎟ = exp − ω

2τ tot2

4⎛⎝⎜

⎞⎠⎟

τ tot = τ12 + τ 2

2 + τ 32 + ... τ FWHM f3dB = 2ln2

π= 0.312

τ FWHM ps[ ] ≈ 312 GHzf3dB[GHz]

ps[ ]p. 6-7, full derivation, example

ideal photodiode:


Example: GaAs

dielectric constant:

drift velocity:

transit time (should be short): 1 ps

thickness of insulating layer:

Fast photodiode

Rs

J Cp

J =qηPopthν

C = εε0A

d

RL = 50 Ω

ε = 13υs ≈ 10

7 cm / s

d = υsτ trans ≈ 1 µm

ideal photodiode:


Example: GaAs

dielectric constant:

drift velocity:

transit time (should be short): 1 ps

thickness of insulating layer:

Rs

J Cp

Why do fast photodiodes have a small active area?

C = εε0A

d

RL = 50 Ω

ε = 13υs ≈ 10

7 cm / s

d = υsτ trans ≈ 1 µm

Example: 60 GHz in 50 Ω


2π= 12πRLC

C ≈ 50 fF

⇒ A ≈ π 12 µm( )2 (r = 12 µm)

Sampling Oscilloscope

Δt

Trigger-Signal für N=1

Δt

N

V(t)

V(t)

Δt(N)1 2 ...

Sampling scope measurement

τtot = τ12+τ22+τ32+...

τFWHM ps⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥ ≈ 312 GHz

f3dB [GHz]

0.4ps⎛

⎝ ⎜

⎞

⎠ ⎟

2+ 7.8ps⎛

⎝ ⎜

⎞

⎠ ⎟

2+ 15.6ps⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2=17.5ps

45.645.545.445.345.245.145.0Sampling timeΔt, ns

laser pulse FWHM ≈ 400 fssampling head: 20 GHzdetector: 40 GHz

19 ps!

Time

Ultrafast Signal Waveform @ f

Sampling Pulses @ f+ Δf

Sampled Waveform @ Δf

Equivalent time sampling

Intensity autocorrelation

I2ω τ( ) ∝ E1 t( )E2 t − τ( ) 2 dt−∞

+∞

∫ E1=E2=E⎯ →⎯⎯⎯ ∝ E t( )E t − τ( ) 2 dt−∞

+∞

∫

I2ω τ( ) ∝ I t( ) I t − τ( )−∞

+∞

∫ dt

Autocorrelation

Nichtlinearer Kristall

λ

λλ/2

•  Frequency doubling: blue light intensity depends on the temporal overlap of the two short pulses (in red):

•  Delay of the two pulses due to time of flight in a mechanical delay line:

•  Signal:

16

0

-40 -20 0 20 40

Verzögerung (fs)

10

Sutter et al.: Spektrum der Wissenschaft,Dossier: Laser (1998)

I2ω Δt( ) = Iω t − Δ t

2( )Iω t + Δ t2( )

−∞

+∞

∫ dt

crystal

Nonlinear crystal

Focusing mirror

Beam splitter

Measure autocorrelation:

FWHM pulse duration of autocorrelation:

FWHM pulse duration of original pulse (transform limited):

Discussion p. 13

Intensity autocorrelation

I2ω τ( ) ∝ I t( ) I t − τ( )−∞

+∞

∫ dt

I t( ) x ≡ t T( )

τ p τ A τ p T

1. Rectangle

I t( ) = 1 , t ≤ T 20 , t > T 2

⎧⎨⎪

⎩⎪

1 1

2. Parabola

I t( ) = 1− x2 , t ≤ T 2

0 , t > T 2

⎧⎨⎪

⎩⎪

0.8716 2

3. Diffraction function

I t( ) = sin2xx2

0.7511 2.7811

4. Gaussian I t( ) = e− x2

0.7071 2 ln2

5. Triangle

I t( ) = 1− x , t ≤ T0, t > T

⎧⎨⎪

⎩⎪

0.6922 1

6. Hyperbolic sech I t( ) = sech2x

0.6482 1.7627

τ A

τ p

Translation stage:

True time shift of one of the pulse:

Measured time shift of autocorrelation signal on oscilloscope:

Time calibration:

Calibration of intensity autocorrelation

I2ω τ( ) ∝ I t( ) I t − τ( )−∞

+∞

∫ dt

Δz0

Δttrue =2Δz0c

Δz0

Δttrue ⇔ ΔτΔτ

Interferometric autocorrelation (IAC)

IInt = 2I + 2IcosΔφ , with Δφ = kΔz = ω0τ

I2ω τ( ) = E t( ) + E t − τ( ) 22dt∫

Appl. Phys. B 65, 175 (‘97)

Appl. Phys. B 65, 189 (‘97)

Appl. Phys. Lett. 74, 2268 (‘99)

Opt. Lett. 24, 631 (‘99)

8

6

4

2

0

IAC

(a.u

.)

