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用白光纳米显微镜在50纳米横向分辨率下的光学虚拟成像

2019/08/27

用白光纳米显微镜在50纳米横向分辨率下的光学虚拟成像

Article | Published: 01 March 2011


Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope

Zengbo Wang, Wei Guo, Lin Li, Boris Luk'yanchuk, Ashfaq Khan, Zhu Liu, Zaichun Chen & Minghui Hong


The imaging resolution of a conventional optical microscope is limited by diffraction to ~ 200 nm in the visible spectrum. Efforts to overcome such limits have stimulated the development of optical nanoscopes using metamaterial superlenses, nanoscale solid immersion lenses and molecular fl uorescence microscopy. These techniques either require an illuminating laser beam to resolve to 70 nm in the visible spectrum or have limited imaging resolution above 100 nm for a white-light source. Here we report a new 50-nm-resolution nanoscope that uses optically transparent microspheres (for example, SiO 2 , with 2 μ m < diameter < 9 μ m) as far-fi eld superlenses (FSL) to overcome the white-light diffraction limit. The microsphere nanoscope operates in both transmission and refl ection modes, and generates magnifi ed virtual images with a magnifi cation up to × 8. It may provide new opportunities to image viruses and biomolecules in real time.


Optical microscopy is one of the most important scientifi c achievements in the history of mankind. It has revolutionized the fi eld of life sciences and remains indispensible in many areas of scientifi c research. However, because of the diffraction limit, the imaging resolution of a classical optical microscope is limited to about half of the illuminating wavelengths λ . Th e root of the diff raction limit stems from the loss of evanescent waves in the far-fi eld. Th ese evanescent waves carry high spatial frequency subwavelength information of an object and decay exponentially with distance. In 2000, Pendry 1 proposed a theoretical ‘ superlens ’ that produces perfect diff raction-free images. Such superlenses are engineered from a slab of artifi cial negative-refraction medium in which the evanescent waves, instead of decaying, are enhanced across the slab. Th is off ers the possibility to restore the nanoscale information in the far-fi eld and therefore a nearly perfect image can be recovered 1 . Th e fi rst laboratory optical superlens was made of a thin slab of silver material. Th rough the resonant coupling of evanescence waves to surface plasmon polaritons (SPP) in silver, objects as small as 60 nm were successfully recorded on a near-fi eld photoresist layer in the ultraviolet spectrum ( λ / 6 near-fi eld resolution at λ = 365 nm) 2 . Soon aft er, a SiC superlens working at mid-infrared frequency range ( λ = 11 μ m, λ / 20 near-fi eld resolution) was demonstrated to resolve 540 nm holes 3 . However, these superlenses are ‘ nearsighted ’ , as the images can only be picked up in the near-fi eld 4 . To project a near-fi eld image into the far-fi eld, a far-FSL was shortly proposed and demonstrated 5,6 . Th e FSL used a silver slab to enhance the evanescent waves and an attached line grating to convert the evanescent waves into propagating waves in the farfi eld. Th e FSL did not magnify objects. An approach to the making of a magnifying superlens is to use two-dimensional SPP confi ned by a concentric polymer grating placed on a gold surface. It generates a × 3 magnifi cation and a resolution of 70 nm at 495 nm wavelength ( λ / 7 far-fi eld resolution) 7 . Hyperlens is another type of magnifying superlens. Th e hyperlens uses an anisotropic medium with a hyperbolic dispersion that gene rates a magnifi cation eff ect through cylindrical or spherically curved multilayer stacks 5,8,9 . Th e hyperlens resolution reached 130 nm for 365 nm ultraviolet wavelength ( λ / 3 far-fi eld resolution) and 160 nm for 410 nm visible wavelength ( λ / 2.6 far-fi eld resolution), both with less than × 3 magnifi cation 9 . Because of the SPP energy loss and sophisticated nanofabrication process, the resolutions of existing SPP superlens and hyperlens are limited at about ( λ / 3 – λ / 7) within the visible spectrum. Th e other practical limit is that the SPP superlenses must be excited / illuminated with a specifi c laser source and parameter confi gurations (wavelength, polarization and incident angle). Th ese superlenses would not function under a standard white-light source. Furthermore, the specifi c laser source required for SPP excitation could heat up, absorbing samples and damaging them. Heating due to SPP loss in superlenses could be another undesired eff ect that aff ects target materials in optical imaging 10 . It is therefore of signifi cant appeal for scientists and engineers to develop a white-light optical nanoscope that works across the visible spectrum. In contrast to the SPP superlens, nanolenses (thickness < 800 nm, diameter < 3 μ m) in plano-spherical-convex shape made of dielectric materials, for example, calix hydroquinone, are naturally loss-free and have been recently fabricated using sophisticated techniques for subwavelength imaging. Th ese nanolenses were nanoscale solid immersion lenses (nSILs) 11 that resolve 220 nm line objects at 475 nm imaging wavelength ( λ / 2.2 far-fi eld resolution, × 2 magnifi cation) 12 . Compared with macroscopic SILs, wavelength-scale nSILs can produce a 25 % smaller focus spot, which enhances the resolution 11 . However, it remains practically impossible for SILs to resolve nano-objects below 100 nm with visible light sources on the basis of solid immersion mechanism due to the shortage of high-index lens materials 11,12 .

