Subwavelength Far Field Imaging of Nanoparticles with Parametric

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Subwavelength Far Field Imaging of Nanoparticles with Parametric Indirect Microscopic Imaging Kaleem Ullah, Xuefeng Liu, Muhammad Habib, and Zhe Shen ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b01406 • Publication Date (Web): 23 Jan 2018 Downloaded from http://pubs.acs.org on January 23, 2018

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Subwavelength Far Field Imaging of Nanoparticles with Parametric Indirect Microscopic Imaging Kaleem Ullah1, ‡, Xuefeng Liu1, ‡, *, Muhammad Habib2 and Zhe Shen1 1

School of electronic Engineering and Optoelectronic Technology, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, China 2

National Synchrotron Radiation Lab, University of Science and Technology of China, Hefei, Anhui, China. *[email protected] In this work, we propose a polarization modulation technique that employs a reconstruction method to map the subwavelength scattering field distributions in the form of polarization parameters. The spatial signature of these indirect parameters delivers an extra scattering information that helps us to resolve scattering modes information of the sample under test. We apply this method to single and dimer spherical particles and we successfully resolve their spatial scattering distribution. In particular, we explore the subwavelength scattering modes information provided by the spatial signature of these polarization parameters. The experimental results have been verified by Mie theory and finite difference time domain (FDTD) method.

Keywords: Scattering, spatial signature, polarization modulation, optical modes, indirect parameters, nanoparticles.

The detection and visualization of sub-wavelength features of the object have numerous applications in imaging, spectroscopy, material science, biology, healthcare, and security

1–5

. In

conventional optical microscopy, the diffractive nature of light exhibits a fundamental limitation on the resolution of electromagnetic wave-based imaging systems

6–12

. This "diffraction limit"

has been well understood since the times and contributions of Abbe and Rayleigh

13,14

. Several

fluorescent super-resolution methods can achieve a λ/10 resolution and single-molecule imaging sensitivity but they need photo-active or photo-switchable fluorophores. Strict assessment of fluorescent probes is required before being used in applications. Moreover, these methods cannot be usable for the study of non-fluorescence samples 15–22.

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The foundation of the super-resolution of an optical microscopy depends on the detection of the near field signals which contains the sub-wavelength features of the sample under test (SUT) 33,34

. It is true that near-field scanning optical microscopy (NSOM) can collect the near field

information by scanning with a sharp tip, a few nanometer away from the SUT to form the image which is beyond the diffraction limit

23–26

. However, NSOM is difficult to operate in non-

invasive mode and only limited to the surface imaging

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. Furthermore, its area of mapping the

scattering field with subwavelength features is narrow which prevents it to image the subdiffraction scattering field to a wider range. Newly proposed super and hyper-lens can also achieve nanoscale scattering features in a clever way by utilizing the evanescent wave spectrum. However, a subsequent study demonstrated that due to the resonant nature of enhancing evanescent waves, resolving capability of the super-lens is seriously weaken by the material loss. Furthermore, evanescent waves could not be focused by using the conventional optics 28–32.

In this work, we applied polarization parametric indirect microscopic imaging (PIMI)

35

that

utilizes a polarization modulation illumination scheme to obtain the scattering far field changes. These changes produced as a result of the near to far field coupling occurs due to the anisotropic features present in SUT. This near to far field coupling in PIMI and careful filtering and fitting of the curve during the reconstruction process narrowed down the point spread function (PSF) width, and therefore we can obtain the nanoscale scattering features of the SUT. We report the ability of the PIMI to map the sub-diffraction scattering distribution in the form of polarization PIMI parameters of an isolated and dimer nanospheres. Using this method, we obtain very fine details about the scattering field distribution of the SUT that cannot be achieved by the conventional optical microscopy.

Several works have been reported based on wide and far field microscopy. They use the polarization modulation and fitting process to increase the resolving power of their system

41-43

.

