Abstract

The optical discontinuities located at domain walls in low-symmetry ferroelastics are responsible for the light-deflection phenomenon and for subsequent impairments of the intensity, the phase coherence, and the polarization of the direct beam transmitted through the domain structure. Here, intensity losses are studied. Degradations of the coherence and the polarization are addressed in a companion paper. The deflected intensities are calculated as a function of the domain-wall density and of the average deformation of the polydomain sample. At first, a random phase hypothesis is assumed, then the calculation is refined by a two-wave interference model. Dichroic effects in deflection are predicted.

© 2002 Optical Society of America

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  1. T. Tsukamoto, J. Hatano, and H. Futama, “Refraction and reflection of light at ferroelastic domain walls in Rochelle salt crystals,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
    [CrossRef]
  2. T. Tsukamoto, M. Komukae, S. Suzuki, H. Futama, 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, “Deflection of light by ferroelectric-ferroelastic RbHSeO4,” Jpn. J. Appl. Phys. 23, 424–427 (1984).
    [CrossRef]
  4. T. Tsukamoto, J. Hatano, and H. Futama, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and Bi4Ti3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
    [CrossRef]
  5. T. Tsukamoto and H. Futama, “REVIEW: light deflection induced by ferroelastic layered domains,” Phase Transit. 45, 59–76 (1993).
    [CrossRef]
  6. J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal,” J. Phys. Condens. Matter 12, 653–667 (2000).
    [CrossRef]
  7. P. Staniorowski and J. Bornarel, “Light deflection in gadolinium molybdate ferroelastic crystals,” J. Phys. Condens. Matter 12, 669–676 (2000).
    [CrossRef]
  8. P. Kolata, L. Guilbert, M. D. Fontana, J. P. Salvestrini, and Z. Czapla, “Birefringence measurements by means of light deflection at domain walls in ferroelastic crystals,” J. Opt. Soc. Am. B 17, 1973–1979 (2000).
    [CrossRef]
  9. J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–5140 (1975).
    [CrossRef]
  10. K. Aizu, “Possible species of “ferroelastic” crystals and of simultaneously ferroelectric and ferroelastic crystals,” J. Phys. Soc. Jpn. 27, 387–396 (1969).
    [CrossRef]
  11. K. Aizu, “Determination of the state parameters and formulation of spontaneous strain for ferroelastics,” J. Phys. Soc. Jpn. 28, 706–716 (1970).
    [CrossRef]
  12. L. Guilbert, J. P. Salvestrini, P. Kolata, F. X. Abrial, and M. D. Fontana, “Optical characteristics of triclinic rubidium hydrogen selenate,” J. Opt. Soc. Am. B 15, 1009–1016 (1998).
    [CrossRef]
  13. T. Horie, K. Kawabe, M. Tachiki, and S. Sawada, “Thermal transition of transparency in ferroelectric single crystal of barium titanate,” J. Phys. Soc. Jpn. 10, 541–549 (1955).
    [CrossRef]
  14. L. Guilbert and Z. Czapla, “Interferences in light deflection by ferroelastic domain walls,” Appl. Opt. 40, 125–128 (2001).
    [CrossRef]
  15. J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals,” J. Appl. Crystallogr. 16, 204–219 (1983).
    [CrossRef]
  16. M. Kremers and H. Meekes, “The interpretation of HAUP measurements: a study of the systematic errors,” J. Phys. D 28, 1195–1211 (1995).
    [CrossRef]
  17. L. Guilbert, “Physical optics in low-symmetry ferroelastics. II. Coherence losses and polarization impairments in the transmitted light,” J. Opt. Soc. Am. B 19, 2987–2994 (2002).
    [CrossRef]
  18. L. Guilbert, J. P. Salvestrini, H. Hassan, and M. D. Fontana, “Combined effects due to phase, intensity and contrast in electrooptic modulation. application to ferroelectric materials,” IEEE J. Quantum Electron. 35, 273–280 (1999).
    [CrossRef]

2002 (1)

2001 (1)

2000 (3)

J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal,” J. Phys. Condens. Matter 12, 653–667 (2000).
[CrossRef]

P. Staniorowski and J. Bornarel, “Light deflection in gadolinium molybdate ferroelastic crystals,” J. Phys. Condens. Matter 12, 669–676 (2000).
[CrossRef]

P. Kolata, L. Guilbert, M. D. Fontana, J. P. Salvestrini, and Z. Czapla, “Birefringence measurements by means of light deflection at domain walls in ferroelastic crystals,” J. Opt. Soc. Am. B 17, 1973–1979 (2000).
[CrossRef]

1999 (1)

