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In optics, polarized light can be described using the Jones calculus, discovered by R. C. Jones in 1941. Polarized light is represented by a Jones vector, and linear optical elements are represented by Jones matrices. When light crosses an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light. Note that Jones calculus is only applicable to light that is already fully polarized. Light which is randomly polarized, partially polarized, or incoherent must be treated using Mueller calculus.

Jones vectors

The Jones vector describes the polarization of light.

The x and y components of the complex amplitude of the electric field of light travel along z-direction, $E_{x} (t)$ and $E_{y} (t)$ , are represented as

(\begin{matrix} E_{x} (t) \\ E_{y} (t) \end{matrix}) = (\begin{matrix} E_{0 x} e^{i (k z - ω t + ϕ_{x})} \\ E_{0 y} e^{i (k z - ω t + ϕ_{y})} \end{matrix}) = (\begin{matrix} E_{0 x} e^{i ϕ_{x}} \\ E_{0 y} e^{i ϕ_{y}} \end{matrix}) e^{i (k z - ω t)}

.

Here ${(\begin{matrix} E_{0 x} e^{i ϕ_{x}} & E_{0 y} e^{i ϕ_{y}} \end{matrix})}^{⊤}$ is the Jones vector ( $i$ is the imaginary unit with $i^{2} = - 1$ ). Thus, the Jones vector represents (relative) amplitude and (relative) phase of electric field in x and y directions.

The sum of the squares of the absolute values of the two components of Jones vectors is proportional to the intensity of light. It is common to normalize it to 1 at the starting point of calculation for simplification. It is also common to constrain the first component of the Jones vectors to be a real number. This discards the phase information needed for calculation of interference with other beams. Note that all Jones vectors and matrices on this page assumes that the phase of the light wave is $ϕ = k z - ω t$ , which is used by Hecht. In this definition, increase in $ϕ_{x}$ (or $ϕ_{y}$ ) indicates retardation (delay) in phase, while decrease indicates advance in phase. For example, a Jones vectors component of $i$ ( $= e^{i π / 2}$ ) indicates retardation by $π / 2$ (or 90 degree) compared to 1 ( $= e^{0}$ ). Collett uses the opposite definition ( $ϕ = ω t - k z$ ). The reader should be wary when consulting references on Jones calculus.

The following table gives the 6 common examples of normalized Jones vectors.

Polarization	Corresponding Jones vector	Typical ket Notation
Linear polarized in the x-direction Typically called 'Horizontal'	$(\begin{matrix} 1 \\ 0 \end{matrix})$	$\| H ⟩$
Linear polarized in the y-direction Typically called 'Vertical'	$(\begin{matrix} 0 \\ 1 \end{matrix})$	$\| V ⟩$
Linear polarized at 45° from the x-axis Typically called 'Diagonal' L+45	$\frac{1}{\sqrt{2}} (\begin{matrix} 1 \\ 1 \end{matrix})$	$\| D ⟩ = \frac{1}{\sqrt{2}} (\| H ⟩ + \| V ⟩)$
Linear polarized at −45° from the x-axis Typically called 'Anti-Diagonal' L-45	$\frac{1}{\sqrt{2}} (\begin{matrix} 1 \\ - 1 \end{matrix})$	$\| A ⟩ = \frac{1}{\sqrt{2}} (\| H ⟩ - \| V ⟩)$
Right Hand Circular Polarized Typically called RCP or RHCP	$\frac{1}{\sqrt{2}} (\begin{matrix} 1 \\ - i \end{matrix})$	$\| R ⟩ = \frac{1}{\sqrt{2}} (\| H ⟩ - i \| V ⟩)$
Left Hand Circular Polarized Typically called LCP or LHCP	$\frac{1}{\sqrt{2}} (\begin{matrix} 1 \\ + i \end{matrix})$	$\| L ⟩ = \frac{1}{\sqrt{2}} (\| H ⟩ + i \| V ⟩)$

When applied to the Poincaré sphere (also known as the Bloch sphere), the basis kets ( $| 0 ⟩$ and $| 1 ⟩$ ) must be assigned to opposing (antipodal) pairs of the kets listed above. For example, one might assign $| 0 ⟩$ = $| H ⟩$ and $| 1 ⟩$ = $| V ⟩$ . These assignments are arbitrary. Opposing pairs are

The $| ψ ⟩$ ket is a general vector that points to any place on the surface. Any point not in the table above and not on the circle that passes through $| H ⟩, | D ⟩, | V ⟩, | A ⟩$ is collectively known as elliptical polarization.

