Abstract

The deflection of light in ferroelastic crystals results from refraction and reflection at domain walls. When the tilt angle of the principal axes in neighboring domains is small, simple relationships between the crystal birefringences and the angles of the deflected beams can be deduced from Snell’s law of refraction. As a rule, this condition is satisfied at W-domain walls in ferroelastic species that have a biaxial prototype phase. In this case, measurement of the deflection angles permits one to determine the birefringences easily. This method has as its main advantages independence of the sample thickness and the need for only rough sample preparation. It is absolutely insensitive to temperature fluctuations. We have applied the method to crystals of rubidium hydrogen selenate and dihydrated barium chloride as illustrative examples.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Tsukamoto, J. Hatano, and H. Futuma, in “Proceedings of the 2nd Japanese–Soviet Symposium on Ferroelectricity, Kyoto 1980,” J. Phys. Soc. Jpn. 49, Suppl. B155–157 (1980).
  2. T. Tsukamoto, M. Komuake, S. Suzuki, H. Futuma, and Y. Makita, “Domain structure and deflection of light at domain walls in RbHSeO4,” J. Phys. Soc. Jpn. 52, 3966–3973 (1983).
    [CrossRef]
  3. T. Tsukamoto, J. Hatano, and H. Futuma, “Refraction and reflection of light at ferroelastic domain walls in rochelle salt crystal,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
    [CrossRef]
  4. T. Tsukamoto, J. Hatano, and H. Futuma, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
    [CrossRef]
  5. T. Tsukamoto and H. Futuma, “Light deflection induced by ferroelastic layered domains,” Phase Transit. 45, 59–76 (1993).
    [CrossRef]
  6. J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–55140 (1975).
    [CrossRef]
  7. R. Poprawski, J. Mroz, Z. Czapla, and L. Sobczyk, “Ferroelectrics properties and domain structure in RbHSeO4,” Acta Phys. Pol. A 55, 641–645 (1979).
  8. I. Brach, D. J. Jones, and J. Roziére, “The crystal structure of RbHSeO4: a neutron diffraction study of the paraelectric phase,” J. Solid State Chem. 48, 401–406 (1983).
    [CrossRef]
  9. L. Guilbert, J. P. Salvestrini, P. Kolata, F. X. Abrial, M. D. Fontana, and Z. Czapla, “Optical characteristics of triclinic rubidium hydrogen selenate,” J. Opt. Soc. Am. B 15, 1009–1016 (1998).
    [CrossRef]
  10. J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in APFA ferroelastic crystals,” J. Phys.: Condens. Matter 12, 653–667 (2000).

2000 (1)

J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in APFA ferroelastic crystals,” J. Phys.: Condens. Matter 12, 653–667 (2000).

1998 (1)

1993 (1)

T. Tsukamoto and H. Futuma, “Light deflection induced by ferroelastic layered domains,” Phase Transit. 45, 59–76 (1993).
[CrossRef]

1984 (1)

T. Tsukamoto, J. Hatano, and H. Futuma, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

1983 (2)

T. Tsukamoto, M. Komuake, S. Suzuki, H. Futuma, and Y. Makita, “Domain structure and deflection of light at domain walls in RbHSeO4,” J. Phys. Soc. Jpn. 52, 3966–3973 (1983).
[CrossRef]

I. Brach, D. J. Jones, and J. Roziére, “The crystal structure of RbHSeO4: a neutron diffraction study of the paraelectric phase,” J. Solid State Chem. 48, 401–406 (1983).
[CrossRef]

1982 (1)

T. Tsukamoto, J. Hatano, and H. Futuma, “Refraction and reflection of light at ferroelastic domain walls in rochelle salt crystal,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
[CrossRef]

1980 (1)

T. Tsukamoto, J. Hatano, and H. Futuma, in “Proceedings of the 2nd Japanese–Soviet Symposium on Ferroelectricity, Kyoto 1980,” J. Phys. Soc. Jpn. 49, Suppl. B155–157 (1980).

1979 (1)

R. Poprawski, J. Mroz, Z. Czapla, and L. Sobczyk, “Ferroelectrics properties and domain structure in RbHSeO4,” Acta Phys. Pol. A 55, 641–645 (1979).

1975 (1)

J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–55140 (1975).
[CrossRef]

Abrial, F. X.

Bornarel, J.

J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in APFA ferroelastic crystals,” J. Phys.: Condens. Matter 12, 653–667 (2000).

Brach, I.

I. Brach, D. J. Jones, and J. Roziére, “The crystal structure of RbHSeO4: a neutron diffraction study of the paraelectric phase,” J. Solid State Chem. 48, 401–406 (1983).
[CrossRef]

Czapla, Z.

J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in APFA ferroelastic crystals,” J. Phys.: Condens. Matter 12, 653–667 (2000).

L. Guilbert, J. P. Salvestrini, P. Kolata, F. X. Abrial, M. D. Fontana, and Z. Czapla, “Optical characteristics of triclinic rubidium hydrogen selenate,” J. Opt. Soc. Am. B 15, 1009–1016 (1998).
[CrossRef]

R. Poprawski, J. Mroz, Z. Czapla, and L. Sobczyk, “Ferroelectrics properties and domain structure in RbHSeO4,” Acta Phys. Pol. A 55, 641–645 (1979).

