Response to 'Comment on 'Design of acoustic devices with isotropic material via conformal transformation'' [Appl. Phys. Lett. 100, 066101 (2012)]

摘要

Designing the meta-devices is an inverse problem, whose solutions could be non-unique. The transformation method just gives one possible solution. Equation (7) in this comment1 is generally correct. Equation (6) in our original letter~2 and Eq. (8) in this comment~1 are both special solutions to Eq. (7) (Ref. 1): ρ~'▽~' .(1/ρ~′▽~′ρ~′) +ω~2ρ~′/λ~′P′ = 0. This can be clarified as follows: Substituting Eq. (6)~,2 i.e., ρ~′ = ρο/|ζ~′(z)| and λ = λο|ζ~′(z)|, into Eq. (7) (Ref. 1) obtains wherez=x + iy is a point in the original configuration, which is transformed to another point denoted by ζ(z) = u{z) + iv(z). Since this is a conformal mapping, the Cauchy-Riemann condition should be satisfied.