Abstract
The problem of inverse design is rooted to the classical problem of inverse scattering. In general, these highly nonlinear and often ill-posed problems are solved via extensive optimization techniques. In this paper, we suggest an optimization-free method for the inverse design of a one-dimensional medium with spatially inhomogeneous dielectric constant $ϵ(z)$. In addition, we derive the governing equation of an analog problem---a time-dependent homogeneous medium---and use the same technique for inverse design of the temporal profile $ϵ(t)$ of a spatially homogeneous medium that is required to achieve a desired frequency response in $k$-space. Lastly, we use this optimization-free inversion approach to demonstrate the design of the reflection response such that the reflected wave undergoes a desired filtering, such as of Tchebychev type, differentiator, and a matched filter for chirp signal detection over additive Gaussian noise, which is of high potential significance in chirp radar and sonar applications.
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