Optical Hybrid-Superlens Hyperlens for Superresolution ... - IEEE Xplore

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IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 19, NO. 3, MAY/JUNE 2013

Optical Hybrid-Superlens Hyperlens for Superresolution Imaging Bo Han Cheng, You Zhe Ho, Yung-Chiang Lan, and Din Ping Tsai, Fellow, IEEE

Abstract—This study proposes an innovative device called “Hybrid-Superlens Hyperlens” with superresolution imaging ability and confirms it by using simulation. This device consists of two multilayered metal-dielectric anisotropic metamaterials: the upper planar superlens and the lower cylindrical hyperlens with different signs in their dielectric tensors and different isofrequency dispersion curves. In our simulation, 100-nm center-to-center resolution is obtained by using an incident wavelength of 405 nm, which is smaller than the optical diffraction limit. Index Terms—Anisotropic media, artificial materials, electromagnetic propagation in anisotropic media, image resolution, metal-insulator structures, microscopy, optical imaging, plasmons, surface waves.

I. INTRODUCTION N 1873, Ernst Abbe discovered that when an object is imaged by an optical system such as the lens of a camera, features smaller than half the wavelength of the light are permanently lost in the image, thus introducing the so-called diffraction limit [1]. This imperfect image occurs since the waves that carry information about the subwavelength details of the object have transverse wave vectors larger than k0 will decay exponentially in free space. Therefore, using the conventional optical microscopy cannot capture the minuscule details of the object in the far field region. Recently, the super-resolution near-field optical structures [2]–[10], superlens structures [11]–[13], including the multilayered metal-dielectric structure [14]–[17] and the metal nanorod array structures [18]–[20], have been proposed to collect subwavelength information or details. Their ability of subwavelength resolution is contributed to the constituents such as metal materials (possess the negative permittivity, due to excitation of surface plasmons) or metamaterials which possess the

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Manuscript received July 14, 2012; revised October 11, 2012; accepted October 25, 2012. Date of publication January 4, 2013; date of current version April 25, 2013. This work was supported by National Science Council, Taiwan, under Grant 99-2120-M-002-012, Grant 99-2911-I-002-127, Grant 100-2120M-002-008, and Grant 100-2923-M-002-007-MY3. B. H. Cheng and Y.-C. Lan are with the Institute of Electro-Optical Science and Engineering, National Cheng Kung University, Tainan 701, Taiwan (e-mail: [email protected]; [email protected]). Y. Z. Ho is with the Department of Physics, National Taiwan University, Taipei 10617, Taiwan (e-mail: [email protected]). D. P. Tsai is with the Department of Physics, and the Graduate Institute of Applied Physics, National Taiwan University, Taipei 10617, Taiwan, and also with the Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTQE.2012.2230152

effective anisotropic relative permittivity. However, these lenses are near sighted [21], i.e., the images can only be picked up in the near field. Hence, they are considered as near-field superlens. The hyperlens with hyperbolic dispersion isofrequency curve that is made of cylindrical or spherically curved multilayer stacks is another approach of magnifying the subwavelength features [22]–[26]. The evanescent waves 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. Therefore, this hyperlens is viewed as a far-field hyperlens. However, the cylindrical shaped stage design [23], [24] being a disadvantage, we cannot put all the resolution objects on the curved platform. Furthermore, the semicircle space constructed by metal forms a cavity, influencing the resolution at specific operation wavelength. In this investigation, we theoretically propose an innovative device magnifying far-field image and prove it by finite element method (FEM) simulation. It possesses ability to image subwavelength object at the far field position and compensate the drawbacks of hyperlens aforementioned. This device is integrated with two anisotropic metamaterial components, the upper planar superlens and the lower cylindrical hyperlens, in which their permittivity tensors have opposite signs. Since the dispersion relations with hyperbolic dispersion curve in these two components are different, our proposed imaging device is named as the hybrid-superlens hyperlens. The device is capable of deriving the high spatial-frequency components excited by the objects on one flat surface and transfer it to the far field. Moreover, the planar shaped design is more practical for real applications such as photolithography and planar integrated optical devices [27]–[29]. II. GEOMETRIC MODEL AND SIMULATION METHOD Fig. 1(a) shows the conceptual objective lens, which is composed of the hybrid-superlens hyperlens and the conventional lens. Fig. 1(b) illustrates the front view of the hybrid-superlens hyperlens for our simulation work. Two 50-nm wide slits with 100-nm center-to-center separation on a thick Cr layer serve as objects (which is put on the top of planar superlens) to be resolved. Below the Cr layer, we use two components to constitute our hybrid-superlens hyperlens. The upper component (planar superlens) consists of six pairs of alternately stacked Ag (30 nm) and Al2 O3 (30 nm) layers, which is capable of extracting the evanescent waves (that carry fine details of the objects) and transferring them to the interface between the upper and the lower components. While the lower component (cylindrical hyperlens) is composed of eight pairs of alternately stacked Ag (30 nm) and HfO2 (30 nm) layers that further transfer the signal

