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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 7 — Aug. 1, 2013
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Breaking Optical diffraction limitation using Optical Hybrid-Super-Hyperlens with Radially Polarized Light

Bo Han Cheng, Yung-Chiang Lan, and Din Ping Tsai  »View Author Affiliations


Optics Express, Vol. 21, Issue 12, pp. 14898-14906 (2013)
http://dx.doi.org/10.1364/OE.21.014898


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Abstract

We propose and analyze an innovative device called “Hybrid-Super-Hyperlens”. This lens is made of two hyperbolic metamaterials with different signs in their dielectric tensor and different isofrequency dispersion curves. The ability of the proposed lens to break the optical diffraction limit is demonstrated using numerical simulations (with the resolution power of about λ/6). Both a pair of nano-slits and a nano-ring can be imaged and resolved by the proposed lens using the radially polarized light source. Such a lens has great potential applications in photolithography and real-time nanoscale imaging.

© 2013 OSA

1. Introduction

Ernst Abbe first introduced so-called diffraction limit d=λ/2(nsinθ), whereλis the wavelength,d is the distance between two objects, and nsinθis the numerical aperture (NA) [1

1. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Press, 1999).

]. Generally, features smaller than half wavelength of the light are permanently lost in the image because the waves which carry information of the sub-wavelength details are transverse waves with their wave vectors larger than free space wave vectork0=ω/c. Those wave vectors decay exponentially from the surface of the object in free space [2

2. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

]. This is the key reason for conventional optical microscopy cannot capture the minuscule details of the object in the far field region. In order to improve the optical imaging resolution, and make good use of the optical evanescent wave or near field, photon scanning tunneling microscopy [3

3. D. P. Tsai, H. E. Jackson, R. Reddick, S. Sharp, and R. J. Warmack, “Photon scanning tunneling microscope study of optical wave-guides,” Appl. Phys. Lett. 56(16), 1515–1517 (1990). [CrossRef]

5

5. D. P. Tsai, J. Kovacs, and M. Moskovits, “Applications of apertured photon scanning-tunneling-microscopy (APSTM),” Ultramicroscopy 57(2-3), 130–140 (1995). [CrossRef]

] and near-field scanning optical microscopy [6

6. E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991). [CrossRef] [PubMed]

8

8. B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000). [CrossRef]

] are the major paths to achieve near-field super-resolution image. However, low throughput, poor compatibility with various environment/samples, and inability to obtain the whole image at one scan are the drawbacks need to be overcome.

According to Pendry’s conceptual model, using a slab with the refractive index n=1, both propagating and evanescent waves excited from the objects can contribute to the resolution image [9

9. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

]. The perfect lens should be realized by tuning the parameters of constituent elements (thin metal wires and split ring) which provide the potential to fulfill the super-resolution condition as mentioned above [10

10. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]

, 11

11. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

]. However, it is difficult to materialize at present due to the feasibility of simultaneously reaching negative permittivity and permeability, as well as the impedance mismatch between the perfect lens and surrounding medium [12

12. D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003). [CrossRef]

]. Some other lenses which are similar to perfect lens named superlens have shown the ability of breaking diffraction limit theoretically [13

13. W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005). [CrossRef]

] and experimentally [14

14. A. Schilling, J. Schilling, C. Reinhardt, and B. Chichkov, “A superlens for the deep ultraviolet,” Appl. Phys. Lett. 95(12), 121909 (2009). [CrossRef]

]. However, in these so-called superlenses, all the fine features (evanescent waves) cannot be brought to focus by conventional optical devices and instruments.