-20 -10 0 10 20

Delay (fs)

8

6

4

2

0

-20 -10 0 10 20

A B

C D

OPA COMP.I

COMP.II LASER

Sources of two-cycle pulses (Science 286, 1507, 1999)

Nonlinear interaction is required for pulse measurement

Without nonlinear interaction we measure interferogram of fundamental pulse:

Fourier transform of this interferogram gives the optical intensity spectrum:

(Fourier spectrography)

I τ( ) =E t( ) + E t − τ( )∫

2dt

2 E t( ) 2 dt∫= 1+

E∗ t( )E t − τ( ) + E t( )E∗ t − τ( )⎡⎣ ⎤⎦∫ dt

2 E t( ) 2 dt∫

F I τ( ) = F 1 +E∗ −ω( ) E −ω( ) + E ω( ) E∗ ω( )

2 E t( ) 2 dt∫= F 1 + I −ω( ) + I ω( )

2 E t( ) 2 dt∫


I2ω τ( ) = E t( ) + E t − τ( ) 22dt∫

I0 ≡ A t( ) 4 dt∫I1 τ( ) ≡ A t( )A t − τ( ) 2 dt∫I2 τ( ) ≡ A t( ) 2 A t( )A∗ t − τ( )dt∫I3 τ( ) ≡ A2 t( )∫ A2 t − τ( )( )∗ dt

IIAC τ( ) = 1+ 1I1 0( ) 2I1 τ( ) + 2Re I2 τ( ) + I2∗ −τ( )( )eiω0τ + Re I3e

i2ω0τ A t( ) t→±∞⎯ →⎯⎯ 0

I0 : background part of radiation

I1 : normal intensity autocorrelation

I2 and I3: interference terms


8

6

4

2

0

-60 -40 -20 0 20 40 60Time [fs]

Calculation:

10 fs sech2-pulse

Measurement:

Modelocked Ti:sapphire laser

8

6

4

2

0

Inte

nsity

[a.u

.]

-40 -20 0 20 40Time delay o [fs]

ideal 10 fs sech2

experimental

Interferometric autocorrelation (IAC) 8

6

4

2

0

-60 -40 -20 0 20 40 60Time [fs]

IIAC τ( ) = IIAC −τ( )

IIAC τ → ±∞( ) = 1IIAC τ( )

max= IIAC 0( ) = 8

IIAC τ( )min

= 0

Non-background free intensity autocorrelation I2ωcollinear τ = 0( )

I2ωcollinear τ → ∞( ) =

31

IAC provides some information about chirped pulses 8

6

4

2

0

-80 -60 -40 -20 0 20 40 60 80Time [fs]

GDD = 50 fs2

8

6

4

2

0

-80 -60 -40 -20 0 20 40 60 80Time [fs]

GDD = 100 fs2

8

6

4

2

0

-80 -60 -40 -20 0 20 40 60 80Time [fs]

GDD = 200 fs2

Δν > ΔνTB

⇒ τ coh =1Δν

< 1ΔνTB

≈ τ p

⇒ τ coh <τ p

TB: time bandwidth limited

coh: coherence time

Different geometries for autocorrelations Noncollinear geometry •  standard autocorrelation

•  background free

•  limits resolution

Collinear geometry, type I •  interference of the pulse replicas

•  no geometrical limits in time resolution

•  interferometric autocorrelation (IAC)

Collinear geometry, type II •  GVM-effects: asymmetric autocorrelations

•  no interference

•  no geometrical limits in time resolution

Temporal resolution in noncollinear setups

θ

0−τ +τ

x

z

ωω

2ω

0

δt = θ0w0c

τm2 = τ p

2 +δt2

The classical (partial) solution

 Measure the pulse with itself: Autocorrelation

  In sub-10-fs regime: Interferometric autocorrelation

Iac(τ ) = I(t)I(t −τ )dt−∞

∞

∫ I( t) = E(t)2with!

