Special issue on transformation optics
The transformation behavior of physical fields is important both in physics and in engineering. For electromagnetic fields, the natural invariance of Maxwell’s equations under coordinate transformations was first proposed by H. Weyl as early as 1902 [1], where the equivalence between geometry and medium was discussed. According to the theory, light in a medium defined by a particular coordinate system can propagate as if in a second medium defined by a different coordinate system. This kind of invariance not only leads to a better understanding of physics, but also provides a powerful method to deal with the electromagnetic problems in complex geometries [2]. However, the theory might have remained in the stages of theoretical research or as an interesting simulation tool until the metamaterial concept [3,4] and its experimental realization [5,6,7,8,9] was introduced. In 2006, J. B. Pendry, D. Schurig, and D. R. Smith proposed a strategy to design an electromagnetic “invisibility cloak,” that would exclude all electromagnetic fields from a given volume of space and eliminate all scattering.The cloak design was based on a coordinate transformation combined with the invariance of Maxwell’s equation, and also leveraged the expanded range of material properties unique to metamaterials [10]. The design technique was dubbed “transformation optics,” and quickly applied to the design of various electromagnetic devices. At the same time, the concept of “transformation optics” has been extended into many other branches of physics, including acoustics, elasticity, and thermal flow.
This special issue contains 29 papers that highlight the field of transformation optics, from theoretical analysis to experimental realization. The issue begins with three reviews. One of these reviews summarizes the two of the most compelling applications of transformation optics: cloaking and imaging [11]; while the other two reviews introduce the recent development of transformation thermodynamics [12,13]. This collection of papers also contains 26 research articles spanning a variety of topics. First, various cloaks are designed usingthe technique of transformation optics, including open active cloaks [14], surface wave cloaks [15], and magnetic carpet cloaks [16]. Additionally, cloaks based on photonic crystals are discussed [17] and the free-space singular boundary conditions in an invisibility cloak are experimentally verified [18]. Second, a set of imaging methods are presented along with practical lens designs. Within this subtopic area, the ideas of integral imaging [19], all-dielectric microwave lenses [20], superlenses [21], optical translational projectors [22], and invisible lenses [23] are presented. Third, transformation optics can be used to design concentrators [24] and metasurface-loaded waveguides [25], and to study wave propagation in complex coordinates [26] and the refractive index of reciprocal electromagnetic media [27]. Fourth, some properties in transformation optics are studied, including the preservation of omnidirectionality [28], surrogate models [29], the all-angle reflectionless property [30], optical forces [31], and some new physical phenomena [32]. Finally, the concept of “transformation optics” has been extended into branches of physics, including transformation plasmonics [33,34], transformation acoustics [35], transformation thermodynamics [36], non-Hermitian transformation optics [37,38], and transformation quantum optics [39].
In summary, we hope this collection of articles will continue to provoke thought regarding the basic aspects of transformation optics, as well as stimulate the experimental design of more practical and functional electromagnetic devices using this fascinating methodology. We also look forward to the continuingexpansion of “transformation optics” to “transformation physics”, as the ideas of geometrical transformations are increasingly applied to a more diverse set of phenomena.
References
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[9] Linden Stefan, Enkrich Christian, Wegener Martin, Zhou Jiangfeng, Koschny Thomas, Soukoulis Costas M 2004 Magnetic Response of Metamaterials at 100 Terahertz Science306 1351.
[10] Pendry J B, Schurig D, and Smith D R 2006 Controlling Electromagnetic Fields Science312 1780.
