Publication details

The Lissajous Lens: A Three-Dimensional Absolute Optical Instrument without Spherical Symmetry

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DANNER Aaron James DAO H. L. TYC Tomáš

Year of publication 2015
Type Article in Periodical
Magazine / Source Optics Express
MU Faculty or unit

Faculty of Science

Field Optics, masers and lasers
Keywords absolute optical instrument; perfect imaging; Lissajous curves; geodesics
Description We propose a three dimensional optical instrument with an isotropic gradient index in which all ray trajectories form Lissajous curves. The lens represents the first absolute optical instrument discovered to exist without spherical symmetry (other than trivial cases such as the plane mirror or conformal maps of spherically-symmetric lenses). An important property of this lens is that a three-dimensional region of space can be imaged stigmatically with no aberrations, with a point and its image not necessarily lying on a straight line with the lens center as in all other absolute optical instruments. In addition, rays in the Lissajous lens are not confined to planes. The lens can optionally be designed such that no rays except those along coordinate axes form closed trajectories, and conformal maps of the Lissajous lens form a rich new class of optical instruments.
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