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Figure 1 | Experimental confi guration of white-light microsphere nanoscope with  / 8 –  / 14 imaging resolution. Schematic of the transmission mode microsphere superlens integrated with a classical optical microscope. The spheres collect the near-fi eld object information and form virtual images that can be captured by the conventional lens.


In this study, we present a new 50-nm-resolution optical nanoscope that uses ordinary glass microspheres ( n = 1.46, 2 μ m < diameter < 9 μ m) as FSL to overcome the white-light diff raction limit, attaining a resolution between λ / 8 and λ / 14 (far-fi eld resolution) and a magnifi cation between × 4 and × 8. Such a super-resolution white-light nanoscope would open up new opportunities for imaging viruses, DNA and molecules in real time. Results Microsphere nanoscope and experimental imaging performance . Figure 1 illustrates the schematic of a transmission mode whitelight microsphere nanoscope. Th e microspheres are placed on the top of the object surface by self-assembly 13 . A halogen lamp with a peak wavelength of 600 nm is used as the white-light illumination source. Th e microsphere superlenses collect the underlying nearfi eld object information, magnify it (forming virtual images which keep the same orientation as the objects in the far-fi eld) and pick it up by a conventional × 80 objective lens (numerical aperture NA = 0.9, Olympus MDPlan). In the experiments, gratings consisting of 360- nm-wide lines, spaced 130 nm apart, were imaged using 4.74- μ mdiameter microspheres ( Fig. 2a ). Th e virtual image plane was 2.5 μ m beneath the substrate surface and inside substrate. As can be seen from Figure 2a , only those lines with particles on top of them have been resolved. Th e lines without particles on top mix together and form a bright spot, which cannot be directly resolved by the optical microscope because of the diff raction limit (for the lowest visible wavelength λ = 400 nm, the best diff raction-limited resolution is estimated to be 215 nm in air using the vector theory of Richards and Wolf 14 , and to be 152 nm by taking the solid immersion eff ect of a particle into account. For the main peak of a white-light source at λ = 600 nm, the limits are 333 nm in air and 228 nm with solid immersion eff ect, respectively. Here, one should also note that the focal planes for lines with and without particles on top are diff erent). Th e magnifi ed image in Figure 2a corresponds to a × 4.17 magnifi cation factor. Figure 2b shows a fi shnet gold-coated anodic aluminium oxide (AAO) membrane imaged with 4.74- μ mdiameter microspheres. Th e pores are 50 nm in diameter and spaced 50 nm apart. As it can be seen, the microsphere nanoscope resolves these tiny pores that are well beyond the diff raction limit, giving a resolution of between λ / 8 ( λ = 400 nm) and λ / 14

