Results and Discussions An effective method to realize various LPPCs in DBD with the advantages of simple devices and dynamical tunability is proposed in this paper (Fig. 1). In addition, novel double-circle Lieb lattice, double-diamond Lieb lattice, diamond-circle Lieb lattice, and diamond-rectangle Lieb lattice have been achieved. Reconfiguration of different LPPCs has been realized by varying the discharge parameters including the applied voltage, gas pressure, and gas compositions. In-situ control of the shape, size, and fine structures of primitive elements in LPPCs is achieved, while the symmetry and lattice constant are well preserved (Fig. 2). The spatial-temporal dynamics of the LPPCs are studied by using photomultipliers. It is shown that the LPPCs are composed of two different square sublattices nested with each other, with the emerging sequence of the filament at corner sites-edge center sites-corner sites-edge center sites (Fig. 3). The LPPCs exhibit high spatial-temporal stability and periodicity, which is attributed to the spatial periodic electric field distribution produced by the square array electrode. With the changes of lattice constant and gas gap spacing, LPPCs with different configurations can be generated in different regions as presented in the phase diagram in Fig. 4. Moreover, the photonic band gaps change significantly with the reconfiguration of LPPCs with disparate scattering elements (Fig. 5). The different geometric configurations give rise to different numbers, positions, and sizes of omnidirectional band gaps and unidirectional band gaps. More importantly, accidental degenerate Dirac cones have been obtained in the double-circle Lieb lattice, diamond-circle Lieb lattice, and diamond-rectangle Lieb lattice. Such remarkable features may lead to the promising development of functional and dynamic devices for electromagnetic waves.

Lieb lattice has been demonstrated to have many striking properties due to its unique Dirac-flat band structure. It has been realized in various systems, such as photonic waveguide arrays, cold atom systems, condensed matter physics, and organic materials. Since the Dirac-flat band structure relies heavily on the structural configurations of the Lieb lattice, it is essential to fabricate tunable Lieb lattices, so as to allow for on-demand control of band structures. Recently, there is a growing interest in plasma photonic crystals (PPCs) comprised of periodic arrays of plasmas and dielectrics. By modulating the plasma density, lattice constant, or lattice symmetry, the PPCs can be tuned dynamically. Various one-dimensional PPCs, two-dimensional PPCs with square or triangular geometries, and three-dimensional woodpile-type PPCs have been realized in previous studies, which possess band gaps to manipulate microwaves. However, the PPCs with a Lieb lattice structure have been less concerned so far. Particularly, it is still a challenge to realize PPCs with tunable scattering elements, whose size, shape, and microstructure can be controlled dynamically. In this study, the Lieb plasma photonic crystals (LPPCs) and the in-situ manipulation of plasma scattering elements in dielectric barrier discharge (DBD) are realized. It provides an effective platform to investigate the universal properties of Lieb lattices and may offer inspiration for designing tunable Lieb lattices in other systems.

The LPPCs have been studied both experimentally and numerically. In the experiment, a uniquely designed DBD system with array-liquid electrodes is proposed. The array electrode induces a two-dimensional periodic electric field to give a constrained symmetry and lattice constant for the Lieb lattice. The water not only serves as the coolant medium to ensure high stability of the plasma structure but also is a transparent medium beneficial for optical detection. By changing the discharge parameters such as the applied voltage, gas pressure, gas composition, and so on, various LPPCs can be obtained, and rapid configuration between Lieb lattices with different primitive elements has been realized. In addition, the spatial-temporal dynamics of the LPPCs are studied by using the photomultipliers. The light emitted from the individual discharge filament is detected by a lens-aperture-photomultiplier tube system and recorded with an oscilloscope. In the simulation, to demonstrate the formation mechanism of LPPCs, the two-dimensional distribution of Laplacian field intensity induced by the square array electrode is calculated by COMSOL software. Moreover, the dispersion relations of different LPPCs are studied by using COMSOL software based on the finite element method. Floquet periodic boundary conditions are utilized for the primitive cell in the Lieb lattice. The normalized eigenfrequencies ωa/2πc for each wave vector k along the irreducible Brillouin zone boundary X?M?Γ?X are calculated. By examining the photonic band structures, the complete bandgaps, incomplete bandgaps, and Dirac cones at different positions are discussed. The results provide theoretical support for the application of LPPCs in the field of electromagnetic wave manipulation.

LPPCs in DBD with uniquely designed array-liquid electrodes are realized, and an in-situ control on the size, shape, and fine structures of plasma scattering elements has been achieved. The spatial-temporal dynamics of LPPCs are studied by using photomultipliers. Through the finite element method, changes in photonic band diagrams with the reconfiguration of different plasma elements have been analyzed in detail. The results show that LPPCs result from the superposition of two different sets of square sublattices that are nested with each other. They exhibit high spatial-temporal stability and periodicity. With changes of the plasma element configurations, the photonic band diagrams change significantly, which leads to accidental degenerate Dirac cone band structures, omnidirectional band gaps, and unidirectional band gaps at different positions. The number, positions, and sizes of the band gaps are greatly affected by the geometry of plasma elements. The realization of in-situ manipulation of plasma elements is beneficial for wide applications of LPPCs and provides inspiration for designing new types of photonic devices.