Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and...

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Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier synthesis Spatial-light modulators Acousto-optic modulators Deformable mirrors Acousto-optic shaping Phase-only pulse shaping Genetic algorithms Simulated annealing Adaptive pulse-shaping grating grating out E in E Masks

Transcript of Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and...

Page 1: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Grating

SphericalMirror

Deformable mirror

14. Pulse Shaping

What do we mean by pulse shaping and why do we care about it?

Methods of pulse shapingFourier synthesis

Spatial-light modulatorsAcousto-optic modulators

Deformable mirrorsAcousto-optic shaping

Phase-only pulse shapingGenetic algorithmsSimulated annealing

Adaptive pulse-shaping

gratinggrating

outE inE Masks

Page 2: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Why pulse-shape?

To compress pulses with complex phase

To generate pulses that control chemical reactions or other phenomena

To generate trains of pulses for telecommunications

To precompensate for distortions that occur in dispersive media

gratinggrating

outE inE Masks

Page 3: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Pulse Shaping: A loose definition

Loosely defined: Pulse shaping includes anything that changes the pulse shape.

i tE t I t e iE S e

Altering any of pulse’s parameters changes the pulse.

Recall that a pulse is defined by its intensity and phase in either the time or frequency domain.

Page 4: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

What do we really mean by pulse shaping?

Tailoring a pulse shape in a specific controlled manner.

Pulse Shaper

Experiment

Pulse Results

1 45

2 37

3 12

4 80

By changing the pulse shape we can alter the results of an experiment.

Page 5: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

How do we modulate an ultrashort pulse?

We could try to modulate the pulse directly in time.

Unfortunately, modulators are too slow.

Alternatively, we can modulate the spectrum.

out inE H E

So all we have to do is to frequency-disperse the pulse in space and modulate the spectrum and spectral phase by creating a spatially varying transmission and phase delay.

out inE t h t E t

Page 6: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

An All-Optical Fourier Transform:The Zero-Dispersion Stretcher

How it works:The grating disperses the light, mapping color onto angle.

The first lens maps angle (hence wavelength) to position.

The second lens and grating undo the spatio-temporal distortions.

The trick is to place a mask in the Fourier transform plane.

( )xx

Fourier Transform

Plane

f

ff f

f

f

gratinggrating

John Heritage, UC DavisAndrew Weiner, Purdue

Page 7: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

The Fourier-Synthesis Pulse-shaper

We can control both the amplitude and phase of the pulse.

The two masks or “spatial light modulators” together can yield any desired pulse.

Amplitude maskTransmission = T(x) = T()

Phase maskPhase delay = (x) = ()

Fourier Transform Plane

( ) exp[ ( )]H T i

f

ff f

f

f

gratinggrating

outE inE

Page 8: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Some common spatial light modulators.

Early pulse shapers used masks created using lithographic techniques and that couldn’t be modified once created.

More recent shapers use “spatial light modulators,” which can be programmed on the fly.

Types of spatial light modulators

Liquid crystal arrays

Acousto-optic modulators

Deformable mirrors

Page 9: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Liquid-crystal spatial light modulators

Liquid crystals orient along a an applied dc E-field. They yield a phase delay (or birefringence) that depends on an applied voltage. They can yield both phase and amplitude masks.

Page 10: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Liquid crystal arrays

Front view

Liquid crystal modulators (LCMs) consist of two liquid crystal arrays at 90° to each other and at 45° to the incoming light.

The first array rotates the polarization of the light in one direction and the second in the opposite direction.

Rotating each the same amount (in opposite directions) yields a phase only modulation.

Rotating one more than the other yields an amplitude and phase modulation of the light.

PixelDead Space

The pixels in LCMs limit the resolution of the modulation. The finite width covers a range of wavelengths, reducing the fidelity of the shaping.The dead spaces (gaps between electrodes) also add artifacts to the pulse train (effectively an unshaped pulse).

Page 11: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

[1] A.M.Weiner et. al., IEEE J. Quantum Electron., 28 (1992) 908.[2] K. Takasago et. al., IEEE J. Select. Topics in Quantum Electron., 4 (1998) 346.

SLM: 128 pixels (pixel width: 97 m, pixel gap 3 m)Groove interval of the grating d-1=651 lines/mm,Input angle: 6.5 deg (100 nm bandwidth)Focal length of the achromatic lens f = 145 mm

Parameters

Spatial-light-modulator pulse shaper: details

grating

lens

grating

lens

f f f f

spatial light modulator

(SLM)input pulse shaped pulse

Takasumi Tanabe, Kimihisa Ohno,

Tatsuyoshi Okamoto, Fumihiko Kannari

Page 12: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Spatial Light Modulator Example

FROG trace

A sinusoidal spectral phase

Spectrum and spectral phase

Omonetto and coworkers, LANL

Pulse illumination of SLM

Page 13: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Acousto-optic spatial light modulators

Acousto-optic modulators (AOM) offer a method of modulating the light.

