FM2C.3.pdf
CLEO:2015 © OSA 2015
Optical Imaging with Photonic Hypercrystals Zun Huang and Evgenii E. Narimanov Birck Nanotechnology Center, School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907
[email protected]
Abstract: We present an optical imaging system based on photonic hypercrystal, an artificial optical medium combining the properties of hyperbolic materials and photonic crystals. This system functions as a negative refraction lens with substantially reduced image aberrations. OCIS codes: (160.3918) Metamaterials; (160.5298) Photonic crystals; (110.0110) Imaging systems.
The conventional lens, made out of transparent dielectrics and featured by positive refraction, represents one of the most fundamental optical elements in microscopy and biomedical imaging. However, it has now reached the fundamental limits. Among many new alternative optical imaging methods, a planar type of negative refraction lens, known as Veselago lens or Superlens [1, 2], has become one of the most promising candidates. Such a lens has shown a striking capability of super-resolution imaging [1] and tremendous potentials in subdiffraction-limit nano-photolithography and large-scale nano-patterning design [3]. Owing to these intriguing features, Veselago lens has been proposed by various methods [4], from negative index metamaterials (NIMs) to photonic crystals (PCs), to periodic structure of plasmonic waveguides and hyperbolic metamaterials (HMMs). Each of these methods, however suffers from serious limitations that plague the imaging performance. The double-resonance (simultaneously negative permittivity and permeability) required in NIMs leads to unavoidable critical losses. The PCs and HMMs fail to yield an image free of spherical aberrations since those non-magnetic materials don’t offer a constant refractive index. Here, we present a new approach of realizing the negative refraction lens by photonic “hypercrystals" (PHCs) [5]. Our device demonstrates significantly improved image quality and a nearly constant negative refractive index. x
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Fig. 1: (a-b): Schematics of the structure and IFS of a planar PHC (a), with HMM (b) as one of its periodic elements, in the lossless limit. The latter usually consists of alternating dielectric and metal layers with subwavelength thicknesses. In panel (a), the first and also the widest propagating band of PHC (green hyperboloid) is surrounded by the second propagating band (translucent orange outline). (c-d): Ray trajectories of light from a point slot source located in silicon through two slab media: sapphire (c) as the natural hyperbolic medium and PHC (d) as the proposed negative refraction lens. While the optical beams become divergent through the hyperbolic medium (c), the PHC focuses most of the incident beams perfectly. The distance of point source from the slab is f1 = 51.45 µm ≈ 2.5λ0 and the two imaging slab lengths are both L = 2f1 .
PHCs are essentially photonic crystals with the unit cell containing hyperbolic dispersion elements which operate in subwavelength regime [6]. These hyperbolic elements can be formed by HMMs or natural materials at a certain spectrum (e.g. sapphire [7] at vacuum wavelength λ0 = 20 µm). Fig. 1(a-b) shows the schematic structure of the planar PHC and its iso-frequency surface (IFS). With appropriate selection of the material and geometric parameters, the first and also the widest propagating band in PHC can be tailored to resemble a semi-circle, indicating that all
FM2C.3.pdf
CLEO:2015 © OSA 2015
the incident beams can be perfectly focused to one point (Fig. 1(d), [5]). If such a PHC is used as Veselago lens for point source imaging (see Fig. 2), a nearly constant negative index of refraction independent of incident angles can be achieved (Fig. 2(d)), even with the actual material losses included. single line source
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Fig. 2: (a) Schematic illustration of imaging a TM polarized line source by a multilayered Si-Al2 O3 PHC at λ0 = 20 µm. The PHC contains 30 unit cells (≈ 44.1 µm) with optimal component layer thicknesses d1 (Si) = 1 µm and d2 (Al2 O3 ) = 0.47 µm. The line source is represented by a magnetic current aligned in y-axis and located in Si at 22.05 µm above the PHC. (b-c) Full numerical simulations of the electromagnetic field intensity by COMSOL Multiphysics for lossless (b) and lossy (c) PHCs. In both cases, two foci are clearly observed inside and outside the PHC, validating the Veselago lensing. (d) The calculated relative refractive indices (defined by n∗ ≡ sin(θt )/sin(θinc ) for a hyperbolic medium (e.g. sapphire, blue dashed) and the PHC (red solid). The latter is almost a constant value of -1 independent of all incident angles. (e-f) The normalized field intensity distributions If (x) at the image plane along the x-axis without (e) and with (f) actual material losses. In the lossless case, the ∆FWHM approaches the diffraction limit of 0.15λ0 , and with losses it is slightly broadened to 0.22λ0 .
We consider a PHC composed of interleaved layers of Si (dielectric element) and Al2 O3 (hyperbolic element) at λ0 = 20 µm. Fig. 2 shows the full numerical simulation of the electromagnetic field distributions when the PHC is used as a Veselago lens to image a TM polarized line source. As seen in Fig. 2 (a-c), all the incident waves emanating from the line source are focused by the PHC, forming two foci located close to the predicted positions inside and outside the PHC. Such "double-foci" phenomenon verifies our device can be used as a Veselago lens for far-field imaging. In the lossless case, the imaging resolution of this Veselago lens approaches the classical diffraction limit, given by the full width at half maximum (∆FWHM ) of the field intensity If (x) at the image plane. As shown in Fig. 2(e), the ∆FWHM is approximately 0.15λ0 ≈ λ0 /(2n0 ), where n0 is the refractive index of Si (∼ 3.4). When the actual material losses are considered (Fig. 2(f)), the If (x) becomes slightly broadened and the corresponding ∆FWHM is increased to 0.22λ0 . In conclusion, we present a new negative refraction lens based on the PHC, which significantly improves the practical spherical aberration issues in the Veselago lenses by PCs or HMMs. The planar nature of PHC enables a feasible fabrication in just one direction, offering many significant engineering applications such as large-throughput nanolithography. The imaging resolution of our device can be further enhanced by coupling to degenerate surface plasmons which will be shown in the future work. This work was partially supported by Gordon and Betty Moore Foundation, NSF Center for Photonic and Multiscale Nanomaterials, and ARO MURI. References J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000). V. G. Veselago, Sov. Phys. Uspekhi 10, 509 (1968). H. Liu, B. Wang, L. Ke, J. Deng, C. C. Chum, S. L. Teo, L. Shen, S. A. Maier and J. Teng, Nano. Lett. 12, 1549 (2012). V. Shalaev, Nat. Photon. 1, 41 (2007); P. V. Parimi, W. T. Lu, P. Vodo, S. Sridhar, Nature 426, 404 (2003); T. Xu, A. Agrawal, M. Abashin, K. J. Chau and H. J. Lezec, Nature 497, 470 (2013); D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, App. Phys. Lett. 84, 2244 (2004). 5. Z. Huang and E. E. Narimanov, Appl. Phys. Lett. 105, 31101 (2014); Z. Huang and E. E. Narimanov, J. Opt. 16, 114009 (2014). 6. E. E. Narimanov, Phys. Rev. X 4 (2014). 7. M. Schubert, T. E. Tiwald, and C. M. Herzinger, Phys. Rev. B 61, 8187 (2000).
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