Abstract

Deflection of light is studied in a crystal of glycine phosphite containing two twin walls. When the crystal is rotated in the incident laser beam, interferences are observed in both the direct beam and in the main deflected beam (A or B) for both polarizations of the incident light. The contrast is especially high, because the mutual tilt angle of the principal axes is close to 45° in this twinned crystal. On this principle, fundamental-harmonic beam splitters could be built from as-grown twin crystals. Furthermore, the electrical modulation of the light deflected by ferroelectric–ferroelastic crystals can be now explained in terms of interference effects.

© 2001 Optical Society of America

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References

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  1. T. Tsukamoto, J. Hatano, H. Futama, “Light deflection from ferroelastic domains,” J. Phys. Soc. Jpn. 49 Suppl. B, 155–159 (1980).
  2. T. Tsukamoto, J. Hatano, H. Futama, “Refraction and reflection of light at ferroelastic domain walls in Rochelle salt crystal,” J. Phys. Soc. Jpn. 51, 3948–3952 (1982).
    [CrossRef]
  3. T. Tsukamoto, M. Komuake, S. Suzuki, H. Futama, Y. Makita, “Domain structure and deflection of light at domain walls in RbHSeO4,” J. Phys. Soc. Jpn. 52, 3966–3973 (1983).
    [CrossRef]
  4. T. Tsukamoto, J. Hatano, 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, H. Futama, “Review: light deflection induced by ferroelastic layered domains,” Phase Transit. 45, 59–76 (1993).
    [CrossRef]
  6. P. Kolata, L. Guilbert, M. D. Fontana, J. P. Salvestrini, 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]
  7. L. Guilbert, J. P. Salvestrini, H. Hassan, 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]

2000

1999

L. Guilbert, J. P. Salvestrini, H. Hassan, 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]

1993

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

1984

T. Tsukamoto, J. Hatano, 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

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

1982

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

1980

T. Tsukamoto, J. Hatano, H. Futama, “Light deflection from ferroelastic domains,” J. Phys. Soc. Jpn. 49 Suppl. B, 155–159 (1980).

Czapla, Z.

Fontana, M. D.

P. Kolata, L. Guilbert, M. D. Fontana, J. P. Salvestrini, 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, H. Hassan, 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]

Futama, H.

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

T. Tsukamoto, J. Hatano, 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. Komuake, S. Suzuki, H. Futama, 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, H. Futama, “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, H. Futama, “Light deflection from ferroelastic domains,” J. Phys. Soc. Jpn. 49 Suppl. B, 155–159 (1980).

Guilbert, L.

P. Kolata, L. Guilbert, M. D. Fontana, J. P. Salvestrini, 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, H. Hassan, 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]

Hassan, H.

L. Guilbert, J. P. Salvestrini, H. Hassan, 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, 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, H. Futama, “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, H. Futama, “Light deflection from ferroelastic domains,” J. Phys. Soc. Jpn. 49 Suppl. B, 155–159 (1980).

Kolata, P.

Komuake, M.

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

Salvestrini, J. P.

P. Kolata, L. Guilbert, M. D. Fontana, J. P. Salvestrini, 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, H. Hassan, 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]

Suzuki, S.

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

T. Tsukamoto, J. Hatano, 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. Komuake, S. Suzuki, H. Futama, 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, H. Futama, “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, H. Futama, “Light deflection from ferroelastic domains,” J. Phys. Soc. Jpn. 49 Suppl. B, 155–159 (1980).

IEEE J. Quantum Electron.

L. Guilbert, J. P. Salvestrini, H. Hassan, 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. Opt. Soc. Am. B

J. Phys. Soc. Jpn.

T. Tsukamoto, J. Hatano, H. Futama, “Light deflection from ferroelastic domains,” J. Phys. Soc. Jpn. 49 Suppl. B, 155–159 (1980).

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

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

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Figures (5)

Fig. 1
Fig. 1

Deflection phenomenon and experimental setup.

Fig. 2
Fig. 2

Two-wave interferences evidenced in the direct beam (D) and in the main deflected beam (A or B) for both polarizations of the incident beam. For slow polarization (lower plot) B beams appear above 25° of incidence, whereas for fast polarization A beams are always present. Reflected beams (R, A′, B′) have been ignored in this experiment.

Fig. 3
Fig. 3

Splitting of the incident wave after two walls. (a) Fast wave gives two deflected waves (DA, AD) and two direct waves (DD, BA). (b) Slow wave gives two deflected waves (DB, BD) and two direct waves (DD, AB). Each letter designates a refraction process at a twin wall: A from fast to slow, B from slow to fast, D from slow to slow or from fast to fast. Conventionally, letters combine with one another from right to left, as is usual for operator symbols. For clarity, reflections processes (R, A′, B′) have been omitted here.

Fig. 4
Fig. 4

Illustration of Tsukamoto’s approximation. The field of the incident wave in the first domain (assumed here to be polarized along the fast axis) projects itself on the two neutral lines in the second domain, with respective amplitudes cos 2ϕ for the direct wave (D) and sin 2ϕ for the deflected wave (A or B). In this approximation the refraction is not taken into account, and the reflected waves are totally ignored.

Fig. 5
Fig. 5

Principle of a harmonic splitter based on light deflection in GPI. The twinned crystal is conveniently cut so that the amplitudes of both waves (direct and deflected) generated at a twin wall are equal. In configuration (a) or (c) the interference order is half-integer for the fundamental beam, whereas it is practically full integer for the harmonic beam. So, the fundamental beam is fully deflected, and the harmonic beam is fully transmitted. In the other configuration (b) or (d) both interference orders m ω and m are integers, so both beams are fully transmitted.

Equations (8)

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

Δlwsin χi-sin i,
sin2 χA,Bsin2 i±sin2 χ0 + for A, - for B,
sin2 χ0n12-n22=2n¯.Δn,
ϕD=2πΔlλ2πmA,B, ϕA,B=2πΔlλ+π2πmA,B+1/2,
mA,Bw/λ sin χA,Bi-sin i,
ΔiA,Brad=mA,Bi-1λwsin χA,Bcos isin χA,B - sin i.
DD: d2cos2 2ϕ,  BA: aba2sin2 2ϕ DA, AD: dasin 2ϕ cos 2ϕ.
γD=2d2a2d4+a4.

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