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Wave Optics

Mueller Matrices for Polarizing Elements

What Are Mueller Matrices? Mueller matrices are 4x4 matrices that describe the linear relationship between polarization states of the incident light beam and the emerging light beam after passing through some polarizing elements, i.e., polarizers, waveplates, rotators. Mueller matrices are used together with Stokes parameters (Stokes vectors). Please check out this article if you need a review of Stokes parameters. Now let's look at figure 1 below.   Figure 1: Interaction of a polarized beam with a polarizing element The incident beam is characterized by its Stokes parameters S:   The incident beam interacts with the polarizing element, and the...

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Poincaré Sphere

What is Poincaré Sphere? The Poincaré sphere, shown in the figure below, is a graphical tool in real, three-dimensional space that allows convenient description of polarized light and of polarization transformations caused by propagation through devices.   Any state of polarization can be uniquely represented by a point on or within a unit sphere centered on a rectangular xyz-coordinate system as shown below. The coordinates (x,y,z) of a point within or upon this sphere are the normalized Stokes parameters (S1, S2, S3). For more information about Stokes parameters, please check out this article. Note: Normalized Stokes parameters always have S0 =...

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What Are Optically Active Materials?

Optical rotation or optical activity (sometimes referred to as rotary polarization) is the rotation of the plane of polarization of linearly polarized light as it travels through certain materials as shown below. The materials that can do so are called optically active materails. Optical activity occurs only in chiral materials, those lacking microscopic mirror symmetry. When we view the light head-on, some optically active materials rotate the electric field clockwise, called dextrorotatory. And some optically active materials rotate the electric field counterclockwise, called levorotatory. Unlike other sources of birefringence which alter a beam's state of polarization, optical activity can be...

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How to Measure Stokes Polarization Parameters

We will introduce the methods for measurement of Stokes polarization parameters. For the tutorial of Stokes Polarization Parameters, please check out this article. The Stokes polarization parameters are based on intensity quantities and thus are directly measurable. This make it very useful. The measurement is done by passing an optical beam through a retarder (waveplate) and a linear polarizer as shown below.   A monochromatic light beam incidents on a retarder, then followed by a linear polarizer with its transmission axis aligned at an angle θ to the x axis. We are now going to use the complex representation of the...

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Stokes Vector

The Definition of Stokes Vector We introduced Stokes parameters in this article. Please click on the link to learn more. As shown in it, Stokes parameters are defined as:   We can arrange the four Stokes parameters into a column matrix as:   Mathematically, it is not a vector, but through custom it is called the Stokes vector. From the Stokes parameters definition (12), (13), (14), (15) above, the Stokes vector for elliptically polarized light is written as:   (2) is also called the Stokes vector for a plane wave.   Stokes Vectors for Linearly and Circularly Polarized Light Just...

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