An Investigation of Influencing Factors on Practical

nanomaterials Article

An Investigation of Influencing Factors on Practical Sub-Diffraction-Limit Focusing of Planar Super-Oscillation Lenses Yiting Yu 1,2, *, Wenli Li 1,2 , Haoyong Li 1,2 , Muyuan Li 1,2 and Weizheng Yuan 1,2 1

2

*

Key Laboratory of Micro/Nano Systems for Aerospace, Ministry of Education, Xi’an 710072, China; [email protected] (W.L.); [email protected] (H.L.); [email protected] (M.L.); [email protected] (W.Y.) Key Laboratory of Micro- and Nano-Electro-Mechanical Systems of Shaanxi Province, Northwestern Polytechnical University, Xi’an 710072, China Correspondence: [email protected]; Tel.: +86-29-8846-0353 (ext. 617)

Received: 31 January 2018; Accepted: 21 March 2018; Published: 22 March 2018

Abstract: Planar super-oscillation lenses (SOLs) can fulfill super-resolution focusing and nanoscopic imaging in the far field without the contribution of evanescent waves. Nevertheless, the existing deviations between the design and experimental results have been seldomly investigated, leaving the practical applications of SOLs unpredictable and uncontrollable. In this paper, some application-oriented issues are taken into consideration, such as the inevitable fabrication errors and the size effect of the designed SOLs, with the aim of providing an engineering reference to elaborately customize the demanded focusing light field. It turned out that a thicker structural film makes the focal spots enlarged, while the sloped sidewalls just weaken the intensity of the focal hotspot. Furthermore, the focal lengths are diminished with the decrease of device size, while the focal spots are enlarged. This research will promote the wide-spread applications of SOLs for sub-diffraction-limit far-field focusing in the areas of nanoscopy and high-density optical storage. Keywords: super-oscillation lenses; focusing; sub-diffraction-limit; influencing factors

1. Introduction Optical lenses play an absolutely indispensable role in the optics-related industry, in which their focusing properties are of vital importance for the imaging quality and accuracy of the post-processing data. The resolving power of traditional optical lenses is subjected to the physical limit due to the loss of the spatial high-frequency Fourier components in the far field, which is the famous Rayleigh diffraction limit, defined as 0.61λ/NA (λ being the working wavelength, and NA being the numerical aperture of the lens) [1]. To solve this problem, scientists have made great efforts in the past decades. They have tried to take advantage of the manipulation of the surface plasmons of evanescent waves to realize super-resolution in the near field, such as the near-field scanning optical microscope [2] (NSOM), superlens [3], and plasmonic lens [4,5], mainly for the applications of super-resolution imaging [6,7] and nanolithography [8,9]. However, the evanescent waves attenuate exponentially due to the energy loss in the medium and cannot propagate to the far field or even the quasi-far field, imposing a fatal restriction for practical purposes. Our recent research on utilizing the polarization state of incident light to achieve the superfocusing capability in the quasi-far field may provide a feasible solution [10, 11]. On the other hand, the optical super-oscillation phenomenon is the delicate interference of the far-field propagating waves, and it can be engineered to achieve a sub-diffarction-limit-focusing hotspot without the contribution of evanescent waves [12,13]. Besides, the experimental results are obtained in the far field from the output surface of super-oscillation lenses (SOLs) [14–16]. Currently, Nanomaterials 2018, 8, 185; doi:10.3390/nano8040185

