Abstract

High-resolution and fast-paced optical microscopy is a requirement for current trends in biotechnology and materials industry. The most reliable and adaptable technique so far to obtain higher resolution than conventional microscopy is near-field scanning optical microscopy (NSOM), which suffers from a slow-paced nature. Stemming from the principles of diffraction imaging, we present fast-paced graphene-based scanning-free wide-field optical microscopy that provides image resolution that competes with NSOM. Instead of spatial scanning of a sharp tip, we utilize the active reconfigurable nature of graphene’s surface conductivity to vary the diffraction properties of a planar digitized atomically thin graphene sheet placed in the near field of an object. Scattered light through various realizations of gratings is collected at the far-field distance and postprocessed using a transmission function of surface gratings developed on the principles of rigorous coupled wave analysis. We demonstrate image resolutions of the order of λ0/16 using computational measurements through binary graphene gratings and numerical postprocessing. We also present an optimization scheme based on the genetic algorithm to predesign the unit cell structure of the gratings to minimize the complexity of postprocessing methods. We present and compare the imaging performance and noise tolerance of both grating types. While the results presented in this article are at terahertz frequencies (λ0=10  μm), where graphene is highly plasmonic, the proposed microscopy principle can be readily extended to any frequency regime subject to the availability of tunable materials.

© 2017 Optical Society of America

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2016 (7)

S. N. Shirodkar and E. Kaxiras, “Li intercalation at graphene/hexagonal boron nitride interfaces,” Phys. Rev. B 93, 245438 (2016).
[Crossref]

A. Forouzmand and H. Mosallaei, “Tunable two dimensional optical beam steering with reconfigurable indium tin oxide plasmonic reflectarray metasurface,” J. Opt. 18, 125003 (2016).
[Crossref]

W. Fan, B. Yan, Z. Wang, and L. Wu, “Three-dimensional all-dielectric metamaterial solid immersion lens for subwavelength imaging at visible frequencies,” Sci. Adv. 2, e1600901 (2016).
[Crossref]

S. Inampudi, M. Nazari, A. Forouzmand, and H. Mosallaei, “Manipulation of surface plasmon polariton propagation on isotropic and anisotropic two-dimensional materials coupled to boron nitride heterostructures,” J. Appl. Phys. 119, 025301 (2016).
[Crossref]

M. Zeng, Y. Xiao, J. Liu, W. Lu, and L. Fu, “Controllable fabrication of nanostructured graphene towards electronics,” Adv. Electron. Mater. 2, 1500456 (2016).
[Crossref]

C. M. Roberts, N. Olivier, W. P. Wardley, S. Inampudi, W. Dickson, A. V. Zayats, and V. A. Podolskiy, “Interscale mixing microscopy: far-field imaging beyond the diffraction limit,” Optica 3, 803–808 (2016).
[Crossref]

J. Cheng, S. Jafar-Zanjani, and H. Mosallaei, “Real-time two-dimensional beam steering with gate-tunable materials: a theoretical investigation,” Appl. Opt. 55, 6137–6144 (2016).
[Crossref]

2015 (6)

S. Inampudi, N. Kuhta, and V. A. Podolskiy, “Interscale mixing microscopy: numerically stable imaging of wavelength-scale objects with sub-wavelength resolution and far field measurements,” Opt. Express 23, 2753–2763 (2015).
[Crossref]

C. M. Roberts, S. Inampudi, and V. A. Podolskiy, “Diffractive interface theory: nonlocal susceptibility approach to the optics of metasurfaces,” Opt. Express 23, 2764–2776 (2015).
[Crossref]

Z. Li, K. Yao, F. Xia, S. Shen, J. Tian, and Y. Liu, “Graphene plasmonic metasurfaces to steer infrared light,” Sci. Rep. 5, 12423 (2015).
[Crossref]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, and M. Polini, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14, 421–425 (2015).
[Crossref]

