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  • Measuring Ultrashort Laser Pulses

    Rick Trebino

    School of Physics

    Georgia Institute of Technology

    Atlanta, GA 30332 USA

    1. Background, Phase Retrieval, and Autocorrelation

    2. Frequency-Resolved Optical Gating

    3. Interferometric Methods

    These slides are available at http://public.me.com/ricktrebino.

  • The vast majority of humankinds greatest

    discoveries have resulted directly from

    improved techniques for measuring light.

    Spectrometers led to quantum mechanics.

    Interferometry led to relativity.

    Microscopes led to biology.

    Telescopes led

    to astronomy.

    X-ray crystallography

    solved DNA.

    And technologies, from medical imaging to

    GPS, result from light measurement!

  • Most light is broadband, and hence

    ultrafast, and also highly complex.

    Ultrabroadband supercontinuum

    Arbitrary waveforms

    Ultrafast and complex in time

    " in time and space

    Nearly every pulse near a focus

    Pulses emerging from almost any medium

    Well learn much by measuring such light pulses.

    Focusing pulse seen

    from the side

    Complex pulse

    Time

    I

    n

    t

    e

    n

    s

    i

    t

    y

    P

    h

    a

    s

    e

  • To determine the temporal resolution of an experiment using it.

    To determine whether a pulse can be

    made even shorter.

    To better understand the lasers that

    emit them and to verify models

    of ultrashort pulse generation.

    To better study media: the better

    we know the light in and light

    out, the better we know the

    medium we study with them.

    To use shaped pulses to control

    chemical reactions: Coherent control.

    Because its there.

    Why measure light with ultrafast variations?

    As a molecule dissociates,

    its emission changes color

    (i.e., the phase changes),

    revealing much about the

    molecular dynamics, not avail-

    able from the mere spectrum,

    or even the intensity vs. time.

    Excitation to excited state

    Emission

    Ground state

    Excited

    state

  • In order to measure

    an event in time,

    you need a shorter one.

    To study this event, you need a

    strobe light pulse thats shorter.

    But then, to measure the strobe light pulse,

    you need a detector whose response time is even shorter.

    And so on9

    So, now, how do you measure the shortest event?

    Photograph taken by Harold Edgerton, MIT

    The Dilemma

  • The shortest events ever created are

    ultrashort laser pulses.

    So how do you measure the pulse itself?

    You must use the pulse to measure itself.

    But that isnt good enough. Its only as short as the pulse. Its not shorter.

    1 minute

    10 fs light

    pulse Age of universe

    Time (seconds)

    Computer

    clock cycle

    Camera

    flash

    Age of

    pyramids

    One

    monthHuman existence

    10-15 10-12 10-9 10-6 10-3 100 103 106 109 1012 1015 1018

    1 femtosecond 1 picosecond

  • Intensity Autocorrelation1D Phase Retrieval

    Single-shot autocorrelation

    The Autocorrelation and SpectrumAmbiguities

    Third-order Autocorrelation

    Interferometric Autocorrelation

    Measuring Ultrashort Laser Pulses I:

    Background, Phase Retrieval, and

    AutocorrelationThe dilemma

    The goal: measuring the intensity and phase vs. time (or frequency)

    Why?

    The Spectrometer and Michelson Interferometer1D Phase Retrieval

  • Its electric field can be written:

    Intensity Phase

    [ ]{ }0Re exp ( (( ))( )) iE It tt t =

    Alternatively, in the frequency domain:

    Spectral

    PhaseSpectrum

    [ ]( ) exp ))( (SE i = %

    We need to measure both the temporal (or spectral) intensity and

    phase.

    A laser pulse has an intensity and phase

    vs. time or frequency.

    S

    p

    e

    c

    t

    r

    a

    l

    p

    h

    a

    s

    e

    ,

    (

    )

    FrequencySp

    e

    c

    t

    r

    u

    m

    ,

    S

    (

    )

    P

    h

    a

    s

    e

    ,

    (t

    )

    Time

    I

    n

    t

    e

    n

    s

    i

    t

    y

    ,

    I

    (

    t

    )

  • The instantaneous frequency:Example: Linear chirp P

    h

    a

    s

    e

    ,

    (t

    )

    time

    time

    F

    r

    e

    q

    u

    e

    n

    c

    y

    ,

    (

    t

    )

    time

    The phase determines the pulses

    frequency (i.e., color) vs. time.

