Acoustic demonstration of virtual impedance matching by transiently echoless complex frequency waves

The ability of a wave to pass through a material boundary can be improved by adding a tuned middle layer, known as an impedance-matching layer. However, in many situations, it is unfeasible to modify the physical system itself. This paper demonstrates that virtual impedance matching without added tuned layers is possible by allowing the frequencies of incident waves to take on complex values. The resulting tailored waveforms directly excite the zeros of the reflection coefficient and lead to complex generalizations of Fabry-Pérot resonances and quarter-wavelength matching. This is demonstrated experimentally whereby the reflection coefficient for an ultrasound beam incident on a bi-layer plate immersed in water is reduced by more than an order of magnitude. While the technique is naturally limited in temporal duration due to the quasi-steady state nature of the signals, it provides an alternative approach to traditional impedance matching by eliminating the need for extra tuned layers and may prove useful in applications where reduction of reflections is desired without modifying the system itself.