A. Forouzmand, H. M. Bernety, and A. B. Yakovlev, “Graphene-loaded wire medium for tunable broadband subwavelength imaging,” Phys. Rev. B 92, 085402 (2015).
[Crossref]

A. Forouzmand and A. B. Yakovlev, “Tunable dual-band subwavelength imaging with a wire medium slab loaded with nanostructured graphene metasurfaces,” AIP Adv. 5, 077108 (2015).
[Crossref]

2014 (10)

Z. Jacob, “Nanophotonics: hyperbolic phonon-polaritons,” Nat. Mater. 13, 1081–1083 (2014).
[Crossref]

P. Doradla, K. Alavi, C. Joseph, and R. Giles, “Single-channel prototype terahertz endoscopic system,” J. Biomed. Opt. 19, 080501 (2014).
[Crossref]

C. S. Joseph, R. Patel, V. A. Neel, R. H. Giles, and A. N. Yaroslavsky, “Imaging of ex vivo nonmelanoma skin cancers in the optical and terahertz spectral regions optical and terahertz skin cancers imaging,” J. Biophoton. 7, 295–303 (2014).
[Crossref]

C. Park, J.-H. Park, C. Rodriguez, H. Yu, M. Kim, K. Jin, S. Han, J. Shin, S. H. Ko, and K. T. Nam, “Full-field subwavelength imaging using a scattering superlens,” Phys. Rev. Lett. 113, 113901 (2014).
[Crossref]

H. W. Lee, G. Papadakis, S. P. Burgos, K. Chander, A. Kriesch, R. Pala, U. Peschel, and H. A. Atwater, “Nanoscale conducting oxide PlasMOStor,” Nano Lett. 14, 6463–6468 (2014).
[Crossref]

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
[Crossref]

S. Inampudi, D. Adams, T. Ribaudo, D. Slocum, S. Vangala, W. Goodhue, D. Wasserman, and V. Podolskiy, “ϵ-near-zero enhanced light transmission through a subwavelength slit,” Phys. Rev. B 89, 125119 (2014).
[Crossref]

G. Popescu, L. L. Goddard, P. S. Carney, T. Kim, R. Zhou, M. A. Mir, and S. D. Babacan, “White light diffraction tomography of unlabeled live cells,” Nat. Photon. 8, 256–263 (2014).
[Crossref]

J. Cheng and H. Mosallaei, “Optical metasurfaces for beam scanning in space,” Opt. Lett. 39, 2719–2722 (2014).
[Crossref]

J. Cheng, D. Ansari-Oghol-Beig, and H. Mosallaei, “Wave manipulation with designer dielectric metasurfaces,” Opt. Lett. 39, 6285–6288 (2014).
[Crossref]

2013 (5)

M. Farmahini-Farahani, J. Cheng, and H. Mosallaei, “Metasurfaces nanoantennas for light processing,” J. Opt. Soc. Am. B 30, 2365–2370 (2013).
[Crossref]

Z. Fei, A. Rodin, W. Gannett, S. Dai, W. Regan, M. Wagner, M. Liu, A. McLeod, G. Dominguez, and M. Thiemens, “Electronic and plasmonic phenomena at graphene grain boundaries,” Nat. Nanotechnol. 8, 821–825 (2013).
[Crossref]

P. Doradla, K. Alavi, C. S. Joseph, and R. H. Giles, “Continuous wave terahertz reflection imaging of human colorectal tissue,” Proc. SPIE 8624, 86240O (2013).
[Crossref]

P. Doradla, K. Alavi, C. Joseph, and R. Giles, “Detection of colon cancer by continuous-wave terahertz polarization imaging technique,” J. Biomed. Opt. 18, 090504 (2013).
[Crossref]

J. Cheng, W. L. Wang, H. Mosallaei, and E. Kaxiras, “Surface plasmon engineering in graphene functionalized with organic molecules: a multiscale theoretical investigation,” Nano Lett. 14, 50–56 (2013).
[Crossref]