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Nanomaterials 2018, 8, 185

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SOLs have found various uses in super-resolution imaging [17–19], high-density optical storage [20], Nanomaterials 2018, 8, x FOR PEER REVIEW 2 of 12 and biomedicine [21]. Note that the high-quality fabrication of nanoscale devices still remains a worldwide challenge, (SOLs) [14–16]. Currently, SOLs have found various uses in super-resolution imaging [17–19], highand the fabrication imperfections more or less work on the performance of the micro/nano devices. density optical storage [20], and biomedicine [21]. Furthermore, it has been a common phenomenon that the experimental results do not always come Note that the high-quality fabrication of nanoscale devices still remains a worldwide challenge, out the same as the theoretical ones; we just summarize the deviation between the theoretical results and the fabrication imperfections more or less work on the performance of the micro/nano devices. and the measured itones recent phenomenon publications that [22–29], as shown inresults Figuredo 1. not What we can clearly Furthermore, has from been athe common the experimental always come observe 1 is most ofones; the deviation is abovethe 6%, while the relatively high deviation outin theFigure same as thethat theoretical we just summarize deviation between the theoretical results may impose certain restriction on the application[22–29], of the as devices. the literature anda the measured ones from thepractical recent publications shown Meanwhile, in Figure 1. What we can on clearly observe in Figure 1generated is that most of focused the deviation is above 6%, while such the relatively high the fabrication imperfections from ion beam (FIB) milling as the slot width deviation may impose a certain restriction on the practical application of the devices. Meanwhile, the error [30], the surface roughness error [9,31], and the sloped sidewalls [32–34], will be discussed. literature on the fabrication imperfections fromprecise focused customization ion beam (FIB) milling as thelight To provide some valuable practical advice generated for the more of the such required slot width error [30], the surface roughness error [9,31], and the sloped sidewalls [32–34], will be contours, three planar SOLs with distinct focal lengths are designed and fabricated to investigate the discussed. To provide some valuable practical advice for the more precise customization of the far-field focusing properties. It is noteworthy that we employ a multi-objective and multi-constraint required light contours, three planar SOLs with distinct focal lengths are designed and fabricated to optimization model to fulfill the sub-diffraction-limit light patterns through the vectorial and angular investigate the far-field focusing properties. It is noteworthy that we employ a multi-objective spectrum (VAS) theory. To rapidly acquire a precise control over the light field farthrough away from multi-constraint optimization model to fulfill the sub-diffraction-limit light patterns the the lens surface, fast spectrum Hankel transformation also applied, and thecontrol method reported vectorial the angular (VAS) theory. To is rapidly acquire a precise overhas the been light field far in our previous research consequence, both the simulated and and measured focalhas sizes, away from the lens[35,36]. surface, As the afast Hankel transformation is also applied, the method beenalong reported in our previous As a consequence, both the simulated and measured focalfrom with the theoretical ones, allresearch beat the[35,36]. calculated Rayleigh diffraction limit. More significantly, sizes, alongofwith the theoretical ones,we allmainly beat the calculated Rayleighondiffraction limit. More the perspective practical application, place an emphasis the application-oriented the perspective of practical application, mainly place an emphasis on the issuessignificantly, such as the from fabrication imperfections and size effect. To we investigate the detailed error-tolerances application-oriented issues such as the fabrication imperfections and size effect. To investigate the generated from the fabrication imperfections of the SOLs, the specific error sources such as the structual detailed error-tolerances generated from the fabrication imperfections of the SOLs, the specific error layer thickness and the sloped sidewalls are investigated, and the fabrication errors are all characterized sources such as the structual layer thickness and the sloped sidewalls are investigated, and the through the Atomic Force Microscopy (AFM). Furthermore, corresponding simulations are finished fabrication errors are all characterized through the Atomicthe Force Microscopy (AFM). Furthermore, to acquire a quantitative analysis of the fabrication imperfections. The results tell us that the slot width the corresponding simulations are finished to acquire a quantitative analysis of the fabrication and surface roughness exhibit little influence on the focusing performance, but the film thickness imperfections. The results tell us that the slot width and surface roughness exhibit little influence on and sloped sidewalls seem tobut influence the focusing properties of SOLs. Moreover, the focusing performance, the filmgreatly thickness and sloped sidewalls seem to influence greatlythrough the focusing properties Moreover, through exploring and the size effect, we find out that the exploring the size effect,of weSOLs. find out that both the simulated measured focal lengths areboth diminished simulated and measured focal lengths are diminished with the decrease of device size, while the fullwith the decrease of device size, while the full-width at half-maximum (FWHM) of the foci is enlarged. width at half-maximum (FWHM) of the foci enlarged. studies The conclusions in accordance with provide our The conclusions are in accordance with ourisprevious [37,38].are This research will previous studies [37,38]. This research will provide an indispensable technological reference for the an indispensable technological reference for the design of the planar SOLs, which may find their design of the planar SOLs, which may find their promising applications during the integration into promising applications during the integration into compact and cost-effective optical systems. compact and cost-effective optical systems.

Figure 1. The deviation of the focusing properties of SOLs in recent publications.

Figure 1. The deviation of the focusing properties of SOLs in recent publications. 2. Design and Experimental Preparations

2. Design and Experimental Preparations

The focusing behavior of planar SOLs can be ascribed to the delicate interference of diffracted

beams in the light field of by planar the specifically designed structural and interference the schematicofofdiffracted subThe focusing behavior SOLs can be ascribed to themask, delicate diffraction-limit seen in Figure 2. The structural specific optimization process has been of beams in the light focusing field bycan thebespecifically designed mask, and the schematic


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Nanomaterials 2018, focusing 8, x FOR PEERcan REVIEW 3 of has 12 been sub-diffraction-limit be seen in Figure 2. The specific optimization process implemented through a multi-objective and multi-constraint genetic algorithm (GA) based on the VAS implemented through a multi-objective and multi-constraint genetic algorithm (GA) based on the theory. The fast Hankel transformation is applied to accelerate the computational processes, and the VAS theory. The fast Hankel transformation is applied to accelerate the computational processes, and whole algorithm has beenhas elaboratedly depicted in our recent research the whole algorithm been elaboratedly depicted in our recent research[35,36]. [35,36].

Figure 2. Schematic illustration of sub-diffraction-limit focusing by a planar super-oscillatory lens

Figure 2. Schematic illustration of sub-diffraction-limit focusing by a planar super-oscillatory (SOLs). lens (SOLs).

