Waveplate

Or a delay -wave plate (also λ / n- platelets) is an optical component, the polarization and the phase of electromagnetic waves passing therethrough (mostly optical ) may change. The following types are available:

• A delayed 4 plate light which is polarized parallel to a component - specific axis, by a quarter wavelength - or π / 2 - with respect to this perpendicular polarized light. It can make when properly irradiation of linearly polarized light, circularly or elliptically polarized light and circularly polarized light from linearly polarized again.
• A λ/2-Plättchen delayed light that is polarized parallel to a component - specific axis, by a half wavelength - or π - with respect to this perpendicular polarized light. It can rotate the polarization direction of linearly polarized light by a selectable angle.

Polarization changes are due to the fact that the light can be decomposed into two perpendicular polarization directions that pass through the retardation plate at different speeds, of which phases are shifted from each other so. Such a plate is typically made of a birefringent crystal (e.g., calcite ) with a suitably selected thickness and orientation. Nowadays however it achieves the same effect even in films, so that it is also retardation films. But still it seems to stay with the usage of the " plate ".

Operation

At a retardation plate is a thin disc of optically anisotropic material, that is material having different polarized light for various propagation velocities c / n (or different refractive indices n ) in different directions. Materials commonly used are optically uniaxial, that is, there are two mutually perpendicular axes in the crystal, along which the refractive indices are different. These are called ordinary ( e- vector of the light is polarized perpendicular to the optical axis ) and extraordinary axis (the E- vector of the light is polarized parallel to the optical axis ). The vibration direction of the light, wherein a shaft has the large propagation velocity is called the " fast axis " that is perpendicular to the direction corresponding to " slow axis ." For retardation plates, the crystals are cut so that their optical axis lies in the plane of the polished entrance surface. On commercially available plates usually the fast axis is marked so that the alignment can be precisely defined.

The functioning of such a wave plate to be described from an optically positive uniaxial material (eg quartz). In this case, the slow axis coincides with the optical axis of the crystal ( high symmetry axis in the crystal lattice ). The refractive indices along these axes are denoted by and.

Light which is polarized parallel to the fast axis, takes less time to traverse the plate as light which is polarized perpendicularly thereto. The light can be imagined divided to the optical axis into two linearly polarized components perpendicular ( ordinary ray ) and parallel ( extraordinary ray ). After passing through the plate, the two waves have a phase shift to each other of:

Where d is the thickness of the plate and λ is the wavelength of the incident light. The two waves are superimposed behind the crystal (interference ) to the outgoing light. Due to the (coherent ) superposition of these two waves, a new polarization of light results ( frequency and wavelength are preserved; see next section). As can be seen in the equation, the thickness of a retardation plate has a decisive influence on the type of overlay. For this reason, such a delay plate is always designed for a specific wavelength.

It should be noted that the splitting is only a kind of computational trick into two beams. In reality, these two beams overlap, of course, at any point of the crystal. The electrons for the atoms of the crystal form and local current dipoles vibrate in a superposition of the two polarization directions of the beams.

4 plate

If we choose d in the above formula so that a phase shift of π / 2 results, we obtain a 4 plate.

Then applies a linearly polarized light beam whose polarization direction is rotated by 45 ° to the optical axis, onto the wafer, the result is circularly polarized light. If the setting is 45 ° different, the result is elliptically polarized light in the general case. The reason for this is that the light beam is split into two orthogonally polarized components that moves at the output of the wafer by a quarter phase overlap again. This creates for the resulting field vector of the outgoing light beam, a Lissajous figure ( circle, or ellipse), which causes a complete rotation of the plane of polarization through 360 ° during each cycle of oscillation. It's called a 4 plate therefore circular polarizer. Conversely 4 plate also turns a circularly polarized light into linearly polarized light.

If the polarization direction of the incident light, however, parallel to one of the axes, one obtains after platelets again linearly polarized, but phase-shifted light.

Two cascaded 4 plate give a λ/2-Plättchen in parallel alignment of their optical axes.

λ/2-Plättchen

Follows up a shift by π, we get a λ/2-Plättchen. One can use such a plate to rotate the polarization direction. Light is radiated at the angle α to an optical axis, the light is at an angle - α ( that is to say the angle 2α to the optical axis rotated ) out again.

Mathematical Description

Consider linearly polarized in the y- direction, a plane wave in the z- direction

To describe a physically real size one uses only the real part of complex description above, ie:

The vector is a vector in the x -y plane. This now meet at right angles to a retardation plate whose fast axis is tilted at an angle α to the y- direction ( see drawing above). We now move to the coordinate system of the axes of the retardation plate! Then is projected onto the axes, and to obtain:

The wave plate then causes a phase delay of the slow axis ( component) with respect to the fast axis, is thus obtained:

For a 4 plate. Considering then only the real part of the complex notation ( corresponds to the real physical quantity, such as the E-field ), we obtain:

However, this corresponds to a movement of the E- field vector in the XY plane in time and space. For α = 45 ° and obtained a circular orbit for the tip of the E-field vector. For other angles results in an ellipse.

In a λ/2-Plättchen and applies accordingly:

This corresponds to a rotation of the polarization by an angle α 2.