Invisibility cloaking via non-smooth transformation optics and ray tracing

Asymptotics of near-cloaking

“…α n i n (2n + 1) h (1) n (k 0 r) P n (cos θ) , r > b (17) and (1) n (k sh (r − a)) P n (cos θ) , a < r < b,…”

“…where we have used h (1) ν and h (2) ν instead of j ν , and we wish to study this integral in the independent but simultaneous limits K → ∞ and k 0 r → ∞. Following Nussenzveig [16], the first term (involving h (2) ν (k 0 r)) does not contribute at all at leading order and what remains is to obtain appropriate estimates of the second term, which is given by the approximate integral representation…”

“…). This allows standard asymptotic results to be quoted and used without any modifications being necessary to account for the half-integer that would otherwise have been present in the order (it is very tempting, for example, to say that h (1,2) μ (z) as μ → ∞, but doing so will in general lead to the omission of O(1) contributions to the phases of some terms within our integrand, especially when Debye-type limits are being taken).…”

“…A widely studied (Cummer et al [3], Greenleaf et al [6]) non-dimensional model for cloaking a sphere of radius a insonified by plane acoustic waves is (r − a) 2 ∂ 2 p ∂r 2 + 2 (r − a)…”

Evaluation and design of a large-scale cloaking device by the Hamiltonian-based ray-tracing method Part I: full-mesh representation

“…So far various cloaking devices with not only regular shapes such as sphere, cylinder, and cone [10,11] but also arbitrary shapes [12][13][14][15][16] have been designed. For ideal cases, the cloaking effects are verified based on full-wave simulations.…”