The laws of geometrical optics for two-dimensional geometries of anisotropic materials and structures are presented through the analysis of the geometrical and mathematical properties of various isofrequency dependences which are also called sections of the wavevector surface. Relations are analyzed between certain peculiarities of these dependences, such as the presence of asymptotes, points of inflection, central or axial symmetry, single- or multiple valuedness, and the existence of certain phenomena, such as nonreciprocal propagation, unidirectional propagation, the emergence of two (or several) reflected or refracted beams, the absence of reflection, and the irreversibility of reflection or refraction. It is shown that simple rules based on seeking the extrema of the isofrequency dependences enable one to find out, for each given geometry, which angles of incidence correspond to positive reflection or refraction of the wave, and which to negative ones.

PACS: 42.15.−i, 42.25.Gy, 78.20.Ci (all) DOI: 10.1070/PU2008v051n04ABEH006460 URL: https://ufn.ru/en/articles/2008/4/d/ 000258187900004 2-s2.0-49249084761 2008PhyU...51..375L Citation: Lock E H "The properties of isofrequency dependences and the laws of geometrical optics" Phys. Usp. 51 375–393 (2008) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Локк Э Г «Свойства изочастотных зависимостей и законы геометрической оптики» УФН 178 397–417 (2008); DOI: 10.3367/UFNr.0178.200804d.0397