    0( ) /t d dt =

    Time

    L

    i

    g

    h

    t

    e

    l

    e

    c

    t

    r

    i

    c

    f

    i

    e

    l

    d

  • The group delay:Example: Linear chirp S

    p

    e

    c

    t

    r

    a

    l

    p

    h

    a

    s

    e

    ,

    (

    )

    frequency

    frequency

    G

    r

    o

    u

    p

    d

    e

    l

    a

    y

    ,

    g(

    )

    time

    The group delay vs. frequency is

    approximately the inverse of the

    instantaneous frequency vs. time.

    The spectral phase also yields a pulses

    color evolution: the group delay vs. .

    ( ) /g d d =

    Wed like to be able to measure,

    not only linearly chirped pulses,

    but also pulses with arbitrarily complex

    phases and frequencies vs. time.

  • The spectrometer measures the spectrum, of course. Wavelength varies

    across the camera, and the spectrum can be measured for a single pulse.

    Pulse Measurement in the Frequency Domain:

    The Spectrometer

    Collimating

    Mirror

    Czerny-Turner

    arrangement

    Entrance

    Slit

    Camera or

    Linear Detector Array

    Focusing

    Mirror

    Grating

    Broad-

    band

    pulse

  • One-dimensional phase retrieval

    E.J. Akutowicz, Trans. Am. Math. Soc. 83, 179 (1956)

    E.J. Akutowicz, Trans. Am. Math. Soc. 84, 234 (1957)

    Retrieving it is called the 1D phase retrieval problem.

    Its more interesting than it appears

    to ask what we lack when we know

    only the pulse spectrum S().

    Obviously, what we lack is the spectral phase ().

    Even with extra information,

    its impossible.

    Recall:

    time

    S

    p

    e

    c

    t

    r

    a

    l

    p

    h

    a

    s

    e

    ,

    (

    )

    FrequencySp

    e

    c

    t

    r

    u

    m

    ,

    S

    (

    )

    [ ]( ) exp ))( (SE i = %

  • Pulse Measurement in the Time Domain: Detectors

    Examples: Photo-diodes, Photo-multipliers

    Detectors are devices that emit electrons in response to photons.

    Detectors have very slow rise and fall times: ~ 1 nanosecond.

    As far as were concerned, detectors have infinitely slow responses.

    They measure the time integral of the pulse intensity from to +:

    The detector output voltage is proportional to the pulse energy (or fluence).

    By themselves, detectors tell us little about a pulse.

    2( )detectorV E t dt

    Another symbol

    for a detector:

    Detector

    Detector

  • Translation stage

    Pulse Measurement in the Time Domain:

    Varying the pulse delay

    Since detectors are essentially infinitely slow, how do we make time-

    domain measurements on or using ultrashort laser pulses?

    Well delay a pulse in time.

    And how will we do that?

    By simply moving a mirror!

    Since light travels 300 m per ps, 300 m of mirror displacement

    yields a delay of 2 ps. This is very convenient.

    Moving a mirror backward by a distance L yields a delay of:

    = 2 L /cDo not forget the factor of 2!

    Light must travel the extra distance

    to the mirrorand back!

    Input

    pulse E(t)

    E(t)

    Mirror

    Output

    pulse

  • We can also vary the delay using

    a mirror pair or corner cube.

    Mirror pairs involve two

    reflections and displace

    the return beam in space:

    But out-of-plane tilt yields

    a nonparallel return beam.

    Corner cubes involve three reflections and also displace the return

    beam in space. Even better, they always yield a parallel return beam:

    Hollow corner cubes avoid propagation through glass.

    Translation stage

    Input

    pulse

    E(t)

    E(t)

    MirrorsOutput

    pulse

    Apollo 11

  • Measuring the interferogram is equivalent to measuring the spectrum.

    Pulse Measurement in the Time Domain:

    The Michelson Interferometer

    2 2 *( ) ( ) 2Re[ ( ) ( )]E t E t E t E t dt

    = +

    2( ) ( ) ( )MIV E t E t dt

    2

    *

    ( ) 2 ( )

    2Re ( ) ( )

    MIV E t dt

    E t E t dt

    Pulse energy

    Field autocorrelation: (2)(). Looks interesting, but the Fourier transform of

    (2)() is just the spectrum!

    Beam-splitter

    Input

    pulse

    Delay

    Slow

    detector

    Mirror

    Mirror

    E(t)

    E(t)

    VMI( )

    Interfer-

    ogram

    VM

    I

    (

    )

    0 Delay

    The detected voltage will be:

  • Can we use these methods to measure a pulse?

    V. Wong & I. A. Walmsley, Opt. Lett. 19, 287-289 (1994)

    I. A. Walmsley & V. Wong, J. Opt. Soc. Am B, 13, 2453-2463 (1996)

    Result: Using only time-independent, linear components, complete

    characterization of a

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