Recently, the multi-layered metal-dielectric structures [15

15. D. Schurig and D. R. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys. 7, 162 (2005). [CrossRef]

17

17. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]

] and the metal nanorod array structures [18

18. A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005). [CrossRef] [PubMed]

20

20. Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-Mediated Radiative Energy Transfer across a Silver Nanowire Array via Resonant Transmission and Subwavelength Imaging,” ACS Nano 4(9), 5003–5010 (2010). [CrossRef] [PubMed]

] have been proposed to have the ability of delivering evanescent information to far-field space optical microscopy. Due to their unusual optical property, the fine features with evanescent mode can be changed into propagation mode [2

2. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

]. They can be understood by considering the isofrequency curve (dispersion relation between the frequency and the wave vector) with hyperbolic forms which are known as hyperbolic metamaterials. Especially, the hyperbolic metamaterials with multi-layered metal-dielectric shape used for super-resolution are named hyperlens and have caught the eye and drawn attention to their potential applications since its first demonstration in 2007 [21

21. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007). [CrossRef] [PubMed]

, 22

22. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

].

The hyperlens with cylindrically or spherically curved multilayer stacks uses an approach of magnifying the sub-wavelength features [2

2. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

]. The evanescent waves excited from the objects (placed near or on the curved hyperlens) are magnified and transformed into the propagating waves in such anisotropic medium with a hyperbolic dispersion. However, the cylindrical structure has shortcomings [2

2. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

, 21

21. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007). [CrossRef] [PubMed]

, 22

22. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

], since it is inconvenient to put the objects on the curved platform for practical applications. Further, the semicircle space that is constructed by metal will form a cavity and affect the resolution ability at specific operation wavelength.

In this investigation, the proposed hybrid-super-hyperlens [23

23. B. H. Cheng, Y. Z. Ho, Y. C. Lan, and D. P. Tsai, “Optical hybrid-superlens-hyperlens for superresolution imaging,” IEEE J. Sel. Top. Quantum Electron. (to be published).

, 24

24. Y. T. Wang, B. H. Cheng, Y. Z. Ho, Y. C. Lan, P. G. Luan, and D. P. Tsai, “Gain-assisted Hybrid-superlens Hyperlens for Nano Imaging,” Opt. Express 20(20), 22953–22960 (2012). [CrossRef] [PubMed]

] with linearly and radially polarized incident light is theoretically investigated. The capability of this lens to break optical diffraction limit is proved by finite element method (FEM) and finite-difference time-domain (FDTD) simulation. The challenge relative to resolve complicated nano pattern is also investigated. Basically, the polarization of light source is an important factor which affects the integrity of the resolution image results from exciting surface plasmon polarions (SPPs) near the patterned region. We demonstrate that the whole magnifying far-field images can be obtained at one scan procedure by using radially polarized light source. That is, superposition of the images under incident light with different polarized directions is unnecessary. The applicability and superiority of hybrid-super-hyperlens for real applications such as photolithography and planar integrated optical devices [25

25. H. Wu, T. W. Odom, and G. M. Whitesides, “Reduction Photolithography Using Microlens Arrays: Applications in Gray Scale Photolithography,” Anal. Chem. 74(14), 3267–3273 (2002). [CrossRef] [PubMed]

, 26

26. E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012). [CrossRef] [PubMed]

] will also be discussed.

2. Analytical model structure and simulation method

Figure 1(a)
Fig. 1 Schematic of the hybrid-super-hyperlens which is composed of two hyperbolic metamaterials (i.e., superlens and hyperlens) with different dielectric tensor under TM wave illumination at 405 nm. The upper part is superlens which consists of 6 paris of alternately stacked Ag (30 nm) and Al2O3 (30 nm) layers, the lower part is hyperlens that is composed of 8 pairs of alternately stacked Ag (30 nm) and HfO2 (30 nm) layers. The orange parts are observed sample with thickness t = 60 nm. The width of grooves carved on the Chromium (Cr) is 50 nm.
shows the conceptual objective lens which is composed of two hyperbolic metamaterials i.e., superlens and hyperlens. For TM polarized wave, both of the optical dispersion relations of the superlens and hyperlens can be obtained by the transfer matrix method [27

27. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, Oxford, 2006).