L. Guilbert, J. P. Salvestrini, H. Hassan, and M. D. Fontana, “Combined effects due to phase, intensity and contrast in electrooptic modulation. application to ferroelectric materials,” IEEE J. Quantum Electron. 35, 273–280 (1999).
[CrossRef]

1998 (1)

1995 (1)

M. Kremers and H. Meekes, “The interpretation of HAUP measurements: a study of the systematic errors,” J. Phys. D 28, 1195–1211 (1995).
[CrossRef]

1993 (1)

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

1984 (2)

T. Tsukamoto, “Deflection of light by ferroelectric-ferroelastic RbHSeO4,” Jpn. J. Appl. Phys. 23, 424–427 (1984).
[CrossRef]

T. Tsukamoto, J. Hatano, and H. Futama, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and Bi4Ti3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

1983 (2)

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

J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals,” J. Appl. Crystallogr. 16, 204–219 (1983).
[CrossRef]

1982 (1)

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

1975 (1)

J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–5140 (1975).
[CrossRef]

1970 (1)

K. Aizu, “Determination of the state parameters and formulation of spontaneous strain for ferroelastics,” J. Phys. Soc. Jpn. 28, 706–716 (1970).
[CrossRef]

1969 (1)

K. Aizu, “Possible species of “ferroelastic” crystals and of simultaneously ferroelectric and ferroelastic crystals,” J. Phys. Soc. Jpn. 27, 387–396 (1969).
[CrossRef]

1955 (1)

T. Horie, K. Kawabe, M. Tachiki, and S. Sawada, “Thermal transition of transparency in ferroelectric single crystal of barium titanate,” J. Phys. Soc. Jpn. 10, 541–549 (1955).
[CrossRef]

Abrial, F. X.

Aizu, K.

K. Aizu, “Determination of the state parameters and formulation of spontaneous strain for ferroelastics,” J. Phys. Soc. Jpn. 28, 706–716 (1970).
[CrossRef]

K. Aizu, “Possible species of “ferroelastic” crystals and of simultaneously ferroelectric and ferroelastic crystals,” J. Phys. Soc. Jpn. 27, 387–396 (1969).
[CrossRef]

Bornarel, J.

J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal,” J. Phys. Condens. Matter 12, 653–667 (2000).
[CrossRef]

P. Staniorowski and J. Bornarel, “Light deflection in gadolinium molybdate ferroelastic crystals,” J. Phys. Condens. Matter 12, 669–676 (2000).
[CrossRef]

Czapla, Z.

Fontana, M. D.

Futama, H.

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

T. Tsukamoto, J. Hatano, and H. Futama, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and Bi4Ti3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

T. Tsukamoto, M. Komukae, S. Suzuki, H. Futama, 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. Futama, “Refraction and reflection of light at ferroelastic domain walls in Rochelle salt crystals,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
[CrossRef]

Guilbert, L.

Hassan, H.

L. Guilbert, J. P. Salvestrini, H. Hassan, and M. D. Fontana, “Combined effects due to phase, intensity and contrast in electrooptic modulation. application to ferroelectric materials,” IEEE J. Quantum Electron. 35, 273–280 (1999).
[CrossRef]

Hatano, J.

T. Tsukamoto, J. Hatano, and H. Futama, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and Bi4Ti3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

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

Horie, T.

T. Horie, K. Kawabe, M. Tachiki, and S. Sawada, “Thermal transition of transparency in ferroelectric single crystal of barium titanate,” J. Phys. Soc. Jpn. 10, 541–549 (1955).
[CrossRef]

Kawabe, K.

T. Horie, K. Kawabe, M. Tachiki, and S. Sawada, “Thermal transition of transparency in ferroelectric single crystal of barium titanate,” J. Phys. Soc. Jpn. 10, 541–549 (1955).
[CrossRef]

Kobayashi, J.

J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals,” J. Appl. Crystallogr. 16, 204–219 (1983).
[CrossRef]

Kolata, P.

Komukae, M.

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

Kremers, M.

M. Kremers and H. Meekes, “The interpretation of HAUP measurements: a study of the systematic errors,” J. Phys. D 28, 1195–1211 (1995).
[CrossRef]

Makita, Y.

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

Meekes, H.

M. Kremers and H. Meekes, “The interpretation of HAUP measurements: a study of the systematic errors,” J. Phys. D 28, 1195–1211 (1995).
[CrossRef]

Salvestrini, J. P.

Sapriel, J.

J. Sapriel, “Domain-wall orientations in ferroelastics,” Phys. Rev. B 12, 5128–5140 (1975).
[CrossRef]

Sawada, S.

