Abstract

New physical aspects of collinear acousto-optical interaction, occurred by acoustic waves of finite amplitude, are revealed and analyzed in crystalline materials exhibiting moderate linear acoustic losses. The analysis is performed in the regime of continuous traveling waves allowing a specific mechanism of the acousto-optic nonlinearity. Our consideration has shown that such nonlinearity together with linear acoustic losses is able to affect the transmission function inherent in collinear interaction. In particular, the mere presence of linear acoustic losses by themselves leads to broadening the width of the transmission function beginning already from very low levels of the applied acoustic power. Moreover, the transmission function exhibits a marked and quasi-periodical dependence on the applied acoustic power density, and that periodicity is governed by the linear acoustic losses. As a result, the transmission function can be significantly narrowed near isolated points at the cost of decreasing the interaction efficiency. These novelties related to collinear acousto-optical interaction accompanied by moderate linear acoustic losses have been studied and confirmed experimentally with an advanced acousto-optical cell based on calcium molybdate (CaMoO4) single crystal and controlled by acoustic waves of finite amplitude.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. W. Dixon, “Acoustic diffraction of light in anisotropic media,” IEEE J. Quantum Electron. QE-3, 85–93 (1967).
    [CrossRef]
  2. S. E. Harris and R. W. Wallace, “Acousto-optic tunable filter,” J. Opt. Soc. Am. 59, 744–747 (1969).
    [CrossRef]
  3. S. E. Harris, S. T. K. Nich, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223–225 (1970).
    [CrossRef]
  4. I. C. Chang, “Tunable acousto-optic filter utilizing acoustic beam walk-off in crystal quartz,” Appl. Phys. Lett. 25, 323–324 (1974).
    [CrossRef]
  5. J. A. Kusters, D. A. Wilson, and D. L. Hammond, “Optimum crystal orientation for acoustically tuned optical filters,” J. Opt. Soc. Am. 64, 434–440 (1974).
    [CrossRef]
  6. E. T. Aksenov, N. A. Esepkina, and A. S. Shcherbakov, “Acousto-optical filter with a LiNbO3-crystal,” Tech. Phys. Lett. 2, 83–84 (1976).
  7. J. D. Fichter, M. Gottlieb, and J. J. Conroy, “Tl3AsSe3 noncollinear acousto-optic filter operation at 10 μm,” Appl. Phys. Lett. 34, 1–3 (1979).
    [CrossRef]
  8. V. N. Parygin, A. V. Vershubskii, and K. A. Kholostov, “Control of the characteristics of a calcium molybdate collinear acousto-optic filter,” Tech. Phys. 44, 1467–1471 (1999).
    [CrossRef]
  9. V. I. Balakshy, V. N. Parygin, and L. I. Chrkov, Physical Principles of Acousto-Optics (Radio I Svyaz, 1985).
  10. A. Korpel, Acousto-Optics, 2nd ed. (Dekker, 1997).
  11. F. T. S. Yu, Introduction to Information Optics (Academic, 2001).
  12. See, for example A. Mahieux, V. Wilquet, R. Drummond, D. Belyaev, A. Federova, and A. C. Vandaele, “A new method for determining the transfer function of an acousto optical tunable filter,” Opt. Express 17, 2005–2014 (2009).
    [CrossRef]
  13. A. S. Shcherbakov and A. Aguirre Lopez, “Shaping the optical components of solitary three-wave weakly coupled states in a two-mode waveguide,” Opt. Express 11, 1643–1649 (2003).
    [CrossRef]
  14. A. S. Shcherbakov and A. Aguirre Lopez, “Binary encoded modulation of light based on collinear three-wave acousto-optical weakly coupled states,” J. Opt. A 5, 471–477 (2003).
    [CrossRef]
  15. A. S. Shcherbakov, J. Maximov, and S. E. Balderas Mata, “Shaping the dissipative collinear three-wave coupled states in a two-mode medium with a square-law nonlinearity and linear non-optical losses,” J. Opt. A 10, 025001 (2008).
    [CrossRef]
  16. M. P. Shaskolskaya, ed., Handbook “Acoustic Crystals” (Nauka, 1988).
  17. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals3rd ed. (Springer, 1999).
  18. A. A. Blistanov, Crystals for Quantum and Nonlinear Optics, 2nd ed. (MISIS, 2007).

