THESIS
2022
1 online resource (xx, 128 pages) : illustrations (chiefly color)
Abstract
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...[
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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.
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