They use different polarization varying field to get near to far field coupling from the SUT to increase the imaging sensitivity. In comparison to these methods, our proposed method is different in two aspects. Firstly, in our post processing algorithm, our method enables to calculate the Stokes parameters with the interconnection of Jones and Muller models. Secondly, due to the controllability on the modulation speed, far field variation quantification and filtering

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off the extra diffraction, our method has the ability to detect the nano-scattering field which is confirmed by FDTD simulations.

Theoretical and Experimental Basis PIMI system is built by modifying a conventional optical far field microscope such that the variation of the polarization status of incident light can be precisely controlled, imaging was subsequently obtained by analyzing the dependency of the optical intensity transmitted through or reflected from the SUT. As due to the rotation of the polarizer, there are intensity variations, the intensity on the CCD can be described by the following equation as 36,37: I=

I0 [1 + sin 2(α − φ ) sin δ ] 2

(1)

Where I0 is the un-polarized intensity, ɑ is the incident angle, ϕ is the angle of polarization also called as the angle along the slow vibration axis

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and δ is the optical retardation (phase shift

between the Ey and Ex). If we expand the equation 1 trigonometrically, then we obtained: I=

1 1 1 I 0 + I 0 sin δ cos 2φ sin 2α + I 0 sin δ sin 2φ cos 2α 2 2 2

(2)

We can derive the required parameters after the fitting by the following equation:

I i = a 0 + a 1 sin α + a 2 c o s α

(3)

Comparison of equation (2) and (3) gives us: a0 =

1 1 1 I 0 , a1 = I 0 sin δ cos 2φ , a 2 = − I 0 sin δ sin 2φ 2 2 2

(4)

If we rotate the polarization to total 360o angles, then a total number of angles are N= 360o and ɑ0, ɑ1 and ɑ2 calculated: N N N 1 2 2 a0 = ∑ Ii , a1 = ∑ Ii sin αi , a2 = ∑ Ii sin αi i =1 N i =1 N i =1 N

(5)

Using these parameters, we can find our desired quantities as: 1  2 2 2  (a + a ) (a + a ) 1 I dp = a0 , sin δ = , φ = arccos  + 1 2    a0 2 a0     2 1

1 2 2 2

3


(6)

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By using the equation 6, we calculated Stokes parameters by a mutual relationship between Jones and Muller model which are given by equation 7 as: S0 = I dp (1 + sin δ ) = E02x + E02y S1 = I dp (1 + sin δ ) cos 2φ = E02x − E02y S 2 = 2 I dp (1 + sin δ ) cos 2φ = 2 E0 x E0 y sin δ

(7)

S3 = 2 I dp (1 + sin δ ) sin 2φ = 2 E0 x E0 y cos δ

Field intensities at each pixel of the CCD recorded after impinging the linear polarization field from 0 to 2π and fit at each pixel using the equation 3. After fitting the curve, by following the equations 4 to 6, the quantities Idp, sinδ, and ϕ have been derived from the fitting curve. By utilizing these derived quantities, we calculated the Stokes parameters as described by equation 7. E0x and E0y are the amplitude of the electric field components in x and y-direction. δ is the phase shift between these orthogonal electric field components also named as optical retardation. Idp is the average of all polarization intensities as given by equation 6. In PIMI, due to the polarization modulation, we can sinusoidally formulate the intensity variation at each spatial point that the PSF covers. Also, we can analyze and check that whether the spatial point of the experimental data follows the coupling principle according to the equation 3 or not. The data points following the near to far field coupling principle fit well with equation 3 according to the fitting criteria such as adjusted root square 35 and those don’t follow, filter out as noise. As a result, the width of the PSF is narrowed down and the optical diffraction limit is broken. In this way, we become able to map the sub-diffraction scattering features of the SUT. A schematic of how the filtering and fitting process in the PIMI system makes us able to differentiate between two closely situated points is shown in Fig. 1. In PIMI, only the middle portion of the PSF confirms the near to far field coupling principle and fit well with the fitting criteria 35. In Fig. 1(a), a blurry image recorded by a diffraction limited system is shown. The two points in this diffraction limited spot are not resolved as can be visualized from Fig. 1(a). Figure 1(b, c) illustrates that how the PIMI fitting and filtration process resolves two close ranged points. The width of the PSF decreases due to goodness of the fit that avoid extra scattering

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signals from the neighboring objective field points and we become able to break the diffraction limit.

