Abstract

A number of spectral imagers using acousto-optic tunable filters (AOTFs) operating from the UV to the longwave infrared (LWIR) using KDP, MgF2, TeO2, and Tl3AsSe3 crystals to cover different spectral regions have been developed. In the LWIR there is a lack of high quality acousto-optic (AO) materials. Mercurous halide (Hg2Cl2 and Hg2Br2) crystals are highly anisotropic with a high AO figure of merit due to slow acoustic velocities and high photoelastic constants and are transparent over a wide spectral region from 0.35 to 20μm for Hg2Cl2 and from 0.4 to 30μm for Hg2Br2. AO modulators, deflectors, and AOTFs based on these crystals can operate over a wide spectral range. Single crystals of these materials are being grown and some prototype devices have been fabricated. Results are presented from device characterization for an AO cell fabricated in Hg2Cl2 based on longitudinal acoustic mode propagation. This device was very useful in demonstrating the AO interaction as well as soundness of the transducer bonding technique. Acoustic phase velocity is calculated and measured, diffraction efficiency is obtained from experiments, and the AO figure of merit of the sample is evaluated.

© 2009 Optical Society of America

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  1. N. Gupta and V. B. Voloshinov, “Hyperspectral imaging performance of a TeO2 imaging acousto-optic tunable filter in the ultraviolet region,” Opt. Lett. 30, 985-987 (2005).
    [CrossRef] [PubMed]
  2. V. B. Voloshinov and N. Gupta, “Investigation of magnesium fluoride crystals for imaging acousto-optic tunable filter applications,” Appl. Opt. 45, 3127-3135 (2006).
    [CrossRef] [PubMed]
  3. V. Voloshinov and N. Gupta, “Ultraviolet/visible imaging acousto-optic tunable filters in KDP,” Appl. Opt. 43, 3901-3909 (2004).
    [CrossRef] [PubMed]
  4. N. Gupta and V. Voloshinov, “Hyperspectral imager from ultraviolet to visible using KDP AOTF,” Appl. Opt. 43, 2752-2759 (2004).
    [CrossRef] [PubMed]
  5. N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible-to-near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033-1038 (2002).
    [CrossRef]
  6. D. R. Suhre and N. Gupta, “Acousto-optic tunable filter sidelobe analysis and reduction using telecentric confocal optics,” Appl. Opt. 44, 5797-5801 (2005).
    [CrossRef] [PubMed]
  7. D. R. Suhre, L. J. Denes, and N. Gupta, “Telecentric confocal optics for aberration correction of acousto-optic tunable filters,” Appl. Opt. 43, 1255-1260 (2004).
    [CrossRef] [PubMed]
  8. N. Gupta and D. R. Suhre, “AOTF imaging spectrometer with full Stokes polarimetric capability,” Appl. Opt. 46, 2632-2037(2007).
    [CrossRef] [PubMed]
  9. V. B. Voloshinov and N. Gupta, “Acousto-optic imaging in the mid-infrared region of the spectrum,” Proc. SPIE 3900, 62-73(1999).
    [CrossRef]
  10. N. Gupta, “Development of agile wide spectral range hyperspectral/polarization imagers,” in Photonic Applications Systems Technologies Conference PhAST (Optical Society of America, 2005), paper PThA3.
  11. N. Gupta, “Hyperspectral and polarization imaging with double-transducer AOTF for wide spectral band coverage,” Int. J. High Speed Electron. Syst. 17, 845-855 (2007).
    [CrossRef]
  12. N. Gupta and V. B. Voloshinov, “Development and characterization of two-transducer imaging acousto-optic tunable filters with extended tuning range,” Appl. Opt. 46, 1081-1088 (2007).
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  14. N. Gupta, “Acousto-optic tunable filters for Infrared Imaging,” Proc SPIE 5953, 59530O (2005).
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  17. J. D. Feichtner, M. Gottlieb, and J. J. Conroy, “Tl3AsSe3 noncollinear acousto-optic filter operation at 10 μm,” Appl. Phys. Lett. 34, 1-3 (1979).
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  20. D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.
  21. D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
    [CrossRef]
  22. D. J. Knuteson, N. B. Singh, M. Gottlieb, D. Suhre, and N. Gupta, “Crystal growth, fabrication and design of mercurous bromide acousto-optic tunable filters,” Opt. Eng. 46, 064001 (2007).
    [CrossRef]
  23. J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Development of mercurous halide crystals for acousto-optic devices,” Proc. SPIE 666166610B (2007).
    [CrossRef]
  24. J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Growth of Hg2Cl2 and Hg2Br2 single crystals by physical vapor transport,” J. Cryst. Growth 310, 2457-2463 (2008).
    [CrossRef]
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    [CrossRef]
  26. M. Silvestrova, C. Barta, G. Dobrshansky, L. Belyaev, and Y. V. Pisarevsky, “Acousto-optic properties of calomel crystal Hg2Cl2,” Sov. Phys. Crystallogr. 20, 649-651 (1975).
  27. C. Barta, P. M. Sileverstova, N. A. Moiseeva, and Yu. V. Pisarevskiy, “Propagation of acoustic waves in crystals of univalent halides,” Krist. Tech. 15, 843-848(1980).
    [CrossRef]
  28. N. B. Singh, M. Gottlieb, and A. Goutzoulis, “Devices made from vapor-phase grown mercurous chloride crystals,” J. Cryst. Growth 82, 274-278 (1987).
    [CrossRef]
  29. M. Gottlieb, A. P. Goutzoulis, and N. B. Singh, “Fabrication and characterization of mercurous chloride acoustooptic devices,” Appl. Opt. 26, 4681-4687 (1987).
    [CrossRef] [PubMed]
  30. A. P. Goutzoulis and M. Gottlieb, “Characteristics and design of mercurous halide Bragg cells for optical signal processing,” Opt. Eng. 27, 157-163 (1988).
  31. M. Gottlieb, A. Goutzoulis, and N. Singh, “High-performance acousto-optic materials: Hg2Cl2 and PbBr2,” Opt. Eng. 31, 2110-2117 (1992).
    [CrossRef]
  32. N. B. Singh and R. Mazelsky, “Development of mercurous halides for acousto-optic devices,” Curr. Top. Cryst. Growth Res. 2, 435-444 (1995).
  33. A. Goutzoulis and D. Pape, Designing and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).
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2008 (4)