Jones matrices

The Jones matrices are the operators that act on the Jones Vectors as listed above. These matrices are implemented by various optical elements such as lenses, beam splitters, mirrors, etc. The following table gives examples of Jones matrices for polarizers:

Optical element	Corresponding Jones matrix
Linear polarizer with axis of transmission horizontal^[1]	$(\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix})$
Linear polarizer with axis of transmission vertical^[1]	$(\begin{matrix} 0 & 0 \\ 0 & 1 \end{matrix})$
Linear polarizer with axis of transmission at ±45° with the horizontal^[1]	$\frac{1}{2} (\begin{matrix} 1 & \pm 1 \\ \pm 1 & 1 \end{matrix})$
Right circular polarizer^[1]	$\frac{1}{2} (\begin{matrix} 1 & i \\ - i & 1 \end{matrix})$
Left circular polarizer^[1]	$\frac{1}{2} (\begin{matrix} 1 & - i \\ i & 1 \end{matrix})$
Linear polarizer with axis of transmission at angle $θ$ with the horizontal. (Shown construction from rotating up from the horizontal into the polarizing element, the polarizing element, and then rotating back down into the horizontal.)	$(\begin{matrix} \cos^{2} (θ) & \cos (θ) \sin (θ) \\ \sin (θ) \cos (θ) & \sin^{2} (θ) \end{matrix}) =$ $(\begin{matrix} \cos (θ) & - \sin (θ) \\ \sin (θ) & \cos (θ) \end{matrix}) (\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}) (\begin{matrix} \cos (- θ) & - \sin (- θ) \\ \sin (- θ) & \cos (- θ) \end{matrix})$

Phase retarders

Phase retarders introduce a phase shift between the vertical and horizontal component of the field and thus change the polarization of the beam. Phase retarders are usually made out of birefringent uniaxial crystals such as calcite, MgF₂ or quartz. Uniaxial crystals have one crystal axis that is different from the other two crystal axes (i.e., n_i ≠ n_j = n_k). This unique axis is called the extraordinary axis and is also referred to as the optic axis. An optic axis can be the fast or the slow axis for the crystal depending on the crystal at hand. Light travels with a higher phase velocity through an axis that has the smallest refractive index and this axis is called the fast axis. Similarly, an axis which has the highest refractive index is called a slow axis since the phase velocity of light is the lowest along this axis. Negative uniaxial crystals (e.g., calcite CaCO₃, sapphire Al₂O₃) have n_e < n_o so for these crystals, the extraordinary axis (optic axis) is the fast axis whereas for positive uniaxial crystals (e.g., quartz SiO₂, magnesium fluoride MgF₂, rutile TiO₂), n_e > n _o and thus the extraordinary axis (optic axis) is the slow axis.

Any phase retarder with fast axis vertical or horizontal has zero off-diagonal terms and thus can be conveniently expressed as

(\begin{matrix} e^{i ϕ_{x}} & 0 \\ 0 & e^{i ϕ_{y}} \end{matrix})

where, $ϕ_{x}$ and $ϕ_{y}$ are the phases of the electric fields in $x$ and $y$ directions respectively. In the phase convention $ϕ = k z - ω t$ , the relative phase between the two waves when represented as $ϵ = ϕ_{y} - ϕ_{x}$ suggests that a positive $ϵ$ (i.e., $ϕ_{y}$ > $ϕ_{x}$ ) means that $E_{y}$ doesn't attain the same value as $E_{x}$ until a later time i.e., $E_{x}$ leads $E_{y}$ . Similarly, if $ϵ < 0$ i.e., $ϕ_{x}$ > $ϕ_{y}$ , $E_{y}$ leads $E_{x}$ . For e.g., if the fast axis of a quarter wave plate is horizontal, this suggests that the phase velocity along the horizontal direction is faster than that in the vertical direction i.e., $E_{x}$ leads $E_{y}$ . Thus, $ϕ_{x} < ϕ_{y}$ which for a quarter wave plate suggests that $ϕ_{y} = ϕ_{x} + π / 2$ .

In the opposite convention $ϕ = ω t - k z$ , the relative phase when defined as $ϵ = ϕ_{x} - ϕ_{y}$ suggests that a positive $ϵ$ means that $E_{y}$ doesn't attain the same value as $E_{x}$ until a later time i.e., $E_{x}$ leads $E_{y}$ .