]
cos(kxΛ)=cos(k1xd1)cos(k2xd2)12(ε1k2xε2k1x+ε2k1xε1k2x)sin(k1xd1)sin(k2xd2)
(1)
where Λ=d1+d2 is the period of one pair of alternately stacked metal and dielectric (d1andd2are the thickness of metal and dielectric region with relative permittivityε1and ε2respectively); k1x=(ε1k02kz2) and k2x=(ε2k02kz2) denote the x-directional wave vector in the metal and dielectric regions, respectively. The relations between the wavevectors (kx,kz)and the effectively parallel and perpendicular relative permittivities (εxeff,εzeff) can be further established.

Considering the long-wavelength approximation (λ>>Λ) and using Taylor expansion to the first-order term, the terms cos(kxΛ), cos(k1xd1)cos(k2xd2), and sin(k1xd1)sin(k2xd2) in Eq. (1) will be replaced by 1(kxΛ)2/2, 1(k1xd1)2/2(k2xd2)2/2, and (k1xd1)(k2xd2),respectively. Then Eq. (1) is transformed to the following form:
kx2εzeff+kz2εxeff=k02
(2)
where εxeff = ε1d1+ε2d2d1+d2and εzeff = (d1d1+d21ε1+d2d1+d21ε2)1. Equation (2) denotes an anisotropic metamaterial with extraordinary relative permittivity in different propagating directions.

Based on the superresolution conditions of the hybrid-super-hyperlens that is shown in Ref. 23

23. B. H. Cheng, Y. Z. Ho, Y. C. Lan, and D. P. Tsai, “Optical hybrid-superlens-hyperlens for superresolution imaging,” IEEE J. Sel. Top. Quantum Electron. (to be published).

and 24

24. Y. T. Wang, B. H. Cheng, Y. Z. Ho, Y. C. Lan, P. G. Luan, and D. P. Tsai, “Gain-assisted Hybrid-superlens Hyperlens for Nano Imaging,” Opt. Express 20(20), 22953–22960 (2012). [CrossRef] [PubMed]

, the calculated isofrequency dispersion curves of the uper planar-superlens for the incident light of 405 nm are shown in Fig. 2
Fig. 2 Isofrequency dispersion curves for light propagating in superlens structure with λ = 405 nm. The solid red and dashed blue lines denote the isofrequency curves obtained from Eq. (1) and Eq. (2), respectively. The constructed parameters of superlens are listed in caption of Fig. 1.
. Figure 2 exhibits that the isofrequency dispersion curves obtained from Eq. (1) and Eq. (2) are essentially the same in their characters. Hence, under the long-wavelength approximation, it is plausible to apply Eq. (2) to design the multi-layered metal-dielectric shape superlens and hyperlens.

The numerical results shown in this paper are obtained by computational electromagnetism program Lumerical and COMSOL MultiphysicsTM 3.5a which are based on the FDTD and FEM numerical methods respectively. The silver in the visible region is described by the Lorentz -Drude model [28

28. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]

]
ε(ω)=1ωp2ω2+iγpω+j=1kfjωj2ωj2ω22iγjω
(3)
with ωpthe plasma frequency and γpthe damping constant. ωjand γjare the resonant frequency and the damping constants of the j-th Lorentz oscillator, respectively. The perfectly matched layers are applied outside the hybrid-super-hyperlens device. The incident wave with linearly/radially polarization is launched from the top of the simulation region. For the linearly polarized incident wave, the electric field perpendicular to the groove-shaped pattern (i.e. y-direction in Fig. 1) is adopted. Since the SPPs only exist for TM polarization, only the grooves that aligned to x axis can be resolved (the corresponding simulation results are shown in Section 3). In contrary, for the beams with radially polarized mode, every position in the beam has the polarization vector (electric field) pointing towards the center of the beam. In cylindrical coordinates system, the electric field distributions (on xy-plane) of the radially beam can be expressed by [29

29. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000). [CrossRef]

]
Ex(r,θ)=er2/4σ2cosθ
(4)
Ey(r,θ)=er2/4σ2sinθ
(5)
where θ=arctan(y/x), cosθ and sinθ are used to create radially polarized beam; the exponential term er2/4σ2 represents the Gaussian envelope of the radial profile of the beam, σ=FWHM/22ln2 with the chosen full width at half maximum FWHM=1.95μm. The imported radially-polarized source is depicted in Fig. 3
Fig. 3 Plots of polarization directions of imported radially-polarized beam used in simulation.
, in which the arrows indicate the polarization direction of the electric fields on xy-plane.