<100 fs laser pulse in

Shaped laser pulse out

Acousto-optic Modulator (TeO2, InP)

Amplitude/frequency modulated R.F. pulses (200

MHz carrier, 50MHz bandwidth, 1W peak)

10 µs (4 cm in crystal)

1o

Undiffracted beam

<100 fs laser pulse in

Shaped laser pulse out

Acousto-optic Modulator (TeO2, InP)

Amplitude/frequency modulated R.F. pulses (200

MHz carrier, 50MHz bandwidth, 1W peak)

10 µs (4 cm in crystal)

1o

Undiffracted beam

AOMs offer both phase and amplitude modulation.

The strength of the sound wave is directly related to the intensity of the diffracted light.

The phase of the sound wave is also written directly onto the diffracted light.

AOMs have a very high number of effective “pixels,” the number of sound waves that fit across the aperture of the crystal.

AOM efficiency is less than other methods since it relies on the diffracted light.

Warren Warren and coworkers, Princeton

Page 14: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Grating

SphericalMirror

Deformable mirror

Deformable-Mirror Pulse-Shaper

A. Efimov, and D. H. Reitze, Proc. SPIE 2701, 190 (1996)K. F. Wong, D. Yankelevich, K. C. Chu, J. P. Heritage, and A. Dienes, Opt. Lett. 18, 558 (1993)

2( ) 2 ( )x z x

x

z

This modulates the phase but not the amplitude.

Page 15: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Micro-Machined Deformable Mirror (MMDM)

• 600 nm Silicon Nitride Membrane

• Gold or Silver Coated• 1 ms Response Time• ~280 V Drive Voltage• Computer Controlled• 3x13 or 1x19 Actuator

Layout

G.V. Vdovin and P.M. Sarro, ``Flexible mirror micromachined in silicon'', Applied Optics 34, 2968-2972 (1995)

E. Zeek, et. Al., “Pulse compression using deformable mirrors”, Opt. Lett. 24, 493-495 (1999)

Page 16: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Advantages and disadvantages of the various types of spatial light modulators

Liquid-Crystal ArraysPhase and amplitude

modulation

Pixellated with dead spaces

EfficientAcousto-Optic Modulators

Phase and amplitude modulation

No dead spaces

Small pixels

Inefficient

Deformable MirrorsPhase-only modulation

No dead spaces

Large pixels

Efficient

All spatial-light-modulator pulse-shapers induce spatio-temporal distortions in the pulse, which are proportional to the magnitude of the shaping.

Page 17: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Acousto-Optic Pulse-Shaping

This method works without the zero dispersion stretcher and hence without spatio-temporal pulse distortions.

It launches an acoustic wave along the beam in a birefringent crystal.

The input polarization is diffracted to the other by the sound wave. The frequency that has its polarization rotated depends on the acoustic-wave frequency. Its relative delay at the crystal exit depends on the relative group velocities of the two polarizations.

different from the acousto-optic SLM!

Page 18: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Acousto-optic pulse shaping: theory

a b c

( )z

y

x

z

a b c

Input optical wave

Interaction length

Acoustic wave

(ordinary axis)

(extraordinary axis)

Diffracted optical wave

S(z)

E1(t)

E2(t)

( ( )[ ( )2

( ) { ) ]( }) eo nn z L z

The extra phase delay seen by each wavelength depends on how far into the crystal the acoustic wave takes on that wavelength and the ordinary and extraordinary refractive indices.

The strength of the acoustic

wave at each wavelength

determines the amplitude of

the output wave at that wavelength.

Page 19: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

[1] F. Verluise et. al., Opt. Lett. 8 (2000) 575.[2] K. Ohno et. al., J. Opt. Soc. Am. B, 19 (2002) in press

ParametersRF signal: center frequency:52.5 MHz, Bandwidth > 10 MHz dynamic range > 50 dBCrystal: TeO2 Crystal length: 25 mm (corresponds to 3 ps)Operation frequency: 1 kHzComplex programming (control data 4096×16 bits)

Acousto-Optic Pulse-Shaping: details

Takasumi Tanabe, Kimihisa Ohno,

Tatsuyoshi Okamoto, Fumihiko Kannari

Commercial device: the “Dazzler”

Acousto-optic pulse shaping yields intensity-and-phase shaping, it induces no spatio-temporal pulse distortions, and it is available commercially.

Page 20: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Results using the Dazzler

Compensating the phase of an ultrashort pulse

The resulting pulse length is reduced from 30 fs to 17 fs.