For clarity, three SOLs with various focal lengths, i.e., f1 = 4 μm, f2 = 7 μm, and f3 = 10 μm, are denoted as the sample #1, #2, #3 in the following discussion, respectively. All the SOLs immersed in Forthe clarity, with various lengths, i.e., fThe 4 µm, f 2 = 7 µm, andmask f 3 =is10 1 = maximum oil (n =three 1.515)SOLs are illuminated by thefocal 640 nm laser source. radius of the setµm, are denotedtoasbethe in the following discussion, respectively. All(ring the SOLs in 10 sample μm, with#1, the #2, total#3ring number of 100, making a minimum feature size width)immersed of 100 nm. The detailed design parameters and thenm corresponding calculated Raleigh diffraction limit formask is the oil (n = 1.515) are illuminated by the 640 laser source. The maximum radius of the #1~#3 are given in Table from which we can see thata with the increase of focal set to beSOLs 10 µm, with the total ring1,number of 100, making minimum feature sizelength, (ring the width) of corresponding imaging quality is degraded, and the resolving power is reduced. According to the 100 nm. The detailed design parameters and the corresponding calculated Raleigh diffraction limit proposed optimization procedure, the transmittance distributions of the amplitude-type masks are for SOLsachieved #1~#3 according are giventointhe Table 1, from which we can see that with the increase of focal length, different requirements, which are also listed in Table 1. For the binary the corresponding imaging quality is degraded, and theare resolving power is reduced.and According to amplitude annular mask, the contained concentric rings initially set to be equidistant, each the proposed optimization procedure, the transmittance distributions the amplitude-type ring can have either unit or zero transmittance, so the binary amplitude of transmittance is encoded masks straightforward thedifferent two digits {0, 1}. To describe theare SOLs (which contain several are achieved accordingusing to the requirements, which also listedmight in Table 1. For the binary hundred rings) more compactly, the transmittance value t i is encoded from the first ring (innermost) amplitude annular mask, the contained concentric rings are initially set to be equidistant, and each to the Nth ring (outermost) by continuously transforming every fourth successive binary digit into ring can have either unit or zero transmittance, so the binary amplitude transmittance is encoded one hexadecimal digit. Take the sample SOL #2, for instance; the first hexadecimal digit “A” denotes straightforward using the two digits {0, 1}. To describe the SOLs (which might contain several hundred the real transmittance values of “1010”. rings) more In compactly, the transmittance valueby ti the is encoded from theamplitude-type first ring (innermost) this study, all the samples are fabricated FIB milling, and the structures to the characterizedby with an 80-nm-thick aluminium film deposited the glass substrate via the Nth ringare(outermost) continuously transforming every fourthon successive binary digit into one electron-beam evaporation. A 10-nm-thick chromium layer is deposited on the substrate to enhance hexadecimal digit. Take the sample SOL #2, for instance; the first hexadecimal digit “A” denotes the the adhesionvalues between glass substrate and the aluminium film. Figure 3 shows the scanning real transmittance of the “1010”. electron microscopy (SEM) images for the three samples and the enlarged view of sample #2, seeing the1.minimum annular radius 101.2 nm. In view of theofinherent problems brought by the fabrication Table Design parameters and is transmittance functions the optimized binary amplitude-type masks. techniques such as the dimensional deviation, the surface roughness, the sloped sidewalls seen from the SEM images, the influence of these imperfections, and the size effect on the focusing properties Calculated Rayleigh Diffraction Transmittance R be (µm) (µm) ofSOL SOLs will further fdiscussed in the following. Limit Function t i

04FF2 90754 FDFA2 Design parameters and transmittance functions #1Table 1. 10 4 0.44λ of the optimized binary amplitude-type FD503 B198C masks. FFFD 41351 22B24 #2 R (μm) 10 f (μm) Calculated 7 0.49λ Limit SOL Rayleigh Diffraction Transmittance Function ti BDA80 E89663 #1 10 4 0.44λ 04FF2 90754 FDFA2 FD503 B198C CE4CE EB177 #3 10 0.57λ #2 10 10 7 0.49λ FFFD 41351 22B24 BDA80 5217C 14904E89663 8478E #3

10

10

0.57λ

CE4CE EB177 5217C 14904 8478E

In this study, all the samples are fabricated by the FIB milling, and the amplitude-type structures are characterized with an 80-nm-thick aluminium film deposited on the glass substrate via the electron-beam evaporation. A 10-nm-thick chromium layer is deposited on the substrate to enhance the adhesion between the glass substrate and the aluminium film. Figure 3 shows the scanning electron microscopy (SEM) images for the three samples and the enlarged view of sample #2, seeing the minimum annular radius is 101.2 nm. In view of the inherent problems brought by the fabrication techniques such as the dimensional deviation, the surface roughness, the sloped sidewalls seen from


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the SEM images, the influence of these imperfections, and the size effect on the focusing properties of SOLs will be further discussed in the following. Nanomaterials 2018, 8, x FOR PEER REVIEW

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Figure 3. SEM diagrams of (a) SOL #1; (b) SOL #2; (c) SOL #3; and (d) the enlarged view of SOL #2.

Figure 3. SEM diagrams of (a) SOL #1; (b) SOL #2; (c) SOL #3; and (d) the enlarged view of SOL #2. 3. Results and Discussions

3. Results and Discussions

3.1. Characterization of Focusing Properties

3.1. Characterization of the Focusing Properties To explore far-field electromagnetic focusing characteristics of the designed planar SOLs, an analytical model is established firstly, as previously depicted in Figure 2. The simulation model is

