XXXVI Workshop on Geometric Methods in Physics | 2-8.07.2017 |

VI School on Geometry and Physics | 26-30.06.2017 |

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## Ali Mostafazadeh## Transfer Matrix Formulation of Scattering Theory, Invisibility, and Reciprocity in Two and Three DimensionsWe 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 allows for establishing a genuinely multidimensional generalization of the Lorentz reciprocity principle and unidirectional invisibility. The former follows as a corollary of a theorem revealing a symplectic nature of the transfer matrix operator. It implies 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. We offer concrete physical applications of our mathematical findings. In particular, we construct a physical model for an active optical wire with a rectangular cross-section that is invisible from one direction but scatters light coming from the opposite direction. References: F. Loran and A. Mostafazadeh, Phys. Rev. A 93, 042707 (2016) and Proc. R. Soc. A 472, 20160250 (2016). |

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