# Structural Tunable Plasma Photonic Crystals in Dielectric Barrier Discharge
## 3 Results and Discussion  
We started with the symmetry modulation of the plasma photonic crystals from a triangular lattice to a square lattice when increasing the applied voltage, as shown in Figure 2. These plasma structures are produced in pure air at atmospheric pressure, which are cost-effective and provide stirring potential in real applications. As displayed in Figure 2a, when the voltage is low at \(U=5.3\) kV, some bright filaments are ignited and they self-organize into a triangular lattice with the lattice constant \(a=1.5\) mm. With an increase of the applied voltage, the triangular structure becomes unstable and it will transit to a well-defined square lattice with the lattice constant \(a=1.2\) mm, as shown in Figure 2d. The symmetrical deformation can also be clearly identified in the spatial Fourier spectra as shown in Figure 2b,e. The voltage-current waveforms associated with different plasma structures are demonstrated in Figure 2c-f. One can see that a group of current spikes are produced with the time interval about several microseconds in each half cycle of the applied voltage. Moreover, the discharge density and discharge interval are increased by increasing the applied voltage. It is worth pointing out here that the plasma lattices as shown in Figure 2a,d are complete and stable, which are actually the time-averaged structures over thousands of AC cycles. The time-resolved measurements of these plasma structures with sub-microsecond scale have been performed, which are not presented here. The results indicate instantly that the crystal lattice is not so perfect and some vacancies may occur, which is caused by the temporal shifts of the micro-discharges living several tens of nanoseconds while forming a lattice within the discharge interval about several microseconds long. The dynamical plasma structures composed of different spatiotemporal sublattices that are ignited at different time instants were also observed in our previous studies [35; 36; 37]. In the preliminary work presented here, we did not take account of these complicated spatio-temporal behaviors, and the changes of the band diagrams are examined when the time-averaged structures of the plasma photonic crystals have been changed. Similar plasma lattices were observed by [PERSON] et al., with similar discharge conditions to our experiments [38]. Band gaps between 17.5-20.0 GHz were detected and the anisotropic behavior of the plasma lattices was observed. It is proved that such plasma lattices could be used as a promising material to manipulate the propagation of microwaves. Figure 1: Schematic diagram of the experimental setup. Figure 3 presents the schematic views of the triangular lattice and the square lattice as well as their corresponding irreducible Brillouin zones. The plasma photonic crystal consists of circular plasma columns immersed in air with the dielectric constant \(\epsilon_{\text{a}}=1\). For the plasmas, its dielectric constant is frequency-dependent, which can be written as:  
\[\epsilon_{\text{P}}(\omega)=1-\frac{\omega_{\text{pe}}^{2}}{\omega\big{(}\omega- \text{j}\
u_{\text{m}}\big{)}} \tag{1}\]  
where \(\omega_{\text{pe}}\), \(\
u_{\text{m}}\), and \(\omega\) are the plasma frequency, the electron collision frequency, and the frequency of the incident EM waves, respectively. \(\omega_{\text{pe}}=\left(\text{e}^{2}n_{\text{e}}/\varepsilon_{\text{0}}m \right)^{1/2}\) where \(n_{\text{e}}\) is the electron density, which can be measured by the spectrum method as discussed in our previous papers [39; 40]. In general, the electron density \(n_{\text{e}}\) is increased by increasing of the applied voltage and the gas pressure. For the discharges operated in a mixture of Ar/air, \(n_{\text{e}}\) increases with the content of air. The electron collision frequency \(\
u_{\text{m}}=N\delta_{\text{C}}(\
u)\upsilon\), where \(\upsilon\) is the speed of the electrons, N is the density of neutral atoms per unit volume, and \(\sigma_{\text{C}}(\upsilon)\) is the collision cross section between the electrons and neutrals.