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 nmin the visible spectrum. Efforts to overcome such limits have stimulated the development ofoptical nanoscopes using metamaterial superlenses, nanoscale solid immersion lenses andmolecular fl uorescence microscopy. These techniques either require an illuminating laserbeam to resolve to 70 nm in the visible spectrum or have limited imaging resolution above100 nm for a white-light source. Here we report a new 50-nm-resolution nanoscope that usesoptically transparent microspheres (for example, SiO 2 , with 2 μ m < diameter < 9 μ m) as far-fi eldsuperlenses (FSL) to overcome the white-light diffraction limit. The microsphere nanoscopeoperates in both transmission and refl ection modes, and generates magnifi ed virtual images witha magnifi cation up to × 8. It may provide new opportunities to image viruses and biomoleculesin real time.

Optical microscopy is one of the most important scientifi cachievements in the history of mankind. It has revolutionizedthe fi eld of life sciences and remains indispensible inmany areas of scientifi c research. However, because of the diffractionlimit, the imaging resolution of a classical optical microscopeis limited to about half of the illuminating wavelengths λ .Th e root of the diff raction limit stems from the loss of evanescentwaves in the far-fi eld. Th ese evanescent waves carry high spatialfrequency subwavelength information of an object and decayexponentially 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-refractionmedium in which the evanescent waves, instead ofdecaying, are enhanced across the slab. Th is off ers the possibilityto restore the nanoscale information in the far-fi eld and thereforea nearly perfect image can be recovered 1 . Th e fi rst laboratoryoptical superlens was made of a thin slab of silver material.Th rough the resonant coupling of evanescence waves to surfaceplasmon polaritons (SPP) in silver, objects as small as 60 nmwere successfully recorded on a near-fi eld photoresist layer in theultraviolet spectrum ( λ / 6 near-fi eld resolution at λ = 365 nm) 2 .Soon aft er, a SiC superlens working at mid-infrared frequencyrange ( λ = 11 μ m, λ / 20 near-fi eld resolution) was demonstratedto 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 wasshortly proposed and demonstrated 5,6 . Th e FSL used a silver slabto enhance the evanescent waves and an attached line grating toconvert the evanescent waves into propagating waves in the farfield. Th e FSL did not magnify objects. An approach to the makingof a magnifying superlens is to use two-dimensional SPP confined by a concentric polymer grating placed on a gold surface. Itgenerates a × 3 magnifi cation and a resolution of 70 nm at 495 nmwavelength ( λ / 7 far-fi eld resolution) 7 . Hyperlens is another type ofmagnifying superlens. Th e hyperlens uses an anisotropic mediumwith a hyperbolic dispersion that gene rates a magnifi cation eff ectthrough cylindrical or spherically curved multilayer stacks 5,8,9 .Th e hyperlens resolution reached 130 nm for 365 nm ultravioletwavelength ( λ / 3 far-fi eld resolution) and 160 nm for 410 nmvisible wavelength ( λ / 2.6 far-fi eld resolution), both with less than × 3 magnifi cation 9 . Because of the SPP energy loss and sophisticatednanofabrication process, the resolutions of existing SPPsuperlens and hyperlens are limited at about ( λ / 3 – λ / 7) within thevisible spectrum. Th e other practical limit is that the SPP superlensesmust be excited / illuminated with a specifi c laser source andparameter confi gurations (wavelength, polarization and incidentangle). Th ese superlenses would not function under a standardwhite-light source. Furthermore, the specifi c laser source requiredfor SPP excitation could heat up, absorbing samples and damagingthem. Heating due to SPP loss in superlenses could be anotherundesired eff ect that aff ects target materials in optical imaging 10 .It is therefore of signifi cant appeal for scientists and engineersto develop a white-light optical nanoscope that works across thevisible spectrum. In contrast to the SPP superlens, nanolenses(thickness < 800 nm, diameter < 3 μ m) in plano-spherical-convexshape made of dielectric materials, for example, calix hydroquinone,are naturally loss-free and have been recently fabricatedusing sophisticated techniques for subwavelength imaging. Th esenanolenses were nanoscale solid immersion lenses (nSILs) 11 thatresolve 220 nm line objects at 475 nm imaging wavelength ( λ / 2.2far-fi eld resolution, × 2 magnifi cation) 12 . Compared with macroscopicSILs, wavelength-scale nSILs can produce a 25 % smallerfocus spot, which enhances the resolution 11 . However, it remainspractically impossible for SILs to resolve nano-objects below100 nm with visible light sources on the basis of solid immersionmechanism due to the shortage of high-index lens materials 11,12 .

