Appendix A: Catenary function for a freely hanging chain -- Appendix B: Matlab codes for GDSII file generation -- Appendix C: Matlab codes for vectorial diffraction -- Appendix D: Quasi-stationary catenary optical fields -- Appendix E: Matlab codes for the transfer matrix method -- Appendix F: Gallery of pictures for catenary -- References.
Chapter 1. Introduction -- 1.1 Concepts and brief history -- 1.2 Catenary function in optics and electromagnetics -- 1.2.1 The mirage -- 1.2.2 Solar concentrator -- 1.2.3 Optical and quantum tunneling -- 1.2.4 Geodesic antenna -- 1.2.5 Wireless energy transfer -- 1.2.6 Accelerated charges in uniform electric fields -- 1.2.7 Coupling between atoms and meta-atoms -- 1.3 Misconceptions and controversies -- 1.3.1 FAST -- 1.3.2 Brachistochrone -- 1.3.3 Glacial valley -- 1.3.4 Freely supported beam and cantilever beam -- 1.4 Overview of the book -- References.
Chapter 2. Spin-controlled beam shaping with catenary subwavelength structures -- 2.1 Introduction to spin, linear and angular momentum of light -- 2.2 Spin-momentum locking in free space and guided waves -- 2.2.1 Guided wave: surface plasmon polaritons -- 2.2.2 Free space: circularly polarized beam at oblique incidence -- 2.3 Spin hall effect generated by a single catenary aperture -- 2.4 Integration design of the catenary array -- 2.5 Wide-angle lenses and airy beam generation -- 2.5.1 Wide-angle flat lens --2.5.2 Airy beam generation based on cubic phase -- 2.6 Optical vortex and high-order bessel beam generation -- 2.6.1 Achromatic optical vortex -- 2.6.2 Bessel beam carrying optical vortex -- 2.7 catenary devices with maximized efficiency -- 2.7.1 Metal-dielectric composites -- 2.7.2 All-metallic catenary meta-mirror -- 2.7.3 All-dielectric catenary devices -- 2.8 Coherent control of the diffraction efficiency of catenary metasurface -- References.
Chapter 3. Catenary structures for spin-dependent coupling of waveguide modes -- 3.1 Catenary apertures for unidirectional excitation of SPP -- 3.1.1 Discrete spin-controlled unidirectional coupler -- 3.1.2 Catenary unidirectional coupler -- 3.2 Spin-controlled router for SOI waveguide -- 3.3 Catenary-shaped waveguides -- References.
Chapter 4. Catenary plasmons for sub-diffraction-limited imaging and nanolithography -- 4.1 Catenary optical fields in plasmonic waveguides -- 4.1.1 Transfer matrix analysis of metal-dielectric multilayer -- 4.1.2 Catenary optical fields as plasmonic eigenmodes -- 4.1.3 Catenary plasmons in superlens -- 4.2 Sub-diffraction-limited nanolithography with planar lens -- 4.2.1 Reflective superlens -- 4.2.2 Plasmonic imaging of dense lines -- 4.2.3 Plasmonic imaging of complex patterns -- 4.3 Demagnifying imaging based on curved hyperlens -- 4.3.1 Numerical simulation -- 4.3.2 Experimental demonstration -- 4.4 Interference lithography of periodic patterns -- 4.4.1 Normal incidence -- 4.4.2 Oblique incidence -- 4.5 Interference lithography of aperiodic patterns -- 4.5.1 Polarization-dependent catenary optical fields -- 4.5.2 Interference of circular polarizations -- 4.6 Plasmonic direct writing based on catenary plasmons -- 4.6.1 Metallic tip -- 4.6.2 Bowtie-shaped nanoapertures -- 4.6.3 Virtual scanning tip -- References.
Chapter 5. Catenary plasmons for flat lensing, beam deflecting, and shaping -- 5.1 Young's double slits interference with unequal widths -- 5.1.1 Far-field EYI -- 5.1.2 Near-field EYI -- 5.2 Wavefront shaping via plasmonic slits -- 5.2.1 Plasmonic deflector and generalized Snell's law -- 5.2.2 Flat lens based on plasmonic nanoslits -- 5.2.3 Tunable plasmonic nanoslits lens -- 5.3 Plasmonic hole lens -- 5.3.1 Rectangular holes -- 5.3.2 Circular holes -- 5.4 Achromatic optical lens based on nanoslits array -- 5.5 Super-oscillatory metalens -- 5.6 Structural colors and color holography -- 5.6.1 Structural colors based on linear dispersion of catenary plasmons -- 5.6.2 Structural colors based on polarization conversion -- 5.6.3 Color holography -- References.