Phase retarders	Corresponding Jones matrix
Quarter-wave plate with fast axis vertical^[2]^{[note 1]}	$e^{i π / 4} (\begin{matrix} 1 & 0 \\ 0 & - i \end{matrix})$
Quarter-wave plate with fast axis horizontal^[2]	$e^{i π / 4} (\begin{matrix} 1 & 0 \\ 0 & i \end{matrix})$
Half-wave plate with fast axis at angle $θ$ w.r.t the horizontal axis^[3]	$(\begin{matrix} \cos 2 θ & \sin 2 θ \\ \sin 2 θ & - \cos 2 θ \end{matrix})$
Any birefringent material (phase retarder)^[4]	$(\begin{matrix} e^{i ϕ_{x}} \cos^{2} θ + e^{i ϕ_{y}} \sin^{2} θ & (e^{i ϕ_{x}} - e^{i ϕ_{y}}) \cos θ \sin θ \\ (e^{i ϕ_{x}} - e^{i ϕ_{y}}) \cos θ \sin θ & e^{i ϕ_{x}} \sin^{2} θ + e^{i ϕ_{y}} \cos^{2} θ \end{matrix})$

The special expressions for the phase retarders can be obtained by using the general expression for a birefringent material. In the above expression:

Phase retardation induced between $E_{x}$ and $E_{y}$ by a birefringent material is given by $ϕ_{y} - ϕ_{x}$
$θ$ is the orientation of the fast axis with respect to the x-axis.
$ϕ$ is the circularity (For linear retarders, $ϕ$ = 0 and for circular retarders, $ϕ$ = ± $π$ /2. For elliptical retarders, it takes on values between - $π$ /2 and $π$ /2).

Rotated elements

Assume an optical element has its optic axis perpendicular to the surface vector for the plane of incidence and is rotated about this surface vector by angle θ/2 (i.e., the principal plane, through which the optic axis passes, makes angle θ/2 with respect to the plane of polarization of the electric field of the incident TE wave). Recall that a half-wave plate rotates polarization as twice the angle between incident polarization and optic axis (principal plane). Therefore, the Jones matrix for the rotated polarization state, M(θ), is

M (θ) = R (θ) M R (- θ),

where

R (θ) = (\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix}) .

This agrees with the expression for a half-wave plate in the table above. These rotations are identical to beam unitary splitter transformation in optical physics given by

R (θ) = (\begin{matrix} r & t^{'} \\ t & r^{'} \end{matrix})

where the primed and unprimed coefficients represent beams incident from opposite sides of the beam splitter. The reflected and transmitted components acquire a phase θ_r and θ_t, respectively. The requirements for a valid representation of the element are ^[5]

θ_{t} - θ_{r} + θ_{t'} - θ_{r'} = \pm π

and $r^{*} t^{'} + t^{*} r^{'} = 0 .$

Both of these representations are unitary matrices fitting these requirements; and as such, are both valid.

Notes

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References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

E. Collett, Field Guide to Polarization, SPIE Field Guides vol. FG05, SPIE (2005). ISBN 0-8194-5868-6.
D. Goldstein and E. Collett, Polarized Light, 2nd ed., CRC Press (2003). ISBN 0-8247-4053-X.
E. Hecht, Optics, 2nd ed., Addison-Wesley (1987). ISBN 0-201-11609-X.
Frank L. Pedrotti, S.J. Leno S. Pedrotti, Introduction to Optics, 2nd ed., Prentice Hall (1993). ISBN 0-13-501545-6
A. Gerald and J.M. Burch, Introduction to Matrix Methods in Optics,1st ed., John Wiley & Sons(1975). ISBN 0-471-29685-6
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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

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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
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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
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
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
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
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
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
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
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
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
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
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

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External links

Jones Calculus written by E. Collett on Optipedia

↑ ^1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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↑ ^2.0 ^2.1 ^2.2 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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↑ Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix, Optik, Jose Jorge Gill and Eusebio Bernabeu,76, 67-71 (1987).
↑ Am. J. Phys. 57 (1), 66 (1988).

Cite error: <ref> tags exist for a group named "note", but no corresponding <references group="note"/> tag was found

[fowles-1] 1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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[hecht-2] 2.0 ^2.1 ^2.2 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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[4] 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

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[5] Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix, Optik, Jose Jorge Gill and Eusebio Bernabeu,76, 67-71 (1987).

[hong-ou-mandel-6] Am. J. Phys. 57 (1), 66 (1988).

