Structural Tunable Plasma Photonic Crystals in Dielectric Barrier Discharge

: We demonstrate a kind of structural tunable plasma photonic crystal in a dielectric barrier discharge by self-organization of the plasma ﬁlaments. The symmetry, the lattice constant and the orientations of di ﬀ erent plasma photonic crystals can be deliberately controlled by changing the applied voltage. The plasma structures can be tuned from a square lattice to a triangular lattice, the lattice constant is reduced and the crystal orientation varies π 6 when the applied voltage is increased. The band diagrams of the plasma photonic crystals under a transverse-magnetic wave have been studied, which shows that the positions and sizes of the band gaps change signiﬁcantly for di ﬀ erent plasma structures. We suggest a ﬂexible way for the fabrication of tunable plasma photonic crystals, which may ﬁnd wide application in the manipulation of microwaves or terahertz waves.


Introduction
Photonic crystals can be used to selectively reflect specific frequencies of electromagnetic radiation. It is a significant tool to control the propagation of electromagnetic (EM) waves, which has been widely used in Bragg mirrors, optical waveguide, optical switch, solar cells, sensors and light-emitting diodes (LEDs) [1][2][3][4][5][6][7][8][9][10]. In recent years, there appears to have been great interest in fabricating tunable photonic crystals for real-time and on-demand control of the photonic band structures [11,12]. One of the most interesting applications of tunable photonic crystals is in designing novel sensing devices, such as highly sensitive temperature and refractive index sensors [9,10]. So far, different methods of producing reconfiguring photonic crystals have been demonstrated, including mechanical, thermal, biological, and opto-fluidic methods [13][14][15][16]. As a new kind of tunable photonic crystal, the plasma photonic crystal (PPC) has attracted considerable attention recently. It is a periodic structure with the plasma and dielectric material or the spatially periodic arrangement of the plasma density [17,18]. The PPCs not only have characteristic band gaps as in the conventional photonic crystals, but also possess a number of unique features such as the strong dispersion around the electron plasma frequency and the dynamic time-varying controllability [19,20]. Depending on the incident EM wave frequency and electron density, the relative permittivity of the plasmas can be tuned from strongly negative to positive values of less than unity (passing through zero) [21,22]. Moreover, it affords the possibility of rapidly controlling the band gap at rates determined only by the time to form or recombine the plasma [22]. These superior properties lead to development of dynamic and functional devices for EM waves ranging from microwaves to terahertz (THz) waves, which can find wide applications in microwave filter, optical switch, wireless communications, millimeter-wave spectroscopy, plasmas stealth aircraft and so on [23][24][25][26].

Experimental Setup
The schematic diagram of the experimental setup is illustrated in Figure 1. Two cylindrical containers with diameter of 7.5 cm filled with tap water were used as the electrodes. The water also served as a coolant and transparent media for observation and measurement of discharge filaments. The water electrodes were sealed with the glass plates with a thickness of 1.5 mm. A metallic ring was immersed in each container and connected to a power supply. A sinusoidal alternating current (AC) voltage at the frequency 10-100 kHz was applied to the left electrode and the right electrode was grounded. A square glass spacing was clamped between two parallel electrodes, serving as a lateral boundary, which determines the distance of the gas gap. The whole apparatus was enclosed in a big container filled with the static gas of different components and different pressures. The voltage waveform and current waveform were detected using a high-voltage probe (Tektronix P6015A 1000×) and a current probe (Tektronix TCP0030A), respectively, which were recorded using a digital phosphor oscilloscope (Tektronix TDS3054B). A camera (EOS 6D) was placed at one end of the electrode to record the images of PPCs. Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 10

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 Matlis 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.

