Circularpolarization

In many respects, light can be described as a wave phenomenon (→ wave optics). More specifically, light waves are recognized as electromagnetic transverse waves, i.e., with transverse oscillations of the electric and magnetic field.

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Circularly polarizedlight

Of course, the polarization can have any other direction perpendicular to the beam axis. Note that a rotation of the polarization by 180° does not lead to a physically distinct state.

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On the other hand, the polarization state of the laser output can be disturbed e.g. by random (and temperature-dependent) birefringence, such as occurs e.g. in optical fibers (if they are not polarization-maintaining or single-polarization fibers) and also in laser crystals or glasses as a result of thermal effects (→ depolarization loss). If the laser gain is not polarization-dependent, small drifts of the birefringence may lead to large changes in the polarization state, and also a significant variation in the polarization state across the beam profile.

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If the oscillations of the horizontal and vertical electric field vector do not have the same strengths, one has the case of an elliptical polarization, where the electric field vector, projected to a plane perpendicular to the propagation direction, moves along an ellipse.

In many cases, the output of a laser is a linearly polarized laser beam. Different mechanisms can be responsible for that:

A circular polarization state can mathematically be obtained as a superposition of electric field oscillations in the vertical and horizontal direction, both with equal strength but a relative phase change of 90°. Effectively, this leads to a rapid rotation of the electric field vector – once per optical cycle – which maintains a constant magnitude.

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We offer a wide range of polarizers and polarization optics for many different uses. Choosing the right polarization optic for your application can be a bewildering task, as we offer a wide range for many different uses.

Electricpolarization

There are also partially polarized states of light. These can be described with Stokes vectors (but not with Jones vectors). Further, one can define a degree of polarization which can be calculated from the Stokes vector and can vary between 0 (unpolarized) and 1 (fully polarized).

There are cases where polychromatic light can be described with a single Jones vector, since all its frequency components have essentially the same polarization state. However, the polarization state is substantially frequency-dependent in other cases.

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Note that a very small gain or loss difference for the two polarization directions can be sufficient for obtaining a stable linear polarization, provided that there is no significant coupling of polarization modes within the laser resonator.

Frequently, however, one requires a propagation direction which is not aligned with one of the crystal axes – for example, in the context of critical phase matching. The article on critical phase matching contains an example case for type I phase matching of frequency doubling in LBO, where the pump and second-harmonic beams propagate within the XY plane with an angle ($\varphi$) against the X axis). In this situation, polarization can be either ordinary or extraordinary:

Polarized light is made up of waves that vibrate in a single plane (Fig. 2). There are three types of polarized lights, linearly, circularly, and elliptically ...

Linearly polarized light can be depolarized (made unpolarized) with a polarization scrambler, which applies the mentioned random polarization changes, or at least quasi-random changes.

Sppolarization

polarization中文

Fully polarized states can be associated with points on the so-called Poincaré sphere. Partially polarized states correspond to points inside that sphere; unpolarized light is represented by the point at its center.

A light beam is called unpolarized when the analysis with a polarizer results in 50% of the power to be in each polarization state, regardless of the rotational orientation. Microscopically, this usually means that the polarization state is randomly fluctuating, so that on average no polarization is detected. Note that such fluctuations are not possible for strictly monochromatic light.

The degree of linear polarization is often quantified with the polarization extinction ratio (PER), defined as the ratio of optical powers in the two polarization directions. It is often specified in decibels, and measured by recording the orientation-dependent power transmission of a polarizer. Of course, the extinction ratio of the polarizer itself must be higher than that of the laser beam.

In the previous cases, the direction of the electric field vector was assumed to be constant over the full beam profile. However, there are light beams where that is not the case. For example, there are beams with radial polarization, where the polarization at any point on the beam profile is oriented in the radial direction, i.e., away from the beam axis.

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In simple cases, one has a polarization direction along one of the axes of the crystal lattice. One may then call this c polarization, for example, if it is along the crystal's c axis. (Unfortunately, for one type of crystal, there are sometimes different ways of labeling the crystal axes.)

I would have been glad to finally remove a serious mistake, but I believe my equations are correct. They agree with those in various textbooks and e.g. also in Wikipedia. Your argument concerning energy swapping back and forth between the electric and magnetic fields looks somewhat plausible but is not accurate.

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20211127 — Unpolarised light would be modelled as an equal mixture of p- and s-polarised light with random, rapidly varying phase differences between them.

When light propagates in a non-isotropic medium, such as a nonlinear crystal, the direction of polarization relative to the crystal axes is relevant. This is not the direction of beam propagation, but rather perpendicular to that.

