The ins and outs of conical refraction

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.