The ins and outs of conical refraction
The ins and outs of conical refraction
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圆锥折射的来龙去脉
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发表时间：
2006
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通讯作者：
D. Weaire
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作者：
J. Lunney;D. Weaire
爱国的骄傲，他在回忆录中的一段华丽的段落中称锥形折射为“辐射的陌生人”。负责圆锥折射的理论预测和实验证实的两位物理学家是威廉·罗恩汉密尔顿（1805-1865）和汉弗莱·劳埃德（1800-1881），他们都是都柏林Trinity学院的教授（图1）。爱尔兰最近的汉密尔顿年（2005年）为重新审视和庆祝他们的成就提供了机会。图2显示了两种圆锥形折射的基本原理，改编自托马斯普雷斯顿的光理论（1890年）[1]。在这两种情况下，晶体使一束窄光束发展成一个中空的圆锥体，根据双折射理论，可能会出现一对光线。在汉密尔顿的洞察力和正式理论揭示这一现象之前，其他研究人员似乎对这一奇怪的效应没有任何模糊的预感，这在科学界是不寻常的。到1832年，菲涅耳的光的波动理论已经成为物理学中最受关注的话题之一，然而，一个重要的细节在理论和实验中都没有引起注意。也许在实验中忽略这种效应是可以原谅的，因为它需要一个既双轴又具有良好光学质量的晶体。此外，实际上这种影响很小：图2中的圆锥通常只有几度的角度。至于理论，汉密尔顿同时代的许多人肯定对他们没有注意到这种反常现象感到失望。Trinity的一位同事詹姆斯·麦卡拉（James MacCullagh，1809-1847）心烦意乱，以至于发起了一场毫无意义的追溯信贷的运动。这一失败，以及他的一般黯然失色汉密尔顿，可能有助于最终自杀的麦卡拉在1847年。菲涅尔（1788-1827）没有活得足够长，遭受任何痛苦的悔恨，他的疏忽。对汉密尔顿来说，这是一个至高无上的成就，实现了他早熟的承诺。对于一般的数学物理学来说，这是一个重要的里程碑：可以说是第一个数学预测的新物理性质，随后被实验证实。有人说，汉密尔顿声称，他的理论是如此安全，它没有必要的实验验证。如果他真的这么说了，那一定是这个严肃的人罕见的玩笑，因为他并不认为这个理论是一本封闭的书。他尽一切努力鼓励和帮助劳埃德完成艰巨的任务。艾萨克·托德亨特（Isaac Todhunter，1820-1884）曾经开玩笑地说，他一生都在教这个学科，不想让一个演示打乱他的想法。这些想法很可能会被下面的一些事情所颠覆。圆锥折射的故事是否是光的波动理论（与那些基于粒子的理论不同）的胜利在当时还存在争议，但汉密尔顿的成功无疑为它日益被接受增添了动力。尽管完全出乎意料，但这一发现并不是范式转变。这是一个日益增长的正统的确认。詹姆斯·奥哈拉在1982年讲述这个故事时写道：“这只不过是一种奇怪的光学现象，没有任何可以想象的应用”。在19世纪的一些光学教科书中，圆锥折射被强调了出来，但实际上却被束之高阁，成了各种各样的小玩意儿。普雷斯顿简明扼要的著作中就包括了圆锥折射，但没有什么戏剧性。大约在同一时间，弗莱彻似乎已经完全忽略了它在他的其他详尽的治疗双折射，光学指标和传输的光在晶体（1892年）。然而，这一主题没有引起注意的拉曼在20世纪40年代，当他调查锥形折射结晶萘，并作出了重要贡献，其理解[4]。但是最近圆锥折射已经被去掉了。就像物理学中的大多数古董一样，如果仔细研究，它包含了更多有趣的细节。Berry指出，圆锥折射是科学文献中讨论的第一个波奇点的例子[5]。在激光和光通信时代，人们正在寻找新的应用。晶体光学器件制造商Vision Crystal Technology AG正在销售一种基于内部锥形折射的激光束整形设备。利用锥形折射所能产生的强度和偏振的独特空间分布，很可能会出现新的应用。
patriotic pride, who called conical refraction “the radiant stranger” in a florid passage in his memoirs. The two physicists responsible for the theoretical prediction and experimental confirmation of conical refraction were William Rowan Hamilton (1805-1865) and Humphrey Lloyd (1800-1881), both professors of Trinity College Dublin (fig. 1). Ireland’s recent Year of Hamilton (2005) provided an opportunity for re-examining and celebrating their achievement. Stripped to their essentials, two versions of conical refraction are shown in figure 2, adapted from Thomas Preston’s Theory of Light (1890) [1]. In both cases a crystal causes a narrow beam of light to develop into a hollow cone, where a pair of rays might be expected from the theory of double refraction. Unusually in science, other researchers do not seem to have had any vague premonition of the curious effect before Hamilton’s insight and formal theory exposed it. By 1832 Fresnel’s wave theory of light had become one of the most worked-over topics in physics, yet an important detail had escaped attention in both theory and experiment. Perhaps it is more excusable to overlook the effect in experiment since it requires a crystal that is both biaxial and of good optical quality. Moreover the effect is a small one in practice: the cones in figure 2 normally have angles of only a few degrees. As