150 Years of Maxwell's Equations Nader Engheta Science 349, 136 (2015); DOI: 10.1126/Science.Aaa7224

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150 years ago James Clerk Maxwell wrote down a set of equations that allow us to control light and other electromagnetic excitations. www.sciencemag.org OPTICS 150 years of Maxwell’s equations Powerful tools are available for the manipulation of electromagnetic fields Downloaded from By Nader Engheta in taming these waves for the purpose of such as permittivity and/or permeability. A inventing new functional devices. Early ex- good example of such photon traffic con- n page 499 of his 1865 paper (1), amples include radio-frequency antennas, trol can be achieved with defects within James Clerk Maxwell wrote, “The lenses and mirrors, microwave waveguides, photonic crystals (2 ), where periodic arrays agreement of the results seems to optical fibers, and telegraph transmission of permittivity variations with photonic show that light and magnetism are lines, to name just a few. Recent develop- band gaps analogous to the electronic band affections of the same substance, and ments in nanoscience and nanotechnology, structures for electrons, provide paths for that light is an electromagnetic dis- materials science and technology, and con- light to propagate (see the figure, panel A). Oturbance propagated through the field ac- densed matter physics has made it possible Although bending light has been tradition- cording to electromagnetic laws.” With that to conceive materials and structures with ally done by reflection and refraction of knowledge, he changed the world forever. atomic-level controllability and with un- rays through surfaces based on Snell’s law, In the span of 150 years since his celebrated precedented properties not otherwise pres- the advent of metamaterials and metasur- paper, numerous scientific discoveries and ent in naturally available materials. These faces is now supplying us with transforma- technological innovations have originated developments have opened doors to numer- tion optics (3 ) and generalization of Snell’s from Maxwell’s equations. Electromagnetic ous opportunities to shape and sculpt light law (4, 5) for tailoring fields at subwave- and optical waves can be manipulated, tai- at the nano-, micro- and mesoscales in a length scales, opening up possibilities for lored, and controlled by means of materi- desired fashion. exciting scenarios such as cloaking, light als, and consequently, during the past one Ushering photons into desired paths re- concentration, optical illusion, and flat and a half centuries, materials science and quires the design of structures with proper photonics. Another paradigm for manipu-

engineering has always played the key roles inhomogeneity in material parameters lation of light at the nanoscale is achieved DUBASSY/THINKSTOCK IMAGE:

136 10 JULY 2015 • VOL 349 ISSUE 6244 sciencemag.org SCIENCE

Published by AAAS by optical metatronics ( 6), in which deeply as new platforms for manipulating light. For example, two waveguides linked by subwavelength structures function as Another extreme scenario is highly confined a near-zero effective-index junction would “lumped” optical circuit elements (analo- concentration of light using plasmonic operate as though they were connected di- gous to the resistor, inductor, and capaci- nanoantennas ( 10). Antennas, which have rectly to each other (see the figure, panel tor elements in electronics). This unifying been traditionally used to convert the con- C). This may have important implication in circuit paradigm furnishes “common al- fined electromagnetic energy in subwave- both classical and quantum optics, in which phabets” between electronics and photon- length regions into the far-field radiation, the distance between two points (two ob- ics, allowing transfer of ideas and designs have been instrumental in the develop- servers, two emitters, or an observer and an between these two fields. Collections of ment of numerous fields, such as wireless emitter), although they may be physically nanoparticles, when properly designed and communications and satellite technology. far apart, would behave as if they were close suitably juxtaposed, form optical nano- Shrinking conventional radio frequency an- together. This effect will present interesting circuits with unprecedented capability of tennas into the nanophotonics arena raises possibilities for long-range collective emis-

