Topological photonics: Fundamental concepts, recent developments, and future directions

Topological photonics is emerging as a new paradigm for the development of both classical and quantum photonic architectures. What makes topological photonics remarkably intriguing is the built-in protection as well as intrinsic unidirectionality of light propagation, which originates from the robustness of global topological invariants. In this Perspective, we present an intuitive and concise pedagogical overview of fundamental concepts in topological photonics. Then we review the recent developments of the main activity areas of this field, categorized into linear, nonlinear, and quantum regimes. For each section, we discuss both current and potential future directions, as well as remaining challenges and elusive questions regarding the implementation of topological ideas in photonics systems.

Figure 1

Selection of emerging topological photonic systems categorized based on photon number and photon-photon-interaction strength, focused on the optical and infrared domain. Reproduced here taken from Refs. [21, 22, 25, 33, 38, 40, 43, 44, 53, 54].

Figure 2

Number of laps when starting from a point (marked by the red cross) and going around an (a) island is a positive or a negative integer, while it is zero for (b) a peninsula. Note that this integer number is invariant regarding the island's shape, swimming direction, or path taken.

Figure 3

(a) Periodic (honeycomb) photonic crystal with sublattices A and B. (b) Band structure of the photonic crystal, with an energy band gap separating the valence (blue) and conduction (yellow) bands. (c) Eigenvectors of the system in a unit sphere.

Figure 4

(a) Cyclotron motion of electrons with a radius of $R$ in a 2D electron gas under a perpendicular magnetic field which generates a quantum of flux due to each electron orbit. (b) Energy levels of the system, with $N_{\varphi }$-fold degeneracy. Note that the adjacent levels are separated by $\hslash {\omega }_c$. (c) Wave-function concentric orbits. (d) Accumulated phase for a particle looping on the sites of a lattice.

Figure 5

(a), (b) The spectrum of Eq. (11) on a $10\times 10$ lattice, for a closed and open boundary condition, respectively. The lower panel illustrates light intensity on the lattice corresponding to three typical states. Apart from the localized bulk states in the middle, in the open boundary case, edge states can form, while propagating in a clockwise (red) and counterclockwise (blue) fashion.

Figure 6

(a) Pair of coupled ring resonators described by Eq. (14). (b) Ring resonator coupled to a waveguide that can be described by the input-out formalism described in the text. (c) Two resonators coupled to each other using another resonator that is antiresonant with the side resonators. By positioning the middle resonator and creating a differential optical path one gets Eq. (17). (d) Clockwise (left) and counterclockwise (right) propagation under opposite magnetic fields, as illustrated by the blue arrows.

Figure 7

Illustration of formation of in-gap edge states at the interface between two topologically distinct mediums with inverted band structure. Adapted from Refs. [83, 84].

Figure 8

Implementation of topological photonic edge states in the linear regime. (a) Passive suspended valley-Hall photonic crystal waveguide. (Image reproduced from Ref. [26].) (b) Topological photonic mode taper [87]. (c) Valley-Hall topological ring resonator with access bus waveguide, forming an all-pass filter. (Image reproduced from Ref. [90].) (d) Topological add-drop filter, comprising a valley-Hall resonator and access waveguides. (Image reproduced from Ref. [157].)

Figure 9

(a)–(c) Schematic of the 2D array of coupled waveguides and variation of their coupling strengths, used to observe spatial topological bulk solitons. (e)–(h) Intensity profile in the array showing soliton behavior. (i) Schematic of the 1D array of coupled waveguides used for pumping of topological solitons and the variation of the coupling strength between the waveguides. (j) Topological pumping in the linear regime. (k) Topological pumping of solitons at higher pump powers, and (l) trapping of solitons at very high pump powers. Taken from Refs. [54, 103].

Figure 10

(a) Schematic of the 2D array of ring resonators used to generate temporal nested solitons. The resonator array simulates the anomalous quantum Hall model for photons. The pump laser is coupled to the array using the input-output waveguide. The nested comb output is collected using the same waveguide. (b) Phase-locked Turing rolls along the edge of the 2D array. (c) Phase-locked nested solitons propagating along the edge of the array. Note that there is a single soliton in each ring resonator that is a part of the nested soliton. (d) Comb spectrum in the regime of phase-locked Turing rolls showing oscillation of a single edge mode in each FSR. (e) Comb spectrum in the regime of nested solitons showing the oscillation of multiple edge modes in each FSR. Taken from Ref. [53].

Figure 11

(a) 2D ring resonator array used to realize a topological source of correlated photon pairs generated via SFWM. Because of the synthetic magnetic field, photons acquire a nonzero, direction-dependent phase $\varphi$ when they circulate around a closed path of four site rings (cyan) and four links (yellow) rings. The clockwise (CW) and the counterclockwise (CCW) edge states are highlighted in color. (b) Measured transmission spectrum showing edge and bulk bands. (c)–(f) Measured spectral correlations, that is, the number of photons generated as a function of the pump and signal frequencies. The dashed lines indicate the edge band region. The spectral correlations for 2D topological devices are very similar in the edge band region. (g)–(j) Measured spectral correlations for 1D devices. The correlations differ significantly across devices because of disorder. Taken from Ref. [38]. (k) Schematic of the SSH waveguide array used to generate correlated photon pairs. The waveguide array supports an edge state at the interface between two SSH domains. Spatial correlations between generated photons for (l)–(n) a topological array and a topologically trivial array (o)–(q), in the absence and presence of disorder. The zeros of the spatial correlation function for a topological source are robust against disorder in coupling strengths. Taken from Ref. [39].

Figure 12

(a), (b) SEM image, and the band structure of the shrunken and expanded honeycomb lattice used to realize a topological interface between quantum dots and helical edge states. (c) An applied magnetic field introduces a Zeeman splitting between the pseudospin (right and left-circular) polarized photons. (d)–(f) The pseudospin polarized edge states propagate along the interface in opposite directions, where they are collected using grating couplers. (g), (h) The measured second-order correlation function $g_2\left(\tau \right)$ shows the operation of quantum dots as single photon sources. Taken from Ref. [150].