To explore far-field electromagnetic focusing characteristics of the designed planar SOLs, physicallythe solved through a rigorous full-wave three-dimensional (3D) finite-difference time-domain an analytical model is established firstly, as previously depicted in Figure 2.mask Theimmersed simulation model is (FDTD) electromagnetic method with the metallic-film-coated nanostructured in the oil solved medium. The whole device is full-wave normally illuminated in the Z axis by finite-difference a linearly polarizedtime-domain plane physically through a rigorous three-dimensional (3D) wave along the X axis of 640with nm wavelength. During the process of simulation, the anti-symmetric (FDTD) electromagnetic method the metallic-film-coated nanostructured mask immersed in the and symmetric boundary conditions are applied in the X axis and Y axis to make the whole oil medium. The whole device is normally illuminated in the Z axis by a linearly polarized plane wave computation storage drop sharply. The mesh sizes for X axis, Y axis, and the optical axis (Z axis) are along the X axis of 640 nm wavelength. During the process of simulation, the anti-symmetric and all set to 20 nm. The values of permittivity (ε) and permeability (μ) for the metallic material are taken symmetric boundary from Ref. [39]. conditions are applied in the X axis and Y axis to make the whole computation storage drop During sharply. mesh sizes formeasurement, X axis, Y axis, and thesub-diffraction-limit optical axis (Z axis) are all set to 20 nm. theThe process of practical the desired focusing hotspots are captured through the optical setup as shown in Figure 4. The transmitted light patterns through The values of permittivity (ε) and permeability (µ) for the metallic material are taken from Ref. [39]. the samples are collected by a 100×/1.4 Nikon inverted oil immersion microscope objective (Nikon, During the process of practical measurement, the desired sub-diffraction-limit focusing hotspots Tokyo, Japan). Additionally, the image contours are recorded by a CCD camera (Nikon, Tokyo, Japan, are captured through the optical setup as shown in Figure 4. The transmitted light patterns through the minimum image size is 0.3 μm) and scanned in Z axis with the step of 0.02 μm driven by the Ethe samples are collected by a 100×/1.4 Nikon inverted oil immersion microscope objective (Nikon, 816 piezo controller (Physik Instrument, PI, Karlsruhe, Germany). In Figure 5, the simulated and Tokyo, Japan). Additionally, image contours are recorded by awith CCD (Nikon, Tokyo, Japan, measured light contoursthe in the Y-Z planes are presented compared thecamera theoretical light intensity the minimum image size is 0.3intensity µm) and scanned ininZthe axis with the step of 0.02 by the profiles. The normalized distributions transverse focal plane alongµm the driven dashed line A- E-816 A passing throughInstrument, the focal points the three cases are also demonstrated 5, which shows piezo controller (Physik PI,inKarlsruhe, Germany). In Figure 5, in theFigure simulated and measured that the focal planes agree much better with calculations, while some light contours in simulated the Y-Z planes are presented compared withthe the VAS theoretical light intensity profiles. discrepancies can be seen in the measured results. Note that the measured intensity of side lobes in The normalized intensity distributions in the transverse focal plane along the dashed line A-A passing the focal planes seems to be much larger than both the VAS calculated results and simulated contours, through which the focal in thetothree cases are also in Figure 5, which shows that the can points be attributed the background noisedemonstrated of the circumstances, making the focal details simulated focal planes agree much better with the VAS calculations, while some discrepancies blurred. To quantitatively analyze the hotspots in the focal plane, the VAS calculation and simulated can be normalized intensity of Note the FWHMs aremeasured numerically derived to with results. seen in the measured results. that the intensity ofcompare side lobes inthe themeasured focal planes seems to the theoretical, simulated, and experimental focal lengths and FWHMs are all be much Furthermore, larger than both the VAS calculated results and simulated contours, which can be shown attributed to in Table 2, respectively. The non-conformity of the focal lengths between the simulated and the the background noise of the circumstances, making the focal details blurred. To quantitatively analyze experimental ones might be accounted for by the imprecise estimation of the structural surface during the hotspots in the focal plane, the VAS calculation and simulated normalized intensity of the FWHMs the process of experiment. Although the side lobes of the experimental testing look much more severe are numerically derived to compare measuredtheresults. Furthermore, the theoretical, simulated, than the VAS calculation and with FDTDthe simulation, focusing FWHMs acquired from the three and experimental lengths FWHMs are alldiffraction shown in Table 2, respectively. samples arefocal all beyond theand calculated Rayleigh limit in the focal planes. The non-conformity of the focal lengths between the simulated and the experimental ones might be accounted for by the imprecise estimation of the structural surface during the process of experiment. Although the side lobes of the experimental testing look much more severe than the VAS calculation and FDTD simulation, the


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focusing FWHMs acquired from the three samples are all beyond the calculated Rayleigh diffraction limit inNanomaterials the focal2018, planes. 8, x FOR PEER REVIEW 5 of 12 Nanomaterials 2018, 8, x FOR PEER REVIEW

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Figure 4. Schematic of optical measurement setup for SOLs’ electromagnetic focusing properties.

FigureCCD: 4. Schematic of optical measurement setup for SOLs’ electromagnetic focusing properties. CCD: Charge Coupled Device. PZT: Piezoelectric Transducer. Figure 4. Schematic of optical measurement setup for SOLs’ electromagnetic focusing properties. Charge Coupled Device. PZT: Piezoelectric Transducer. CCD: Charge Coupled Device. PZT: Piezoelectric Transducer.

