We consider a 1D PC with the periodic structure embedded in air, as shown in Fig. 1. Here, represents an isotropicdielectric layer with the permittivity, permeability, and thickness, and is a uniaxial indefinitemetamaterial with thickness. N is the period number, and a plane wave is incident at an angle upon the 1DPC from air.

Theinterfaces of the layers are parallel to the plane, and the axis is normal to the structure.We assume that the optical axis of the indefinite medium lies in the plane and makes angle with the axis. In this case, thepermittivity and permeability tensors of the indefinite metamaterial medium aregiven by 24, 33, Fig.

1. Schematic of proposed ofthe 1DPC consisting of alternate layers of isotropic material (B) and uniaxialindefinite metamaterial (A), and is thenumber of periods. , (1)Where, (2) Here, , , and are the principle elements ofthe permittivity and permeability tensors of the layer along the optical axis andperpendicular to the optical axis, respectively, and is the angle between the opticalaxis and the -axis. The permittivity and permeability of layer A are complex given by34, 35: (3) Where is the angular frequency of theincident wave, and is measured in units of (109 rad ? s).Consider anelectromagnetic wave with frequency of, electric and magnetic fields of and, respectively, incident to the structure with angle with respect to the -axis. The fundamental equations for an electromagnetic wave are givenby the following Maxwell equations: (4)where and is the relative permittivity and permeability tensors, which, for anisotropic metamaterial witharbitrary optical axis is described Eq. (1).

At first, we focus only on the TEwaves. According to the Maxwell equations, the electric field inside the indefinite layersatisfies the wave equation:, (5) where is the vacuum wave vector. Byimposing the continuity condition on and at the interfaces and introducing a wave function as, , (6) The following relation is derived betweenthe electric and magnetic fields at any two positions and of the same medium: (7) here, is the transfer matrix of theindefinite medium, (8) where, and .Similar results can beobtained for the isotropic layer : , (9) where is the component of the wave vector inthe medium B , and c is the light speed in vacuum, and .For the waves, the wave equation in the metamaterial layer can be obtained similarlyas: , (10) here, is the transfer matrix of theindefinite medium for TM polarization: , (11) Where, and . By means of the transfermatrix method 29, we obtain the transmission of the structure as, , (12) where are the elements of the totalmatrix , and for the surrounding medium (air). We consider a 1D PC with the periodic structure embedded in air, as shown in Fig.

1. Here, represents an isotropicdielectric layer with the permittivity, permeability, and thickness, and is a uniaxial indefinitemetamaterial with thickness. N is the period number, and a plane wave is incident at an angle upon the 1DPC from air. Theinterfaces of the layers are parallel to the plane, and the axis is normal to the structure.We assume that the optical axis of the indefinite medium lies in the plane and makes angle with the axis.

In this case, thepermittivity and permeability tensors of the indefinite metamaterial medium aregiven by 24, 33, Fig. 1. Schematic of proposed ofthe 1DPC consisting of alternate layers of isotropic material (B) and uniaxialindefinite metamaterial (A), and is thenumber of periods. , (1)Where, (2) Here, , , and are the principle elements ofthe permittivity and permeability tensors of the layer along the optical axis andperpendicular to the optical axis, respectively, and is the angle between the opticalaxis and the -axis. The permittivity and permeability of layer A are complex given by34, 35: (3) Where is the angular frequency of theincident wave, and is measured in units of (109 rad ? s).

Consider anelectromagnetic wave with frequency of, electric and magnetic fields of and, respectively, incident to the structure with angle with respect to the -axis. The fundamental equations for an electromagnetic wave are givenby the following Maxwell equations: (4)where and is the relative permittivity and permeability tensors, which, for anisotropic metamaterial witharbitrary optical axis is described Eq. (1). At first, we focus only on the TEwaves. According to the Maxwell equations, the electric field inside the indefinite layersatisfies the wave equation:, (5) where is the vacuum wave vector.

Byimposing the continuity condition on and at the interfaces and introducing a wave function as, , (6) The following relation is derived betweenthe electric and magnetic fields at any two positions and of the same medium: (7) here, is the transfer matrix of theindefinite medium, (8) where, and .Similar results can beobtained for the isotropic layer : , (9) where is the component of the wave vector inthe medium B , and c is the light speed in vacuum, and .For the waves, the wave equation in the metamaterial layer can be obtained similarlyas: , (10) here, is the transfer matrix of theindefinite medium for TM polarization: , (11) Where, and . By means of the transfermatrix method 29, we obtain the transmission of the structure as, , (12) where are the elements of the totalmatrix , and for the surrounding medium (air).