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Register a new userHomotopy analysis method applied to second-order frequency mixing in nonlinear optical dielectric media
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The classical problem of three-wave mixing in a nonlinear optical medium is investigated using the homotopy analysis method (HAM). We show that the power series basis builds a generic polynomial expression that can be used to study three-wave mixing for arbitrary input parameters. The phase-mismatched and perfectly phase matched cases are investigated. Parameters that result in generalized sum- and difference-frequency generation are studied using HAM with a power series basis and compared to an explicit finite-difference approximation. The convergence region is extended by increasing the auxiliary parameter.
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Second-harmonic and sum-frequency mixing phenomena associated with 3D-localized photonic modes are studied in InP-based planar photonic crystal microcavities excited by short-pulse radiation near 1550 nm. Three-missing-hole microcavities that support two closely-spaced modes exhibit rich second-order scattering spectra that reflect intra- and inter-mode mixing via the bulk InP chi(2) during ring-down after excitation by the broadband, resonant pulse. Simultaneous excitation with a non-resonant source results in tunable second-order radiation from the microcavity.
Polarization-resolved second-harmonic spectra are obtained from the resonant modes of a two-dimensional planar photonic crystal microcavity patterned in a free-standing InP slab. The photonic crystal microcavity is comprised of a single missing-hole defect in a hexagonal photonic crystal host formed with elliptically-shaped holes. The cavity supports two orthogonally-polarized resonant modes split by 60 wavenumbers. Sum-frequency data are reported from the nonlinear interaction of the two coherently excited modes, and the polarization dependence is explained in terms of the nonlinear susceptibility tensor of the host InP.
Higher-order topological insulators (HOTI) are a novel topological phase beyond the framework of the conventional bulk-boundary correspondence. In these peculiar systems, the topologically nontrivial boundary modes are characterized by a co-dimension of at least two. Despite several promising preliminary considerations regarding the impact of nonlinearity in such systems, the flourishing field of experimental HOTI research has thus far been confined to the linear evolution of topological states. As such, the observation of the interplay between nonlinearity and the dynamics of higher-order topological phases in conservative systems remains elusive. In our work, we experimentally demonstrate nonlinear higher-order topological corner states. Our photonic platform enables us to observe nonlinear topological corner states as well as the formation of solitons in such topological structures. Our work paves the way towards the exploration of topological properties of matter in the nonlinear regime, and may herald a new class of compact devices that harnesses the intriguing features of topology in an on-demand fashion.
Small perturbations in the dielectric environment around a high quality whispering gallery mode resonator usually lead to a frequency shift of the resonator modes directly proportional to the polarizability of the perturbation. Here, we report experimental observations of strong frequency shifts that can be opposite and even exceed the contribution of the perturbations polarizability. The mode frequencies of a lithium niobate whispering gallery mode resonator are shifted using substrates of refractive indices ranging from 1.50 to 4.22. Both blue- and red-shifts are observed, as well as an increase in mode linewidth, when substrates are moved into the evanescent field of the whispering gallery mode. We compare the experimental results to a theoretical model by Foreman et al. and provide an additional intuitive explanation based on the Goos-Hanchen shift for the optical domain.
We investigate numerically the effect of long-range interaction on the transverse localization of light. To this end, nonlinear zigzag optical waveguide lattices are applied, which allows precise tuning of the second-order coupling. We find that localization is hindered by coupling between next-nearest lattice sites. Additionally, (focusing) nonlinearity facilitates localization with increasing disorder, as long as the nonlinearity is sufficiently weak. However, for strong nonlinearities, increasing disorder results in weaker localization. The threshold nonlinearity, above which this anomalous result is observed grows with increasing second-order coupling.
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