Topological aspects in nonlinear optical frequency conversion
arXiv:2210.11526 · doi:10.1103/PhysRevA.106.053503
Abstract
Nonlinear optical frequency conversion, observed more than half a century ago, is a corner stone in modern applications of nonlinear and quantum optics. It is well known that frequency conversion processes are constrained by conservation laws, such as momentum conservation that requires phase matching conditions for efficient conversion. However, conservation laws alone could not fully capture the features of nonlinear frequency conversion. Here it is shown that topology can provide additional constraints in nonlinear multi-frequency conversion processes. Unlike conservation laws, a topological constraint concerns with the conserved properties under continuous deformation, and can be regarded as a new indispensable degree of freedom to describe multi-frequency processes. We illustrate such a paradigm by considering sum frequency generation under a multi-frequency pump wave, showing that, akin topological phases in topological insulators, topological phase transitions can be observed in the frequency conversion process both at classical and quantum level.
arXiv comment16 pages, 4 figures, to appear in Physical Review A
References in corpus (35)
- Topological insulators and superconductors
- Topological Insulators with Inversion Symmetry
- Topological Photonics
- Topological Photonics
- Classification of topological quantum matter with symmetries
- Bidirectional and efficient conversion between microwave and optical light
- Nonlinear topological photonics
- Topological nature of nonlinear optical effects in solids
- Synthetic Dimension in Photonics
- Novel Topological Phase with Zero Berry Curvature
- Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
- Heralded generation of entangled photon pairs
- Topological characterization of chiral models through their long time dynamics
- Topological characterizations of an extended Su-Schrieffer-Heeger model
- Interplay between long range hopping and disorder in topological systems
- Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime
- Theory of Two-Photon Interactions with Broadband Down-Converted Light and Entangled Photons
- Topological quantum fluctuations and travelling wave amplifiers
- Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices
- Direct Observation of Topology from Single-photon Dynamics on a Photonic Chip
- Multistep Parametric Processes in Nonlinear Optics
- Probing one-dimensional topological phases in waveguide lattices with broken chiral symmetry
- An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model
- Quantum frequency conversion between infrared and ultraviolet
- Topological origin of edge states in two-dimensional inversion-symmetric insulators and semimetals
- Experimental realization of two-dimensional weak topological insulators
- Interaction of Independent Single Photons based on Integrated Nonlinear Optics
- Theory of high-efficiency sum-frequency generation for single-photon waveform conversion
- Photonic Nonlinearities via Quantum Zeno Blockade
- Two-dimensional weak-type topological insulators in inversion symmetric crystals
- Flat Energy Bands within Antiphase and Twin Boundaries and at Open Edges in Topological Materials
- Zitterbewegung of optical pulses in nonlinear frequency conversion
- Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials
- Single-photon frequency conversion in nonlinear crystals
- Transparency in nonlinear frequency conversion