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Modeling and simulations of a nonlinear granular metamaterial: application to geometric phase-based mass sensing
Abstract Dynamical simulations of an externally harmonically driven model granular metamaterial composed of four linearly and nonlinearly coupled granules show that the nonlinear normal mode can be expressed in a linear normal mode orthonormal basis with time dependent complex coefficients. These coefficients form the components of a state vector that spans a 2 2 dimensional Hilbert space parametrically with time. Local π jumps in the phase of these components occurring periodically are indicative of topological features in the manifold spanned by the geometric phase of the vibrational state of the metamaterial. We demonstrate that these topological features can be exploited to realize high sensitivity mass sensor. The effect of dissipation on sensitivity is also reported. Nonlinear granular metamaterials with very low dissipation could serve as mass sensors with considerable sensitivity to small mass changes via large changes in geometric phase.
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Award ID(s):
Publication Date:
NSF-PAR ID:
10354800
Journal Name:
Modelling and Simulation in Materials Science and Engineering
Volume:
30
Issue:
7
Page Range or eLocation-ID:
074002
ISSN:
0965-0393
3. Recently, our groups have introduced the notion of optical parametric amplification based on non-Hermitian phase matching wherein the incorporation of loss can lead to gain in this nonlinear optical process. Previous simulation results using second-order nonlinear optical coupled-mode theory have demonstrated the potential of this technique as an alternative to the stringent phase-matching condition, which is often difficult to achieve in semiconductor platforms. Here we fortify this notion for the case of third-order nonlinearity by considering parametric amplification in silicon nanowires and illustrate the feasibility of these devices by employing rigorous finite-difference time-domain analysis using realistic materials and geometric parameters. Particularly, we demonstrate that by systematic control of the optical loss of the idler in a four-wave mixing process, we can achieve efficient unidirectional energy conversion from the pump to the signal component even when the typical phase-matching condition is violated. Importantly, our simulations show that a signal gain of$∼<#comment/>9dB$for a waveguide length of a few millimeters is possible over a large bandwidth of several hundreds of nanometers ($∼<#comment/>600nm$). This bandwidth is nearly 2 orders of magnitude larger than what can be achieved in the conventionalmore »