[1]

[2]

[note 1]

[3]

[4]

[5]

Just intonation: Difference between revisions

Revision as of 16:07, 3 February 2014

Contents

Jones vectors

Jones matrices

Phase retarders

Rotated elements

See also

Notes

References

External links

Navigation menu

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+In [[optics]], [[polarized light]] can be described using the '''Jones calculus''', discovered by [[Robert Clark Jones|R. C. Jones]] in 1941. Polarized light is represented by a '''Jones vector''', and linear optical elements are represented by ''Jones [[matrix (mathematics)|matrices]]''. When light crosses an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light.
+Note that Jones calculus is only applicable to light that is already fully polarized. Light which is randomly polarized, partially polarized, or incoherent must be treated using [[Mueller calculus]].
+== Jones vectors ==
+The Jones vector describes the polarization of  light.
+The ''x'' and ''y'' components of the complex amplitude of the electric field of light travel along ''z''-direction, <math>E_x(t)</math> and <math>E_y(t)</math>, are represented as
+:<math>\begin{pmatrix} E_x(t) \\ E_y(t)\end{pmatrix}
+= \begin{pmatrix} E_{0x} e^{i(kz- \omega t+\phi_x)} \\ E_{0y} e^{i(kz- \omega t+\phi_y)} \end{pmatrix}
+=\begin{pmatrix} E_{0x} e^{i\phi_x} \\ E_{0y} e^{i\phi_y} \end{pmatrix}e^{i(kz- \omega t)}  </math>.
+Here <math>\begin{pmatrix} E_{0x} e^{i\phi_x} & E_{0y} e^{i\phi_y} \end{pmatrix}^\top </math> is the Jones vector (<math> i </math> is the [[imaginary unit]] with <math>i^2=-1</math>).
+Thus, the Jones vector represents (relative) amplitude and (relative) phase of electric field in ''x'' and ''y''  directions.
+The sum of the squares of the absolute values of the two components of Jones vectors is proportional to the intensity of light.  It is common to normalize it to 1 at the starting point of calculation for simplification.  It is also common to constrain the first component of the Jones vectors to be a [[real number]]. This discards the phase information needed for calculation of [[Interference (wave propagation)|interference]] with other beams.  Note that all Jones vectors and matrices on this page assumes that the phase of the light wave is <math>\phi = kz - \omega t</math>, which is used by Hecht.  In this definition, increase in <math>\phi_x</math> (or <math>\phi_y</math>) indicates retardation (delay) in phase, while decrease indicates advance in phase.  For example, a Jones vectors component of <math>i</math> (<math>=e^{i\pi/2}</math>) indicates retardation by <math> \pi/2</math> (or 90 degree) compared to 1 (<math>=e^{0}</math>).  Collett uses the opposite definition (<math>\phi = \omega t - kz</math>).  The reader should be wary when consulting references on Jones calculus.
+The following table gives the 6 common examples of normalized Jones vectors.
+{| class="wikitable"
+| '''Polarization''' || '''Corresponding Jones vector''' || '''Typical [[Bra-ket notation|ket]] Notation'''
+|-
+| Linear polarized in the x-direction<BR>Typically called 'Horizontal' || <math>\begin{pmatrix} 1 \\ 0 \end{pmatrix}</math> || <math> |H\rangle </math>
+|-
+| Linear polarized in the y-direction<BR>Typically called 'Vertical' || <math>\begin{pmatrix} 0 \\ 1 \end{pmatrix}</math> || <math> |V\rangle </math>
+|-
+| Linear polarized at 45° from the x-axis<BR>Typically called 'Diagonal' L+45 || <math>\frac{1}{\sqrt2} \begin{pmatrix} 1 \\ 1 \end{pmatrix}</math> || <math> |D\rangle = \frac{1}{\sqrt2} ( |H\rangle + |V\rangle ) </math>
+|-
+| Linear polarized at −45° from the x-axis<BR>Typically called 'Anti-Diagonal' L-45 || <math>\frac{1}{\sqrt2} \begin{pmatrix} 1 \\ -1 \end{pmatrix}</math> || <math> |A\rangle = \frac{1}{\sqrt2} ( |H\rangle - |V\rangle ) </math>
+|-
