Abstract

Coherence losses that are due to secondary deflection by domain walls in low-symmetry ferroelastics are calculated by the two-wave interference model introduced in the companion paper. Impairments on the polarization are calculated by means of Jones matrix formalism. Subsequent losses of contrast are estimated in various situations of practical interest. The results show that the tilt angle of the neutral lines, the domain-wall density, and the average deformation of the polydomain crystal have considerable influence on the characteristics of the transmitted beam. The results also stress the necessity to choose the propagation direction close to an axis of quasi-optical continuity of the domain structure to preserve the coherence and the polarization in any optical device that makes use of polydomain crystals.

© 2002 Optical Society of America

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References

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  1. L. Guilbert, “Physical optics in low-symmetry ferroelastics. I. Intensity losses and dichroism caused by deflection,” J. Opt. Soc. Am. B 19, 2978–2986 (2002).
    [CrossRef]
  2. 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]
  3. M. Kremers and H. Meekes, “The interpretation of HAUP measurements: a study of the systematic errors,” J. Phys. D 28, 1195–1211 (1995).
    [CrossRef]
  4. J. P. Salvestrini, M. D. Fontana, M. Aillerie, and Z. Czapla, “New material with strong electro-optic effect: Rubidium hydrogen selenate (RbHSeO4),” Appl. Phys. Lett. 64, 1920–1922 (1994).
    [CrossRef]
  5. J. P. Salvestrini, L. Guilbert, M. D. Fontana, and Z. Czapla, “Electro-optical properties of rubidium hydrogen selenate: influence of the dc electric field and origin of the large electro-optic coefficient,” J. Opt. Soc. Am. B 14, 2818–2822 (1997).
    [CrossRef]
  6. L. Guilbert, J. P. Salvestrini, M. D. Fontana, and Z. Czapla, “Correlation between dielectric and electro-optic properties related to domain dynamics in RbHSeO4 crystals,” Phys. Rev. B 58, 2523–2528 (1998).
    [CrossRef]
  7. L. Guilbert, J. P. Salvestrini, and Z. Czapla, “Indirect Pockels effect in rubidium hydrogen selenate: measurement of the large r42 coefficient,” J. Opt. Soc. Am. B 17, 1980–1985 (2000).
    [CrossRef]
  8. 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]
  9. 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]
  10. J. Przeslawski, R. Lingard, and Z. Czapla, “Linear and circular birefringence of RbHSeO4,” Ferroelectr. Lett. Sect. 20, 131–135 (1996).
    [CrossRef]
  11. 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]
  12. T. Tsukamoto and H. Futama, “REVIEW: light deflectioninduced by ferroelastic layered domains,” Phase Transit. 45, 59–76 (1993).
    [CrossRef]
  13. 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]
  14. P. Staniorowski and J. Bornarel, “Light deflection in gadolinium molybdate ferroelastic crystals,” J. Phys. Condens. Matter 12, 669–676 (2000).
    [CrossRef]
  15. 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]

2002

2000

L. Guilbert, J. P. Salvestrini, and Z. Czapla, “Indirect Pockels effect in rubidium hydrogen selenate: measurement of the large r42 coefficient,” J. Opt. Soc. Am. B 17, 1980–1985 (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]

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]

1998

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]

L. Guilbert, J. P. Salvestrini, M. D. Fontana, and Z. Czapla, “Correlation between dielectric and electro-optic properties related to domain dynamics in RbHSeO4 crystals,” Phys. Rev. B 58, 2523–2528 (1998).
[CrossRef]

1997

1996

J. Przeslawski, R. Lingard, and Z. Czapla, “Linear and circular birefringence of RbHSeO4,” Ferroelectr. Lett. Sect. 20, 131–135 (1996).
[CrossRef]

1995

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

1994

J. P. Salvestrini, M. D. Fontana, M. Aillerie, and Z. Czapla, “New material with strong electro-optic effect: Rubidium hydrogen selenate (RbHSeO4),” Appl. Phys. Lett. 64, 1920–1922 (1994).
[CrossRef]

1993

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

1984

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

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

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]

Abrial, F. X.

