Moti Fridman1, Alessandro Farsi2 and Alexander L. Gaeta2

1School of Engineering, Bar Ilan University, Ramat Gan, 52900, Israel

2School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA

Multistage Accelerating Beams

CausticsMenaechmus  ~ 400 BC

Accelerating beam of light

G. A. Siviloglou et. al. (2007)

Accelerating beam in space

Input beam

Mask imposingcubic phase

Accelerating beam

Lens

Accelerating beam of electrons

N. V. Bloch et. al. (2012)

Akhmanov, Sukhorukov, and Chirkin, Sov. Phys. - JETP, 28, 748, (1969).Kolner, IEEE J. Quantum Electron. 30, 1951 (1994).

Optical processing based on time-space duality

Spatial diffraction Dispersive propagation

Spatial domain

Temporal domain

x

z

z

diffraction

dispersive broadening

Imaging in space

• Imaging achieved by adding a quadratic phase to wavefront.

lensquadratic phase

shift in space

Temporal imaging

• Imaging achieved by adding a quadratic phase to the signal.

quadratic phase shiftin time

dispersive elements

Accelerating beam in timecubic phase shift in time and a lens

dispersion

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

200

400

600

800

1000

1200

1400

1600

1800

2000

• Parametric mixing with a quadratic chirped pump

D

quadratic frequency shift

Quadratic dispersion

pumppulse

• Look for interaction that imparts quadratic phase shift.

Imposing cubic phase in time

Imposing cubic phase in time

PumpDiffracting grating

Reflecting stairs

Accelerating beam in time

Multistage accelerating beam

FWM

Stage 1

signal

idler

Multistage accelerating beam

FWM

Stage 1

FWM

signal

idler

Idler #2

Stage 2

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.