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CHENG et al.: OPTICAL HYBRID-SUPERLENS HYPERLENS FOR SUPERRESOLUTION IMAGING

Fig. 1. (a) Schematic of the proposed hybrid hyperlens conceptual structure. (b) Cross section of the hybrid hyperlens.

to the far field and magnify it. In Fig. 1, the thickness of Cr layer (t), total thickness of the planar superlens (H1 ), and total thickness of the cylindrical hyperlens (H2 ) are 70, 360, and 480 nm, respectively. The thickness ratios of Ag, Al2 O3 , and HfO2 are based on the geometry parameters as in [23]. In the meantime, the space left for the planar superlens can also be fit into six pairs of alternately stacked Ag (30 nm) and Al2 O3 (30 nm) layers. In our simulation, the relative permittivities of Al2 O3 and HfO2 are set to be 3.217 [30] and 3.9 [31], respectively. For Ag, the Lorentz–Drude model is adopted in the simulation with the parameters given by as in [32]. The FEM commercial solver COMSOL Multiphysics 3.5 a is used in this 2-D simulation. The transverse magnetic (TM) polarization is considered with the incident electric field (x direction) perpendicular to the axis of an infinitely long cylinder (along y direction). The surrounding boundaries are perfectly matched layers. III. THEORY AND DESIGN METHOD A. Design of Component One (Planar Superlens) At first, we examine the operation wavelength that can transfer the high-order spatial components being excited from the slits to the interface between upper and lower elements. The upper component (planar superlens) is composed of alternative metal (ε1 ) and dielectric (ε2 ) layers. It can be viewed as an

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Fig. 2. (a) Real part of permittivity of the planar superlens structure as a function of operation wavelength (η = 1) for effective perpendicular permittivity (εz , orange line) and effective parallel permittivity (εx , green line). Blue dashed line denotes εz and εx equal to zero. Black dashed line indicates the wavelength (λ = 397 nm) when εz and εx are equal to zero. (b) Isofrequency dispersion curves of light propagating in planar-superlens structure for λ = 350 nm (blue line) and 405 nm (red line).

anisotropic medium with effective parallel (εx ) and perpendicular (εz ) relative permittivities given by [14] ε1 + ηε2 1+η 1 1 1 η = + εz 1 + η ε1 ε2 εx = ε y =

(1) (2)

where η is the ratio of the widths of the metal and dielectric layers in the system (here we have set η = 1). Fig. 2(a) shows the real part of this anisotropic permittivity versus incident wavelength. When the incident wavelength λ is shorter than below 397 nm, the effective parallel permittivity and perpendicular permittivity are positive and negative, respectively. On the contrary, the signs of these permittivities are reversed as the wavelength is longer than 397 nm. According to [15], if the parameters η, ε1 , and ε2 are chosen such that εx → 0, the field distribution in the incident plane is one-to-one transferred to any other plane by the parallel rays. Since Fig. 2(b) shows that this condition can be satisfied when λ approaches 397 nm from both sides, therefore λ = 350 and 405 nm are chosen as the operation wavelengths. It means Re(εx ) → 0+ & Re(εz ) < 0 at λ = 350 nm, and Re(εx ) → 0− & Re(εz ) > 0 at λ = 405 nm, respectively. The isofrequency dispersion curve of light in the upper planar

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Fig. 3. Calculated transmission coefficient versus k x at λ = 350 nm (blue line) and 405 nm (red line).

