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6 January 2015Focusing properties of diffractive lenses constructed with the aperiodic m-bonacci sequence
In this contribution we present a new family of diffractive lenses which are designed using the m-bonacci sequence.
These lenses are a generalization of the Fibonacci Zone Plates previously reported. Diffractive elements of this type are
called aperiodic zone plates because they are characterized by a radial profile that follows a given deterministic aperiodic
sequence (Cantor set, Thue-Morse, Fibonacci...). Aperiodic lenses have demonstrated new interesting focusing and
imaging properties that have found applications in different fields such as soft X-ray microscopy and spectral domain
optical coherence tomography. Here, we show that m-bonacci zone plates are inherently bifocal lenses. We demonstrate
that the relative separation of their foci depends on the m-value of the sequence and also can be correlated with the
generalized golden ratio. As a particular case, the properties of the m-bonacci sequence with m=2 and m=3, called
Fibonacci and Tribonacci Zone Plates respectively are discussed.
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Walter D. Furlan, Vicente Ferrando, Juan A. Monsoriu, "Focusing properties of diffractive lenses constructed with the aperiodic m-bonacci sequence," Proc. SPIE 9450, Photonics, Devices, and Systems VI, 945014 (6 January 2015); https://doi.org/10.1117/12.2070434