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Introduction

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Catenary Optics
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Abstract

Catenary optics is a newly emerging branch in optics and nanophotonics, which focuses on the applications of catenary functions in optical and electromagnetic devices. In a more general sense, it may be called catenary electromagnetics to highlight the electromagnetic nature of light. This book is devoted to the physics and applications of catenary optics and catenary electromagnetics. Section 1.1 gives a brief description of the developing history of catenary optics. Section 1.2 describes typical examples which illustrate the universal relation between catenary and optics. Section 1.3 discusses some common misconceptions related to catenary function. Section 1.4 is an overview of this book.

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References

  1. Catenary, http://www.en.wikipedia.org/wiki/Catenary

  2. M. Hirano, M. Aniya, A rational explanation of cross-profile morphology for glacial valleys and of glacial valley development. Earth Surf. Process. Landf. 13, 707–716 (1988)

    Article  Google Scholar 

  3. U shaped valley, http://www.en.wikipedia.org/wiki/U_shaped_valley

  4. The Lady with an Ermine, https://commons.wikimedia.org/wiki/File:The_Lady_with_an_Ermine.jpg

  5. Jin Wu Di, https://commons.wikimedia.org/wiki/File:Jin_Wu_Di.jpg

  6. Bodhisattva Leading the Way, https://upload.wikimedia.org/wikipedia/commons/2/28/Anonymous-Bodhisattva_Leading_the_Way.jpg

  7. Court Ladies Wearing Flowered Headdresses, https://upload.wikimedia.org/wikipedia/commons/0/06/Zhou_Fang._Court_Ladies_Wearing_Flowered_Headdresses._%2846x180%29_Liaoning_Provincial_Museum%2C_Shenyang.jpg

  8. D. Gilbert, On the mathematical theory of suspension bridges, with tables for facilitating their construction. Philos. Trans. R. Soc. Lond. 116, 202–218 (1826)

    Article  Google Scholar 

  9. C.R. Calladine, An amateur’s contribution to the design of Telford’s Menai Suspension Bridge: a commentary on Gilbert (1826) ‘On the mathematical theory of suspension bridges’, Philos. Transact. A Math. Phys. Eng. Sci. 373, 20140346 (2015)

    Article  Google Scholar 

  10. “Robert Hooke,” https://commons.wikimedia.org/wiki/Robert_Hooke

  11. R.K. Temple, The Genius of China: 3,000 Years of Science, Discovery, and Invention (Inner Traditions Rochester, VT, 2007)

    Google Scholar 

  12. Poem of Du Fu, https://zhuanlan.zhihu.com/p/43666691

  13. Anlan Suspension Bridge, https://commons.wikimedia.org/wiki/File:Anlan_Suspension_Bridge-3.jpg

  14. Luding Bridge, https://en.wikipedia.org/wiki/Luding_Bridge

  15. Q. Chen, X. Yao, L. Xu, Q. Li, Y. Song, L. Jiang, Capillary force restoration of droplet on superhydrophobic ribbed nano-needles arrays. Soft Matter 6, 2470–2474 (2010)

    Article  CAS  Google Scholar 

  16. P.A. Kralchevsky, K. Nagayama, Capillary bridges and capillary-bridge forces, in Particles at Fluid Interfaces and Membranes (Elsevier, 2001), pp. 469–502

    Google Scholar 

  17. Capillary bridges, http://www.en.wikipedia.org/wiki/Capillary_bridges

  18. Catenoid, https://en.wikipedia.org/wiki/catenoid

  19. G.A. Rottigni, Concentration of the sun’s rays using catenary curves. Appl. Opt. 17, 969–974 (1978)

    Article  CAS  Google Scholar 

  20. Eye, http://www.en.wikipedia.org/wiki/Eye

  21. D.J. Coleman, R.H. Silverman, H. Lloyd, IV.D. Physiology of Accommodation and Role of the Vitreous Body, in Vitreous: In Health and Disease, ed. by J. Sebag, (Springer New York, 2014), pp. 495–507

