Abstract

The acousto-optical crystals are frequently used, indispensable elements of high technology and modern science, and yet their precise numerical description has not been available. In this paper an accurate, rapid and quite general model of the AO interaction in a Bragg-cell is presented. The suitability of the simulation is intended to be verified experimentally, for which we wanted to apply the most convincing measurement methods. The difficulty of the verification is that the measurement contains unknown parameters. Therefore we performed an elaborated series of measurements and developed a method for the estimation of the unknown parameters.

© 2014 Optical Society of America

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References

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  1. J. Xu and R. Stroud, “Acousto-Optic Interaction,” in Acousto-Optic Devices (Wiley-Interscience, 1992). pp. 61–94.
  2. A. Korpel, Acousto-Optics (Marcel Dekker Inc., 1997).
  3. G. Mihajlik, P. Maák, A. Barocsi, P. Richter, “Novel accurate computer algorithm for modeling light propagation and diffraction in inhomogeneous, anisotropic medium – Applied to the acousto-optic interaction,” Opt. Commun. 282(10), 1961–1968 (2009).
    [CrossRef]
  4. G. Mihajlik, P. Maák, A. Barocsi, “Simulation of light propagation in anisotropic, optically active and slightly inhomogeneous medium, concerning the acousto-optic interaction,” Opt. Commun. 285(9), 2255–2265 (2012).
    [CrossRef]
  5. G. Mihajlik, A. Barocsi, P. Maák, “Measurement and general modeling of optical rotation in anisotropic crystal,” Opt. Commun. 310(1), 31–34 (2014).
    [CrossRef]
  6. Y. Hao and R. Mittra, FDTD Modeling of Metamaterials, Theory and Applications (Artech House, Inc., 2009).
  7. A. Deinega, S. Belousov, I. Valuev, “Hybrid transfer-matrix FDTD method for layered periodic structures,” Opt. Lett. 34(6), 860–862 (2009).
    [CrossRef] [PubMed]
  8. G. Dhatt, E. Lefrançois, and G. Touzot, Finite Element Method (Wiley, 2012).
  9. R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (SIAM, 2007).
  10. B. A. Auld, Acoustic Fields and Waves in Solids (Krieger Pub Co. 1990).
  11. B. E. A. Saleh and M. C. Teich, “Polarization and Crystal Optics,” in Fundamentals of Photonics (Wiley & Sons Inc. 1991). pp. 216, 6.310–6.311.

2014 (1)

G. Mihajlik, A. Barocsi, P. Maák, “Measurement and general modeling of optical rotation in anisotropic crystal,” Opt. Commun. 310(1), 31–34 (2014).
[CrossRef]

2012 (1)

G. Mihajlik, P. Maák, A. Barocsi, “Simulation of light propagation in anisotropic, optically active and slightly inhomogeneous medium, concerning the acousto-optic interaction,” Opt. Commun. 285(9), 2255–2265 (2012).
[CrossRef]

2009 (2)

G. Mihajlik, P. Maák, A. Barocsi, P. Richter, “Novel accurate computer algorithm for modeling light propagation and diffraction in inhomogeneous, anisotropic medium – Applied to the acousto-optic interaction,” Opt. Commun. 282(10), 1961–1968 (2009).
[CrossRef]

A. Deinega, S. Belousov, I. Valuev, “Hybrid transfer-matrix FDTD method for layered periodic structures,” Opt. Lett. 34(6), 860–862 (2009).
[CrossRef] [PubMed]

Barocsi, A.

G. Mihajlik, A. Barocsi, P. Maák, “Measurement and general modeling of optical rotation in anisotropic crystal,” Opt. Commun. 310(1), 31–34 (2014).
[CrossRef]

G. Mihajlik, P. Maák, A. Barocsi, “Simulation of light propagation in anisotropic, optically active and slightly inhomogeneous medium, concerning the acousto-optic interaction,” Opt. Commun. 285(9), 2255–2265 (2012).
[CrossRef]

G. Mihajlik, P. Maák, A. Barocsi, P. Richter, “Novel accurate computer algorithm for modeling light propagation and diffraction in inhomogeneous, anisotropic medium – Applied to the acousto-optic interaction,” Opt. Commun. 282(10), 1961–1968 (2009).
[CrossRef]

Belousov, S.

