Department of MathematicsDepartment of Physics2024-11-0920141050-294710.1103/PhysRevA.90.0558032-s2.0-84914811644https://hdl.handle.net/20.500.14288/415In [Phys. Rev. A 90, 023833 (2014)], we offer a solution to the problem of constructing a scattering potential v(x) which possesses scattering properties of one's choice at an arbitrarily prescribed wave number. This solution involves expressing v(x) as the sum of n <= 6 finite-range unidirectionally invisible potentials. We improve this result by reducing the upper bound on n from 6 to 4. In particular, we show that we can construct v(x) as the sum of up to n = 3 finite-range unidirectionally invisible potentials, unless if it is required to be bidirectionally reflectionless.pdfOpticsPhysicsJournal Article1094-1622https://doi.org/10.1103/PhysRevA.90.055803349462100014N/ANOIR00288