Diffractive m-bonacci lenses

Abstract

Fibonacci zone plates are proving to be promising candidates in image forming devices. In this letter we show that the set of Fibonacci zone plates are a particular member of a new family of diffractive lenses which can be designed on the basis of a given m-bonacci sequence. These lenses produce twin axial foci whose separation depends on the m-golden mean. Therefore, with this generalization, bifocal systems can be freely designed under the requirement at particular focal planes. Experimental results support our proposal.

Design of Binary-Sequence Zone Plates in High Wavelength Domains

“…As shown in [ 8 ], Fibonacci binary sequences produce ZPs with two-foci focusing profiles, while Fractal binary sequences based on the Cantor set result in multi-foci focusing profiles, which can be used to minimize chromatic aberration [ 9 ]. Other binary sequences with additional properties can also be used for building ZPs with different focusing profiles [ 10 , 11 ]. Table 1 shows three binary sequences that result in ZPs of different natures; here, N states for the length of the sequence.…”

“…Table 1 shows three binary sequences that result in ZPs of different natures; here, N states for the length of the sequence. The procedure to obtain the binary sequences for these ZPs can be found in [ 8 , 11 ].…”

“…However, conventional FZPs are severely limited in their focusing profile flexibility. Recently, new types of Zone Plates (ZPs) employing a Binary-Sequence Method (BSM) have been proposed [ 8 , 9 , 10 , 11 ]. Among the different lenses that can be implemented using this method, Fibonacci ZPs [ 8 ], which allow two-foci focusing profiles, and Cantor ZPs [ 9 ], which produce multiple foci reproducing the self-similarity of the ZP, should be highlighted.…”

Bifocal Ultrasound Focusing Using Bi-Fresnel Zone Plate Lenses

“…In [23], J. Kim et al presented a method to achieve multifocal focusing profiles based on the phase conjugation principle and the phase-opposition blocking criterion used in conventional FZPs. Recently, novel lenses based on traditional FZPs have been introduced in optics [ [24][25][26][27] and later demonstrated in acoustics [28][29][30], which increases the versatility of these devices.…”

Fibonacci terahertz imaging by silicon diffractive optics

“…To conclude, the silicon-based Fibonacci (bifocal) diffractive zone plate for 0.6 THz frequency has been developed, and its employment for bifocal THz imaging with the wavelength resolution was demonstrated. It not only enriched a family bifocal focusing elements like bifocal zoom lenses using plasmonic metasurfaces [18], fractal zone planes with reduced aberration in visible range [19], plates based on generalized m-bonacci sequence [20], but also extended routes to manipulate with THz beam [21] in continuous wave mode using diffractive optics components providing thus an additional tool for further development of compact and alignment-free THz imaging systems.…”