Abstract
We apply the transformation optical technique to modify or improve conventional refractive and gradient index optical imaging devices. In particular, when it is known that a detector will terminate the paths of rays over some surface, more freedom is available in the transformation approach, since the wave behavior over a large portion of the domain becomes unimportant. For the analyzed configurations, quasi-conformal and conformal coordinate transformations can be used, leading to simplified constitutive parameter distributions that, in some cases, can be realized with isotropic index; index-only media can be low-loss and have broad bandwidth. We apply a coordinate transformation to flatten a Maxwell fish-eye lens, forming a near-perfect relay lens; and also flatten the focal surface associated with a conventional refractive lens, such that the system exhibits an ultra-wide field-of-view with reduced aberration.
Highlights
Transformation optics (TO) is a recently appreciated design approach for electromagnetic and optical materials [1]
If a solution to the wave equation is found using a particular coordinate system, a coordinate transformation cannot change this underlying wave solution; if the wave solution is expressed in a different set of coordinates and plotted in the new coordinate system, it will appear identical to the original field distribution
We show that the TO methodology allows an intuitive design procedure that holds the potential for greatly improved imaging systems
Summary
Transformation optics (TO) is a recently appreciated design approach for electromagnetic and optical materials [1]. An arbitrary coordinate transformation typically results in a medium that is anisotropic and with both permittivity and permeability tensor elements that vary independently throughout space. Such media are akin to gradient index (GRIN) media, though considerably more demanding. An important type of optimization was introduced by Li and Pendry [16], who suggested the use of a numerical scheme to achieve quasi-conformal transformations These numerical methods seek transformations that minimize the anisotropy of the constitutive tensors and, at least in two-dimensional geometries, can produce index-only TO designs that have small absorption and broad bandwidth. In this paper we describe the QCTO approach and apply it to reduce the anisotropy associated with the configurations considered
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