Figure 5. Top: electric intensity distributions in Y-Z planes of the three samples through VAS, FDTD simulation, and experiment. Bottom: Intensity profiles in the focal planes of the three samples obtained fromelectric VAS, intensity FDTD simulation, andinexperiment. Besides, thesamples corresponding Figure 5. Top: distributions Y-Z planes of through normalized VAS, FDTD Figure 5. Top: electric intensity distributions in Y-Z planes ofthe thethree three samples through VAS, FDTD intensity distributions in the focal planes of the three samples are focal also shown. simulation, and experiment. Bottom: Intensity profiles in the planes of the three samples

simulation, and experiment. Bottom: Intensity profiles in the focal planes of the three samples obtained from VAS, FDTD simulation, and experiment. Besides, the corresponding normalized obtained from VAS, FDTD simulation, and experiment. Besides, the corresponding normalized intensity intensity distributions in the focal planes of the three samples are also shown. distributions in the focal planes of the three samples are also shown.


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Table 2. The VAS, simulated, and experimental focal lengths, and FWHMs, for the three samples. f (µm)

SOL #1 #2 #3

FWHM

VAS

FDTD

EXP

VAS

FDTD

EXP

4.00 7.00 9.97

3.92 6.90 9.76

4.21 6.80 10.12

0.33λ 0.40λ 0.42λ

0.34λ 0.40λ 0.43λ

0.33λ 0.39λ 0.47λ

The above simulation and experiment are carried out at the wavelength of 640 nm without considering the chromatic effect. Chromatism may cause serious performance degradation of the optical imaging system, especially for the diffraction imaging. For practical application, the dispersion features of the diffractive devices cannot be ignored. The focusing property of the SOLs sample #1, #2, and #3 at other two wavelengths, λ = 532 nm and 730 nm, is examined. To quantitatively analyze the dispersion features of the SOLs, the experimental focal lengths and FWHMs are presented in Table 3. Obviously, the focal lengths are shortened as the wavelength increases, while the focal spots are enlarged, making the imaging quality degraded. Table 3. The experimental dispersion features of the SOLs at three distinct wavelengths. f (µm)

SOL λ (nm)

532

#1 #2 #3

5.06 9.28 12.50

730

532

640 a

730

4.21 6.80 10.12

3.28 5.46 7.80

0.32λ 0.34λ 0.40λ

0.33λ 0.39λ 0.47λ

0.41λ 0.49λ 0.55λ

640

a

FWHM

a

Denotes the designed wavelength of SOLs.

3.2. Fabrication Imperfections Actually, there indeed exist some distinctions between the theoretical results and experimental ones as the Figure 1 shows above, in which the fabrication errors may play a non-ignorable role. To investigate the error-tolerance of the focusing properties of planar SOLs, we paid much attention to the common fabrication imperfections of FIB milling such as the slot width, surface roughness, structural layer thickness, and the sloped sidewalls. Although the chromium layer is just applied to enhance the adhesive force between the glass substrate and the aluminum film, its thickness should also be examined to see whether it affects the focusing properties of SOLs. According to our process capability, the thickness deviation of the customized metal film can be controlled within ±5 nm by employing electron-beam evaporation. To acquire much more complete influencing rules about the film thickness, we changed it from 5 nm to 40 nm with a 5-nm interval to investigate the variation of the focusing properties of SOLs in the simulation. For clarity, we just took the sample whose focal length is 7 µm as an example in the following discussion. The corresponding results can be seen in Figure 6, in which the axial intensity distribution shows no big difference with the increased thickness of adhesive layer. Furthermore, the maximum intensity of the focal spot gradually decreases as the adhesive layer becomes thicker due to the growing of propagation loss in the metal. However, the FWHMs are gradually enlarged when the adhesive layer is increased. Figure 7 gives the AFM diagrams for the three SOLs with different focal lengths, and the corresponding slot width error is shown as well. It should be pointed out that we obtained the AFM diagrams via the curve fitting method, in case the probe did not reach the bottom of the grooves during the measurement. From the cross-sectional view of the as-fabricated SOLs’ geometrical profiles, we can obviously see that the FIB milling encountered a severe problem showing sloped sidewalls [32–34], attributed to its intrinsic physically sputtering etching mechanism. This issue has been neglected before by many researchers and has a close relationship with the aspect ratio (depth to width) of the etched