2009 (1)

2008 (1)

A. S. Shcherbakov, J. Maximov, and S. E. Balderas Mata, “Shaping the dissipative collinear three-wave coupled states in a two-mode medium with a square-law nonlinearity and linear non-optical losses,” J. Opt. A 10, 025001 (2008).
[CrossRef]

2003 (2)

A. S. Shcherbakov and A. Aguirre Lopez, “Shaping the optical components of solitary three-wave weakly coupled states in a two-mode waveguide,” Opt. Express 11, 1643–1649 (2003).
[CrossRef]

A. S. Shcherbakov and A. Aguirre Lopez, “Binary encoded modulation of light based on collinear three-wave acousto-optical weakly coupled states,” J. Opt. A 5, 471–477 (2003).
[CrossRef]

1999 (1)

V. N. Parygin, A. V. Vershubskii, and K. A. Kholostov, “Control of the characteristics of a calcium molybdate collinear acousto-optic filter,” Tech. Phys. 44, 1467–1471 (1999).
[CrossRef]

1979 (1)

J. D. Fichter, M. Gottlieb, and J. J. Conroy, “Tl3AsSe3 noncollinear acousto-optic filter operation at 10 μm,” Appl. Phys. Lett. 34, 1–3 (1979).
[CrossRef]

1976 (1)

E. T. Aksenov, N. A. Esepkina, and A. S. Shcherbakov, “Acousto-optical filter with a LiNbO3-crystal,” Tech. Phys. Lett. 2, 83–84 (1976).

1974 (2)

I. C. Chang, “Tunable acousto-optic filter utilizing acoustic beam walk-off in crystal quartz,” Appl. Phys. Lett. 25, 323–324 (1974).
[CrossRef]

J. A. Kusters, D. A. Wilson, and D. L. Hammond, “Optimum crystal orientation for acoustically tuned optical filters,” J. Opt. Soc. Am. 64, 434–440 (1974).
[CrossRef]

1970 (1)

S. E. Harris, S. T. K. Nich, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223–225 (1970).
[CrossRef]

1969 (1)

1967 (1)

R. W. Dixon, “Acoustic diffraction of light in anisotropic media,” IEEE J. Quantum Electron. QE-3, 85–93 (1967).
[CrossRef]

Aguirre Lopez, A.

A. S. Shcherbakov and A. Aguirre Lopez, “Shaping the optical components of solitary three-wave weakly coupled states in a two-mode waveguide,” Opt. Express 11, 1643–1649 (2003).
[CrossRef]

A. S. Shcherbakov and A. Aguirre Lopez, “Binary encoded modulation of light based on collinear three-wave acousto-optical weakly coupled states,” J. Opt. A 5, 471–477 (2003).
[CrossRef]

Aksenov, E. T.

E. T. Aksenov, N. A. Esepkina, and A. S. Shcherbakov, “Acousto-optical filter with a LiNbO3-crystal,” Tech. Phys. Lett. 2, 83–84 (1976).

Balakshy, V. I.

V. I. Balakshy, V. N. Parygin, and L. I. Chrkov, Physical Principles of Acousto-Optics (Radio I Svyaz, 1985).

Balderas Mata, S. E.

A. S. Shcherbakov, J. Maximov, and S. E. Balderas Mata, “Shaping the dissipative collinear three-wave coupled states in a two-mode medium with a square-law nonlinearity and linear non-optical losses,” J. Opt. A 10, 025001 (2008).
[CrossRef]

Belyaev, D.

Blistanov, A. A.

A. A. Blistanov, Crystals for Quantum and Nonlinear Optics, 2nd ed. (MISIS, 2007).

Chang, I. C.

I. C. Chang, “Tunable acousto-optic filter utilizing acoustic beam walk-off in crystal quartz,” Appl. Phys. Lett. 25, 323–324 (1974).
[CrossRef]

Chrkov, L. I.

V. I. Balakshy, V. N. Parygin, and L. I. Chrkov, Physical Principles of Acousto-Optics (Radio I Svyaz, 1985).

Conroy, J. J.

J. D. Fichter, M. Gottlieb, and J. J. Conroy, “Tl3AsSe3 noncollinear acousto-optic filter operation at 10 μm,” Appl. Phys. Lett. 34, 1–3 (1979).
[CrossRef]

Dixon, R. W.

