The caustics of two- and three-dimensional parabolic reflectors

被引：8
|
作者：
Bell, C. G. [1 ]
Ockendon, H. [1 ]
Ockendon, J. R. [1 ]
机构：
[1] Univ Oxford, Inst Math, Oxford OX1 3LB, England
来源：
JOURNAL OF OPTICS | 2010年 / 12卷 / 06期
基金：
英国工程与自然科学研究理事会;
关键词：
caustic; hyperbolic umbilic; paraboloid; paraboloid of revolution; elliptic paraboloid; parabolic cylinder; parabola; Tschirnhausen cubic; catastrophe; GEOMETRICAL-OPTICS; RAY PROPAGATION; FLUX DENSITY; WAVE-FRONT; SURFACE; CURVE;
D O I：
10.1088/2040-8978/12/6/065703
中图分类号：
O43 [光学];
学科分类号：
070207 ; 0803 ;
摘要：
The caustic of a two-dimensional parabola illuminated off-axis is the Tschirnhausen cubic and does not contain any singular points. The caustic of a three-dimensional paraboloid of revolution similarly illuminated consists of two cusped sheets containing a hyperbolic umbilic singularity. We relate these two situations by considering a suitable sequence of illuminated elliptic paraboloids.
引用
收藏
页数：12
相关论文
共 50 条
  • [1] The formation of caustics in two- and three-dimensional media
    Spetzler, J
    Snieder, R
    [J]. GEOPHYSICAL JOURNAL INTERNATIONAL, 2001, 144 (01) : 175 - 182
  • [2] The decoherence of the two- and three-dimensional parabolic quantum dot qubit
    Chen, Shi-Hua
    [J]. PHYSICA B-CONDENSED MATTER, 2010, 405 (03) : 843 - 845
  • [3] Two- and three-dimensional surfaces
    Hauck, J
    Mika, K
    [J]. ZEITSCHRIFT FUR PHYSIKALISCHE CHEMIE-INTERNATIONAL JOURNAL OF RESEARCH IN PHYSICAL CHEMISTRY & CHEMICAL PHYSICS, 2002, 216 (11): : 1281 - 1293
  • [4] Coexistence of a two- and three-dimensional Landau states in a wide parabolic quantum well
    Sergio, CS
    Gusev, GM
    Leite, JR
    Olshanetskii, EB
    Bykov, AA
    Moshegov, NT
    Bakarov, AK
    Toropov, AI
    Maude, DK
    Estibals, O
    Portal, JC
    [J]. PHYSICAL REVIEW B, 2001, 64 (11)
  • [5] Bioinspired two- and three-dimensional nanostructures
    Mirkin, Chad A.
    [J]. JOURNAL OF NANOPARTICLE RESEARCH, 2000, 2 (02) : 121 - 122
  • [6] Two- and three-dimensional tetrathiafulvalene macrocycles
    Nielsen, MB
    Becher, J
    [J]. LIEBIGS ANNALEN-RECUEIL, 1997, (11): : 2177 - 2187
  • [7] Percolation on two- and three-dimensional lattices
    Martins, PHL
    Plascak, JA
    [J]. PHYSICAL REVIEW E, 2003, 67 (04)
  • [8] Two- and three-dimensional parametric packing
    Miyazawa, F. K.
    Wakabayashi, Y.
    [J]. COMPUTERS & OPERATIONS RESEARCH, 2007, 34 (09) : 2589 - 2603
  • [9] Bioinspired Two- and Three-Dimensional Nanostructures
    Chad A. Mirkin
    [J]. Journal of Nanoparticle Research, 2000, 2 : 121 - 122
  • [10] Three-Dimensional Leaf Edge Reconstruction Combining Two- and Three-Dimensional Approaches
    Murata, Hidekazu
    Noshita, Koji
    [J]. PLANT PHENOMICS, 2024, 6
12345