Related Experiment Video
Updated: Apr 16, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Three-mode coupling of symmetric and antisymmetric Lamb waves in plates with finite corrugations
Abstract:
Coupled-mode equations governing the amplitudes of the higher-order symmetric Lamb modes S1 and S2 with the antisymmetric mode A2 in an infinite elastic plate with sinusoidal surface corrugation over a finite length are obtained via multiple-scales analysis. This phenomenon of threemode coupling is observed when the wavenumbers k(s1) and k(s2) of the symmetric modes and k(A2) of the antisymmetric mode satisfy the simultaneous resonance conditions k(s1) - k(A2) = k(w) and k(A2) - k(s2) = k(w), where k(w) is the wavenumber of the sinusoidal corrugation. Near resonance, the coupled amplitude equations are solved exactly as an initial-value problem and it is seen that the modes are transmitted through the grating without reflection. Complete conversion from the symmetric modes into the antisymmetric mode is observed at periodic intervals along the grating when the resonance conditions are exactly satisfied. The effect of detuning away from resonance also shows propagation without reflection with periodic energy exchange. In the latter case, the modes couple without complete conversion. This phenomenon of mode conversion is confirmed by the results of an experiment on an aluminum plate with a triangular grating excited with the S2 symmetric mode at 2.7 MHz.
Related Concept Videos
Standing Waves in a Cavity
Symmetry in Maxwell's Equations
Symmetric Member in Bending
Steady, Laminar Flow Between Parallel Plates
Modes of Standing Waves: II
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end....
Gauss's Law: Planar Symmetry

