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[[Image:Fig1wikiXPW.png|thumb|right|325px|Fig. 1.]]
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'''Cross polarized wave''' (XPW) generation is a [[nonlinear optics|nonlinear optical process]] that can be classified in the group of  frequency degenerate [four wave mixing] processes. It can take place only in media with anisotropy of third order nonlinearity. As a result of such nonlinear optical interaction at the output of the nonlinear crystal it is generated a new linearly polarized wave at the same [[frequency]], but with polarization oriented perpendicularly to the polarization of input wave
 
<math>\omega^{(\perp)}~=~\omega^{(\|)}~+~\omega^{(\|)}~-~\omega^{(\|)}</math>.
 
Simplified optical scheme for XPW generation is shown on Fig. 1. It consists of a nonlinear crystal plate (thick 1-2&nbsp;mm) sandwiched between two crossed polarizers. The intensity of generated XPW  has cubic dependence with respect to the intensity of the input wave. In fact this is the main reason this effect is so successful for improvement of the contrast of the temporal and spatial profiles of femtosecond pulses. Since  cubic crystals are used as nonlinear media they are isotropic with respect to linear properties (there is no birefringence) and because of that the phase and group velocities of both waves XPW and the fundamental wave(FW) are equal:V<sub>XPW</sub>=V<sub>FW</sub> and V<sub>gr,XPW</sub>=V<sub>gr,FW</sub>. Consequence of that is ideal phase and group velocity matching for the two waves propagating along the crystal. This property allows obtaining very good efficiency of the XPW generation process with minimum distortions of the pulse shape and the spectrum.
 
==Description of the process==
Let us consider the case of interaction of two perpendicularly polarized waves in nonlinear  media with cubic nonlinearity [1]. The equations describing the self phase modulation of the fundamental wave '''A''' and the generation of new wave perpendicularly polarized wave '''B''' in condition that |B| << |A| (i.e. when the depletion of the fundamental wave is neglected, self and cross phase modulation of wave '''B''')  can be written in following form:
 
[[Image:Fig2wikiXPW.png|thumb|right|325px|Fig. 2. Dependence of the efficiency of XPW generation for three different time and spatial profiles: rectangular (top hat) in space and Gaussian in time (gray solid line); Gaussian in time and space (dash line); rectangular in time and space, i. e. plane wave (black solid line).]]
 
:<math>\frac{d A}{dz} =-i \gamma_{\|}|A|^2A</math>,
 
:<math>\frac{d B}{dz} =-i \gamma_{\perp}|A|^2A</math>,
 
where <math>\gamma_{\|}</math> and <math>\gamma_{\perp}</math> are coefficients that depend on (i) the orientation of the sample with respect to the crystal axes (see [3] for the expressions for two popular orientations:  Z-cut  and for holographic cut); (ii) the component  <math>\chi^{(3)}_{xxxx} </math> and (iii) anisotropy of <math>\chi^{(3)}_{} </math> tensor.
 
The solution of this simplified system with initial conditions А(0)=А<sub>0</sub> and B&nbsp;(0)&nbsp;=&nbsp;0 is:
 
:<math> A = A_0 e^{-i \gamma_{||} |A|^2L} </math>,
 
:<math> B = A_0 \frac{\gamma_{\perp}}{\gamma_{||}}(e^{-i \gamma_{||} |A|^2L}-1) </math>,
 
where L is the length of the nonlinear media. In case of CW pump, the efficiency <math>\eta</math>, that is defined as ratio of  XPW intensity I<sub>out</sub> at the output of the nonlinear media to the intensity of the input wave I<sub>in</sub> can be described by sin<sup>2</sup> function of input intensity × length product:
 
(1)    &nbsp; &nbsp;  &nbsp; &nbsp;  <math>\eta=\frac{|B(L)|^2}{|A_0|^2}=\frac{I_{out}}{I_{in}} =4(\frac{\gamma_{\perp}}{\gamma_{||}})^2 \sin^2(\gamma_{||} |A|^2L/2)</math>.
 
If self phase modulation is relatively small  <math>\gamma_{\|} |A|^{2}L \leq 1</math> then:
 
(2)    &nbsp; &nbsp; &nbsp; &nbsp;  <math>\eta =({\gamma_{\perp}})^2 |A|^4L^2 \propto \gamma_{\perp}^2I_{in}^2L^2</math>.
 
