Techniques for Characterizing Radially Polarized ......Techniques for Characterizing Radially Polarized Femtosecond Pulses for Direct Laser Electron Acceleration Abdurahim Rakhman

Outline Radially Polarized Pulses Pulse Characterization Measurement of Radially Polarized Pulse

Techniques for Characterizing Radially Polarized Femtosecond Pulses forDirect Laser Electron Acceleration

Abdurahim Rakhman

Department of Mechanical & Nuclear EngineeringPenn State University

September 21, 2012

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Techniques for Characterizing Radially Polarized Femtosecond Pulses for Direct Laser Electron Acceleration


Outline

1 Radially Polarized PulsesWhat is a radially polarized beam?How we create radially polarized laser pulse?Radially polarized field & Direct laser accelerationImportance of characterizing radially polarized pulses

2 Pulse CharacterizationWhat is pulse characterization?Pulse characterization techniquesTechniques for polarization shaped pulses

3 Measurement of Radially Polarized Pulse

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Outline




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Outline




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Outline




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What is a radially polarized beam?

Cylindrical vector-beam solution of Maxwell’s equation

Obey axial symmetry in both amplitude & phase

Superposition of orthogonally polarized HG01 & HG10 modes

~Er = HG10~ex + HG01~ey

Q. Zhan, Adv.Opt.Photon. 1, 1 (2009)

As it is focused, the fields in space are:1 transverse electric field Er2 axial electric field Ez3 azimuthal magnetic field Bθ

Er Ez BθY. Salamin, New J. Phy. 8, 133 (2006)

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How we create radially polarized laser pulse?

There are many methods to create radially polarized beams

It can be active or passive depending on the generation methods involve media

Active: use of laser intracavity devices to force the laser to oscillate in desiredmode

Passive: convert spatially homogeneous polarizations (such as linear/circular)into spatially inhomogeneous polarizations in free space

We use a liquid crystal polarization converter to create femtosecond RP beam

M. Stalder, et al., Opt. Lett. 21, 1948 (1996)

CCD images of radially polarized light in our lab

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Radially polarized field & Direct laser acceleration

Radially polarized field:

1 Transverse field Er cannot accelerate forward accelerating electrons

2 Can be focused to a much smaller spot than the linearly/circularly polarized light

3 Results in a more intense axial electric field Ez , where

Ez,max = E0θ20, divergence angle: θ0 = ω0

zr, Power: P0 =

πω20

2

E20

cµ0

(θ02

)2

Direct Laser Acceleration (DLA):

1 Uses the intense axial electric field Ez of radially polarized pulse

2 Periodic density varying plasma structure to phase-match electrons & laser pulses

B. Layer et. al., PRL 99, 035001 (2007)

3 High acceleration gradients at modest laser powers

4 ∼5 orders of magnitude increase in rep. rate & ∼2 order of magnitude increasein average power compared to LWFA

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Direct laser acceleration in our lab

BS

1

Machining beam

Interferometer

Radially pump beam

Machining beam image

Relay image

Side scatteringimage

Optical & mechanical design by M. Lin

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Importance of characterizing radially polarized pulses

Temporal & spatial characterization:

1 Understanding the interaction between a radially polarized fs pulse & corrugatedplasma channel is crucial to achieve QPM in DLA

2 A study of the propagation of radially polarized beams in plasma channels hasnot been reported

3 Only a standalone radially polarized beam characterized by FROG in the past

K.J.Moh, et. al., Appl. Phy. Lett. 89, 251114 (2006)

4 Polarization & pulse duration preservation is important to achieve acceleration

5 Comparing the measured fields of the laser pulse as it propagates in a preformedplasma waveguide w/ simulation is important to understand our theoretical model

6 Laser pulse characterization may be used to diagnose the plasma parameters

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Outline




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What is pulse characterization?