T. Horie, K. Kawabe, M. Tachiki, and S. Sawada, “Thermal transition of transparency in ferroelectric single crystal of barium titanate,” J. Phys. Soc. Jpn. 10, 541–549 (1955).
[CrossRef]

Staniorowski, P.

P. Staniorowski and J. Bornarel, “Light deflection in gadolinium molybdate ferroelastic crystals,” J. Phys. Condens. Matter 12, 669–676 (2000).
[CrossRef]

J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal,” J. Phys. Condens. Matter 12, 653–667 (2000).
[CrossRef]

Suzuki, S.

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

Tachiki, M.

T. Horie, K. Kawabe, M. Tachiki, and S. Sawada, “Thermal transition of transparency in ferroelectric single crystal of barium titanate,” J. Phys. Soc. Jpn. 10, 541–549 (1955).
[CrossRef]

Tsukamoto, T.

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

T. Tsukamoto, J. Hatano, and H. Futama, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and Bi4Ti3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

T. Tsukamoto, “Deflection of light by ferroelectric-ferroelastic RbHSeO4,” Jpn. J. Appl. Phys. 23, 424–427 (1984).
[CrossRef]

T. Tsukamoto, M. Komukae, S. Suzuki, H. Futama, 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. Futama, “Refraction and reflection of light at ferroelastic domain walls in Rochelle salt crystals,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
[CrossRef]

Uesu, Y.

J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals,” J. Appl. Crystallogr. 16, 204–219 (1983).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

L. Guilbert, J. P. Salvestrini, H. Hassan, and M. D. Fontana, “Combined effects due to phase, intensity and contrast in electrooptic modulation. application to ferroelectric materials,” IEEE J. Quantum Electron. 35, 273–280 (1999).
[CrossRef]

J. Appl. Crystallogr. (1)

J. Kobayashi and Y. Uesu, “A new optical method and apparatus HAUP for measuring simultaneously optical activity and birefringence of crystals,” J. Appl. Crystallogr. 16, 204–219 (1983).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. Condens. Matter (2)

J. Bornarel, P. Staniorowski, and Z. Czapla, “Light deflection and birefringence in (NH4)2Sb2F5 ferroelastic crystal,” J. Phys. Condens. Matter 12, 653–667 (2000).
[CrossRef]

P. Staniorowski and J. Bornarel, “Light deflection in gadolinium molybdate ferroelastic crystals,” J. Phys. Condens. Matter 12, 669–676 (2000).
[CrossRef]

J. Phys. D (1)

M. Kremers and H. Meekes, “The interpretation of HAUP measurements: a study of the systematic errors,” J. Phys. D 28, 1195–1211 (1995).
[CrossRef]

J. Phys. Soc. Jpn. (6)

K. Aizu, “Possible species of “ferroelastic” crystals and of simultaneously ferroelectric and ferroelastic crystals,” J. Phys. Soc. Jpn. 27, 387–396 (1969).
[CrossRef]

K. Aizu, “Determination of the state parameters and formulation of spontaneous strain for ferroelastics,” J. Phys. Soc. Jpn. 28, 706–716 (1970).
[CrossRef]

T. Horie, K. Kawabe, M. Tachiki, and S. Sawada, “Thermal transition of transparency in ferroelectric single crystal of barium titanate,” J. Phys. Soc. Jpn. 10, 541–549 (1955).
[CrossRef]

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

T. Tsukamoto, M. Komukae, S. Suzuki, H. Futama, 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. Futama, “Deflection of light by ferroelastic domains in Gd2(MoO4)3 and Bi4Ti3O12 crystals,” J. Phys. Soc. Jpn. 53, 838–843 (1984).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Tsukamoto, “Deflection of light by ferroelectric-ferroelastic RbHSeO4,” Jpn. J. Appl. Phys. 23, 424–427 (1984).
[CrossRef]

Phase Transit. (1)

T. Tsukamoto and H. Futama, “REVIEW: 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, 5128–5140 (1975).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Optical symmetry of neighbor domains with respect to a W wall.

Fig. 2
Fig. 2

Deflection phenomenon in a FEL domain structure: A, B, refractive transmissions; A, B, refractive reflections; D, R, nonrefractive processes.

Fig. 3
Fig. 3

Elementary processes of transmission and reflection at a FEL DW, shown separately for the fast incident wave (F0) and for the slow incident wave (S0). Under unpolarized light, direct waves (F) and (S) constitute direct beam D, and reflected waves (F) and (S) constitute reflected beam R.

Fig. 4
Fig. 4

Illustration of Tsukamoto’s approximation.

