Over the past two decades, acoustic metamaterials have demonstrated extraordinary wave manipulation capabilities, including negative refraction, cloaking, super-resolution imaging, and oneway topological propagation. Conventionally, most metamaterials are passive and require tailor-made designs to achieve these extraordinary capabilities. Once designed and fabricated, the resultant material properties are often locked into place with limited tunability. Furthermore, imposed by the constraints of passivity and reciprocity, losses inherent in resonating structures inevitably reduce the power efficiency. On the other hand, time-varying metamaterials have been recently proposed with exciting new possibilities in breaking time-reversal symmetry, achieving non-reciprocal wave propagation and...[ Read more ]

Over the past two decades, acoustic metamaterials have demonstrated extraordinary wave manipulation capabilities, including negative refraction, cloaking, super-resolution imaging, and oneway topological propagation. Conventionally, most metamaterials are passive and require tailor-made designs to achieve these extraordinary capabilities. Once designed and fabricated, the resultant material properties are often locked into place with limited tunability. Furthermore, imposed by the constraints of passivity and reciprocity, losses inherent in resonating structures inevitably reduce the power efficiency. On the other hand, time-varying metamaterials have been recently proposed with exciting new possibilities in breaking time-reversal symmetry, achieving non-reciprocal wave propagation and controllable frequency conversion. However, conventional passive metamaterials may not offer the required real-time tunability, so most of the proposed non-reciprocal phenomena enabled by time-varying material parameters remain as theoretical proposals.

To realize time-varying metamaterials for more non-reciprocal phenomena and to solve the power efficiency issue, I develop an active metamaterial platform using virtualized metamaterials in this thesis. These metamaterials adopt digital feedback through external microcontrollers to achieve real-time tunable resonating responses through programmable digital convolution. Such an approach is feasible in air-borne acoustics in the kHz regime by using fast microcontrollers to complete digital convolution within one sampling period. Such an approach is also suitable for constructing active metamaterials by instructing an anti-Lorentzian resonance which exhibits gain around the resonating frequency while the system poles can still be maintained on the lower half of the complex frequency plane to ensure system stability. These constitute a general way to construct the so-called non- Hermitian metamaterials.

Using virtualized metamaterials with real-time tunability, we can investigate a series of extraordinary wave phenomena enabled by either gain, time-varying material parameters, or both. First, I achieved decoupled control of all the four constitutive parameters in a one-dimensional acoustic metamaterial, including the effective bulk modulus, density, and the two Willis coupling terms as an analogy of bianisotropy in electromagnetism. These parameters can be non-Hermitian, that is, passive or active, with arbitrary control of the resonating frequency, bandwidth and strength. The Willis coupling terms can be reciprocal or non-reciprocal and their values can go beyond the limits imposed by passive metamaterials. Second, these material parameters can be tuned in real-time. For example, the time-varying properties can be instructed at a modulation speed far faster than the signal frequency, enabling the first experimental realization of the concept of the temporal effective medium in acoustics.

Next, by combining non-Hermiticity with time-varying capability, I investigated a temporal modulation between gain and loss to obtain a unique phenomenon called unidirectional amplification. In one incident direction, the frequency conversion on the reflection signal was diminished while it was amplified in the opposite direction. Analogous to quantum interference, such an effect is enabled by the interference between different frequency conversion paths using a modulation phase delay between neighboring atoms. The exploration of this path interference also enables non-reciprocal frequency conversion.

Finally, I also investigated the extension of the virtualized metamaterial concept to two dimensions. Specifically, by enclosing a detector with an active metasurface shell, localized field amplification can be achieved within the shell without causing additional scattering outside the metasurface. Such localized amplification can be used for non-reciprocal communication and sensing. As a whole, the development of active and time-varying acoustic metamaterials in this thesis could further extend the horizon in designing future metamaterial devices, especially in applications about non-reciprocal sensing, isolation, signal modulation, multiplexing and demultiplexing. The development may also benefit further investigation of non-Hermitian topology in dynamic systems.