**5. Plasma in photonic crystal**

In this section experimental study on plasma added photonic crystal (hybrid plasm photonic crystal) is presented. We have seen that negative refraction at microwave frequencies was also observed in both dielectric and metallic PCs. Although, research indicates that the MPC is suitable for negative refraction (Kumar 2011a), however, to date tunability in the fabricated MPC to control the wave propagation has not been achieved. From this aspect, plasma can be a good candidate to replace metal or dielectrics from PCs because plasma is a frequency dependent dispersive medium and its refractive index can be determined by electromagnetic wave frequency and plasma frequency (Ginzberg, 1970; Hojo et.al 2003; Hojo and Mase, 2004) has proposed that plasma photonic crystals (PPCs) are artificially made periodic arrays composed of alternating discharge plasma and other dielectric materials (including vacuum). On the bases of different approaches, two types of PPC are being studied. In the first type of PPC, cylindrical glass rods or dielectrics forming a crystal lattice are immersed in discharge background plasma (Laxmi and Parmanand, 2005; Liu, et al, 2006; Hojo et al, 2006; LIU et al, 2009) while the second type consists of cylindrical rods of discharge plasma that constitutes a crystal lattice in vacuum or air (Sakai, et al, 2005; Sakai et al, 2005; Sakai and Tachibana, 2007). It can also be composed of plasma with spatially periodic density variation, which can be induced naturally in plasmas i.e in the presence of laser pulses in underdense plasmas (Botton and Ron, 1991 ; Zhang et al, 2003; Wu et al, 2005 ; Yin et al, 2009), dust plasma crystals (Rosenberg et al, 2006), self-organised small plasma blobs or patterns (Fan et al, 2009 ; Kumar and Bora, 2010a ; Kumar, 2011c), etc. However theoretical and experimental studies have been going on since last few years to find out the possible applications of PPC over the conventional PCs, although there is no strong evidence of negative refractive index or metamaterial properties of PPC. Meanwhile, difficulties in the construction of PPC have been experienced during experimental realizations. Even after a long research history of MPC and PCC, a number of problems related to controllability and fabrications in both PCs are still unresolved. There is, however, plenty of scope to work on a hybrid PCs (Kumar , 2009a; 2009b, 2011b, 2011d) of MPC and PPC in such a manner so that properties of both PCs can be utilized. Hence, the motivation of this study is to investigate the effect of a plasma column to control the microwave propagation through MPC as presented in Fig 3.

Plasma Photonic Crystal 287

where *pe* is the electron plasma angular frequency, is the angular frequency of the incident wave and *<sup>m</sup>* is the electron-neutral collision frequency. We see that in order to obtain a significant effect of the plasma for reasonable values of the plasma channel diameter, the plasma density should be in the range of 5 x 1012 cm-3. Plasma parameters are precisely chosen to full fill the conditions. Possible precautions for cut-off criteria, collisionality and skin depth effect have been considered. The calculated values of these are

To accomplish the motivation of this study an experimental set-up is made (This experiemnt was performed in GREPHE, LAPALCE, Toulouse, France). A schematic of experimental setup for measuring the microwave transmission through metallic photonic crystal (MPCs) with and without plasma column is shown in Fig.6, where a MPC, glass chamber, horn antennas, etc. are presented. A triangular MPC is made by 33 copper rods of diameter 2 mm and length of 100 mm, which are fixed with lattice constant of 10mm in two flanges or discs made by dielectrics in such a way so that different structures of MPC can be configured. Metallic photonic crystal is placed in a glass chamber to carry out experiments with and without plasma column. MPC is kept at the centre of the glass chamber in such a manner that transmitter and receivers can be aliened with the MPC and plasma columns. Two suitable canonical horn antennas are used as transmitter and receiver for X-band microwave. Transmitting horn antenna is fixed and receiving horn antenna can be moved around the MPC form 00 to 3600. Both antennas are used in far-field region form the MPC. The heights of both the antennas are same from the ground. A microwave generator is used to generate X-band microwave (2 GHz-28GHz). A vector network analyzer (VNA) is attached with both the antennas to measure the transmission coefficient. An angle chart is made on the ground level to measure the angle of the position of the receiver from the origin of the MPC. A microwave absorber is used to absorb the microwave so that reflected microwave cannot affect the measurements. In order to investigate the application of plasmas in MPC experiments are conducted with and without plasma column at different places; thus, experimental set-up is modified as follows. In the first set of experiments in which plasma column is formed at the place of central rod of the front row in MPC and in the second set of experiments plasma column is formed between MPC and position of

