Huygens principle of double refraction

While the Huygens' principle of double refraction explains the phenomenon of double refraction in an optically anisotropic medium, the Huygens–Fresnel principle pertains to the propagation of waves in an optically isotropic medium.^[3][4] According to the Huygens–Fresnel principle, each point on a wavefront can be considered a secondary point source of waves, so a new wavefront is formed after the secondary wavelets have traveled for a period equal to one vibration cycle. This new wavefront can be described as an envelope or tangent surface to these secondary wavelets.^[5] Understanding and forecasting the classical wave propagation of light is based on the Huygens-Fresnel principle.^[3]

Polarization of light

The electromagnetic wave equation's sinusoidal solution has the following form:^[7]

$${\displaystyle {\begin{aligned}\mathbf {E} (\mathbf {r} ,t)&=\mathbf {E} _{0}\cos(\omega t-\mathbf {k} \cdot \mathbf {r} +\phi _{0})\\\mathbf {B} (\mathbf {r} ,t)&=\mathbf {B} _{0}\cos(\omega t-\mathbf {k} \cdot \mathbf {r} +\phi _{0})\end{aligned}}}$$

• t is time (in seconds),
• ω is the angular frequency (in radians per second),
• ${\displaystyle \phi _{0}}$ is the phase angle constant (in rad), and
• k = (k_x, k_y, k_z) is the wave vector of the wave (in rad/m).

The wave vector is related to the angular frequency and speed of light c by

$${\displaystyle k=|\mathbf {k} |={\omega \over c}={2\pi \over \lambda }}$$

where k is the wavenumber (the magnitude of the wave vector) and λ is the wavelength.

Unpolarized light

If we were able to observe a light wave originating from an ordinary source and directed toward us, such as the light emitted by an incandescent bulb, we would find that it consists of mixture of light waves. These waves exhibit electric field components that fluctuate at a rapid pace, nearly matching the optical frequency itself, with a time scale of approximately 10⁻¹⁴ seconds. Consequently, the direction of oscillation of the electric field vector occurs in all possible planes perpendicular to the direction of the light beam. Unpolarized light is a type of light wave where the electric field vector oscillates in multiple planes. Light emitted by the sun, incandescent lamps, or candle flames is considered to be unpolarized.^[1][5]

Types of polarization

The light wave

${\displaystyle \mathbf {E} }$

The light may also be partially polarized in addition to these. The polarization of light cannot be determined by the human eye on its own. However, some animals and insects have a vision that is sensitive to polarization.^[1]

Plane linear polarized light

A frequent notion in the study of anisotropic materials, particularly in the context of optics, is the optical axis. It refers to a particular axis within the material along which certain optical characteristics remain unaltered. To put it in another way, the light that travels along the optical axis does not experience anisotropic behaviours on the transverse plane.^[10]

It is possible to further divide anisotropic materials into two categories:

extraordinary ray (E-ray) has an ellipsoidal wavefront due to its refractive index, which varies with the propagation direction within the uniaxial material, leading to different velocities in different directions. The two wavefronts come into contact at the points where they intersect with the optical axis.^[1]