OutlineOutline MotivationMotivation Experimental Set-UpExperimental Set-Up Theory behind the set-upTheory behind the set-up ResultsResults AcknowledgementsAcknowledgements

MotivationMotivation Attosecond pulses could be used to Attosecond pulses could be used to

study time-dependence of atomic study time-dependence of atomic dynamics. dynamics.

Greater control of pulse duration Greater control of pulse duration gives a better control of the power gives a better control of the power produced from each pulse as well.produced from each pulse as well.

The Set-UpThe Set-Up

Diffraction Grating Diffraction Grating

Con

cave

Mirr

or

Con

cave

Mirr

or

BBO CrystalSHG Prism

Direction of grating (235 grooves/mm)

Incoming Pulse

SLM

500 nm

1000 nm

SpectrometerConcave mirror

F=500mm

AlignmentAlignmentGrating

Green laser 532nm

first order diffraction(532nm)

second order diffraction(1064nm

)

64mm

Make 1 order and 2 order Make 1 order and 2 order spots overlap on the output spots overlap on the output

gratinggrating

Spots overlap

Use CCD cameras to detect the

overlap

Change the inclination of input grating to adjust vertical position of two spots on the output grating.

Adjust the location of this reflecting mirror to overlap spots horizontally.

Trials-green laser and Trials-green laser and spectrometerspectrometer

For SHG For SHG Two photons Two photons γγ enter the BBO. Each enter the BBO. Each γγ has a frequency has a frequency

ΔΔ. One photon leaves the BBO with frequency (2. One photon leaves the BBO with frequency (2ΔΔ). ). The contribution of each initial photon The contribution of each initial photon γγ1, 1, γγ2 2 is as is as

followsfollows ΔΔ11 = = ΔΔ + + ΩΩ ; ; ΔΔ22= = ΔΔ – – ΩΩ ; 2 ; 2ΔΔ= = ΔΔ11 + + ΔΔ22Where Where ΩΩ is just a way of expressing the energy is just a way of expressing the energy

difference between the contributions of each photondifference between the contributions of each photonThe spectrum of a beam is given byThe spectrum of a beam is given by

…… ……

2( ) { ( )}S E t F(Δ)(2)

2 3

2 3

2

( ) ( )

( )2 6

( )2 6

2 ( )

2(2)(2 ) ( ) ( ) exp{ [ ( ) ( )]}S E E i d

MIIPS (Multiphoton Intrapulse Interference Phase Scan) MIIPS (Multiphoton Intrapulse Interference Phase Scan)

Let frequency=Δ ; difference=Ω ; parameters=γ,α ; phase= φ ; phase correction = f

Take a Taylor approximation

And

You get

Let frequencyLet frequency==ΔΔ ; difference ; difference==ΩΩ ; parameters ; parameters==γγ,,αα ; phase ; phase== φφ ; ; phase correction phase correction = = ff

A maximum SHG signal corresponds to flat phase. If we can modulate some phase Δ make set α,γ, and scan δ

( ) cos( )f 2( ) cos( )f

( ) ( )f

0( ) 0

0( ) 0

( )

0f

Data obtained using the Data obtained using the 10% beam10% beam

Am

plitudeA

mplitude

Fourier TransformFourier Transform By performing an By performing an

inverse Fourier inverse Fourier transform we can transform we can change the change the information from a information from a graph showing graph showing frequency frequency ωω to a to a graph showing graph showing time t.time t.

1( ) ( ) exp( )2

f t F i t d

Inte

nsity

(cou

nts)

202

1( ) [ 2( ) ]

22ln(2)

1.177411.17741 32.2454537.9661 fs

x xf x

WW

FWHM WW

Original Phase

Flat Phase

Inte

nsity

(cou

nts)

The Full-The Full-Width-Half-Width-Half-MaximumMaximumFull-width-half-Full-width-half-maximummaximum is the distance is the distance between the half-between the half-maximum points.maximum points.

Also: we can define these widths in terms of f(t) or of its intensity, |f(t)|2.Define spectral widths () similarly in the frequency domain (t ).

t

tFWHM

1

0.5

With some small phase With some small phase correctionscorrections

The last week’s workThe last week’s work

Inte

nsity

(cou

nts)

MIIPS after 9 phase correction MIIPS after 9 phase correction attemptsattempts

ComparisonComparison

AcknowledgementsAcknowledgementsandand

CitationsCitations Professor Zenghu ChangProfessor Zenghu Chang He Wang, Yi WuHe Wang, Yi Wu Dr. Larry WeaverDr. Larry Weaver Dr. Kristan CorwinDr. Kristan Corwin Kansas State UniversityKansas State University Trebino, Rick. "FROG:Lecture Files." Trebino, Rick. "FROG:Lecture Files." Georgia Georgia

Institute of Technology School of PhysicsInstitute of Technology School of Physics. Georgia . Georgia Tech Phys Dept. 29 Jul 2007 Tech Phys Dept. 29 Jul 2007 <http://www.physics.gatech.edu/gcuo/lectures/>. <http://www.physics.gatech.edu/gcuo/lectures/>.