[[Image:Fig3wikiXPW.png|thumb|left|325px|Fig. 3. Experimentally measured XPW generation efficiency as a function of input energy (in μJ) with use of BaF2 crystal(s) for one crystal scheme (upper plot) and two crystal scheme (lower plot).]]
 
The last expression (2) indicates that when nonlinear phase shift of the fundamental wave <math>\gamma_{\|} |A|^{2}L</math> is relatively small the efficiency grows as square of input intensity. The increase of the nonlinear phase shift above 3 prevents the coherent growing of XPW signal and leads in principle to periodical dependence of the efficiency as a function of input intensity. The use of two crystal scheme [2,3] allows this problem to be overcome.
 
Accounting the temporal and spatial shapes leads to reduction of the predicted by expression (1) efficiency. This is illustrated on Fig. 2 where  the exact solution with all processes accompanying the effect of generation of XPW taken into account is given. The maximum XPW efficiency obtained with single crystal scheme approaches 12% for Gaussian in  space and in time, while for top-hat spatial profile and Gaussian in time the maximum achieved efficiency is 29%. This behavior is direct consequence of the nonlinearity of the process.  Typical experimental results for generation of XPW in BaF2 crystal are shown in Fig. 3. It is seen the efficiency of XPW process in single crystal scheme saturates close to 10%, while with two crystal scheme one can achieve 20–30% efficiency for XPW generation [2,3].  
 
The effect of XPW generation is finding application for enhancement of the temporal contrast of femtosecond pulses [4] and for their monitoring and control. The approach of XPW generation for cleaning femtosecond pulses will be used in the '''Extreme Light Infrastructure''' European project.
 
==For additional reading==
 
[1] N. Minkovski et al., Opt. Lett., vol. 27, pp. 2025–2027 (2002); N. Minkovski et al., J. Opt. Soc. Am. B, vol. 21, pp. 1659–1664 (2004).
 
[2] A. Jullien et al., Opt. Express, vol. 14, pp. 2760–2769 (2006); A. Jullien et al., Appl. Phys. B, vol. 84, pp. 409–414 (2006).
 
[3] L. Canova et al., Appl. Phys. Lett., vol. 92, pp. 231102_1-3 (2008).
 
[4] A. Jullien et al.,Opt. Lett., vol. 30, pp.920–922 (2005);  V. Chvykov et al., Opt.
Lett., vol. 31, pp. 1456–1458 (2006).
 
[[Category:Nonlinear optics|Cross polarized wave generation]]

Revision as of 08:56, 5 March 2014

If an existing Word - Press code is found vulnerable, Word - Press will immediately issue an update for that. It is thus, on these grounds that compel various web service provider companies to integrate the same in their packages too. Should you go with simple HTML or use a platform like Wordpress. 2- Ask for the designs and graphics that will be provided along with the Word - Press theme. The number of options offered here is overwhelming, but once I took the time to begin to review the video training, I was amazed at how easy it was to create a squeeze page and a membership site.

Word - Press is known as the most popular blogging platform all over the web and is used by millions of blog enthusiasts worldwide. Wordpress have every reason with it which promote wordpress development. Some plugins ask users to match pictures or add numbers, and although effective, they appear unprofessional and unnecessary. So, if you are looking for some option to build a giant e-commerce website, then e-shopping preferable CMS tools will be helpful for you. Word - Press makes it possible to successfully and manage your website.

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If all else fails, please leave a comment on this post with the issue(s) you're having and help will be on the way. As an example, if you are promoting a product that cures hair-loss, you most likely would not wish to target your adverts to teens. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. The company gains commission from the customers' payment. Wordpress template is loaded with lots of prototype that unite graphic features and content area.

Every single module contains published data and guidelines, usually a lot more than 1 video, and when pertinent, incentive links and PDF files to assist you out. Being a Plugin Developer, it is important for you to know that development of Word - Press driven website should be done only when you enable debugging. It's not a secret that a lion share of activity on the internet is takes place on the Facebook. Page speed is an important factor in ranking, especially with Google. Should you have virtually any queries regarding where as well as the best way to employ wordpress dropbox backup, you can e mail us at our own website. For your information, it is an open source web content management system.

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