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The '''spin angular momentum of light''' (SAM) is the component of [[angular momentum]] of a light beam that can be associated with its [[circle|circular]] or elliptical [[Polarization (waves)|polarization]].
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A number of the great things about these fatty acids are minimizing irritation and reducing cholesterol.<br><br>Nourishment is often forgotten by many people, and a lot people also aren't knowledgeable enough concerning the proper nutrients selections. After you have read this information and facts, you happen to be now prepared to make much better alternatives. Remember the following tips whenever you go food shopping.
[[File:Sam v1.png|thumb|right|400px|Left and right handed circular polarization, and their associate angular momenta.]]
An [[electromagnetic wave]] is said to have [[circular polarization]] when its [[electric]] and [[magnetic field]]s rotate continuously around the beam axis during the propagation. The [[circular polarization]] is left (<math>L</math>) or right (<math>R</math>) depending on the field rotation direction (but be careful that both conventions are used in science, depending on the subfield).
 
When a light beam is circularly polarized, each of its [[photon]]s carries a spin angular momentum of <math>\pm\hbar</math>, where <math>\hbar</math> is the [[reduced Planck constant]] and the <math>\pm</math> sign is positive for '''Left''' and negative for '''Right''' circular polarizations (this is adopting the convention most commonly used in [[optics]]). This SAM is directed along the beam axis (parallel if positive, antiparallel if negative).
The above figure shows the instantaneous structure of the electric field of left (<math>L</math>) and right (<math>R</math>) circularly polarized light in space. The green arrows indicate the [[Wave propagation|propagation]] direction.              
 
The mathematical expressions reported under the figures give the three electric field components of circularly polarized plane wave propagating in the <math>z</math>-direction, in [[complex number|complex]] notation.
 
== Mathematical expression ==
In the following the main formula used for the spin angular momentum of light are given: General expression (paraxial limit only):<ref>{{cite journal|last=Belintante|first=F. J.|title=On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields|journal=Physica|year=1940|volume=7|pages=449|doi=10.1016/S0031-8914(40)90091-X|issue=5|bibcode = 1940Phy.....7..449B }}</ref>
 
:<math>\mathbf{S}=\epsilon_0\int \left(\mathbf{E}\times\mathbf{A}\right)d^{3}\mathbf{r} ,</math>
 
where <math>\mathbf{E}</math> and <math>\mathbf{A}</math> are the [[electric field]] and [[vector potential]], respectively, <math>\epsilon_0</math> is the [[vacuum permittivity]] and we are using SI units.
 
Monochromatic wave case:<ref>{{cite journal|last=Humblet|first=J.|title=Sur le moment d'impulsion d'une onde electromagnetique|journal=Physica (Utrecht)|year=1943|volume=10|pages=585|doi=10.1016/S0031-8914(43)90626-3|issue=7|bibcode = 1943Phy....10..585H }}</ref>
 
:<math>\mathbf{S}= \frac{\epsilon_0}{2i\omega}\int \left(\mathbf{E}^\ast\times\mathbf{E}\right)d^{3}\mathbf{r} .</math>
 
In particular, this expression shows that the SAM is nonzero when the light polarization is elliptical or circular, while it vanishes if the light polarization is linear. In the [[quantum mechanics|quantum theory]] of the electromagnetic field, the SAM is a quantum observable, described by a corresponding operator.
 
:<math>\mathbf{S}=\sum_{\mathbf{k}}\hbar\mathbf{u}_{\mathbf{k}}\left(\hat{a}^{\dagger}_{\mathbf{k},L}\hat{a}_{\mathbf{k},L}-\hat{a}^{\dagger}_{\mathbf{k},R}\hat{a}_{\mathbf{k},R}\right),</math>
 
where <math>\mathbf{u}_{\mathbf{k}}</math> is the unit vector in the propagation direction, <math>\hat{a}^{\dagger}_{\mathbf{k},\pi}</math> and <math>\hat{a}_{\mathbf{k},\pi}</math> are the creation and annihilation operators for photons in the mode {{math|'''k'''}} and polarization state <math>\pi</math>, respectively.  
 