R. W. Dixon, “Acoustic diffraction of light in anisotropic media,” IEEE J. Quantum Electron. QE-3, 85–93 (1967).
[CrossRef]

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals3rd ed. (Springer, 1999).

Drummond, R.

Esepkina, N. A.

E. T. Aksenov, N. A. Esepkina, and A. S. Shcherbakov, “Acousto-optical filter with a LiNbO3-crystal,” Tech. Phys. Lett. 2, 83–84 (1976).

Federova, A.

Fichter, J. D.

J. D. Fichter, M. Gottlieb, and J. J. Conroy, “Tl3AsSe3 noncollinear acousto-optic filter operation at 10 μm,” Appl. Phys. Lett. 34, 1–3 (1979).
[CrossRef]

Fiegelson, R. S.

S. E. Harris, S. T. K. Nich, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223–225 (1970).
[CrossRef]

Gottlieb, M.

J. D. Fichter, M. Gottlieb, and J. J. Conroy, “Tl3AsSe3 noncollinear acousto-optic filter operation at 10 μm,” Appl. Phys. Lett. 34, 1–3 (1979).
[CrossRef]

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals3rd ed. (Springer, 1999).

Hammond, D. L.

Harris, S. E.

S. E. Harris, S. T. K. Nich, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223–225 (1970).
[CrossRef]

S. E. Harris and R. W. Wallace, “Acousto-optic tunable filter,” J. Opt. Soc. Am. 59, 744–747 (1969).
[CrossRef]

Kholostov, K. A.

V. N. Parygin, A. V. Vershubskii, and K. A. Kholostov, “Control of the characteristics of a calcium molybdate collinear acousto-optic filter,” Tech. Phys. 44, 1467–1471 (1999).
[CrossRef]

Korpel, A.

A. Korpel, Acousto-Optics, 2nd ed. (Dekker, 1997).

Kusters, J. A.

Mahieux, A.

Maximov, J.

A. S. Shcherbakov, J. Maximov, and S. E. Balderas Mata, “Shaping the dissipative collinear three-wave coupled states in a two-mode medium with a square-law nonlinearity and linear non-optical losses,” J. Opt. A 10, 025001 (2008).
[CrossRef]

Nich, S. T. K.

S. E. Harris, S. T. K. Nich, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223–225 (1970).
[CrossRef]

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals3rd ed. (Springer, 1999).

Parygin, V. N.

V. N. Parygin, A. V. Vershubskii, and K. A. Kholostov, “Control of the characteristics of a calcium molybdate collinear acousto-optic filter,” Tech. Phys. 44, 1467–1471 (1999).
[CrossRef]

V. I. Balakshy, V. N. Parygin, and L. I. Chrkov, Physical Principles of Acousto-Optics (Radio I Svyaz, 1985).

Shcherbakov, A. S.

A. S. Shcherbakov, J. Maximov, and S. E. Balderas Mata, “Shaping the dissipative collinear three-wave coupled states in a two-mode medium with a square-law nonlinearity and linear non-optical losses,” J. Opt. A 10, 025001 (2008).
[CrossRef]

A. S. Shcherbakov and A. Aguirre Lopez, “Binary encoded modulation of light based on collinear three-wave acousto-optical weakly coupled states,” J. Opt. A 5, 471–477 (2003).
[CrossRef]

A. S. Shcherbakov and A. Aguirre Lopez, “Shaping the optical components of solitary three-wave weakly coupled states in a two-mode waveguide,” Opt. Express 11, 1643–1649 (2003).
[CrossRef]

E. T. Aksenov, N. A. Esepkina, and A. S. Shcherbakov, “Acousto-optical filter with a LiNbO3-crystal,” Tech. Phys. Lett. 2, 83–84 (1976).

Vandaele, A. C.

Vershubskii, A. V.

V. N. Parygin, A. V. Vershubskii, and K. A. Kholostov, “Control of the characteristics of a calcium molybdate collinear acousto-optic filter,” Tech. Phys. 44, 1467–1471 (1999).
[CrossRef]

Wallace, R. W.

Wilquet, V.

Wilson, D. A.

Yu, F. T. S.

