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Speaker:       Prof. 
Ali Mostafazadeh Departments of Mathematics and Physics,Koç University, Istanbul, Turkey                   
Title:             Transfer matrix, nonreciprocal transmission, and unidirectional invisibility in arbitrary dimensions
Date/Time:    Oct. 25, 2016 Tuesday @ 15:40 
Place:            Sabanci University, FENS L062


Abstract:  We outline an alternative to the S-matrix formulation of scattering theory in two and three dimensions that relies on a multidimensional notion of transfer matrix. This enables us to obtain an exact solution of the scattering problem for delta function potentials in two and three dimensions. It also extends the transfer matrix based numerical scattering methods to higher dimensions and allows for establishing a genuinely multidimensional generalization of the Lorentz reciprocity principle and unidirectional invisibility. We show that in dimensions other than one the reciprocity principle does not prohibit nonreciprocal transmission. This is of particular significance for constructing linear optical and acoustic diodes, which was previously considered impossible. As concrete applications of our findings we give an analytic description of the effect of a surface line defect for a mirrorless slab laser and construct a unidirectionally invisible potential in two dimensions that displays nonreciprocal transmission. The latter provides a concrete physical model for an active optical wire with a rectangular cross-section that is invisible from one direction but displays nontrivial reflection and transmission from the opposite direction. 

References: F. Loran and A. Mostafazadeh, Phys. Rev. A 93, 042707 (2016) and Proc. R. Soc. A 472, 20160250 (2016).

contact:           Inanc Adagideli, adagideli@sabanciuniv.edu