In general, the radially-polarized source has been used to produce a smaller focused spot and in other applications such as optical trapping [30

30. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004). [CrossRef] [PubMed]

]. Here, we employ the characteristics of the radially polarized beam that possesses electric components with arbitrary polarization directions. Using the radially-polarized incident wave, the SPPs along all directions of the pattern carved on the sample plate can be excited. Therefore, the whole pattern is expected to be resolved on the image plane. (The corresponding simulation results are shown below in Section 3).

3. Numerical simulation results

The abilities of the hybrid-super-hyperlens to break optical diffraction limit are demonstrated first. Here the simulated object is a pair of nano-slits and the two-dimensional FEM (COMSOL) is utilized in the simulation. The metal in the hybrid-super-hyperlens is silver. The other simulation parameters are listed in Table 1

Table 1. Parameters of the hybrid-super-hyperlens at variant incident wavelength

table-icon
View This Table
. The relative permittivity values are designed based on Eq. (2), and the thickness ratio (d1/d2) is 1 in the simulation. The corresponding material can be prepared by using available nano-fabrication techniques. (Note that the constituent parameters of the planar superlens and cylindrical (sphere) hyperlens fulfilled the requirement given in [23

23. B. H. Cheng, Y. Z. Ho, Y. C. Lan, and D. P. Tsai, “Optical hybrid-superlens-hyperlens for superresolution imaging,” IEEE J. Sel. Top. Quantum Electron. (to be published).

]).

Figures 4(a)
Fig. 4 Simulated time-averaged power flow contours (left) and normalized power intensity versus x position measured at the cross section dashed line (right) for incident wavelengths of (a) 532 nm (b) 632.8 nm and (c) 650 nm. Green dotted lines in right figures indicate positions of slits with 50 nm width.
-4(c) plot the simulated time-averaged power flows (left) and the normalized power intensities as a function of x position measured along the dotted line (right) with the incident wavelengths of 532 nm, 632.8 nm and 650 nm, respectively. The figures show that the pair of slit pair whose center-to-center distance smaller than λ/4 can be resolved by the hybrid-super-hyperlens. The resolution powers for various incident wavelengths are also listed in Table 1. The figures also display that the signals extracted from the slits can propagate in the planar superlens and in the cylindrical hyperlens, and finally transfer into the far field. This is the reason why the hybrid-super-hyperlens can break the optical diffraction limit.

Next, the images of three-dimensional nano-patterns formed by the proposed hybrid-super-hyperlens are examined by FDTD (Lumerical) simulations. Figures 5(a)
Fig. 5 Simulated Power flow images of (a) a pair of nano-slits and (b) a nano-ring that covered on the Chromium with linearly polarized incident light. The center to center distance of the nano-slits pattern is 140 nm, and the width of the slit is 50 nm. The inner and outer radius of the nano-ring is 70 and 120 nm, respectively. Images are recorded at 20 nm below the outer surface of sphere-shape hyperlens.
and 5(b) plot the simulated time-averaged power flows images below the bottom facet of the spherical hyperlens for a pair of nano-slits and a nano-ring, respectively, carved on the chromium sample stage and illuminated by linearly polarized light with the incident wavelength of 405 nm. (Note that, the sample stage design such as the thickness (width) of slits and type of material can be found in Ref [31

31. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12(25), 6106–6121 (2004). [CrossRef] [PubMed]

, 32

32. N. Yao, Z. Lai, L. Fang, C. Wang, Q. Feng, Z. Zhao, and X. Luo, “Improving resolution of superlens lithography by phase-shifting mask,” Opt. Express 19(17), 15982–15989 (2011). [CrossRef] [PubMed]

