Outline Motivation Experimental Set-Up Theory behind the set-up - - PowerPoint PPT Presentation

Outline

• Motivation
• Experimental Set-Up
• Theory behind the set-up
• Results
• Acknowledgements

Motivation

• Attosecond pulses could be used to study

time-dependence of atomic dynamics.

• Greater control of pulse duration gives a

better control of the power produced from each pulse as well.

The Set-Up

Diffraction Grating Diffraction Grating

Direction of grating (235 grooves/mm)

1000 nm Concave Mirror Concave Mirror BBO Crystal SHG Prism SLM Incoming Pulse

Spectrometer

500 nm

Concave mirror F=500mm

What it really looks like

Getting Ready

More set up

Alignment

Grating

first order diffraction(532nm) second order diffraction(1064nm) 64mm Green laser 532nm

Make 1 order and 2 order spots

• verlap on the output grating

Adjust the location of this reflecting mirror to

• verlap spots

horizontally. Change the inclination

• f input grating to

adjust vertical position

• f two spots on the
• utput grating.

Spots overlap Use CCD cameras to detect the

• verlap

Trials-green laser and spectrometer

For SHG

• Two photons γ enter the BBO. Each γ has a frequency

∆. One photon leaves the BBO with frequency (2∆).

• The contribution of each initial photon γ1, γ2 is as follows

∆1 = ∆ + Ω ; ∆2= ∆ – Ω ; 2∆= ∆1 + ∆2 Where Ω is just a way of expressing the energy difference between the contributions of each photon The spectrum of a beam is given by ……

2

( ) { ( )} S E t ω ≡ F

(∆)

(2)

MIIPS (Multiphoton Intrapulse Interference Phase Scan) Let frequency= ∆ ; difference= Ω ; parameters= γ,α ; phase= φ ; phase correction = f

2 3 2 3 2

( ) ( ) ( ) 2 6 ( ) 2 6 2 ( ) ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ∆ + Ω + ∆ − Ω ′′ ′′′ ′ = ∆ + Ω + Ω + Ω ′′ ′′′ ′ + ∆ − Ω + Ω − Ω ′′ = ∆ + Ω

2 (2)(2 )

( ) ( ) exp{ [ ( ) ( )]} S E E i d ϕ ϕ ∆ ∝= ∆ + Ω ∆ − Ω × ∆ + Ω + ∆ − Ω Ω

∫

Take a Taylor approximation And You get

Let frequency=∆ ; difference=Ω ; parameters=γ,α ; phase= φ ; phase correction = f A maximum SHG signal corresponds to flat phase. If we can modulate some phase Δ make set α,γ, and scan δ

( ) cos( ) f α γ δ ∆ = ∆ −

2

( ) cos( ) f αγ γ δ ′′ ∆ = − ∆ −

( ) ( ) f ϕ′′ ′′ ∆ = − ∆

( ) ϕ′ ∆ =

( ) ϕ ∆ =

( ) ϕ ∆

f ϕ ′′ ′′ + =

Data obtained using the 10% beam

Amplitude Amplitude

Fourier Transform

• By performing an

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

1 ( ) ( )exp( ) 2 f t F i t d ω ω ω π

∞ −∞

=

∫

Intensity (counts)

2 2

1 ( ) [ 2( ) ] 2 2ln(2) 1.17741 1.17741 32.24545 37.9661 fs x x f x W W FWHM W W π − = − = ≈ = × =

Original Phase Flat Phase

t ∆tFWHM

1 0.5

The Full-Width- Half-Maximum

Full-width-half-maximum is the distance between the half-maximum points.

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

With some small phase corrections The last week’s work

MIIPS after 9 phase correction attempts

Comparison

Acknowledgements and Citations

• Professor Zenghu Chang
• He Wang, Yi Wu
• Dr. Larry Weaver
• Dr. Kristan Corwin
• Kansas State University
• Trebino, Rick. "FROG:Lecture Files." Georgia Institute of

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

• Lozovoy, Vadim. "Multiphoton Intrapulse Interference."

Optics Letters 29.7(2004): 775-777.

Grating Grating

64mmX5mm

SLM Concave Mirror Concave Mirror f=500mm

α

ο ο ο ο ο ο ο ο

45 . 49 2 / ) 90 ( / ] ) / ( sin[arctan 169 . 9 748 . 6 421 . 3 842 . 6 748 . 6 59 . 13 ≈ + = = + = + = = − = β γ λ β β α a f x

β γ

X

D

BBO (β- Barium Borate) Crystal

Why is the BBO crystal used??

– Used to separate the beam into it’s fundamental and second harmonic frequencies

For SHG

• Two photons γ enter the BBO. Each γ has a frequency

∆. One photon leaves the BBO with frequency (2∆).

• The contribution of each initial photon γ1, γ2 is as follows

∆1 = ∆ + Ω ; ∆2= ∆ – Ω ; 2∆= ∆1 + ∆2 Where Ω is just a way of expressing the difference between the contributions of each photon The spectrum of a beam is given by The spectrum of the beam is given by S2 of 2 ∆ is

2 (2)(2 )

( ) ( ) exp{ [ ( ) ( )]} S E E i d ϕ ϕ ∆ ∝= ∆ +Ω ∆ −Ω × ∆ +Ω + ∆ −Ω Ω

∫

2

( ) { ( )} S E t ω ≡ F

(∆)

(2)

We used MIIPS (Multiphoton Intrapulse Interference Phase Scan) to get a picture of the phase of each wavelength contained in the pulse Let frequency=∆ difference=Ω parameters=γ,α phase= φ phase correction =f

( ) cos( ) f α γ δ ∆ = ∆ −

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

2

( ) cos( ) f αγ γ δ ′′ ∆ = − ∆ −

( ) ( ) f ϕ′′ ′′ ∆ = − ∆

( ) ϕ′ ∆ =

( ) ϕ ∆ =

( ) ϕ ∆

f ϕ ′′ ′′ + =

2 3 2 3 2

( ) ( ) ( ) 2 6 ( ) 2 6 2 ( ) ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ∆ + Ω + ∆ − Ω ′′ ′′′ ′ = ∆ + Ω + Ω + Ω ′′ ′′′ ′ + ∆ − Ω + Ω − Ω ′′ = ∆ + Ω

2 (2)(2 )

( ) ( ) exp{ [ ( ) ( )]} S E E i d ϕ ϕ ∆ ∝= ∆ + Ω ∆ − Ω × ∆ + Ω + ∆ − Ω Ω

∫

Project Goals

During the summer of 2007, I spent approximately ten weeks studying and researching at Kansas State University Physics Department. My project during this time was to work with two graduate students to shape laser

• 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

• 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 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 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

• 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 attosecond pulses through this method. 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, 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

• 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 would be useful to our experiment with it.