Same discharge mechanism can be used to form the plasma column in all the experiments, so the details of discharge mechanism and formation of plasma columns are common. It is well known that micro-discharge can be used to produce large volume plasma columns up to atmospheric pressure (Kunhard, 2000 ; Park et al, 2003; JING and WANG, 2006). Therefore, micro-discharge is also used to form plasma column in and out of MPC (Kumar, 2009b). For this purpose, three electrodes are made of molybdenum foil and alumina is used as a dielectric to make sandwich of electrodes with the hole diameter of 0.5 mm to 1 mm. High temperature glue is used to pack the electrodes and alumina. Two DC power supplies are used to produce voltage differences between electrodes. Length of the plasma column is equal to the separation between electrodes and, of course, length of plasma column can be varied by changing the separation of electrodes. Typical cathode voltage is 800 V and anode voltage varies form 1 KV to 2 KV maintaining current up to 15 mA. Argon and helium gases are used as background gases in the glass chamber. Experiments are carried out with

given below in Fig. 5.

transmitter.

**5.2 Experimental set-up** 

Fig. 3. Hybrid plasma photonic crystal

#### **5.1 Selection of plasma parameters**

Our motivation for the study to use plasma column in place of copper rods lies in the fact that by switching OFF and ON plasma, which can be formed and destroyed rapidly, and microwave refraction can be controlled. Hence, to accomplish such purpose it is required to study the characteristics of plasma at X-band frequency microwave (18 GHz) to obtain its behavior close to the metallic copper rods. Hence phase difference in 18 GHz microwave is calculated using reflection coefficient of copper and plasma with the help of relative reflective index ( 0.40 1.26 *<sup>r</sup> i* ) and conductivity ( 1.24 1.4 *i* ). Reflection behavior of microwave from metal and plasma is shown in Fig. 4. The phase difference and path difference are achieved as 2.5 radian and 6 mm respectively.

Fig. 4. Reflection of 18 GHz microwave from metal and plasma medium

The plasma is considered as a homogeneous cylindrical channel with complex relative electric permittivity given as

$$\varepsilon(r) = 1 - \left(\frac{\alpha\_{pe}}{\alpha}\right)^2 \left(1 - i\frac{\upsilon\_m}{\alpha}\right)^{-1} \tag{3}$$

Our motivation for the study to use plasma column in place of copper rods lies in the fact that by switching OFF and ON plasma, which can be formed and destroyed rapidly, and microwave refraction can be controlled. Hence, to accomplish such purpose it is required to study the characteristics of plasma at X-band frequency microwave (18 GHz) to obtain its behavior close to the metallic copper rods. Hence phase difference in 18 GHz microwave is calculated using reflection coefficient of copper and plasma with the help of relative reflective index ( 0.40 1.26 *<sup>r</sup> i* ) and conductivity ( 1.24 1.4 *i* ). Reflection behavior of microwave from metal and plasma is shown in Fig. 4. The phase difference and path

Fig. 3. Hybrid plasma photonic crystal

**5.1 Selection of plasma parameters** 

electric permittivity given as

difference are achieved as 2.5 radian and 6 mm respectively.

