20 August 2009 Field method for concentrator design
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Abstract
We study the analogy between the geometrical vector flux, the light vector introduced by A. Gershun and Pharosage vector introduced by P. Moon. From this analogy we present a treatment of the design of concentrators in terms of field theory. We study first the symmetry of concentrators in different coordinate systems. In particular, we study concentrators in elliptical cylindrical coordinates as asymmetric concentrators linking rotational and translational concentrators. Following that symmetry we study the light field produced by an elliptical disk, and we show that onesheet hyperboloids behave as ideal 3D asymmetric concentrators. This result can be generalized to orthogonal surfaces by using field theory. Finally, we find higher order field lines by the study of the light field produced by a 2-D truncated wedge, which can be used to define a new higher order concentrator, the Hyperparabolic Concentrator (HPC). This concentrator has the profile of a hyperbola continuously joined with a tilted parabola. In the limit of infinite focal length of the hyperbola, the 3D HPC reaches the thermodynamic limit of concentration.
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Angel Garcia-Botella, Angel Garcia-Botella, Antonio A. Fernandez-Balbuena, Antonio A. Fernandez-Balbuena, Daniel Vázquez-Moliní, Daniel Vázquez-Moliní, Eusebio Bernabeu, Eusebio Bernabeu, Agustin Gonzalez-Cano, Agustin Gonzalez-Cano, } "Field method for concentrator design", Proc. SPIE 7423, Nonimaging Optics: Efficient Design for Illumination and Solar Concentration VI, 742307 (20 August 2009); doi: 10.1117/12.825989; https://doi.org/10.1117/12.825989
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