Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers

摘要: [1] The kd–βd (dispersion) equations are found for traveling waves on two- and three-dimensional infinite periodic arrays of small lossless acoustic monopoles, electric or magnetic dipoles, magnetodielectric spheres. Using Floquet mode expansions then expressions the rapid summation Schlomilch series, prohibitively slowly convergent summations converted to forms that can be used efficient calculation equations. Computer programs have been written obtain diagrams all treated, representative numerical results presented discussed. Expressions, more accurate than Clausius-Mossotti relations, obtained effective bulk permittivity permeability utilizing quantities readily available from solutions Exact computable fields lossy sphere finite in direction array axis, illuminated by a plane wave parallel analyses performed curves arrays.