Deinega, A.

Maák, P.

G. Mihajlik, A. Barocsi, P. Maák, “Measurement and general modeling of optical rotation in anisotropic crystal,” Opt. Commun. 310(1), 31–34 (2014).
[CrossRef]

G. Mihajlik, P. Maák, A. Barocsi, “Simulation of light propagation in anisotropic, optically active and slightly inhomogeneous medium, concerning the acousto-optic interaction,” Opt. Commun. 285(9), 2255–2265 (2012).
[CrossRef]

G. Mihajlik, P. Maák, A. Barocsi, P. Richter, “Novel accurate computer algorithm for modeling light propagation and diffraction in inhomogeneous, anisotropic medium – Applied to the acousto-optic interaction,” Opt. Commun. 282(10), 1961–1968 (2009).
[CrossRef]

Mihajlik, G.

G. Mihajlik, A. Barocsi, P. Maák, “Measurement and general modeling of optical rotation in anisotropic crystal,” Opt. Commun. 310(1), 31–34 (2014).
[CrossRef]

G. Mihajlik, P. Maák, A. Barocsi, “Simulation of light propagation in anisotropic, optically active and slightly inhomogeneous medium, concerning the acousto-optic interaction,” Opt. Commun. 285(9), 2255–2265 (2012).
[CrossRef]

G. Mihajlik, P. Maák, A. Barocsi, P. Richter, “Novel accurate computer algorithm for modeling light propagation and diffraction in inhomogeneous, anisotropic medium – Applied to the acousto-optic interaction,” Opt. Commun. 282(10), 1961–1968 (2009).
[CrossRef]

Richter, P.

G. Mihajlik, P. Maák, A. Barocsi, P. Richter, “Novel accurate computer algorithm for modeling light propagation and diffraction in inhomogeneous, anisotropic medium – Applied to the acousto-optic interaction,” Opt. Commun. 282(10), 1961–1968 (2009).
[CrossRef]

Valuev, I.

Opt. Commun. (3)

G. Mihajlik, P. Maák, A. Barocsi, P. Richter, “Novel accurate computer algorithm for modeling light propagation and diffraction in inhomogeneous, anisotropic medium – Applied to the acousto-optic interaction,” Opt. Commun. 282(10), 1961–1968 (2009).
[CrossRef]

G. Mihajlik, P. Maák, A. Barocsi, “Simulation of light propagation in anisotropic, optically active and slightly inhomogeneous medium, concerning the acousto-optic interaction,” Opt. Commun. 285(9), 2255–2265 (2012).
[CrossRef]

G. Mihajlik, A. Barocsi, P. Maák, “Measurement and general modeling of optical rotation in anisotropic crystal,” Opt. Commun. 310(1), 31–34 (2014).
[CrossRef]

Opt. Lett. (1)

Other (7)

J. Xu and R. Stroud, “Acousto-Optic Interaction,” in Acousto-Optic Devices (Wiley-Interscience, 1992). pp. 61–94.

A. Korpel, Acousto-Optics (Marcel Dekker Inc., 1997).

Y. Hao and R. Mittra, FDTD Modeling of Metamaterials, Theory and Applications (Artech House, Inc., 2009).

G. Dhatt, E. Lefrançois, and G. Touzot, Finite Element Method (Wiley, 2012).

R. J. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (SIAM, 2007).

B. A. Auld, Acoustic Fields and Waves in Solids (Krieger Pub Co. 1990).

B. E. A. Saleh and M. C. Teich, “Polarization and Crystal Optics,” in Fundamentals of Photonics (Wiley & Sons Inc. 1991). pp. 216, 6.310–6.311.

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Figures (11)

Fig. 1
Fig. 1

Arrangement of the measurement.