Lozovoy, Vadim. "Multiphoton Intrapulse Lozovoy, Vadim. "Multiphoton Intrapulse Interference." Interference." Optics LettersOptics Letters 29.7(2004): 775-777. 29.7(2004): 775-777.

SLM

Grating Grating

Concave Mirror

Concave Mirror

f=500mm

α

Supplementary and extended Supplementary and extended materialmaterial

45.492/)90(

/])/(sin[arctan169.9748.6421.3

842.6748.659.13

afx

D

64mmX5mm

X

β

γ

BBO (BBO (ββ- Barium Borate- Barium Borate) ) CrystalCrystal

Why is the BBO crystal used??Why is the BBO crystal used?? Used to separate the beam into it’s Used to separate the beam into it’s

fundamental and second harmonic fundamental and second harmonic frequenciesfrequencies

For SHG For SHG Two photons Two photons γγ enter the BBO. Each enter the BBO. Each γγ has a frequency has a frequency

ΔΔ. One photon leaves the BBO with frequency (2. One photon leaves the BBO with frequency (2ΔΔ). ). The contribution of each initial photon The contribution of each initial photon γγ1, 1, γγ2 2 is as is as

followsfollows ΔΔ11 = = ΔΔ + + ΩΩ ; ; ΔΔ22= = ΔΔ – – ΩΩ ; 2 ; 2ΔΔ= = ΔΔ11 + + ΔΔ22Where Where ΩΩ is just a way of expressing the difference is just a way of expressing the difference

between the contributions of each photonbetween the contributions of each photonThe spectrum of a beam is given byThe spectrum of a beam is given by

The spectrum of the beam is given by SThe spectrum of the beam is given by S22 of 2 of 2 ΔΔ is is2

(2)(2 ) ( ) ( ) exp{ [ ( ) ( )]}S E E i d

2( ) { ( )}S E t F(Δ)(2)

( ) cos( )f

Maximum SHG signal correspond to flat phase. If we can modulate some phase Δ make set α,γ, and scan δ

2( ) cos( )f

( ) ( )f

0( ) 0

0( ) 0

( )

0f

2 3

2 3

2

( ) ( )

( )2 6

( )2 6

2 ( )

2(2)(2 ) ( ) ( ) exp{ [ ( ) ( )]}S E E i d

We used MIIPS (Multiphoton Intrapulse Interference Phase Scan) to We used MIIPS (Multiphoton Intrapulse Interference Phase Scan) to get a picture of the phase of each wavelength contained in the pulseget a picture of the phase of each wavelength contained in the pulse

Let frequency=Δ difference=Ω parameters=γ,α phase= φ phase correction =f

Project GoalsProject GoalsDuring the summer of 2007, I spent approximately ten weeks studying and During the summer of 2007, I spent approximately ten weeks studying and

researching at Kansas State University Physics Department. My project researching at Kansas State University Physics Department. My project during this time was to work with two graduate students to shape laser during this time was to work with two graduate students to shape laser pulses. Specifically, we designed and set up a system that (hopefully) pulses. Specifically, we designed and set up a system that (hopefully)

allows us to adjust the phase of each separate frequency of a laser light allows us to adjust the phase of each separate frequency of a laser light pulse. Using a device called an SLM, Spatial Light Modifier, we were able to pulse. Using a device called an SLM, Spatial Light Modifier, we were able to apply different voltages to each pixel on a liquid crystal screen. Each pixel apply different voltages to each pixel on a liquid crystal screen. Each pixel corresponds to a different frequency of light. When we apply the different corresponds to a different frequency of light. When we apply the different voltages, we change the phase of each frequency, our goal is to make the voltages, we change the phase of each frequency, our goal is to make the phase of each frequency the same. Then applying a Fourier Transform we phase of each frequency the same. Then applying a Fourier Transform we were able to see how this phase shift changed the time-dependence of the were able to see how this phase shift changed the time-dependence of the pulse. Our goal is to be able to control the pulse as we choose, thus making pulse. Our goal is to be able to control the pulse as we choose, thus making

it possible to control the duration of each pulse. We are hoping to attain it possible to control the duration of each pulse. We are hoping to attain attosecond pulses through this method. attosecond pulses through this method.

As a part of this research, I was also given the opportunity to learn many As a part of this research, I was also given the opportunity to learn many different styles of programming, including, C, C++ ,and LabView. To many, different styles of programming, including, C, C++ ,and LabView. To many, these programs might seem basic, but I had not yet encountered them in these programs might seem basic, but I had not yet encountered them in my normal studies, so this presented a new and interesting challenge for my normal studies, so this presented a new and interesting challenge for me. LabView especially proved to be quite the ordeal and I spent a good me. LabView especially proved to be quite the ordeal and I spent a good

deal of time learning this program and attempting to write a program that deal of time learning this program and attempting to write a program that would be useful to our experiment with it.would be useful to our experiment with it.