Figure 1. (a) A diffraction limited spot in which two points are un-resolved. (b) Fitting process represents the fitting curve in red solid line fitting the experimental data points shown in blue square shape. (c) Two points are resolved after the fitting process in PIMI system.

A schematic of the PIMI system with the whole process has been displayed in Fig. 2. As we can see that in Fig. 2(c), different polarizations obtained different anisotropic structural characteristics and scattering information from the SUT. Based on the different scattering information enabled by different linearly polarized light illumination, every PIMI parameter exhibits different spatial signature that is different from the conventional microscopic (CM) scattering signature and depends on the atomic arrangement of the SUT as well as on the shape and size. The spatial signature of every PIMI parameter is plotted in Fig. 2(e, g) for the data extracted in the form of a line shown in Fig. 2(d, f). As we can observe that away from the particle boundary, the curve of CM is decayed and delivered no angular scattering information as can be observed from Fig. 2(e, g). In Fig. 2(e), we can observe that unlike the CM, away from the particle, spatial scattering signatures of the PIMI parameters S0 and S1 are different. This spatial variation trend of the scattering field is even more remarkable in the spatial signatures of the S2, S3, sinδ and ϕ parameters as shown in Fig. 2(e). These spatial signatures, unlike CM, conveyed scattering information within the boundary of the particle as well as away from the particle as can be visualized from Fig. 2(e).

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Figure 2. (a) Schematic of the PIMI system. (b) A fitting method representation, the rectangular blue points are the experimental data points and the solid black curve is the fitting curve. (c) Scattering field distribution of a Cu2O particle at 532 nm wavelength for an angle range starts from 0o to 360o with 36o angle width under bright field illumination using 100x objective of the numerical aperture of 0.90. (d, f) A representation of the horizontal and vertical line on a PIMI parameter S0 describes that how the data has been extracted from every PIMI parameter and from CM. (e, g) The data points plotted for every spatial signature delivered by PIMI parameters and for CM. We also plotted the intensity profiles by drawing the data in the form of a vertical line as shown in Fig. 2(f). We can analyze that the intensity field variation trend in CM is also the same as like in horizontal line data plotting shown in Fig. 2(e). However, the S0 and S1 spatial signatures are changed from the horizontal line case as can be observed with the comparison of Fig. 2(e &g). The spatial signatures of S2, S3, sinδ and ϕ parameters are also changed from horizontal line curves as displayed in Fig. 2(g). The same spatial signature of CM in both cases proved that its scattering distribution is isotropic and it does not contain any angular scattering information of the SUT whereas in case of spatial signature delivered by PIMI parameters contains angular scattering distribution as well as the polarization status information. The spatial signature of the

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PIMI parameter “Idp” is the same as of the CM, the reason may lie in the fact that it is an average effect of all the polarization intensities as shown in Fig. 2(e, g).

We have illustrated the working principle of PIMI system in Fig. 2. The simple schematic of the system has been shown in Fig. 2(a). The modulator rotated in a fine mechanical controlled atmosphere and a highly sensitive CCD recorded the images under different polarization illuminations. We recorded every image on the CCD with a step width of 18o in order to remove minor errors by averaging. A representation of bright field images for an angle range of 360o has been shown in Fig. 2(c) with a step width of 36o. After recording these images, the filtering and fitting process continuously removes the extra diffraction offered by the neighboring source points at every pixel of the CCD. In the fitting process, the spatial points which located in the middle of the PSF distribution follow the coupling principle. These points are called the authentic points whereas the other points filtered off. In this way, the width of the PSF narrowed down and we can differentiate between two close ranged points.

