An elegant and rare wire model of the wave (or ray) surface of a biaxial crystal - possibly dating from the time of Humphrey Lloyd.* |
The Irish poet Aubrey de Vere called conical refraction "the radiant stranger", and it was apt enough. It was a totally unanticipated theoretical prediction by William Rowan Hamilton that met with immediate experimental confirmation - the very model of idealised modern science.
In conical refraction, a cone of rays is observed instead of the two rays in double refraction by a crystal.
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. The latter is the more excusable lapse, because the experiment requires a suitable crystal of good quality- one that is biaxial. Moreover the effect is a small one in practice: the cones of refraction have angles of a few degrees at most and the two forms of the effect (internal, external) require a ray to be incident on the crystal in particular directions.
Inspired by the dramatic prediction, Humphrey Lloyd lost no time in verifying it. This excellent physicist is also remembered for other work in optics and in geomagnetism.
Many of Hamilton's contemporaries must have felt disappointed that they had been less assiduous. A Trinity colleague, James MacCullagh, 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 did not live quite long enough to suffer any pangs of remorse at his oversight.
Whether the conical refraction story was a triumph for the wave theory of light (as distinct from those that are based on particles) was debatable, as Stokes insisted, 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.
For Hamilton it was a crowning achievement, a realisation of his precocious promise, and surely the motivation for the conferral of a knighthood by the Lord Lieutenant of Ireland at the BAAS meeting which followed in Dublin.
It has been said that Hamilton claimed that his theory was so secure that it had no need of experimental validation. If so, 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 did make the 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.
James O'Hara, in his 1982 telling of the story, wrote that it was "it was little more than a curious optical phenomenon which had no conceivable application". After being highlighted in some of the optical textbooks of the 19th 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).
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. And in the age of lasers and optical communication the search is on for novel applications.
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An elegant and rare wire model of the wave (or ray) surface of a biaxial crystal - possibly dating from the time of Humphrey Lloyd.* |
A radial line drawn in most directions will encounter two parts of the wave surface, the inverse radii giving the velocities of two possible waves in that direction, having different polarisation.
But two directions (together with their opposites) are very special: only a single velocity is found, because the inner and outer surface meet in a cusp consisting of two opposed cones. These special lines are called the optic axes, or binormals (or indeed several other names).
At first sight these binormals might seem less interesting than the general directions that yield two distinct wave velocities and hence are associated with double refraction, but Hamilton saw that even more exotic extraordinary refractive properties are associated with the binormals.
Conical refraction arises from the properties of these two kinds of special directions in the crystal.
The original experiment of Lloyd was that of external conical refraction, which produces a diverging hollow cone of light emerging from the crystal. He had no success until he obtained a particularly good crystal of aragonite from a commercial supplier. With this he demonstrated external conical refraction, measuring a cone angle of about 3 degrees, as predicted.
His experimental arrangements may today be simplified, if a crystal is cut so that its faces are normal to either one of the special directions. And lasers provide convenient bright beams, making demonstrations possible even on a large scale.
Lloyd was a thorough experimentalist, a fitting counterpart to Hamilton, the systematic theorist. Not content with seeing the phenomenon as predicted, he examined the polarisation of the emergent light, and was surprised to find that "every ray of the cone was polarised in a different plane".
The finer details
As early as 1839, the bright ring exhibited by internal conical refraction
was resolved by the experiments of Poggendorf into two concentric rings.
(Everything seems to come in twos in this subject.) The same is true of the
external case. With modern equipment additional, fainter rings are
discernible, and Lloyd's simple manifestation of the effect becomes a
complex pattern and a fresh challenge to theory.
The extra structure appears because the light beams that are used are of
finite extent, rather than those idealised rays, mere lines, upon which the
elementary theory is based.
A singular case
Often in constructing (or deconstructing) the history of science, its manner
of progress is falsified for the sake of clarity. The electron was not
discovered by JJ Thomson on a certain day in Cambridge, but we tell it so.
The case of conical refraction is an exception for which the revelatory
process is unambiguous, and priority is sharply defined - in spite of the
anguished protestations of MacCullagh. It is a tale of two virtuous and
dedicated scientists who richly deserved the accolades that they received; a
tale worth recounting for generations to come. The emergence of the radiant
stranger can still startle, entertain and educate us.
A full version of this article is to be submitted to Europhysics News.
See also David Wilkins' article 'William Rowan Hamilton: mathematical genius' in the August 2005 issue of Physics World.