Fig. 4. Isofrequency dispersion curve in cylindrical-hyperlens structure (at λ = 405 nm).

superlens is expressed as [14]

of resolution will be affected by the dispersion characteristic of planar superlens. We select the planar-superlens structure with East–West opening hyperbola as the resolution component of hybrid-superlens hyperlens [see Fig. 2(b)].

kx2 εz

+

kz2 εx

= k02

(3)

where kx and kz are the parallel and perpendicular components of the wavevector, and k0 the wavevector of light in air. Equation (3) exhibits that the upper planar superlens possesses hyperbola dispersion feature. Fig. 2(b) shows the isofrequency dispersion curve of light in the upper planar superlens for λ = 350 nm (blue line) and 405 nm (red line), in which the propagation characteristic of the upper planar superlens for λ = 350 nm is different from that for λ = 405 nm. The propagation property of the wave in the z direction is governed by kz (if kz is imaginary, the wave decays exponentially with z). For λ = 350 nm, kz is real for all kx values. Conversely, Fig. 2(b) displays that a higher spatial frequency, i.e., kx larger than 13 × 107 (1/m), propagates in the planar superlens for λ = 405 nm. As shown in Fig. 2(b), the degree of transmission of the high spatial-frequency components (the detailed feature) cannot be obtained. In principle, it is fundamentally related to the transmission coefficient. Therefore, the transmission ability of the high spatial-frequency components (kx ) at different operating wavelengths should be determined. We assume that such a medium (without Chromium plane) is embedded into free space. The transmission coefficient for TM wave can be express as [14] t(kx , ω) =

2 cos kz d − i

2 k z

εx kz ε

+

kz ε k z ε x

(4) sin(kz d)

where εx , εz , kx , and kz are defined in (1)–(3), ε the permittivity of the surrounding medium (air), ω the incident frequency, d the total thickness of the upper planar superlens, and kz the wave vector in the surrounding medium (air). Fig. 3 shows the transmission coefficients as a function of kx for incident wavelength λ = 350 and 405 nm, from which, for λ = 405 nm, the transmission coefficient is still significant for larger wavevector kx . On the other hand, the transmission coefficient of the high spatial-frequency components decays more quickly for λ = 350 nm. It means the signals containing the fine features excited from the slits propagate in this planar superlens at the operational wavelength λ = 405 nm. In other words, the ability

B. Design of Component Two (Cylindrical Hyperlens) Next, the propagation behavior in the lower cylindrical hyperlens for λ = 405 nm is considered. In order to receive and transfer the subwavelength signal spreading from the upper planar superlens, the anisotropic medium needs to be in the form of North–South opening hyperbola [23]. Hence, we adopt a multilayered anisotropic structure with curved geometry as the lower component (cylindrical hyperlens). Moreover, the slope (i.e., dkr /dkθ , where kr and kθ are the r- and θ-components, respectively) of the wavevector [see Fig. 1(b)] in the isofrequency dispersion relation of the cylindrical hyperlens must be nearly flat so that the waves excited by the slits with different transverse wave vectors all propagate at the same phase velocity along the radial direction, which is important in forming an undistorted image in the far field [21]. The isofrequency dispersion curve of light in the lower cylindrical hyperlens is expressed as [23] k2 kr2 + θ = k02 εθ εr

(5)

where kr and kθ are wavevectors, εr and εθ permittivities in radial and tangential direction, respectively, in cylindrical coordinates. Fig. 4 shows the isofrequency dispersion relation of the cylindrical hyperlens for the incident wavelength of 405 nm, from which the previous relation is satisfied. Therefore, the cylindrical hyperlens shown in Fig. 1(b) is adequate for our proposed hybrid-superlens hyperlens. IV. SIMULATION RESULTS AND DISCUSSION Finally, the overall optical properties of the proposed hybridsuperlens hyperlens are investigated. Fig. 5(a) plots the simulated time-average power flow for λ = 405 nm. Fig. 5(b) plots the normalized power intensity as a function of the x position measured along the dotted line shown in Fig. 5(a). It can be seen from Fig. 5(a) that the signal extracted from the slits are

CHENG et al.: OPTICAL HYBRID-SUPERLENS HYPERLENS FOR SUPERRESOLUTION IMAGING

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hyperlens, with different dispersion relations. The proposed hybrid-superlens hyperlens can not only resolve the subwavelength fine structures but also utilize its anisotropic feature to enhance and transfer the high spatial frequencies to the far field. Moreover, the desired operation wavelength can be achieved by controlling the metal filling factor in the hybrid-superlens hyperlens. Numerical simulation has further verified the design methodology. The parameters for the geometry and material being chosen are within the capability of current nanofabrication techniques. Since the hybrid-superlens hyperlens has the ability to project an image (constructed by a flat geometry of objective plane) with extremely fine features to the far field, this device can be combined with the conventional lens to form a kind of novel objective lens. Although this simulation work is accomplished by a cylindrical shape geometry, it is possible to design a spherical one and to use the light source with radial polarization to magnify the subwavelength structures with arbitrary shapes in three dimensions. This device has potential applications in different areas, such as photolithography, planar integrated optical devices, and DVD technology. ACKNOWLEDGMENT

