Synthetic dimensions in photonic structures provide unique opportunities for actively manipulating light in multiple degrees of freedom. Here, we theoretically explore a dispersive waveguide under the dynamic phase modulation that supports single pul
se manipulations in the synthetic (2+1) dimensions. Compared with the counterpart of the conventional (2+1) space-time, we explore temporal diffraction and frequency conversion in a synthetic time-frequency space while the pulse evolves along the spatial dimension. By introducing the effective gauge potential well for photons in the synthetic time-frequency space with the control of the modulation phase, we show that a rich set of pulse propagation behaviors can be achieved, including confined pulse propagation, fast/slow light, and pulse compression. With the additional nonlinear oscillation subject to the effective force along the frequency axis of light, we provide an exotic approach for actively manipulating the single pulse in both temporal and spectral domains, which shows the great promise for applications of the pulse processing and optical communications in integrated photonics.
The concept of synthetic dimensions in photonics has attracted rapidly growing interest in the past few years. Among a variety of photonic systems, the ring resonator system under dynamic modulation has been investigated in depth both in theory and e
xperiment, and has proven to be a powerful way to build synthetic frequency dimensions. In this tutorial, we start with a pedagogical introduction to the theoretical approaches in describing the dynamically modulated ring resonator system, and then review experimental methods in building such a system. Moreover, we discuss important physical phenomena in synthetic dimensions, including nontrivial topological physics. Our tutorial provides a pathway towards studying the dynamically modulated ring resonator system, understanding synthetic dimensions in photonics, and discusses future prospects for both fundamental research and practical applications using synthetic dimensions.
Topological photonics has emerged as a novel paradigm for the design of electromagnetic systems from microwaves to nanophotonics. Studies to date have largely focused on the demonstration of fundamental concepts, such as non-reciprocity and waveguidi
ng protected against fabrication disorder. Moving forward, there is a pressing need to identify applications where topological designs can lead to useful improvements in device performance. Here we review applications of topological photonics to ring resonator-based systems, including one- and two-dimensional resonator arrays, and dynamically-modulated resonators. We evaluate potential applications such as quantum light generation, disorder-robust delay lines, and optical isolation, as well as future research directions and open problems that need to be addressed.
The concept of synthetic dimensions, which has enabled the study of higher-dimensional physics on lower-dimensional physical structures, has generated significant recent interest in many branches of science ranging from ultracold-atomic physics to ph
otonics, since such a concept provides a versatile platform for realizing effective gauge potentials and novel topological physics. Previous experiments demonstrating this concept have augmented the real-space dimensionality by one additional physical synthetic dimension. Here we endow a single ring resonator with two independent physical synthetic dimensions. Our system consists of a temporally modulated ring resonator with spatial coupling between the clockwise and counterclockwise modes, creating a synthetic Hall ladder along the frequency and pseudospin degrees of freedom for photons propagating in the ring. We experimentally observe a wide variety of rich physics, including effective spin-orbit coupling, magnetic fields, spin-momentum locking, a Meissner-to-vortex phase transition, and chiral currents, completely in synthetic dimensions. Our experiments demonstrate that higher-dimensional physics can be studied in simple systems by leveraging the concept of multiple simultaneous synthetic dimensions.
We show that a single ring resonator undergoing dynamic modulation can be used to create a synthetic space with an arbitrary dimension. In such a system the phases of the modulation can be used to create a photonic gauge potential in high dimensions.
As an illustration of the implication of this concept, we show that the Haldane model, which exhibits non-trivial topology in two dimensions, can be implemented in the synthetic space using three rings. Our results point to a route towards exploring higher-dimensional topological physics in low-dimensional physical structures. The dynamics of photons in such synthetic spaces also provides a mechanism to control the spectrum of light.
We study a one-dimensional photonic resonator lattice with Kerr nonlinearity under the dynamic modulation. With an appropriate choice of the modulation frequency and phase, we find that this system can be used to create anyons from photons. By coupli
ng the resonators with external waveguides, the anyon characteristics can be explored by measuring the transport property of the photons in the external waveguides.