Fig. 4. Reflection of 18 GHz microwave from metal and plasma medium

The plasma is considered as a homogeneous cylindrical channel with complex relative

1 1 *pe <sup>m</sup> r i*

2 1

(3)

where *pe* is the electron plasma angular frequency, is the angular frequency of the incident wave and *<sup>m</sup>* is the electron-neutral collision frequency. We see that in order to obtain a significant effect of the plasma for reasonable values of the plasma channel diameter, the plasma density should be in the range of 5 x 1012 cm-3. Plasma parameters are precisely chosen to full fill the conditions. Possible precautions for cut-off criteria, collisionality and skin depth effect have been considered. The calculated values of these are given below in Fig. 5.

### **5.2 Experimental set-up**

To accomplish the motivation of this study an experimental set-up is made (This experiemnt was performed in GREPHE, LAPALCE, Toulouse, France). A schematic of experimental setup for measuring the microwave transmission through metallic photonic crystal (MPCs) with and without plasma column is shown in Fig.6, where a MPC, glass chamber, horn antennas, etc. are presented. A triangular MPC is made by 33 copper rods of diameter 2 mm and length of 100 mm, which are fixed with lattice constant of 10mm in two flanges or discs made by dielectrics in such a way so that different structures of MPC can be configured. Metallic photonic crystal is placed in a glass chamber to carry out experiments with and without plasma column. MPC is kept at the centre of the glass chamber in such a manner that transmitter and receivers can be aliened with the MPC and plasma columns. Two suitable canonical horn antennas are used as transmitter and receiver for X-band microwave. Transmitting horn antenna is fixed and receiving horn antenna can be moved around the MPC form 00 to 3600. Both antennas are used in far-field region form the MPC. The heights of both the antennas are same from the ground. A microwave generator is used to generate X-band microwave (2 GHz-28GHz). A vector network analyzer (VNA) is attached with both the antennas to measure the transmission coefficient. An angle chart is made on the ground level to measure the angle of the position of the receiver from the origin of the MPC. A microwave absorber is used to absorb the microwave so that reflected microwave cannot affect the measurements. In order to investigate the application of plasmas in MPC experiments are conducted with and without plasma column at different places; thus, experimental set-up is modified as follows. In the first set of experiments in which plasma column is formed at the place of central rod of the front row in MPC and in the second set of experiments plasma column is formed between MPC and position of transmitter.

Same discharge mechanism can be used to form the plasma column in all the experiments, so the details of discharge mechanism and formation of plasma columns are common. It is well known that micro-discharge can be used to produce large volume plasma columns up to atmospheric pressure (Kunhard, 2000 ; Park et al, 2003; JING and WANG, 2006). Therefore, micro-discharge is also used to form plasma column in and out of MPC (Kumar, 2009b). For this purpose, three electrodes are made of molybdenum foil and alumina is used as a dielectric to make sandwich of electrodes with the hole diameter of 0.5 mm to 1 mm. High temperature glue is used to pack the electrodes and alumina. Two DC power supplies are used to produce voltage differences between electrodes. Length of the plasma column is equal to the separation between electrodes and, of course, length of plasma column can be varied by changing the separation of electrodes. Typical cathode voltage is 800 V and anode voltage varies form 1 KV to 2 KV maintaining current up to 15 mA. Argon and helium gases are used as background gases in the glass chamber. Experiments are carried out with

Plasma Photonic Crystal 289

Experiments are carried out to study the electromagnetic bands gaps (EBGs) of X-band microwave through different configurations of triangle structure of MPC with and without

It has been studied that flat and forbidden bands at 18 GHz can be formed by MPC and defaulted MPC (Kumar 2011a, Kumar 2011b). Although this research work has potential to improve the tunability of PCs, it seems that enhancement in the tunability and controllability in this MPC is required because for tuning the MPC one needs to physically remove the metallic rods by mechanical effort (Kumar 2011a). For this concern, attention is paid to use a plasma column in the hole or default of MPC because plasma can be created and destroyed by switching ON and OFF. With the help of this approach, tunability of MPC

