The frequency modes of photonic resonators offer tantalizing possibilities for analog simulators of Hamiltonians both in the quantum and classical realm. We show how synthetic frequency dimensions can be formed by coupling such modes through external drives, enabling experimental demonstrations of a wide variety of topologically nontrivial effects that are challenging in other platforms. Harnessing the long-range coupling, coherent phase control and unprecedented reconfigurability afforded by synthetic dimensions, we observe phenomena such as the 2D quantum Hall effect and topological phase transitions in 0D structures consisting of one or two resonators. Our work elucidates how higher-dimensional physics can be implemented in simpler, experimentally feasible lower-dimensional structures. We also highlight the potential of scalably constructing new phenomena such as topological energy pumps showing quantized transport that is robust to dissipation by introducing an additional Floquet dimension in coupled resonators.
We present the creation of a two-dimensional frequency comb in a single integrated microring resonator through its dual pumping. We demonstrate experimentally and theoretically that dual-pumping allows for the creation of a multi-color soliton with a single group rotation velocity yet multiple phase rotation velocities, yielding multiple soliton eigenfrequencies (i.e. colors). We show that, thanks to the material's nonlinearity, its eigenfrequencies can cascade through four-wave mixing, creating a comb. Because this dimension is orthogonal to the azimuthal mode number dimension, the extracted frequency comb is ultimately a two-dimensional one.
Implementing frequency-encoded photonic linear transformations can be of significant interest not only for quantum information processing and machine learning hardware accelerators, but also for optical signal processing, communications, and spectrotemporal shaping of light. We present a flexible, reconfigurable architecture to implement such arbitrary linear transformations for photons using the synthetic frequency dimension of dynamically modulated microring resonators. Inverse design of the coupling between the frequency modes enables arbitrary scattering matrices to be scalably implemented with high fidelity, allowing for nonreciprocal frequency translation, unitary and nonunitary transformations. Our results introduce new functionalities for linear transformations beyond those possible with real-space architectures that are typically time-invariant.
Higher-order topological insulators (HOTIs), originating from quantized quadrupole and octupole moments, have attracted significant interest since they support boundary states that are two or more dimensions lower than their bulk. However, previous HOTIs have been restricted to real-space dimensions. Here we construct photonic HOTIs using synthetic dimensions, comprising frequency modes of dynamically modulated rings. We show how quadrupole and octupole HOTIs supporting topologically protected corner modes emerge in a lattice of modulated photonic molecules and predict a dynamical topological phase transition in this system. Additionally, we propose a quantized hexadecapole (16-pole) insulator by leveraging synthetic dimensions to create a 4D hypercubic lattice that cannot be realized in real space.
We calculate optical forces on colloidal particles over a photonic crystal slab. We show numerically that exciting a
guided resonance mode of the slab yields a resonantly-enhanced, attractive optical force. Optical forces in the lateral
direction result in a two-dimensionally periodic pattern of stable trapping positions. Trapping patterns can be
reconfigured by changing the wavelength or polarization of incident light. We study the dependence of optical forces on
particle size, particle dielectric constant, and photonic-crystal slab parameters. Finally, we describe the fabrication and
measurement of a photonic crystal slab with a Q ~ 370.
Conference Committee Involvement (2)
Laser Resonators, Microresonators, and Beam Control XXVII
28 January 2025 | San Francisco, California, United States
Laser Resonators, Microresonators, and Beam Control XXVI
30 January 2024 | San Francisco, California, United States
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