Fourier optics with linearly tapered waveguides: Light trapping and focusing

An optical pulse asymptotically reaching zero group velocity in tapered waveguides can ultimately stop at a certain position the taper accompanied by strong spatial compression. This phenomenon also be observed spatiotemporal systems where reaches of front. The first system is well known from plasmonic adiabatic nano-focusing light observed. Its counterpart push broom effect nonlinear front collects and compresses signal. Here, we use slowly varying envelope approximation to describe such systems. We demonstrate an analytical solution for linear piecewise dispersion show that this case resembles lens paraxial approximation. In particular, distribution focused represents Fourier transform signal input.