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 Matlis 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. Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 10  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 εa = 1. For the plasmas, its dielectric constant is frequency-dependent, which can be written as: where ω , ν , and ω are the plasma frequency, the electron collision frequency, and the frequency of the incident EM waves, respectively. ω = (e n /ε m) / where n 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 ne is increased by increasing of the applied voltage and the gas pressure. For the discharges operated in a mixture of Ar/air, ne increases with the content of air. The electron collision frequency ν = Nδ (υ)υ, where υ is the speed of the electrons, N is the density of neutral atoms per unit volume, and σ (υ) is the collision cross section between the electrons and neutrals. The real part of the relative dielectric constant ε given in Equation (2) is used to calculate the dispersion relations of the plasma photonic crystals, while the imaginary part is responsible for dissipation and absorption of the EM waves, which is not taken into account here.
Re ε = 1 − ω ω + ν (2) Simulations of the plasma photonic crystals with different configurations were completed by use of COMSOL Multiphysics software based on the finite element method. The Lorentz-Drude model was employed. The mesh division is selected as a free triangle mesh, and the largest mesh  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 ε a = 1. For the plasmas, its dielectric constant is frequency-dependent, which can be written as: where ω pe , ν m , and ω are the plasma frequency, the electron collision frequency, and the frequency of the incident EM waves, respectively. ω pe = e 2 n e /ε 0 m where n 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 e is increased by increasing of the applied voltage and the gas pressure. For the discharges operated in a mixture of Ar/air, n e increases with the content of air. The electron collision frequency ν m = Nδ C (υ)υ, where υ is the speed of the electrons, N is the density of neutral atoms per unit volume, and σ C (υ) is the collision cross section between the electrons and neutrals. The real part of the relative dielectric constant ε p given in Equation (2) is used to calculate the dispersion relations of the plasma photonic crystals, while the imaginary part is responsible for dissipation and absorption of the EM waves, which is not taken into account here.
Appl. Sci. 2020, 10, 5572 5 of 10 rhombus in Figure 3a,c indicate the basic units of different plasma photonic crystals. Floquet periodic boundary conditions are applied at two sets of opposite edges of the square and rhombus. According to Bloch's theorem, the eigenvalue frequencies corresponding to different wave vectors k along the irreducible Brillouin zone boundaries M-Γ-X-M and M-Γ-K-M are calculated, respectively. By scanning the coefficient k through the parameterized sweep built in COMSOL, the dispersion relations of EM waves for different plasma structures can be obtained.   [36,[38][39][40]. Obviously, one can see that an increase of the electron density leads to formation of more band gaps for both of the square and triangular plasma photonic crystals. Moreover, the positions of the band gaps move to the higher frequency and the sizes of the band gaps are increased remarkably. Here we take the band diagram at the electron density n = 10 cm for example, which order of magnitude most commonly occurs in the discharges [39,40]. We can see that three unidirectional band gaps form for the triangular lattice as shown in Figure 4c. They locate at the position of 0.58-0.76ωa/2πc in M − Γ direction, and at 0.74-0.99ωa/2πc and 1.08-1.26ωa/2πc in K-M direction, respectively. When the plasma photonic crystal is tuned to the square lattice by increasing the applied voltage as shown in Figure 4g, a remarkably different band structure forms. An absolute band gap is produced at the position of 0.72-0.77ωa/2πc, and the EM waves within this frequency range cannot pass through the plasma crystals. Consequently, with the symmetrical deformation from the triangular lattice to square lattice, the band structures change significantly, which can be utilized to modulate the propagation of EM waves of different frequencies. Simulations of the plasma photonic crystals with different configurations were completed by use of COMSOL Multiphysics software based on the finite element method. The Lorentz-Drude model was employed. The mesh division is selected as a free triangle mesh, and the largest mesh element is set as 8.33 × 10 −5 m, the curvature factor is 0.25. The areas enclosed by the black and rhombus in Figure 3a,c indicate the basic units of different plasma photonic crystals. Floquet periodic boundary conditions are applied at two sets of opposite edges of the square and rhombus. According to Bloch's theorem, the eigenvalue frequencies corresponding to different wave vectors k along the irreducible Brillouin zone boundaries M-Γ-X-M and M-Γ-K-M are calculated, respectively. By scanning the coefficient k through the parameterized sweep built in COMSOL, the dispersion relations of EM waves for different plasma structures can be obtained. Figure 4 illustrates the band diagrams of the triangular and the square plasma photonic crystals corresponding to the plasma structures shown in Figure 