title: Localization-delocalization wavepacket transition in Pythagorean aperiodic potentials.
abstract: We introduce a composite optical lattice created by two mutually rotated square patterns and allowing observation of continuous transformation between incommensurate and completely periodic structures upon variation of the rotation angle θ. Such lattices acquire periodicity only for rotation angles cos θ = a/c, sin θ = b/c, set by Pythagorean triples of natural numbers (a, b, c). While linear eigenmodes supported by lattices associated with Pythagorean triples are always extended, composite patterns generated for intermediate rotation angles allow observation of the localization-delocalization transition of eigenmodes upon modification of the relative strength of two sublattices forming the composite pattern. Sharp delocalization of supported modes for certain θ values can be used for visualization of Pythagorean triples. The effects predicted here are general and also take place in composite structures generated by two rotated hexagonal lattices.
authors: Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.|Key Laboratory for Laser Plasma (Ministry of Education), IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240, China.
authors: Changming
authors: C
authors: Huang
authors: Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.|Key Laboratory for Laser Plasma (Ministry of Education), IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240, China.
authors: Fangwei
authors: F
authors: Ye
authors: Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.|Key Laboratory for Laser Plasma (Ministry of Education), IFSA Collaborative Innovation Center, Shanghai Jiao Tong University, Shanghai 200240, China.
authors: Xianfeng
authors: X
authors: Chen
authors: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.|Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Region, 142190, Russia.
authors: Yaroslav V
authors: YV
authors: Kartashov
authors: Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande 2, Edifício C8, Lisboa 1749-016, Portugal.
authors: Vladimir V
authors: VV
authors: Konotop
authors: ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.|Universitat Politecnica de Catalunya, 08034, Barcelona, Spain.
authors: Lluis
authors: L
authors: Torner