Open waveguides in a thin Dirichlet lattice: II. localized waves and radiation conditions

  • S. A. NazarovEmail author


Wave processes localized near an angular open waveguide obtained by thickening two perpendicular semi-infinite rows of ligaments in a thin square lattice of quantum waveguides (Dirichlet problem for the Helmholtz equation) are investigated. Waves of two types are discovered: the first are observed near the lattice nodes and almost do not affect the ligaments, while the second, on the contrary, excite oscillations in the ligaments, whereas the nodes stay relatively at rest. Asymptotic representations of the wave fields are derived, and radiation conditions are imposed on the basis of the Umov–Mandelstam energy principle.


open waveguides square lattice Dirichlet problem for the Helmholtz equation asymptotic representations of wave fields Umov–Mandelstam principle 


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© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Peter the Great St. Petersburg State Polytechnical UniversitySt. PetersburgRussia
  3. 3.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia

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