2. Due to the facts that there may have fluctuations of electron densities in the ensemble of filaments forming the crystal lattice, the band diagrams under different electron densities are studied. For similar conditions to the present experiments, 10 13 ≤ n e ≤ 10 16 cm −3 [36,[38][39][40]. Obviously, one can see that an increase of the electron density leads to formation of more band gaps for both of the square and triangular plasma photonic crystals. Moreover, the positions of the band gaps move to the higher frequency and the sizes of the band gaps are increased remarkably. Here we take the band diagram at the electron density n e = 10 15 cm −3 for example, which order of magnitude most commonly occurs in the discharges [39,40]. We can see that three unidirectional band gaps form for the triangular lattice as shown in Figure 4c. They locate at the position of 0.58-0.76ωa/2πc in M-Γ direction, and at 0.74-0.99ωa/2πc and 1.08-1.26ωa/2πc in K-M direction, respectively. When the plasma photonic crystal is tuned to the square lattice by increasing the applied voltage as shown in Figure 4g, a remarkably different band structure forms. An absolute band gap is produced at the position of 0.72-0.77ωa/2πc, and the EM waves within this frequency range cannot pass through the plasma crystals. Consequently, with the symmetrical deformation from the triangular lattice to square lattice, the band structures change significantly, which can be utilized to modulate the propagation of EM waves of different frequencies.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 10 By changing the applied voltage, the lattice constant of the plasma structures can be dynamically controlled. As shown in Figure 5, the triangular lattices with different lattice constants are obtained in our experiment. More filaments are ignited and the lattice constants decrease by increasing the applied voltage. All these plasma structures are very stable, which can last for tens of minutes unless the discharge parameters are changed. To quantitatively characterize the spatial order of the plasma structures, the pair correlation functions (PCF) are calculated from the discharge density distributions. The PCFs have been used to characterize complex plasma crystals to show the probability density (ρ ) to find a filament at distance r from a given filament [41]. One can clearly see that the pair correlation function displays a series of isolated peaks, in which the first peak is the strongest, giving the value of the lattice constant. The lattice constant a = 2.68 mm, 2.59 mm, 2.48 mm, respectively, which decreases with an increase of the applied voltage. The positions of ρ peaks for the ideal triangular lattices are given by the red short lines at the bottom of Figure 5d-f. Obviously, they matched well with the ρ peaks of the plasma structures obtained in our experiment, By changing the applied voltage, the lattice constant of the plasma structures can be dynamically controlled. As shown in Figure 5, the triangular lattices with different lattice constants are obtained in our experiment. More filaments are ignited and the lattice constants decrease by increasing the applied voltage. All these plasma structures are very stable, which can last for tens of minutes unless the discharge parameters are changed. To quantitatively characterize the spatial order of the plasma structures, the pair correlation functions (PCF) are calculated from the discharge density distributions. The PCFs have been used to characterize complex plasma crystals to show the probability density (ρ r ) to find a filament at distance r from a given filament [41]. One can clearly see that the pair correlation function displays a series of isolated peaks, in which the first peak is the strongest, giving the value of the lattice constant. The lattice constant a = 2.68 mm, 2.59 mm, 2.48 mm, respectively, which decreases with an increase of the applied voltage. The positions of ρ r peaks for the ideal triangular lattices are given by the red short lines at the bottom of Figure 5d-f. Obviously, they matched well with the ρ r peaks of the plasma structures obtained in our experiment, indicating that these plasma lattices are very regular and close to the ideal triangular lattices. The voltage-current waveforms for different plasma photonic crystals are illustrated in Figure 5g-i. One can see that more current spikes appear with an increase of the applied voltage, owing to the formation of more discharge filaments. As expected, the band diagrams change correspondingly when the lattice constant is reduced with increasing of the applied voltage. One can find in Figure 5j that a complete band gap is produced when a = 2.68 mm, which locates at the position of 1.18-1.22ωa/2πc. Besides, two unidirectional band gaps form in the M-Γ direction at the positions of 0.74-0.90ωa/2πc and 1.47-1.63ωa/2πc, respectively, and two unidirectional band gaps are produced in the K-M direction at the positions of 1.23-1.47ωa/2πc and 1.68-1.76ωa/2πc. When the lattice constant is reduced from 2.68 mm to 2.48 mm, as shown in Figure 5l, the width of the complete band gap becomes larger and its position is changed to 1.19-1.27ωa/2πc. In addition, the positions of the other four unidirectional band gaps are also changed, which locate at 0.78-0.94ωa/2πc and 1.51-1.71ωa/2πc in the M-Γ direction and at 1.28-1.52ωa/2πc and 1.71-1.82ωa/2πc, in the K-M direction, respectively. Obviously, the photonic bands move towards higher frequencies with a decrease of the lattice constant and the size of each band gap is increased. Thus, by changing the lattice constant, the plasma photonic crystals can be used to selectively control the propagation of EM waves of different frequencies.