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

In this study, we present a new 50-nm-resolution optical nanoscopethat uses ordinary glass microspheres ( n = 1.46, 2 μ m < diameter < 9 μ m) as FSL to overcome the white-light diff raction limit, attaininga resolution between λ / 8 and λ / 14 (far-fi eld resolution) and a magnification between × 4 and × 8. Such a super-resolution white-light nanoscopewould open up new opportunities for imaging viruses, DNAａnd molecules in real time. ResultsMicrosphere nanoscope and experimental imaging performance . Figure 1 illustrates the schematic of a transmission mode whitelightmicrosphere nanoscope. Th e microspheres are placed on thetop of the object surface by self-assembly 13 . A halogen lamp with apeak wavelength of 600 nm is used as the white-light illuminationsource. Th e microsphere superlenses collect the underlying nearfield object information, magnify it (forming virtual images whichkeep the same orientation as the objects in the far-fi eld) and pick it upby 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 mdiametermicrospheres ( Fig. 2a ). Th e virtual image plane was 2.5 μ mbeneath the substrate surface and inside substrate. As can be seenfrom Figure 2a , only those lines with particles on top of them havebeen resolved. Th e lines without particles on top mix together andform a bright spot, which cannot be directly resolved by the opticalmicroscope because of the diff raction limit (for the lowest visiblewavelength λ = 400 nm, the best diff raction-limited resolution isestimated to be 215 nm in air using the vector theory of Richardsａnd Wolf 14 , and to be 152 nm by taking the solid immersion eff ectof a particle into account. For the main peak of a white-light sourceat λ = 600 nm, the limits are 333 nm in air and 228 nm with solidimmersion eff ect, respectively. Here, one should also note thatthe focal planes for lines with and without particles on top arediff erent). Th e magnifi ed image in Figure 2a corresponds to a × 4.17magnifi cation factor. Figure 2b shows a fi shnet gold-coated anodicaluminium oxide (AAO) membrane imaged with 4.74- μ mdiametermicrospheres. Th e pores are 50 nm in diameter andspaced 50 nm apart. As it can be seen, the microsphere nanoscoperesolves these tiny pores that are well beyond the diff ractionlimit, giving a resolution of between λ / 8 ( λ = 400 nm) and λ / 14

Figure 2 | Microsphere superlens imaging in transmission mode.( a ) Microsphere superlens imaging of 360-nm-wide lines spaced 130 nmapart (top left image taken by scanning electron microscope (SEM)),the optical nanoscope (ON) image (top right image) shows that the linesare clearly resolved. ( b ) A gold-coated fi shnet AAO sample imaged witha microsphere ( a = 2.37 μ m, borders of two spheres are shown by whitelines) superlens. The nanoscope clearly resolves the pores that are 50 nmin diameter and spaced 50 nm apart (bottom left SEM image). The size ofthe 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 notethat the magnifi cation in this case is around × 8, which is almosttwo times of that in the grating samples as shown in Figure 2a . Th isimplies that the performance of microsphere superlens is aff ectedby the near-fi eld interaction of the sphere and the substrate. Inour experiment, we have confi rmed that the gold coating layer onthe AAO surface not only enhanced the resolving power but alsoincreased the magnifi cation factor of the microsphere superlens.As self-assembled particles are easy to spread over a large surfacearea and meanwhile each particle can work as a superlens, theimages produced by each particle can be stitched together to forma large image. Th ese are the cases seen in Figure 2a,b , in whicha hexagonal array of particles functions as an array of superlenscovering a large area. Our previous calculations reveal the fact that the Poyntingvector of the radiation refl ected by the surface transfers throughthe particle 15 , which permits the formation of an image in therefl 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 mdiametermicrospheres in the refl ection mode using the halogen lightillumination. Th e subdiff raction-limited lines are clearly observed. Figure 3b shows another example of refl ection mode imaging ofa star structure made on SbTe DVD disk. Th e complex shape ofthe star, including the 90 nm corners of the star, was clearly resolvedby the microsphere superlens. Further experiments have confirmed that complex shape structures can also be well imaged in thetransmission mode and that both the transmission and refl ectionmodes can achieve 50 nm resolution. Indeed, the microsphere nanoscopehas proven its practicability and versatility in nano imaging ofvarious samples.

