Abstract

Birefringence of ice causes the inner edges of refraction halos to be polarized. The direction of this polarization relates directly to the projection of the crystal main axis onto the sky. This implies that the inner-edge polarization can serve as an observational diagnostic for determining the actual nature of a halo arc if two competing explanations exist. The direction and the visibility of the inner-edge polarization of arcs and circular halos arising from usual ice crystals and from ice crystals with pyramidal ends are calculated. It is found that the observation of inner-edge polarization can be decisive for the identification of a spot that might be either a 44° parhelion or a 46° parhelion, of an arc that might be either a 22° sunvex Parry arc or a 20° Parroid arc arising from plate-oriented pyramidal crystals, and of an arc that might be either a 22° suncave Parry arc or a 23° Parroid arc from plate-oriented pyramidal crystals. (With a Parroid arc, a halo is that which arises from an ice wedge made up of two faces of a crystal that rotates about a vertically oriented spin axis, and the edge of the wedge is perpendicular to this spin axis.) Polarization properties of other rare arcs are discussed. Practical hints are given for observing visually the inner-edge polarization of halos.

© 1998 Optical Society of America

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References

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  1. R. G. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, 1980).
  2. F. Pattloch, E. Tränkle, “Monte Carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. A 1, 520–526 (1984).
    [CrossRef]
  3. R. G. Greenler, E. Tränkle, “Anthelic arcs from airborne ice crystals,” Nature (London) 311, 339–343 (1984).
    [CrossRef]
  4. W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).
  5. J. Veldkamp, Continenten op Drift [privately published by Veldkamp, Bilthoven, The Netherlands, 1988; available from the Royal Netherlands Meteorological Institute (KNMI), P.O. Box 201, 3730 AE De Bilt, The Netherlands].
  6. W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
    [CrossRef]
  7. S. W. Visser, “Die Haloerscheinung,” in Handbuch der Geophysik, F. Möller, ed. (Bornträger, Berlin, 1960), Vol. 8, pp. 1027–1081.
  8. A. Bravais, “Mémoire sur les halos et les phénomènes optiques qui les accompagnent,” J. Éc. R. Polytech. 31, 1–270 (1847).
  9. E. Tränkle, R. G. Greenler, “Multiple-scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591–599 (1987).
    [CrossRef]
  10. W. Tape, G. P. Können, “A general setting for halo theory,” submitted to Appl. Opt.; see Abstract, 37, 1434 (1998).
  11. G. P. Können, J. Tinbergen, “Polarimetry of a 22° halo,” Appl. Opt. 30, 3382–3400 (1991).
    [CrossRef] [PubMed]
  12. G. P. Können, S. H. Muller, J. Tinbergen, “Halo polarization profiles and the interfacial angles of ice crystals,” Appl. Opt. 33, 4569–4579 (1994).
    [CrossRef] [PubMed]
  13. P. V. Hobbs, Ice Physics (Clarendon, Oxford, 1974), pp. 200–202.
  14. G. Szivessy, “Kristaloptik,” in Handbuch der Physik, H. Konen, ed. (Springer-Verlag, Berlin, 1920), Vol. 20, pp. 689–709.
  15. F. Schaaf, “A field guide to atmospheric optics,” Sky Telesc. 77, 254–259 (1989).
  16. G. P. Können, “Polarization and intensity distributions of refraction halos,” J. Opt. Soc. Am. 73, 1629–1640 (1983).
    [CrossRef]
  17. M. V. Berry, “Supernumery ice-crystal halos?” Appl. Opt. 33, 4563–4568 (1994).
    [CrossRef] [PubMed]

1994 (2)

G. P. Können, S. H. Muller, J. Tinbergen, “Halo polarization profiles and the interfacial angles of ice crystals,” Appl. Opt. 33, 4569–4579 (1994).
[CrossRef] [PubMed]

M. V. Berry, “Supernumery ice-crystal halos?” Appl. Opt. 33, 4563–4568 (1994).
[CrossRef] [PubMed]

1991 (1)

1989 (1)

F. Schaaf, “A field guide to atmospheric optics,” Sky Telesc. 77, 254–259 (1989).

1987 (1)

1984 (2)

F. Pattloch, E. Tränkle, “Monte Carlo simulation and analysis of halo phenomena,” J. Opt. Soc. Am. A 1, 520–526 (1984).
[CrossRef]

R. G. Greenler, E. Tränkle, “Anthelic arcs from airborne ice crystals,” Nature (London) 311, 339–343 (1984).
[CrossRef]

1983 (1)

G. P. Können, “Polarization and intensity distributions of refraction halos,” J. Opt. Soc. Am. 73, 1629–1640 (1983).
[CrossRef]

1972 (1)

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
[CrossRef]

1847 (1)

A. Bravais, “Mémoire sur les halos et les phénomènes optiques qui les accompagnent,” J. Éc. R. Polytech. 31, 1–270 (1847).