As we have explained, how PIMI makes us enable to resolve two close ranged points. In Fig. 3, the same particle with different fitting level has been displayed. Fig. 3(a) represents the different reconstruction curves with the different fitting level of the experimental data points. The curve that exhibits more authentic points corresponds to a better resolved image and narrow width of the PSF. PIMI bright field image of parameter ϕ with different fitting level has been displayed in Fig. 3(b). When less number of experimental data points reach the fitting criteria, the resolution of the image is low as shown in Fig. 3(b) and a high number of fitting points correspond to better sensing of the scattering distribution as can be seen from the Fig. 3(b). If we increase the number of points follows the equation 3, the width of the PSF decreases and hence, we can record the sub-diffraction scattering signal including the structural information of the SUT as shown in Fig. 3(c).

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Figure 3. (a) Fitting curve with different level of fitting, the rectangular points represent the experimental data points whereas the solid curves represent the fitting curve. (b) Bright field scattering distribution of a zirconium iron (ZrFe) spherical particle by PIMI method using 100x objective of the numerical aperture equal to 0.90. The length of the scale bar is ~ 200 nm and wavelength used for the measurement is 532 nm. (c) The 3D Gaussian distribution represents an order of decreasing the width of the PSF i.e. the best fitting curve corresponds to lower width and lower fitting curve represents the larger width of the PSF.

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Results and Discussion We apply PIMI method for recording the scattering distributions of the ZrFe particles dispersed on the silicon substrate. Fig. 4 shows the CM and PIMI parameters “ϕ” results. In order to compare the resolving power and subwavelength far field sensing ability between CM and the PIMI, we extract several particles out from the full field distribution image shown in Fig. 4(a, b). A particle from the same position has been extracted from images provided by Fig. 4(a, b). This particle has been shown in Fig. 4(c & f). As we can see that PIMI resolves the inner scattering features of that SUT which are lacked by the CM. These results proved a remarkable resolving power of the PIMI system. We plotted the line intensity graph as shown in Fig. 4(d, e) by extracting the data with help of an insertion of line on both the images (Fig. 4(c, f)).

It can be seen a huge difference in the images of the CM and the PIMI system regarding resolving features of the SUT. The full width at half maximum (FWHM) in the intensity line profile plot of PIMI is about 42 and 48 nm. This is about 5 to 6 times less than the calculated FWHM of the intensity profile plot delivered by the CM images shown in Fig. 4(d). An exceptional sensing and resolving ability of the PIMI can be analyzed from Fig. 4(g-i). The field distributions of three particles have been displayed from CM and PIMI full spot image provided in Fig. 4(a, b). The length of the scale bar is about 200 nm in these images which proves the capability of the PIMI to sense the subwavelength scattering signals from the SUT beyond the diffraction limit.

PIMI utilizes the polarization modulation field in a controlled way before impinging on the SUT. Polarization modulation adds information to the super-resolution

38, 39

and different polarization

extracts different scattering information based on optical anisotropy of the SUT. We apply PIMI method in order to investigate the angular scattering distributions around a Cu2O sphere and a dimer. In Fig. 5(a), we have displayed the scanning electron microscope (SEM) micrograph which shows a perfect spherical submicron particle (radius= 450 nm). We can see a difference in the scattering field distribution between CM and our PIMI parameter ϕ in Fig. 5(b and c). The distribution given by the CM is almost isotropic whereas the field distributions delivered by our PIMI method resolve the scattering angular distribution of the Cu2O sphere as can be seen in Fig. 5(c). In Fig. 5(c), the inner lobe information within the boundary of the Cu2O sphere can be seen

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which only can be viewable in near field optical microscopy. We have proved this inner lobe information through our FDTD simulation as can be seen in Fig. 5(d). The two lower intensity lobes as indicated by arrow are well resolved and two higher intensity lobes appeared in red color at the vertical edges of the sphere. The two outer higher intensity and lower intensity lobes indicated by arrow symbol can also be seen in Fig. 5(c). Our FDTD simulation also showed these two outer lobes but far away from the edges of the sphere, the lobes are again inverted which is not like as we get in the experimental distribution. However, the inner and very close outer lobe pattern of the simulated results indicated by arrow symbol matched with the experimental results.

