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Jones Vector Representation of Polarization States

Complex Amplitudes of a Monochromatic Beam in Isotropic and Homogeneous Medium When a light beam propagates in an isotropic and homogeneous medium, the beam can be represented by its electric field E(r,t), which can be written: E(r,t) = A cos(ωt - k • r)                     (1) where A is a constant vector representing the amplitude, ω is the angular frequency, k is the wave vector (wave number), and r is the position in space. For mathematical simplicity, the monochromatic plane wave in (1) is often written:   Note: Only the real part of the right side represents...

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Complex-Number Representation of Polarization States

As we've seen from the article about polarization states, a light beam can be represented by its electric field vector E(r,t), which can be written: E = A cos(ωt - k • r) Being a transverse wave, the electric field vector must lie in the xy plane. So it can be decomposed into two mutually independent orthogonal components Ex and Ey: Ex = Ax cos(ωt - kz + δx)Ey = Ay cos(ωt - kz + δy) where we have used two independent and positive amplitudes Ax and Ay, and have added two independent initial phases δx and δy. Since the x component and the...

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Polarization States

Polarized Light A polarized lightwave signal that is propagating in fiber or in free space is represented by electric and magnetic field vectors that lie at right angles to one another in a transverse plane (a plane perpendicular to light's propagation direction). Polarization is defined in terms of the pattern traced out in the transverse plane by the electric field vector as a function of time, as shown in Figure 1 below. Figure 1: Three-dimensional and "polarization ellipse" representations of polarized light These are snapshots in time, showing the electric field as a function of distance. As time passes, the...

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Phase Velocity and Group Velocity

Superposition of Light Waves When we analyze the resultant of two or more simple harmonic vibrations (monochrome light waves), we usually can treat it as the simple sum of the individual vibrations (waves) as shown below. Note: This linear treatment is only true for low power intensity lights. When the power intensities are very high (such as with an electric field strength at 1012 volts/meter), non-linear effects will be excited and the simple sum method should not be used. However, in this discussion, we can use the simple sum method. Superposed Wave of Different Frequencies (very small difference) and Beats We will now...

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Faraday Effect

Faraday effect describes such a phenomenon: If a magnetic field is applied to a medium in a direction parallel with light’s propagation direction, a rotation of the light’s polarization direction happens. This is best shown in a picture. The essence of Faraday effect or Faraday rotation is that it shows the interaction between light and a magnetic field in a medium. In 1845 Faraday discovered that a magnetic field in the direction of propagation of a light beam in a transparent medium produces the effects of circular birefringence. Thus he established for the first time a direct connection between optics and electromagnetism...

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