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. 2024 Jun 20;14(1):14249.
doi: 10.1038/s41598-024-64800-3.

Bifocal diffractive lenses based on the aperiodic Kolakoski sequence

Adrián Garmendía-Martínez  1 , Francisco M Muñoz-Pérez  1   2 , Walter D Furlan  2 , Vicente Ferrando  1 , Juan A Monsoriu  3
Affiliations

Bifocal diffractive lenses based on the aperiodic Kolakoski sequence

Adrián Garmendía-Martínez et al. Sci Rep. .

Abstract

In this work, we present a new family of Zone Plates (ZPs) designed using the self-generating Kolakoski sequence. The focusing and imaging properties of these aperiodic diffractive lenses coined Kolakoski Zone Plates (KZPs) are extensively studied. It is shown that under monochromatic plane-wave illumination, a KZP produces two main foci of the same intensity along the axial axis. Moreover, one of the corresponding focal lengths is double the other, property correlated with the involved aperiodic sequence. This distinctive optical characteristic is experimentally confirmed. We have also obtained the first images provided by these bifocal new diffractive lenses.

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Conflict of interest statement

The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

Figures

Figure 1
Figure 1
Length LS of the Kolakoski sequence of order S (red points). The result of the linear-logarithmic fit is also included in the figure (blue line).
Figure 2
Figure 2
Ratio between the lengths of two consecutive Kolakoski sequences, LS/LS-1.
Figure 3
Figure 3
Phase transmission function ϕS(ζ) of the KZP of order S=7. The associated Kolakoski sequence is K7={1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1}. Note that the phase function takes values π or 2π (phase 0) at the j-th sub-intervals of K7 where K7,j is “1” or “2”, respectively.
Figure 4
Figure 4
Kolakoski diffractive lens generated from the 1-D function ϕ7(ζ). Gray and white rings correspond to a phase π and 0, respectively.
Figure 5
Figure 5
Numerically computed normalized axial irradiances produced by KZPs of orders S = 7, 8, and 9.
Figure 6
Figure 6
Comparison between the axial irradiances distributions produced by Kolakoski, Fibonacci, Tribonacci and a periodic ZPs.
Figure 7
Figure 7
Scheme of the experimental setup used to evaluate (a) the focusing and (b) imaging properties of the KZP.
Figure 8
Figure 8
Theoretical and experimental axial irradiance profiles of the Kolakoski lens of order S=8. Both of these distributions are normalized with respect to the maximum intensity..
Figure 9
Figure 9
Evolution of the transverse intensity distribution produced by a KZP of order 8.
Figure 10
Figure 10
Images provided by a KZP of order 8 at its corresponding focal lengths.
See this image and copyright information in PMC

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