Abstract

We present a comprehensive study of the acoustic-to-optic phase transfer during anisotropic Bragg diffraction. Our results refine the operating theory of widely used acousto-optic implementations such as pulse shapers, delay lines, and phase modulators.

© 2010 Optical Society of America

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  1. P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).
  2. F. Verluise, V. Laude, J. P. Huignard, P. Tournois, and A. Migus, “Arbitrary dispersion control of ultrashort optical pulses with acoustic waves,” J. Opt. Soc. Am. B 17, 138-145(2000).
    [CrossRef]
  3. V. Molchanov, S. Chizhikov, O. Makarov, N. Solodovnikov, V. Ginzburg, E. Katin, E. Khazanov, V. Lozhkarev, and I. Yakovlev, “Adaptive acousto-optic technique for femtosecond laser pulse shaping,” Appl. Opt. 48, C118-C124 (2009).
    [CrossRef]
  4. A. VanderLugt, Optical Signal Processing, Wiley Series in Pure and Applied Optics (Wiley, 2005).
  5. W. D. Jemison, “Analysis of the AO-FDPC optical heterodyne technique for microwave time delay and phased array beam steering applications,” IEEE Trans. Microwave Theory Tech. 50, 1832-1843 (2002).
    [CrossRef]
  6. Y. Jiang, Y. Leng, X. Chen, X. Li, and Z. Xu, “Active phase control and frequency chirp effects on supercontinuum generation in high birefringence photonic crystal fiber,” Opt. Commun. 281, 2449-2453 (2008).
    [CrossRef]
  7. J. P. Lee, “Simple phase tracking measurement technique for multichannel Bragg cells,” Opt. Eng. 27, 677-683(1988).
  8. N.J.Berg, ed., Acousto-Optic Signal Processing (Marcel Dekker, 1983).
  9. V. B. Voloshinov, A. V. Tchernyatin, E. Blomme, and O. J. Leroy, “A dozen of Bragg effects in tellurium dioxide single crystal,” Proc. SPIE 3581, 141-152 (1998).
  10. V. B. Voloshinov, “Elastic anisotropy of acousto-optic interaction medium,” Proc. SPIE 4514, 8-19 (2001).
  11. M. Pushkareva and V. N. Parygin, “Quasi-collinear AOTF with improved resolution,” Proc. SPIE 4514, 147-152 (2001).
  12. Y. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear acousto-optic interaction of divergent beams in paratellurite crystal,” Proc. SPIE 5828, 16-24 (2004).
  13. Y. Dobrolenskiy, V. Voloshinov, Y. Zyuryukin, and E. Djakonov, “Nonreciprocity of acousto-optic interaction in collinear tunable acousto-optic filters,” Appl. Opt. 48, C67-C73 (2009).
    [CrossRef]
  14. V. B. Voloshinov and N. V. Polikarpova, “Acousto-optic investigation of propagation and reflection of acoustic waves in paratellurite crystal,” Appl. Opt. 48, C55-C66 (2009).
    [CrossRef]
  15. P. Maák, I. Frigyes, L. Jakab, I. Habermayer, M. Gyukics, and P. Richter, “Realization of true-time delay lines based on acoustooptics,” J. Lightwave Technol. 20, 730-739 (2002).
    [CrossRef]
  16. P. Kwiek and R. Reibold, “Additional phase shifts in ultrasound diffraction,” Acustica 80, 294-299 (1994).
  17. P. Kwiek and R. Reibold, “Determination of the phase of an ultrasound field using light diffraction,” Acustica 82, 376-378 (1996).

2009 (3)

2008 (1)

Y. Jiang, Y. Leng, X. Chen, X. Li, and Z. Xu, “Active phase control and frequency chirp effects on supercontinuum generation in high birefringence photonic crystal fiber,” Opt. Commun. 281, 2449-2453 (2008).
[CrossRef]

2006 (1)

P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).

2004 (1)

Y. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear acousto-optic interaction of divergent beams in paratellurite crystal,” Proc. SPIE 5828, 16-24 (2004).