In order to understand the angular distribution of a sub-micron Cu2O particle delivered by PIMI, we calculated the multipolar scattering contributions to the scattering efficiency using Mie theory 45

provided in Fig. 5(e). The scattering efficiency value of magnetic dipolar (MD) is slightly

higher than the electric dipolar (ED) at a wavelength equal to 532 nm. Reversely, electric quadrupole (EQ) value is much higher than the magnetic quadrupole (MQ). The magnetic octupole (MO) resonance mode contribution is higher than the electric octupole (EO) and having the highest scattering efficiency in the resonance modes provided in Fig. 5(e) calculated by the Mie theory. From the multipolar decomposition delivered by Mie calculations, we can observe that the distribution delivered by PIMI for a submicron Cu2O sphere is actually a sum of different multipolar modes with magnetic hexapolar as a dominant mode.

We calculated the Stokes parameters using FDTD method which confirms the nanoscale scattering field mapping ability of the PIMI system. Figure 6 showed the experimental scattering distribution in terms of Stokes parameters provided by PIMI and the simulation results delivered by FDTD. In S0 result, the horizontal inner lower intensity lobe is well matched between the experimental and simulated results as indicated by small arrow in Fig. 6(a, e). The higher intensity lobe indicated by arrow symbol in the experimental image appeared on the vertical edge of the particle whereas this edge is also can be seen in S0 simulation result. The higher intensity outer lobe distribution in S0 as indicated by arrow is well matched, however, the outer low intensity lobe in the simulation result tends to split into two lobes as shown in Fig 6(b).

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Figure 4. Full spot image was taken by the 100x objective of the numerical aperture 0.90. (a) CM system. (b) PIMI method. (c, f) One particle extracted from CM and PIMI in analyzing the resolving power comparison. (d, e) Intensity profile plotting by drawing a line in the same position of both the images as shown in (c & f). (g-i) The images extracted from the (a) and (b) for showing a comparison of the resolving power between the CM and PIMI method regarding the far field sensing signals. The length of the scale bar is 200 nm in (g-i) whereas it is equal to 1 microns in (c, f) images. The measurement is taken at a wavelength of 532 nm.

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Figure 5. (a) SEM image of the Cu2O sphere of radius 450 nm. (b) The conventional microscopic image was taken with 100x objective of the numerical aperture of 0.90 with a bright field illumination at 532 nm wavelength. (c) PIMI parameter “ϕ” image taken with the same optics as we used in the conventional image. (d) Near field scattering image of PIMI parameter “ϕ” calculated by FDTD at 532 nm wavelength. (e) Multipolar scattering contribution to the scattering efficiency of a Cu2O Sphere of radius equal to 450 nm calculated by Mie theory.

Figure 6. (a-d) PIMI Stokes parameters images of Cu2O submicron particle taken with 100x objective of the numerical aperture of 0.90 with a bright field illumination at 532 nm wavelength. (e-h) Calculated FDTD near field Stokes parameters at wavelength of 532 nm.

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Similarly, the S1 result delivered by the PIMI also resolved the angular scattering distribution within the boundary of the particle as well as in the outer area as can be visualized from the Fig. 6(b, f). The matching between the simulation and experimental results in case of S2 and S3 parameters is remarkable as can be seen from the comparison of the Fig. 6(c, d) and Fig. 6(g, h). Along with the inner lobe distribution, the outer lobe scattering distribution is also well matched as indicated by the small arrows in Fig. 6(c, g). The similarities in the scattering field mapping provided by PIMI and FDTD method proved the ability of our method to map the localization of the optical modes in nanoscale area which cannot be obtained with conventional far field microscopy.