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Figure 2 | Microsphere superlens imaging in transmission mode. ( a ) Microsphere superlens imaging of 360-nm-wide lines spaced 130 nm apart (top left image taken by scanning electron microscope (SEM)), the optical nanoscope (ON) image (top right image) shows that the lines are clearly resolved. ( b ) A gold-coated fi shnet AAO sample imaged with a microsphere ( a = 2.37 μ m, borders of two spheres are shown by white lines) superlens. The nanoscope clearly resolves the pores that are 50 nm in diameter and spaced 50 nm apart (bottom left SEM image). The size of the optical image between the pores within the image plane is 400 nm (bottom right ON image). It corresponds to a magnifi cation factor of M≈ 8. Scale bar, 5 μ m.


( λ = 750 nm) in the visible spectrum range. It is important to note that the magnifi cation in this case is around × 8, which is almost two times of that in the grating samples as shown in Figure 2a . Th is implies that the performance of microsphere superlens is aff ected by the near-fi eld interaction of the sphere and the substrate. In our experiment, we have confi rmed that the gold coating layer on the AAO surface not only enhanced the resolving power but also increased the magnifi cation factor of the microsphere superlens. As self-assembled particles are easy to spread over a large surface area and meanwhile each particle can work as a superlens, the images produced by each particle can be stitched together to form a large image. Th ese are the cases seen in Figure 2a,b , in which a hexagonal array of particles functions as an array of superlens covering a large area. Our previous calculations reveal the fact that the Poynting vector of the radiation refl ected by the surface transfers through the particle 15 , which permits the formation of an image in the refl ection mode as well. Figure 3a demonstrates a Blu-ray DVD disk (200-nm-wide lines separated 100 nm apart) imaged with 4.74- μ mdiameter microspheres in the refl ection mode using the halogen light illumination. Th e subdiff raction-limited lines are clearly observed. Figure 3b shows another example of refl ection mode imaging of a star structure made on SbTe DVD disk. Th e complex shape of the star, including the 90 nm corners of the star, was clearly resolved by the microsphere superlens. Further experiments have confi rmed that complex shape structures can also be well imaged in the transmission mode and that both the transmission and refl ection modes can achieve 50 nm resolution. Indeed, the microsphere nanoscope has proven its practicability and versatility in nano imaging of various samples.


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Figure 3 | Microsphere nanoscope refl ection mode imaging. ( a ) Microsphere superlens refl ection mode imaging of a commercial Blu-ray DVD disk. The 100- μ m-thick transparent protection layer of the disk was peeled off before using the microsphere ( a = 2.37 μ m). The subdiffractionlimited 100 nm lines (top left SEM image) are resolved by the microsphere superlens (top right ON image). ( b ) Refl ection mode imaging of a star structure made on GeSbTe thin fi lm for DVD disk (bottom left SEM image). The complex shape of the star including 90 nm corner was clearly imaged (bottom right ON image). Scale bar: SEM (500 nm), ON (5 μ m).