F. T. S. Yu, Introduction to Information Optics (Academic, 2001).

Appl. Phys. Lett. (3)

S. E. Harris, S. T. K. Nich, and R. S. Fiegelson, “CaMoO4 electronically tunable optical filter,” Appl. Phys. Lett. 17, 223–225 (1970).
[CrossRef]

I. C. Chang, “Tunable acousto-optic filter utilizing acoustic beam walk-off in crystal quartz,” Appl. Phys. Lett. 25, 323–324 (1974).
[CrossRef]

J. D. Fichter, M. Gottlieb, and J. J. Conroy, “Tl3AsSe3 noncollinear acousto-optic filter operation at 10 μm,” Appl. Phys. Lett. 34, 1–3 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. W. Dixon, “Acoustic diffraction of light in anisotropic media,” IEEE J. Quantum Electron. QE-3, 85–93 (1967).
[CrossRef]

J. Opt. A (2)

A. S. Shcherbakov and A. Aguirre Lopez, “Binary encoded modulation of light based on collinear three-wave acousto-optical weakly coupled states,” J. Opt. A 5, 471–477 (2003).
[CrossRef]

A. S. Shcherbakov, J. Maximov, and S. E. Balderas Mata, “Shaping the dissipative collinear three-wave coupled states in a two-mode medium with a square-law nonlinearity and linear non-optical losses,” J. Opt. A 10, 025001 (2008).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Express (2)

Tech. Phys. (1)

V. N. Parygin, A. V. Vershubskii, and K. A. Kholostov, “Control of the characteristics of a calcium molybdate collinear acousto-optic filter,” Tech. Phys. 44, 1467–1471 (1999).
[CrossRef]

Tech. Phys. Lett. (1)

E. T. Aksenov, N. A. Esepkina, and A. S. Shcherbakov, “Acousto-optical filter with a LiNbO3-crystal,” Tech. Phys. Lett. 2, 83–84 (1976).

Other (6)

V. I. Balakshy, V. N. Parygin, and L. I. Chrkov, Physical Principles of Acousto-Optics (Radio I Svyaz, 1985).

A. Korpel, Acousto-Optics, 2nd ed. (Dekker, 1997).

F. T. S. Yu, Introduction to Information Optics (Academic, 2001).

M. P. Shaskolskaya, ed., Handbook “Acoustic Crystals” (Nauka, 1988).

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals3rd ed. (Springer, 1999).

A. A. Blistanov, Crystals for Quantum and Nonlinear Optics, 2nd ed. (MISIS, 2007).

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 (16)

Fig. 1.
Fig. 1.

2D plot on the plane (αx,σx) with lines corresponding to N=0, 1, 2.

Fig. 2.
Fig. 2.

Restricting the number N of unit-valued maxima; the particular case of α=0.1cm1, σ=1cm1, and N2 is shown.

Fig. 3.
Fig. 3.

Graphical solution to Eq. (5a); positions for the unit-valued maxima as a function of collinear interaction length. σ is a parameter for N=0 and α=0.1cm1.

Fig. 4.
Fig. 4.

Normalized scattered light distributions versus the dimensional length of interaction with α=0.1cm1; the dashed line is for σ=0.5cm1, and the solid line is for σ=1cm1.

Fig. 5.
Fig. 5.

3D plots for the absolute values of the scattered light intensity profile with α0 and q0/q11 on the interval 0σx3π: (a) αx=0.1 and (b) αx=0.5.

Fig. 6.
Fig. 6.

2D profiles |C1[(σx),(ηx)]|2 with q0/q11: (a) α=0.1cm1 and σ=0.5cm1 with X0=3.768cm and X1=28.55cm, (b) α=0.1cm1 and σ=1cm1 wherein X0=1.709cm, X1=6.372cm, and X2=15.39cm.

Fig. 7.
Fig. 7.

First combined diagram expressed in the coordinates R=η/α and S=σ/α on a plane corresponding to the 0.405 level.

Fig. 8.
Fig. 8.

Second combined diagram expressed in the coordinates s=σx and r=ηx with the parameter a=αx on a plane related to the 0.405 intensity level. The plots for the dimensionless mismatch ηx, which represents half of the TFW, are shown by solid lines. The plots for |C1(η=0)|2 are drawn by dotted lines.

