Abstract
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 experiment 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. This Tutorial provides a pathway toward studying the dynamically modulated ring resonator system and understanding synthetic dimensions in photonics and discusses future prospects for both fundamental research and practical applications using synthetic dimensions.
Highlights
In physics, dimensionality, i.e., the number of independent directions in a system, is a key factor for characterizing a broad range of physical phenomena, affecting a variety of physical dynamics.1 Physical phenomena can have very different characteristics depending on the dimensions of the physical systems
Significant efforts have focused on developing the concept of synthetic dimensions, which uses degrees of freedom of the physical system other than spatial dimensions to augment the spatial dimensions in order to explore higher dimensional physics
The first experimental demonstration of quantum Hall physics in photonic synthetic space was reported in a 2D waveguide array, with the synthetic dimension formed by the transverse spatial supermodes of the array
Summary
Dimensionality, i.e., the number of independent directions in a system, is a key factor for characterizing a broad range of physical phenomena, affecting a variety of physical dynamics. Physical phenomena can have very different characteristics depending on the dimensions of the physical systems. Physical phenomena can have very different characteristics depending on the dimensions of the physical systems Both Anderson localization and recurrence properties of random walks have different characteristics in one or two dimensions as compared to three or more dimensions.. Significant efforts have focused on developing the concept of synthetic dimensions, which uses degrees of freedom of the physical system other than spatial dimensions to augment the spatial dimensions in order to explore higher dimensional physics.. We provide a tutorial on the creation of synthetic frequency dimensions in the dynamically modulated ring resonator system. We focus on this system since there have been significant developments in experimental implementation of synthetic dimensions using this system.. We hope that our work gives an illustrative picture of constructing synthetic dimensions with engineered connectivity along the frequency axis of light and can trigger more interesting ideas associated with synthetic dimensions in photonics
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