Experimental comparison with SILs imaging . It is important to mention that we have also conducted comparison experiments using two SILs ( Supplementary Fig. S1 ), and confi rmed that none of them can be used to resolve our samples with feature sizes between 50 and 130 nm ( Supplementary Fig. S2 ). Immersion of samples ‘ into ’ solids, attained by positioning the samples in close contact with the fl at bottom surface of the lens, provides a means to access a shorter working wavelength in lens materials, and thus higher resolution beyond that in air. Th e resolution limit of the SILs used in our experiments was ~ 152 nm, which makes it impossible to resolve the 100 nm objects. Th e imaging mechanism of the microsphere nanoscope . In principle, the imaging resolution and magnifi cation of the microsphere superlenses are fundamentally related to their focus properties 16 . It is well known that small spheres can generate ‘ photonic nanojets ’ with super-resolution foci 17 , less well known is that such superresolution foci are only achievable for a narrow window of ( n , q ) parameters, where n is the refractive index of the sphere and q is the size parameter defi ned as q = 2 πa / λ , according to Mie theory 16 . Figure 4a shows the calculated super-resolution window for diff erent n and q parameters for spheres immersed in air. Th e y axis was calculated as (focus spot size − Rayleigh diff raction limit) / radius, which we name as super-resolution strength. For the n = 1.46 spheres used in this study, super-resolution occurs for q < 70, which corresponds to smaller than 9.0- μ m-diameter spheres at a wavelength of λ = 400 nm. From our experiments, it was verifi ed that 10 and 50 μ m spheres are not successful in 100-nm-resolution imaging tests, whereas 3.0 μ m spheres produce clear 50-nm-resolution images as achieved by the 4.74 μ m spheres. We also examined the use of 1 μ m spheres for imaging. It is found that because of the small-view windows of such particles, high-resolution imaging was not successful. Th erefore, the limit for 1 μ m sphere is a practical conclusion rather than a theoretical one. Th e practical size window for n = 1.46 microspheres is recommended as 2 μ m < diameter < 9 μ m for 50-nm-resolution imaging. From Figure 4a , it can also be seen that refractive index has a strong eff ect on super-resolution foci; with n = 1.8, the size window for super-resolution extends up to q ~ 250, which implies that particles as big as 30 μ m could be used for nanoimaging. Th is would facilitate the experiments because of wider view windows off ered by bigger particles. Moreover, one can see that the superresolution strength is maximized at n = 1.8. When refractive index increases further to n = 2.0, the super-resolution strength reduces and super-resolution window shrinks, making it undesirable to use n > 1.8 high-index materials for nanoimaging in our technique. On the contrary, high-index ( n > 1.8) materials are important for SILs as their imaging resolution is determined by the refractive index of lens materials because of the solid immersion mechanism. Figure 4b,c compares the | E | 2 intensity distribution for SIL, sphere and particle on surface calculated with the same parameters, that is, n = 1.46, diameter = 4.74 μ m and λ = 600 nm. Here, one important diff erence between SIL and sphere was demonstrated: a super-resolution focus outside of sphere and a diff raction-limited focus for the same-diameter SIL. Truncating of sphere into SIL causes the loss of super-resolution focus, and diff raction-limited spot of SIL makes it impossible to resolve below 100 nm objects. Super-resolution foci are the key requirement of our technique. With the presence of a substrate, the focus at particle – substrate contact region generally becomes sharper. Th is is evidenced by our particle on surface calculation ( Fig. 4b,c ). Such eff ects could enhance the imaging resolution according to the reciprocity principle 18 .

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Figure 4 | Super-resolution foci and virtual magnifi cation factor analyses. ( a ) Super-resolution strength, defi ned as (focus spot size − Rayleigh limit) / radius, as a function of size parameter q for different refractive index particles. The inset shows q up to 300 for n = 1.46. ( b ) The intensity distributions calculated for SIL (left image, height H = a (1 + n − 1 )), sphere (middle image) and particle on surface(right image) of a 40-nm-thick gold fi lm for the sphere with radius a = 2.37 μ m and refractive index n = 1.46 at the wavelength λ = 600 nm. ( c ) Full width at half maximum of foci for SIL (blue solid), sphere (red dot) and sphere on substrate (green solid). ( d ) Virtual image magnifi cation versus particle size for sphere with n = 1.46 at the wavelength λ = 600 nm.


