Both explicit analysis and FEM numerical simulation are used to analyze the field distribution of a line current in the so-called Maxwell's fish eye lens [bounded with a perfectly electrical conductor (PEC) boundary]. We show that such a 2D Maxwell's fish eye lens cannot give perfect imaging due to the fact that high order modes of the object field can hardly reach the image point in Maxwell's fish eye lens. If only zeroth order mode is excited, a good image of a sharp object may be achieved in some cases, however, its spot-size is larger than the spot size of the initial object field. The image resolution is determined by the field spot size of the image corresponding to the zeroth order component of the object field. Our explicit analysis consists very well with the FEM results for a fish eye lens. Time-domain simulation is also given to verify our conclusion. Multi-point images for a single object point are also demonstrated.
2. Luneburg, R. K., Mathematical Theory of Optics, University of California Press, Berkeley, CA, 1964.
3. Born, M. and E.Wolf, Principles of Optics, 5 Ed., Pergamon, Oxford, 1975.
4. Leonhardt, U., "Perfect imaging without negative refraction," New J. Phys., Vol. 11, 093040-093051, 2009.
5. Leonhardt, U. and T. G. Philbin, "Perfect imaging with positive refraction in three dimensions," Phys. Rev. A, Vol. 81, 011804, 2010.
6. Erdélyi, A., W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, 1981.
7. Jackson, J. D., Classical Electrodynamics, 3 Ed., Wiley, New York, 1998.
8. Jacob, Z., L. V. Alekseyev, and E. Narimanov, "Optical hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express, Vol. 14, 8247-8256, 2006.
9. Blaikie, R. J., "Comment on `Perfect imaging without negative refraction'," New Journal of Physics, Vol. 12, 058001, 2010.
10. Leonhardt, U., "Reply to comment on `Perfect imaging without negative refraction'," New Journal of Physics, Vol. 12, 058002, 2010.