2012 (3)

M. Osada and T. Sasaki, “Two-dimensional dielectric nanosheets: novel nanoelectronics from nanocrystal building blocks,” Adv. Mater. 24, 210–228 (2012).
[Crossref]

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7, 699–712 (2012).
[Crossref]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, and P. Godignon, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

2011 (5)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, and Y. R. Shen, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

C. H. Lui, Z. Li, K. F. Mak, E. Cappelluti, and T. F. Heinz, “Observation of an electrically tunable band gap in trilayer graphene,” Nat. Phys. 7, 944–947 (2011).
[Crossref]

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref]

C.-F. Chen, C.-H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, and S. G. Louie, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471, 617–620 (2011).
[Crossref]

Y. Yang, G. Yu, J. J. Cha, H. Wu, M. Vosgueritchian, Y. Yao, Z. Bao, and Y. Cui, “Improving the performance of lithium–sulfur batteries by conductive polymer coating,” ACS Nano 5, 9187–9193 (2011).
[Crossref]

2010 (2)

S. Thongrattanasiri, N. Kuhta, M. Escarra, A. Hoffman, C. Gmachl, and V. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
[Crossref]

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105, 256805 (2010).
[Crossref]

2009 (1)

Y. Zhang, T.-T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, “Direct observation of a widely tunable bandgap in bilayer graphene,” Nature 459, 820–823 (2009).
[Crossref]

2008 (5)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103, 064302 (2008).
[Crossref]

T. Stauber, N. Peres, and A. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78, 085432 (2008).
[Crossref]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101, 196405 (2008).
[Crossref]

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ACS Nano (1)

Y. Yang, G. Yu, J. J. Cha, H. Wu, M. Vosgueritchian, Y. Yao, Z. Bao, and Y. Cui, “Improving the performance of lithium–sulfur batteries by conductive polymer coating,” ACS Nano 5, 9187–9193 (2011).
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Adv. Mater. (1)

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AIP Adv. (1)

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Appl. Opt. (2)

Appl. Phys. Lett. (2)

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93, 131905 (2008).
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Figures (4)

Fig. 1.
Fig. 1. (a) Schematic setup of GNOM. Objects are placed on a substrate (ε=2.25). Graphene sheet slices with electrodes are placed at a distance h on top of the object. Red and black colors of the graphene slices represent different values of surface conductivity. The inset is the schematic for transmission function calculation. (b), (c) The relative variation in field amplitude at angles of 0° and 30°, respectively, for five different objects numbered 1–5 shown as insets. Object 1total size(5λ0), Object 2total size(3λ0), Object 3total size(2λ0), Object 4total size(2λ0) with subwavelength features (λ0/8, λ0/4, λ0/2, λ0/8, λ0/4), and Object 5total size(2λ0) with subwavelength feature sizes (λ0/16, λ0/8, λ0/4, λ0/2, λ0/16, λ0/4). The gaps between the subwavelength features are of relative size. For objects with the smallest subwavelength features (more evanescent spectrum) the variation in relative amplitude is high and irregular (nonredundant) in pattern. |H| and |H0| represent the amplitude of the field with and without a grating, respectively.
Fig. 2.
Fig. 2. Image reconstruction using binary graphene gratings. (a) Transmitted far-field intensity “measurements” of the test object (calculated using COMSOL) in the normal direction with grating periodicity reconfigured from Λ=λ0 to Λ=λ0/16 in 300 steps, λ0=10  μm. The unit cell has two equal size components with σ1Ef and σ2=104. The object-to-grating distance is h=100  nm. (b) The corresponding transmission function matrix (TG) with rows as the rows of the transmission function of each grating in the normal direction calculated using Eq. (10), where color represents the magnitude of the matrix element. Upper and lower sections represent gratings with the two Fermi levels of graphene. (c) The test object (dotted line) and the reconstructed image (solid line) using Eq. (13). The overall size of the object is 2λ0, and the subwavelength feature sizes are (λ0/16, λ0/8, λ0/4, λ0/2, λ0/4) with gaps of relative size between them. The reconstructed image resolves the gaps and features of the object.
Fig. 3.
Fig. 3. Image reconstruction using gratings with optimized unit cells. (a) Fermi level, consequently the surface conductivity, profile of unit cells optimized to maximize the coupling of each wave vector (kxa) to the corresponding diffraction order in the propagation regime (Λ=λ0, λ0=10  μm). Each unit cell has 32 elements. A color bar is displayed for clarity. (b) Line plots of the same quantity for three representative wave vectors. (c) The elements of composite transmission matrix TG, where each row is the row of the transmission function calculated using Eq. (10) for corresponding transmission direction of each optimized grating. (d) The real part of the magnetic field of the object (black dashed line) from COMSOL and the corresponding image (solid and dotted lines) recovered analytically using Eqs. (3) and (15) with no numerical postprocessing. The inset shows the corresponding amplitude spectrum of the object and image. The electric and magnetic fields of the image are computed using Eq. (4) as H=Hz and E=Ex2+Ez2.
Fig. 4.
Fig. 4. Noise tolerance of the image reconstruction. Image reconstruction using (a) binary graphene gratings and (b) gratings with optimized unit cells by adding multiple realizations of random noise to the measured far-field intensity. The dotted line represents the object; the solid line and the shaded region represent the mean image and the standard deviation of all noise patterns, respectively. The addition of noise to the “measured” intensity is performed as Imeas;noise=|Hmeas+Nrmax(|Hmeas|)|2, where I represents intensity, H represents complex field, N is the noise percent level, and r is a random number between 1 and 1. In comparison to (a), (b) has less artifacts surrounding the object and reconstructs all the features of the object at noise levels as high as 20%.