We also applied our method to resolve the spatial scattering information of the Cu2O dimer. In case of the dimer, we received an isotropic scattering information around the dimer using CM as shown in Fig. 7(a). But the parameters of sinδ and ϕ of the PIMI, make us able to resolve their angular spatial distribution as shown in Fig. 7(c, d). The lobe information in the big sphere is quite clear but in case of the smaller sphere, one of the small intensity lobes has been perturbed. This might be caused due to the field interaction between the particles. Idp has no lobe information, the reason may lie in the fact that it is the average of all polarization intensities, that is why it showed a contour like distributions around the dimer as shown in Fig. 7(b).

The Stokes parameters for this dimer structure is given in Fig. 7(e-h). In scattering information delivered by the Stokes parameters, S0 represents here the total intensity of the scattered field because it adds all the polarization including un-polarized light

40

. S0 clearly shows the two

higher intensity lobes of the big particle and also of the smaller particle. S0 also provides the information of the external field which may be formed due to the interference of the external scattering distribution of both particles. S0 resolved the external scattering lobes to a certain scattering range as shown in Fig 7(e). S1 which belongs to the linear polarization 40 adds just an isotropic information and provides no angular distribution as shown in Fig 7(f). In S2 spatial distribution, there is a clear lobe information as displayed in Fig. 7(g), similarly, the S3 also offers us a clear lobe information as shown in Fig. 7(h). S3 gives the information about the

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chirality because it is equal to the difference in the left and right hand circularly polarized lights 40

.

Figure 7. (a) CM scattering field image of the Cu2O dimer taken at 532 nm wavelength using 100x objective of the numerical aperture 0.90. (b-h) Scattered field distribution delivered by PIMI parameters using the same optics as used for CM image.

We can extract electric field spatial distributions from these Stokes parameters calculated by equation 7. These electric field distribution images extracted from the PIMI Stokes parameters consists of spatial angular information which contains nano-scattering information of the SUT. In order to validate our experimental findings, FDTD simulations have been carried out which verified that our super resolution method can record the subwavelength scattering field signals.

We calculated the magnitudes of the Ex and Ey from the Stokes parameters by using the equation 7. The scattering field of Ex represents the contour like ring structure within the boundary of two spheres of the dimer as represented in Fig. 8(a). The simulation result provided by Fig. 8(d), there are two ring-like structures which have quite resolved field distribution as compared to the

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experimental result. The difference should exist because, in simulation, we sliced the particle from the center. However, the overall pattern of the experimental scattering field distributions resembles with the simulation results. The field distribution carried by Ey is quite matching with the simulation result of Ey as shown in Fig. 8(b, e). The higher intensity lobes area in the experimental result of Ey is narrow as compared to simulation result. A remarkable resemblance is found in the experimental and simulated results of the ϕ as shown in Fig. 8(c, f). This distribution represents a quadrupolar dominant scattering mode.

Figure 8. (a,b) Experimental orthogonal components of the electric field Ex and Ey derived by the PIMI Stokes parameters, the measurement performed at 532 nm wavelength using 100x objective of the numerical aperture 0.90. (d,e) FDTD simulated near field Ex and Ey. (c,f) Experimental and simulated image of the azimuthal angle.

For studying more about the angular distribution of dimer resolved by PIMI, we calculated its extinction cross section by FDTD method. The lower amplitude peak has been appeared near our working wavelength, whereas two higher intensity peaks can be visualized at wavelengths of 650

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and 725 nm as displayed in Fig. 9(a). We plotted polar distribution at 532 nm wavelength in Fig. 9(b). In this far field distribution, the three lobes are well resolved, however, the lobe which corresponds to the forward direction is perturbed and try to split into two lobes as shown in Fig. 9(b). The splitting of this lobe might be due to the interaction between two particles. We further resolved the scattering response of these two particles independently with the Mie theory by calculating their multipolar contribution to the extinction cross section. From Fig. 9(c), it is obvious that major contribution is of EQ in R= 220 nm sphere, whereas in R=300 nm sphere, the major contribution is of MQ as presented in Fig. 9(d). From the Mie theory, the independent analysis of two spheres in dimer structure also showed the quadrupolar dominancy, which is in accordance with the PIMI dimer angular distribution resolving results.

