## INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS A: PURE AND APPLIED OPTICS (2006)

### BibTeX

@MISC{Berry06instituteof,

author = {M V Berry and M R Jeffrey},

title = {INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS A: PURE AND APPLIED OPTICS},

year = {2006}

}

### OpenURL

### Abstract

refraction

### Citations

35 |
Stegun I A 1972
- Abramowitz
(Show Context)
Citation Context ...grals A±, defined in (2.25), begins by assuming that ρ is not very close to one of the branch-points (2.24), and applying the following standard large-argument forms for the Bessel functions in (2.22)=-=[31]-=-: ρ 0 ξ J0 (˜κ ˜ρ) cos (˜κρ0) ± J1 (˜κ ˜ρ) sin (˜κρ0) √ 2 ≈ π ˜ρ cos { ˜κ ( ˜ρ ∓ ρ0) − 1 4 π } . (3.1) Thus A± ≈ √ 2 π ˜ρ ∫ ∞ 0 d˜κ ˜κ 1/2 { exp − 1 2 i˜ζ ˜κ 2 } cos{˜κ ( ˜ρ ∓ ρ0) − 1 π}. (3.2) 4 The ... |

22 |
Uniform asymptotic smoothing of Stokes’s discontinuities
- Berry
- 1989
(Show Context)
Citation Context ...ticaTM , which we have used for all computations). The phases in A± are determined by careful consideration of the steepest-descent integration contours; in A+, the sign switches across a Stokes line =-=[32, 33]-=-, where the exponential is subdominant relative to the end-point contribution to be considered later. The result (3.3) reveals the reason for working with A+ and A−, rather than B0 and B1: in this lea... |

17 | The optical singularities of birefringent dichroic chiral crystals
- Berry, Dennis
(Show Context)
Citation Context ..., and the corresponding directions generated by Im η, are distinct, which is true in general for (1.1). With polar coordinates θ, φ in direction space, one pair of singular axes is conveniently given =-=[20]-=- in stereographic coordinates Z by Z = tan 1 θ exp(iφ) = 2 √ η1 − η3 − √ η2 − η3 √ , η1 − η2 and Z ∗ = tan 1 θ exp(−iφ). 2 (1.3) For a transparent crystal (Im η = 0), the optic axis lies in the plane ... |

10 |
Physics of nonhermitian degeneracies
- Berry
(Show Context)
Citation Context ...refracts into a hollow cylinder beyond [13, 14]. With absorption (but without chirality [10]), the matrix is complex symmetric, that is, non-Hermitian. This changes the degeneracy structure radically =-=[15]-=-: each conical intersection splits into two branch-points, which in optics are called the singular axes [14, 16–20]. We will study beam propagation associated with these singular axes. The effect of d... |

10 |
phenomenon; smoothing a Victorian discontinuity, Publ
- Berry, Stokes’
(Show Context)
Citation Context ...ticaTM , which we have used for all computations). The phases in A± are determined by careful consideration of the steepest-descent integration contours; in A+, the sign switches across a Stokes line =-=[32, 33]-=-, where the exponential is subdominant relative to the end-point contribution to be considered later. The result (3.3) reveals the reason for working with A+ and A−, rather than B0 and B1: in this lea... |

8 |
Secondary dark rings of internal conical refraction,” Phys
- Warnick, Arnold
- 1997
(Show Context)
Citation Context ...examination reveals that the ring is really two thin rings, separated by the Poggendorff [29] dark ring: an anti-caustic. Still-finer resolution reveals that inside the inner ring are Warnick– Arnold =-=[6]-=- fringes: interference between a geometrical ray and a wave diffracted by the diabolical point on the wave surface. At the centre of the rings, and getting more prominent further from the screen, is a... |

5 |
Internal conical refraction of light beams in biaxial gyrotropic crystals, Opt
- Belsky, Stepanov
- 2002
(Show Context)
Citation Context ...xiality [1, 5]; understanding the phenomena implied by the theory [6–8]; experimental demonstration of the theoretical predictions [9]; extension of the theory to include chirality (optical activity) =-=[10, 11]-=-; and extension of the theory to include nonlinearity [12]. Conical refraction is associated with degeneracy of the matrix generating the wave surface [13] (polar plot of the two refractive indices as... |

4 |
The prediction and discovery of conical refraction by William Rowan Hamilton and Humphrey
- O’Hara
- 1982
(Show Context)
Citation Context ...o the theory of conical diffraction [1, 2], that is, conical refraction and the associated wave effects. This will extend the physical theory of conical diffraction that was begun by Hamilton in 1832 =-=[3, 4]-=-. Interest in the phenomenon has revived, partly as a result of the bicentenary in 2005 of Hamilton’s birth, and there have been several recent developments. These include: definitive formulation of t... |

4 |
1837, Third Supplement to an Essay on the Theory of Systems of Rays, Trans
- Hamilton
(Show Context)
Citation Context ...o the theory of conical diffraction [1, 2], that is, conical refraction and the associated wave effects. This will extend the physical theory of conical diffraction that was begun by Hamilton in 1832 =-=[3, 4]-=-. Interest in the phenomenon has revived, partly as a result of the bicentenary in 2005 of Hamilton’s birth, and there have been several recent developments. These include: definitive formulation of t... |

4 | Orbital and spin angular momentum in conical diffraction - Berry, Jeffrey, et al. - 2005 |

