ABSTRACT
Christian Huygens was the first to suggest that light was not a scalar quantity, based on his work on the propagation of light through crystals; it appeared that light had “sides” in the words of Newton. This vectorial nature of light is called polarization. If we follow mechanics and equate an optical medium to an isotropic elastic medium, it should be capable of supporting three independent oscillations (optical disturbances): ux(r, t), uy(r, t), and uz(r, t). Correspondingly, three independent wave equations are then required to describe the propagation of the optical disturbance,
∇ = ∂ ∂
1 u r t
v
u r t
t i x y zi
i( , ) ( , )
, , , (4.1)
where ν is the velocity of propagation of the oscillation and r = r(x, y, z). In a Cartesian system, the components ux(r, t) and uy(r, t) are said to be the transverse components, and the component uz(r, t) is said to be the longitudinal component when the propagation is in the z direction. According to Equation 4.1 the optical field components should be
u t u tx x xr k r, ( · ),( ) = − +0 cos ω δ (4.2)
u t u ty y yr k r, ( · ),( ) = − +0 cos ω δ (4.3)
u t u tz z zr k r, ( · ).( ) = − +0 cos ω δ (4.4)
In 1818, Fresnel and Arago carried out a series of fundamental investigations on Young’s interference experiment using polarized light. After a considerable amount of experimentation, they were forced to conclude that the longitudinal component Equation 4.4 did not exist. That is, light consisted only of the transverse components Equations 4.2 and 4.3. If we take the direction of propagation to be in the z direction, then the optical field in free space must be described only by
u z t u t kzx x x, cos( ),( ) = − +0 ω δ (4.5)
u z t u t kzy y y, ( ),( ) = − +0 cos ω δ (4.6)
where u0x and u0y are the maximum amplitudes and δx and δy are arbitrary phases. There is no reason, a priori, for the existence of only transverse components on the basis of an elastic medium (the “luminiferous aether” in optics). It was considered to be a defect in Fresnel’s theory. Nevertheless, Equations 4.5 and 4.6 were found to describe satisfactorily the phenomenon of interference using polarized light.