Aillerie, M.

J. P. Salvestrini, M. D. Fontana, M. Aillerie, and Z. Czapla, “New material with strong electro-optic effect: Rubidium hydrogen selenate (RbHSeO4),” Appl. Phys. Lett. 64, 1920–1922 (1994).
[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.

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. 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]

L. Guilbert, J. P. Salvestrini, and Z. Czapla, “Indirect Pockels effect in rubidium hydrogen selenate: measurement of the large r42 coefficient,” J. Opt. Soc. Am. B 17, 1980–1985 (2000).
[CrossRef]

L. Guilbert, J. P. Salvestrini, M. D. Fontana, and Z. Czapla, “Correlation between dielectric and electro-optic properties related to domain dynamics in RbHSeO4 crystals,” Phys. Rev. B 58, 2523–2528 (1998).
[CrossRef]

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]

J. P. Salvestrini, L. Guilbert, M. D. Fontana, and Z. Czapla, “Electro-optical properties of rubidium hydrogen selenate: influence of the dc electric field and origin of the large electro-optic coefficient,” J. Opt. Soc. Am. B 14, 2818–2822 (1997).
[CrossRef]

J. Przeslawski, R. Lingard, and Z. Czapla, “Linear and circular birefringence of RbHSeO4,” Ferroelectr. Lett. Sect. 20, 131–135 (1996).
[CrossRef]

J. P. Salvestrini, M. D. Fontana, M. Aillerie, and Z. Czapla, “New material with strong electro-optic effect: Rubidium hydrogen selenate (RbHSeO4),” Appl. Phys. Lett. 64, 1920–1922 (1994).
[CrossRef]

Fontana, M. D.

Futama, H.

T. Tsukamoto and H. Futama, “REVIEW: light deflectioninduced 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, 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.

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]

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.

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]

Lingard, R.

J. Przeslawski, R. Lingard, and Z. Czapla, “Linear and circular birefringence of RbHSeO4,” Ferroelectr. Lett. Sect. 20, 131–135 (1996).
[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]

Przeslawski, J.

J. Przeslawski, R. Lingard, and Z. Czapla, “Linear and circular birefringence of RbHSeO4,” Ferroelectr. Lett. Sect. 20, 131–135 (1996).
[CrossRef]

Salvestrini, J. P.

Staniorowski, P.

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]

Tsukamoto, T.

T. Tsukamoto and H. Futama, “REVIEW: light deflectioninduced 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, 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. Phys. Lett.

J. P. Salvestrini, M. D. Fontana, M. Aillerie, and Z. Czapla, “New material with strong electro-optic effect: Rubidium hydrogen selenate (RbHSeO4),” Appl. Phys. Lett. 64, 1920–1922 (1994).
[CrossRef]

Ferroelectr. Lett. Sect.

J. Przeslawski, R. Lingard, and Z. Czapla, “Linear and circular birefringence of RbHSeO4,” Ferroelectr. Lett. Sect. 20, 131–135 (1996).
[CrossRef]

J. Appl. Crystallogr.

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

J. Phys. Condens. Matter

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

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.

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, 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]

Phase Transit.

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

Phys. Rev. B

L. Guilbert, J. P. Salvestrini, M. D. Fontana, and Z. Czapla, “Correlation between dielectric and electro-optic properties related to domain dynamics in RbHSeO4 crystals,” Phys. Rev. B 58, 2523–2528 (1998).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Secondary deflection in a direct beam.

Fig. 2
Fig. 2

Phase contrast losses that are due to secondary deflection, calculated for a RHSe crystal cut at an optimal angle for EO modulation (propagation at 35.3° from the normal to DWs). Wavelength, 633 nm; average thickness of the domains, 3 µm. (a) Coercive state (P=0). The dashed curve corresponds to the random-phase approximation (here pessimistic). (b) Partially saturated state (P/PS=0.7). The tilt angle 2ϕ of the neutral lines should be as small as possible to reduce deflection and thus preserve the contrast.

Fig. 3
Fig. 3

Gradual rotation of the polarization that is due to the tilt of neutral lines from domain to domain.