for theory, many of Hamilton’s contemporaries must have felt disappointed that they had failed to notice the anomaly. A Trinity colleague, James MacCullagh (1809-1847), was distraught to the point of launching a pointless retrospective campaign for credit. That failure, and his general eclipse by Hamilton, may have contributed to the eventual suicide of MacCullagh in 1847. Fresnel (1788-1827) did not live quite long enough to suffer any pangs of remorse at his oversight. For Hamilton it was a crowning achievement, a realisation of his precocious promise [2]. For mathematical physics in general it was a significant milestone: arguably the first mathematical prediction of a novel physical property that was subsequently confirmed by experiment. It has been said that Hamilton claimed that his theory was so secure that it had no need of experimental validation. If he did say this, it must have been a rare jest from this serious man, for he did not regard the theory as a closed book. He did everything he could to encourage and assist Lloyd in his difficult task. Isaac Todhunter (1820-1884) once made a jocular remark that, having taught this subject all his life he did not want to have his ideas upset by a demonstration. Those ideas might well have been upset by some of what follows below. Whether the conical refraction story was a triumph for the wave theory of light (as distinct from those theories based on particles) was debated at the time, but Hamilton’s success certainly added momentum to its growing acceptance. The discovery was no paradigm shift, despite being totally unexpected. It was a confirmation of a growing orthodoxy. James O’Hara, in his 1982 telling of the story, wrote that “it was little more than a curious optical phenomenon which had no conceivable application” [3]. After being highlighted in some of the optical textbooks of the 19 century, conical refraction had indeed been consigned to the lumber-room of miscellaneous minor curiosities.Preston’s compendious work included it,but with no great drama. At about the same time Fletcher seems to have completely ignored it in his otherwise exhaustive treatment of double refraction, The Optical Indicatrix and the Transmission of Light in Crystals (1892). However the topic did catch the attention of Raman in the 1940s when he investigated conical refraction in crystalline naphthalene and made an important contribution to its understanding [4]. But lately conical refraction has been taken out and dusted off. Like most antique curiosities in physics, it contains further layers of intriguing detail if closely examined. Berry has pointed out that conical refraction is the first example of a wave singularity to be discussed in the scientific literature [5].And in the age of lasers and optical communication the search is on for novel applications. A manufacturer of crystal optics, Vision Crystal Technology AG, is marketing a laser beam shaping device based on internal conical refraction. It seems likely that new applications will emerge to exploit the unique spatial distribution of intensity and polarisation which can be produced by conical refraction.