1. L. Corner and T. Hird John Adams Institute for Accelerator Science, Oxford University, UK 1AAC, USA, 2016 The efficient generation of radially polarised beams by coherent combination of higher order fibre waveguide modes

2. AAC, USA, August 20162 What are radially polarised beams? Why are they interesting for accelerators? How do you make them? Outline

3. AAC, USA, August 20163 Cylindrical Vector Beams Non spatially homogeneous polarisation state - annular intensity spatial profile. Radially polarised beam Azimuthally polarised beam

4. AAC, USA, August 20164 Motivation Acceleration! Conventional/advanced accelerators use a medium – rf cavity/plasma/dielectric – all have associated difficulties. What about direct laser acceleration? Generate longitudinal field by manipulating light – acceleration in vacuum. Focusing radially polarised beams produces strong longitudinal fields. Theory and experimental work – for example: F. Pierre-Louis et al. ‘Direct-field electron acceleration with ultrafast radially polarized laser beams: Scaling laws and optimization’, J. Phys. B 43, 025401 (2010); L. J. Wong and F. X. Kärtner, ‘Direct acceleration of an electron in infinite vacuum by a pulsed radially polarized laser beam’, Opt. Express 18, 25035 (2010); S. Carbajo at. al. ‘Direct longitudinal laser acceleration of electrons in free space’, PR STAB 19, 021303 (2016) – report a gradient of 3GeV/m – energy gain of 12keV from initial energy of 40keV, 30% modulation from focused radial pulse, 600  J, 1.2  m, NA = 1 OAP focusing optic. Can we make radially polarised beams efficiently?

5. AAC, USA, August 20165 Making radial and azimuthal beams Segmented wave plate

6. AAC, USA, August 20166 Generating radial beams by mode overlap Proposed by Tidwell et. al., ‘Generating radially polarized beams interferometrically’, Appl. Opt. 29, 2234 (1990). Inteferometrically combined two TEM 01 modes of an Ar ion laser together. No phase control, so polarisation output not always radial as arms of interferometer move wrt each other by /2. Reliable method of producing radial beams this way requires phase locking.

7. AAC, USA, August 20167 Fibre laser modes Fig: RP Photonics Encyclopedia Don’t have an Ar ion laser with a wire in the cavity. Do have some (slightly) multimode fibre lasers. Can we excite higher order modes in two fibres and combine them to make a radially polarised beam? And even amplify the modes to produce high power output? Yb doped double clad fibre, 15  m core diameter, multimode for 1  m light, polarisation maintaining.

8. AAC, USA, August 20168 Exciting higher order modes in multimode fibre Lowest order mode coupling LP 11 mode coupling

9. Dove prism Analysis Two fibre combination 9 1053nm, 8ps, 2nJ, 32MHz Seed laser Double clad Yb fibres Piezo mounted mirror HC detector /4 Closed feedback system /4 Dove prism /2

10. Phase Locking 10

11. Testing the beam 11 Segmented wave plate radial beamCombined fibre mode radial beam Clearly created radial beam but quality not great – issues with different divergence of output from each fibre as distance from end of each fibre to combination cube is different.

12. AAC, USA, August 201612 Single fibre combination 1053nm, 8ps, 2nJ, 32MHz Pump diode Piezo mounted mirror Analysis HC detector /4 Closed feedback system Dove prisms /4 /2 Seed laser Double clad Yb fibre

13. AAC, USA, August 201613 Single fibre combination output Is the locked combined beam radial?

14. AAC, USA, August 201614 Amplification of higher order mode Amplification of higher order mode: Very clean – no noticeable degradation of mode quality. Increase of factor 2, limited by short length ( ~ 40 cm) of fibre.

15. AAC, USA, August 201615 Amplification results Amplification – same exposure with and without pumping

16. AAC, USA, August 201616 Summary Proposed an efficient new method to produce radially polarised beams. Combined higher-order modes from two fibres and phase- locked them. Generated a truly radial beam from higher-order modes in one fibre and shown it can be amplified and maintain its polarisation.

17. AAC, USA, August 201617 Axicon focusing Axicon focusing of radial beam produces strong longitudinal accelerating field. Designed high refractive index (n = 1.8) and high apex angle (32 degree) axicon. transverselongitudinal

18. AAC, USA, August 201618 A high ‐ energy, laser accelerator for electrons using the inverse Cherenkov effect (Fontana 1983) Modelling of inverse Cerenkov laser acceleration with axicon laser-beam focusing (Romea 1989) Generating radially polarized beams interferometrically (Tidwell 1990) Transporting and focusing radially polarized laser beams (Tidwell 1991) Efficient radially polarized laser beam generation with a double interferometer (Tidwell 1993) Direct longitudinal laser acceleration of electrons in free space (Carbajo 2016) References