Polarization examples

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.

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.

Polarization oflightnotes PDF

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.

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.

Infrared heating uses infrared lamps, commonly called heat lamps, to transmit infrared radiation to the body that is being heated. When a body with a large surface area needs to be heated, an array of infrared lamps is often used. The lamp commonly contains an incandescent bulb that produces infrared radiation. Infrared lamps have many industrial applications including curing coatings and preparing plastic for forming, commercial applications such as cooking and browning food, and personal applications such as providing heat (especially in bathrooms and for pets) [6] as well as for commercial and industrial heating.[7]

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 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.

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.

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.

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.

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.

Infrared lamps are electrical devices which emit infrared radiation. Infrared lamps are commonly used in radiant heating for industrial processes and building heating.[1] Infrared LEDs are used for communication over optical fibers and in remote control devices. Infrared lamps are also used for some night vision devices where visible light would be objectionable. Infrared lamp sources are used in certain scientific and industrial instrument for chemical analysis of liquids and gases; for example, the pollutant sulfur dioxide in air can be measured using its infrared absorption characteristics. IR radiant energy emitted by lamps cover a wide spectrum of wavelengths, ranging from 0.7 μm (micrometers) to a longer wavelength of 400 μm.[2]

Plane polarizedlight

Polarized and unpolarizedlight

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Polarization by reflection

Solid-state light emitting diodes can be produced to be efficient sources of near-monochromatic infrared energy. Such sources can be rapidly modulated for communication systems and control signals. A light emitting diode can be closely coupled to an optical fiber, allowing infrared signals to be sent up to scores of kilometres without amplification.

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.

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.

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.

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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.

IR data transmission is also employed in short-range communication among computer peripherals and personal digital assistants. These devices usually conform to standards published by IrDA, the Infrared Data Association. Remote controls and IrDA devices use infrared light-emitting diodes (LEDs) to emit infrared radiation which is focused by a plastic lens into a narrow beam. The beam is modulated, i.e. switched on and off, to encode the data. The receiver uses a silicon photodiode to convert the infrared radiation to an electric current. It responds only to the rapidly pulsing signal created by the transmitter, and filters out slowly changing infrared radiation from ambient light. Infrared communications are useful for indoor use in areas of high population density. IR does not penetrate walls and so does not interfere with other devices in adjoining rooms. Infrared is the most common way for remote controls to command appliances.

Some applications use the heat generated by the standard incandescent lamps, such as incubators, brooding boxes for poultry,[4] heat lights for reptile tanks,[5] novelty lamps such as lava lamps, and the Easy-Bake Oven toy. Heat lamps may have a red coating to reduce the visible light emitted.

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 electric and magnetic fields looks somewhat plausible but is not accurate.

Further, we have many interesting case studies on the same page, with topics mostly in fiber optics. Concrete examples cases, investigated quantatively, often give you much more insight!

What is polarizing lightin physics

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What ispolarization

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.

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).

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.

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.

Circularly polarizedlight

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.

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!

Incandescent light bulbs use a tungsten filament heated to high temperature to produce visible light and, necessarily, even more infrared radiation. Round bulbs, often tinted red to reduce visible light, provide infrared radiant heat suitable for warming of people or animals, but the power density available is low. The development of quartz halogen linear lamps allowed much higher power density up to 200 watts/inch of lamp (8 w/mm), useful for industrial heating, drying and processing applications.[3] By adjusting the voltage applied to incandescent lamps, the spectrum of the radiated energy can be made to reduce visible light and emphasize infrared energy production. Different wavelengths of infrared radiation are differently absorbed by different materials.[2]

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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 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.

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 of the polarization state, and also a significant variation in the polarization state across the beam profile.

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