    Google Scholar 

  22. J. Evans, M. Rosenquist, “F = ma” optics. Am. J. Phys. 54, 876–883 (1986)

    Article  Google Scholar 

  23. D.J. Coleman, On the hydraulic suspension theory of accommodation. Trans. Am. Ophthalmol. Soc. 84, 846 (1986)

    CAS  Google Scholar 

  24. R. Nan, G. Ren, W. Zhu, Y. Lu, Adaptive cable-mesh reflector for the FAST. Acta Astron. Sin. 44, 13–18 (2003)

    Google Scholar 

  25. R. Nan, Five hundred meter aperture spherical radio telescope (FAST). Sci. China, Ser. G 49, 129–148 (2006)

    Article  Google Scholar 

  26. H. Fang, M. Lou, L.-M. Hsia, P. Leug, Catenary systems for membrane structures, in 19th AIAA Applied Aerodynamics Conference. Fluid Dynamics and Co-Located Conferences (American Institute of Aeronautics and Astronautics, 2001)

    Google Scholar 

  27. H.G. Kosmahl, G.M. Branch, Generalized representation of electric fields in interaction gaps of klystrons and traveling-wave tubes. IEEE Trans. Electron Devices 20, 621–629 (1973)

    Article  Google Scholar 

  28. X. Luo and T. Ishihara, Sub 100 nm lithography based on plasmon polariton resonance, in 2003 International Microprocesses and Nanotechnology Conference (IEEE, 2003), pp. 138–139

    Google Scholar 

  29. K. Tanaka, M. Tanaka, Simulations of nanometric optical circuits based on surface plasmon polariton gap waveguide. Appl. Phys. Lett. 82, 1158–1160 (2003)

    Article  CAS  Google Scholar 

  30. X. Luo, T. Ishihara, Surface plasmon resonant interference nanolithography technique. Appl. Phys. Lett. 84, 4780–4782 (2004)

    Article  CAS  Google Scholar 

  31. X. Luo, T. Ishihara, Subwavelength photolithography based on surface-plasmon polariton resonance. Opt. Express 12, 3055–3065 (2004)

    Article  Google Scholar 

  32. C. Wang, C. Du, X. Luo, Refining the model of light diffraction from a subwavelength slit surrounded by grooves on a metallic film. Phys. Rev. B 74, 245403 (2006)

    Article  Google Scholar 

  33. B. Wood, J.B. Pendry, D.P. Tsai, Directed subwavelength imaging using a layered metal-dielectric system. Phys. Rev. B 74, 115116 (2006)

    Article  Google Scholar 

  34. J. Khurgin, W.-Y. Tsai, D.P. Tsai, G. Sun, Landau damping and limit to field confinement and enhancement in plasmonic dimers. ACS Photonics 4, 2871–2880 (2017)

    Article  CAS  Google Scholar 

  35. M. Pu, Y. Guo, X. Li, X. Ma, X. Luo, Revisitation of extraordinary Young’s interference: from catenary optical fields to spin-orbit interaction in metasurfaces. ACS Photonics 5, 3198–3204 (2018)

    Article  Google Scholar 

  36. M. Pu, X. Ma, Y. Guo, X. Li, X. Luo, Theory of microscopic meta-surface waves based on catenary optical fields and dispersion. Opt. Express 26, 19555–19562 (2018)

    Article  CAS  Google Scholar 

  37. R. Chikkaraddy, B. de Nijs, F. Benz, S.J. Barrow, O.A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, J.J. Baumberg, Single-molecule strong coupling at room temperature in plasmonic nanocavities. Nature 535, 127 (2016)

    Article  CAS  Google Scholar 

  38. M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, X. Luo, Catenary optics for achromatic generation of perfect optical angular momentum. Sci. Adv. 1, e1500396 (2015)

    Article  Google Scholar 

  39. X. Luo, M. Pu, X. Li, X. Ma, Broadband spin Hall effect of light in single nanoapertures. Light Sci. Appl. 6, e16276 (2017)

    Article  CAS  Google Scholar 

  40. S. Pancharatnam, Generalized theory of interference, and its applications. Part I. Coherent pencils. Proc. Indian Acad. Sci. 44, 247–262 (1956)