N. Gupta, “Hyperspectral imager development at Army Research Laboratory,” Proc. SPIE 6940, 69401P (2008).
[CrossRef]

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Growth of Hg2Cl2 and Hg2Br2 single crystals by physical vapor transport,” J. Cryst. Growth 310, 2457-2463 (2008).
[CrossRef]

V. B. Voloshinov, V. I. Balakshy, L. A. Kulakova, and N. Gupta, “Acousto-optic properties of tellurium that are useful in anisotropic diffraction,” J. Opt. A 10, 095002 (2008).
[CrossRef]

2007 (5)

D. J. Knuteson, N. B. Singh, M. Gottlieb, D. Suhre, and N. Gupta, “Crystal growth, fabrication and design of mercurous bromide acousto-optic tunable filters,” Opt. Eng. 46, 064001 (2007).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Development of mercurous halide crystals for acousto-optic devices,” Proc. SPIE 666166610B (2007).
[CrossRef]

N. Gupta, “Hyperspectral and polarization imaging with double-transducer AOTF for wide spectral band coverage,” Int. J. High Speed Electron. Syst. 17, 845-855 (2007).
[CrossRef]

N. Gupta and V. B. Voloshinov, “Development and characterization of two-transducer imaging acousto-optic tunable filters with extended tuning range,” Appl. Opt. 46, 1081-1088 (2007).
[CrossRef] [PubMed]

N. Gupta and D. R. Suhre, “AOTF imaging spectrometer with full Stokes polarimetric capability,” Appl. Opt. 46, 2632-2037(2007).
[CrossRef] [PubMed]

2006 (1)

2005 (5)

D. R. Suhre and N. Gupta, “Acousto-optic tunable filter sidelobe analysis and reduction using telecentric confocal optics,” Appl. Opt. 44, 5797-5801 (2005).
[CrossRef] [PubMed]