Hence experiments are carried out to measure the transmitted power at 18 GHz through MPC with and without plasma column. For this purpose electrodes of separation 20 mm are kept at the centre hole and well connected with the power-supplies. Finally, a plasma column of density of 5 x 1012 cm-3 and electron temperature of 2eV is formed around atmospheric pressure. Transmitted power of microwave is measured at different angles. Plasma is characterized [Kumar 2009b] as a collisional medium, which shows cut-off for 18 GHz microwave. A schematic of measurement method with electrode and with plasma in

Measurements of transmitted power of 18 GHz with electrodes and with plasma column are presented in Fig.9. Results of this figure show that transmitted power –38dBm at + 450 for

Fig. 6. A photo of experimental set up for plasma added MPC

plasma columns. Measurement method is shown in Fig.7.

can be increased as rapidly as the plasma can be formed and destroyed.

**5.3.1 Without and with plasma in central default** 

electrodes is shown in Fig. 8 (a) and (b) respectively.

**5.3 Measurements and results** 

Plasma Column Copper rods

different cathode-anode configurations at different background pressures. Turbo pumps and needle valves are used to control the gas pressure inside the glass chamber respectively. For transmitting microwave a horn antenna is fixed at the flange of one of the ports of glass chamber and properly aligned according to the position of plasma column and MPC. Flange of the second port of glass chamber is used to take the electrical connections between power supplies and electrodes. For receiving the transmitted microwave power, another horn antenna is fixed on a stand outside the glass chamber. Such horn antenna can be moved on the angle chart form +900 to -900. Microwave is fed to the transmitting antenna using microwave generator and receiving antenna is fitted to a spectrum analyzer. Transmitter, MPC and plasma column are arranged in a glass chamber in such a way that the experiments can be carried out for different positions of plasma column.

$$n\_c = 1.24 \times 10^4 \times \left\{ f \left( MHz \right) \right\}^{\frac{1}{n\_c}} \text{cm}^{-3} \quad \quad n\_c = 4 \times 10^{12} \text{cm}^{-3} \quad \text{for } f = 18 \text{GHz}$$

$$\rho(1.13 \times 10^{11}) \gg \nu\_w \left(3 \times 10^{10}\right) \quad \text{Collisionless plasma for 18 GHz}$$

$$\nu\_n(\mathfrak{S}\times 10^{11}) \ge \mathcal{O}(1\times 10^{11})$$

$$
\sigma = 2.82 \times 10^{-4} \times \frac{n\_\star}{\phi^2} \nu\_\pi
$$

$$\sigma-1.1 \times 10^{-3} \, Ohm^{-1} \, Gm^{-1}$$

$$\delta' = \frac{\text{s.c.s}}{\left(\sigma(Ohm^{-1}cm^{-1}), f(MHz)\right)^{\frac{1}{\frac{1}{\sigma}}}}$$

$$\delta = 11 \text{ mm} \text{ for } f = 18 \text{ GHz}$$

Fig. 5. Calculations for plasma parameters

different cathode-anode configurations at different background pressures. Turbo pumps and needle valves are used to control the gas pressure inside the glass chamber respectively. For transmitting microwave a horn antenna is fixed at the flange of one of the ports of glass chamber and properly aligned according to the position of plasma column and MPC. Flange of the second port of glass chamber is used to take the electrical connections between power supplies and electrodes. For receiving the transmitted microwave power, another horn antenna is fixed on a stand outside the glass chamber. Such horn antenna can be moved on the angle chart form +900 to -900. Microwave is fed to the transmitting antenna using microwave generator and receiving antenna is fitted to a spectrum analyzer. Transmitter, MPC and plasma column are arranged in a glass chamber in such a way that the

experiments can be carried out for different positions of plasma column.

Fig. 5. Calculations for plasma parameters

Fig. 6. A photo of experimental set up for plasma added MPC