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nanostructures. In order to verify the error-tolerance of the slot width for the planar SOLs, we just set the deviation of each ring from 5 nm to 30 nm with a 5 nm interval. The simulated results are shown in Figure 8a,b; we can demonstrate that with the increase of slot width, the focal lengths stay almost the same, while the FWHMs are slightly enlarged. Figure 7 shows that the FIB milling will make obvious sloped sidewalls of the structure. By setting the sloped angle from 0 to 30◦ , the simulated focusing characteristics are presented in Figure 8c,d, from which we can see that with the increase of the sloped angle, the focal lengths almost keep constant while the FWHMs are enlarged, deteriorating the imaging quality of SOLs. However, the maximum intensity of the main focal spot weakens gradually as the sloped angle increases, also making the practical focusing performance degraded to some extent. It should be noted that the sloped sidewalls in the practical FIB milling will not be as large as 30◦ ; we just try to declare obvious influencing rule. Nanomaterials 2018, 8, xan FOR PEER REVIEW 7 of 12 A smooth metallic film can always help to reduce the surface scattering loss during the focusing the focal lengths almost the same, while themetallic FWHMsfilm are does slightly Figure 7 smoothly shows that process, but the surface quality of the deposited notenlarged. always behave Nanomaterials 2018, 8,stay x FOR PEER REVIEW 7 of 12[9,31]. the FIB milling will make obvious sloped sidewalls of the structure. By setting the sloped angle from Taking this into account, we characterize the surface topography of the aluminum film utilizing the to focal 30°, the simulated focusing areFWHMs presented in Figureenlarged. 8c,d, from which7 we see lengths stay almost the characteristics same, whileare the arein slightly Figure that AFM.0the The corresponding measured results displayed Figure 9a,b. What we shows cancan infer from that with the increase of the slopedsloped angle,sidewalls the focal of lengths almost keep constant FWHMs the FIB milling will make obvious the structure. By setting thewhile slopedthe angle from Figure 9 is that the root mean square (RMS) for surface roughness of the film is around 2 nm over a are deteriorating the imaging qualityare of presented SOLs. However, the8c,d, maximum intensity of the 0 toenlarged, 30°, the simulated focusing characteristics in Figure from which we can see 5 × 5main µm2 focal region. Toweakens make agradually survey of the error-tolerance of the surface roughness, the RMS is changed spot the sloped angle increases, making thewhile practical that with the increase of the sloped as angle, the focal lengths almostalso keep constant the focusing FWHMs fromperformance 0 toenlarged, 20 nm with a 2-nm interval. The simulated results can found in Figure from which degraded to some extent. Itquality should of be SOLs. noted that thebesloped sidewalls in 9c,d, the practical are deteriorating the imaging However, the maximum intensity of the we can see thatspot the focusing properties almost keep as the increases. FIB milling will not be as gradually large as 30°; we just try to declare anunchanged obvious influencing rule. main focal weakens as of theSOLs sloped angle increases, also making theroughness practical focusing performance degraded to some extent. It should be noted that the sloped sidewalls in the practical FIB milling will not be as large as 30°; we just try to declare an obvious influencing rule.

Figure 6. The changing rules of (a) the focusing properties, (b) the maximum intensity of the main

Figure 6. Theand changing rules with of (a)the the focusing properties, (b) thelayer. maximum intensity of the main hotspot, (c) the FWHM increased thickness of adhesive hotspot, and (c) the FWHM with the increased thickness of adhesive layer. Figure 6. The changing rules of (a) the focusing properties, (b) the maximum intensity of the main hotspot, and (c) the FWHM with the increased thickness of adhesive layer.

Figure 7. The fitted AFM cross-sectional diagram of the three SOLs with different focal lengths: (a) f = 4 μm, (b) f = 7 μm, (c) f = 10 μm. Figure 7. The fitted AFM cross-sectional diagram of the three SOLs with different focal lengths: (a) f

Figure 7. The fitted AFM cross-sectional diagram of the three SOLs with different focal lengths: (a) f = = 4 μm, (b) f = 7 μm, (c) f = 10 μm. 4 µm, (b) f = 7 µm, (c) f = 10 µm.

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A smooth metallic film can always help to reduce the surface scattering loss during the focusing

Figure 7.the The cross-sectional diagram of the film threedoes SOLsnot with different focal smoothly lengths: (a)[9,31]. f8 of 13 Nanomaterials 8, fitted 185 AFM process, but2018, surface quality of the deposited metallic always behave = 4this μm,into (b) f account, = 7 μm, (c)we f = characterize 10 μm. Taking the surface topography of the aluminum film utilizing the AFM. The corresponding measured results are displayed in Figure 9a,b. What we can infer from Figure 9 is that the root mean square (RMS) for surface roughness of the film is around 2 nm over a 5 × 5 μm2 region. To make a survey of the error-tolerance of the surface roughness, the RMS is changed from 0 to 20 nm with a 2-nm interval. The simulated results can be found in Figure 9c,d, from which we can see that the focusing properties of SOLs almost keep unchanged as the roughness increases. Taking account of these kinds of amplitude-type annular nanostructures, the thickness of the structural film may impose a significant role on the focusing characteristics of SOLs. In this situation, we change the thickness theREVIEW aluminum film from 25 nm to 300 nm with a 25-nm interval8 to obtain Nanomaterials 2018, 8, x FORofPEER of 12 the light distribution along the optical axis, which can be seen in Figure 10a. Figure 10a shows that A smooth film can always while help tothe reduce the surface lossfoci during the focusingas the the designed main metallic foci keep unchanged, intensity of thescattering secondary are enhanced Figure 8. (a,b) The focusing performance of slot width deviation changing from 0 nm to 30 nm; (c,d) process, but the surface quality of the deposited metallic film does not always behave smoothly [9,31]. Figure 8. (a,b) The focusing performance of slot width deviation changing from 0 nm to nm; (c,d) that film thickness increases, weakening the imaging property of SOLs. Figure 10b clearly 30 illustrates The focusing performance with the inclined sidewalls changing from 0 toaluminum 30°. ◦ Taking this into account, we characterize the surface topography of the film utilizing the The focusing performance inclined sidewalls changingAs from to 30 . the optimal thickness the focal spots are enlarged with withthethe increasing thickness. a 0result, is AFM. The corresponding measured results are displayed in Figure 9a,b. What we can infer from suggested to be 80 nm considering the skin depth of the structural material. Figure 9 is that the root mean square (RMS) for surface roughness of the film is around 2 nm over a 5 × 5 μm2 region. To make a survey of the error-tolerance of the surface roughness, the RMS is changed from 0 to 20 nm with a 2-nm interval. The simulated results can be found in Figure 9c,d, from which we can see that the focusing properties of SOLs almost keep unchanged as the roughness increases. Taking account of these kinds of amplitude-type annular nanostructures, the thickness of the structural film may impose a significant role on the focusing characteristics of SOLs. In this situation, we change the thickness of the aluminum film from 25 nm to 300 nm with a 25-nm interval to obtain the light distribution along the optical axis, which can be seen in Figure 10a. Figure 10a shows that the designed main foci keep unchanged, while the intensity of the secondary foci are enhanced as the film thickness increases, weakening the imaging property of SOLs. Figure 10b clearly illustrates that the focal spots are enlarged with the increasing thickness. As a result, the optimal thickness is suggested to be 80 nm considering the skin depth of the structural material. Figure 9. (a,b) The surface roughness characterized by AFM; The axial intensity distribution (c) and Figure 9. (a,b) The surface roughness characterized by AFM; The axial intensity distribution (c) and the transverse intensity distribution (d) of SOLs with the increase of surface roughness. the transverse intensity distribution (d) of SOLs with the increase of surface roughness.