[11] Wu Kedi, and Cheng Qiluan, Wang Guo Ping Fourier analysis: from cloaking to imaging
[12] Raza Muhammad, Liu Yichao, Lee El Hang, Ma Yungui, Transformation Thermodynamics and Heat Cloaking: A Review
[13] Han Tiancheng and Qiu Cheng-Wei Transformation Laplacian metamaterials: Recent advances in manipulating thermal and dc fields
[14] Ma Qian, Yang Fan, Jin Tian Yu, Mei Zhong Lei and Cui Tie Jun Open active cloaking and illusion devices for the Laplace equation
[15] McManus T M, Spada L La and Hao Y On isotropic and anisotropic surface wave cloaks
[16] Deng Ye, Xu Su, Zhang Runren, Zheng Bin, Chen Hua, Gao Fei, Yu Faxin, Zhang Baile, and Chen Hongsheng Ultra-Broadband Magnetic Carpet Cloak for Transverse-Electric Polarization
[17] Semouchkina Elena, Duan Ran, Gandji Navid P, Jamilan Saeid, Semouchkin George, and Pandey Ravi Superluminal Media Formed by Photonic Crystals for Transformation Optics-Based Invisibility Cloaks
[18] Wu Qiannan, Gao Fei, Song Zhengyong, Lin Xiao, Zhang Youming, Chen Huanyang, Zhang Baile Experimental verification of free-space singular boundary conditions in an invisibility cloak
[19] Oxburgh Stephen, White Chris D, Antoniou Georgios, Orife Ejovbokoghene, Sharpe Tim, and Courtial Johannes Large-scale, white-light, transformation optics using integral imaging
[20] YI Jianjia, BUROKUR Shah Nawaz, PIAU Gérard-Pascal, and LUSTRAC André de 3D printed broadband transformation optics based all-dielectric microwave lenses
[21] Wee W H, Ye Y J and Luo Y Towards a practical superlens - a simple simplical design
[22] Sun Fei, Liu Yichao, and He Sailing True dynamic imaging and image composition/division by the optical translational projector
[23] Aaron Danner and Tomas Tyc Visual defects when extending two-dimensional invisible lenses with circular symmetry into the third dimension
[24] Prokopeva L J and Kildishe A V Expanding the theory of circular omnidirectional light concentrators to elliptic and spheroidal designs
[25] Wei Pengjiang, Xiao Shiyi, Xu Yadong, Chen Huanyang, Chu Sai Tak and Li Jensen Metasurface-loaded waveguide for transformation optics applications
[26] Simon Horsley, Christopher King, and Thomas Philbin, Wave propagation in complex coordinates
[27] McCall Martin W, Kinsler Paul and Topf David The Refractive Index of Reciprocal Electromagnetic Media
[28] Popa Bogdan-Ioan, Cummer Steven A Preserving omnidirectionality in optimized asymmetric transformation optics designs
[29] Campbell Sawyer D, Nagar Jogender, Brocker Donovan E, and Werner Douglas H On the use of surrogate models in the analytical decompositions of refractive index gradients obtained through quasiconformal transformation optics
[30] Gok Gurkan, Grbic Anthony A Physical Explanation for the All-Angle Reflectionless Property of Transformation Optics Designs
[31] Novitsky A V Scattered field generation and optical forces in transformation optics
[32] Jiang Wei Xiang, Bao Di, and Cui Tie Jun Exploring new physical phenomena with transformation optics
[33] Meriam Aloui, Kaizad Rustomji, Tieh-Ming Chang, Gerard Tayeb, Pierre Sabouroux, Romain Quidant, Stefan Enoch, Sebastie Guenneau, Redha Abdeddaim Cyclic concentrator, carpet cloaks and fisheye lens via transformation plasmonics
[34] Huidobro P A, Kraft M, Kun R, Maier S A, and Pendry J B Graphene, plasmons and transformation optics
[35] Bowen Patrick T, Urzhumov Yaroslav A Three Forms of Omnidirectional Acoustic Invisibility Engineered Using Fast Elastodynamic Transfer-Matrix Method
[36] Garcia-Meca Carlos and Barcel Carlos Dynamically-tunable transformation thermodynamics
[37] Savoia S, Castaldi G, Galdi V Complex-coordinate non-Hermitian transformation optics
[38] Andrea Alu, Costas Valagiannopoulos, Francesco Monticone, PT-Symmetric Planar Devices for Field Transformation and Imaging
[39] Zhang Jingjing, Wubs Martijn, Ginzburg Pavel, Wurtz Gregory, Zayats Anatoly V Transformation quantum optics: Designing spontaneous emission using coordinate transformations