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arXiv 2103.01680physics.optics

线性锥形波导中的傅里叶光学:光捕获与聚焦

Fourier optics with linearly tapered waveguides: light trapping and focusing

Mahmoud A. Gaafar, Hagen Renner, Manfred Eich, Alexander Yu. Petrov

AI总结:

本文利用慢变包络近似研究线性锥形波导中的光捕获与聚焦,给出线性锥形和分段线性色散下的解析解,证明其聚焦光场空间分布等价于输入信号的傅里叶变换,揭示了锥形波导与傍轴光学透镜之间的对应关系。

摘要:

光脉冲在锥形波导中渐近地达到零群速度时,最终会在锥形区域的某一位置停止,并伴随强烈的空间压缩。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。第一种系统在锥形等离子体波导中广为人知,其中可以观察到光的绝热纳米聚焦。它在时空系统中的对应现象是光学推帚效应,其中非线性前沿收集并压缩信号。在这里,我们使用慢变包络近似来描述这类系统。我们展示了线性锥形和分段线性色散情况下的解析解,并证明这种情况下的解类似于傍轴近似下的光学透镜。特别是,聚焦光的空间分布代表了输入信号的傅里叶变换。

英文摘要:

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 be also observed in spatio-temporal 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 spatio-temporal 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.

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