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Conical Refraction and the Radiant Stranger

Internal conical refraction is a striking optical phenomenon which arises when a beam of light is incident along one of the optic axes of a slab of transparent biaxial crystal. The beam propagates as a skewed hollow cone inside the crystal, and on leaving the crystal it refracts into a hollow cylinder of light, as shown in Figure 1. Conical refraction was predicted by William Rowan Hamilton in 1832 [1], and experimentally verified by Humphrey Lloyd [2], later that year.

Figure 1. Ray diagram to illustrate internal conical refraction from Ref. 3.

At the time of discovery, conical refraction was widely celebrated: arguably the first example of a mathematical prediction of a new physical phenomenon that was quickly followed by experimental confirmation. A non-technical introduction to physics and the history of conical diffraction is presented in Ref. 4. The year 2005 was the bicentenary of Hamilton’s birth, and the School of Physics at TCD took part in the Year of Hamilton celebration. James Lunney set up a demonstration of internal conical refraction using a small laser and a high quality synthetic biaxial crystal.  This demonstration is now on display in the Fitzgerald Library in the School of Physics. While this demonstration was being prepared, a rare and beautiful 19th century wire model of the ray surface in a biaxial crystal was discovered in the Department of Geology and is also now displayed in the Fitzgerald Library.  A large-scale sculpture based on the wire model was constructed in the School of Physics and is wall-mounted in the stairwell of the Fitzgerald Building.

Figure 2. Radiant Stranger: A large-scale sculpture based on the wire model of the ray surface in a biaxial crystal. The sculpture is on display on the second floor of the Fitzgerald Building.

The full description of conical refraction requires a wave optics approach [5, 6], as described by Sir Michael Berry and others, hence the alternative name “conical diffraction”. Berry’s main result was a paraxial solution for the optical field which can be numerically evaluated at any plane normal to the propagation direction. It shows that the conically diffracted beam has a narrow double-ring profile in the focal image plane and then diffracts to yield a beam which has a maximum on axis and is described by a superposition of 0th and 1st order diverging Bessel beams with opposite circular polarizations (Figure 3)

 

 

Figure 3. Photograph of a magnified image of the double-ring formed at the focal image plane by internal conical diffraction of a Gaussian laser beam [7].

These calculations were compared with experiment and the agreement was very close [7].  With support from Science Foundation Ireland, John Donegan and James Lunney used a single Gaussian mode laser beam and a high quality synthetic biaxial crystal to reveal the finer details of conical diffraction and explore potential applications [8, 9].

The Radiant Stranger sculpture inspired by conical refraction can be seen on the second floor of the Fitzgerald Building.

 

 

Sources

  1. R. Hamilton, “Third supplement to an essay on the theory of systems of rays” Transactions of the Royal Irish Academy 17, 1–144 (1837).
  2. Lloyd, “On the phenomena presented by light in its passage along the axes of biaxial crystals” Phil. Mag. 1, 112–120 and 207–210 (1833).
  3. G. Lunney, and D. W. Weaire, “The ins and outs of conical refraction” Europhys. News 37(3), 26–29 (2006).
  4. V. Berry, “Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike” J. Opt. A, Pure Appl. Opt. 6(4), 289–300 (2004).
  5. V. Berry, and M. R. Jeffrey, “Conical diffraction: Hamilton’s diabolical point at the heart of crystal optics” Prog. Opt. 50, 13–50 (2007).
  6. V. Berry, M. R. Jeffrey, and J. G. Lunney, “Conical diffraction: Observations and theory” Proc. R. Soc. A462(2070), 1629–1642 (2006).
  7. F. Phelan, D. P. O’Dwyer, Y. P. Rakovich, J. F. Donegan and J. G. Lunney “Conical diffraction and Bessel beam formation with a high optical quality biaxial crystal” Optics Express, 17, 1289 –12898 (2009).
  8. F. Phelan, J. F. Donegan and J. G. Lunney “Conical diffraction of linearly polarised light controls the angular position of a microscopic object” Optics Express, 18, 2 7310-27326(2010)
  9. O’Dwyer, C. F. Phelan, K. E. Ballantine, Y. Rakovich, J. G. Lunney and J. F. Donegan, “Generation of a radially polarised light beam using internal conical refraction” Optics Express, 19, 21793 – 21801 (2011).