Iiac(τ ) = E(t) + E(t − τ)( )22dt

−∞

∞

∫

8

6

4

2

0-30 -20 -10 0 10 20 30

Delay (fs)

interferometric intensity ac

Pulse characterization: phase information? Autocorrelation - noncollinear: no phase information - collinear: interferometric autocorrelation has very limited phase information FROG - Frequency-Resolved Optical Gating - Spectrally resolved autocorrelation gives amplitude & phase information - D. J. Kane, R. Trebino, IEEE J. Quantum Electron. 29, 571, 1993 SPIDER - Spectral Phase Interferometry for Direct Electric-Field Reconstruction - Spectral interferogram of two identical but spectrally shifted pulses gives phase information - combined with independently measured spectrum gives amplitude info - C. Iaconis, I. A. Walmsley, Opt. Lett. 23, 792 (1998)

Limitations of autocorrelation   Not very sensitive on pulse shape

  Contain very limited phase information  Becomes a problem with complex phase structures or pulse shapes

  Limited value with complex pulse shapes

8

6

4

2

0

-20 -10 0 10 20Delay (fs)

SPIDER8

6

4

2

0

-20 -10 0 10 20Delay (fs)

sech2-fit

1.0

0.8

0.6

0.4

0.2

0.0-100 -50 0 50 100

Time (fs)

sech2

FROG

1.0

0.8

0.6

0.4

0.2

0.0-100 -50 0 50 100

Delay (fs)

sech2-fit FROG

FROG

Here: Second-harmonic generation FROG Spectrally resolved intensity autocorrelation Iterative "fitting" procedure yields E-field of input pulse

(Frequency-resolved optical gating)!Kane et al.: IEEE J. Quantum Electron. 29, 571 (1993)"

⇔!

Knowledge ofsignal generation

process!

Measured data!

SFROGSHG (ω,τ ) = E(t)E(t −τ )

−∞

∞

∫ exp( iωt)dt2

EsigSHG(t, τ )

FROG

Here: Second-harmonic generation FROG Spectrally resolved intensity autocorrelation Iterative "fitting" procedure yields E-field of input pulse

(Frequency-resolved optical gating)!Kane et al.: IEEE J. Quantum Electron. 29, 571 (1993)"

⇔!

SFROGSHG (ω,τ ) = E(t)E(t −τ )

−∞

∞

∫ exp( iωt)dt2

EsigSHG(t, τ )

Esig t,τ( ) ∝

E t( )E t − τ( ) for SHG

E t( ) E t − τ( ) 2 for PG

E t( )2 E* t − τ( ) for SD

E t( )2 E t − τ( ) for THG

⎧

⎨

⎪⎪

⎩

⎪⎪

Many kinds of nonlinearity work:

PG-FROG

Polarization gating (PG): polarizers are oriented at 0° and 90° an intense 45°-polarized beam (at frequency w2) induces birefringence and therefore a polarization rotation of the 0°-polarized beam (at frequency w1), which can then leak through the second 90° polarizer. The pulse at the output indicates the signal pulse, again collinear with one of the input beams, but here with the orthogonal polarization.

R. Trebino, Kluwer Academic Publishers, Boston, 2002, ISBN 1-4020-7066-7

Esig t,τ( ) ∝E t( )E t − τ( ) for SHG

E t( ) E t − τ( ) 2 for PG

⎧⎨⎪

⎩⎪

SD-FROG

Self-diffraction: The two beams interfere and yield a sinusoidal intensity pattern, which induces a refractive index grating inside the medium.

Then each beam diffracts off the grating.

The pulses at the output indicate the signal pulses, here in the and directions.



E t( )2 E* t − τ( ) for SD

⎧⎨⎪

⎩⎪

2k1 − k2 2k2 − k1

THG-FROG

Third harmonic generation:

While each beam individually can produce third harmonic, it can also be produced by two factors of one field and one of the other.

These latter two cases are shown here.



E t( )2 E t − τ( ) for THG

⎧⎨⎪

⎩⎪

FROG


SHG-FROG-trace

FROG projections algorithm

E ω ,τ( ) = F Esig t,τ( ) = Esig t,τ( )∫ exp −iωt( )dt

IFROG ω ,τ( ) = Esig t,τ( )exp −iωt( )dt∫2

IFROG ω ,τ( )eiφ ω ,τ( ) = Esig t,τ( )exp −iωt( )dt∫

Measurement of pulses in the two-cycle regime

transform limit: 5.3 fs sech2-fit: 4.5 fs!!

