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arXiv 0909.5305physics.optics
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无负折射的完美成像

Perfect imaging without negative refraction

Ulf Leonhardt

摘要:

完美的成像一直被认为依赖于负折射,但在这里,我们表明,一个普通的正折射光学介质也可以形成完美的图像。特别是,我们建立了一个数学证明,麦克斯韦的鱼眼在二维集成光学,使一个完美的仪器,分辨率不受光波长的限制。我们还展示了如何修改鱼眼,使完美的成像设备可以在实践中。我们的完美聚焦方法也可以在光学之外的领域,如声学、流体力学或量子物理学中找到应用,只要波服从二维亥姆霍兹方程。

英文摘要:

Perfect imaging has been believed to rely on negative refraction, but here we show that an ordinary positively-refracting optical medium may form perfect images as well. In particular, we establish a mathematical proof that Maxwell's fish eye in two-dimensional integrated optics makes a perfect instrument with a resolution not limited by the wavelength of light. We also show how to modify the fish eye such that perfect imaging devices can be made in practice. Our method of perfect focusing may also find applications outside of optics, in acoustics, fluid mechanics or quantum physics, wherever waves obey the two-dimensional Helmholtz equation.

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