Fig. 5. (a) Simulated time-average power flow contours for incident wave of 405 nm. (b) Normalized power intensity versus x position measured at the cross-section dashed line shown in Fig. 5(a). The green dotted lines indicate the positions of the two slits.

successfully transferred to the far field and magnified. Furthermore, Fig. 5(b) displays that the image is enlarged by a factor M = 228/100 = 2.28. The enlargement factor M is also predicted by M = rout /rin = 2.33, where rout = H1 + H2 and rin = H1 denote the radii of the output face and input face of the lower cylindrical hyperlens, respectively [15], [22]. According to Figs. 2(b) and 3, the larger kx remain propagation mode and the amount of transmission coefficient is sufficient to undergo the upper component. Hence, this device provides the potential for resolving the smaller objects. Our simulated enlargement factor is consistent with the predicted enlarged factor (rout /rin ). According to the simulation results, the smallest details on the order of λrin /2nrout can be resolved in our proposed hybrid-superlens hyperlens (where n is the refraction index of the medium surrounding the object) [15]. The optimization of the proposed device (i.e., the constituent parameters η, ε1 , ε2 ) would result in better resolution. Therefore, a conventional microscopy can equip with our hybrid-superlens hyperlens to receive the magnified propagation wave and obtain the images of the slits engraved on the Chromium plane. V. CONCLUSION We have demonstrated that a hybrid-superlens hyperlens can be developed by employing two periodic metal-dielectric composites, the upper planar superlens and the lower cylindrical

The authors are grateful to National Center for Theoretical Sciences, Taipei Office, Molecular Imaging Center of National Taiwan University, Taipei, Taiwan, and Research Center for Applied Sciences, Academia Sinica, Taipei, for their support. REFERENCES [1] E. Abbe, “Beitr¨age zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikr. Anat., vol. 9, pp. 413–468, 1873. [2] D. P. Tsai and W. C. Lin, “Probing the near fields of the super-resolution near-field optical structure,” Appl. Phys. Lett., vol. 77, pp. 1413–1415, 2000. [3] D. P. Tsai, C. W. Yang, W. C. Lin, F. H. Ho, H. J. Huang, M. Y. Chen, T. F. Tseng, C. H. Lee, and C. J. Yeh, “Dynamic aperture of near-field super resolution structures,” Jpn. J. Appl. Phys., vol. 39, pp. 982–983, 2000. [4] W. C. Liu, C. Y. Wen, K. H. Chen, W. C. Lin, and D. P. Tsai, “Nearfield images of the AgOx-type super-resolution near-field structure,” Appl. Phys. Lett., vol. 78, pp. 685–687, 2001. [5] T. C. Chu, D. P. Tsai, and W. C. Liu, “Readout contrast beyond diffraction limit by a slab of random nanostructures,” Opt. Exp., vol. 15, pp. 12–23, 2007. [6] K. P. Chiu, K. F. Kai, and D. P. Tsai, “Application of surface polariton coupling between nano recording marks to optical data storage,” Opt. Exp., vol. 16, pp. 13885–13892, 2008. [7] R. Bukasov, T. A. Ali, P. Nordlander, and J. S. Shumaker-Parry, “Probing the plasmonic near-field of gold nanocrescent antennas,” ACS Nano, vol. 4, pp. 6639–6650, 2010. [8] C. Georgi, A. A. Green, M. C. Hersam, and A. Hartschuh, “Probing exciton localization in single-walled carbon nanotubes using high-resolution near-field microscopy,” ACS Nano, vol. 4, pp. 5914–5920, 2010. [9] M. Fleischer, A. Weber-Bargioni, M. V. P. Altoe, A. M. Schwartzberg, P. J. Schuck, S. Cabrini, and D. P. Kern, “Gold nanocone near-field scanning optical microscopy probes,” ACS Nano, vol. 5, pp. 2570–2579, 2011. [10] J. M. Stiegler, Y. Abate, A. Cvitkovic, Y. E. Romanyuk, A. J. Huber, S. R. Leone, and R. Hillenbrand, “Nanoscale infrared absorption spectroscopy of individual nanoparticles enabled by scattering-type near-field microscopy,” ACS Nano, vol. 5, pp. 6494–6499, 2011. [11] J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett., vol. 85, pp. 3966–3969, 2000. [12] D. O. S. Melville and R. J. Blaikie, “Super-resolution imaging through a planar silver layer,” Opt. Exp., vol. 13, pp. 2127–2134, 2005.