8

6

4

2

0

Norm

alize

d IA

C

-60 -40 -20 0 20 40 60Delay (fs)

calculated measured

1.0

0.8

0.6

0.4

0.2

0.0

Norm

alize

d in

tens

ity

-60 -40 -20 0 20 40 60Time (fs)

-60 -40 -20 0 20 40 60Delay (fs)

5.5

5.0

4.5

4.0

Angu

lar f

requ

ency

(fs

-1)

Measured

-60 -40 -20 0 20 40 60Delay (fs)

5.5

5.0

4.5

4.0

Angu

lar f

requ

ency

(fs

-1)

Reconstructed

tFWHM = 6.6 fs

FROG vs SPIDER

SPIDER!

FROG!

SPIDER: Straightforward to extend to significantly shorter pulses !

FROG: One setup may cover a large range of pulse durations!

Interpretation of the spectral phase ϕ(ω)

ϕ (ω ) =ϕ0 +dϕdω ω0

ω − ω0( ) + 12d 2ϕdω 2

ω 0

(ω − ω0 )2 + 1

6d 3ϕdω 3

ω 0

(ω −ω 0 )3 + ...

3.0

2.8

2.6

2.42.2

2.0

1.8

-40 0 40Time (fs)

Transform limited3.0

2.8

2.6

2.4

2.2

2.0

1.8

-40 0 40Time (fs)

GDD = 50 fs23.0

2.8

2.6

2.42.2

2.0

1.8

-40 0 40Time (fs)

TOD = 500 fs3

The spectral phase rearranges the frequency components in the temporal domain!

Linear chirp! Nonlinear chirp!Transform limited(shortest possible pulse)!

Chirp!

SPIDER (Spectral phase interferometry for direct electric-field reconstruction)!

Iaconis et al.: Opt. Lett. 23, 792 (1998)" Gallmann et al.: Opt. Lett. 24, 1314 (1999)"

T >> τ >> τp(3 ps >> 300 fs >> 6 fs)!

SFG"

3.0

2.8

2.6

2.4

2.2

2.0

1.8

-1500 -1000 -500 0 500 1000 1500Time (fs)

τ

δω

1.0

0.8

0.6

0.4

0.2

0.0

5.25.04.84.64.44.2Frequency (fs-1)

δω

S(ω ) = E(ω )2 + E(ω +δω )2 + 2E(ω )E(ω + δω) cos ϕ(ω +δω ) −ϕ (ω ) +ωτ( )

OMA

GDD

Δt

PRBS

SPIDER

Slow variations in conversion efficiency over the pulse spectrum do not influence the reconstructed spectral phase!

τ

ω+δω" ω"

BBO-crystal!

Iaconis et al.: Opt. Lett. 23, 792 (1998)" Gallmann et al.: Opt. Lett. 24, 1314 (1999)"

1.0

0.5

0.0

Inte

rfer

ogra

m

460400340Wavelength (nm)

Only phase term - No amplitude information used!!!φ(ω) from SPIDER + independently measured pulse spectrum!+ Fourier transformation results in E(t) and P(t)!

Spectral Interferogram SFG: two spectrally shifted pulses with φ(ω+δω) and φ (ω) !Interference of these pulses: phase difference, then φ (ω) !Chirped pulses produce spectrally dependent fringe separations!

"

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

spe

ctru

m

800750700Frequency (THz)

ω!

t!

ω!

unchirped!

chirped!

t!

