Multistage Accelerating Beams Moti Fridman 1, Alessandro Farsi 2 and Alexander L. Gaeta 2 1 School of Engineering, Bar Ilan University, Ramat Gan, 52900, Israel 2 School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA
Caustics Menaechmus ~ 400 BC
Accelerating beam of light G. A. Siviloglou et. al. (2007)
Accelerating beam in space Mask imposing cubic phase Input beam Lens Accelerating beam
Accelerating beam of electrons N. V. Bloch et. al. (2012)
Optical processing based on time-space duality Spatial domain x z diffraction Temporal domain z dispersive broadening Spatial diffraction Dispersive propagation Akhmanov, Sukhorukov, and Chirkin, Sov. Phys. - JETP, 28, 748, (1969). Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).
Imaging in space lens quadratic phase shift in space • Imaging achieved by adding a quadratic phase to wavefront.
Temporal imaging dispersive elements quadratic phase shift in time • Imaging achieved by adding a quadratic phase to the signal.
Accelerating beam in time cubic phase shift in time and a lens dispersion
Imposing cubic phase in time • Look for interaction that imparts quadratic phase shift. • Parametric mixing with a quadratic chirped pump Quadratic dispersion D quadratic frequency shift pump pulse
Imposing cubic phase in time Pump Diffracting grating
Reflecting stairs
Accelerating beam in time
Multistage accelerating beam Stage 1 idler signal FWM
Multistage accelerating beam Stage 1 Stage 2 Idler #2 idler signal FWM
Experimental setup
Accelerating beam in time
Multistage accelerating beam in time
Conclusions • Accelerating beam in time. • Multistage acceleration. • More complex dispersion relations. • Space-time equivalent can open a rout for many more novel demonstrations.
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