**3. Plasma photonic crystal (PPC)**

In previous section, we have seen that negative refraction of electromagentic wave is possible by photonic crystal. We now interested to study the plasma photonic crystal due to its applications over the convetional PCs. The plasma photonic crystals (PPCs) are artificially periodic array composed of alternating thin unmagnetised or magnetized plasmas and dielectric materials or vacuum (Hojo and Mase, 2004). It is well known that nonmagnetised plasma can be characterized by a complex frequency-dependent permittivity medium. On the other hand, the unmagnetised plasma is frequency dispersive medium. The refractive index of collisionless unmagnetised plasma that is determined by electromagnetic wave frequency and plasma frequency is less than one. Dispersion relation of propagating electromagnetic waves in nonmagnetised plasma can be modified if bulk plasma is replaced by a microplasma array (Park et al, 2002), which is analogically

Thus, calculating band structure of a PC numerically leads to calculation of . From the experimental point of view can be calculated by Snell's law. Hence, the negative refraction can be realized also with PCs that is in contrast to the composite metamaterials pave inhomogeneous media with a lattice constant comparable to the wavelength. Although both and µ are positive in dielectric PCs and metallic photonic crystals (MPCs), phenomenon of negative refraction and super resolution can be expected from peculiarities of the dispersion characteristics of certain PCs. The main advantage of PCs over composite metamaterials (CMMs) currently is that they can be more easily scaled to 3D and adapted to visible frequencies (Parimi et al, 2004). Negative refraction at microwave frequencies was observed in both dielectric and metallic PCs, for example, using a square array of alumina rods in air (Cubukcu et al, 2003). 2D and 3D PCs consisting of alumina rods were used for the demonstration of negative refraction in the microwave and millimeter wave range. Two techniques namely, manual assembly of alumina rods and rapid phototyping were used in this study for fabricating low-loss PCs (investigated in the wave range form 26 GHz to 60 GHz). The negative refraction in a metallic PC with hexagonal lattice acting as a flat lens with out optical axis at microwave frequencies was reported at 10.4 GHz for TM mode (Parimi et. al, 2004). Such PC contains cylindrical copper rods, are in triangular lattice, in which negative refraction was found for both TM and TE mode propagation between 8.6 and 11 GHz (TM mode) and between 6.4 and 9.8 GHz (TE mode). Hence, extensive experimental and simulation results were achieved, which pave the way to a variety of well tailored PCs structures. However, the advantages of metallic PC were reported to be highest dielectric constant, low attenuation, and the possibility of focusing. Most of efforts have been dedicated to the engineering and extension of the functionalities of metamaterials or PCs at terahertz (Yen et al, 2004 ; Padilla et al, 2006, Chen et al, 2006) and optical frequencies (Linden et al, 2004; Soukoulis et al, 2007). Negative refraction of surface plasmons was also demonstrated but was confined to a two-dimensional waveguide (Lezec et al, 2007). Three dimensional optical metamaterials have come into focus recently, including the realization of negative refraction in semiconductor metamatetrials and a 3D magnetic metamaterial in the infra red frequencies. However neither of these had a negative index of refraction (Liu et al, 2008 ; Hoffman et al, 2007). Three dimensional optical metamaterial with a negative refractive index has been also demonstrated recently (Valentine et al, 2008). Negative and positive refaction tubability of x-band microwve in MPC have been achieved recently by

In previous section, we have seen that negative refraction of electromagentic wave is possible by photonic crystal. We now interested to study the plasma photonic crystal due to its applications over the convetional PCs. The plasma photonic crystals (PPCs) are artificially periodic array composed of alternating thin unmagnetised or magnetized plasmas and dielectric materials or vacuum (Hojo and Mase, 2004). It is well known that nonmagnetised plasma can be characterized by a complex frequency-dependent permittivity medium. On the other hand, the unmagnetised plasma is frequency dispersive medium. The refractive index of collisionless unmagnetised plasma that is determined by electromagnetic wave frequency and plasma frequency is less than one. Dispersion relation of propagating electromagnetic waves in nonmagnetised plasma can be modified if bulk plasma is replaced by a microplasma array (Park et al, 2002), which is analogically

making defults or holes (Kumar, 2011a).

**3. Plasma photonic crystal (PPC)** 

understood from the extensive studies of photonic crystal. Hence in plasma photonic crystal, array of periodic micro plasmas are used at the place of array of dielectrics or metals in the conventional photonic crystals. One or two dimensional layers of array of micro plasmas make forbidden bands for wave propagation are formed beyond the bulk cut of frequency (electron plasma frequency) due to periodicity, where one can refer to such a functional structures as plasma photonic crystal. A photo of plasma photonic crystal is given below in Fig.1.

Fig. 1. Plasma photonic crystal

We know that plane-wave-expansion method has been widely used to analytically derive photonic band diagram of two-and three-dimensional dielectric periodic structures (Ho et al, 1990; Phihal et al, 1991). Dielectric constant of plasma can be obtained considering the field components in electromagnetic waves proportional to exp.[ ( . )] *j t kx* , where *k* and *x* are the complex wave number and spatial position vector, respectively. The dielectric constant as a function of frequency *<sup>p</sup>* inside a cold plasma column with electron plasma frequency *pe* is written as

$$\mathfrak{e}\_p = \mathbf{1} - \left(\frac{\mathrm{co}\_{pe}}{\mathrm{co}}\right)^2 \frac{\mathbf{1}}{\mathbf{1} - j(\mathrm{co}\_m/\mathrm{co})} \tag{2}$$

where *<sup>m</sup>* is the electron elastic collision frequency determined by neutral gas pressure and elastic collision cross section. In metal cases, a similar value ( ) to *m* was used as an inverse of electron relaxation time, and was much smaller than and *pe* (Kuzmiak and 1997) it is also possible that *<sup>m</sup>* is comparable to and *pe* where electron density is around 1013 cm-3 at a gas pressure around atmospheric pressure. Therefore plane-wave expansion method with Drude model in collision plasma has been studied (Sakai et al, 2007) for plasma photonic crystals. Experimental demonstrations have also been performed (Sakai et al, 2005 ; Sakaguchi et al, 2007) those typical parameters are summarized below,


Plasma Photonic Crystal 285

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

Fig. 2. A prototype to present EM wave transition from plasma crystal

**5. Plasma in photonic crystal** 

propagation through MPC as presented in Fig 3.


Several experimental studied have been conducted with the help of given experimental setup and parameters. Important results which emerged from the studied are listed below,

