Ultratransparent Media: Towards the Ultimate Transparency

From left to right: (top row) Jie Luo, Yuting Yang, Zhongqi Yao, Weixin Lu; (bottom row) Bo Hou, Zhi Hong Hang, C. T. Chan, and Yun Lai.

Authors: Jie Luo¹, Yuting Yang¹, Zhongqi Yao¹, Weixin Lu¹, Bo Hou¹, Zhi Hong Hang¹, Che Ting Chan², Yun Lai¹

Affiliation:
¹College of Physics, Optoelectronics and Energy & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China
²Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong.

Transparent media are the foundation of almost all optical instruments, such as optical lens, etc. However, perfect transparency has never been realized in natural transparent solid materials such as glass because of the impedance mismatch with free space or air. As a consequence, there generally exist unwanted reflected waves at the surface of a glass slab, as illustrated in Fig. 1(a). It is well known that non-reflection only occurs at a particular incident angle for a specific polarization, which is known as the Brewster angle effect [1]. Our question is: is it possible to extend the Brewster angle from a particular angle to a wide range of or all angles, so that there is no reflection for any incident angle.

In addition, the virtual image formed by a glass slab placed in air is usually blurred to a certain extent [Fig. 1(a)]. Such a blur indicates the aberration of virtual images, and is caused by the mismatch of equal frequency contours (EFCs) between air (grey lines) and the glass (blue lines).

Figure 1: (a) Virtual image formation through a glass slab, with general reflection and aberration. (b) Aberration-free virtual image formation through an ultratransparent photonic crystal without any reflection due to omnidirectional impedance matching. The black arrows and blue dashed lines in represent the light rays from a point source, and the back tracing lines, respectively. The yellow dashed curves in (b) indicate equal phase surfaces of transmitted rays. The inset graphs show the corresponding EFCs. The figure is adapted from Reference [2].

The purpose of our work [2] is to explore the possibility of realizing the ultimate transparency by artificial optical structures such as photonic crystals (PhCs) [3] and metamaterials [4]. In other words, we pursue the realization of transparent media with the extreme property of omnidirectional impedance matching and the ability of forming aberration-free virtual images, which are hereby denoted as ultratransparent media.

In this work, we propose that omnidirectional impedance matching can be realized by utilizing effective medium with nonlocal parameters, i.e. permittivity and permeability that are dependent on the incident angle. Interestingly, such an effective medium can be realized by using pure dielectric PhCs. Moreover, the EFC of the ultratransparent PhC can be tuned to be a shifted ellipse (red lines) with the same height of the EFC of air (grey lines). By using ray optics, we prove that such an EFC endows the valuable ability of forming aberration-free virtual images, as presented in Fig. 1(b).

Because of the shift of EFC, the PhC is beyond the local medium framework, and effective parameters are nonlocal (i.e. spatially dispersive). Interestingly, such nonlocality leads to additional phase modulation p d, where p is the shift magnitude and d is the slab thickness [Fig. 1(b)].

Figure 2: (a) Illustration of the unit cell of the ultratransparent PhC. (b) The EFC of the PhC. (c) Transmittance through the PhC slab with N (=4, 5, 6, 15) layers of unit cells as functions of the incident angle. The figure is adapted from Reference [2].

An extreme example with almost complete transparency (T>99%) for nearly all incident angles (-89^o, +89^o) is shown in Fig. 2. The PhC is two-dimensional and its unit cell is shown in Fig. 2(a). For transverse electric polarization, at the working frequency, the EFC is a shifted ellipse (red dashed curve) with the same height as that in free space (grey dashed curve), as shown in Fig. 2(c). The transmittance through such a PhC slab is always near unity (>99%) for nearly all incident angles (<89^o), and is almost irrespective of the layer number, N.

Figure 3: (a) Photo of the simplified PhC composed of alumina bars (white) placed inside the microwave field mapper. (b) The EFC of the PhC. (c) Transmittance through the PhC slab in simulations (solid lines) and experiments (triangular dots) and an alumina slab having the same thickness (dashed lines) as the function of incident angles. The figure is adapted from Reference [2].