A B C

n = 1 n Ӎ 0 ef

n = 1

Manipulating electromagnetic fields and waves. (A) Photonic crystals as a platform for photon traffic control. (B) Optical metatronics, i.e., a collection of nanostructures with properly selected shapes, sizes, and materials, as lumped circuit elements for manipulating and processing optical fields and waves at subwavelength scales. (C) “Extreme” metamaterials with near-zero effective refractive index, providing a spatially uniform phase in a bounded region of space that functions as an “electromagnetic point” connecting two distant ports ( 12). information processing at subwavelength the possibility of using suitably designed sion, quantum entanglement, and cavity regions (see the figure, panel B). One can metallic nanostructures to concentrate light quantum electrodynamics, involving such then envision designing materials that in deeply subwavelength volumes with high extreme structures. tailor light-matter interaction in order to field intensity. This has opened new fron- James Clerk Maxwell could not have perform optical signal processing at the tiers in detection, sensing, and emission imagined that 150 years later his predicted nanoscale, e.g., performing mathematical control, such as nanoantenna-enhanced electromagnetic waves would be manipu- operations such as differentiation and inte- surface-enhanced Raman spectroscopy, and lated in numerous manners due to devel- gration as light passes through such mate- engineering spontaneous emission of quan- opments in science and technology. One rials and structures ( 7). Perhaps the notion tum dots ( 11). would wonder where our world would have of doing math with light in materials might Adding nonreciprocity to the optics of been without his ingenious and elegant also be extended to solving equations with nanoantennas by using magnetized mag- equations. ■ light if properly designed nanostructures neto-optical materials results in phenomena could be used. such as near-field optical energy rotation. REFERENCES AND NOTES The ability to synthesize materials with These effects would be enhanced due to the 1. J. C. Maxwell, Philos. Trans. R. Soc. Lond. 155, 499 (1865). 2. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987). desired parameters now offers opportu- plasmonic resonance of such nanoantennas 3. J. B. Pendry, D. Schurig, D. R. Smith, Science 312, 1780 nities to take manipulating the Maxwell and the high intensity of optical fields in (2006). equations to the “extreme.” For example, their vicinity. This can be a basis for nonre- 4. N. Yu et al., Science 334, 333 (2011). two-dimensional materials such as the gra- ciprocal optical devices, such as circulators, 5. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, V. M. Shalaev, Science 335, 427 (2012). phene have brought previously unimagina- at the nanoscale. As a final example of ex- 6. N. Engheta, Science 317, 1698 (2007). ble possibilities to photonics. treme manipulation of waves, metamaterials 7. A. Silva et al., Science 343, 160 (2014). The propagation of highly confined elec- with effective parameters near zero bring an 8. Z. Fei et al., Nature 487, 82 (2012). tromagnetic surface waves in the form of entirely new set of mechanisms for tailoring 9. J. Chen et al., Nature 487, 77 (2012). 10. M. Agio, A. Alù, Optical Antennas (Cambridge Univ. Press, surface plasmon polaritons along the gra- fields and waves ( 12). As relative permittivity Cambridge, 2013). phene sheet has been demonstrated ( 8, 9), and/or relative permeability attain near-zero 11. Y. C. Jun, R. Pala, M. Brongersma, J. Phys. Chem. C 114, which makes it possible to envision opti- values in a properly designed metamaterial, 7269 (2010). cal devices just one atom thick. Other low- the effective refractive index approaches 12. A. M. Mahmoud, N. Engheta, Nat. Commun. 5, 5638 (2014). dimensional materials such as hexagonal zero, causing the effective wavelength to be- boron nitride (hBN) and molybdenum di- come very large for the operating frequency. ACKNOWLEDGMENTS This work is supported in part by the U.S. Air Force Office of sulfide (MoS2) are also attracting attention Therefore, the phase of steady-state signals within such a structure is spatially uniform, Scientific Research (AFOSR) Multidisciplinary University Research Initiatives (MURI) grant numbers FA-9550-12-1-0488 implying that the structure appears to be University of Pennsylvania, Department of Electrical and and FA9550-14-1-0389. Systems Engineering, Philadelphia, PA 19104, USA. subwavelength electromagnetically regard- E-mail: [email protected] less of its shape and size. 10.1126/science.aaa7224

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Published by AAAS 150 years of Maxwell's equations Nader Engheta Science 349, 136 (2015); DOI: 10.1126/science.aaa7224

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