2002 (2)

P. Maák, I. Frigyes, L. Jakab, I. Habermayer, M. Gyukics, and P. Richter, “Realization of true-time delay lines based on acoustooptics,” J. Lightwave Technol. 20, 730-739 (2002).
[CrossRef]

W. D. Jemison, “Analysis of the AO-FDPC optical heterodyne technique for microwave time delay and phased array beam steering applications,” IEEE Trans. Microwave Theory Tech. 50, 1832-1843 (2002).
[CrossRef]

2001 (2)

V. B. Voloshinov, “Elastic anisotropy of acousto-optic interaction medium,” Proc. SPIE 4514, 8-19 (2001).

M. Pushkareva and V. N. Parygin, “Quasi-collinear AOTF with improved resolution,” Proc. SPIE 4514, 147-152 (2001).

2000 (1)

1998 (1)

V. B. Voloshinov, A. V. Tchernyatin, E. Blomme, and O. J. Leroy, “A dozen of Bragg effects in tellurium dioxide single crystal,” Proc. SPIE 3581, 141-152 (1998).

1996 (1)

P. Kwiek and R. Reibold, “Determination of the phase of an ultrasound field using light diffraction,” Acustica 82, 376-378 (1996).

1994 (1)

P. Kwiek and R. Reibold, “Additional phase shifts in ultrasound diffraction,” Acustica 80, 294-299 (1994).

1988 (1)

J. P. Lee, “Simple phase tracking measurement technique for multichannel Bragg cells,” Opt. Eng. 27, 677-683(1988).

Barócsi, A.

P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).

Blomme, E.

V. B. Voloshinov, A. V. Tchernyatin, E. Blomme, and O. J. Leroy, “A dozen of Bragg effects in tellurium dioxide single crystal,” Proc. SPIE 3581, 141-152 (1998).

Chen, X.

Y. Jiang, Y. Leng, X. Chen, X. Li, and Z. Xu, “Active phase control and frequency chirp effects on supercontinuum generation in high birefringence photonic crystal fiber,” Opt. Commun. 281, 2449-2453 (2008).
[CrossRef]

Chizhikov, S.

Djakonov, E.

Dobrolenskiy, Y.

Dobrolenskiy, Y. S.

Y. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear acousto-optic interaction of divergent beams in paratellurite crystal,” Proc. SPIE 5828, 16-24 (2004).

Frigyes, I.

Ginzburg, V.

Gyukics, M.

Habermayer, I.

Huignard, J. P.

Jakab, L.

P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).

P. Maák, I. Frigyes, L. Jakab, I. Habermayer, M. Gyukics, and P. Richter, “Realization of true-time delay lines based on acoustooptics,” J. Lightwave Technol. 20, 730-739 (2002).
[CrossRef]

Jemison, W. D.

W. D. Jemison, “Analysis of the AO-FDPC optical heterodyne technique for microwave time delay and phased array beam steering applications,” IEEE Trans. Microwave Theory Tech. 50, 1832-1843 (2002).
[CrossRef]

Jiang, Y.

Y. Jiang, Y. Leng, X. Chen, X. Li, and Z. Xu, “Active phase control and frequency chirp effects on supercontinuum generation in high birefringence photonic crystal fiber,” Opt. Commun. 281, 2449-2453 (2008).
[CrossRef]

Katin, E.

Khazanov, E.

Kovács, A. P.

P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).

Kurdi, G.

P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).

Kwiek, P.

P. Kwiek and R. Reibold, “Determination of the phase of an ultrasound field using light diffraction,” Acustica 82, 376-378 (1996).

P. Kwiek and R. Reibold, “Additional phase shifts in ultrasound diffraction,” Acustica 80, 294-299 (1994).

Laude, V.

Lee, J. P.

J. P. Lee, “Simple phase tracking measurement technique for multichannel Bragg cells,” Opt. Eng. 27, 677-683(1988).

Leng, Y.

Y. Jiang, Y. Leng, X. Chen, X. Li, and Z. Xu, “Active phase control and frequency chirp effects on supercontinuum generation in high birefringence photonic crystal fiber,” Opt. Commun. 281, 2449-2453 (2008).
[CrossRef]

Leroy, O. J.