In this case, for a single [[photon]] the SAM can only have two values ([[eigenvalues]] of the SAM operator):
:<math>\mathbf{S}_z=\pm\hbar .</math>
 
The corresponding eigenfunctions describing photons with well defined values of SAM are described as circularly polarized waves:
 
:<math>|\pm\rangle=\frac{1}{\sqrt{2}}\left(\begin{array}[l]{c}
    1\\
    \pm i
    \end{array}\right).</math>
 
==See also==
<div style="-moz-column-count:3; -webkit-column-count:3; column-count:3;">
* [[Angular momentum]]
* [[Angular momentum of light]]
* [[Circular polarization]]
* [[Electromagnetic wave]]
* [[Elliptical polarization]]
* [[Helmholtz equation]]
* [[Light orbital angular momentum]]
* [[Polarization (waves)]]
</div>
 
== References ==
<!--- See http://en.wikipedia.org/wiki/Wikipedia:Footnotes on how to create references using <ref></ref> tags which will then appear here automatically -->
{{Reflist}}
 
==Further reading==
*{{Cite book |last=Born |first=M. |lastauthoramp=yes |last2=Wolf |first2=E. |title=Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light |edition=7th |publisher=Cambridge University Press |location=Cambridge |year=1999 |isbn=0-521-64222-1 }}
*{{Cite book |last=Allen |first=L. |lastauthoramp=yes |last2=Barnnet |first2=Stephen M.|last3=Padgett |first3=Miles J. |title=Optical Angular Momentum |publisher=Institute of Physics |location=Bristol |year=2003 |isbn=978-0-7503-0901-1 }}
*{{Cite book |last= Torres |first=Juan P. |lastauthoramp=yes |last2=Torner |first2= Lluis|title=Twisted Photons: Applications of Light with Orbital Angular Momentum |publisher= Wiley-VCH |location=Bristol |year=2011 |isbn=978-3-527-40907-5 }}
 
== External links ==
* [http://www.phorbitech.eu/ Phorbitech]
* [http://www.physics.gla.ac.uk/Optics/ Glasgow Optics Group]
* [http://www.molphys.leidenuniv.nl/qo/ Leiden Institute of Physics]
* [http://www.icfo.es/ ICFO]
* [http://people.na.infn.it/~marrucci/softmattergroup/ Università Di Napoli "Federico II"]
* [http://quantumoptics.phys.uniroma1.it/homepage.htm Università Di Roma "La Sapienza"]
 
<!--- Categories --->
 
[[Category:Articles created via the Article Wizard]]
[[Category:Light]]

Latest revision as of 12:26, 12 January 2015

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Eat well prior to working out. When you do, it must be dinner which is packed with nutritional vitamins and easy to break down as you may burn fat. Fruit does the work properly. Fats should be eliminated since they have a tendency to sit weighty in the abdomen.

Tend not to consume any snack food items that are bad for you, eliminate them. Buy items that are good for you prefer popcorn, legumes, whole grain products, or greens.

If you have had troubles with irregularity, incorporating far more fresh fruits to your diet can help. Fruit diets provide you with fiber content and are generally delicious.

Eat a healthful meal just before working out. Follow a dinner which will process quickly, but supply a lot of swift vitality. An effective instance of this particular meals are fruit. Try to avoid consuming foods which can be high in excess fat articles before working out since your system has got to continue to work harder to approach high-excess fat food products.

Ingesting a healthy diet regime is a crucial part of nutrition. Whenever you strategy meals and snack food items, it is important to hold the appropriate percentage of your primary nutritional components. For every single dish, 50% of your own unhealthy calories need to originate from carbohydrate food, 20Per cent ought to come from protein, and 30Per cent ought to are derived from fat.

Adding do-it-yourself juices for your diet regime is a wonderful way of getting extra nutritional supplements, along with the fruit and veggies that could be lacking. Introducing veggies to your liquid gives it an added strike. Ginger herb is another wonderful accessory for fruit juices, it brings a zip to juices made from carrots and apples. If you love spicy meals, consider juicing 50 % of a jalapeno and add it to your beverage.

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Eat a healthful treat well before exercising. Choose one thing that will be quickly broken down to get a speedy vitality boost. Fresh fruits is a superb selection. Unhealthy fats should be averted given that they usually rest hefty inside the belly.

A thing that young people need to take into account making use of their diet is incorporating fish-oil nutritional supplements to their diet regime. Seafood skin oils contain important omega3 fatty acids not quickly extracted from other meat. A number of the great things about these fatty acids are minimizing irritation and reducing cholesterol.

Nourishment is often forgotten by many people, and a lot people also aren't knowledgeable enough concerning the proper nutrients selections. After you have read this information and facts, you happen to be now prepared to make much better alternatives. Remember the following tips whenever you go food shopping.