Linear polarization

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A magneto-optic effect is any one of a number of phenomena in which an electromagnetic wave propagates through a medium that has been altered by the presence of a quasistatic magnetic field. In such a material, which is also called gyrotropic or gyromagnetic, left- and right-rotating elliptical polarizations can propagate at different speeds, leading to a number of important phenomena. When light is transmitted through a layer of magneto-optic material, the result is called the Faraday effect: the plane of polarization can be rotated, forming a Faraday rotator. The results of reflection from a magneto-optic material are known as the magneto-optic Kerr effect (not to be confused with the nonlinear Kerr effect).

In general, magneto-optic effects break time reversal symmetry locally (i.e. when only the propagation of light, and not the source of the magnetic field, is considered) as well as Lorentz reciprocity, which is a necessary condition to construct devices such as optical isolators (through which light passes in one direction but not the other).

Two gyrotropic materials with reversed rotation directions of the two principal polarizations, corresponding to complex-conjugate ε tensors for lossless media, are called optical isomers.

Gyrotropic permittivity

In particular, in a magneto-optic material the presence of a magnetic field (either externally applied or because the material itself is ferromagnetic) can cause a change in the permittivity tensor ε of the material. The ε becomes anisotropic, a 3×3 matrix, with complex off-diagonal components, depending of course on the frequency ω of incident light. If the absorption losses can be neglected, ε is a Hermitian matrix. The resulting principal axes become complex as well, corresponding to elliptically-polarized light where left- and right-rotating polarizations can travel at different speeds (analogous to birefringence).

More specifically, for the case where absorption losses can be neglected, the most general form of Hermitian ε is:

$\varepsilon ={\begin{pmatrix}\varepsilon _{xx}'&\varepsilon _{xy}'+ig_{z}&\varepsilon _{xz}'-ig_{y}\\\varepsilon _{xy}'-ig_{z}&\varepsilon _{yy}'&\varepsilon _{yz}'+ig_{x}\\\varepsilon _{xz}'+ig_{y}&\varepsilon _{yz}'-ig_{x}&\varepsilon _{zz}'\\\end{pmatrix}}$

or equivalently the relationship between the displacement field D and the electric field E is:

$\mathbf {D} =\varepsilon \mathbf {E} =\varepsilon '\mathbf {E} +i\mathbf {E} \times \mathbf {g}$

where $\varepsilon '$ is a real symmetric matrix and $\mathbf {g} =(g_{x},g_{y},g_{z})$ is a real pseudovector called the gyration vector, whose magnitude is generally small compared to the eigenvalues of $\varepsilon '$. The direction of g is called the axis of gyration of the material. To first order, g is proportional to the applied magnetic field:

$\mathbf {g} =\varepsilon _{0}\chi ^{(m)}\mathbf {H}$

where $\chi ^{(m)}\!$ is the magneto-optical susceptibility (a scalar in isotropic media, but more generally a tensor). If this susceptibility itself depends upon the electric field, one can obtain a nonlinear optical effect of magneto-optical parametric generation (somewhat analogous to a Pockels effect whose strength is controlled by the applied magnetic field).

The simplest case to analyze is the one in which g is a principal axis (eigenvector) of $\varepsilon '$, and the other two eigenvalues of $\varepsilon '$ are identical. Then, if we let g lie in the z direction for simplicity, the ε tensor simplifies to the form:

$\varepsilon ={\begin{pmatrix}\varepsilon _{1}&+ig_{z}&0\\-ig_{z}&\varepsilon _{1}&0\\0&0&\varepsilon _{2}\\\end{pmatrix}}$

Most commonly, one considers light propagating in the z direction (parallel to g). In this case the solutions are elliptically polarized electromagnetic waves with phase velocities $1/{\sqrt {\mu (\varepsilon _{1}\pm g_{z})}}$ (where μ is the magnetic permeability). This difference in phase velocities leads to the Faraday effect.

For light propagating purely perpendicular to the axis of gyration, the properties are known as the Cotton-Mouton effect and used for a Circulator.

Kerr Rotation and Kerr Ellipticity

Kerr Rotation and Kerr Ellipticity are changes in the polarization of incident light which comes in contact with a gyromagnetic material. Kerr Rotation is a rotation in the angle of transmitted light, and Kerr Ellipticity is the ratio of the major to minor axis of the ellipse traced out by elliptically polarized light on the plane through which it propagates. Changes in the orientation of polarized incident light can be quantified using these two properties.

Circular Polarized Light

According to classical physics, the speed of light varies with the permittivity of a material:

$v_{p}={\frac {1}{\sqrt {\epsilon \mu }}}$

where $v_{p}$ is the velocity of light through the material, $\epsilon$ is the material permittivity, and $\mu$ is the material permeability. Because the permittivity is anisotropic, polarized light of different orientations will travel at different speeds.

This can be better understood if we consider a wave of light that is circularly polarized (seen to the right). If this wave interacts with a material at which the horizontal component (green sinusoid) travels at a different speed than the vertical component (blue sinusoid), the two components will fall out of the 90 degree phase difference (required for circular polarization) changing the Kerr Ellipticity.

A change in Kerr Rotation is most easily recognized in linearly polarized light, which can be separated into two Circularly polarized components: Left-Handed Circular Polarized (LCP) light and Right-Handed Circular Polarized (RCP) light. The anisotropy of the Magneto Optic material permittivity causes a difference in the speed of LCP and RCP light, which will cause a change in the angle of polarized light. Materials that exhibit this property are known as Birefringent

From this rotation, we can calculate the difference in orthogonal velocity components, find the anisotropic permittivity, find the gyration vector, and calculate the applied magnetic field $\mathbf {H}$.

Wavelength parallel measurement of magneto-optical effect

Because the MO activity is usually very small, normally less than 1°,in conventional systems, the monochromator produces quasi-monochromatic light in a narrow wavelength window since the amplitude of modulation is wavelength dependent. Therefore, to measure the spectroscopic MO activity, a large number of measurements over the full spectra is required to obtain satisfactory wavelength resolution and thus is very time consuming. To obtain the spectroscopic information of the MO activity, light wavelength is varied by the monochromator. Therefore, these methods cost huge amount of time though provide high sensitivity to small MO activities. Fast spectroscopic characterization of the MO activity is thus desirable. Can we use white light source and perform wavelength-parallel measurement such as that in the state-of-art ellipsometry for the characterization of refractive index?

It is well established that when this linear polarized light passes through another polarizer, also called analyzer, the transmitted light intensity could be varied depending on their relative angle θ governed by a cos²(θ) law. Based on this simple idea, now researcher has developed a fast spectroscopic MO system, they can get full spectral range MO activity in a single magnetic field scan. The system requires only stable continuous spectral light source, two polarizers, an achromatic quarter-wave plate and a spectrometer.

Fast magneto-optical spectrometry

It is low cost and flexible for application in full spectral range from UV to IR, or even in THz applications.This new system would booster the exploration to the MO characteristics of a large variety of materials in the full spectral range. The minimum resolvable angle depends on the full scale signal of light source and is limited by the instability and dark noise of the spectrometer. A minimum resolvable angle of 0.004° has been demonstrated in the their configuration.

See also

• Zeeman effect
• QMR effect
• Magneto-optic Kerr effect
• Faraday effect
• Voigt Effect
• Photoelectric effect

References

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  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• Broad band magneto-optical spectroscopy