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 wave number, 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 discuss their utility in making v(x) bidirectionally invisible at k(0) and demonstrate the application of our method to obtain antireflection and invisibility cloaks for a Bragg reflector.