To prove the theory, we performed proof-of-principle microwave experiments by utilizing a simplified PhC consisting of rectangular alumina bars in a square lattice, as shown in Fig. 3(a). Such a PhC exhibits a shifted elliptical EFC [Fig. 3(b)] and a wide-angle impedance matching effect. The measured transmission data (triangular dots) and simulation results (solid lines) both show high transmittance, which is great enhancement compared to the transmittance through an alumina slab with the same thickness (dashed lines).

Finally, we also note that such ultratransparent media can extend transformation optics (TO) [5, 6] to the general realm of nonlocal media. The traditional TO was founded in the local medium framework and require local media. Here, we demonstrate that ultratransparent media with controllable refractive indexes are also good candidates for TO applications such as invisibility cloaks. Interestingly, due to the nonlocality, the ultratransparent media also enable additional freedom in phase modulation, which is absent in the traditional TO. At optical frequencies, ultratransparent PhCs exhibit the significant advantages of omnidirectional impedance matching, low loss and micro fabrication requirement.

The concept and theory of ultratransparency gives a guideline for realizing the ultimate transparency which is broadband, omnidirectional and polarization-insensitive. Recently, we designed broadband, wide-angle and polarization-insensitive transparent media by using one-dimensional dielectric PhCs [7]. In the future, ultratransparent solid materials may be optimized to exhibit an unprecedented level of transparency and produce no reflection at all in certain ranges of frequencies.

References:
[1] John D. Jackson, "Classical Electrodynamics" (3rd edition, Wiley, New York, 1975).
[2] J. Luo, Y. Yang, Z. Yao, W. Lu, B. Hou, Z. H. Hang, C. T. Chan, and Y. Lai, "Ultratransparent media and transformation optics with shifted spatial dispersions", Physical Review Letters, 117, 223901 (2016). Abstract.
[3] John D. Joannopoulos, Steven G. Johnson, Joshua N. Winn, Robert D. Meade, "Photonic Crystals: Molding the Flow of Light" (2nd edition, Princeton University Press, Princeton, USA, 2008).
[4] Yongmin Liu, Xiang Zhang, "Metamaterials: a new frontier of science and technology", Chemical Society Reviews, 40, 2494-2507 (2011). Abstract.
[5] J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields", Science, 312, 1780-1782 (2006). Abstract.
[6] Ulf Leonhardt, "Optical conformal mapping", Science, 312, 1777-1780 (2006). Abstract.
[7] Zhongqi Yao, Jie Luo, Yun Lai, "Photonic crystals with broadband, wide-angle, and polarization-insensitive transparency", Optics Letters, 41, 5106 (2016). Abstract.

Diffusive-Light Invisibility Cloaking

[From Left to Right] Robert Schittny, Muamer Kadic, Tiemo Bückmann, Martin Wegener

Authors:
Robert Schittny^1,2, Muamer Kadic^1,3, Tiemo Bückmann^1,2, Martin Wegener^1,2,3

Affiliations:
¹Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), Germany, 
²DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), Germany, 
³Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Germany.

In an invisibility cloak [1–5], light is guided on a detour around an object such that it emerges behind unchanged, thus making the object invisible to an outside observer. An ideal cloak should be macroscopic and work perfectly for any direction, polarization, and wavelength of the incoming light. To make up for the geometrical detour, light has to travel faster inside the cloak than outside, that is, faster than the vacuum speed of light for cloaking in air or vacuum. Furthermore, the absence of wavelength dependence means that energy velocity and phase velocity are strictly equal. However, general relativity forbids energy velocities higher than the vacuum speed of light. Thus, macroscopic, omnidirectional, and broadband invisibility cloaking is fundamentally impossible in air [4, 5]. Consistently, all experimental demonstrations of optical cloaking so far came with a drawback in terms of operation bandwidth, size, or both [6–10].