Page 21: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Phase-only pulse shaping is more efficient. But can it achieve the desired pulse shape?

Recall that the spectral phase is more important than the amplitude for determining E(t). So can we generate a given pulse with only a phase mask? Mostly. But calculating a phase-only mask is difficult.

Generally we’re given a target wave-form.Direct calculation of H() requires a phase and amplitude mask.

We must calculate the best possible phase-only mask.

out

in

EH

E

There now exist a whole class of optimization algorithms that specialize in such difficult (or impossible) problems.

The most common are Evolutionary (also called “Genetic”) Algorithms

Page 22: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Evolutionary Algorithms: What are they?

Evolutionary algorithms base their optimization on a simple axiom:

Survival of the fittest.Evolutionary algorithms perform a pseudo random search.

1. Start with a set of parents (initially random).

2. Make a set of children. Using crossover to combine parts of parents.

3. Add random mutations.

4. Evaluate the fitness of the individuals. If we keep the parents from the last generation, it’s called “elitism.”

5. Select the parents for the next generation.

Initial Parents

Mutate

Check Fitness

Select Parents

Make Childrenwith cross over Children

Elitism

Parents

MutatedChildren

Evolutionary algorithms provide a simple and robust optimization method.

Page 23: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Second GenerationFirst Generation

Evolutionary Algorithm Example

Parameter 1

Par

am

eter

2

1. The first generation evenly samples the parameter space. From this we select the parents for the next generation

2. The second generation is concentrated around the first set of parents, and from this we select the next set of parents.

Evolutionary algorithms are very reliable, but they are slow.

Page 24: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Okay, so we can pulse-shape. But what if we want to amplify, too?

Amplification will distort the pulse shape.

So amplify first and shape second.

But shaping is inefficient (remember the gratings…).

So shape first and amplify second.

Hmm… Worse, we may not actually know the input pulse shape.

The solution is Adaptive Pulse Shaping.

Page 25: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

450 mW @ 1 kHz0 = 800 nm, = 20 nm~40 fs pulse length

1.88 ps

Takasumi Tanabe, Kimihisa Ohno,

Tatsuyoshi Okamoto, Fumihiko Kannari

Adaptive pulse-shaping with amplification…

Pulse-shape, then amplify, then measure. Feed back on the FROG or SI (TADPOLE) trace.

Amplifier

Page 26: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Target

Shaped pulseInitial FROG traceOptimization

1 10-5

2 10-5

3 10-5

4 10-5

5 10-5

6 10-5

7 10-5

0

2 10-6

0 1000 2000 3000

Iteration #

Simulated Annealing

Calculate the difference(No waveform reconstruction in each loop)

Adaptive pulse shaping using the FROG trace

0

1

-5

0

5

10

15

-300 -150 0 150 300

Time [fs]

targetshaped

Iterate on the FROG trace.

Page 27: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

0

0.2

0.4

0.6

0.8

1

1.2

-4

-3

-2

-1

0

1

2

3

4

-300 -150 0 150 300

Time [fs]

Initial FROG trace

Calculate the difference(No waveform reconstruction in each loop)

Target FROG

Optimized FROG trace

0

0.2

0.4

0.6

0.8

1

1.2

-2

0

2

4

6

8

10

-300 -150 0 150 300

Time [fs]

Shaped pulse

Simulated Annealing

Wave-form reconstruction

Optimization

1 10-5

2 10-5

3 10-5

4 10-5

5 10-5

6 10-5

7 10-5

0

2 10-7

4 10-7

6 10-7

8 10-7

1 10-6

0 1000 2000 3000

Iteration #

-20

-15

-10

-5

0

5

10

0 20 40 60 80 100 120

Pixel #

Mast Function

Adaptive pulse shaping: a double pulse

Target pulse

Page 28: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Target FROG trace

ShapedFROG trace

Phase-only pulse-shaping cannot achieve a perfect square pulse.

Phase-only adaptive pulse shaping: a square pulse

Shaped in 3000 iterations

FROG error: 0.6% (128×128)

Target trace was obtained by adding only phase modulation.

Page 29: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Pulse shaping with TADPOLE feedback: 300 fs double pulse

Red: shaped pulseBlue: target pulse

Fast optimizationEqual peak intensityShaped phase mask agrees well with targetBut not quite as reliable as FROG

Temporal waveform Mask function

Conclusions

Page 30: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

Pulse-shaping for telecommunications

The goal is to create multiple pulses with variable separations.

Page 31: Grating Spherical Mirror Deformable mirror 14. Pulse Shaping What do we mean by pulse shaping and why do we care about it? Methods of pulse shaping Fourier.

A shaped pulse for telecommunications

Ones and zeros…

Andrew Weiner and coworkers