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

中文翻译：

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具有线性锥形波导的傅立叶光学器件：光捕获和聚焦

在锥形波导中渐近达到零群速度的光脉冲最终会停在锥形的某个位置，并伴随着强烈的空间压缩。这种现象也可以在时空系统中观察到，其中脉冲速度渐近地达到锥形前沿的速度。第一个系统是众所周知的锥形等离子体波导，其中观察到光的绝热纳米聚焦。它在时空系统中的对应物是光学推扫效应，其中非线性前沿收集并压缩信号。在这里，我们使用缓慢变化的包络近似来描述这样的系统。我们展示了线性锥度和分段线性色散的解析解，并表明这种情况下的解类似于近轴近似中的光学透镜的解。