Magnifi cation factor of the microsphere nanoscope . In cases of macroscopic spheres and SILs, in which geometrical optics applies, the virtual image magnifi cation factor can be calculated through ray tracing as M = f / ( f − a ) for an object in contact with the lens surface, where f is the focal length and a is the distance between the object and the centre of the lens. Characteristically, spheres ( M≈n / (2 − n )) produce a higher magnifi cation over the SILs counterparts ( M≈n2 ) for n < 2.0 because of their shorter focal length f ( Supplementary Figs S3 and S4 ). As sphere size reduces to the super-resolution size window (2 μ m < diameter < 9 μ m, n = 1.46), geometrical ray tracing becomes invalid as evidenced by two signs. First, it fails to predict the magnifi cation factor for those super-resolution spheres with f = a , as M = f / ( f − a ) becomes infi nite in these cases. Second, optical rays going through such small spheres could form optical vortices and singularities inside the sphere. ( Supplementary Figs S5 and S6 ). A mathematical model for near-fi eld magnifi cation with fi eld singularities is still not available in literature. Here, we propose a fi tting formula based on maximal fi eld enhancement with some exponent, M≈ ( Imax / I0 ) β . We found that the factor β≈ 0.34 yields excellent agreement ( < 1 % deviation) with exact virtual image magnifi cation for geometrical optics approximation ( Supplementary Fig. S4 ). Using this simplifi ed estimation, one can determine the magnifi cation factor for the particle on surface to be M≈ 5.5, which is in reasonable agreement with experimental values between 4 and 8 for diff erent samples. In a similar manner, we found that magnifi cation increases with particle size within superresolution size window from M≈ 4 for 2 μ m spheres to M≈ 7 for 9 μ m spheres ( Fig. 4d ). Th e magnifi cation-increasing tendency was also confi rmed by experiments using 3.0 μ m and 4.74 μ m spheres; the magnifi cation of 4.74 μ m is about 1.2 times that of 3.0 μ m spheres.


Discussion Th e microsphere nanoscope demonstrated by us has a far-fi eld resolution between λ / 8 and λ / 14 and a magnifi cation between × 4 and × 8 Such resolution and magnifi cation have greatly surpassed those of existing visible wavelength SPP hyperlens 7,8 (resolution λ / 7, magnifi cation × 2.4) and nSILs 11,12 (resolution λ / 2.2, magnifi cation × 2) within the visible spectrum; note that the SiC superlens resolution of λ / 20, as demonstrated in the literature 3 , is not far-fi eld resolution but a near-fi eld resolution in mid-infrared spectrum range. Th e microsphere superlenses operate in a virtual imaging mode, and can be easily integrated with an ordinary optical microscope in both transmission and refl ection modes, and work under a standard white-light illumination. From our estimations, it follows that maximal virtual image magnifi cation can be attained with a refractive index n≈ 1.8. With 5 μ m particles, it should resolve arbitrary structures < 20 nm, making it possible to directly observe viruses and the inside of living cells under white light without the need to excite fl uorescence using proper lasers as in molecular fl uorescence nanoscopy 19 . As a fi nal note, particles in other shapes, such as elliptical particles, could also be considered for below 50 nm imaging as near-fi eld foci strongly depend on particle shape. In conclusion, we have demonstrated that optically transparent microspheres are highperformance optical superlens that could resolve 50 nm objects by near-fi eld virtual imaging under a white-light source illumination. Th e microsphere nanoscope is robust, economical and is also easy to accommodate diff erent kinds of samples with potential applications for imaging biological objects such as virus, DNA and molecules. Methods Imaging samples fabrication and preparation . Th e gratings used in Figure 2a were fabricated using a focused ion beam machine ( Quanta 200 3D , FEI ). Th e sample consists of 30-nm-thick chrome fi lm coated on fused silica substrates. Th e AAO used in Figure 2b was fabricated by two steps anodizing in oxalic acid (0.3 mol l − 1 ), under a constant voltage of 40 V. A porous 20-nm-thick metallic fi lm (gold) was then formed by using a 300- μ m-thick AAO as the template. Th e star sample used in Figure 3b was fabricated using contact particle lens array technique, which was developed by us recently 20 . Th e diluted SiO 2 sphere suspension was applied onto the substrate surface by drop coating. Th e colloidal silica spheres ( Bangs Laboratories ) form an ordered monolayer through self-assembly. An Olympus microscope ( MX-850 ), fi tted with an × 80 objective lens (numerical aperture NA = 0.9, Olympus MDPlan) was used to focus through the microsphere into the substrate and virtual images were collected and reported. All scanning electron microscopic images were taken by Hitachi S-3400N . SILs imaging . Both 2.5-mm-diameter and 0.5-mm-diameter fused silica half-ball SILs) from Edmund Optics have been used for the control experiments ( Supplementary Fig. S1 ). Th e SILs were placed directly onto imaging sample surface by careful manual handling, attaining an experimental confi guration similar to that for the microsphere. An × 80 objective lens was used for the 0.5-mm-diameter SIL and a × 40 lens for the 2.5-mm-diameter SIL, as limited by the available gap between lens and sample. All samples as in Figures 2 and 3 have been tested with SILs without success. Example results on Blu-ray disk imaging without SILs and particles, with 0.5 mm SIL, with 2.5 mm SIL and with 4.74 μ m sphere were shown for comparison in Supplementary Figure S2 . Simulation method . Th e geometrical optical ray tracing analysis ( Supplementary Fig. S3 ) was carried out using Mathematica 7.0 soft ware, and fi eld distributions in Figure 4 were calculated by Mie theory for sphere and fi nite diff erence in time domain technique for SIL and sphere and particle on surface, respectively.


