Reflectionless excitation of arbitrary photonic structures: a general theory
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A. Douglas Stone
Abstract
We outline and interpret a recently developed theory of impedancematching or reflectionless excitation of arbitrary finite photonic structures in any dimension. The theory includes both the case of guided wave and free-space excitation. It describes the necessary and sufficient conditions for perfectly reflectionless excitation to be possible and specifies howmany physical parameters must be tuned to achieve this. In the absence of geometric symmetries, such as parity and time-reversal, the product of parity and time-reversal, or rotational symmetry, the tuning of at least one structural parameter will be necessary to achieve reflectionless excitation. The theory employs a recently identified set of complex frequency solutions of theMaxwell equations as a starting point, which are defined by having zero reflection into a chosen set of input channels, and which are referred to as R-zeros. Tuning is generically necessary in order to move an R-zero to the real frequency axis, where it becomes a physical steady-state impedancematched solution, which we refer to as a reflectionless scattering mode (RSM). In addition, except in singlechannel systems, the RSM corresponds to a particular input wavefront, and any other wavefront will generally not be reflectionless. It is useful to consider the theory as representing a generalization of the concept of critical coupling of a resonator, but it holds in arbitrary dimension, for arbitrary number of channels, and even when resonances are not spectrally isolated. In a structure with parity and time-reversal symmetry (a real dielectric function) or with parity-time symmetry, generically a subset of the R-zeros has real frequencies, and reflectionless states exist at discrete frequencies without tuning. However, they do not exist within every spectral range, as they do in the special case of the Fabry-Pérot or two-mirror resonator, due to a spontaneous symmetry-breaking phenomenon when two RSMs meet. Such symmetry-breaking transitions correspond to a new kind of exceptional point, only recently identified, at which the shape of the reflection and transmission resonance lineshape is flattened. Numerical examples of RSMs are given for one-dimensional multimirror cavities, a two-dimensionalmultiwaveguide junction, and a multimode waveguide functioning as a perfect mode converter. Two solution methods to find R-zeros and RSMs are discussed. The first one is a straightforward generalization of the complex scaling or perfectly matched layer method and is applicable in a number of important cases; the second one involves a mode-specific boundary matching method that has only recently been demonstrated and can be applied to all geometries for which the theory is valid, including free space andmultimode waveguide problems of the type solved here.
Abstract
We outline and interpret a recently developed theory of impedancematching or reflectionless excitation of arbitrary finite photonic structures in any dimension. The theory includes both the case of guided wave and free-space excitation. It describes the necessary and sufficient conditions for perfectly reflectionless excitation to be possible and specifies howmany physical parameters must be tuned to achieve this. In the absence of geometric symmetries, such as parity and time-reversal, the product of parity and time-reversal, or rotational symmetry, the tuning of at least one structural parameter will be necessary to achieve reflectionless excitation. The theory employs a recently identified set of complex frequency solutions of theMaxwell equations as a starting point, which are defined by having zero reflection into a chosen set of input channels, and which are referred to as R-zeros. Tuning is generically necessary in order to move an R-zero to the real frequency axis, where it becomes a physical steady-state impedancematched solution, which we refer to as a reflectionless scattering mode (RSM). In addition, except in singlechannel systems, the RSM corresponds to a particular input wavefront, and any other wavefront will generally not be reflectionless. It is useful to consider the theory as representing a generalization of the concept of critical coupling of a resonator, but it holds in arbitrary dimension, for arbitrary number of channels, and even when resonances are not spectrally isolated. In a structure with parity and time-reversal symmetry (a real dielectric function) or with parity-time symmetry, generically a subset of the R-zeros has real frequencies, and reflectionless states exist at discrete frequencies without tuning. However, they do not exist within every spectral range, as they do in the special case of the Fabry-Pérot or two-mirror resonator, due to a spontaneous symmetry-breaking phenomenon when two RSMs meet. Such symmetry-breaking transitions correspond to a new kind of exceptional point, only recently identified, at which the shape of the reflection and transmission resonance lineshape is flattened. Numerical examples of RSMs are given for one-dimensional multimirror cavities, a two-dimensionalmultiwaveguide junction, and a multimode waveguide functioning as a perfect mode converter. Two solution methods to find R-zeros and RSMs are discussed. The first one is a straightforward generalization of the complex scaling or perfectly matched layer method and is applicable in a number of important cases; the second one involves a mode-specific boundary matching method that has only recently been demonstrated and can be applied to all geometries for which the theory is valid, including free space andmultimode waveguide problems of the type solved here.
