Three-dimensional single-shell dielectric lens design using complex coordinates and local axis-displaced confocal quadrics
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Universidade Federal de Minas Gerais
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This study proposes an analytical formulation in complex coordinates to synthesise three-dimensional single-shell dielectric lens surfaces. An exact formulation based on geometrical optics is developed, and the synthesis problem is modelled as a non-linear second-order partial differential equation of the Monge–Ampère (MA) type. An alternative numerical scheme based on axis-displaced confocal quadrics is used to locally represent the surface of dielectric lens. The advantage of this approach is to analytically obtain the partial derivatives present in the MA equation. To validate the proposed methodology, numerical results are obtained by an iterative algorithm that allows the simultaneous control of the transmitted beam width and the power density amplitude in the far-field region. To illustrate the synthesis effectiveness, two examples of lens antennas are simulated and analysed.
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Lentes dielétricas, Síntese e Análise de Antenas, Óptica Geométrica, In recent years, several works have proposed the use of dielectric lenses to design antennas for microwave and millimetre wave applications. In these frequency ranges, conventional dielectric lenses can be designed to be small and low-weighted, increasing the set of lenses' advantages. These antennas are quite inexpensive, have good fabrication tolerances, wide-band capabilities, as well as very low dissipative losses. In this scenario, it is expected that proper modelling of dielectric lenses' surfaces may yield designs capable of assisting telecommunication services demanding higher data rates at increasingly higher frequencies., Teoria Eletromagnética Aplicada, Telecomunicações
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https://ietresearch.onlinelibrary.wiley.com/doi/10.1049/mia2.12365