In contrast to this, more recently, we have demonstrated [11] close to ideal macroscopic and broadband invisibility cloaking in diffusive light scattering media at visible wavelengths.

Past 2Physics articles by this Group:
May 06, 2012: "A Cloak for Elastic Waves in Thin Polymer Plates"
     by Nicolas Stenger, Manfred Wilhelm, Martin Wegener
June 19, 2011:
"3D Polarization-Independent Invisibility Cloak at Visible Wavelengths"
     by Tolga Ergin, Joachim Fischer, Martin Wegener
April 11, 2010: "3D Invisibility Cloaking Device at Optical Wavelengths"
     by Tolga Ergin, Nicolas Stenger, Martin Wegener

Fig. 1 [11] illustrates the principle and results of invisibility cloaking in diffusive media. In such media, many scattering particles are randomly distributed, causing each photon to travel along a random path (see artistic illustration in the magnifying glass in Fig. 1). This effectively slows down light with respect to the vacuum speed of light, making perfect cloaking possible. In contrast to “ballistic” light propagation in vacuum or air as described by Maxwell’s equations, light propagation in such a medium can be described by diffusion of photons [12].

Figure 1 (Ref.[11]): Principle of diffusive-light cloaking. Computer-generated image of an illuminated cuboid diffusive medium with a zero-diffusivity obstacle (left-hand side) and a core-shell cloak (right-hand side). The magnifying glass shows an artistic illustration of a photon’s random walk inside the diffuse medium. The black streamline arrows are simulation results illustrating the photon current around obstacle and cloak. Corresponding measurement results are projected onto the front side of the cuboid volume, showing a diffuse shadow for the obstacle (left-hand side) and its elimination for the cloak (right-hand side). The euro coin illustrates the macroscopic dimensions of the cloak.

If a diffusive medium is illuminated from one side, any object with a different diffusivity inside this medium will cause perturbations of the photon flow. On the left-hand side of Fig. 1, a hollow cylinder with a diffusivity of exactly zero (the “obstacle”) suppresses any photon flow inside and casts a pronounced shadow, reducing the photon current on the downstream side (see black streamline arrows in Fig. 1). To compensate for this, a thin layer with a higher diffusivity than in the surrounding medium is added to the cylinder on the right-hand side of Fig. 1 (the “cloak”). Intuitively, a higher diffusivity (that is, a lower concentration of scattering particles) leads to an effectively higher light propagation speed and thus makes up for the geometrical detour the light has to take on its way around the obstacle. The black streamline arrows show that the photon current behind the cloak is unchanged. In other words, the shadow cast by the obstacle vanishes.

Such a core-shell cloak design can be thought of as the reduction of more complex multilayer designs based on transformation optics [1–3] to just two layers. It is known theoretically [13, 14] to work perfectly in the static case and for spatially constant gradients of the photon density across the cloak. Core-shell cloaks have been demonstrated before in magnetostatics [15], thermodynamics [16, 17], and elastostatics [18], recently even for non-constant gradients [16, 17].

For our experiments, we used a hollow aluminum cylinder as the obstacle, coated with a thin layer of white paint that acted as a diffusive reflector. For the cloaking shell, we coated the cylinder with a thin layer of a transparent silicone doped with dielectric microparticles. Obstacle and cloak are truly macroscopic, as indicated by the euro coin in Fig. 1 for comparison. We realized the diffusive background medium by mixing de-ionized water and white wall-paint. By changing the paint concentration, we could easily vary the surrounding’s diffusivity to find good cloaking performance. Other common examples of diffusive media are clouds, fog, paper or milk.

The samples were submerged in a Plexiglas tank filled with the water-paint mixture. The tank was illuminated from one side with white light coming from a computer monitor; photographs of the other side of the tank were taken with an optical camera. Two of these photographs are projected onto the front side of the cuboid volume shown in Fig. 1. The left-hand side shows the case with just the obstacle inside, exhibiting a pronounced diffuse shadow as expected from the discussion above. This shadow vanishes almost completely on the right-hand side, where the cloak is inside the tank. The yellowish tint of the photographs is caused by partial absorption of blue light in the water-paint mixture. Furthermore, we could trace the small remaining intensity variations for the cloaking case back to a finite absorption of light at the core-shell interface.

