Huygens principle of double refraction, named after Dutch physicist Christiaan Huygens, explains the phenomenon of double refraction observed in uniaxial anisotropic material such as calcite. When unpolarized light propagates in such materials (along a direction different from the optical axis), it splits into two different rays, known as ordinary and extraordinary rays. The principle states that every point on the wavefront of birefringent material produces two types of wavefronts or wavelets: spherical wavefronts and ellipsoidal wavefronts. These secondary wavelets, originating from different points, interact and interfere with each other. As a result, the new wavefront is formed by the superposition of these wavelets.
History The systematic exploration of light polarization began during the 17th century. In 1669, Rasmus Bartholin made an observation of double refraction in a calcite crystal and documented it in a published work in 1670. Later, in 1690, Huygens identified polarization as a characteristic of light and provided a demonstration using two identical blocks of calcite placed in succession. Each crystal divided an incoming ray of light into two, which Huygens referred to as "regular" and "irregular" (in modern terminology: ordinary and extraordinary). However, if the two crystals were aligned in the same orientation, no further division of the light occurred.
Huygens–Fresnel principle
While the Huygens's 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. 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. Understanding and forecasting the classical wave propagation of light is based on the Huygens-Fresnel principle.
Polarization of light
Electric and magnetic fields that are mutually perpendicular and fluctuating give rise to the transverse electromagnetic wave known as light. Electric and magnetic fields are perpendicular to the propagation direction of the wave. For example, if the wave propagation is in the z-direction, both the electric field and the magnetic field lie in the xy-plane. The electric field points in a specific direction in space since it is a vector. The direction of an electromagnetic wave's electric field vector E is referred to as polarization. If the electric field oscillates in the x-direction, the polarization of the light will be linear, along the x-direction.
Plane wave equation of the light The electromagnetic wave equation's sinusoidal solution has the following form: E ( r , t ) = E 0 cos ( ω t − k ⋅ r + ϕ 0 ) B ( r , t ) = B 0 cos ( ω t − k ⋅ r + ϕ 0 ) {\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}}} where
t is time (in seconds), ω is the angular frequency (in radians per second),
ϕ 0 {\displaystyle \phi _{0}} is the phase angle constant (in rad), and k = (kx, ky, kz) 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 k = | k | = ω c = 2 π λ {\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.
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