V. B. Voloshinov, A. V. Tchernyatin, E. Blomme, and O. J. Leroy, “A dozen of Bragg effects in tellurium dioxide single crystal,” Proc. SPIE 3581, 141-152 (1998).

Li, X.

Y. Jiang, Y. Leng, X. Chen, X. Li, and Z. Xu, “Active phase control and frequency chirp effects on supercontinuum generation in high birefringence photonic crystal fiber,” Opt. Commun. 281, 2449-2453 (2008).
[CrossRef]

Lozhkarev, V.

Maák, P.

P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).

P. Maák, I. Frigyes, L. Jakab, I. Habermayer, M. Gyukics, and P. Richter, “Realization of true-time delay lines based on acoustooptics,” J. Lightwave Technol. 20, 730-739 (2002).
[CrossRef]

Makarov, O.

Migus, A.

Molchanov, V.

Osvay, K.

P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).

Parygin, V. N.

Y. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear acousto-optic interaction of divergent beams in paratellurite crystal,” Proc. SPIE 5828, 16-24 (2004).

M. Pushkareva and V. N. Parygin, “Quasi-collinear AOTF with improved resolution,” Proc. SPIE 4514, 147-152 (2001).

Polikarpova, N. V.

Pushkareva, M.

M. Pushkareva and V. N. Parygin, “Quasi-collinear AOTF with improved resolution,” Proc. SPIE 4514, 147-152 (2001).

Reibold, R.

P. Kwiek and R. Reibold, “Determination of the phase of an ultrasound field using light diffraction,” Acustica 82, 376-378 (1996).

P. Kwiek and R. Reibold, “Additional phase shifts in ultrasound diffraction,” Acustica 80, 294-299 (1994).

Richter, P.

P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).

P. Maák, I. Frigyes, L. Jakab, I. Habermayer, M. Gyukics, and P. Richter, “Realization of true-time delay lines based on acoustooptics,” J. Lightwave Technol. 20, 730-739 (2002).
[CrossRef]

Solodovnikov, N.

Tchernyatin, A. V.

V. B. Voloshinov, A. V. Tchernyatin, E. Blomme, and O. J. Leroy, “A dozen of Bragg effects in tellurium dioxide single crystal,” Proc. SPIE 3581, 141-152 (1998).

Tournois, P.

VanderLugt, A.

A. VanderLugt, Optical Signal Processing, Wiley Series in Pure and Applied Optics (Wiley, 2005).

Verluise, F.

Voloshinov, V.

Voloshinov, V. B.

V. B. Voloshinov and N. V. Polikarpova, “Acousto-optic investigation of propagation and reflection of acoustic waves in paratellurite crystal,” Appl. Opt. 48, C55-C66 (2009).
[CrossRef]

Y. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear acousto-optic interaction of divergent beams in paratellurite crystal,” Proc. SPIE 5828, 16-24 (2004).

V. B. Voloshinov, “Elastic anisotropy of acousto-optic interaction medium,” Proc. SPIE 4514, 8-19 (2001).

V. B. Voloshinov, A. V. Tchernyatin, E. Blomme, and O. J. Leroy, “A dozen of Bragg effects in tellurium dioxide single crystal,” Proc. SPIE 3581, 141-152 (1998).

Xu, Z.

Y. Jiang, Y. Leng, X. Chen, X. Li, and Z. Xu, “Active phase control and frequency chirp effects on supercontinuum generation in high birefringence photonic crystal fiber,” Opt. Commun. 281, 2449-2453 (2008).
[CrossRef]

Yakovlev, I.

Zyuryukin, Y.

Acustica (2)

P. Kwiek and R. Reibold, “Additional phase shifts in ultrasound diffraction,” Acustica 80, 294-299 (1994).

P. Kwiek and R. Reibold, “Determination of the phase of an ultrasound field using light diffraction,” Acustica 82, 376-378 (1996).

