Asymptotic theory of bimodal quarter-wave impedance matching for full mode-converting transmission

A quarter-wave impedance-matching element inserted between two dissimilar media allows full-power transmission, but this phenomenon occurs only when the mode of the incident and transmitted waves remains unaltered, either longitudinal (L) or transverse (T). Here, we report our asymptotic bimodal quarter-wave impedance-matching theory for full-power mode-converting transmission. It requires that two coupled quarter waves should be simultaneously formed inside a matching element possessing specific anisotropy for phase matching and L-to-T (T-to-L) mode conversion. Simulations using designed metamaterial matching elements show that nearly full mode-converting transmissions can be realized within a single medium or between two dissimilar media. We expect that our theory can be critically useful for medical and industrial ultrasonic applications wherever highly efficient mode conversion and high-powered transverse waves are required.