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[13] H. Liu, B. Wang, L. Ke, J. Deng, C. C. Chum, S. L. Teo, L. Shen, S. A. Maier, and J. Teng, “High aspect subdiffraction-limit photolithography via a silver superlens,” Nano Lett., vol. 12, pp. 1549–1554, 2012. [14] B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B, vol. 74, p. 115116, 2006. [15] A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B, vol. 74, p. 075103, 2006. [16] W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based metal-dielectric composites,” Phys. Rev. B, vol. 72, p. 193101, 2005. [17] D. Schurig and D. R. Smith, “Sub-diffraction imaging with compensating bilayers,” New J. Phys., vol. 7, p. 162, 2005. [18] 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. Exp., vol. 17, pp. 22380–22385, 2009. [19] A. Ono, J. Kato, and S. Kawata, “Subwavelength optical imaging through a metallic nanorod array,” Phys. Rev. Letts., vol. 95, p. 267407, 2005. [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, “Plasmonmediated radiative energy transfer across a silver nanowire array via resonant transmission and subwavelength imaging,” ACS Nano, vol. 4, pp. 5003–5010, 2010. [21] X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater., vol. 7, pp. 435–441, 2008. [22] Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Exp., vol. 14, pp. 8247–8256, 2006. [23] H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Exp., vol. 15, pp. 15886–15891, 2007. [24] Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science, vol. 315, p. 1686, 2007. [25] S. Schwaiger, M. Brll, A. Krohn, A. Stemmann, C. Heyn, Y. Stark, D. Stickler, D. Heitmann, and S. Mendach, “Rolled-up three-dimensional metamaterials with a tunable plasma frequency in the visible regime,” Phys. Rev. Lett., vol. 102, p. 163903, 2009. [26] I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science, vol. 315, pp. 1699–170, 2007. [27] H. Wu, T. W. Odom, and G. M. Whitesides, “Reduction photolithography using microlens arrays: Applications in gray scale photolithography,” Anal. Chem., vol. 74, pp. 3267–3273, 2002. [28] E. U. Haq, Z. Liu, Y. Zhang, S. A. A. Ahmad, L. S. Wong, S. P. Armes, J. K. Hobbs, G. J. Leggett, J. Micklefield, C. J. Roberts, and J. M. R. Weaver, “Parallel scanning near-field photolithography: The Snomipede,” Nano Lett., vol. 10, pp. 4375–4380, 2010. [29] 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., vol. 11, pp. 432–435, 2012. [30] E. D. Palik, Handbook of Optical Constants of Solids. San Francisco, CA: Academic Press, 1998. [31] D. Smith and P. Baumeister, “Refractive index of some oxide and fluoride coating materials,” Appl. Opt., vol. 18, pp. 111–115, 1979. [32] 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., vol. 37, pp. 5271–5283, 1998.

Bo Han Cheng received the M.S. degree in photonics from National Cheng Kung University, Tainan, Taiwan, in 2008, where he is currently working toward the Ph.D. degree in photonics. His current research interests include simulation and calculation of nanophotonic devices and metamaterials.

You Zhe Ho received the Bachelor’s degree from the Tunghai University, Taichung, Taiwan, in 2010, and is currently working toward the Master’s degree in the Department of Physics, National Taiwan University, Taipei, Taiwan, studying under Professor Din Ping Tsai. His research interests include developing theory and simulating the plasmonic systems for predicting the experiment results.

Yung-Chiang Lan received the Ph.D. degree in engineering and system science from the National Tsing Hua University, Hsinchu City, Taiwan, in 2002. In February 2004, he joined the Faculty of Institute of Electro-Optical Science and Engineering at National Cheng Kung University, Tainan, Taiwan. His research interests include the simulations of plasmonics, plasma and nano, and optical devices.

Din Ping Tsai (S’89–M’90–SM’04–F’12) received the Ph.D. degree in physics from the University of Cincinnati, Cincinnati, OH, in 1990. He is currently a Distinguished Professor in the Department of Physics, National Taiwan University, Taipei, Taiwan, and the Director and Distinguished Research Fellow at the Research Center for Applied Sciences, Academia Sinica, Taipei. His current research interests include nanophotonics, plasmonics, metamaterials, and biophotonics. Dr. Tsai is a Fellow of the American Physical Society, the Optical Society of America, the International Society of Optical Engineering, and the Electro Magnetics Academy.