Fontana, M. D.

Futuma, H.

T. Tsukamoto and H. Futuma, “Light deflection induced by ferroelastic layered domains,” Phase Transit. 45, 59–76 (1993).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

T. Tsukamoto, M. Komuake, S. Suzuki, H. Futuma, and Y. Makita, “Domain structure and deflection of light at domain walls in RbHSeO4,” J. Phys. Soc. Jpn. 52, 3966–3973 (1983).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, “Refraction and reflection of light at ferroelastic domain walls in rochelle salt crystal,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, in “Proceedings of the 2nd Japanese–Soviet Symposium on Ferroelectricity, Kyoto 1980,” J. Phys. Soc. Jpn. 49, Suppl. B155–157 (1980).

Guilbert, L.

Hatano, J.

T. Tsukamoto, J. Hatano, and H. Futuma, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, “Refraction and reflection of light at ferroelastic domain walls in rochelle salt crystal,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, in “Proceedings of the 2nd Japanese–Soviet Symposium on Ferroelectricity, Kyoto 1980,” J. Phys. Soc. Jpn. 49, Suppl. B155–157 (1980).

Jones, D. J.

I. Brach, D. J. Jones, and J. Roziére, “The crystal structure of RbHSeO4: a neutron diffraction study of the paraelectric phase,” J. Solid State Chem. 48, 401–406 (1983).
[CrossRef]

Kolata, P.

Komuake, M.

T. Tsukamoto, M. Komuake, S. Suzuki, H. Futuma, and Y. Makita, “Domain structure and deflection of light at domain walls in RbHSeO4,” J. Phys. Soc. Jpn. 52, 3966–3973 (1983).
[CrossRef]

Makita, Y.

T. Tsukamoto, M. Komuake, S. Suzuki, H. Futuma, and Y. Makita, “Domain structure and deflection of light at domain walls in RbHSeO4,” J. Phys. Soc. Jpn. 52, 3966–3973 (1983).
[CrossRef]

Mroz, J.

R. Poprawski, J. Mroz, Z. Czapla, and L. Sobczyk, “Ferroelectrics properties and domain structure in RbHSeO4,” Acta Phys. Pol. A 55, 641–645 (1979).

Poprawski, R.

R. Poprawski, J. Mroz, Z. Czapla, and L. Sobczyk, “Ferroelectrics properties and domain structure in RbHSeO4,” Acta Phys. Pol. A 55, 641–645 (1979).

Roziére, J.

I. Brach, D. J. Jones, and J. Roziére, “The crystal structure of RbHSeO4: a neutron diffraction study of the paraelectric phase,” J. Solid State Chem. 48, 401–406 (1983).
[CrossRef]

Salvestrini, J. P.

Sapriel, J.

J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–55140 (1975).
[CrossRef]

Sobczyk, L.

R. Poprawski, J. Mroz, Z. Czapla, and L. Sobczyk, “Ferroelectrics properties and domain structure in RbHSeO4,” Acta Phys. Pol. A 55, 641–645 (1979).

Staniorowski, P.

J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in APFA ferroelastic crystals,” J. Phys.: Condens. Matter 12, 653–667 (2000).

Suzuki, S.

T. Tsukamoto, M. Komuake, S. Suzuki, H. Futuma, and Y. Makita, “Domain structure and deflection of light at domain walls in RbHSeO4,” J. Phys. Soc. Jpn. 52, 3966–3973 (1983).
[CrossRef]

Tsukamoto, T.

T. Tsukamoto and H. Futuma, “Light deflection induced by ferroelastic layered domains,” Phase Transit. 45, 59–76 (1993).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

T. Tsukamoto, M. Komuake, S. Suzuki, H. Futuma, and Y. Makita, “Domain structure and deflection of light at domain walls in RbHSeO4,” J. Phys. Soc. Jpn. 52, 3966–3973 (1983).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, “Refraction and reflection of light at ferroelastic domain walls in rochelle salt crystal,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, in “Proceedings of the 2nd Japanese–Soviet Symposium on Ferroelectricity, Kyoto 1980,” J. Phys. Soc. Jpn. 49, Suppl. B155–157 (1980).

Acta Phys. Pol. A (1)

R. Poprawski, J. Mroz, Z. Czapla, and L. Sobczyk, “Ferroelectrics properties and domain structure in RbHSeO4,” Acta Phys. Pol. A 55, 641–645 (1979).

J. Opt. Soc. Am. B (1)

J. Phys. Soc. Jpn. (4)

T. Tsukamoto, J. Hatano, and H. Futuma, in “Proceedings of the 2nd Japanese–Soviet Symposium on Ferroelectricity, Kyoto 1980,” J. Phys. Soc. Jpn. 49, Suppl. B155–157 (1980).

