Interacting Airy and nonlinear beams Yiqi Zhang and Milivoj Belić Xi’an Jiaotong University and TAMUQ, Doha SOPO, Suzhou, August 2014

Outline Accelerating light beams? Quantum-mechanical Airy wave-packets Nonlinear Airy beams in optics Interacting accelerating beams Summary

Courtesy of D. Christodoulides Yes, but…

Yes, of course! But, can light accelerate?

M.V. Berry and N. L. Balazs, “Nonspreading wave packets, In quantum mechanics: Airy wave packet M.V. Berry and N. L. Balazs, “Nonspreading wave packets, Am. J. Phys. 47, 264 (1979) Free-particle Schrödinger equation Airy wave-packet solution |Ψ|2 x Non-spreading Airy wave-packet t>0 acceleration Courtesy of Ady Arie

From Quantum Mechanics to Optics Scaled paraxial wave equation s |Φ|2 Siviloglou and Christodulides, 2007 Finite energy beam Nearly non diffracting Freely accelerating Free particle Schrödinger equation |Ψ|2 x Infinite energy wave packet Berry and Balzas, 1979 Non diffracting Freely accelerating Berry and Balzas, Am. J. Phys, 47, 264 (1979) Siviloglou, Broky, Dogariu, & Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).

Airy beam: What is accelerating there? Siviloglou et al.,PRL 99, 213901 (2007) Berry and Balazs, Am J Phys 47, 264 (1979)

Airy beam – a manifestation of caustic Caustic: An envelope of light rays reflected or refracted by a curved surface or object or the projection of that envelope of rays on another surface. In ray description, the rays are tangent to the parabolic line but do not cross it. The Airy beam is a beam with curving propagation trajectory Kaganovsky and Heyman, Opt. Exp. 18, 8440 (2010) 8

Curved caustics in everyday life

Airy beams propagating in NL media Equation Input beam No trunca- tion, a=0 Truncated a=0.2

Counterpropagating Airy beams Linear medium: Interference of beams Upper row: In-phase Lower row: Out-of-phase

Counterpropagating Airy beams Kerr medium: Generation of solitons No acceleration! Upper row: In-phase (attraction) Lower row: Out-of-phase (repulsion)

Counterpropagating Airy beams Kerr medium: Generation of solitons No acceleration! Black lines: Trajectories of the main lobes

Interacting Airy beam and a soliton Kerr medium: NL interference Top: In-phase Bottom: Out-of-phase

Summary Thank you for your attention! Introduced interacting Airy wave-packets and beams In linear media: Superposition and interference; no solitons In NL optics: Nonlinear interference and generation of solitons Depicted counterpropagating Airy beams in Kerr media Cosidered interactions of solitons and Airy beams Thank you for your attention! 15