Symmetry in optics and photonics: a group theory approach
arXiv:1803.00121 · doi:10.1016/j.scib.2017.12.020
Abstract
Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles (such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.
arXiv comment20 page, 5 figures
References in corpus (55)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- Photonic Floquet Topological Insulators
- Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
- Unidirectional Invisibility induced by PT-Symmetric Periodic Structures
- Imaging topological edge states in silicon photonics
- Robust optical delay lines via topological protection
- Coherent Perfect Absorbers: Time-reversed Lasers
- Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
- Loss-induced suppression and revival of lasing
- PT-symmetry breaking and laser-absorber modes in optical scattering systems
- PT-symmetric laser-absorber
- Experimental Study of Active LRC Circuits with PT-Symmetries
- Probing topological invariants in the bulk of a non-Hermitian optical system
- PT-Symmetric Phonon Laser
- Observation of photonic anomalous Floquet Topological Insulators
- Reversing the Pump-Dependence of a Laser at an Exceptional Point
- Pump-induced Exceptional Points in Lasers
- Topologically protected midgap states in complex photonic lattices
- Nonparaxial Mathieu and Weber accelerating beams
- Observation of dynamic localization in periodically-curved waveguide arrays
- Non-Paraxial Accelerating Beams
- Supersymmetric Optical Structures
- Supersymmetric mode converters
- Constant-intensity waves and their modulation instability in non-Hermitian potentials
- Supersymmetry-generated complex optical potentials with real spectra
- Quantum Mechanical Properties of Bessel Beams
- Nonlinear modal interactions in parity-time () symmetric lasers
- Exceptional points and lasing self-termination in photonic molecules
- SUSY-inspired one-dimensional transformation optics
- Quantum noise and mode nonorthogonality in nonhermitian PT-symmetric optical resonators
- Bloch-like waves in random-walk potentials based on supersymmetry
- Supersymetric laser arrays
- Light transport in PT-invariant photonic structures with hidden symmetries
- Non-Hermitian engineering of single mode two dimensional laser arrays
- Optomechanical interactions in non-Hermitian photonic molecules
- Observation of supersymmetric scattering in photonic lattices
- Arbitrary non-paraxial accelerating periodic beams and spherical shaping of light
- Spherical fields as nonparaxial accelerating waves
- The quantum Arnold transformation
- Nonhermitian transport effects in coupled-resonator optical waveguides
- Jacobi photonic lattices and their SUSY partners
- Revisiting the optical -symmetric dimer
- Ermakov-Lewis symmetry in photonic lattices
- Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry
- Dynamical constants of structured photons with parabolic-cylindrical symmetry
- Supersymmetric Bragg gratings
- The Quantum Arnold Transformation and the Ermakov-Pinney equation
- Gilmore-Perelomov symmetry based approach to photonic lattices
- An introduction to arrays of coupled waveguides
- Optical finite representation of the Lorentz group
- Propagation and perfect transmission in three-waveguide axially varying couplers
- Wei-Norman equations for a unitary evolution
- A single structured light beam as an atomic cloud splitter
- SUSY Transformations for Quasinormal Modes of Open Systems
- Chaotic dynamics of thermal atoms in labyrinths created by optical lattices
Cited by in corpus (12)
- Parity-Time Symmetry in Non-Hermitian Complex Optical Media
- Spontaneous -symmetry breaking and exceptional points in cavity quantum electrodynamics systems
- Symmetric supermodes in cyclic multicore fibers
- Necklaces of -symmetric dimers
- Optical non-Hermitian para-Fermi oscillators
- Isospectral and square root Cholesky photonic lattices
- Lasing in para-Fermi class-B microring resonator arrays
- Optical trimer: A theoretical physics approach to waveguide couplers
- Optical simulation of atomic decay enhancement and suppression
- Reconfigurable multiport switch in coupled mode devices
- Euler--Poincaré reduction and the Kelvin--Noether theorem for discrete mechanical systems with advected parameters and additional dynamics
- Compound symmetries and double antisymmetry groups in linear time-invariant photonic systems