N. Gupta and V. B. Voloshinov, “Hyperspectral imaging performance of a TeO2 imaging acousto-optic tunable filter in the ultraviolet region,” Opt. Lett. 30, 985-987 (2005).
[CrossRef] [PubMed]

N. Gupta, “Acousto-optic tunable filters for Infrared Imaging,” Proc SPIE 5953, 59530O (2005).

N. Gupta, D. R. Suhre, and M. Gottlieb, “LWIR spectral imager with an 8 cm−1 passband acousto-optic tunable filter,” Opt. Eng. 44094601 (2005).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

2004 (3)

2002 (1)

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible-to-near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033-1038 (2002).
[CrossRef]

2001 (1)

N. B. Singh, D. Suhre, N. Gupta, W. Rosch, and M. Gottlieb, “Performance of TAS cystal for AOTF iaging,” J. Cryst.Growth 225, 124-128 (2001).
[CrossRef]

1999 (1)

V. B. Voloshinov and N. Gupta, “Acousto-optic imaging in the mid-infrared region of the spectrum,” Proc. SPIE 3900, 62-73(1999).
[CrossRef]

1998 (1)

1995 (1)

N. B. Singh and R. Mazelsky, “Development of mercurous halides for acousto-optic devices,” Curr. Top. Cryst. Growth Res. 2, 435-444 (1995).

1992 (1)

M. Gottlieb, A. Goutzoulis, and N. Singh, “High-performance acousto-optic materials: Hg2Cl2 and PbBr2,” Opt. Eng. 31, 2110-2117 (1992).
[CrossRef]

1988 (1)

A. P. Goutzoulis and M. Gottlieb, “Characteristics and design of mercurous halide Bragg cells for optical signal processing,” Opt. Eng. 27, 157-163 (1988).

1987 (2)

N. B. Singh, M. Gottlieb, and A. Goutzoulis, “Devices made from vapor-phase grown mercurous chloride crystals,” J. Cryst. Growth 82, 274-278 (1987).
[CrossRef]

M. Gottlieb, A. P. Goutzoulis, and N. B. Singh, “Fabrication and characterization of mercurous chloride acoustooptic devices,” Appl. Opt. 26, 4681-4687 (1987).
[CrossRef] [PubMed]

1980 (1)

C. Barta, P. M. Sileverstova, N. A. Moiseeva, and Yu. V. Pisarevskiy, “Propagation of acoustic waves in crystals of univalent halides,” Krist. Tech. 15, 843-848(1980).
[CrossRef]

1979 (1)

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

1975 (1)

M. Silvestrova, C. Barta, G. Dobrshansky, L. Belyaev, and Y. V. Pisarevsky, “Acousto-optic properties of calomel crystal Hg2Cl2,” Sov. Phys. Crystallogr. 20, 649-651 (1975).

Auld, B. A.

B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, 1973), Vol. 1.

Balakshy, V. I.

V. B. Voloshinov, V. I. Balakshy, L. A. Kulakova, and N. Gupta, “Acousto-optic properties of tellurium that are useful in anisotropic diffraction,” J. Opt. A 10, 095002 (2008).
[CrossRef]

Barta, C.

C. Barta, P. M. Sileverstova, N. A. Moiseeva, and Yu. V. Pisarevskiy, “Propagation of acoustic waves in crystals of univalent halides,” Krist. Tech. 15, 843-848(1980).
[CrossRef]

M. Silvestrova, C. Barta, G. Dobrshansky, L. Belyaev, and Y. V. Pisarevsky, “Acousto-optic properties of calomel crystal Hg2Cl2,” Sov. Phys. Crystallogr. 20, 649-651 (1975).

Belyaev, L.

M. Silvestrova, C. Barta, G. Dobrshansky, L. Belyaev, and Y. V. Pisarevsky, “Acousto-optic properties of calomel crystal Hg2Cl2,” Sov. Phys. Crystallogr. 20, 649-651 (1975).

Berghmans, A.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Choy, S.

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible-to-near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033-1038 (2002).
[CrossRef]

Conroy, J. J.

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

Dahmani, R.

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible-to-near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033-1038 (2002).
[CrossRef]

Denes, L. J.