Taking account of these kinds of amplitude-type annular nanostructures, the thickness of the structural film may impose a significant role on the focusing characteristics of SOLs. In this situation, we change the thickness of the aluminum film from 25 nm to 300 nm with a 25-nm interval to obtain the light distribution along the optical axis, which can be seen in Figure 10a. Figure 10a shows that the designed main foci keep unchanged, while the intensity of the secondary foci are enhanced as the film thickness increases, weakening the imaging property of SOLs. Figure 10b clearly illustrates that the focal spots are enlarged with the increasing thickness. As a result, the optimal thickness is suggested Figure 9. (a,b) The surface roughness characterized by AFM; The axial intensity distribution (c) and to be 80 nm considering the skin depth of the structural material. the transverse intensity distribution (d) of SOLs with the increase of surface roughness.

Figure 10. (a) The axial light intensity curve and (b) the changing FWHMs of the main foci as the thickness of structural film grows.

3.3. Size Effect The plasmonic lens formed by 2D nanometric cross-shaped aperture arrays for Fresnel-region focusing was investigated by truncating the size of the arrays to vary the NA of the lens [40]. In addition, we also investigated the effect of lens size on the focusing performance of plasmonic lenses before and concluded that a larger lens size makes for better focusing behavior as a design [37]. To investigate the size effect on the focusing characteristics of SOLs, the radius of the sample #2 is Figure 10. (a) The axial light intensity curve and (b) the changing FWHMs of the main foci as the Figure 10. (a)ofThe axial10 light intensity and (b) the changing FWHMs of the main foci as thecases gradually truncated from μmgrows. to 6 μmcurve at a 2-μm interval and the corresponding truncated thickness structural film thickness of structural film grows. 3.3. Size Effect The plasmonic lens formed by 2D nanometric cross-shaped aperture arrays for Fresnel-region focusing was investigated by truncating the size of the arrays to vary the NA of the lens [40]. In addition, we also investigated the effect of lens size on the focusing performance of plasmonic lenses before and concluded that a larger lens size makes for better focusing behavior as a design [37]. To

Nanomaterials 2018, 8, 185 Nanomaterials 2018, 8, x FOR PEER REVIEW

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are as #2-1, #2-2, #2-3, respectively. Figure 11a–c displays the SEM diagrams of the three 3.3.labeled Size Effect samples for different radii. Meanwhile, the axial light intensity distributions for the three samples are The plasmonic lens formed by 2D nanometric cross-shaped aperture arrays for Fresnel-region demonstrated in Figure 11d–f, and some differences can be seen between the simulated results and focusing was investigated by truncating the size of the arrays to vary the NA of the lens [40]. In the experimental ones, which can be attributed to the approximate determination of the structural addition, we also investigated the effect of lens size on the focusing performance of plasmonic lenses surface during the optical characterization. In addition, the transverse focusing properties are before and concluded that a larger lens size makes for better focusing behavior as a design [37]. investigated by calculating the simulated and experimental normalized intensity distributions in the To investigate the size effect on the focusing characteristics of SOLs, the radius of the sample #2 is focal planes, which are shown in Figure 11g–i. The derived focal lengths and FHWMs are listed in gradually truncated from 10 µm to 6 µm at a 2-µm interval and the corresponding truncated cases Table 4, from which we can acquire that as the size decreases for SOL #2, focal shift phenomenon are labeled as #2-1, #2-2, #2-3, respectively. Figure 11a–c displays the SEM diagrams of the three happens. It turns out that the FWHMs in the focal plane are gradually enlarged with the decrease of samples for different radii. Meanwhile, the axial light intensity distributions for the three samples are the device size, and this may be due to the enhanced diffraction effect [37,38]. demonstrated in Figure 11d–f, and some differences can be seen between the simulated results and the experimental can and be attributed to the approximate of thedecreases. structural surface Table ones, 4. Thewhich simulated experimental FWHMs and focaldetermination lengths as the radius during the optical characterization. In addition, the transverse focusing properties are investigated f (μm) FWHM distributions in the focal planes, by calculating the simulated and experimental normalized intensity SOL which are shown in Figure 11g–i. The derived lengths and FHWMs are listed in Table 4, from FDTDfocal EXP FDTD EXP which we can acquire that asRthe size SOL #2, focal shift phenomenon happens. It turns = 10 μmdecreases 6.90 for6.80 0.38λ 0.39λ out that the FWHMs in the focal gradually the decrease of the device size, R = 8plane μm are6.88 7.34 enlarged 0.44λ with 0.51λ and this may be due to the enhanced R = 6 μmdiffraction 6.72 effect 6.54 [37,38]. 0.55λ 0.56λ