Figure 3 | Microsphere nanoscope refl ection mode imaging. ( a )Microsphere superlens refl ection mode imaging of a commercial Blu-rayDVD disk. The 100- μ m-thick transparent protection layer of the disk waspeeled off before using the microsphere ( a = 2.37 μ m). The subdiffractionlimited100 nm lines (top left SEM image) are resolved by the microspheresuperlens (top right ON image). ( b ) Refl ection mode imaging of a starstructure 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 tomention that we have also conducted comparison experimentsusing two SILs ( Supplementary Fig. S1 ), and confi rmed that none ofthem can be used to resolve our samples with feature sizes between50 and 130 nm ( Supplementary Fig. S2 ). Immersion of samples ‘ into ’ solids, attained by positioning the samples in close contactwith the fl at bottom surface of the lens, provides a means to access ashorter working wavelength in lens materials, and thus higher resolutionbeyond that in air. Th e resolution limit of the SILs used in ourexperiments was ~ 152 nm, which makes it impossible to resolve the100 nm objects.Th e imaging mechanism of the microsphere nanoscope . In principle,the imaging resolution and magnifi cation of the microspheresuperlenses 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 superresolutionfoci are only achievable for a narrow window of ( n , q )parameters, where n is the refractive index of the sphere and q is thesize parameter defi ned as q = 2 πa / λ , according to Mie theory 16 . Figure 4a shows the calculated super-resolution window for diff erentn and q parameters for spheres immersed in air. Th e y axis was calculatedas (focus spot size − Rayleigh diff raction limit) / radius, which wename as super-resolution strength. For the n = 1.46 spheres used inthis study, super-resolution occurs for q < 70, which corresponds tosmaller 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 spheresare not successful in 100-nm-resolution imaging tests, whereas3.0 μ m spheres produce clear 50-nm-resolution images as achievedby the 4.74 μ m spheres. We also examined the use of 1 μ m spheresfor imaging. It is found that because of the small-view windows ofsuch 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 microspheresis recommended as 2 μ m < diameter < 9 μ m for 50-nm-resolutionimaging. From Figure 4a , it can also be seen that refractive indexhas a strong eff ect on super-resolution foci; with n = 1.8, the sizewindow for super-resolution extends up to q ~ 250, which impliesthat particles as big as 30 μ m could be used for nanoimaging. Th iswould facilitate the experiments because of wider view windowsoff ered by bigger particles. Moreover, one can see that the superresolutionstrength is maximized at n = 1.8. When refractive indexincreases further to n = 2.0, the super-resolution strength reducesａnd super-resolution window shrinks, making it undesirable to usen > 1.8 high-index materials for nanoimaging in our technique. Onthe contrary, high-index ( n > 1.8) materials are important for SILsas their imaging resolution is determined by the refractive index oflens materials because of the solid immersion mechanism. Figure 4b,c compares the | E | 2 intensity distribution for SIL, sphereａnd particle on surface calculated with the same parameters, thatis, n = 1.46, diameter = 4.74 μ m and λ = 600 nm. Here, one importantdiff erence between SIL and sphere was demonstrated: a super-resolutionfocus outside of sphere and a diff raction-limited focus for thesame-diameter SIL. Truncating of sphere into SIL causes the loss ofsuper-resolution focus, and diff raction-limited spot of SIL makes itimpossible to resolve below 100 nm objects. Super-resolution fociare the key requirement of our technique. With the presence of a substrate, the focus at particle – substrate contact region generallybecomes sharper. Th is is evidenced by our particle on surfacecalculation ( Fig. 4b,c ). Such eff ects could enhance the imaging resolutionaccording to the reciprocity principle 18 .