Dobrshansky, G.

M. Silvestrova, C. Barta, G. Dobrshansky, L. Belyaev, and Y. V. Pisarevsky, “Acousto-optic properties of calomel crystal Hg2Cl2,” Sov. Phys. Crystallogr. 20, 649-651 (1975).

Feichtner, J. D.

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

Fitelson, M.

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

Gottlieb, M.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

D. J. Knuteson, N. B. Singh, M. Gottlieb, D. Suhre, and N. Gupta, “Crystal growth, fabrication and design of mercurous bromide acousto-optic tunable filters,” Opt. Eng. 46, 064001 (2007).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

N. Gupta, D. R. Suhre, and M. Gottlieb, “LWIR spectral imager with an 8 cm−1 passband acousto-optic tunable filter,” Opt. Eng. 44094601 (2005).
[CrossRef]

N. B. Singh, D. Suhre, N. Gupta, W. Rosch, and M. Gottlieb, “Performance of TAS cystal for AOTF iaging,” J. Cryst.Growth 225, 124-128 (2001).
[CrossRef]

M. Gottlieb, A. Goutzoulis, and N. Singh, “High-performance acousto-optic materials: Hg2Cl2 and PbBr2,” Opt. Eng. 31, 2110-2117 (1992).
[CrossRef]

A. P. Goutzoulis and M. Gottlieb, “Characteristics and design of mercurous halide Bragg cells for optical signal processing,” Opt. Eng. 27, 157-163 (1988).

M. Gottlieb, A. P. Goutzoulis, and N. B. Singh, “Fabrication and characterization of mercurous chloride acoustooptic devices,” Appl. Opt. 26, 4681-4687 (1987).
[CrossRef] [PubMed]

N. B. Singh, M. Gottlieb, and A. Goutzoulis, “Devices made from vapor-phase grown mercurous chloride crystals,” J. Cryst. Growth 82, 274-278 (1987).
[CrossRef]

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

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Goutzoulis, A.

M. Gottlieb, A. Goutzoulis, and N. Singh, “High-performance acousto-optic materials: Hg2Cl2 and PbBr2,” Opt. Eng. 31, 2110-2117 (1992).
[CrossRef]

N. B. Singh, M. Gottlieb, and A. Goutzoulis, “Devices made from vapor-phase grown mercurous chloride crystals,” J. Cryst. Growth 82, 274-278 (1987).
[CrossRef]

A. Goutzoulis and D. Pape, Designing and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).

Goutzoulis, A. P.

A. P. Goutzoulis and M. Gottlieb, “Characteristics and design of mercurous halide Bragg cells for optical signal processing,” Opt. Eng. 27, 157-163 (1988).

M. Gottlieb, A. P. Goutzoulis, and N. B. Singh, “Fabrication and characterization of mercurous chloride acoustooptic devices,” Appl. Opt. 26, 4681-4687 (1987).
[CrossRef] [PubMed]

Gupta, N.

V. B. Voloshinov, V. I. Balakshy, L. A. Kulakova, and N. Gupta, “Acousto-optic properties of tellurium that are useful in anisotropic diffraction,” J. Opt. A 10, 095002 (2008).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Growth of Hg2Cl2 and Hg2Br2 single crystals by physical vapor transport,” J. Cryst. Growth 310, 2457-2463 (2008).
[CrossRef]

N. Gupta, “Hyperspectral imager development at Army Research Laboratory,” Proc. SPIE 6940, 69401P (2008).
[CrossRef]

N. Gupta, “Hyperspectral and polarization imaging with double-transducer AOTF for wide spectral band coverage,” Int. J. High Speed Electron. Syst. 17, 845-855 (2007).
[CrossRef]

N. Gupta and V. B. Voloshinov, “Development and characterization of two-transducer imaging acousto-optic tunable filters with extended tuning range,” Appl. Opt. 46, 1081-1088 (2007).
[CrossRef] [PubMed]

N. Gupta and D. R. Suhre, “AOTF imaging spectrometer with full Stokes polarimetric capability,” Appl. Opt. 46, 2632-2037(2007).
[CrossRef] [PubMed]