+| Right Hand Circular Polarized<BR>Typically called RCP or RHCP || <math>\frac{1}{\sqrt2} \begin{pmatrix} 1 \\ -i \end{pmatrix}</math> || <math>| R\rangle = \frac{1}{\sqrt2} ( |H\rangle - i |V\rangle ) </math>
+|-
+| Left Hand Circular Polarized<BR>Typically called LCP or LHCP || <math>\frac{1}{\sqrt2} \begin{pmatrix} 1 \\ +i \end{pmatrix}</math> || <math> |L\rangle  = \frac{1}{\sqrt2} ( |H\rangle + i |V\rangle ) </math>
+|}
+When applied to the [[Poincaré sphere]] (also known as the [[Bloch sphere]]), the basis kets (<math>|0\rangle</math> and <math>|1\rangle</math>) must be assigned to opposing ([[Antipodal points|antipodal]]) pairs of the kets listed above.  For example, one might assign <math>|0\rangle</math> = <math>|H\rangle</math> and <math>|1\rangle</math> = <math>|V\rangle</math>.  These assignments are arbitrary.  Opposing pairs are
+* <math>|H\rangle</math> and <math>|V\rangle</math>
+* <math>|D\rangle</math> and <math>|A\rangle</math>
+* <math>|R\rangle</math> and <math>|L\rangle</math>
+The <math>|\psi\rangle</math> [[Bra-ket notation|ket]] is a general vector that points to any place on the surface.  Any point not in the table above and not on the circle that passes through <math>|H\rangle, |D\rangle, |V\rangle, |A\rangle</math> is collectively known as [[elliptical polarization]].
+== Jones matrices ==
+The Jones matrices are the operators that act on the Jones Vectors as listed above.  These matrices are implemented by various optical elements such as lenses, beam splitters, mirrors, etc.  The following table gives examples of Jones matrices for polarizers:
+{| class="wikitable" style="text-align:center"
+| '''Optical element''' || '''Corresponding Jones matrix'''
+|-
+| Linear [[polarizer]] with axis of transmission horizontal<ref name="fowles">{{cite book|author=Fowles, G.|title=Introduction to Modern Optics|edition=2nd|publisher=Dover|year=1989|page=35}}</ref> ||
+<math>\begin{pmatrix}
+& 0 \\ 0 & 0
+\end{pmatrix}</math>
+|-
+| Linear polarizer with axis of transmission vertical<ref name="fowles" /> ||
+<math>\begin{pmatrix}
+& 0 \\ 0 & 1
+\end{pmatrix}</math>
+|-
+| Linear polarizer with axis of transmission at ±45° with the horizontal<ref name="fowles" /> ||
+<math>\frac{1}{2} \begin{pmatrix}
+& \pm 1 \\ \pm 1 & 1
+\end{pmatrix}</math>
+|-
+| Right circular polarizer<ref name="fowles" /> ||
+<math>\frac{1}{2} \begin{pmatrix}
+& i \\ -i & 1
+\end{pmatrix}
+</math>
+|-
+| Left circular polarizer<ref name="fowles" /> ||
+<math>\frac{1}{2} \begin{pmatrix}
+& -i \\ i & 1
+\end{pmatrix}</math>
+|-
+| Linear polarizer with axis of transmission at angle <math>\theta</math> with the horizontal. (Shown construction from rotating up from the horizontal into the polarizing element, the polarizing element, and then rotating back down into the horizontal.) ||
+<math>\begin{pmatrix}
+\cos^2(\theta) & \cos(\theta)\sin(\theta) \\
+\sin(\theta)\cos(\theta) & \sin^2(\theta)
+\end{pmatrix} =
+</math>
+<br>
+<math>
+\begin{pmatrix}
+\cos(\theta) & -\sin(\theta) \\
+\sin(\theta) & \cos(\theta)
+\end{pmatrix}
+\begin{pmatrix}
+& 0 \\
+& 0
+\end{pmatrix}
+\begin{pmatrix}
+\cos(-\theta) & -\sin(-\theta) \\
+\sin(-\theta) & \cos(-\theta)
+\end{pmatrix}</math>
+<br />
+|}
+== Phase retarders ==
+Phase retarders introduce a phase shift between the vertical and horizontal component of the field and thus change the polarization of the beam. Phase retarders are usually made out of [[birefringent]] [[uniaxial crystal]]s such as [[calcite]], MgF<sub>2</sub> or [[quartz]]. Uniaxial crystals have one crystal axis that is different from the other two crystal axes (i.e., ''n<sub>i</sub>'' ≠ ''n<sub>j</sub>'' = ''n<sub>k</sub>''). This unique axis is called the extraordinary axis and is also referred to as the [[optic axis of a crystal|optic axis]]. An optic axis can be