Chapter 6. Beam shaping via microscopic meta-surface-wave -- 6.1 Microscopic meta-surface-wave -- 6.1.1 Catenary theory of the microscopic m-waves -- 6.1.2 Application of m-wave in amplitude and phase modulation -- 6.2 All-metallic surface structure for virtual shaping -- 6.3 Broadband virtual shaping via layered metasurfaces -- 6.4 Achromatic skin cloak -- 6.5 Wide-angle beam steering -- 6.6 Switchable beam manipulation via phase-change materials -- References.
Chapter 7. Catenary optical fields and dispersion for perfect absorption of light -- 7.1 Critical coupling associated with catenary optical fields -- 7.2 Broadband absorption based on coupled resonators -- 7.2.1 Structure and generalized impedance theory -- 7.2.2 Fano resonance induced by coupled modes -- 7.2.3 Design of broadband absorbers -- 7.3 Dispersion engineering for broadband metasurface absorber -- 7.4 Catenary dispersion model for broadband absorption -- 7.4.1 Microwave absorber -- 7.4.2 Terahertz absorber -- 7.5 Coherent perfect absorption in metallic thin films -- 7.6 Catenary plasmons for solar cell enhancement -- 7.6.1 Localized field enhancement in plasmonic grating -- 7.6.2 Catenary model for the localized field enhancement -- References.
Chapter 8. Catenary optical fields for thermal emission engineering -- 8.1 Introduction -- 8.2 Beyond Planck's thermal radiation law -- 8.2.1 Near-field thermal radiation with flat surfaces -- 8.2.2 Near-field thermal radiation with structured surfaces -- 8.2.3 Far-field super-Planckian thermal radiation -- 8.3 Coherent thermal radiation -- 8.3.1 Coherent thermal radiation based on surface waves -- 8.3.2 Coherent thermal radiation in graphene -- 8.4 Perfect thermal radiation -- 8.4.1 Metamaterials -- 8.4.2 Metal-dielectric multilayers -- 8.5 Reduction of thermal radiation in pseudo- Brewster angle -- References.
Chapter 9. From catenary optics to engineering optics 2.0 -- 9.1 Basic laws of traditional engineering optics -- 9.2 Young's interferences of photons, electrons and coupled plasmons -- 9.2.1 Shrunk interference patterns in EYI -- 9.2.2 Shifted interference patterns in EYI -- 9.2.3 Modulated transmission in EYI -- 9.2.4 Extraordinary vertical Fabry-Perot interference -- 9.3 Generalized optical theories and their applications -- 9.3.1 Generalized diffraction theory based on catenary optical fields -- 9.3.2 Generalized laws of reflection and refraction -- 9.3.3 Generalized theory for absorption and radiation -- 9.4 Conclusions and outlooks -- References.
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This book offers the first comprehensive introduction to the optical properties of the catenary function, and includes more than 200 figures. Related topics addressed here include the photonic spin Hall effect in inhomogeneous anisotropic materials, coupling of evanescent waves in complex structures, etc. After familiarizing readers with these new physical phenomena, the book highlights their applications in plasmonic nanolithography, flat optical elements, perfect electromagnetic absorbers and polarization converters. The book will appeal to a wide range of readers: while researchers will find new inspirations for historical studies combining mechanics, mathematics, and optics, students will gain a wealth of multidisciplinary knowledge required in many related areas. In fact, the catenary function was deemed to be a "true mathematical and mechanical form" in architecture by Robert Hooke in the 1670s. The discovery of the mathematical form of catenaries is attributed to Gottfried Leibniz, Christiaan Huygens and Johann Bernoulli in 1691. As the founders of wave optics, however, Hooke and Huygens did not recognize the importance of catenaries in optics. It is only in recent decades that the link between catenaries and optics has been established.