Fig. 5: Guided-mode theory for waveguides.
From: Realization of ultrathin waveguides by elastic metagratings

a Schematic of omnidirectional wave reflection in a waveguide excited by a point source S placed in the middle of the waveguide. Points A and E are located symmetrically at the boundary of waveguide. Wave fields in points A and point C have the same phase with their projections B and D, respectively. φ represents the phase shift when total reflection appears at the waveguide boundary. b The guided-mode order β as functions of the ratio l/λ and the incident angle θi. The whole region is divided into three parts (0.2–1.2, 1.2–2.2, and 2.2–3.2), which represent different patterns in standing wave fields. c Simulated displacement fields |w| in the waveguides with l/λ = 0.5,1.5,2.5, respectively. The amplitude |w| on a typical line (dashed yellow line) crossing the waveguide (the orange curve) is examined in each subplot.