    Article  Google Scholar 

  41. M.V. Berry, Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. Math. Phys. Eng. Sci. 392, 45–57 (1984)

    Article  Google Scholar 

  42. K.Y. Bliokh, D. Smirnova, F. Nori, Quantum spin Hall effect of light. Science 348, 1448–1451 (2015)

    Article  CAS  Google Scholar 

  43. Y. Zhao, M.A. Belkin, A. Alù, Twisted optical metamaterials for planarized ultrathin broadband circular polarizers. Nat. Commun. 3, 870 (2012)

    Article  CAS  Google Scholar 

  44. J.K. Gansel, M. Thiel, M.S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, M. Wegener, Gold helix photonic metamaterial as broadband circular polarizer. Science 325, 1513–1515 (2009)

    Article  CAS  Google Scholar 

  45. J. Kaschke, L. Blume, L. Wu, M. Thiel, K. Bade, Z. Yang, M. Wegener, A helical metamaterial for broadband circular polarization conversion. Adv. Opt. Mater. 3, 1411–1417 (2015)

    Article  CAS  Google Scholar 

  46. Y. Guo, X. Ma, M. Pu, X. Li, Z. Zhao, X. Luo, High-efficiency and wide-angle beam steering based on catenary optical fields in ultrathin metalens. Adv. Opt. Mater. 6, 1800592 (2018)

    Article  Google Scholar 

  47. M. Zhang, M. Pu, F. Zhang, Y. Guo, Q. He, X. Ma, Y. Huang, X. Li, H. Yu, X. Luo, Plasmonic metasurfaces for switchable photonic spin-orbit interactions based on phase change materials. Adv. Sci. 5, 1800835 (2018)

    Article  Google Scholar 

  48. X. Li, M. Pu, Z. Zhao, X. Ma, J. Jin, Y. Wang, P. Gao, X. Luo, Catenary nanostructures as highly efficient and compact Bessel beam generators. Sci. Rep. 6, 20524 (2016)

    Article  CAS  Google Scholar 

  49. Y. Wang, M. Pu, Z. Zhang, X. Li, X. Ma, Z. Zhao, X. Luo, Quasi-continuous metasurface for ultra-broadband and polarization-controlled electromagnetic beam deflection. Sci. Rep. 5, 17733 (2015)

    Article  CAS  Google Scholar 

  50. X. Li, M. Pu, Y. Wang, X. Ma, Y. Li, H. Gao, Z. Zhao, P. Gao, C. Wang, X. Luo, Dynamic control of the extraordinary optical scattering in semicontinuous 2D metamaterials. Adv. Opt. Mater. 4, 659–663 (2016)

    Article  CAS  Google Scholar 

  51. A. Poddubny, I. Iorsh, P. Belov, Y. Kivshar, Hyperbolic metamaterials. Nat. Photonics 7, 948–957 (2013)

    Article  CAS  Google Scholar 

  52. C. Wang, P. Gao, X. Tao, Z. Zhao, M. Pu, P. Chen, X. Luo, Far field observation and theoretical analyses of light directional imaging in metamaterial with stacked metal-dielectric films. Appl. Phys. Lett. 103, 031911 (2013)

    Article  Google Scholar 

  53. D. de Klerk, J. Murugan, and J.-P. Uzan, The catenary revisited: from Newtonian strings to superstrings, arXiv:1103.0788 (2011)

  54. Mirage, https://en.wikipedia.org/wiki/Mirage

  55. Z. Wang, An explanation of mirage with linearly varying index of refraction. Coll. Phys. 20, 24–27 (2001)

    Google Scholar 

  56. Z. Zhao, M. Pu, Y. Wang, X. Luo, The generalized laws of refraction and reflection. Opto-Electron. Eng. 44, 129–139 (2017)

    Google Scholar 

  57. A. Kalvach, Z. Szabó, Aberration-free flat lens design for a wide range of incident angles. J. Opt. Soc. Am. B 33, A66–A71 (2016)