Chapters in this book
- Frontmatter i
- Preface v
- Contents vii
-
Part I: Optoelectronics and Integrated Photonics
- Disorder effects in nitride semiconductors: impact on fundamental and device properties 3
- Ultralow threshold blue quantum dot lasers: what’s the true recipe for success? 23
- Waiting for Act 2: what lies beyond organic lightemitting diode (OLED) displays for organic electronics? 31
- Waveguide combiners for mixed reality headsets: a nanophotonics design perspective 41
- On-chip broadband nonreciprocal light storage 75
- High-Q nanophotonics: sculpting wavefronts with slow light 83
- Thermoelectric graphene photodetectors with sub-nanosecond response times at terahertz frequencies 89
- High-performance integrated graphene electro-optic modulator at cryogenic temperature 99
- Asymmetric photoelectric effect: Auger-assisted hot hole photocurrents in transition metal dichalcogenides 105
- Seeing the light in energy use 115
-
Part II: Lasers, Active optical devices and Spectroscopy
- A high-repetition rate attosecond light source for time-resolved coincidence spectroscopy 119
- Fast laser speckle suppression with an intracavity diffuser 131
- Active optics with silk 139
- Nanolaser arrays: toward application-driven dense integration 151
- Two-dimensional spectroscopy on a THz quantum cascade structure 173
- Homogeneous quantum cascade lasers operating as terahertz frequency combs over their entire operational regime 183
- Toward new frontiers for terahertz quantum cascade laser frequency combs 189
- Soliton dynamics of ring quantum cascade lasers with injected signal 197
-
Part III: Fiber Optics and Optical Communications
- Propagation stability in optical fibers: role of path memory and angular momentum 213
- Perspective on using multiple orbital-angularmomentum beams for enhanced capacity in freespace optical communication links 229
-
Part IV: Biomedical Photonics
- A fiber optic–nanophotonic approach to the detection of antibodies and viral particles of COVID-19 241
- Plasmonic control of drug release efficiency in agarose gel loaded with gold nanoparticle assemblies 253
- Metasurfaces for biomedical applications: imaging and sensing from a nanophotonics perspective 265
- Hyperbolic dispersion metasurfaces for molecular biosensing 301
-
Part V: Fundamentals of Optics
- A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction 323
- Reflectionless excitation of arbitrary photonic structures: a general theory 351
-
Part VI: Optimization Methods
- Multiobjective and categorical global optimization of photonic structures based on ResNet generative neural networks 371
- Machine learning–assisted global optimization of photonic devices 381
- Artificial neural networks for inverse design of resonant nanophotonic components with oscillatory loss landscapes 395
- Adjoint-optimized nanoscale light extractor for nitrogen-vacancy centers in diamond 403
-
Part VII: Topological Photonics
- Non-Hermitian and topological photonics: optics at an exceptional point 415
- Topological photonics: Where do we go from here? 437
- Topological nanophotonics for photoluminescence control 447
- Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems 455
-
Part VIII: Quantum Computing, Quantum Optics, and QED
- Quantum computing and simulation 467
- NIST-certified secure key generation via deep learning of physical unclonable functions in silica aerogels 471
- Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons 479
- Macroscopic QED for quantum nanophotonics: emitter-centered modes as a minimal basis for multiemitter problems 491
- Generation and dynamics of entangled fermion–photon–phonon states in nanocavities 505
- Polaritonic Tamm states induced by cavity photons 527
- Recent progress in engineering the Casimir effect – applications to nanophotonics, nanomechanics, and chemistry 537
- Enhancement of rotational vacuum friction by surface photon tunneling 551
-
Part IX: Plasmonics and Polaritonics
- Shrinking the surface plasmon 561
- Polariton panorama 565
- Scattering of a single plasmon polariton by multiple atoms for in-plane control of light 595
- A metasurface-based diamond frequency converter using plasmonic nanogap resonators 605
- Selective excitation of individual nanoantennas by pure spectral phase control in the ultrafast coherent regime 613
- Semiconductor quantum plasmons for high frequency thermal emission 623
- Origin of dispersive line shapes in plasmon-enhanced stimulated Raman scattering microscopy 633
- Epitaxial aluminum plasmonics covering full visible spectrum 643
-
Part X: Metaoptics
- Metamaterials with high degrees of freedom: space, time, and more 657
- The road to atomically thin metasurface optics 661
- Active nonlocal metasurfaces 673
- Giant midinfrared nonlinearity based on multiple quantum well polaritonic metasurfaces 685
- Near-field plates and the near zone of metasurfaces 697
- High-efficiency metadevices for bifunctional generations of vectorial optical fields 703
- Printing polarization and phase at the optical diffraction limit: near- and far-field optical encryption 715
- Optical response of jammed rectangular nanostructures 723
- Dynamic phase-change metafilm absorber for strong designer modulation of visible light 731
- Arbitrary polarization conversion for pure vortex generation with a single metasurface 745
- Enhanced harmonic generation in gases using an all-dielectric metasurface 751
- Monolithic metasurface spatial differentiator enabled by asymmetric photonic spin-orbit interactions 759
Chapters in this book
