Special topic on synthetic gauge field photonics

Gauge fields are a fundamental concept in physics that describes the basic interactions between charged particles. Naturally, all neutral particles are decoupled from real gauge fields. Nevertheless, if we properly design a physical system, we can generate synthetic gauge fields that would govern the effective dynamics of the chargeless particles, such as photons. In this way, synthetic gauge fields enable uncharged particles to behave as if affected by external fields. For example, a photon propagating in an elaborately designed photonic lattice will flow in a similar fashion as an electron in a magnetic flux due to the synthetic gauge fields generated by such a lattice. Consequently, synthetic gauge fields allow us to endow photonic systems with a wide range of exciting features that are naturally not expected for them.

Synthetic gauge fields are generally induced through the geometric design of the system, which usually involves some specific external spatial or temporal modulation. In this way, the effective dynamics of the system will behave as if it were governed by a “real” gauge field. Synthetic gauge fields are currently realized in a wide range of physical systems, ranging from ultracold atomic gases^1,2 and photonics^3,4 to mechanical,⁵ acoustic,⁶ and electrical circuits.⁷ In photonics, synthetic gauge fields have been used to generate dynamics that would otherwise be inconceivable for light. The best example is topological photonics, in which synthetic gauge fields are the fundamental building block that enables the realization of photonic topological insulators^3,4 and topological insulator lasers.⁸ A plethora of novel optical devices based on the synthetic gauge field have been proposed, such as negative refraction and one-way mirrors,⁹ and higher order frequency converters.¹⁰ Novel waveguiding mechanisms¹¹ based on synthetic gauge fields have been demonstrated, as well as non-reciprocal devices in silicon photonics,¹² among many other new devices and photonic phenomena only possible by using the synthetic gauge field.

This Special Topic Collection is dedicated to highlighting recent progress in the field of synthetic gauge field photonics. It contains 13 articles that capture the current experimental and theoretical advances in the application of synthetic gauge fields in photonics. It covers a vast range of photonic systems, from linear and nonlinear systems to non-Hermitian and lasing systems.

One of the most interesting applications of synthetic gauge fields is that they can be used to break reciprocity. Kim et al.¹³ demonstrate optical non-reciprocity in an acousto-optically modulated nanophotonic resonator chain. To produce this effect in the microwave regime, they simultaneously generate a synthetic electric field using temporal modulations and a synthetic magnetic field using spatial modulation of a resonator chain. Even without breaking reciprocity, synthetic gauge fields can help us to control the directionality of light. Höckendorf et al.¹⁴ proposed a one-dimensional modulated zigzag photonic waveguide lattice that possesses two transport channels with opposite directionality. Interestingly, the direction of transport can be controlled by controlling the relative phase and angle of incidence between two input beams. These new concepts based on synthetic gauge fields could help in designing new optical steering devices. When the counterpropagating modes of a microring/microdisk wave resonator coalesce into one single traveling mode, a chiral exceptional point emerges. Hashemi et al.¹⁵ present an alternative and complementary approach for describing chiral exceptional points based on a coupled oscillator model and adiabatic elimination. The advantage of this formalism is that it does not use the full-wave scattering analysis that make it useful to apply this concept to discrete photonic arrangements such as coupled resonator and waveguide arrays.

As it is well known, one of the main achievements of synthetic gauge fields in photonics is that these are the fundamental elements to create topological photonic systems. In this regard, the classification of topological systems presents a new challenge. Leykam and Angelakis¹⁶ propose a new way to characterize and optimize band structures of periodic topological photonic media. This new technique opens the door to discovering novel classes of photonic band structures. The search for new classes and implementations of topological photonics structures is very important. Nowadays, even the simplest topological systems, such as the Su-Schrieffer-Heeger (SSH) model, keep finding very interesting applications. For example, Yuan et al.¹⁷ propose an efficient and robust way to transfer photons in a one-dimensional photonic lattice by manipulating the topological defect state of the SSH model.

Synthetic gauge fields can also induce nontrivial dynamics in the bulk of the system. For example, D’Errico et al.¹⁸ demonstrate unusual characteristics of a photonic quantum walk in the presence of a synthetic gauge field. By propagating light through a set of liquid crystal birefringent waveplates, they demonstrate that the action of the synthetic gauge field on the propagating light mimics the action of an electric field on a charge particle.

Apart from linear systems, light–matter interactions in nonlinear synthetic photonic structures exhibit a range of novel features, which can lead to new regimes of optical lasing. Chang et al.¹⁹ analyze the dynamics of waves in a nonlinear diamond chain waveguide lattice. They find, in contrast to perfect Aharonov-Bohm caging in a linear regime supported by a synthetic magnetic flux when all modes are localized and stationary, that nonlinearity can enable the formation of breathing solutions and wave trains with long-range correlations. Zhong et al.²⁰ investigate optical lasing in the Kagome waveguide array with a rhombic configuration, which realizes a second-order photonic topological insulator and supports a zero-dimensional corner state. It is found that nonlinear two-photon absorption can stabilize the lasing states, while their spatial extent can be controlled by specially deforming the structure through the shifts of each second waveguide. Seclì et al.²¹ predict that frequency-dependent gain in topological systems can provide a flexible selection of lasing modes and, in particular, stabilize single-mode lasing into an edge state. Detailed analysis is performed for the Harper–Hofstadter lattice structure with gain provided by embedded two-level atoms, which suggests new directions for future experiments. Liu et al.²² present a general concept for realizing non-Hermitian topological lattices that can facilitate phase locking in laser arrays. It is shown that such structures can be constructed from photonic molecules composed of pairs of microring resonators featuring specially tailored asymmetric coupling.

Synthetic gauge fields can be generated through various mechanisms, ranging from networks of electric circuits that emulate gauge fields to strain in van der Waals 2D materials. The resulting topological bulk and boundary effects are then useful for photonic applications. Ni and Alù²³ explore how topoelectric systems can be coupled to show the spectral properties of a 3D high-order semimetal, namely, the emergence of nodal line rings and Weyl points in the bulk dispersion, whose projected surfaces and hinges support surface Fermi arcs and flat hinge Fermi arcs. Ornigotti et al.²⁴ explore how a strained 2D graphene flake shows signs of broken centrosymmetry through the generation of even harmonics. Furthermore, the emergent square-root-like Landau level spectrum arising from the pseudomagnetic field gives telltale signatures in the interaction of the material with the electromagnetic pulses through the appearance of half-integer harmonics in the nonlinear signal. Balanov et al.²⁵ explore how free-electron interactions with van der Waals materials and specifically with edge modes can lead to the generation of parametric x-ray radiation. Harnessing the tunability of these 2D materials is shown as a promising path for x-ray pulses with controllable radiation polarizations as well as spatial and temporal distributions.

In conclusion, the field of synthetic gauge fields continues to advance at a rapid pace, especially in photonics due to the plethora of new effects that synthetic gauge fields enable for light. We anticipate that the new concepts and experiments reported in this Special Topic Collection will further extend the potential of synthetic gauge fields in photonics and facilitate a range of practical photonic “toda su ayuda en la preparación” applications. We are grateful to Associate Editor Alexander Szameit for inviting us to prepare this Special Topic Collection and for all his assistance in its preparation.