Perfect imaging without negative refraction

Ulf Leonhardt

Research output: Contribution to journalArticlepeer-review

181 Citations (Scopus)


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 (2D) 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 2D Helmholtz equation.

Original languageEnglish
Article number093040
Number of pages13
JournalNew Journal of Physics
Publication statusPublished - 29 Sept 2009


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