the fast or the slow axis for the crystal depending on the crystal at hand. Light travels with a higher phase velocity through an axis that has the smallest [[refractive index]] and this axis is called the fast axis. Similarly, an axis which has the highest refractive index is called a slow axis since the [[phase velocity]] of light is the lowest along this axis. Negative uniaxial crystals (e.g., [[calcite]] CaCO<sub>3</sub>, [[sapphire]] Al<sub>2</sub>O<sub>3</sub>) have ''n<sub>e</sub>'' < ''n<sub>o</sub>'' so for these crystals, the extraordinary axis (optic axis) is the fast axis whereas for positive uniaxial crystals (e.g., [[quartz]] SiO<sub>2</sub>, [[magnesium fluoride]] MgF<sub>2</sub>, [[rutile]] TiO<sub>2</sub>), ''n<sub>e</sub>'' > ''n <sub>o</sub>'' and thus the extraordinary axis (optic axis) is the slow axis.
+Any phase retarder with fast axis vertical or horizontal has zero off-diagonal terms and thus can be conveniently expressed as
+:<math>
+\begin{pmatrix}
+e^{i\phi_x} & 0 \\ 0 & e^{i\phi_y}
+\end{pmatrix} </math>
+where, <math>\phi_x</math> and <math>\phi_y</math> are the phases of the electric fields in <math>x</math> and <math>y</math> directions respectively. In the phase convention <math>\phi = kz - \omega t</math>, the relative phase between the two waves when represented as <math>\epsilon = \phi_y - \phi_x</math> suggests that a positive <math>\epsilon</math> (i.e., <math>\phi_y</math> > <math>\phi_x</math>) means that <math>E_y</math> doesn't attain the same value as <math>E_x</math> until a later time i.e., <math>E_x</math> leads <math>E_y</math>. Similarly, if <math>\epsilon < 0</math> i.e., <math>\phi_x</math> > <math>\phi_y</math>, <math>E_y</math> leads <math>E_x</math>.
+For e.g., if the fast axis of a quarter wave plate is horizontal, this suggests that the phase velocity along the horizontal direction is faster than that in the vertical direction i.e., <math>E_x</math> leads <math>E_y</math>. Thus, <math>\phi_x < \phi_y</math> which for a quarter wave plate suggests that <math>\phi_y = \phi_x + \pi/2</math>.
+In the opposite convention <math>\phi = \omega t - kz</math>, the relative phase when defined as <math>\epsilon = \phi_x - \phi_y</math> suggests that a positive <math>\epsilon</math> means that <math>E_y</math> doesn't attain the same value as <math>E_x</math> until a later time i.e., <math> E_x</math> leads <math>E_y</math>.
+{| class="wikitable"
+! Phase retarders !! Corresponding Jones matrix
+|-
+| [[wave plate|Quarter-wave plate]] with fast axis vertical<ref name="hecht">{{cite book|author=Hecht, E.|title=Optics|edition=4th|year=2001|page=378|isbn=0805385665}}</ref>{{#tag:ref|The prefactor <math>e^{i\pi/4}</math> appears only if one defines the phase delays in a symmetric fashion; that is, <math>\phi_x = -\phi_y = \pi/4</math>. This is done in Hecht<ref name="hecht" /> but not in Fowles.<ref name="fowles" /> In the latter reference the Jones matrices for a quarter-wave plate have no prefactor.|group="note"}} ||
+<math> e^{i \pi/4}
+\begin{pmatrix}
+& 0 \\ 0 & -i
+\end{pmatrix} </math>
+|-
+| [[wave plate|Quarter-wave plate]] with fast axis horizontal<ref name="hecht" /> ||
+<math> e^{i \pi/4}
+\begin{pmatrix}
+& 0 \\ 0 & i
+\end{pmatrix} </math>
+|-
+| [[wave plate|Half-wave plate]] with fast axis at angle <math>\theta</math> w.r.t the horizontal axis<ref>{{cite book|author=Gerald, A.|author2=Burch, J.M.|title=Introduction to Matrix Methods in Optics|edition=1st|publisher=John Wiley & Sons|year=1975|isbn=0471296856}}</ref>||
+<math>\begin{pmatrix}
+\cos2\theta & \sin2\theta \\ \sin2\theta & -\cos2\theta
+\end{pmatrix}</math>
+|-
+| Any birefringent material (phase retarder)<ref>''Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix'', [[Optik (journal)|Optik]], Jose Jorge Gill and Eusebio Bernabeu,'''76''', 67-71 (1987).</ref> ||