Figure 11. SEM images of the three samples ((a) R = 10 μm, (b) R = 8 μm, (c) R = 6 μm) and the Figure 11. SEM images of the three samples ((a) R = 10 µm, (b) R = 8 µm, (c) R = 6 µm) and the corresponding axial intensity distribution along the optical axis for (d) #2-1, (e) #2-2, and (f) #2-3; corresponding axial intensity distribution along the optical axis for (d) #2-1, (e) #2-2, and (f) #2-3; Bottom: The normalized intensity line of the hotspots with their FWHMs for (g) #2-1, (h) #2-2, and (i) Bottom: The normalized intensity line of the hotspots with their FWHMs for (g) #2-1, (h) #2-2, and (i) #2-3. #2-3.


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Table 4. The simulated and experimental FWHMs and focal lengths as the radius decreases. f (µm)

SOL

FWHM

FDTD

EXP

FDTD

EXP

6.90 6.88 6.72

6.80 7.34 6.54

0.38λ 0.44λ 0.55λ

0.39λ 0.51λ 0.56λ

R = 10 µm R = 8 µm R = 6 µm

Admittedly, the practical structural layer thickness and the specific feature size are not taken into account in the design process, bringing out the fact that the theoretical results are much smaller than those of the FDTD simulation. Figure 11 clearly depicts the size effect of SOLs, and we can clearly observe that the focal spots are enlarged, while the focal lengths are reduced as the radius of SOLs decreases. Since the fabrication imperfections cannot be avoided in the practical sample preparation, we can only make some adjustments to reduce the influence of the fabrication imperfections at the greatest extent. To make the FIB milling results more acceptable, the metal film with a smaller grain size should be used to form the structural layer. The other fabrication imperfections such as the sloped sidewalls, surface roughness, and slot width deviation can be controlled by optimizing the FIB milling process parameters, e.g., energy and diameter of the ion beam. As the device size decreases, namely, the number of transparent rings decreases correspondingly, the manipulation of light field by SOLs is not the same as before. According to the Fourier optics theory in the frequency domain, the sub-diffraction-limit light contours in the focal plane could be explained by the destructive annular-interference of the Fourier frequency components, which can help to bring some valuable information beyond the cut-off frequency caused by the finite aperture size of the lens based on the super-oscillation phenomenon. 4. Conclusions and Outlook In summary, to give some valuable suggestions for the more precise acquisition of the desired focusing properties of planar SOLs, we implement some application-oriented investigations such as the fabrication imperfections and the size effect. Firstly, three SOLs with various focal lengths are designed, and the far-field electromagnetic focusing characteristics are explored experimentally. Both the theoretical and measured results are compared with those obtained from the 3D FDTD simulations; as imagined, all the results beat the Raleigh diffraction limit. Since there always remain some discrepancies between the theoretical results and experimental ones, we investigate the influences of the fabrication imperfections such as the slot width, surface roughness, structural layer thickness, and sloped sidewalls on the focusing properties of the planar SOLs. The results show that a thicker structural layer makes the focal spot enlarged, and the surface roughness seems to impose little influence on the focusing properties of SOLs. Besides, the slot width tolerance can be set less than ±15 nm to keep the focusing properties unchanged, while the sloped sidewalls weaken the intensity of the focal spot, leading to a poor imaging performance. Considering the practical applications, the size effect is also examined. It turns out that the focal lengths are diminished with the decrease of device size, while the FWHMs are enlarged. Note that chromatism may cause serious performance degradation of the optical imaging system, especially for diffraction imaging. Consequently, the operating bandwidth of the SOLs should be expanded to a large extent to satisfy a much wider application need, and the roadmap to realize an achromatic lens for these kinds of nanostructures can be realized through the optimization method [14,28,41]. The study provides a practical reference for the precise customization of the required light patterns of planar SOLs. A further study considering the design of achromatic SOLs will be also performed. Faced with the imperative application requirements in the complex optical system, the transformation from a single lens to a hybrid lens becomes an inevitable trend [12,42]. Furthermore, the manufacturing robustness and morphology errors, as well as the efficiency optimization, are all noteworthy in the future research.


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Acknowledgments: We acknowledge the financial support by the National Natural Science Foundation of China (51375400, 51622509), the Specific Project for the National Excellent Doctorial Dissertations (201430), the Fundamental Research Funds for the Central Universities (Grant No. 3102017jg02007), and the 111 Project (B13044). Author Contributions: The idea of the study was conceived by Yiting Yu. Wenli Li set up the various models, carried out the numerical simulations and experiments, and then wrote the manuscript. Muyuan Li and Haoyong Li helped in checking the whole simulations and finishing the experiments. Weizheng Yuan gave constructive suggestions during the preparation of the manuscript. All authors read and reviewed the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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