Phase extraction in SPIDER S ω( ) = E ω( ) 2 + E ω + δω( ) 2 + 2 E ω( )E ω + δω( ) cos ϕ ω + δω( ) −ϕ ω( ) +ωτ( )

1.0

0.8

0.6

0.4

0.2

0.0

5.25.04.84.64.44.2Frequency (fs-1)

δω

A

C* C

g ω( ) = a ω( ) + b ω( )cos φ ω( ) +ωτ( )

g ω( ) = a ω( ) + c ω( )eiωτ + c* ω( )e− iωτ ,

with c ω( ):= 12b ω( )eiφ ω( )

FFT ⇒ G t( ) = A t( ) + C t − τ( ) + C* t + τ( )

IFFT of C t − τ( ) ⇒ c ω( )eiωτ

Im log c ω( )eiωτ⎡⎣ ⎤⎦ = Im log 12 b ω( )⎡⎣ ⎤⎦ + i φ ω( ) +ωτ⎡⎣ ⎤⎦ = φ ω( ) +ωτ

S ω( ) = E ω( ) 2 + E ω + δω( ) 2 + 2 E ω( )E ω + δω( ) cos ϕ ω + δω( ) −ϕ ω( ) +ωτ( )Phase reconstruction from interferogram phase

known: relative phase between blue pulses

φ ωn( ) = ϕ ωn + δω( ) −ϕ ωn( ) measured at ω1,..,ωn with spacing Δω

Now we interpolate to spacing δω (>Δω ) : φ ωn( ) = ϕ ωn+1( ) −ϕ ωn( )

It follows: ϕ(ωn+1) = ϕ(ωn ) + φ(ωn ) = ϕ(ωn−1) + φ(ωn−1) + φ(ωn )

= ϕ(ω1):=0 + φ(ω1) +…+ φ(ωn ) = φ(ω i )

i=1

n

∑Reconstructed phase together with measured spectrum yields pulse:

E(t) = F−1 I(ω )eiϕ (ω )

From calibration with δω = 0

Measurement of pulses in the two-cycle regime

transform limit: 5.3 fs

1.0

0.8

0.6

0.4

0.2

0.0Norm

alize

d sp

ectru

m

440420400380360Wavelength (nm)

tFWHM = 5.9 fs

3.0

2.8

2.6

2.4

2.2

2.0

150100500-50-100Time (fs)

1.0

0.8

0.6

0.4

0.2

0.0

1000900800700600Wavelength (nm)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

1.0

0.8

0.6

0.4

0.2

0.0-60 -40 -20 0 20 40 60

Time (fs)

D. H. Sutter, et al., Opt. Lett. 24, 631, 1999 and Appl. Phys. B 70, S5, 2000

Accuracy of SPIDER measurements 8

6

4

2

0

Norm

alize

d IA

C

-40 -20 0 20 40Delay (fs)

calculated measured

1.0

0.8

0.6

0.4

0.2

0.03.02.82.62.42.22.0

Angular frequency (fs-1)

-1.0

0.0

1.0σwa = 0.017 rad 1.0

0.8

0.6

0.4

0.2

0.0-40 -20 0 20 40

Time (fs)

1.0

0.8

0.6

0.4

0.2

0.0

3.02.82.62.42.22.0Frequency (fs-1)

2.5

2.0

1.5

1.0

0.5

0.0

-0.5

calculated measured

Comparison with autocorrelation!

Statistical fluctuations! Statistical fluctuations!

Measurement of known phase!

(Propagation through 275 µm of fused silica)"

(Error in pulse duration < a few percent)"(SPIDER can resolve a few cm of air)"

Need amplitude & phase measurements

Sub-10-fs Ti:sapphire laser: Measured IAC (dotted line) Measured SPIDER - calculated IAC trace (solid line) very good agreement - SPIDER: 5.9 fs FWHM Ideal sech2-fit to IAC (solid line) - no good in the wings! - ideal sech2-fit: 4.5 fs FWHM Measured optical spectrum - transform-limit: 5.3 fs FWHM Other fits to IAC trace - generally underestimating FWHM

8

6

4

2

0-20 -10 0 10 20

Delay (fs)

sech2-fitτ = 4.5 fs

8

6

4

2

0

SPIDERτ = 5.9 fs

Appl. Phys. B 70, S67, 2000 L. Gallmann et al.Techniques for characterization of sub-10-fs pulses: a comparison"

BBO Conversion Efficiency

Noncollinear geometry has not been taken into account in the efficiency calculations

(due to the very small crossing angles) - Opt. Lett. 24, 1314 (1999)

Effic

ienc

y (a

rb.u

.)

1.61.41.21.00.80.60.4Input wavelength (µm)

θ = 41.5° θ = 44.5° θ = 47.5° θ = 50.5°

30µm type II BBO

30 µm BBO extraordinary axis (narrow-band) ordinary axis

θSFGnegligible: noncollinear beam-crossing angle 3-4°

“quasi-cw”

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9 Pulse Measurement

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