    Article  CAS  Google Scholar 

  58. M. Pu, X. Li, Y. Guo, X. Ma, X. Luo, Nanoapertures with ordered rotations: symmetry transformation and wide-angle flat lensing. Opt. Express 25, 31471–31477 (2017)

    Article  CAS  Google Scholar 

  59. W. Liu, Z. Li, H. Cheng, C. Tang, J. Li, S. Zhang, S. Chen, J. Tian, Metasurface enabled wide-angle Fourier lens. Adv. Mater. 30, 1706368 (2018)

    Article  Google Scholar 

  60. A. Arbabi, E. Arbabi, S.M. Kamali, Y. Horie, S. Han, A. Faraon, Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations. Nat. Commun. 7, 13682 (2016)

    Article  CAS  Google Scholar 

  61. B. Groever, W.T. Chen, F. Capasso, Meta-lens doublet in the visible region. Nano Lett. 17, 4902–4907 (2017)

    Article  CAS  Google Scholar 

  62. M. Pu, N. Yao, C. Hu, X. Xin, Z. Zhao, C. Wang, X. Luo, Directional coupler and nonlinear Mach-Zehnder interferometer based on metal-insulator-metal plasmonic waveguide. Opt. Express 18, 21030–21037 (2010)

    Article  CAS  Google Scholar 

  63. E. Merzbacher, The early history of quantum tunneling. Phys. Today 55, 44–50 (2002)

    Article  CAS  Google Scholar 

  64. M. Razavy, Quantum Theory of Tunneling, 2nd ed. (World Scientific, 2014)

    Google Scholar 

  65. J.L. McFarland, Catenary geodesic lens antenna, U.S. patent 3,383,691 (1968)

    Google Scholar 

  66. J.S. Ajioka, J.L. McFarland, Beam-forming feeds, in Antenna Handbook (Chapman & Hall, 1993), Vol. III

    Google Scholar 

  67. K.H. Teo, D. Huang, J. Zhang, B. Yerazunis, B. Wang, Wireless energy transfer with negative material, U.S. patent US 20110133566 A1 (2011)

    Google Scholar 

  68. S. Assawaworrarit, X. Yu, S. Fan, Robust wireless power transfer using a nonlinear parity–time-symmetric circuit. Nature 546, 387 (2017)

    Article  CAS  Google Scholar 

  69. B. Wang, K.H. Teo, T. Nishino, W. Yerazunis, J. Barnwell, J. Zhang, Experiments on wireless power transfer with metamaterials. Appl. Phys. Lett. 98, 254101 (2011)

    Article  Google Scholar 

  70. L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1984)

    Google Scholar 

  71. B. Averill, P. Eldredge, Principles of General Chemistry (2012)

    Google Scholar 

  72. B. Zhao, J. Yang, New effects in an ultracompact Young’s double nanoslit with plasmon hybridization. New J. Phys. 15, 073024 (2013)

    Article  Google Scholar 

  73. X. Ma, Y. Guo, M. Pu, X. Li, X. Luo, Refined model for plasmon ruler based on catenary shaped optical fields. Plasmonics (2019)

    Google Scholar 

  74. Five hundred meter Aperture Spherical Telescope, http://www.en.wikipedia.org/wiki/Five_hundred_meter_Aperture_Spherical_Telescope

  75. Brachistochrone Curve, http://www.en.wikipedia.org/wiki/Brachistochrone_curve

  76. Beam Deflection Formulae, www.advancepipeliner.com/Resources/Others/Beams/Beam_Deflection_Formulae.pdf

  77. S.H. Pepe, Polynomial and catenary curve fits to human dental arches. J. Dent. Res. 54, 1124 (1975)

    Article  CAS  Google Scholar 

  78. Y. Guo, M. Pu, X. Li, X. Ma, P. Gao, Y. Wang, X. Luo, Functional metasurfaces based on metallic and dielectric subwavelength slits and stripes array. J. Phys.: Condens. Matter 30, 144003 (2018)

    Google Scholar 

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Luo, X. (2019). Introduction. In: Catenary Optics. Springer, Singapore. https://doi.org/10.1007/978-981-13-4818-1_1

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