1. Accelerator Research Department B Photonic Crystal Laser Acceleration Experiments at ORION Ben Cowan SLAC Second ORION Workshop, 2/19/2003

2. Accelerator Research Department B 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

3. Accelerator Research Department B 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/m Efficiency: Photon-to-electron: 4.2 x 10 -4 Wall-plug in LEAP Experiment: ~ 10 -10 (no staging) Diagram by T. Plettner

4. Accelerator Research Department B Vacuum Laser Acceleration Issues Gradient In free space Maximum E x 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?

5. Accelerator Research Department B 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 Mode can be guided in a defect in a photonic crystal lattice Silicon (ε r = 12.1 for λ = 1.5 μm) Vacuum 2D photonic crystal of vacuum holes in silicon; r/a = 0.427. 2D TE Band Gap a r

6. Accelerator Research Department B 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 guide pad Speed-of-light mode in PC waveguide

7. Accelerator Research Department B 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 E p the damage threshold for 1 ps pulses,

8. Accelerator Research Department B 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 SOL modes exist for most geometries Impedance has power-law dependence on guide width

9. Accelerator Research Department B 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?

10. Accelerator Research Department B Maximum Gradient Maximum gradient appears to have optimum; will be different for other lengths Compare to DWA as more analytically tractable example 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 v g for f D Dielectric waveguide accelerator geometry

11. Accelerator Research Department B 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 *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)

12. Accelerator Research Department B Next Steps Continue to optimize parameters Improve f D 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).

13. Accelerator Research Department B 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)

14. Accelerator Research Department B 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