Berry, M. V.

Bravais, A.

A. Bravais, “Mémoire sur les halos et les phénomènes optiques qui les accompagnent,” J. Éc. R. Polytech. 31, 1–270 (1847).

Evans, W. F. J.

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
[CrossRef]

Greenler, R. G.

E. Tränkle, R. G. Greenler, “Multiple-scattering effects in halo phenomena,” J. Opt. Soc. Am. A 4, 591–599 (1987).
[CrossRef]

R. G. Greenler, E. Tränkle, “Anthelic arcs from airborne ice crystals,” Nature (London) 311, 339–343 (1984).
[CrossRef]

R. G. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, 1980).

Hobbs, P. V.

P. V. Hobbs, Ice Physics (Clarendon, Oxford, 1974), pp. 200–202.

Können, G. P.

G. P. Können, S. H. Muller, J. Tinbergen, “Halo polarization profiles and the interfacial angles of ice crystals,” Appl. Opt. 33, 4569–4579 (1994).
[CrossRef] [PubMed]

G. P. Können, J. Tinbergen, “Polarimetry of a 22° halo,” Appl. Opt. 30, 3382–3400 (1991).
[CrossRef] [PubMed]

G. P. Können, “Polarization and intensity distributions of refraction halos,” J. Opt. Soc. Am. 73, 1629–1640 (1983).
[CrossRef]

W. Tape, G. P. Können, “A general setting for halo theory,” submitted to Appl. Opt.; see Abstract, 37, 1434 (1998).

Muller, S. H.

G. P. Können, S. H. Muller, J. Tinbergen, “Halo polarization profiles and the interfacial angles of ice crystals,” Appl. Opt. 33, 4569–4579 (1994).
[CrossRef] [PubMed]

Pattloch, F.

Schaaf, F.

F. Schaaf, “A field guide to atmospheric optics,” Sky Telesc. 77, 254–259 (1989).

Szivessy, G.

G. Szivessy, “Kristaloptik,” in Handbuch der Physik, H. Konen, ed. (Springer-Verlag, Berlin, 1920), Vol. 20, pp. 689–709.

Tape, W.

W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

W. Tape, G. P. Können, “A general setting for halo theory,” submitted to Appl. Opt.; see Abstract, 37, 1434 (1998).

Tinbergen, J.

G. P. Können, S. H. Muller, J. Tinbergen, “Halo polarization profiles and the interfacial angles of ice crystals,” Appl. Opt. 33, 4569–4579 (1994).
[CrossRef] [PubMed]

G. P. Können, J. Tinbergen, “Polarimetry of a 22° halo,” Appl. Opt. 30, 3382–3400 (1991).
[CrossRef] [PubMed]

Tränkle, E.

Tricker, R. A. R.

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
[CrossRef]

Veldkamp, J.

J. Veldkamp, Continenten op Drift [privately published by Veldkamp, Bilthoven, The Netherlands, 1988; available from the Royal Netherlands Meteorological Institute (KNMI), P.O. Box 201, 3730 AE De Bilt, The Netherlands].

Visser, S. W.

S. W. Visser, “Die Haloerscheinung,” in Handbuch der Geophysik, F. Möller, ed. (Bornträger, Berlin, 1960), Vol. 8, pp. 1027–1081.

Appl. Opt. (1)

G. P. Können, S. H. Muller, J. Tinbergen, “Halo polarization profiles and the interfacial angles of ice crystals,” Appl. Opt. 33, 4569–4579 (1994).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Éc. R. Polytech. (1)

A. Bravais, “Mémoire sur les halos et les phénomènes optiques qui les accompagnent,” J. Éc. R. Polytech. 31, 1–270 (1847).