Fig. 9.
Fig. 9.

Set of 2D plots for the normalized scattered light intensity |C1(x)|2 at the level of 0.405 on the plane (σx,ηx) for various αx taken only within the first quasi-period.

Fig. 10.
Fig. 10.

Dimensionless mismatch ηx versus the acoustic losses αx with infinitely small controlling signal σ0 or s0.

Fig. 11.
Fig. 11.

Acoustic power density P versus the parameter σ in the CaMoO4 cell.

Fig. 12.
Fig. 12.

Schematic arrangement of the experimental setup.

Fig. 13.
Fig. 13.

Scattered light intensity |C1|2 versus the acoustic power density P with α=0.0261cm1 (solid line is for theory and circles are for experiment at f=61.24MHz, λ=532nm) and α=0.0615cm1 (squares are for experiment at fmax=94.34MHz, λ=444nm) in the CaMoO4-cell.

Fig. 14.
Fig. 14.

Digitized oscilloscope traces for the scattered light intensity |C1|2 observed at the output of the collinear CaMoO4 cell for various acoustic losses and acoustic frequencies. Their widths have been measured at the level 0.405 with σL0.2, so that (a) fA=43.47MHz, (αL)A0.0575; (b) fB=61.24MHz, (αL)B0.114; and (c) fC=94.34MHz, (αL)C0.271.

Fig. 15.
Fig. 15.

Combined diagram reflecting both the 2D-theoretical plots with the product αL{0,0.0575,0.114,0.271} and all the above-noted experimental points. The lossless case is αL=0.

Fig. 16.
Fig. 16.

Digitized oscilloscope traces for the scattered light intensity |C1|2 for the green light with λ=532nm observed at the output of the collinear CaMoO4 cell near the central carrier acoustic frequency f0=61.24MHz and estimated at the level 0.405. Reshaping the transmission function is followed at the same optical pump in variable scales: (a) σLπ/2, P0.0365[W/mm2]; (b) σL2.5, P0.0925[W/mm2]; (c) σL3.0, P0.133[W/mm2]; and (d) σL3.2, P0.152[W/mm2].

Equations (23)

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

|C0(x)|2=η2σ2+η2+σ2σ2+η2cos2[G(x)G(0)],
|C1(x)|2=q0q1σ2σ2+η2sin2[G(x)G(0)],
G(x)=1α[η2+σ2exp(2αx)+ηln{2αη2[ηexp(αx)+σ2+η2exp(2αx)]}].
|C1(x)|2=q0q1sin2{σα[1exp(αx)]}.
Maxima:G(x)G(0)=π(N+12),N=0,1,2,,
Zeros:G(x)G(0)=πM,M=1,2,3,,
σα[1exp(αx)]=π(N+12),
σα[1exp(αx)]=πM.
Nσαπ[1exp(αx)]12,
Mσαπ[1exp(αx)];
XN=α1·ln[1απσ(N+12)].
ZM=α1·ln[1απσM].
|C1(x)|2=(q0(σx)2q1)·sin2(ηx)(ηx)2,
G(x,α0)=α1η[αx1+ln(4αη1)],
G(0,α0)=α1η[1+ln(4αη1)].
S2·sin2(R2+S2R2+S2[1πS(N+0.5)]2Rln[1πS(N+0.5)]+Rln{2R2[R+R2+S2[1πS(N+0.5)]2]}Rln{2R2[R+R2+S2]})=0.405·(R2+S2).
s2·sin2(1ar2+s21ar2+s2exp[a]+raln{2ar2[rexp(a)+r2exp(2a)+s2]}raln{2ar2[r+r2+s2]})=0.405·(r2+s2)·sin2{sa[1exp(a)]}.
1r2+s2·sin2(1ar2+s21ar2+s2exp[a]+raln{2ar2[rexp(a)+r2exp(2a)+s2]}raln{2ar2[r+r2+s2]})=0.405·1s2·sin2{sa[1exp(a)]}.
sin2(ηx)(ηx)2=0.405·[1exp(αx)αx]2.
σN(m)=απ(N+0.5)1exp(αXN),
σM(z)=απM1exp(αZM),
σ=U0q0q1πλP2M2,
P2λ2σ2π2M2,

Metrics