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A Christiansen filter realized with a cylindrical lens

A type of Christiansen filter that takes the form of a cylindrical lens is proposed. This kind of Christiansen filter has a pass band narrower than the traditional one, with more means of control of its performance; it could approximate arbitrary functions over a frequency range of interest. An inverse scattering theory for the synthesis of such a filter is developed and a systematic design technique is established. A desired, prescribed response can be tailored by properly configuring the lens of the filter. A Gaussian filter centered at 225 nm with a full width at half maximum of 1 nm is synthesized and is numerically modeled on a computer using the finite difference beam propagation method. The simulation results confirm the feasibility of the proposed Christiansen filter.