On the sign of the refractive index for metamaterials

The concept of the negative refractive index with application to doubly negative metamaterials is critically analyzed. The positive value of the refractive index is consistent with the definition of the refractive-index vector and the wave vector. A simple method for calculating the complex refractive index for dissipative isotropic materials using the concept of the wave-type identifier is presented

Formulation of the Snell-Descartes laws in terms of geometric algebra

A formulation of the laws of reflection and refraction of optical rays by the interface of two isotropic media using the mathematical apparatus of geometric algebra is given. The cases of specular reflection, positive and negative refraction, and refraction in the presence of a metasurface are considered

Fresnel coefficients of forward and backward waves refracting at the interface of isotropic media

The Fresnel coefficients are derived for cross- and co-polarization states of plane electromagnetic wave incident at the interface between two isotropic media. The media can support forward or backward normal waves. Based on introduction of wave type identifiers, without application of the notion of the negative refractive index, phenomena of positive and negative refractions are considered in the general case

Fresnel coefficients of forward and backward waves refracting at the interface of isotropic media

The Fresnel coefficients are derived for cross- and co-polarization states of plane electromagnetic wave incident at the interface between two isotropic media. The media can support forward or backward normal waves. Based on introduction of wave type identifiers, without application of the notion of the negative refractive index, phenomena of positive and negative refractions are considered in the general case

Vector formulations of the laws of reflection and refraction of forward and back-ward waves

Modified vector formulations of the laws of reflection and refraction are presented for forward and backward waves, based on Bhattacharjee’s approach. The new formulas include cases of specular reflection, retroreflection, and positive and negative refraction

Refractive index and wave resistance of homogeneous plane waves in isotropic media with losses and gain

Analytical expressions for complex values of the wave number, refractive index, and the characteristic wave impedance of homogeneous electromagnetic plane waves propagating in a linear, homogeneous, isotropic medium with losses and gain are derived. Formulas for determining the type of normal wave as a function of the values of the real and imaginary parts of the permittivity and permeability are obtained, and conditions for the appearance of positive and negative refraction at the interface of two isotropic media are indicated. In the approach applied here, the concept of a negative refractive index is not used

Vector formulations of the laws of reflection and refraction of forward and back-ward waves

Modified vector formulations of the laws of reflection and refraction are presented for forward and backward waves, based on Bhattacharjee’s approach. The new formulas include cases of specular reflection, retroreflection, and positive and negative refraction