In order to understand an ultrashortpulse we must measure:

1 Energy, peak power & repetition rate:detector, photodiode

2 Spatial distribution: Beam profile,CCD matrix

3 Spectrum: spectrometer

4 Temporal profile: pulse duration,shape, chirp

Complete characterization of ultrashortpulse requires:

1 time-domain spatio-temporal electricfield,

E(t) ={√

I(t)exp[i(ω0t − φ(t))]}

2 frequency-domain spatio-temporalelectric field,

E(ω) ={√

S(ω)exp[−iϕ(ω)]}

3 intensity & phase/spectrum & spectralphase fully determine the pulse

4 the most prominent techniques:SPIDER & FROG

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SI: Spectral Interferometry

Froehly, et al., J. Opt. (Paris) 4, 183 (1973)

SSI (ω) = |F(Eref (t − τ) + Eunk (t))|2

= |Eref (ω)|2 + |Eunk (ω)|2 + |Eref (ω)||Eunk (ω)| cos(ϕref (ω)− ϕunk (ω) + ωτ)

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SI: Spectral Interferometry

Advantages:

1 Simple linear technique & henceextremely sensitive for measuring the∆ϕ(ω) between two light waves

2 Involves simply measuring thespectrum of the sum of the two pulses

3 If Eref (ω) & ϕref (ω) are available, canbe used to completely characterize theunknown pulse

Disadvantages:

1 It measures only the spectral-phasedifference

2 The interferometer must be stable, thebeams must be very well aligned, andthe beams must be mode-matched

3 Requires a reference pulse thatcontains all of the colors of theunknown pulse

4 A separately characterized referencepulse is required to measure the phaseof an unknown pulse

5 Finer fringes caused by larger delaysmy exceed the spectral resolution ofthe spectrometer

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SPIDER: Spectral Phase Interferometry for Direct Electric-fieldReconstruction

Iaconis and Walmsley, IEEE. JQE 35, 501 (1999)

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SPIDER

S(ω0) = |E(ω0)|2 + |E(ω0 + δω)|2 + 2|E(ω0)||E(ω0 + δω)|= × cos[ϕω(ω0 + δω)− ϕω(ω0) + ω0τ ]

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SPIDER

Advantages:

1 Yields the spectral phase of a pulsedirectly & hence fast, providedτ > tfwhm & the resulting frequencyfringes can be resolved by thespectrometer

2 Only one spectrum yields the spectralphase (naturally operates single-shot)

3 SI extracts spectral phase differencewhich is the derivative of the spectralphase ϕω(ω0 + δω)− ϕω(ω0),integration yields ϕω(ω0)

Disadvantages:

1 Apparatus is very complicated. It has12 sensitive alignment parameters

2 Requires very high mechanicalstability, or the fringes wash out

3 Poor beam quality can wash out thefringes, preventing the measurement

4 Cannot measure long or complexpulses: TBP <∼3

5 Poor sensitivity due to the need tosplit and stretch the pulse before thenonlinear medium.

6 The pulse delay must be chosen for theparticular pulse. And pulse structurecan confuse it, yielding ambiguities.

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FROG: Frequency-Resolved Optical Grating

Involves gating the pulse with a variably delayed replica of itself in aninstantaneous nonlinear-optical medium and then spectrally resolving the gatedpulse vs. delay.

Use any ultrafast nonlinearity: Second-harmonic generation, etc.

3 alignment parameters (θ, φ for a mirror & delay τ)

Has many variations of beam geometries (SHG, PG, SD, THG & XFROG etc.)

Can be single-shot & multi-shot with different sensitivity

R. Trebino et. al., Rev. Sci. Instrum., Vol. 68, No.9, (1997)

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FROG: Generalized-projection (GP) Iterative Algorithm

Find the signal field, Es ig(t, τ), that satisfies both of these constraints,

IFROG (ω, τ) =∣∣∣ ∫ +∞

−∞Esig (t, τ)exp(−iωt)dt

∣∣∣2Esig (t, τ) ∝ E(t)|E(t − τ)|2

for the particular beam geometry (PG FROG here)

Requirements on set-up: linear detector response, step size, S/N.

Delay-scanning technique.