Fig. 4
Fig. 4

Extinction contrast between crossed polarizers calculated for a RHSe crystal cut at an optimal angle for EO modulation (propagation at 35.3° from the normal to DWs). Wavelength, 633 nm; average thickness of the domains, 3 µm. (a) Coercive state (P=0) and (b) partially saturated state (P/PS=0.7).

Fig. 5
Fig. 5

Sénarmont’s setup (neutral lines are represented by dash–dot lines for all the components).

Equations (54)

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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),
Fn(co.)=F0(1-α¯2)nF0 exp(-nα¯2),
Sn(co.)=S0(1-β¯2)nS0 exp(-nβ¯2).
γϕ,F=Fn(co.)Fnα¯2+β¯2β¯2 exp(nα¯2)+α¯2 exp(-nβ¯2),
γϕ,S=Sn(co.)Snα¯2+β¯2α¯2 exp(nβ¯2)+β¯2 exp(-nα¯2).
γϕ,Fγϕ,S1cosh(nα¯2).
γϕ,Fγϕ,S1cosh(na2).
Γk±=2πλΔn±δk±
Dk+=exp(iΓk+/2)00exp(-iΓk+/2).
Dk-
=cos Γk-2+i cos 4ϕ sin Γk-2i sin 4ϕ sin Γk-2i sin 4ϕ sin Γk-2 cos Γk-2-i cos 4ϕ sin Γk-2.
Ck=Dk-Dk+=pkqk-qk*pk*,
pk=cos Γk-2+i cos 4ϕ sin Γk-2exp(iΓk+/2),
qk=i sin 4ϕ sin Γk-2 exp(iΓk+/2).
pk=|pk|exp(iφk),qk=i|qk|exp(-iΓk+/2),
|qk|=sin Γk-2sin|4ϕ|,
|pk|=1-|qk|2,
φkΓk++Γk-2.
MN=k=1NCk=PNQN-QN*PN*,
QN=kak(1)qk+k<l<maklm(3)qkql*qm+k<l<m<n<paklmnp(5)qkql*qmqn*qp+,
PN=kpk+k<lakl(2)qk*ql+k<l<m<naklmn(4)qkql*qmqn*+.
akl  z(ν)=j=1Npj°pkpl  pz,
|PN(0)|=k|pk|=k1-|qk|2
ΦNk=1Nφk.
|QN|2=k|ak(1)|2|qk|2+k<l<m|aklm(3)|2|qk|2|ql|2|qm|2+.
|QN|2=p2N(Nr+CN3r3+CN5r5+),
|QN|2=1/2[1-(1-2q2)N].
q2=sin2(Γ-/2)sin2 4ϕ.
|PN|2=1-|QN|2.
T(θ)=RQ2+I2 sin2(2θ-2θ0),
RQ=R(QN),
I2=J2(PN)+J2(QN),
tan 2θ0=J (QN)J (PN).
γ(PA)Tmax-TminTmax+Tmin=I2I2+2R2.
R2(QN)=J2(QN)=|QN|22,
R2(PN)=J2(PN)=|PN|22.
γ(PA)=11+2|QN|2=12-(1-2q2)N.
T(θ)=1/2[1+sin(2θ-Γ)],
T(θ)=12+12[(RP2-RQ2)-(IP2-IQ2)]sin 2θ+[RPIP-RQIQ]cos 2θ,
RP=R(PN),IP=J(PN),
RQ=R(QN),IQ=J(QN).
γ(S)=[1-2(RP2-IP2)(RQ2-IQ2)-8RPIPRQIQ]1/2
γ(S)=[1-2|QN|2(1-|QN|2)]1/2.
T±(θ)=1/2 sin2(2θ2ϕ).
T(x, θ)=1+x4 sin2(2θ-2ϕ)+1-x4 sin2(2θ+2ϕ).
T(x, θ)=1/4{1-γ(x)cos[4θ-4θ0(x)]},
tan 4θ0(x)=x tan 4ϕ,
γ(x)=(cos2 4ϕ+x2 sin2 4ϕ)1/2.
γ(0)=|cos 4ϕ|.

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