T. Tsukamoto, M. Komuake, S. Suzuki, H. Futuma, and Y. Makita, “Domain structure and deflection of light at domain walls in RbHSeO4,” J. Phys. Soc. Jpn. 52, 3966–3973 (1983).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, “Refraction and reflection of light at ferroelastic domain walls in rochelle salt crystal,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futuma, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and BiTi3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

J. Phys.: Condens. Matter (1)

J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in APFA ferroelastic crystals,” J. Phys.: Condens. Matter 12, 653–667 (2000).

J. Solid State Chem. (1)

I. Brach, D. J. Jones, and J. Roziére, “The crystal structure of RbHSeO4: a neutron diffraction study of the paraelectric phase,” J. Solid State Chem. 48, 401–406 (1983).
[CrossRef]

Phase Transit. (1)

T. Tsukamoto and H. Futuma, “Light deflection induced by ferroelastic layered domains,” Phase Transit. 45, 59–76 (1993).
[CrossRef]

Phys. Rev. B (1)

J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–55140 (1975).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Deflection phenomenon at a ferroelastic W-domain wall. A, B, refractive transmission (from low index to high index and vice versa), A and B, the corresponding refractive reflections. D (direct beam) and R (reflected beam), quasi-nonrefractive processes without change of the index magnitude.

Fig. 2
Fig. 2

Definition of the so-called pseudoprincipal axes: x3, perpendicular to the plane of the domain walls; x1, x2, neutral lines in this plane. In the case of monoclinic crystals with orthorhombic protophase (bottom) x1 and x2 coincide with crystallographic axes. One of them is the monoclinic axis; it is a true principal axis that is common in both orientation states.

Fig. 3
Fig. 3

Mutual tilt angle of the neutral lines with respect to a W-domain wall, as seen from pseudoprincipal axes x1 and x2 defined above (see Fig. 2). The figure shows the general case of a triclinic crystal. For monoclinic crystals either ϕ1 or ϕ2 is strictly zero.

Fig. 4
Fig. 4

Deflection processes, shown separately for the fast incident wave (A deflection) and for the slow incident wave (B deflection). For small optical tilts the beams are either quasi ordinary (filled circles) or extraordinary (hatch marks), depending on the refractive index (see Table 1) below. Deflections A and B are reciprocals of each other when the path of the light is reversed. The reflected (R) and retrodeflected (A and B) beams, symmetrical to D, A, and B, respectively, are not represented here.

Fig. 5
Fig. 5

Deflection angles measured in x1-cut and x2-cut RHSe plates. The solid curves are linear regressions. In the experiment, x2-cut beam crossing occurs when the incident wave vector comes close to an optical axis.

Fig. 6
Fig. 6

Deflection angles measured in BCD plates. The solid curves in (a) are linear regressions. The b-cut plate (b) causes no deflection, owing to its monoclinic symmetry; deflection angle αb(0)=11.4° is determined by a parabolic interpolation of angular measurements in the vicinity of the b axis.

Fig. 7
Fig. 7

Systematic error caused by sample thickness. PD, photodetector.

Tables (1)

Tables Icon

Table 1 Characteristics of the Deflected Beams at Small Incidencea

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

sin i=nf (if)sin if,nf (if)cos if=ns(αs)cos αs,
ns(αs)sin αs=sin α,
sin i=ns(is)sin is,ns(is)cos is=nf (βf)cos βf,
nf (βf)sin βf=sin β,
sin2 α-sin2 i=ns2(αs)-nf2(if)(>0),
sin2 β-sin2 i=nf2(βf)-ns2(is)(<0).
1nf2(if)cos2 ifn32+sin2 ifnj2,
sin2 α1(i)n22-n32+n32n12sin2 i,
sin2 α2(i)n12-n32+n32n22sin2 i.
sin2 α1(0)n22-n32Δ1(n2),
sin2 α2(0)n12-n32Δ2(n2),
sin2 αx(0)n2(x)-n32.
1n2(x)cos2 xn22+sin2 xn12
n32n12sin2 β1(i)sin2 i-(n22-n32),
n32n22sin2 β2(i)sin2 i-(n12-n32).
1ns2(αs)cos2 αsn32+sin2 αsnj2,
n32n12sin2 α1(i)n32-n22+sin2 i,
n32n22sin2 α2(i)n32-n12+sin2 i.
sin2 α1(0)n12n32(n32-n22) (x1 cut),
sin2 α2(0)n22n32(n32-n12) (x2 cut).
sin2 β1(i)n32n12sin2 i-(n32-n22),
sin2 β2(i)n32n22sin2 i-(n32-n12).
Δ1(n2)n22-n32=0.1716(12),
n32/n12=0.984(4),
Δ2(n2)n12-n32=0.0420(6),
n32/n22=0.930(2).
Δn1n2-n3=0.0559(4),
Δn2n3-n1=-0.0139(2).
α2(0)=17.2(±0.1)°
Δa(n2)
n32-nb2(n32/na2)sin2 α2(0)=0.0888(10),
α1(0)=11.4(±0.1)°
Δb(n2)
n32-na2(n32/nb2)sin2 α1(0)=0.0404(8).
δαα-αm=t cos3 α2L(tan α-tan αs)t2L(1-1/n)sin α,

Metrics