Accelerator Research Department B Photonic Crystal Laser Acceleration Experiments at ORION Ben Cowan...

Accelerator Research Department B

Photonic Crystal Laser Acceleration Experiments at ORION

Ben CowanSLAC

Second ORION Workshop, 2/19/2003


Overview• Background: The LEAP structure

• Photonic crystals overview

• 2D photonic crystal accelerator structures

• Photonic crystal accelerator parameters and optimization

• Next steps

• Manufacturing

• ORION wish list


Background: The LEAP Structure

• Some relevant parameters:

Modulated bunch charge

~ 1 pC

Peak modulation

15 keV

Interaction length

1.5 mm

Laser pulse energy (at cell)

36 μJ

The LEAP Cell

Gradient: 10 MeV/mEfficiency:

Photon-to-electron: 4.2 x 10-4

Wall-plug in LEAP Experiment: ~ 10-10

(no staging)

Diagram by T. Plettner


Vacuum Laser Acceleration Issues• Gradient

• In free space

• Maximum Ex is determined by damage threshold

• Laser mode size must be comparable to wavelength for best gradient

• Shunt Impedance: effective acceleration length• In free space, small modes diffract quickly and won’t

accelerate for appreciable distance

→ Look for near-field, guided-mode structures• But metals have low breakdown threshold• How do we confine a mode in vacuum using only

dielectrics?

0/~/ wEE xz


Photonic Crystals to the Rescue!• A photonic crystal is a geometry with periodic dielectric

constant

• Like electronic states in solids, EM modes form bands

• Band gaps can form, in which propagation is prohibited

0

0.2

0.4

0.6

0.8

1

TE Band Structure of Crystal

a

/2 c

Position around Brillouin Zone Edge

• Mode can be guided in a defect in a photonic crystal lattice

Silicon (εr = 12.1 forλ = 1.5 μm)Vacuum

2D photonic crystal of vacuumholes in silicon; r/a = 0.427.

2D TE Band Gap

a

r


A 2D Photonic Crystal Accelerator Segment• Intuition-building structure• Accelerator consists of array of

vacuum holes in silicon, with vacuum guide

• Parameters:• Lattice spacing a• Guide width w• “Pad” width δ

• Large bandgap leads to good confinement

• Only frequencies within gap are confined – higher order modes in general escape

• We still need a method of vertical confinement

e-beam

guidepad

Speed-of-light mode in PC waveguide


2D PC Accelerator Parameters• Group velocity

• These are transmission-mode, non-resonant structures to take advantage of ultrafast lasers

• Characteristic impedance (normalized to 1λ height)

• “Damage factor”:

• Maximum gradient: Depends on length L of structure

where for Ep the damage threshold for 1 ps pulses,

material

max

axis /EzD Ef

1

1)( maxmaxmax

gDDz c

LEfEfE

ps10)ps/(750.0

]ps10,ps4.0[)ps/(

ps4.0)ps/(892.0

4/1

8/3

2/1

max

p

p

p

E

E

E

E


Computation Results• A PC waveguide has similar

dispersion characteristics to metallic guide, in the gap

• Can pad the guide to bring SOL modes into center of gap

0.25 0.3 0.35 0.4 0.45 0.50.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

0.46

kza/2

a

/2 c

Dispersion Relations for PC Waveguides (no padding)

Speed-of-light linew = 2.0aw = 3.0aw = 4.0aw = 5.0aw = 6.0aw = 7.0a

• SOL modes exist for most geometries

• Impedance has power-law dependence on guide width

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.60

50

100

150

200

250

300

w/

Zc [

]

PC Waveguide Shunt Impedance for SOL Modes

55.3

~

w

Zc


Dependence of PC Waveguide Parameters

• Trade-off: With wider guide, impedance and damage factor go down, but group velocity goes up• How to optimize overall gradient?

0 0.05 0.1 0.15 0.2 0.250.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

/a

f D

Damage Factor vs. Pad and Guide Witdhs

w = 3.0aw = 4.0aw = 5.0aw = 6.0a

0 0.05 0.1 0.15 0.2 0.250.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

/a

g

Group Velocity vs. Pad and Guide Witdhs

w = 3.0aw = 4.0aw = 5.0aw = 6.0a


Maximum Gradient• Maximum gradient appears to

have optimum; will be different for other lengths

• Compare to DWA as more analytically tractable example

0 0.05 0.1 0.15 0.2 0.250.03

0.04

0.05

0.06

0.07

0.08

0.09

/a

Ezm

ax /E

p

Maximum Accelerating Gradient for 25 mm Segment

w = 3.0aw = 4.0aw = 5.0aw = 6.0a

0 0.5 1 1.5 2 2.5 30

0.05

0.1

0.15

0.2

r/

Ezm

ax /E

p

Maximum Gradient for 25 mm DWA Segment

r

b

• For each r, find b such that lowest mode is SOL

• Compute parameters of mode• Result: For 25 mm segment, it

pays to use narrower guide and trade vg for fD

Dielectric waveguide accelerator geometry


• We use the MIT Photonic-Bands package*• Frequency-domain iterative eigensolver• Public domain, maintained by Joannopoulos group

• Group velocities computed easily using Feynman-Hellmann theorem: For λ an eigenvalue of operator H which depends on parameter α,

• Mode calculation for one geometry takes ~2 hr of CPU time on SLAC Sun farm; subsequent convergence to SOL mode is rapid

Computation Techniques

d

dH

d

d

* Steven G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Optics Express 8, no. 3, 173-190 (2001)


Next Steps• Continue to optimize parameters

• Improve fD by using poorly-confined frequency?

• Wakefield computations (FDTD code)• What happens in the short-wavelength

regime? Quantum effects?

• Coupling to structures (FDTD)

• 3D structures

• Also in progress: Investigation of photonic crystal fibers• Accelerating mode found by X. Lin (SLAC)• Work underway by M. Javanmard (SLAC) to

generalize and optimize

Example of photonic crystal waveguide bend. From A.

Mekis, et. al., Phys. Rev. Lett. 77, pp. 3787 (1996).

X. Lin, Phys. Rev. ST-AB, 4, 051301, (2001).


Manufacturing Issues• 2D structures amenable to lithography

• Feature size of ~0.6 μm possible with optical lithography• High aspect ratio poses an etching challenge

• Photonic crystal fibers can be drawn• Tolerance issues unknown

• 3D photonic crystal structures in NIR possible• Structures have been fabricated in III-V semiconductors

using wafer-fusion technique• Low aspect ratio amenable to plasma etching• Small feature size would require e-beam or DUV lithography

S. Noda et. al., Science 289, 604 (2000)


ORION Wish List• Many requirements same as LEAP I• Optics: May use fiber laser inside experimental hall

• Shielded sub-enclosure for fiber laser• Fiber laser couplers, diagnostics (including streak camera), alignment tools• Timing signal to lock laser available in experimental hall

• E-beam:• Transverse emittance: ~ 2.5 × 10-4 mm-mrad, with collimation• Low energy spread not as crucial• Bunch charge monitor after spectrometer

• Clean prep area, possibly with wet benches• Solvent wetbench; acid wetbench for RCA-type cleans• Requires waste disposal infrastructure• DI water and dry nitrogen

SNF access – facilitated by ORION?• Computing:

Batch farm for simulation/offline analysis• High-performance resources (MP?) for compute-intensive work• Machine(s) for online analysis• Microfab simulation software/CAD tools

• DAQ infrastructure (To be discussed for E163) Cable TV system for video diagnostics

Accelerator Research Department B Photonic Crystal Laser Acceleration Experiments at ORION Ben Cowan...

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