].) The materials and geometry parameters of the proposed lens are also listed in Table 1. Both the nano-slits and nano-ring have the widths of 50 nm and are filled with a dielectric of refractive index n=1. (The structures are depicted in the insets of Figs. 5). Figure 5(a) displays that the far-field magnified image of the nano-slits pair can be obtained via the hybrid-super-hyperlens. Since the z component of electric field of the incident linearly light is perpendicular to the metal (chromium) surface, SPPs in the vicinity of the pair (nano-slits) are excited [33

33. M. Mansuripur, A. R. Zakharian, A. Lesuffleur, S. H. Oh, R. J. Jones, N. C. Lindquist, H. Im, A. Kobyakov, and J. V. Moloney, “Plasmonic nano-structures for optical data storage,” Opt. Express 17(16), 14001–14014 (2009). [CrossRef] [PubMed]

]. The Fabry-Perot-like resonance inside the slits would induce the SPPs coupling between the upper and lower surface of chromium stage. When the multi-layered superlens is close to the chromium, the excited higher order signals (fine features) with evanescent form can be transferred to propagation mode [16

16. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006). [CrossRef]

]. After the signals pass through the superlens and arrive at the interface between superlens and hyperlens, they can be received and delivered by spherical hyperlens from the interface to the outer surface. Because they become a propagating mode, the energy can be detected in the far field through a conventional optical microscope with a magnification factor (rout/rin) [17

17. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]

]. Conversely, Fig. 5(b) shows that the resolvable image of the nano-ring cannot be obtained by the lens with a linearly polarized incident light. This result is attributed to the fact that SPPs are excited at parts of the nano-ring only. That is, the polarization direction of the incident light plays an important role in the ability of the lens to resolve a complicated geometrical pattern. To resolve the nano-ring pattern, all the radial directions of this structure should be “seen”. SPPs along the groove of the nano-ring should be excited and all the corresponding fine feature signals should be delivered to the superlens at the same time.

Figures 6(a)
Fig. 6 Simulated power flow images of (a) a pair of nano-slits and (b) a nano-ring with radially polarized incident light. Simulation parameters and observation plane are the same as in Fig. 5.
and 6(b) depict the time-averaged power flow images of a pair of nano-slits and a nano-ring that are irradiated with radially polarization source (using Lumerical). The images are also extracted at 20 nm below the hybrid-super-hyperlen outer facet. Figures 6(a) and 6(b) exhibit that both of the nano-slits and the nano-ring are resolvable by the radially-polarized incident light, which are significantly different from those in Figs. 5. As we have mentioned, the formation of the images are caused by excitation of SPPs along the groove and transfer of fine-structure signals into the far-field. Notably, an unbroken and completed image can be obtained at one scan procedure by using the proposed hybrib-super-hyperlens. To image more complex nano patterns, the unpolarized light source should be required. Furthermore, all parameters of material presented here are currently existent and available in industry, so that they can be applied to design real and operable devices. The choice of parameters of the material in the hybrid-super-hyperlens is flexible; basically, any values that suit the requirement shown in section 2 will also work well.

4. Conclusion

The hybrid-super-hyperlens is proposed and numerically investigated. In this proposed lens, by using the anisotropic feature of superlens and hyperlens, the high order signals that reveal the fine feature of the resolved object can be transferred and delivered into far field region. The proposed lens has demonstrated the resolution aboutλ/6 that breaks the diffraction limit. Both the nano-slit pair and the nano-ring are successfully resolved using radially incident source. The feasibility of the proposed lens is assured since all the materials are available.

Acknowledgment

This work is supported by the National Science Council of Taiwan under grants NSC100-2923-M-002-007-MY3, 101-2112-M-006-002-MY3, 101-3113-P-002-021, 101-2911-I-002-107 and 101-2112-M-002-023. We also thank National Center for High-Performance Computing, Research Center for Applied Sciences, Academia Sinica, Taiwan, National Center for Theoretical Sciences, Taipei Office, and Molecular Imaging Center of National Taiwan University for their kind support.

References and links

1.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Press, 1999).

2.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

3.

D. P. Tsai, H. E. Jackson, R. Reddick, S. Sharp, and R. J. Warmack, “Photon scanning tunneling microscope study of optical wave-guides,” Appl. Phys. Lett. 56(16), 1515–1517 (1990). [CrossRef]

4.

