Evolution of the hyperbolic umbilic diffraction pattern from Airy rings

Journal of Optics A: Pure and Applied Optics

Volumn 8, Issue 3, 2006, Pages 304-314

  Nye, J F ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Diffraction; Diffraction catastrophes; Fraunhofer; Fresnel; Optical vortices; Singularity optics; Wave dislocations

Indexed keywords

DISLOCATIONS (CRYSTALS); OPTICAL SYSTEMS; TOPOLOGY;

DIFFRACTION CATASTROPHES; FRAUNHOFER; FRESNEL;

ELECTROMAGNETIC WAVE DIFFRACTION;

EID: 33644756923     PISSN: 14644258     EISSN: 17413567     Source Type: Journal    
DOI: 10.1088/1464-4258/8/3/013     Document Type: Article

References (19)

1. Beijersbergen M W 1996 Phase singularities in optical beams Doctoral Dissertation University of Leiden
2. Berry M V 1998 Wave dislocation reactions in non-paraxial Gaussian beams J. Mod. Opt. 45 1845-58
3. Berry M V and Dennis M R 2001 Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime J. Phys. A: Math. Gen. 34 8877-88
4. Berry M V, Nye J F and Wright F J 1979 The elliptic umbilic diffraction catastrophe Phil. Trans. R. Soc. 291 453-84
5. Farnell G W 1957 Calculated intensity and phase distribution in the image space of a microwave lens Can. J. Phys. 35 777-83
6. Farnell G W 1958 Measured phase distribution in the image space of a microwave lens Can. J. Phys. 36 935-43
7. Karman G P, Beijersbergen M W, van Duijl A and Woerdman J P 1997 Creation and annihilation of phase singularities in a focal field Opt. Lett. 22 1503-5
8. Karman G P, Beijersbergen M W, van Duijl A and Woerdman J P 1998 Airy pattern reorganization and sub-wavelength structure in a focus J. Opt. Soc. Am. A 15 884-99
9. Linfoot E H and Wolf E 1956 Phase distribution near focus in an aberration-free diffraction image Proc. Phys. Soc. B 69 823-32
10. Nicholls K W and Nye J F 1987 Three-beam model for studying dislocations in wave pulses J Phys A: Math. Gen. 20 4673-96
11. Nye J F 1998 Unfolding of higher-order wave dislocations J. Opt. Soc. Am. A 15 1132-8
12. Nye J F 2003a Evolution from a Fraunhofer to a Pearcey diffraction pattern J. Opt. A: Pure Appl. Opt. 5 495-502
13. Nye J F 2003b From Airy rings to the elliptic umbilic diffraction catastrophe J. Opt. A: Pure Appl. Opt. 5 503-10
14. Nye J F 2004 Local solutions for the interaction of wave dislocations J. Opt. A: Pure Appl. Opt. 6 S251-4
15. Nye J F 2005 The relation between the spherical aberration of a lens and the spun cusp diffraction catastrophe J. Opt. A: Pure Appl. Opt. 7 95-102
16. Nye J F 2006 Dislocation lines in the hyperbolic umbilic diffraction catastrophe Proc. R. Soc. Lond. A at press
17. Pearcey T 1946 The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic Phil. Mag. 37 311-7
18. Press W H, Flannery B P, Teukolsky S A and Vetterling W T 1986 Numerical Recipes (Cambridge: Cambridge University Press)
19. Wright F J and Berry M V 1984 Wave-front dislocations in the soundfield of a pulsed circular piston radiator J. Acoust. Soc. Am. 75 733-48