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Focusing performance of Fibonacci tiling-based zone plates.

Adrián Garmendía-Martínez1, Francisco M Muñoz Pérez1, Juan C Castro Palacio1

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|February 25, 2026
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Summary
This summary is machine-generated.

We introduce Fibonacci Tiling-Based Zone Plates (FTZPs), a novel optical element with a quasiperiodic pattern of transparent and opaque rectangles. These FTZPs offer unique diffraction properties for advanced optical applications.

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Area of Science:

  • Optics and Photonics
  • Diffraction Optics
  • Quasiperiodic Structures

Background:

  • Conventional Fibonacci zone plates utilize concentric rings for optical manipulation.
  • Quasiperiodic structures offer unique wave-front shaping capabilities.
  • Binary arrays can define complex transmittance functions.

Purpose of the Study:

  • To introduce and characterize Fibonacci Tiling-Based Zone Plates (FTZPs).
  • To explore the optical properties of FTZPs for diffraction-based applications.
  • To investigate the performance of FTZPs through simulation and experimentation.

Main Methods:

  • Generation of a Fibonacci binary array using complementary substitution rules.
  • Defining a transmittance function based on the quasiperiodic array.
  • Numerical simulations to analyze intensity distribution and diffraction patterns.
  • Experimental measurements to validate simulation results.

Main Results:

  • FTZPs exhibit a unique pattern of transparent and opaque rectangles, unlike conventional ring-based zone plates.
  • The quasiperiodic structure influences the diffraction characteristics.
  • Simulations and experiments confirm the predicted intensity distributions and diffraction patterns.

Conclusions:

  • FTZPs represent a novel class of optical elements with distinct diffraction properties.
  • The rectangular, quasiperiodic design offers advantages for specific diffraction applications.
  • Further research can explore advanced applications of FTZP technology.