Temporal filtering with time lenses

Abstract

We propose to use optics for ultrafast serial processing by employing the well known analogy between optical spatial diffraction and temporal dispersion. The essence of this analogy can be stated briefly like this: The temporal frequency corresponds to the spatial frequency in the lateral direction, and the time t corresponds to the lateral coordinate x. In this project, passing through a dispersive delay line is the analog of free space propagation and the action of a spatial lens is mimicked by a time lens, which multiplies the incoming signal by a chirp. The suggested "temporal filtering" system contains two 2-f configurations in cascade. Both of them perform a temporal Fourier transform. Thus the total configuration is equivalent to the well known 4-f spatial processor, and most of its uses, such as spatial correlation and convolution, can be also implemented in the time domain with the temporal filtering system. Each 2-f system consists of three subsystems in cascade: free space propagation, transfer through the lens, and again free space propagation. Accordingly, we let our temporal signal travel over a distance f, then let it interact with the time lens, and finally propogate it over another length f. By using typical parameters for the dispersive medium and the time lenses several systems were designed and computer simulated, such as 4-f correlator, joint transform correlator, and derivator.