像散椭圆高斯光MATLAB代码

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Untitle1是传播距离为零时的像散椭圆高斯光MATLAB代码;Untitle2是传播距离不为零时的像散椭圆高斯光MATLAB代码; 文件夹里的pdf文件是像散椭圆高斯光的相关理论及公式推导。
像散椭圆高斯光.zip
  • 像散椭圆高斯光
  • Vortex astigmatic Fourier-invariant Gaussian.pdf
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内容介绍
<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/6255fbaf47503a0a93f3825e/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6255fbaf47503a0a93f3825e/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">V<span class="_ _0"></span>ortex astigmatic Fourier<span class="_ _1"></span>-invariant Gaussian </div><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls1 ws1">beams </div><div class="t m0 x1 h3 y3 ff1 fs1 fc1 sc0 ls2 ws1">V.<span class="fs2 ls3"> </span><span class="ls4 ws2">V. K</span><span class="fs2 ls5">OTLYAR</span><span class="ls3">,</span></div><div class="t m0 x2 h4 y4 ff1 fs3 fc1 sc0 ls6 ws1">1,2</div><div class="t m0 x3 h3 y3 ff1 fs1 fc1 sc0 ls7 ws3"> A.<span class="fs2 ls3 ws1"> </span><span class="ls8 ws4">A. K<span class="fs2 ls9 ws1">OVALEV<span class="fs1 ls3">,</span></span></span></div><div class="t m0 x4 h4 y4 ff1 fs3 fc1 sc0 ls6 ws1">1,2,*</div><div class="t m0 x5 h3 y3 ff1 fs1 fc1 sc0 ls7 ws3"> A.<span class="fs2 ls3 ws1"> </span><span class="ls4 ws2">P. P<span class="fs2 lsa ws1">ORFIREV</span></span></div><div class="t m0 x6 h4 y4 ff1 fs3 fc1 sc0 ls6 ws1">1,2</div><div class="t m0 x7 h3 y3 ff1 fs1 fc1 sc0 ls3 ws1"> </div><div class="t m0 x1 h5 y5 ff2 fs4 fc0 sc0 ls3 ws1">1</div><div class="t m0 x8 h6 y6 ff2 fs5 fc0 sc0 lsb ws5">Image Processing Systems Institute of the RAS &#8211; <span class="_ _2"></span><span class="lsc ws6">Branch of FSRC &#8220;Crystallography &amp; Photonics&#8221; of </span></div><div class="t m0 x1 h6 y7 ff2 fs5 fc0 sc0 lsd ws7">the RAS, 151 Mo<span class="_ _2"></span>lodogvardeyskaya St., Samara 443001, Russia </div><div class="t m0 x1 h5 y8 ff2 fs4 fc0 sc0 ls3 ws1">2</div><div class="t m0 x8 h6 y9 ff2 fs5 fc0 sc0 lse ws8">Samara National Research University, 34<span class="lsf"> Moskovskoe Shosse, Samara 443086, <span class="_ _2"></span>Russia </span></div><div class="t m0 x1 h5 ya ff2 fs4 fc2 sc0 ls3 ws1">*</div><div class="t m0 x8 h6 yb ff2 fs5 fc2 sc0 ls10 ws1">alexeysmr@mail.ru </div><div class="t m0 x1 h7 yc ff3 fs6 fc0 sc0 ls11 ws1">Abstract:<span class="ff4 ls12 ws9"> We find a two-parameter family of astig<span class="ls13 wsa">matic elliptical Gaussian (AEG) optical </span></span></div><div class="t m0 x1 h7 yd ff4 fs6 fc0 sc0 ls14 wsb">vortices, which are free space modes up to <span class="_ _2"></span>scal<span class="ls15 wsc">e and ro<span class="_ _1"></span>tation. We calculate total normalized </span></div><div class="t m0 x1 h7 ye ff4 fs6 fc0 sc0 ls11 wsd">orbital angul<span class="_ _2"></span>ar momentum<span class="_ _2"></span> of AEG vortices, whic<span class="_ _2"></span>h can be an integer, <span class="_ _2"></span>fractional and zero<span class="_ _2"></span>, and </div><div class="t m0 x1 h7 yf ff4 fs6 fc0 sc0 ls16 wse">which is equal to the algebraic sum of two terms reflecting the contributio<span class="_ _1"></span>n of the vortex and </div><div class="t m0 x1 h7 y10 ff4 fs6 fc0 sc0 ls17 wsf">astigmatic componen<span class="_ _1"></span>ts of the light field. In an<span class="_ _1"></span>y <span class="ls18 ws10">transverse plane, such a beam has an isol<span class="_ _2"></span>ated </span></div><div class="t m0 x1 h7 y11 ff2 fs6 fc0 sc0 ls3 ws1">n<span class="ff4 ls19 ws11">-fold dege<span class="_ _2"></span>nerate intensity<span class="_ _2"></span> null on the opti<span class="_ _2"></span>cal axis (an optical vo<span class="_ _2"></span>rtex) embedded into a<span class="_ _2"></span>n </span></div><div class="t m0 x1 h7 y12 ff4 fs6 fc0 sc0 ls1a ws12">elliptical Gaussian beam. In addition to the qu<span class="_ _1"></span>adratic elliptical phase, a beam has the ph<span class="_ _1"></span>ase of </div><div class="t m0 x1 h7 y13 ff4 fs6 fc0 sc0 ls1b ws13">a cylindrical lens r<span class="_ _2"></span>otated by an angle of 45 de<span class="_ _2"></span><span class="ls1c ws14">grees with respect to th<span class="ls1d ws15">e principal axes of the </span></span></div><div class="t m0 x1 h7 y14 ff4 fs6 fc0 sc0 ls1a ws16">ellipse of the Gaussian beam inten<span class="_ _1"></span>sity distribu<span class="_ _1"></span>tion. The degenerated cen<span class="_ _1"></span>tral intensity null in </div><div class="t m0 x1 h7 y15 ff4 fs6 fc0 sc0 ls1e ws17">these beams does not split it in<span class="_ _1"></span>to <span class="ff2 ls3 ws1">n</span><span class="ls1f ws18"> spatially separated intensity nu<span class="_ _1"></span>lls, as is usually assumed </span></div><div class="t m0 x1 h7 y16 ff4 fs6 fc0 sc0 ls20 ws19">for elliptical astigmatic beams. </div><div class="t m0 x1 h8 y17 ff5 fs3 fc0 sc0 ls21 ws1a">&#169; 2019 Optical Society of America under the terms of the <span class="fc2 ls22 ws1b">OSA Open Access P<span class="ls23 ws1c">ublishing Agreement<span class="_ _1"></span></span></span><span class="ls3 ws1"> </span></div><div class="t m0 x1 h9 y18 ff1 fs6 fc0 sc0 ls1d ws1d">1. Introduction </div><div class="t m0 x1 h7 y19 ff4 fs6 fc0 sc0 ls24 ws1e">It is known [1&#8211;5] t<span class="_ _2"></span>hat a cylindrical lens can be used t<span class="_ _2"></span>o determine the topological<span class="_ _2"></span> charge of an </div><div class="t m0 x1 h7 y1a ff4 fs6 fc0 sc0 ls19 ws1f">optical vortex<span class="_ _2"></span>. This property of<span class="ls13 ws20"> the cylindrical lens was noti<span class="ls14 ws21">ced long ago. For example, a </span></span></div><div class="t m0 x1 h7 y1b ff4 fs6 fc0 sc0 ls25 ws22">Hermite-Gauss<span class="_ _2"></span>ian laser beam of an orde<span class="_ _2"></span>r (0, <span class="ff2 ls3 ws1">n</span><span class="ls26 ws23">) with the zero orbi<span class="_ _2"></span>tal angular m<span class="_ _2"></span>omentum </span></div><div class="t m0 x1 h7 y1c ff4 