Fig. 5
Fig. 5

Weak refraction of the direct wave at a FEL DW (construction on the slowness curves).

Fig. 6
Fig. 6

Axes of optical continuity x0 (in the plane of DWs) and x3 (perpendicular to DWs). Dotted arrows represent axes of quasi-optical continuity (in the case of a triclinic crystal).

Fig. 7
Fig. 7

Exchanges of intensity between the fast component F of the direct beam and the slow deflected beam A at a DW assuming no interference in the deflection phenomenon. a2 and b2 are the elementary deflection factors. A similar scheme (symmetrical to this one) represents the exchanges between the slow component. (S) of the direct beam and the fast deflected beam (B).

Fig. 8
Fig. 8

Transmittance of the direct beam as a function of the number of DWs. (a) Within Tsukamoto’s approximation and random-phase approximation for different values of the tilt angle between the neutral lines. (b) Within the two-wave interference model for a RHSe crystal in different strain states ranging from coercive (x=0) to strongly saturated (x=0.9) at the 633-nm wavelength. A slight dichroism exists between the fast wave (F) and the slow wave (S).

Fig. 9
Fig. 9

Exchanges of intensity between fast component F of the direct beam and slow deflected beam A within a microdomain. 2αk2 and 2βk2 are effective deflection factors that take into account the interferences between the parallel waves deflected by the two walls.

Fig. 10
Fig. 10

Deflection by a microdomain. Each incident wave (fast or slow) splits into a direct wave and a deflected wave at the first wall, then each of the four waves splits again into two at the second wall. Two parallel waves that carry the same polarization interfere with a phase difference that is proportional to thickness δ of the microdomain.

Equations (43)

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

aψAψF0,bψBψS0;
aψAψF0,bψBψS0;
dFψFψF0,dSψSψS0;
rFψFψF0,rSψSψS0.
|a||b|sin 2ϕ;
dFdScos 2ϕ;
Fn=(1-a2)Fn-1+b2An-1,
An=a2Fn-1+(1-b2)An-1,
Sn=(1-b2)Sn-1+a2Bn-1,
Bn=b2Sn-1+(1-a2)Bn-1,
A=S=a2a2+b2,
B=F=b2a2+b2.
An/F0=a2a2+b2[1-(1-a2-b2)n],
Bn/S0=b2a2+b2[1-(1-a2-b2)n],
Fn/F0=b2a2+b2+a2a2+b2(1-a2-b2)n,
Sn/S0=a2a2+b2+b2a2+b2(1-a2-b2)n.
An/F0a2a2+b2{1-exp[-n(a2+b2)]},
Bn/S0b2a2+b2{1-exp[-n(a2+b2)]},
Fn/F0b2a2+b2+a2a2+b2 exp[-n(a2+b2)],
Sn/S0a2a2+b2+b2a2+b2 exp[-n(a2+b2)].
NS2.30a2+b2,
NS1.15(2ϕ)2,
2αk2=2dF2a2(1+cos φA,k),
2βk2=2dS2b2(1+cos φB,k),
φA,k2πmA,k,mA,k=1/2+ηA(i) δkλ,
φB,k2πmB,k,mB,k=1/2+ηB(i) δkλ,
An/F0=α¯2α¯2+β¯2[1-(1-2α¯2-2β¯2)n/2]α¯2α¯2+β¯2{1-exp[-n(α¯2+β¯2)]},
Bn/S0=β¯2α¯2+β¯2[1-(1-2α¯2-2β¯2)n/2]β¯2α¯2+β¯2{1-exp[-n(α¯2+β¯2)]},
Fn/F0=1-An/F0β¯2α¯2+β¯2+α¯2α¯2+β¯2×exp[-n(α¯2+β¯2)],
Sn/S0=1-Bn/S0α¯2α¯2+β¯2+β¯2α¯2+β¯2×exp[-n(α¯2+β¯2)],
α¯2a2(1+cos φA,k),
β¯2b2(1+cos φB,k).
ΔlBA/FF=δ×[ns(α)cos α-nf(i)cos i],
ΔlAB/SS=δ×[ns(i)cos i-nf(β)cos β],
nf(i)sin ins(α)sin α
ns(i)sin inf(β)sin β.
nf(i)nf(β)n1.
1ns2(θ)cos2 θn22+sin2 θn32,
sin2 αn12n22 sin2 i1-n22n32-1 n12n22 sin2 i,
sin2 βn22n12 sin2 i1+n22n32-1sin2 i.
ηA=ΔlBA/FFδ,ηB=ΔlAB/SSδ.
φA=φF+π=2πδληA(i)+π,
φB=φS+π=2πδληB(i)+π.

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