- Frontmatter i
- Preface v
- Contents vii
-
Part I: Optoelectronics and Integrated Photonics
- Disorder effects in nitride semiconductors: impact on fundamental and device properties 3
- Ultralow threshold blue quantum dot lasers: what’s the true recipe for success? 23
- Waiting for Act 2: what lies beyond organic lightemitting diode (OLED) displays for organic electronics? 31
- Waveguide combiners for mixed reality headsets: a nanophotonics design perspective 41
- On-chip broadband nonreciprocal light storage 75
- High-Q nanophotonics: sculpting wavefronts with slow light 83
- Thermoelectric graphene photodetectors with sub-nanosecond response times at terahertz frequencies 89
- High-performance integrated graphene electro-optic modulator at cryogenic temperature 99
- Asymmetric photoelectric effect: Auger-assisted hot hole photocurrents in transition metal dichalcogenides 105
- Seeing the light in energy use 115
-
Part II: Lasers, Active optical devices and Spectroscopy
- A high-repetition rate attosecond light source for time-resolved coincidence spectroscopy 119
- Fast laser speckle suppression with an intracavity diffuser 131
- Active optics with silk 139
- Nanolaser arrays: toward application-driven dense integration 151
- Two-dimensional spectroscopy on a THz quantum cascade structure 173
- Homogeneous quantum cascade lasers operating as terahertz frequency combs over their entire operational regime 183
- Toward new frontiers for terahertz quantum cascade laser frequency combs 189
- Soliton dynamics of ring quantum cascade lasers with injected signal 197
-
Part III: Fiber Optics and Optical Communications
- Propagation stability in optical fibers: role of path memory and angular momentum 213
- Perspective on using multiple orbital-angularmomentum beams for enhanced capacity in freespace optical communication links 229
-
Part IV: Biomedical Photonics
- A fiber optic–nanophotonic approach to the detection of antibodies and viral particles of COVID-19 241
- Plasmonic control of drug release efficiency in agarose gel loaded with gold nanoparticle assemblies 253
- Metasurfaces for biomedical applications: imaging and sensing from a nanophotonics perspective 265
- Hyperbolic dispersion metasurfaces for molecular biosensing 301
-
Part V: Fundamentals of Optics
- A Tutorial on the Classical Theories of Electromagnetic Scattering and Diffraction 323
- Reflectionless excitation of arbitrary photonic structures: a general theory 351
-
Part VI: Optimization Methods
- Multiobjective and categorical global optimization of photonic structures based on ResNet generative neural networks 371
- Machine learning–assisted global optimization of photonic devices 381
- Artificial neural networks for inverse design of resonant nanophotonic components with oscillatory loss landscapes 395
- Adjoint-optimized nanoscale light extractor for nitrogen-vacancy centers in diamond 403
-
Part VII: Topological Photonics
- Non-Hermitian and topological photonics: optics at an exceptional point 415
- Topological photonics: Where do we go from here? 437
- Topological nanophotonics for photoluminescence control 447
- Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems 455
-
Part VIII: Quantum Computing, Quantum Optics, and QED
- Quantum computing and simulation 467
- NIST-certified secure key generation via deep learning of physical unclonable functions in silica aerogels 471
- Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons 479
- Macroscopic QED for quantum nanophotonics: emitter-centered modes as a minimal basis for multiemitter problems 491
- Generation and dynamics of entangled fermion–photon–phonon states in nanocavities 505
- Polaritonic Tamm states induced by cavity photons 527
- Recent progress in engineering the Casimir effect – applications to nanophotonics, nanomechanics, and chemistry 537
- Enhancement of rotational vacuum friction by surface photon tunneling 551
-
Part IX: Plasmonics and Polaritonics
- Shrinking the surface plasmon 561
- Polariton panorama 565
- Scattering of a single plasmon polariton by multiple atoms for in-plane control of light 595
- A metasurface-based diamond frequency converter using plasmonic nanogap resonators 605
- Selective excitation of individual nanoantennas by pure spectral phase control in the ultrafast coherent regime 613
- Semiconductor quantum plasmons for high frequency thermal emission 623
- Origin of dispersive line shapes in plasmon-enhanced stimulated Raman scattering microscopy 633
- Epitaxial aluminum plasmonics covering full visible spectrum 643
-
Part X: Metaoptics
- Metamaterials with high degrees of freedom: space, time, and more 657
- The road to atomically thin metasurface optics 661
- Active nonlocal metasurfaces 673
- Giant midinfrared nonlinearity based on multiple quantum well polaritonic metasurfaces 685
- Near-field plates and the near zone of metasurfaces 697
- High-efficiency metadevices for bifunctional generations of vectorial optical fields 703
- Printing polarization and phase at the optical diffraction limit: near- and far-field optical encryption 715
- Optical response of jammed rectangular nanostructures 723
- Dynamic phase-change metafilm absorber for strong designer modulation of visible light 731
- Arbitrary polarization conversion for pure vortex generation with a single metasurface 745
- Enhanced harmonic generation in gases using an all-dielectric metasurface 751
- Monolithic metasurface spatial differentiator enabled by asymmetric photonic spin-orbit interactions 759
