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

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

3. Courtesy of D. Christodoulides
Yes, but…

4. Yes, of course!
But, can light
accelerate?

5. 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

6. 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, (2007).

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

8. 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

9. Curved caustics in everyday life

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

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

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

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

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

15. 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