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 distributionscalculated 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 spherewith 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 ofmacroscopic spheres and SILs, in which geometrical optics applies,the virtual image magnifi cation factor can be calculated throughray tracing as M = f / ( f − a ) for an object in contact with the lenssurface, where f is the focal length and a is the distance betweenthe 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 lengthf ( Supplementary Figs S3 and S4 ). As sphere size reduces to thesuper-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-resolutionspheres with f = a , as M = f / ( f − a ) becomes infi nite in thesecases. Second, optical rays going through such small spheres couldform optical vortices and singularities inside the sphere. ( SupplementaryFigs S5 and S6 ). A mathematical model for near-fi eldmagnifi cation with fi eld singularities is still not available in literature.Here, we propose a fi tting formula based on maximal fi eldenhancement with some exponent, M≈ ( Imax / I0 ) β . We found that the factor β≈ 0.34 yields excellent agreement ( < 1 % deviation) withexact virtual image magnifi cation for geometrical optics approximation( Supplementary Fig. S4 ). Using this simplifi ed estimation, onecan determine the magnifi cation factor for the particle on surfaceto be M≈ 5.5, which is in reasonable agreement with experimentalvalues between 4 and 8 for diff erent samples. In a similar manner,we found that magnifi cation increases with particle size within superresolutionsize window from M≈ 4 for 2 μ m spheres to M≈ 7 for 9 μ mspheres ( Fig. 4d ). Th e magnifi cation-increasing tendency was alsoconfi rmed by experiments using 3.0 μ m and 4.74 μ m spheres; themagnifi 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 eldresolution between λ / 8 and λ / 14 and a magnifi cation between × 4ａnd × 8 Such resolution and magnifi cation have greatly surpassedthose 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 resolutionof λ / 20, as demonstrated in the literature 3 , is not far-fi eld resolutionbut 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 inboth transmission and refl ection modes, and work under a standardwhite-light illumination. From our estimations, it follows thatmaximal virtual image magnifi cation can be attained with a refractiveindex n≈ 1.8. With 5 μ m particles, it should resolve arbitrarystructures < 20 nm, making it possible to directly observe virusesａnd the inside of living cells under white light without the need toexcite fl uorescence using proper lasers as in molecular fl uorescencenanoscopy 19 . As a fi nal note, particles in other shapes, such as ellipticalparticles, could also be considered for below 50 nm imaging asnear-fi eld foci strongly depend on particle shape. In conclusion, wehave demonstrated that optically transparent microspheres are highperformanceoptical superlens that could resolve 50 nm objects bynear-fi eld virtual imaging under a white-light source illumination.Th e microsphere nanoscope is robust, economical and is also easy toaccommodate diff erent kinds of samples with potential applicationsfor imaging biological objects such as virus, DNA and molecules. MethodsImaging samples fabrication and preparation . Th e gratings used in Figure 2awere fabricated using a focused ion beam machine ( Quanta 200 3D , FEI ). Th e sampleconsists of 30-nm-thick chrome fi lm coated on fused silica substrates. Th e AAOused 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) wasthen formed by using a 300- μ m-thick AAO as the template. Th e star sample usedin Figure 3b was fabricated using contact particle lens array technique, which wasdeveloped by us recently 20 . Th e diluted SiO 2 sphere suspension was applied ontothe 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, OlympusMDPlan) was used to focus through the microsphere into the substrate and virtualimages were collected and reported. All scanning electron microscopic imageswere taken by Hitachi S-3400N .SILs imaging . Both 2.5-mm-diameter and 0.5-mm-diameter fused silica half-ballSILs) from Edmund Optics have been used for the control experiments ( SupplementaryFig. S1 ). Th e SILs were placed directly onto imaging sample surfaceby careful manual handling, attaining an experimental confi guration similar tothat for the microsphere. An × 80 objective lens was used for the 0.5-mm-diameterSIL and a × 40 lens for the 2.5-mm-diameter SIL, as limited by the available gapbetween lens and sample. All samples as in Figures 2 and 3 have been tested withSILs without success. Example results on Blu-ray disk imaging without SILs andparticles, with 0.5 mm SIL, with 2.5 mm SIL and with 4.74 μ m sphere were shownfor comparison in Supplementary Figure S2 .Simulation method . Th e geometrical optical ray tracing analysis ( SupplementaryFig. S3 ) was carried out using Mathematica 7.0 soft ware, and fi eld distributionsin Figure 4 were calculated by Mie theory for sphere and fi nite diff erence in timedomain technique for SIL and sphere and particle on surface, respectively.

Virtual image magnifi cation factor . Magnifi cation factor for virtual imagecan 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 Ais situated at the plane of SIL at yA = y0a , then yimage≈n2y0 , that is, magnifi cationof the virtual image is MSIL≈n2 . At similar conditions, magnifi cation of the virtualimage by the sphere is presented by Msphere≈n / (2 − n ). Th us, the spherical particleeverywhere produces a higher magnifi cation than SIL ( Supplementary Fig. S3 ).Following the focusing properties of the sphere under the approximation ofgeometrical optics 21 , the fi eld enhancement in the focal area is given by Th us, under the approximation of geometrical optics, we have a relationshipbetween 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 beapproximated by a function Msphere≈ ( Imax / I0 ) β , with β≈ 0.34. Th e diff erence betweenthe exact curve and approximated formula for M ( n ) is < 1 % for the whole range ofrefractive index from 1 to 1.95. Note that geometrical optics approximation yieldssingularity 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 doesnot depend on the particle size. However, one can see this dependence under theapproximation of the Mie theory, see Figure 4d in the article.

Energy fl ow simulation . Within the framework of classical Mie theory, the timeaveragedPoynting vector (energy fl ow) is given by S E = × 12 Re[ *] H and fi eld linesare the solutions of the diff erential equation d x / Sx = d y / Sy . We developed a Fortranprogram based on Mie formulation, and in Supplementary Figure S5 , we presentthe Poynting vector lines for the microsphere with radius a = 2.37 μ m and refractiveindex n = 1.46 illuminated by a plane wave with λ = 600 nm. We can construct thevirtual image, using the reciprocity principle and extrapolation of the Poyntingvector, 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 ofvirtual image construction as in geometrical optics. We extrapolate not thestraight ray but plot tangential line to the lines with some curvature. Th is imageconstruction yields a magnifi cation of 2 – 4 times depending on the particularPoynting vector line.