Diffractive Nanophotonics

**Diffractive Nanophotonics** demonstrates the utility of the well-established methods of diffractive computer optics in solving nanophotonics tasks. It is concerned with peculiar properties of laser light diffraction by microoptics elements with nanoscale features and light confinement in subwavelength space regions. Written by recognized experts in this field, the book covers in detail a wide variety of advanced methods for the rigorous simulation of light diffraction. The authors apply their expertise to addressing cutting-edge problems in nanophotonics.Chapters consider the basic equations of diffractive nanophotonics and related transformations and numerical methods for solving diffraction problems under strict electromagnetic theory. They examine the diffraction of light on two-dimensional microscopic objects of arbitrary shape and present a numerical method for solving the problem of diffraction on periodic diffractive micro- and nanostructures. This method is used in modern trends in nanophotonics, such as plasmonics, metamaterials, and nanometrology. The book describes the simulation of electromagnetic waves in nanophotonic devices and discusses two methods of calculating the spatial modes of microstructured photonic crystal fibres—a relatively new class of optical fibres with the properties of photonic crystals.The book explains the theory of paraxial and non-paraxial laser beams with axial symmetry and an orbital angular momentum—called vortex beams—which are used for optical trapping and rotating micro- and nanoparticles in a ring in the cross-sectional plane of the beam. The final chapter discusses methods for calculating the force and torque exerted by the electromagnetic field focused onto the microparticle of arbitrary form, whose dimensions are comparable with the wavelength of light. Basic equations of diffractive nanophotonics Maxwell equations Differential equations of optics Integral theorems of optics Integral transformations in optics Numerical methods for diffraction theory The finite-difference time-domain method for solving Maxwell’s equation Numerical solution of the Helmholtz equations BPM–approach) Diffraction on cylindrical inhomogeneities comparable to the wavelength Analysis of diffraction on inhomogeneities by the combined finite element method and boundary element method Finite element method for solving the two-dimensional integral diffraction equation Diffraction of light on inhomogeneous dielectric cylinders Fast iterative method for calculating the diffraction field of a monochromatic electromagnetic wave on a dielectric cylinder Modelling of periodic diffractive micro- and nanostructures The method of rigorous coupled-wave analysis for solving the diffraction problem in periodic diffractive structures Formation of high-frequency interference patterns of surface plasma polaritons by diffraction gratings Diffractive heterostructures with resonant magneto-optical properties Metrology of periodic micro- and nanostructures by the reflectometry method Photonic crystals and light focusing One- and two-dimensional photonic crystals Two-dimensional photonic crystal gradient Mikaelian lens Sharp focusing of radially-polarized light Three-dimensional photonic crystals Interefence-litographic synthesis of photonic crystals Three-dimensional photonic approximants of quasicrystals and related structures One-dimensional photonic crystal based on a nanocomposite: metal nanoparticles – a dielectric Photonic crystal fibres Calculation of modes of photonic crystal fibres by the method of matched sinusoidal modes Calculation of modes of photonic-crystal light guides by the finite difference method Singular optics and superresolution Optical elements that form wavefronts with helical phase singularities The spiral phase plate Quantized SPP with a restricted aperture, illuminated by a plane wave Helical conical axicon Helical logarithmic axicon Elliptic vortex beams The vortex beams in optical fibres Matrices of optical vortices Simulation of an optical vortex generated by a plane wave diffracted by a spiral phase plate Optical trapping and manipulation of micro- and nano-objects Calculation of the force acting on the micro-object by a focused laser beam Methods for calculating the torque acting on a micro-object by a focused laser beam A geometrical optics method for calculating the force acting by light on a microscopic object Rotation of micro-objects in a Bessel beam Optical rotation using a multiorder spiral phase plate Rotation of microscopic objects in a vortex light ring formed by an axicon Optical rotation in a double light ring Optical rotation in a double ring of light Rotation of micro-objects by means of hypergeometric beams and beams that do not have the orbital angular momentum using the spatial light modulator (SLM) Investigation of rotation of micro-objects in light beams with orbital angular momentum The capture of micro-objects in Airy beams with ballistic properties Conclusion Appendix A Simulation using FULLWAVE Appendix B Simulation using FIMMWAVE Appendix C Simulation using OLYMPIOS program Index Diffractive Nanophotonics demonstrates the utility of the well-established methods of diffractive computer optics in solving nanophotonics tasks. It is concerned with peculiar properties of laser light diffraction by microoptics elements with nanoscale features and light confinement in subwavelength space regions. Written by recognized experts in this field, the book covers in detail a wide variety of advanced methods for the rigorous simulation of light diffraction. The authors apply their expertise to addressing cutting-edge problems in nanophotonics. Chapters consider the basic equations of diffractive nanophotonics and related transformations and numerical methods for solving diffraction problems under strict electromagnetic theory. They examine the diffraction of light on two-dimensional microscopic objects of arbitrary shape and present a numerical method for solving the problem of diffraction on periodic diffractive micro- and nanostructures. This method is used in modern trends in nanophotonics, such as plasmonics, metamaterials, and nanometrology. The book describes the simulation of electromagnetic waves in nanophotonic devices and discusses two methods of calculating the spatial modes of microstructured photonic crystal fibres—a relatively new class of optical fibres with the properties of photonic crystals. The book explains the theory of paraxial and non-paraxial laser beams with axial symmetry and an orbital angular momentum—called vortex beams—which are used for optical trapping and rotating micro- and nanoparticles in a ring in the cross-sectional plane of the beam. The final chapter discusses methods for calculating the force and torque exerted by the electromagnetic field focused onto the microparticle of arbitrary form, whose dimensions are comparable with the wavelength of light. "The authors have offered a comprehensive and accessible reference for computational methods in difractive nanophotonics."--Axel Mainzer in Optics & Photonics News