D. P. Tsai, J. Kovacs, Z. Wang, M. Moskovits, V. M. Shalaev, J. S. Suh, and R. Botet, “Photon scanning tunneling microscopy images of optical excitations of fractal metal colloid clusters,” Phys. Rev. Lett. 72(26), 4149–4152 (1994). [CrossRef] [PubMed]

5.

D. P. Tsai, J. Kovacs, and M. Moskovits, “Applications of apertured photon scanning-tunneling-microscopy (APSTM),” Ultramicroscopy 57(2-3), 130–140 (1995). [CrossRef]

6.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251(5000), 1468–1470 (1991). [CrossRef] [PubMed]

7.

S. Kawata and Y. Inouye, “Scanning probe optical microscopy using a metallic probe tip,” Ultramicroscopy 57(2-3), 313–317 (1995). [CrossRef]

8.

B. Hecht, B. Sick, U. P. Wild, V. Deckert, R. Zenobi, O. J. F. Martin, and D. W. Pohl, “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112(18), 7761–7774 (2000). [CrossRef]

9.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

10.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996). [CrossRef] [PubMed]

11.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]

12.

D. R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S. A. Ramakrishna, and J. B. Pendry, “Limitations on subdiffraction imaging with a negative refractive index slab,” Appl. Phys. Lett. 82(10), 1506–1508 (2003). [CrossRef]

13.

W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005). [CrossRef]

14.

A. Schilling, J. Schilling, C. Reinhardt, and B. Chichkov, “A superlens for the deep ultraviolet,” Appl. Phys. Lett. 95(12), 121909 (2009). [CrossRef]

15.

D. Schurig and D. R. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys. 7, 162 (2005). [CrossRef]

16.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006). [CrossRef]

17.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]

18.

A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Lett. 95(26), 267407 (2005). [CrossRef] [PubMed]

19.

J. Yao, K. T. Tsai, Y. Wang, Z. Liu, G. Bartal, Y. L. Wang, and X. Zhang, “Imaging visible light using anisotropic metamaterial slab lens,” Opt. Express 17(25), 22380–22385 (2009). [CrossRef] [PubMed]

20.

Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-Mediated Radiative Energy Transfer across a Silver Nanowire Array via Resonant Transmission and Subwavelength Imaging,” ACS Nano 4(9), 5003–5010 (2010). [CrossRef] [PubMed]

21.

I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007). [CrossRef] [PubMed]

22.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

23.

B. H. Cheng, Y. Z. Ho, Y. C. Lan, and D. P. Tsai, “Optical hybrid-superlens-hyperlens for superresolution imaging,” IEEE J. Sel. Top. Quantum Electron. (to be published).

24.

Y. T. Wang, B. H. Cheng, Y. Z. Ho, Y. C. Lan, P. G. Luan, and D. P. Tsai, “Gain-assisted Hybrid-superlens Hyperlens for Nano Imaging,” Opt. Express 20(20), 22953–22960 (2012). [CrossRef] [PubMed]

25.

H. Wu, T. W. Odom, and G. M. Whitesides, “Reduction Photolithography Using Microlens Arrays: Applications in Gray Scale Photolithography,” Anal. Chem. 74(14), 3267–3273 (2002). [CrossRef] [PubMed]

26.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11(5), 432–435 (2012). [CrossRef] [PubMed]

27.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, Oxford, 2006).

28.

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef] [PubMed]

29.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett. 77(21), 3322–3324 (2000). [CrossRef]

30.

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004). [CrossRef] [PubMed]

31.

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12(25), 6106–6121 (2004). [CrossRef] [PubMed]

32.

N. Yao, Z. Lai, L. Fang, C. Wang, Q. Feng, Z. Zhao, and X. Luo, “Improving resolution of superlens lithography by phase-shifting mask,” Opt. Express 19(17), 15982–15989 (2011). [CrossRef] [PubMed]

33.