Politicalpolarization

Your first plot shows the magnetic and electric field in phase – which is wrong. The magnetic field is made from the changing electric field. The two fields swap energy back and forth. Hence the magnetic field is at a maximum when the electric field has the largest rate of change, that is, at zero E field. The magnetic field zeros in strength when the electric field rate of change is zero, at it's peak. These are a simple consequence of Maxwell's Equations and is covered in most any text on E&M. The worst error I have found in years of use of your marvelous resource!

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Shalom EO offers various birefringent materials, including: MgF2 crystals, LiNbO3 and alpha-BBO crystals, quartz crystals, calcite crystals, and YVO4 crystals. The crystals exhibit excellent properties when used to make waveplates, Glan and Thompson polarizers, and other optical components. Crystal ingots, blanks, and polished and coated optical elements made of birefringent crystals are offered according to your request.

Linearpolarization

A radially polarized laser beam may be generated from a linearly polarized beam with some optical element, but it is also possible to obtain radially polarized emission directly from a laser. The advantage of this approach, applied in a solid-state bulk laser, is that depolarization loss may be avoided [4]. Furthermore, there are applications benefiting from radially polarized light.

Jones vectors can be used only for fully defined polarization states, not for unpolarized or partially polarized beams (see below) having a stochastic nature.

In the simplest case, a light beam is linearly polarized, which means that the electric field oscillates in a certain linear direction perpendicular to the beam axis, and the magnetic field oscillates in a direction which is perpendicular both to the propagation axis and the electric field direction. The direction of polarization is taken to be the direction of the electric field oscillations (i.e., not the magnetic ones). For example, a laser beam propagating in ($z$) direction may have the electric field oscillations in the vertical (($y$)) direction and the magnetic field oscillations in the horizontal (($x$)) direction (see Figure 1); it can be called vertically polarized or ($y$)-polarized. In a different perspective, this is also shown in the second part of Figure 2.

Polarization

Note that radial or azimuthal polarization state requires a zero electric field strength and thus also a vanishing optical intensity on the beam axis; it is not compatible with a Gaussian beam, for example. Radially polarized beams frequently exhibit a kind of donut profile.

The polarization state of light often matters when light hits an optical surface under some angle. A linear polarization state is then denoted as p polarization when the polarization direction lies in the plane spanned by the incoming beam and the reflected beam. The polarization with a direction perpendicular to that is called s polarization. These indications have a German origin: s = senkrecht = perpendicular, p = parallel.

EKSMA Optics has various kinds of birefringent crystal materials including various nonlinear crystals, some of our laser crystals and Raman crystals and polarizing optics crystals.

One distinguishes left and right circular polarization (see Figure 2). For example, left circular polarization means that the electric (and magnetic) field vector rotates in the left direction, seen in the direction of propagation. For an observer looking against the beam, the rotation of course has the opposite direction.

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As explained above, a waveplate or other birefringent optical element may rotate the direction of linear polarization, but more generally one will obtain an elliptical polarization state after such an element. True polarization rotation, where a linear polarization state is always maintained (just with variable direction), can occur in the form of optical activity. Some optically active substances such as ordinary sugar (saccharose) can produce substantial rotation angles already within e.g. a few millimeters of propagation length. Optical activity can be accurately measured with polarimeters.

The polarization state of monochromatic light is often described with a Jones vector, having complex electric field amplitudes for ($x$) and ($y$) direction, if propagation occurs in ($z$) direction. That Jones vector may be constant over some area across the beam, or it may vary, for example for a radially polarized beam (see above). The effect of optical elements such as waveplates, polarizers and Faraday rotators can be described with Jones matrices, with which the Jones vectors can be transformed by multiplication. (One assumes a linear relationship between input and output amplitudes.) A whole sequence of such optical elements can be described with a single Jones matrix, which is obtained as the product of the matrices corresponding to the components.

For the mentioned phase-matching scheme, which is denoted as XY oo-e, the pump wave has ordinary polarization, while the second-harmonic wave has extraordinary polarization. There are also cases with type II phase matching, e.g. the scheme XY oe-e, where the pump wave has both an ordinary and an extraordinary polarization component.

There are also azimuthally polarized beams, where the electric field direction at any point is tangential, i.e., perpendicular to a line through the point and the beam axis.

While optical activity usually results from the presence of chiral molecules, with a concentration difference between the two possible enantiometers, it can also be induced by a magnetic field in a substance which is not naturally optically active. That is called the Faraday effect, and is exploited in Faraday rotators and Faraday isolators.

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