Roadmap on topological photonics

Abstract

Topological photonics seeks to control the behaviour of the light through the design of protected topological modes in photonic structures. While this approach originated from studying the behaviour of electrons in solid-state materials, it has since blossomed into a field that is at the very forefront of the search for new topological types of matter. This can have real implications for future technologies by harnessing the robustness of topological photonics for applications in photonics devices. This Roadmap surveys some of the main emerging areas of research within topological photonics, with a special attention to questions in fundamental science, which photonics is in an ideal position to address. Each section provides an overview of the current and future challenges within a part of the field, highlighting the most exciting opportunities for future research and developments.

HarmonicBalance.jl: A Julia suite for nonlinear dynamics using harmonic balance

“…Its modular design paves the way for future methodological extensions, including detection of Hopf bifurcations [107], limit cycles and chaos [108], higher-order Krylov-Bogoliubov averaging method [109], as well as interfaces with existing dedicated libraries to treat nonlinear spatially-extended or quantum systems [110,111]. Its usage can assist a breadth of fields, where nonlinear harmonically-driven systems appear, such as modal analysis in structural dynamics [10,33], electric circuits [11,34,35], nonlinear optics [12,[36][37][38][39][40][41][42], optomechanics [22,[43][44][45], micro-and nanomechanics [18,46,[51][52][53][54][55][56][57], oscillator networks [58][59][60][61][62][63], Ising machines [64][65][66][67][68][69], and many-body light-matter systems [70]…”

“…1c]. Our package is readily applicable to a range of active fields where nonlinear harmonically-driven systems appear, such as modal analysis in structural dynamics [10,33], electric circuits [11,34,35], nonlinear optics [12,[36][37][38][39][40][41][42], optomechanics [22,[43][44][45], micro-and nanomechanics [18,[46][47][48][49][50][51][52][53][54][55][56][57], oscillator networks [58][59][60][61][62][63],…”

Nonlinear Topological Photonic Insulator in Synthetic Space

“…where 𝜒 (3) is the third order electrical polarizability and Δk is the wave vector mismatch, which satisfies…”

“…[1,2] Recently, the field of topological phenomena in optics is moving toward broader directions. [3] For example, there are extensive studies focusing on topological properties with different dimensionalities of photonic structures, [4][5][6][7][8][9] with profound explorations into synthetic dimensions that utilize various degrees of freedom of DOI: 10.1002/andp.202200288 light including frequency, [10,11] pulse arrival time, [12,13] orbital angular momentum, [14,15] and others. [16,17] On the other hand, new ingredients such as nonlinearity and non-Hermiticity have been added into topological photonics, which shows increasing importance in optical signal transmissions in media with the nonlinear process, [18][19][20][21][22][23][24][25] and with gain or loss.…”

Fundamental constraints on the observability of non-Hermitian effects in passive systems

“…The design of such systems has received further impetus by the realization that in non-Hermitian systems, modes with predetermined frequencies, life times, and mode profiles can be protected by generalised symmetries [38][39][40][41]. This leads to rich scenarios that transcend Hermitian topological physics [42][43][44], both practically [45] as well as in their mathematical complexity [46][47][48]. However, many of these symmetries can only be realized in active systems, which require a sustained supply of energy and introduce noise.…”