fs6 fc0 sc0 ls27 ws24">(OAM) was transformed by using a cylindrical le<span class="_ _1"></span><span class="ls28 ws25">ns into a Laguerre<span class="_ _2"></span>-Gaussian laser beam<span class="_ _2"></span> [6] </span></div><div class="t m0 x1 h7 y1d ff4 fs6 fc0 sc0 ls13 ws26">that has <span class="ff2 ls3 ws1">n</span><span class="ls1e ws27">-fold degenerate intensity nu<span class="_ _1"></span>ll and possesses the OAM. Using a cylindrical lens, it is </span></div><div class="t m0 x1 h7 y1e ff4 fs6 fc0 sc0 ls19 ws28">possible to generate<span class="_ _2"></span> vortex-free laser beams <span class="ls20 ws29">with the OAM [7,8]. Th<span class="ls29 ws2a">ere are no isolated </span></span></div><div class="t m0 x1 h7 y1f ff4 fs6 fc0 sc0 ls16 ws2b">intensity nulls (singular points) in such<span class="_ _1"></span> beams. These astigmatic beams are described by a </div><div class="t m0 x1 h7 y20 ff4 fs6 fc0 sc0 ls16 ws2c">superposition of an<span class="_ _1"></span> infinite number of optical vo<span class="_ _1"></span>rtices with only even positive and<span class="_ _1"></span> negative </div><div class="t m0 x1 h7 y21 ff4 fs6 fc0 sc0 ls2a ws2d">topological charges [8]. </div><div class="t m0 x9 h7 y22 ff4 fs6 fc0 sc0 ls2b ws2e">It is also known that a linear combination <span class="ls2c ws2f">of even a<span class="_ _2"></span>nd odd Mathieu [9], Ince-<span class="_ _2"></span>Gaussian </span></div><div class="t m0 x1 h7 y23 ff4 fs6 fc0 sc0 ls2c ws30">[10] and Herm<span class="_ _2"></span>ite [11,12] beams wi<span class="_ _2"></span>th a phase shift of <span class="ff6 ls3 ws1">&#960;</span><span class="ls2d ws31">/2 generates elliptical optical vortices </span></div><div class="t m0 x1 h7 y24 ff4 fs6 fc0 sc0 ls1e ws32">with their OAM depending on the degree of<span class="_ _1"></span><span class="ls1a ws33"> ellipticity. Both vortex<span class="_ _1"></span> and astigmatic </span></div><div class="t m0 x1 h7 y25 ff4 fs6 fc0 sc0 ls19 ws34">component<span class="_ _2"></span>s contribute to t<span class="_ _2"></span>he OAM of such beam<span class="_ _2"></span>s and these contributio<span class="_ _2"></span>ns of both </div><div class="t m0 x1 h7 y26 ff4 fs6 fc0 sc0 ls25 ws35">component<span class="_ _2"></span>s (vortex and ast<span class="_ _2"></span>igmatic) to the O<span class="_ _2"></span>AM can change with the <span class="_ _2"></span>propagation of suc<span class="_ _2"></span>h </div><div class="t m0 x1 h7 y27 ff4 fs6 fc0 sc0 ls17 ws36">elliptical beams [2,1<span class="_ _1"></span>3]. </div><div class="t m0 x9 h7 y28 ff4 fs6 fc0 sc0 ls2a ws37">The OAM of optical vortices, <span class="ls1b ws38">including the fractional<span class="_ _2"></span> OAM [14,15], can be m<span class="_ _2"></span>easured not </span></div><div class="t m0 x1 h7 y29 ff4 fs6 fc0 sc0 ls19 ws39">only by using t<span class="_ _2"></span>he cylindrical lens [1&#8211;5]<span class="_ _2"></span>, but also by many<span class="_ _2"></span> other ways, for