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 10 indicating that these plasma lattices are very regular and close to the ideal triangular lattices. The voltage-current waveforms for different plasma photonic crystals are illustrated in Figure 5g-i. One can see that more current spikes appear with an increase of the applied voltage, owing to the formation of more discharge filaments. As expected, the band diagrams change correspondingly when the lattice constant is reduced with increasing of the applied voltage. One can find in Figure 5j that a complete band gap is produced when a = 2.68 mm, which locates at the position of 1.  Next, we examined the angular reorientation of the plasma photonic crystals. As shown in Figure 6a,b, the plasma crystals rotate 6 when slightly increasing the applied voltage, while the other structural parameters are nearly invariant. Figure 6c,d present the voltage-current waveforms corresponding to different plasma structures. One can see that a group of discharge spikes are produced, which occur at both of the falling and rising edge of the applied voltage (passing through the zero-crossing point of the ac voltage waveform). The time intervals of the discharges are about Next, we examined the angular reorientation of the plasma photonic crystals. As shown in Figure 6a,b, the plasma crystals rotate π 6 when slightly increasing the applied voltage, while the other structural parameters are nearly invariant. Figure 6c,d present the voltage-current waveforms corresponding to different plasma structures. One can see that a group of discharge spikes are produced, which occur at both of the falling and rising edge of the applied voltage (passing through the zero-crossing point of the ac voltage waveform). The time intervals of the discharges are about 6.0 us. The discharges occurring at the falling edge of the applied voltage are mainly dominated by the fields of surface charges, while the discharges occurring at the rising edge are initiated by the applied voltage [37]. The voltage-current waveforms change little when the orientation of the plasma has been changed. To some extent, the changes of the crystal orientation are equivalent to varying the incident angle of the EM waves, which may have significant influence on the photonic band diagrams. It was proven in previous studies that a blue shift of the photonic bands as well as a narrowed band gap is achieved when increasing the incident angle of the EM waves [42]. Thus, through modulating the orientation of the plasma structures, we suggest an alternative way to control the reflection and transmission behavior of the EM waves.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 10 6.0 us. The discharges occurring at the falling edge of the applied voltage are mainly dominated by the fields of surface charges, while the discharges occurring at the rising edge are initiated by the applied voltage [37]. The voltage-current waveforms change little when the orientation of the plasma has been changed. To some extent, the changes of the crystal orientation are equivalent to varying the incident angle of the EM waves, which may have significant influence on the photonic band diagrams. It was proven in previous studies that a blue shift of the photonic bands as well as a narrowed band gap is achieved when increasing the incident angle of the EM waves [42]. Thus, through modulating the orientation of the plasma structures, we suggest an alternative way to control the reflection and transmission behavior of the EM waves.

Conclusions
In summary, we demonstrate a rich variety of structural tunable plasma photonic crystals by self-organization of the filaments in DBD. By changing the applied voltage, the plasma structures can be tuned flexibly in three ways, including changing the spatial symmetry, the lattice constant and the crystal orientation. The plasma structures changes from square lattice to triangular lattice, the lattice constant is reduced, and the crystal orientation varies π 6 when the applied voltage is increased. The band diagrams of the plasma photonic crystals under a TM wave are studied by using the finite element method, which shows that the positions and sizes of the band gaps change significantly for different plasma structures. A complete band gap is produced for the square plasma lattice, while a number of unidirectional band gaps are generated when the square lattice is

Conclusions
In summary, we demonstrate a rich variety of structural tunable plasma photonic crystals by self-organization of the filaments in DBD. By changing the applied voltage, the plasma structures can be tuned flexibly in three ways, including changing the spatial symmetry, the lattice constant and the crystal orientation. The plasma structures changes from square lattice to triangular lattice, the lattice constant is reduced, and the crystal orientation varies π 6 when the applied voltage is increased. The band diagrams of the plasma photonic crystals under a TM wave are studied by using the finite element method, which shows that the positions and sizes of the band gaps change significantly for different