Fiber Accelerating StructuresAdvanced Accelerator Research Division

By Andrew P. Hammond

What technology is needed for the next powerful linear accelerator to be built at SLAC?

Photonic bandgap (PBG) fiber for 1 mm telecommunications with a central defect

Basic TheoryA photonic band gap (PBG) is a periodic arrangement of dielectric material that precludes certain wave length from propagating.In a 1D PBG it is a periodic symmetric structure. When solved using the Maxwell equation lead to constructive and destructive interference for certain wavelengths.In a 2D PBG fiber it is confined linearly.

Steven G. Johnson. Photonic Crystals, Periodic surprises in Electromagnetism. (2003)

From: http://ab-initio.mit.edu/photons/tutorial/, Retrieved 8/12/09

Theory of PBG DefectIn a PBG Fiber a defect can be added that allows certain wavelength to propagate near it despite being in the band gap.

There are two major types of propagation in a defect, core and surface modes.

Computer ModelingThe program used to model the PBG fibers that I tested is called CUDOS, made by the University Sydney.

Assumes an infinite fiber with light of a certain wavelength moving down it.

Does not track movement of particular light source.

ProjectsFor an optical fiber to be used as an accelerator, it must over come the

basic difficulties of: Laser Coupling, Accelerator Structure, and Alignment.

To potentially solve these difficulties:

1. The simple fiber accelerator parameters were optimized,

2. A double defect was examined,

3. A perturbed lattice was looked at.

Shift of accelerating mode depending on basic values

I studied how the longitudinal Electric field shifted when basic parameters were shifted.

Pitch can’t be shifted independently

As radius of normal cylinder decrease so does field

As defect radius of defect increases field decreases

Possible to increase defect max by decreasing normal cylinder size

Longitudinal E-Field of Optimal ModesThe E-field of the two maximum modes, defect size and field ratio, properties are:

λ (μm) n neff R(μm) r(μm) P(μm) Ratio

2.0 1.459 1.0017, 3.22E-4 1.4375 0.84 2.55 0.5570

2.0 1.459 1.0196, 1.11E-3 1.08 0.87 2.55 0.7639

The largest defect size has a uniformity in the defect of 3.2%.

The maximum field fiber has a uniformity of 9.8%.

Basic Accelerating Modes for Higher Wavelengths

At higher wavelengths, past ~2.5µm, the refractive index fluctuates a large amount as various absorption peaks are hit. This changes the PBG, so a new structure is needed.

Examined fiber structure at λ=16 µm, where n=1.484.

This wavelength needs a larger defect to support the mode. (Expected defect for radius = 10.52 µm).

Based on previous papers, I expect the higher the refractive index a lower pitch and lower normal radius will be needed.

Analysis of 16 Micron Fiber

λ (μm) n neff R(μm) r(μm) P(μm) Ratio

16.0 1.484 1.0018, 3.67-4 12.50 6.92 20.40 0.4280

16.0 1.484 1.0192, 2.72E-4 11.00 6.92 20.40 0.4938

The 16 micron fiber case shows an increased defect is necessary from a scaled up version to create an accelerating structure.

The higher gradient case has a uniformity of 17.4%.

The higher defect radius has a uniformity of 4.5%.

Double DefectA double defect might serve to couple laser into another defect. It might also help offset the low electron bunch number.

Basic fiber parameters of large defect 2 micron case.

Double Defect ResultsObserve partial coupling for separation of 5 and 7 cylinders. Despite the losses from lack of coverage, there is some coupling.

Past that the memory constraints perturb and remove mode.

Lower and the PBG is offset by values to close to one another.

Perturbed Lattice

In order to create stronger electric fields in the defect and eliminate hot E field spots, it is possible to perturb the lattice and maintain a uniform field.

Conclusion

I. Optimized fiber for two goalA. High E-field, large normal radius small defect radius, but lose

uniformityB. Large defect, small normal radius is more uniform

II. Need to increase defect and decrease normal radius for higher nIII. Two defect can couple and maintain accelerating fieldIV. Lattice can be perturbed to eliminate high E-field without losing mode

References[1] Eric Colby, Gary Lum, Tomas Plettner, and James Spencer. Gamma radiation studies on optical materials. IEEE Transactions on Nuclear Science, 49 (6), 2002.

[2]* John D. Joannopoulos, Robert D. Meade, and Joshua N. Winn. Photonic Crystals, Molding the Flow of Light. Princeton University Press, 1995.

[3] R. Kitamura, L. Pilon, and M Jonasz. Optical constants of fused quartz from extreme ultraviolet to far infrared at near room temperatures. Applied Optics, 46 (33). (8118-8133),2007.

[4]* Robert J. Noble. Dispersion information for photonic fiber modes from CUDOS simulations. ARDB Note 04, SLAC, 2005.

[5]* Robert J. Noble, Eric R. Colby, Benjamin Cowan, Christopher M. Sears, Robert H Siemann, and James E. Spencer. Designing photonic bandgap fibers for particle acceleration. In Particle Accelerator Conference, PAC 07, SLAC-PUB-12571, June 2007.

[6] Burak Temelkuran, Shandon D. Hart, Gilles Benoit, John D. Joannopoulos, and Yoel Flink. Wavelength-scalable hollow optical fibres with large photonic bandgaps for co2 laser transmission. Nature, 420, 2002. 1