On ‘Orbital’ and ‘Spin’ Angular Momentum of Light in Classical and Quantum Theories – A General Framework

Arvind; Chaturvedi S.; Mukunda N.

摘要

Abstract > We develop a general framework to analyze two much discussed questions concerning (a) ‘orbital’ and ‘spin’ angular momentum carried by light and (b) the paraxial approximation of the free Maxwell system both in the classical as well as quantum domains. After formulating the classical free Maxwell system in the transverse gauge in terms of complex analytical signals we derive expressions for the constants of motion (COM) associated with its Poincaré symmetry. In particular, we show that the COM corresponding to the total angular momentum J naturally splits into an ‘orbital’ part L and a ‘spin’ part S each of which is a COM in its own right. We then discuss quantization of the free Maxwell system and construct the operators generating the Poincaré group and analyze their algebraic properties and find that while the quantum counterparts <mat:math display="inline" altimg="urn:x-wiley:00158208:media:prop201800040:prop201800040-math-0001" wiley:location="equation/prop201800040-math-0001.png"> <mat:mover accent="true"> <mat:mi mathvariant="bold">L</mat:mi> <mat:mo>?</mat:mo> </mat:mover> </mat:math> and <mat:math display="inline" altimg="urn:x-wiley:00158208:media:prop201800040:prop201800040-math-0002" wiley:location="equation/prop201800040-math-0002.png"> <mat:mover accent="true"> <mat:mi mathvariant="bold">S</mat:mi> <mat:mo>?</mat:mo> </mat:mover> </mat:math> of L and S go over into bona fide observables, they fail to satisfy the angular momentum algebra making their interpretation as ‘orbital’ and ‘spin’ operators untenable at the quantum level. On the other hand <mat:math </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><abstract type =“main”xml：lang =“en”> <title type =“main”>抽象</ title> >我们开发一般框架来分析有关（a）'orbital'的两个讨论的问题“旋转”角度由光线和（B）在经典以及量子域中的自由麦克斯韦系统的近轴近似。在横向仪中制定经典自由麦克斯韦系统之后，在复杂的分析信号方面，我们推导出与其Poincaré对称相关的运动常数（COM）的表达。特别地，我们表明，对应于总角动量的COM <B> J </ B>自然地分裂成“轨道”部分<B> L </ B>和“旋转”部分<B> S </ b>每个人都有一个com。然后我们讨论空闲麦克斯韦系统的量化，并构建生成Poincaré组的运营商，并分析其代数特性，并发现Quantum Conderparts <Mat：Math Display =“内联”Altimg =“URN：X-Wiley：00158208：媒体：PROP201800040：PROP2018000-MATH-MATH-0001“WIley：Location =”Aquation / Prop201800040-Math-0001.PNG“> <MAT：MIVER ACCENT =”TRUE“> <MAT：MI Mathvariant =”BOLD“> L </ MAT： mi> <mat：mo>？</ mat：mo> </ mat：移动器> </ mat：math>和<mat：math display =“内联”altimg =“urn：x-wiley：00158208：媒体：prop201800040 ：PROP201800040-MATH-0002“WIley：位置=”等式/ PROP201800040-MATH-0002.PNG“> <MAT：MIVER ACCENT =”TRUE“> <MAT：MI MathVariant =”粗体“> S </ MAT：MI> <mat：mo>？</ mat：mo> </ mat：移动器> </ mat：math> l </ b>和 s </ b>返回BONA FIDE可观察到没有满足Y角动位代数使其解释为“轨道”和“旋转”运营商在量子层面无法掌管。另一方面<mat：数学 </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-24639/'>《Fortschritte der Physik》</a> <b style="margin: 0 2px;">|</b><span>2018年第10期</span><b style="margin: 0 2px;">|</b><span>共16页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Arvind&option=202" target="_blank" rel="nofollow">Arvind;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Chaturvedi S.&option=202" target="_blank" rel="nofollow">Chaturvedi S.;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Mukunda N.&option=202" target="_blank" rel="nofollow">Mukunda N.;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Indian Institute of Science Education and Research Mohali;</p> <p>Indian Institute of Science Education and Research Bhopal;</p> <p>Indian Academy of Sciences Bangalore;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/158.html" title="物理学">物理学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=orbital angular momentum&option=203" rel="nofollow">orbital angular momentum;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=single photons&option=203" rel="nofollow">single photons;</a> </p> <div class="translation"> 机译：轨道角动量;单个光子; 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href="/patent-detail/061202611284.html">基于级联半导体光放大器的大角度光偏振旋转系统</a> <b>[P]</b> . <span> 中国专利： CN104505710B </span> <span> . 2017.10.10</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130439498227.html">PHOTONIC SWITCH WORKING IN MOMENTUM-DIVISON-MULTIPLE-ACCESS (MDMA) MODE FOR MICROWAVE AND OPTICAL WAVELENGTHS BASED UPON THE MEASUREMENT OF THE SPIN, THE ORBITAL ANGULAR MOMENTUM AND THE TOTAL ANGULAR MOMENTUM OF THE INVOLVED PHOTONS</a> <b>[P]</b> . <span> 外国专利：  EP1509795A1 </span> <span> . 2005-03-02</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：基于动量-分多址（MDMA）模式的微波和光学波峰光子开关工作，基于所旋转光子的自旋，轨道角动量和总角动量的测量 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130438033534.html">Photonic switch working in momentum-division-multiple-access (mdma) mode for microwave and optical wavelengths based upon the measurement of the spin, the orbital angular momentum and the total angular momentum of the involved photo</a> <b>[P]</b> . <span> 外国专利：  US2005259914A1 </span> <span> . 2005-11-24</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：基于自旋，轨道角动量和所涉及照片的总角动量的测量，对微波和光波长以动量分多址（mdma）模式工作的光子开关 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130442176375.html">PHOTONIC SWITCH WORKING IN MOMENTUM-DIVISON-MULTIPLE-ACCESS (MDMA) MODE FOR MICROWAVE AND OPTICAL WAVELENGTHS BASED UPON THE MEASUREMENT OF THE SPIN, THE ORBITAL ANGULAR MOMENTUM AND THE TOTAL ANGULAR MOMENTUM OF THE INVOLVED PHOTO</a> <b>[P]</b> . <span> 外国专利：  AU2003240054A1 </span> <span> . 2003-12-19</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：基于动量-分多址（MDMA）模式的微波和光学波长的光子开关工作，基于所旋转的光的自旋，轨道角动量和总角动量的测量 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> <div class="right rightcon"> <div class="details_img cardcommon clearfix" style="margin-bottom: 10px;display:none;" > </div> </div> </div> <div id="thesis_get_original1" class="downloadBth" style="bottom: 19px;z-index: 999;" onclick="ywcd('0704023603720','4',7,2,1,'',this,24)" class="delivery" prompt="010401" title="通过人工服务将文献原文发送至邮箱" >获取原文</div> <div class="journalsub-pop-up" style="display: none"> <div class="journal-sub"> <h2>期刊订阅</h2> <img src="https://cdn.zhangqiaokeyan.com/img/loginclose.png" alt="关闭" onclick="$('.journalsub-pop-up').hide()"> <p class="pardon">抱歉，该期刊暂不可订阅，敬请期待！</p> <p class="current">目前支持订阅全部北京大学中文核心（2020）期刊目录。</p> <div style="display: flex;margin-top: 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