Abstract
We propose a novel design method for multi-focal metallic Fresnel zone plates (MFZPs), which exploits the phase selection rule by putting virtual point sources (VPSs) at the desired focal points distant to the MFZP plane. The phase distribution at the MFZP plane reciprocally formed by the VPSs was quantized in a binary manner based on the phase selection rule, thereby leading to a corresponding on-off amplitude pattern for the targeted MFZP. The resultant phase distribution was dependent on the complex amplitudes of the VPSs, so that they could be determined from the perspective of both multi-focal functionality and fabrication feasibility. As a typical example, we utilized the particle swarm optimization algorithm to determine them. Based on the proposed method, we designed and numerically analyzed two types of novel MFZPs—one for a monochromatic multi-focal application and the other for a multi-chromatic mono-focal application—verifying the effectiveness and validity of the proposed method. We also fabricated them onto Au-deposited glass substrates, using electron beam evaporation and a focused ion beam milling process. We experimentally characterized them and also verified that they successfully demonstrated their feasibilities. The former produced distinct hot spots at three different focal distances of 10, 15, and 20 μ m for monochromatic incidence at 650 nm, and the latter produced a single hot spot at a focal distance of 15 μ m for multi-chromatic incidence at 660, 532, and 473 nm. The experimental results were also in good agreement with their corresponding numerical results. We expect that both MFZPs will have various applications, such as laser micromachining, optical trapping, biomedical sensing, confocal collimation, achromatic optics, etc.
Highlights
Fresnel zone plates (FZPs) or metallic Fresnel zone plates (MFZPs) have received considerable attention in recent years as an efficient focusing element for flat optical applications [1,2,3,4,5]
There have been very few attempts to investigate a systematic design method for multi-focal MFZPs even though such a method could have a huge impact on improvements in laser micro-machining, optical trapping, chemical sensing, biomedical sensing, confocal collimation, achromatic optics, etc. [14,15,16,17,18,19,20,21]
Considering that the quantized amplitude pattern manner based on the so-called phase selection rule (PSR), subsequently making the 0 and π regions can considerably vary in a binary manner based on the PSR, given the choice of the complex open and closed, the resultant pattern of the annular slits is the same as specified by Equation (1) for amplitudes of the virtual point sources (VPSs), i.e., their intensity levels and initial phase-offset values, it is necessary to a mono-focal MFZP
Summary
Fresnel zone plates (FZPs) or metallic Fresnel zone plates (MFZPs) have received considerable attention in recent years as an efficient focusing element for flat optical applications [1,2,3,4,5]. MFZPs for multi-focal applications have recently received considerable attention These studies have exploited various authentic mathematical formulae as generating functions for the metallic annular slit structure, such as Fibonacci, fractal, and cantor series [11,12,13]. A more intricate way to realize a multi-focal MFZP is to exploit a pixelated phase pattern on the substrate via dielectric material deposition [26], such that all the combined diffractions eventually form multi-focal spots at different depths Such a highly pixelated phase pattern generally requires a complicated fabrication process, such as plasma-enhanced chemical deposition. We fabricated them and verified their novel characteristics both numerically and experimentally
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