Appl. Opt. (3)

Appl. Phys. B (1)

P. Maák, G. Kurdi, A. Barócsi, K. Osvay, A. P. Kovács, L. Jakab, and P. Richter, “Shaping of ultrashort pulses using bulk acousto-optic filter,” Appl. Phys. B 82, 283-287 (2006).

IEEE Trans. Microwave Theory Tech. (1)

W. D. Jemison, “Analysis of the AO-FDPC optical heterodyne technique for microwave time delay and phased array beam steering applications,” IEEE Trans. Microwave Theory Tech. 50, 1832-1843 (2002).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Commun. (1)

Y. Jiang, Y. Leng, X. Chen, X. Li, and Z. Xu, “Active phase control and frequency chirp effects on supercontinuum generation in high birefringence photonic crystal fiber,” Opt. Commun. 281, 2449-2453 (2008).
[CrossRef]

Opt. Eng. (1)

J. P. Lee, “Simple phase tracking measurement technique for multichannel Bragg cells,” Opt. Eng. 27, 677-683(1988).

Proc. SPIE (4)

V. B. Voloshinov, A. V. Tchernyatin, E. Blomme, and O. J. Leroy, “A dozen of Bragg effects in tellurium dioxide single crystal,” Proc. SPIE 3581, 141-152 (1998).

V. B. Voloshinov, “Elastic anisotropy of acousto-optic interaction medium,” Proc. SPIE 4514, 8-19 (2001).

M. Pushkareva and V. N. Parygin, “Quasi-collinear AOTF with improved resolution,” Proc. SPIE 4514, 147-152 (2001).

Y. S. Dobrolenskiy, V. B. Voloshinov, and V. N. Parygin, “Collinear acousto-optic interaction of divergent beams in paratellurite crystal,” Proc. SPIE 5828, 16-24 (2004).

Other (2)

N.J.Berg, ed., Acousto-Optic Signal Processing (Marcel Dekker, 1983).

A. VanderLugt, Optical Signal Processing, Wiley Series in Pure and Applied Optics (Wiley, 2005).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the heterodyne system.

Fig. 2
Fig. 2

(a) Measured dependence of the heterodyne signal phase shift on the acoustic frequency at two laser wavelengths (measured with two different lasers) caused by a 0.1 mm shift of the cell perpendicular to the laser beam direction. (b) Calculated and measured acoustic frequency dependence of the heterodyne phase, registered at different laser beam–transducer distances. The distance changes in steps of 1.15 mm , which is approximately half of the beam diameter in this configuration.

Fig. 3
Fig. 3

(a) Simulated transfer of the acoustic phase to the heterodyne signal phase at a given frequency ( 80 MHz ). (b) Simulated effect of the acoustic frequency change on the heterodyne phase at different transducer–laser beam distances.

Fig. 4
Fig. 4

Meeting point and relative propagation angles of the acoustic and optical beams within the AO crystal; the angles are exaggerated. The horizontal lines are the phase planes of the acoustic wave, K ¯ denotes the acoustic wave vector, and I ¯ is the direction of the energy propagation.

Equations (8)

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φ i , 1 = π λ L 2 n v a c 2 f 2 ,
Δ φ a c = 2 π f v a c y ,
U ˜ ( x , y ) = e i k z g ( x , y ) U ˜ ( x , y ) g ( x , y ) e i k z ( x x + y y ) d x d y .
U ˜ ( x , y ) = e x 2 + y 2 w 2 e i k Δ n cos ( K y Ω t + Φ ) ,
g ( x , y ) = e i k 2 z ( x 2 + y 2 ) , g ( x , y ) = e i k 2 z ( x 2 + y 2 ) .
| U ˜ 0 + U ˜ 1 | 2 = | U ˜ 0 | 2 + | U ˜ 1 | 2 + Re ( U ˜ 0 U ˜ 1 * ) .
I het ( y ) = Re ( U ˜ 0 ( y ) U ˜ 1 * ( y c ) ) ,
ϕ 0 = 2 π d cos ( ξ + δ ) Λ cos ( δ ) = 2 π d cos ( ξ + δ ) v a c cos ( δ ) f .

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