Figure 9. (a) Extinction cross section of Cu2O dimer calculated by using the FDTD method. (b) Far field polar plot at 532 nm of a dimer delivered by FDTD method. (c, d) Multipolar

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contribution to the extinction cross section (SCS) of the Cu2O small sphere (R= 220 nm) and big sphere (R= 300 nm) respectively calculated by Mie theory at 532 nm wavelength.

Conclusion In summary, we have shown that how the highly defined modulated illumination, far field variation quantification and filtering in our system resolve nanoscale scattering field distribution in the form of polarization parameters. The angular distributions given by PIMI parameters provide us the information about the scattering multipolar modes. Using PIMI, we were able to investigate the scattering optical modes of a Cu2O isolated particle as well as of dimer. The FDTD scattering field simulation verified that the spatial signature offered by PIMI parameters contains the subwavelength information of the SUT that only can be viewable in scanning near field optical microscopy. These spatial signatures have not just provided the information about the scattering field distribution with fine details but also delivers a complete polarization information of this scattering field.

Methods Sample Preparation To synthesize Cu2O nanoparticles a typical solution route was employed 44. For the nanoparticle synthesis, research grade reagents were purchased, from Sigma-Aldrich, and used as it is in the experiment. In the first step, the transparent light green solution was prepared by slowly adding polyvinylpyrrolidone in 100 mL CuCl2.2H2O solution. After that 10 mL sodium hydroxide (NaOH) was added into polyvinylpyrrolidone-CuCl2.2H2O solution and stir for 30 minutes. In the next step ascorbic acid was added into PVP-CuCl2.2H2O solution drop by drop and aged for 3 h. These steps were performed in the water bath with constant stirring and heating. The molarities of polyvinylpyrrolidone, NaOH, and ascorbic acid were 0.01 mol L-1 (PVPMW 30000), 2.0 mol L-1 and 0.6 M respectively while used was. The obtained solution was centrifuged to get the desired precipitate. After that several times, washing was performed with DI water and ethanol to get rid of impurities followed by drying in an oven for several hours.

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Parametric Indirect Microscopic Imaging (PIMI) PIMI system has been built by modifying the conventional microscopy Olympus BX51.A schematic of the PIMI system is displayed in Fig. 1(a). An un-polarized visible source in the form of an incandescent lamp has been used. We have incorporated a homemade system in the optical path which is composed of a polarization modulation module of an angle precision of 0.05 degree and a Basler (PiA2400-17gm) CCD with a pixel resolution of 3.45 micron. The 3.45-micron-pixel CCD resolution leads to an outmost potential resolving power of 34.5nm if diffraction limit is broken and the Nyquist principle is fulfilled in the microscopic system, working with a 100x objective 35. The direct and indirect optical images were carried out at the illumination wavelength of 532nm.

Acknowledgement The authors wish to acknowledge the financial support by National Science Foundation China (NSFC) No. 61275163, 61501239, 61605078, 61604073, Natural Science Foundation of Jiangsu Province (Grant No. BK20160839), National Key Research and Development Program of China (2017YFF0107100), National Natural Science Foundation of China (61501239) and the “Zijin Professor Project” of Nanjing University of Science and Technology. MH thanks the National Natural Science Foundation of China for financial support (Project No. U1532112, 11375198, 11574280). MH and KU are grateful to CSC fellowship and Xiaolei Wen for helping in sample preparation.

Author Contributions These authors ‡ contribute to this work equally.

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Subwavelength Far Field Imaging of Nanoparticles with Parametric

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