Cloaking of the momentum in acoustic waves

A Unified Approach to Nonlinear Transformation Materials

The advances in geometric approaches to optical devices due to transformation optics has led to the development of cloaks, concentrators, and other devices. It has also been shown that transformation optics can be used to gravitational fields from general relativity. However, the technique is currently constrained to linear devices, as a consistent approach to nonlinearity (including both the case of a nonlinear background medium and a nonlinear transformation) remains an open question. Here we show that nonlinearity can be incorporated into transformation optics in a consistent way. We use this to illustrate a number of novel effects, including cloaking an optical soliton, modeling nonlinear solutions to Einstein’s field equations, controlling transport in a Debye solid, and developing a set of constitutive to relations for relativistic cloaks in arbitrary nonlinear backgrounds.

Detecting Thermal Cloaks via Transient Effects

Recent research on the development of a thermal cloak has concentrated on engineering an inhomogeneous thermal conductivity and an approximate, homogeneous volumetric heat capacity. While the perfect cloak of inhomogeneous κ and inhomogeneous ρc_p is known to be exact (no signals scattering and only mean values penetrating to the cloak’s interior), the sensitivity of diffusive cloaks to defects and approximations has not been analyzed. We analytically demonstrate that these approximate cloaks are detectable. Although they work as perfect cloaks in the steady-state, their transient (time-dependent) response is imperfect and a small amount of heat is scattered. This is sufficient to determine the presence of a cloak and any heat source it contains, but the material composition hidden within the cloak is not detectable in practice. To demonstrate the feasibility of this technique, we constructed a cloak with similar approximation and directly detected its presence using these transient temperature deviations outside the cloak. Due to limitations in the range of experimentally accessible volumetric specific heats, our detection scheme should allow us to find any realizable cloak, assuming a sufficiently large temperature difference.

Cloaking a sensor via transformation optics

Ideal transformation optics cloaking at positive frequency, besides rendering the cloaked region invisible to detection by scattering of incident waves, also shields the region from those same waves. In contrast, we demonstrate that approximate cloaking permits a strong coupling between the cloaked and uncloaked regions; careful choice of parameters allows this coupling to be amplified, leading to effective cloaks with degraded shielding. The sensor modes we describe are close to but distinct from interior resonances, which destroy cloaking. As one application, we describe how to use transformation optics to hide sensors in the cloaked region and yet enable the sensors to efficiently measure incident waves on the exterior of the cloak, an effect similar to the plasmon-based approach of Alù and Engheta.