Math 2.0

Optics, electromagnetic theory Definition

Conical refraction

Builds on Fresnel's wave surfaceBirefringenceIndex ellipsoid

Definition

Let a biaxial transparent medium be given, with principal speeds vx,vy,vzv_x, v_y, v_z all distinct. Its Fresnel wave surface WW has four planes that touch WW along a whole circle, and four conical singular points.

  1. Internal conical refraction: let ๐ฌ\mathbf{s} be a wave normal orthogonal to one of these tangent planes. The energy of the waves with normal ๐ฌ\mathbf{s} flows along all the rays from the centre of WW to the circle of contact. So a narrow beam with wave normal ๐ฌ\mathbf{s} spreads into a hollow cone inside the medium.
  2. External conical refraction: let ๐ญ\mathbf{t} be a ray direction through one of the singular points. The waves whose energy flows along ๐ญ\mathbf{t} have a whole cone of wave normals. So a ray along ๐ญ\mathbf{t} leaves the medium as a hollow cone.

Remarks

The directions ๐ฌ\mathbf{s} of clause 1 are the two optic axes, the normals to the circular sections of the index ellipsoid. The directions ๐ญ\mathbf{t} of clause 2 are the two optic ray axes. In internal conical refraction a beam that leaves the crystal through a parallel face emerges as a hollow cylinder of light, seen as a ring on a screen.

Example: a biaxial crystal such as aragonite shows both effects along its axes.

Non-example: a uniaxial crystal shows no conical refraction. There the two sheets of the wave surface touch only at two points on the optic axis, with a common tangent plane. So no circle of contact and no cone appear.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

Show the path as a graph
Birefringence, concept, no evidence levelBirefringenceconceptFresnel's wave surface, concept, no evidence levelFresnel's wave surfaceconceptIndex ellipsoid, concept, no evidence levelIndex ellipsoidconceptConical refraction, definition, no evidence levelConical refractiondefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Birefringence concept
  2. Fresnel's wave surface concept
  3. Index ellipsoid concept
  4. Conical refraction definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Conical_refraction
About this page
TagDVPC28JZ3W
URIm2://DVPC28JZ3W
Kinddefinition
WritingW0 stub
MSC78A10, 78A05
DefinesConical refraction
UsesFresnel's wave surface, Birefringence, Index ellipsoid
Changed3 November 2026

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