+<math>\begin{pmatrix}
+ e^{i\phi_x} \cos^2\theta+e^{i\phi_y} \sin^2\theta & (e^{i\phi_x}-e^{i\phi_y}) \cos\theta \sin\theta \\ (e^{i\phi_x}-e^{i\phi_y}) \cos\theta \sin\theta & e^{i\phi_x} \sin^2\theta+e^{i\phi_y} \cos^2\theta
+\end{pmatrix}
+</math><br />
+|}
+The special expressions for the phase retarders can be obtained by using the general expression for a birefringent material. In the above expression:
+*Phase retardation induced between <math>E_x</math> and <math>E_y</math> by a birefringent material is given by <math> \phi_y - \phi_x </math>
+*<math>\theta</math> is the orientation of the fast axis with respect to the x-axis.
+*<math>\phi</math> is the circularity (For linear retarders, <math>\phi</math> = 0 and for circular retarders, <math>\phi</math> = ± <math>\pi</math>/2. For elliptical retarders, it takes on values between - <math>\pi</math>/2 and <math>\pi</math>/2).
+== Rotated elements ==
+Assume an optical element has its optic axis perpendicular to the surface vector for the plane of incidence and is rotated about this surface vector by angle ''θ/2'' (i.e., the principal plane, through which the optic axis passes, makes angle ''θ/2'' with respect to the plane of polarization of the electric field of the incident TE wave). Recall that a half-wave plate rotates polarization as ''twice'' the angle between incident polarization and optic axis (principal plane). Therefore, the Jones matrix for the rotated polarization state, M(''θ''), is
+:<math>M(\theta )=R(\theta )\,M\,R(-\theta ),</math>
+: where <math>R(\theta ) =
+\begin{pmatrix}
+\cos \theta & -\sin \theta \\
+\sin \theta & \cos \theta
+\end{pmatrix}.</math>
+This agrees with the expression for a half-wave plate in the table above. These rotations are identical to beam unitary splitter transformation in optical physics given by
+:<math>R(\theta ) =
+\begin{pmatrix}
+r & t'\\
+t & r'
+\end{pmatrix}</math>
+where the primed and unprimed coefficients represent beams incident from opposite sides of the beam splitter. The reflected and transmitted components acquire a phase ''θ<sub>r</sub>'' and ''θ<sub>t</sub>'', respectively. The requirements for a valid representation of the element are <ref name=hong-ou-mandel>Am. J. Phys. 57 (1), 66 (1988).</ref>
+:<math>
+\theta_\text{t} - \theta_\text{r} + \theta_\text{t'} - \theta_\text{r'} = \pm \pi
+</math>
+and
+<math>r^*t' + t^*r' = 0.</math>
+:Both of these representations are unitary matrices fitting these requirements; and as such, are both valid.
+==See also==
+* [[Mueller calculus]]
+* [[Stokes parameters]]
+* [[Photon polarization|Polarization]]
+==Notes==
+{{reflist|group="note"}}
+==References==
+{{reflist}}
+* E. Collett, ''Field Guide to Polarization'', SPIE Field Guides vol. '''FG05''', SPIE (2005). ISBN 0-8194-5868-6.
+* D. Goldstein and E. Collett, ''Polarized Light'', 2nd ed., CRC Press (2003). ISBN 0-8247-4053-X.
+* E. Hecht, ''Optics'', 2nd ed., Addison-Wesley (1987). ISBN 0-201-11609-X.
+* Frank L. Pedrotti, S.J. Leno S. Pedrotti, ''Introduction to Optics'', 2nd ed., Prentice Hall (1993). ISBN 0-13-501545-6
+* A. Gerald and J.M. Burch, ''Introduction to Matrix Methods in Optics'',1st ed., John Wiley & Sons(1975). ISBN 0-471-29685-6
+* {{Cite journal
+|first1=R. Clark
+|last1=Jones
+|title=A new calculus for the treatment of optical systems, I. Description and Discussion of the Calculus
+|journal=Journal of the Optical Society of America
+|volume=31
+|issue=7
+|pages=488&ndash;493
+|doi=10.1364/JOSA.31.000488
+|year=1941}}
+* {{Cite journal
+|first1=Henry
+|last1=Hurwitz
+|first2=R. Clark
+|last2=Jones
+|title=A new calculus for the treatment of optical systems, II. Proof of three general equivalence theorems
+|journal=Journal of the Optical Society of America
+|volume=31
+|issue=7