J. Opt. Soc. Am. (1)

G. P. Können, “Polarization and intensity distributions of refraction halos,” J. Opt. Soc. Am. 73, 1629–1640 (1983).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (London) (1)

R. G. Greenler, E. Tränkle, “Anthelic arcs from airborne ice crystals,” Nature (London) 311, 339–343 (1984).
[CrossRef]

Sky Telesc. (1)

F. Schaaf, “A field guide to atmospheric optics,” Sky Telesc. 77, 254–259 (1989).

Weather (1)

W. F. J. Evans, R. A. R. Tricker, “Unusual arcs in the Saskatoon halo display,” Weather 27, 234–238 (1972).
[CrossRef]

Other (7)

S. W. Visser, “Die Haloerscheinung,” in Handbuch der Geophysik, F. Möller, ed. (Bornträger, Berlin, 1960), Vol. 8, pp. 1027–1081.

W. Tape, G. P. Können, “A general setting for halo theory,” submitted to Appl. Opt.; see Abstract, 37, 1434 (1998).

W. Tape, Atmospheric Halos, Vol. 64 of Antarctic Research Series (American Geophysical Union, Washington, D.C., 1994).

J. Veldkamp, Continenten op Drift [privately published by Veldkamp, Bilthoven, The Netherlands, 1988; available from the Royal Netherlands Meteorological Institute (KNMI), P.O. Box 201, 3730 AE De Bilt, The Netherlands].

R. G. Greenler, Rainbows, Halos and Glories (Cambridge U. Press, Cambridge, 1980).

P. V. Hobbs, Ice Physics (Clarendon, Oxford, 1974), pp. 200–202.

G. Szivessy, “Kristaloptik,” in Handbuch der Physik, H. Konen, ed. (Springer-Verlag, Berlin, 1920), Vol. 20, pp. 689–709.

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Figures (4)

Fig. 1
Fig. 1

Pyramidal crystal, the numbering of the faces and the angles of halos of which at least one of the two refracting faces is a pyramidal face. The bottom face has face number 2. The crystal main axis (C axis) coincides with the crystal optic axis. The figure is taken with permission from Ref. 4.

Fig. 2
Fig. 2

Examples of formation of a Parroid arc in pyramidal crystals of different orientations. By definition, a Parroid arc is an arc that arises from refraction through wedges that spin about a vertical axis and the refracting edge of the wedge is perpendicular to this axis (hence horizontal). The two upper diagrams show a light path for a 20° Parroid arc in Parry-oriented crystals (main crystal axis and two prism faces horizontal; left diagram) and in plate-oriented crystals (main crystal axis vertical; right diagram). The two lower diagrams give examples for 23° Parroid arcs. Each Parroid arc has its own shape. In the depicted crystals, ray paths exist for other 20° Parroid arcs or other 23° Parroid arcs and also for Parroid arcs associated with circular halos of other radii. These possibilities are not shown here.

Fig. 3
Fig. 3

Minimum-deviation ray passing though a halo-generating ice wedge consisting of two of the crystal faces of Fig. 1. The scattering plane is perpendicular to the refracting edge and hence in this view is horizontal. The angle γ determines the refractive index of the extraordinary refracted rays [Eq. (1)]. The direction of polarization of the extraordinary refracted rays is in the plane formed by the light ray and the crystal main axis; that of ordinary refracted rays (not shown) is perpendicular to such a plane. The latter rays make up the halo inner edge. For a circular halo, the angle ψ defines the tilt with respect to the scattering plane of the polarization of light of an individual crystal wedge that contributes to the halo inner-edge radiance.

Fig. 4
Fig. 4

Angular displacement Δθ h , as seen through a rotating polarizer, of the inner edges of the upper sunvex and suncave Parry arcs and of their closely resembling counterparts, the upper 20° and 23° Parroid arcs arising from plate-oriented pyramidal crystals. The right axis represents the visibility Vis of the arc’s inner-edge polarization relative to that of the 22° halo. The light paths of the arcs are depicted schematically.

Tables (3)

Tables Icon

Table 1 Inner-Edge Polarization of Circular Halos

Tables Icon

Table 2 Some Pairs of Halo Arcs that may be Mistaken for Each Other, Whose Real Nature may be Determined by their Inner-Edge Polarization

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Table 3 Parroid Arcs from Parry-Oriented Crystals with Pyramidal Ends Compared with 22° (Alternate) Parry Arcs

Equations (4)

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Δ n = n eff - n o = n e - n o sin 2   γ ,
Δ θ h = 180 ° π 2   sin θ h / 2 n o cos θ h / 2 - 1   Δ n ,
P = cos 2 ψ .
Vis = | P | Δ θ h / Δ θ h 22 ° = | P | Δ θ h / 0.106 ° .

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