Measures 2D characteristic (long).

Does not always converge.

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SEA TADPOLE: Spatially Encoded Arrangement TemporalAnalysis by Dispersing a Pair Of Light E-fields

Before SEA TADPOLE SEA TADPOLE

R. Trebino, Nature Photonics, 5,189-192(2011)

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SEA TADPOLE Algorithm

Has all the advantages of TADPOLE & none of the problems.

Single mode fibers assure mode-matching & maintain alignment.

Retrieval algorithm is single shot, so phase stability isn’t essential.

Collinearity is not only unnecessary; its not allowed.

And the crossing angle θ is irrelevant; its okay if it varies.

The pulse is retrieved using spatial fringes, not spectral fringes, with zero delay.

S(ω, x) = Sref (ω) + Sunk (ω) + 2√

Sref (ω)√

Sunk (ω) cos[ϕunk (ω)− ϕref (ω) + 2kx sin θ]

P. Bowlan, PhD Thesis, Georgia Tech(2009)

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POLLIWOG: POLarization Labeled Interference versus Wavelengthfor Only a Glint

light polarization state changes too rapidly with time

Measure E(t) for both polarization vs. time using two TADPOLE apparatus

Walecki, Fittinghoff, Smirl and Trebino, Opt. Lett., 22, 81 (1997)

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SEA TADPOLE measurement of polarization shaped pulses

Three measurements of the field, Ex (ω), Ey (ω), Exy (ω)

A polarizer, a wave plate in front of the unknown arm of the SEA TADPOLE’sentrance fiber

Minimize the rms difference between Ix+y (ω) and Ixy(ω) to find ϕrel

Ix+y (ω) =∣∣∣Ex (ω) + Ey (ω)

∣∣∣2 =∣∣∣Ex (ω) + Ey (ω) exp(iϕrand + iε)

∣∣∣2Ixy (ω) =

∣∣∣Exy (ω)∣∣∣2 =

∣∣∣Ex (ω) exp(iϕrel ) + Ey (ω)∣∣∣2

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SEA TADPOLE measurement of polarization shaped pulses

Linearly Polarized State

Chirped Linearly Polarized State

Circularly Polarized State

Elliptically Polarized State

P. Bowlan, PhD Thesis, Georgia Tech(2009)

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STRIPED FISH: Spatially and Temporally Resolved Intensity andPhase Evaluation Device Full Information from a Single Hologram

R. Trebino, Nature Photonics, 5,189-192(2011)

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Reconstruction Algorithm of STRIPED FISH

E(x, y , t) =1

2π

∑ωk

E(x, y ;ωk )exp(iωk t)δω

P. Gabolde and R. Trebino, JOSAB, Vol.25, No.6 (2008)

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Measurements of the spectral phase by STRIPED FISH

P. Gabolde and R. Trebino, JOSAB, Vol.25, No.6 (2008)

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Outline




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Sampling Technique

Method:

A sampling device with two apertures can be placed in the optical path

It samples the quasi-vertical (quasi-horizontal) portion of the polarization

Each beamlet with a particular polarization combined with correspondingreference beam simultaneously

Two SEA TADPOLE (?) traces correspond to two interferograms analyzed

Up & Down (Left & Right) spectra & temporal intensities w/ phases extractedsimultaneously

Up

Down

Left Right

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Measurement of Radially Polarized Pulse

Methods:

SEA TADPOLE interferometric measurement of Elinear (t) & Eradial (t)

Elinear (t) measurement can be done with FROG or SPIDER

Coupling w/ & w/o plasma waveguide

Input & output measurement

Plan:

Begin with a particular method have a draft schematic

Write a Matlab simulation code to reproduce previous methods used by P.Bowlan and others

Have a linearly/circular polarized case solvable by code

Implement radial polarization & test it with experiment

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Documents

Techniques for Characterizing Radially Polarized ......Techniques for Characterizing Radially Polarized Femtosecond Pulses for Direct Laser Electron Acceleration Abdurahim Rakhman