+|pages=493&ndash;499
+|doi=10.1364/JOSA.31.000493
+|year=1941}}
+* {{Cite journal
+|first1=R. Clark
+|last1=Jones
+|title=A new calculus for the treatment of optical systems, III The Sohncke Theory of optical activity
+|journal=Journal of the Optical Society of America
+|volume=31
+|issue=7
+|pages=500&ndash;503
+|doi=10.1364/JOSA.31.000500
+|year=1941}}
+* {{Cite journal
+|first1=R. Clark
+|last1=Jones
+|title=A new calculus for the treatment of optical systems, IV
+|journal=Journal of the Optical Society of America
+|volume=32
+|issue=8
+|pages=486&ndash;493
+|doi=10.1364/JOSA.32.000486
+|year=1942}}
+* {{Cite journal
+|first1=A. L.
+|last1=Fymat
+|title=Jones's Matrix Representation of Optical Instruments. I: Beam Splitters
+|journal=Applied Optics
+|volume=10
+|issue=11
+|pages=2499&ndash;2505
+|doi=10.1364/AO.10.002499
+|year=1971
+|pmid=20111363|bibcode = 1971ApOpt..10.2499F }}
+* {{Cite journal
+|first1=A. L.
+|last1=Fymat
+|title=Jones's Matrix Representation of Optical Instruments. 2: Fourier Interferometers (Spectrometers and Spectropolarimeters)
+|journal=Applied Optics
+|volume=10
+|issue=12
+|pages=2711&ndash;2716
+|doi=10.1364/AO.10.002711
+|year=1971|bibcode = 1971ApOpt..10.2711F }}
+* {{Cite journal
+|first1=A. L.
+|last1=Fymat
+|title=Polarization Effects in Fourier Spectroscopy. I: Coherency Matrix Representation
+|journal=Applied Optics
+|volume=11
+|issue=1
+|pages=160&ndash;173
+|doi=10.1364/AO.11.000160
+|year=1972
+|pmid=20111472|bibcode = 1972ApOpt..11..160F }}
+* {{Cite journal
+|first1=Jose Jorge
+|last1=Gill
+|first2=Eusebio
+|last2=Bernabeu
+|title=Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar decomposition of its Mueller matrix,
+|journal=Optik
+|volume=76
+|pages=67&ndash;71
+|year=1987}}
+* {{Cite journal
+|first1=Christian
+|last1=Brosseau
+|first2=Clark R.
+|last2=Givens
+|first3=Alexander B.
+|last3=Kostinksi
+|journal=Journal of the Optical Society of America A
+|title=Generalized trace condition on the Mueller-Jones polarization matrix
+|volume=10
+|issue=10
+|pages=2248&ndash;2251
+|doi=10.1364/JOSAA.10.002248
+|year=1993|bibcode = 1993JOSAA..10.2248B }}
+* {{Cite journal
+|first1=James P.
+|last1=McGuire
+|first2=Russel A.
+|last2=Chipman
+|journal=Applied Optics
+|title=Polarization aberrations. 1. Rotationally symmetric optical systems
+|volume=33
+|issue=22
+|pages=5080&ndash;5100
+|doi=10.1364/AO.33.005080
+|year=1994
+|pmid=20935891}}
+* {{Cite journal
+|first1=Natale C.
+|last1=Pistoni
+|journal=Applied Optics
+|title=Simplified approach to the Jones calculus in retracing optical circuits
+|volume=34
+|issue=34
+|pages=7870&ndash;7876
+|doi=10.1364/AO.34.007870
+|year=1995
+|pmid=21068881|bibcode = 1995ApOpt..34.7870P }}
+* {{Cite journal
+|first1=Ignacio
+|last1=Moreno
+|first2=Maria J.
+|last2=Yzuel
+|first3=Juan
+|last3=Campos
+|first4=Asticio
+|last4=Vargas
+|journal=Journal of Modern Optics
+|title=Jones matrix treatment for polarization Fourier optics
+|volume=51
+|issue=14
+|pages=2031&ndash;2038
+|doi=10.1080/09500340408232511
+|year=2004|bibcode = 2000JMOp...51.2031M }}
+* {{Cite journal
+|first1=Ivan
+|last1=Moreno
+|journal=Applied Optics
+|title=Jones matrix for image-rotation prisms
+|volume=43
+|issue=17
+|pages=3373&ndash;3381
+|doi=10.1364/AO.43.003373
+|year=2004
+|pmid=15219016|bibcode = 2004ApOpt..43.3373M }}
+==External links==
+* [http://spie.org/x32380.xml ''Jones Calculus written by E. Collett on Optipedia'']
+{{DEFAULTSORT:Jones Calculus}}
+[[Category:Optics]]
+[[Category:Polarization (waves)]]
+[[Category:Matrices]]

Just intonation: Difference between revisions

Revision as of 16:07, 3 February 2014

Jones vectors

Jones matrices

Phase retarders

Rotated elements

See also

Notes

References

External links

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