Active Invisibility Cloaks in One Dimension

We outline a general method of constructing finite-range cloaking potentials which render a given finite-range real or complex potential $v(x)$ unidirectionally reflectionless or invisible at a wavenumber $k_0$ of our choice. We give explicit analytic expressions for three classes of cloaking potentials which achieve this goal while preserving some or all of the other scattering properties of $v(x)$. The cloaking potentials we construct are the sum of up to three constituent unidirectionally invisible potentials. We also discuss their application in making $v(x)$ bidirectionally invisible at $k_0$, and demonstrate the application of our method to obtain anti-reflection and invisibility cloaks for a Bragg reflector.