4 |
2004b, Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike
- Berry
(Show Context)
Citation Context ...incident beam profile was restricted by a pinhole, but the theory is considerably simplified by studying conical diffraction for Gaussian incident beams, for which the diffraction detail is different =-=[5, 8]-=-. Moreover, Gaussian beams correspond to 1464-4258/06/121043+09$30.00 © 2006 IOP Publishing Ltd Printed in the UK 1043M V Berry and M R Jeffrey current experiments with lasers [9, 25–27]. Therefore w... |

4 | 1955b The propagation of light in absorbing biaxial crystals - Pancharatnam |

4 | On the phenomena presented by light in its passage along the axes of biaxial crystals - Lloyd |

4 |
Gaussian beams as a bundle of complex rays, Electron
- Deschamps
- 1971
(Show Context)
Citation Context ...y are complex. The reason why double refraction in a transparent crystal can mimic the effect of absorption is connected with the fact that a Gaussian beam can be regarded as a bundle of complex rays =-=[28]-=-. Previous theory [1, 5] showed that conical diffraction by a transparent crystal is determined by a single parameter ρ0, defined as the radius of the geometrical cylinder beyond the crystal divided b... |

3 |
Conical diffraction: Hamiltons diabolical point at the heart of crystal optics, Prog
- Berry, Jeffrey
(Show Context)
Citation Context ... Keywords: polarization, birefringence, non-Hermitian, crystal optics 1. Introduction Our main purpose here is to incorporate dichroism (anisotropic absorption) into the theory of conical diffraction =-=[1, 2]-=-, that is, conical refraction and the associated wave effects. This will extend the physical theory of conical diffraction that was begun by Hamilton in 1832 [3, 4]. Interest in the phenomenon has rev... |

3 |
A 1999 Optical beam propagation in biaxial crystals
- Dreger
(Show Context)
Citation Context ... beam direction, specified by a second 2-vector parameter κ 0, representing the transverse wavevector. Of course κ0 could have been incorporated into the theory of ordinary conical diffraction, where =-=[21]-=- it describes the transition from conical to double refraction. In the pioneering observations [22–24], the incident beam profile was restricted by a pinhole, but the theory is considerably simplified... |

3 | 1841, An examination of the phaenomena of conical refraction in biaxial crystals - Potter |

3 | Large scale demonstrations on conical refraction, http://www.demophys. tsu.ru/Original/Hamilton/Hamilton.html - Mikhailychenko - 2005 |

2 |
2006 Conical diffraction: observations and theory
- Berry, Jeffrey, et al.
(Show Context)
Citation Context ...ity between beam direction and dichroism, a more promising strategy is to study images away from the optic axes of a transparent biaxial crystal. (In the images in our experimental study (figure 2 of =-=[9]-=-, close to the crystal, and unpublished additional images for larger values of ζ closer to that simulated in figure 1), the transition between double and conical refraction was evident, but the dynami... |

2 |
2006a, Chiral conical diffraction
- Berry, Jeffrey
(Show Context)
Citation Context ...xiality [1, 5]; understanding the phenomena implied by the theory [6–8]; experimental demonstration of the theoretical predictions [9]; extension of the theory to include chirality (optical activity) =-=[10, 11]-=-; and extension of the theory to include nonlinearity [12]. Conical refraction is associated with degeneracy of the matrix generating the wave surface [13] (polar plot of the two refractive indices as... |

2 | A J and Bloembergen N 1978 Laser studies of internal conical diffraction. I. Quantitative comparison of experimental and theoretical conical intensity dirstribution in aragonite - Schell |

1 |
A and Newell A C 2006 Conical refraction and nonlinearity Opt. Express 14 at press
- Indik
(Show Context)
Citation Context ...ory [6–8]; experimental demonstration of the theoretical predictions [9]; extension of the theory to include chirality (optical activity) [10, 11]; and extension of the theory to include nonlinearity =-=[12]-=-. Conical refraction is associated with degeneracy of the matrix generating the wave surface [13] (polar plot of the two refractive indices as a function of directions of plane waves). For transparent... |

1 | On the behaviour of pleochroitic crystals along directions in the neighbourhood of an optic axis - Voigt - 1902 |

1 | Crystal Optics in Handbuch der Physik vol XXV/I, ed H Flügge (Berlin: Springer) 1050 diffraction complexified: dichroism and the transition to double refraction - Ramachandran, Ramaseshan - 1961 |

1 | Boulanger B and Marnier G 1994 Experimental study of internal and external conical refraction in KTP Opt - Fève |

1 |
C 1839 Ueber die konische refraction Pogg
- Poggendorff
(Show Context)
Citation Context ...der low resolution, consists of a Hamilton [4] bright ring: the geometrical image of the incident beam. Closer examination reveals that the ring is really two thin rings, separated by the Poggendorff =-=[29]-=- dark ring: an anti-caustic. Still-finer resolution reveals that inside the inner ring are Warnick– Arnold [6] fringes: interference between a geometrical ray and a wave diffracted by the diabolical p... |

1 |
D and Harney H L 2001 The chirality of exceptional points Eur
- Heiss
(Show Context)
Citation Context ...he factors 1/2, and the sign change of ˜ρ, d± acquire, in a circuit of each branch-point (2.24), the phase factors ±i familiar around degeneracies (‘exceptional points’) of complex symmetric matrices =-=[30]-=-, making them singularities of index ±1/4[20]. It is easier to observe not D itself but the light intensity I. This is where I = D ∗ · D = 1 4 exp{2ImF0}d ∗ 0 · M · d0, (2.30) M = (A ∗ + m† + + A ∗ − ... |