Virtual image magnifi cation factor . Magnifi cation factor for virtual image can be found by ray tracing under the approximation of geometrical optics ( Supplementary Fig. S3 ). Th e focal lengths of SIL and sphere are fSIL≈an2 / ( n2 − 1) and fsphere≈na / 2( n − 1), respectively, where a is the radius. If a small point object A is situated at the plane of SIL at yA = y0a , then yimage≈n2 y0 , that is, magnifi cation of the virtual image is MSIL≈n2 . At similar conditions, magnifi cation of the virtual image by the sphere is presented by Msphere≈n / (2 − n ). Th us, the spherical particle everywhere produces a higher magnifi cation than SIL ( Supplementary Fig. S3 ). Following the focusing properties of the sphere under the approximation of geometrical optics 21 , the fi eld enhancement in the focal area is given by Th us, under the approximation of geometrical optics, we have a relationship between fi eld enhancement and magnifi cation of virtual image, Msphere = f ( Imax / I0 ), written in a parametric form, where refractive index n has a role of parameter, see in Supplementary Figure S4 . Th is dependence with high accuracy can be approximated by a function Msphere≈ ( Imax / I0 ) β , with β≈ 0.34. Th e diff erence between the exact curve and approximated formula for M ( n ) is < 1 % for the whole range of refractive index from 1 to 1.95. Note that geometrical optics approximation yields singularity at n = 2; thus, it cannot be applied in the vicinity of this point. Also, note that under the approximation of geometrical optics, fi eld enhancement does not depend on the particle size. However, one can see this dependence under the approximation of the Mie theory, see Figure 4d in the article.

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Energy fl ow simulation . Within the framework of classical Mie theory, the timeaveraged Poynting vector (energy fl ow) is given by S E = × 1 2 Re[ *] H and fi eld lines are the solutions of the diff erential equation d x / Sx = d y / Sy . We developed a Fortran program based on Mie formulation, and in Supplementary Figure S5 , we present the Poynting vector lines for the microsphere with radius a = 2.37 μ m and refractive index n = 1.46 illuminated by a plane wave with λ = 600 nm. We can construct the virtual image, using the reciprocity principle and extrapolation of the Poynting vector, on the basis of this angle of vector line on the outer edge of the particle, see in Supplementary Figure S6 . Th is method, in fact, uses the same idea of virtual image construction as in geometrical optics. We extrapolate not the straight ray but plot tangential line to the lines with some curvature. Th is image construction yields a magnifi cation of 2 – 4 times depending on the particular Poynting vector line.

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