exampl<span class="_ _2"></span>e, by using </div><div class="t m0 x1 h7 y2a ff4 fs6 fc0 sc0 ls25 ws3a">interferogram<span class="_ _2"></span>s [8,14] and a tri<span class="_ _2"></span>angular apertur<span class="_ _2"></span>e [16]. </div><div class="t m0 x9 h7 y2b ff4 fs6 fc0 sc0 ls2e ws3b">In this paper, we consider new laser beams with combined properties of vortex elliptic </div><div class="t m0 x1 h7 y2c ff4 fs6 fc0 sc0 ls26 ws3c">Gaussian beam<span class="_ _2"></span>s [9&#8211;13] and of ast<span class="_ _2"></span>igmatic vortex-<span class="ls1c ws3d">free laser beam<span class="_ _2"></span>s [7,8]. We call such a family </span></div><div class="t m0 x1 h7 y2d ff4 fs6 fc0 sc0 ls12 ws3e">of laser beams as astigmatic elliptical Gaussian (AEG) optical vortices. In the initial plan<span class="_ _1"></span>e, </div><div class="t m0 x1 h7 y2e ff4 fs6 fc0 sc0 ls2f ws3f">the AEG-vortex is an <span class="_ _2"></span><span class="ff2 ls3 ws1">n<span class="ff4 ls30 ws40">-fold degenerate circ<span class="_ _2"></span>ularly symme<span class="_ _2"></span>tric intensity null<span class="_ _2"></span> embedded into the<span class="_ _2"></span> </span></span></div><div class="t m0 x1 h7 y2f ff4 fs6 fc0 sc0 ls31 ws41">center of the waist of an ellip<span class="ls2b ws42">tic Gaussian beam, whose waist radii along the Cartesi<span class="_ _2"></span>an axes </span></div><div class="t m0 x1 h7 y30 ff4 fs6 fc0 sc0 ls1e ws43">are related by a certain relation, and then p<span class="_ _1"></span>a<span class="ls32 ws44">ssed through a cylindrical lens rotated in<span class="_ _1"></span> the </span></div><div class="t m0 x1 h7 y31 ff4 fs6 fc0 sc0 ls16 ws45">initial plane around th<span class="_ _1"></span>e optical axis by an a<span class="_ _1"></span>ngl<span class="ls33 ws46">e of 45 degrees with respect to<span class="_ _1"></span> the Cartesian </span></div><div class="t m0 x1 h7 y32 ff4 fs6 fc0 sc0 ls14 ws47">axes. Such a beam propagates in<span class="ls2f ws48"> free space<span class="_ _2"></span> preserving its struct<span class="ls1c ws14">ure up to scale and rotation. </span></span></div><div class="c xa y33 w2 ha"><div class="t m0 x0 hb y34 ff7 fs7 fc0 sc0 ls3 ws1"> Vol. 27, No. 2 | 21 Jan 2019 | OPTICS EXPRESS 657<span class="fc3 sc0"> </span></div></div><div class="c xb y35 w3 hc"><div class="t m0 x0 hd y36 ff8 fs8 fc0 sc0 ls3 ws1">#347499<span class="fc3 sc0"> </span></div></div><div class="c xc y35 w4 hc"><div class="t m0 x0 hd y36 ff8 fs8 fc0 sc0 ls3 ws1">https://doi.org/10.1364/OE.27.000657<span class="fc3 sc0"> </span></div></div><div class="c xb y37 w5 hc"><div class="t m0 x0 hd y36 ff8 fs8 fc0 sc0 ls3 ws1">Journal &#169; 2019</div></div><div class="c xd y37 w6 hc"><div class="t m0 x0 hd y36 ff8 fs8 fc0 sc0 ls3 ws1">Received 8 Oct 2018; revised 14 Nov 2018; accepted 15 Nov 2018; published 8 Jan 2019<span class="fc3 sc0"> </span></div></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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