While the illustration in Fig. 1 only shows results for homogeneous illumination, we also found excellent cloaking performance using an inhomogeneous line-like illumination pattern (not depicted). Furthermore, we also performed successful experiments with spherical samples (not depicted), proving that our cloak is truly three-dimensional and works for any polarization and any direction of incidence.

References:
[1] J. B. Pendry, D. Schurig, D. R. Smith, "Controlling electromagnetic fields". Science, 312, 1780 (2006). Abstract.
[2] Ulf Leonhardt, "Optical conformal mapping". Science, 312, 1777 (2006). Abstract.
[3] Vladimir M. Shalaev, "Transforming light". Science, 322, 384 (2008). Abstract.
[4] David A. B. Miller, "On perfect cloaking". Optics Express, 14, 12457 (2006). Full Article.
[5] Hila Hashemi, Baile Zhang, J. D. Joannopoulos, Steven G. Johnson, "Delay-bandwidth and delay-loss limitations for cloaking of large objects". Physical Review Letters, 104, 253903 (2010). Abstract.
[6] D. Schurig, J.J. Mock, B.J. Justice, S.A. Cummer, J.B. Pendry, A.F. Starr, D.R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies". Science, 314, 977 (2006). Abstract.
[7] R. Liu, C. Ji, J.J. Mock, J.Y. Chin, T.J. Cui, D.R. Smith, "Broadband ground-plane cloak". Science, 323, 366 (2009). Abstract.
[8] Jason Valentine, Jensen Li, Thomas Zentgraf, Guy Bartal, Xiang Zhang, "An optical cloak made of dielectrics". Nature Materials, 8, 568 (2009). Abstract.
[9] Lucas H. Gabrielli, Jaime Cardenas, Carl B. Poitras, Michal Lipson, "Silicon nanostructure cloak operating at optical frequencies". Nature Photonics, 3, 461 (2009). Abstract.
[10] Tolga Ergin, Nicolas Stenger, Patrice Brenner, John B. Pendry, Martin Wegener, "Three-dimensional invisibility cloak at optical wavelengths". Science, 328, 337 (2010). Abstract. 2Physics Article.
[11] Robert Schittny, Muamer Kadic, Tiemo Bückmann, Martin Wegener, "Invisibility Cloaking in a Diffusive Light Scattering Medium". Science, Published Online June 5 (2014). DOI:10.1126/science.1254524.
[12] C. M. Soukoulis, Ed., “Photonic Crystals and Light Localization in the 21st Century”, (Springer, 2001).
[13] Graeme W. Milton, “The Theory of Composites”, (Cambridge Univ. Press, 2002).
[14] Andrea Alù, Nader Engheta, "Achieving transparency with plasmonic and metamaterial coatings". Physical Review E, 72, 016623 (2005). Abstract.
[15] Fedor Gömöry, Mykola Solovyov, Ján Šouc, Carles Navau, Jordi Prat-Camps, Alvaro Sanchez, "Experimental realization of a magnetic cloak". Science, 335, 1466 (2012). Abstract.
[16] Hongyi Xu, Xihang Shi, Fei Gao, Handong Sun, Baile Zhang, "Ultrathin three-dimensional thermal cloak". Physical Review Letters, 112, 054301 (2014). Abstract.
[17] Tiancheng Han, Xue Bai, Dongliang Gao, John T. L. Thong, Baowen Li, Cheng-Wei Qiu, "Experimental demonstration of a bilayer thermal cloak". Physical Review Letters, 112, 054302 (2014). Abstract.
[18] T. Bückmann, M. Thiel, M. Kadic, R. Schittny, M. Wegener, "An elasto-mechanical unfeelability cloak made of pentamode metamaterials". Nature Communications, 5, 4130 (2014). Abstract.