Fig. 2
Fig. 2

Measured and simulated diffraction efficiency values as the function of the angle of in-cidence with vertical (↕) or horizontal (↔) polarizations of the incident beam (P1), in case of the filter. Here the P2 polarizer was not applied.

Fig. 3
Fig. 3

Measured and modeled Bragg angles of the eight different first order diffractions as a function of the acoustic frequency, in case of the filter.

Fig. 4
Fig. 4

The transducer of the measured deflector. Only the left hexagon is factory connected.

Fig. 5
Fig. 5

The parameters of the fitted P IAWF. (a) The parameters of the hexagonal transducer. (b) The absolute value and phase of the fitted polynomial along the symmetric axis. As can be seen the size of the hexagon is not sharp but dithered so as to allow numerical differentiation. The full width at half maximum, FWHM = p2 + 2⋅p3.

Fig. 6
Fig. 6

(a) The absolute value (in arbitrary unit) and (b) phase of the fitted HR IAWF. Here it is important to emphasize that the fitted IAWF is still not the same as the real one, since more different IAWFs can generate the same ηsim(τ, Xi, Y) quantities.

Fig. 7
Fig. 7

The diffraction efficiencies at Bragg angle as a function of the vertical position (Y) of the beam at X = 3 mm and X = 8 mm, where the effect of the ground electrode is eliminated by estimation from the measurement. The green line denotes the simulation assuming the P IAWF.

Fig. 8
Fig. 8

The measured and modeled diffraction efficiencies are shown as functions of the angle of incidence for several X and Y values. The green line represents the simulation assuming P IAWF without the ground electrode, the red line shows calculations assuming the HR IAWF with the ground electrode. The black line represents the measurements. For each value of (XY) there are two subfigures to illustrate the diffraction curves at different scales with 1× and 10× zoom to show the agreement.

Fig. 9
Fig. 9

The measured and modeled diffraction efficiencies are shown as functions of the angle of incidence for several X and Y values. The green line represents the simulation assuming P IAWF without the ground electrode, the red line shows calculations assuming the HR IAWF with the ground electrode. The black line represents the measurements. For each value of (XY) there are four subfigures to illustrate the diffraction curves at different scales with 1×, 10×, 20× and 100× zoom to show the agreement.

Fig. 10
Fig. 10

The measured and modeled diffraction efficiencies are shown as functions of the angle of incidence for several X and Y values. The green line represents the simulation assuming P IAWF without the ground electrode, the red line shows calculations assuming the HR IAWF with the ground electrode. The black line represents the measurements. For each value of (XY) there are four subfigures to illustrate the diffraction curves at different scales with 1×, 10×, 20× and 100× zoom to show the agreement.

Fig. 11
Fig. 11

The measured and modeled diffraction efficiencies are shown as functions of the angle of incidence in the proximity of the Bragg angle. X = 3 mm for all subfigures. The black line represents the measurement, the blue line shows the estimation of the elimination of the ground electrode effect from the measurement. The red line represents the simulation assuming the HR IAWF with the ground electrode, the green line shows calculations assuming the P IAWF without the ground electrode. The same colors denote the same quantities in Figs. 7-11.

Tables (1)

Tables Icon

Table 1 The fitted and measured parameters of the hexagonal transducer for the P IAWF.

Equations (7)

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iK c KL Lj u j =ρ 2 u i / t 2 ,
u i (r,t)=Re{ U i (r)exp(iΩt)}.
K iK c KL K Lj U j =ρ Ω 2 U i .
K iK c KL K Lj U j =( A ¯ ¯ 1 K x 2 + A ¯ ¯ 2 K y 2 +...+ A ¯ ¯ 6 K y K z )U.
( A ¯ ¯ 1 K x 2 + A ¯ ¯ 2 K y 2 +...+ A ¯ ¯ 6 K y K z I ¯ ¯ ρ Ω 2 )U=0.
η(τ,X,Y) k x , k y spot | E ˜ d,spot | 2 ,
S ( x , y ) = ( q 0 + q 1 y + q 2 y 2 + q 3 y 3 + i q 4 y 2 ) e x p ( 2 π i q 5 y ) .

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