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For some periodic waveguides, there are standing waves, which are special guided modes, non-propagating and localized around the waveguide core.These non-propagating waves localized around the waveguide core are special guided modes above the light line with a zero wavenumber, and they are related to transmission anomalies and other resonant phenomena.A recently developed pseudospectral modal method (PSMM) for diffraction gratings is reformulated to analyze standing waves on periodic waveguides.