M. Mansuripur, A. R. Zakharian, A. Lesuffleur, S. H. Oh, R. J. Jones, N. C. Lindquist, H. Im, A. Kobyakov, and J. V. Moloney, “Plasmonic nano-structures for optical data storage,” Opt. Express 17(16), 14001–14014 (2009). [CrossRef] [PubMed]

OCIS Codes
(110.0180) Imaging systems : Microscopy
(160.1190) Materials : Anisotropic optical materials
(350.5730) Other areas of optics : Resolution
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: February 4, 2013
Revised Manuscript: March 1, 2013
Manuscript Accepted: March 5, 2013
Published: June 17, 2013

Virtual Issues
Vol. 8, Iss. 7 Virtual Journal for Biomedical Optics
Hyperbolic Metamaterials (2013) Optics Express

Citation
Bo Han Cheng, Yung-Chiang Lan, and Din Ping Tsai, "Breaking Optical diffraction limitation using Optical Hybrid-Super-Hyperlens with Radially Polarized Light," Opt. Express 21, 14898-14906 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-12-14898


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References

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  19. J. Yao, K. T. Tsai, Y. Wang, Z. Liu, G. Bartal, Y. L. Wang, and X. Zhang, “Imaging visible light using anisotropic metamaterial slab lens,” Opt. Express17(25), 22380–22385 (2009). [CrossRef] [PubMed]
  20. Z. K. Zhou, M. Li, Z. J. Yang, X. N. Peng, X. R. Su, Z. S. Zhang, J. B. Li, N. C. Kim, X. F. Yu, L. Zhou, Z. H. Hao, and Q. Q. Wang, “Plasmon-Mediated Radiative Energy Transfer across a Silver Nanowire Array via Resonant Transmission and Subwavelength Imaging,” ACS Nano4(9), 5003–5010 (2010). [CrossRef] [PubMed]
  21. I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science315(5819), 1699–1701 (2007). [CrossRef] [PubMed]
  22. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science315(5819), 1686 (2007). [CrossRef] [PubMed]
  23. B. H. Cheng, Y. Z. Ho, Y. C. Lan, and D. P. Tsai, “Optical hybrid-superlens-hyperlens for superresolution imaging,” IEEE J. Sel. Top. Quantum Electron. (to be published).
  24. Y. T. Wang, B. H. Cheng, Y. Z. Ho, Y. C. Lan, P. G. Luan, and D. P. Tsai, “Gain-assisted Hybrid-superlens Hyperlens for Nano Imaging,” Opt. Express20(20), 22953–22960 (2012). [CrossRef] [PubMed]
  25. H. Wu, T. W. Odom, and G. M. Whitesides, “Reduction Photolithography Using Microlens Arrays: Applications in Gray Scale Photolithography,” Anal. Chem.74(14), 3267–3273 (2002). [CrossRef] [PubMed]
  26. E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. E. Chad, M. R. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater.11(5), 432–435 (2012). [CrossRef] [PubMed]
  27. A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University Press, Oxford, 2006).
  28. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt.37(22), 5271–5283 (1998). [CrossRef] [PubMed]
  29. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, “The formation of laser beams with pure azimuthal or radial polarization,” Appl. Phys. Lett.77(21), 3322–3324 (2000). [CrossRef]
  30. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express12(15), 3377–3382 (2004). [CrossRef] [PubMed]
  31. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express12(25), 6106–6121 (2004). [CrossRef] [PubMed]
  32. N. Yao, Z. Lai, L. Fang, C. Wang, Q. Feng, Z. Zhao, and X. Luo, “Improving resolution of superlens lithography by phase-shifting mask,” Opt. Express19(17), 15982–15989 (2011). [CrossRef] [PubMed]
  33. M. Mansuripur, A. R. Zakharian, A. Lesuffleur, S. H. Oh, R. J. Jones, N. C. Lindquist, H. Im, A. Kobyakov, and J. V. Moloney, “Plasmonic nano-structures for optical data storage,” Opt. Express17(16), 14001–14014 (2009). [CrossRef] [PubMed]

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