Equations (15)

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kxm=kx0+m2πΛ,
σ=e2Efε0cπ211τiω,
Hobj(x)=a+(kx)eikxxdkx=wl=al+(kxl)eikxlx,
Hy{I,II}(x,z)=m=[am+{I,II}eikzm{I,II}z+am{I,II}eikzm{I,II}z]eikxmx,Ex{I,II}(x,z)=m=kzm{I,II}k0ε{I,II}[am+{I,II}eikzm{I,II}zam{I,II}eikzm{I,II}z]eikxmx,Ez{I,II}(x,z)=m=kxmk0ε{I,II}[am+{I,II}eikzm{I,II}z+am{I,II}eikzm{I,II}z]eikxmx.
kzm{I,II}=k02ε{I,II}kxm2,
ExI(x,z=0)ExII(x,z=0)=0,HyI(x,z=0)HyII(x,z=0)=σ(x)ExII(x,z=0).
1εIKzI(AI+AI)1εIIKzII(AII+AII)=0,(AI+AI)(AII+AII)=1k0εIIΞKzII(AII+AII).
[AIAII+]=[R+TT+R][AI+AII],
R+=[k0(εIIKzI+εIKzII)+KzIIΞKzI]1[k0(εIIKzIεIKzII)+KzIIΞKzI],T=[k0(εIIKzI+εIKzII)+KzIIΞKzI]1[2k0εIKzII],T+=[k0(εIIKzI+εIKzII)+KzIΞKzII]1[2k0εIIKzI],R=[k0(εIIKzI+εIKzII)+KzIΞKzII]1[k0(εIIKzIεIKzII)+KzIΞKzII].
T=[Tm1,n1Tm1,nTm1,n+1Tm,n1Tm,nTm,n+1Tm+1,n1Tm1,nTm+1,n+1],
TgpF=m=TgmGexp(ikxmxp)sin(kxmP/2)/(kxmP/2).
IgC=|ag|2=|pTgpFhp|2.
|IgCImeas|2min.
n|Tbn+δan|2min.
a(kxa)=Ameas(g)(kxb)TabGAmeas(0)(kxb)TaaG,

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