D. J. Knuteson, N. B. Singh, M. Gottlieb, D. Suhre, and N. Gupta, “Crystal growth, fabrication and design of mercurous bromide acousto-optic tunable filters,” Opt. Eng. 46, 064001 (2007).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Development of mercurous halide crystals for acousto-optic devices,” Proc. SPIE 666166610B (2007).
[CrossRef]

V. B. Voloshinov and N. Gupta, “Investigation of magnesium fluoride crystals for imaging acousto-optic tunable filter applications,” Appl. Opt. 45, 3127-3135 (2006).
[CrossRef] [PubMed]

N. Gupta and V. B. Voloshinov, “Hyperspectral imaging performance of a TeO2 imaging acousto-optic tunable filter in the ultraviolet region,” Opt. Lett. 30, 985-987 (2005).
[CrossRef] [PubMed]

D. R. Suhre and N. Gupta, “Acousto-optic tunable filter sidelobe analysis and reduction using telecentric confocal optics,” Appl. Opt. 44, 5797-5801 (2005).
[CrossRef] [PubMed]

N. Gupta, “Acousto-optic tunable filters for Infrared Imaging,” Proc SPIE 5953, 59530O (2005).

N. Gupta, D. R. Suhre, and M. Gottlieb, “LWIR spectral imager with an 8 cm−1 passband acousto-optic tunable filter,” Opt. Eng. 44094601 (2005).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

D. R. Suhre, L. J. Denes, and N. Gupta, “Telecentric confocal optics for aberration correction of acousto-optic tunable filters,” Appl. Opt. 43, 1255-1260 (2004).
[CrossRef] [PubMed]

V. Voloshinov and N. Gupta, “Ultraviolet/visible imaging acousto-optic tunable filters in KDP,” Appl. Opt. 43, 3901-3909 (2004).
[CrossRef] [PubMed]

N. Gupta and V. Voloshinov, “Hyperspectral imager from ultraviolet to visible using KDP AOTF,” Appl. Opt. 43, 2752-2759 (2004).
[CrossRef] [PubMed]

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible-to-near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033-1038 (2002).
[CrossRef]

N. B. Singh, D. Suhre, N. Gupta, W. Rosch, and M. Gottlieb, “Performance of TAS cystal for AOTF iaging,” J. Cryst.Growth 225, 124-128 (2001).
[CrossRef]

V. B. Voloshinov and N. Gupta, “Acousto-optic imaging in the mid-infrared region of the spectrum,” Proc. SPIE 3900, 62-73(1999).
[CrossRef]

N. Gupta, “Development of agile wide spectral range hyperspectral/polarization imagers,” in Photonic Applications Systems Technologies Conference PhAST (Optical Society of America, 2005), paper PThA3.

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Hawkins, J.

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

Hawkins, J. J.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Hedrick, J.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

Kahler, D.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Karr, T.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

Kim, J.

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Growth of Hg2Cl2 and Hg2Br2 single crystals by physical vapor transport,” J. Cryst. Growth 310, 2457-2463 (2008).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Development of mercurous halide crystals for acousto-optic devices,” Proc. SPIE 666166610B (2007).
[CrossRef]

Knuteson, D. J.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

D. J. Knuteson, N. B. Singh, M. Gottlieb, D. Suhre, and N. Gupta, “Crystal growth, fabrication and design of mercurous bromide acousto-optic tunable filters,” Opt. Eng. 46, 064001 (2007).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Kulakova, L. A.

V. B. Voloshinov, V. I. Balakshy, L. A. Kulakova, and N. Gupta, “Acousto-optic properties of tellurium that are useful in anisotropic diffraction,” J. Opt. A 10, 095002 (2008).
[CrossRef]

Lears, C.

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Mazelsky, R.

N. B. Singh and R. Mazelsky, “Development of mercurous halides for acousto-optic devices,” Curr. Top. Cryst. Growth Res. 2, 435-444 (1995).

Moiseeva, N. A.

C. Barta, P. M. Sileverstova, N. A. Moiseeva, and Yu. V. Pisarevskiy, “Propagation of acoustic waves in crystals of univalent halides,” Krist. Tech. 15, 843-848(1980).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Masson, 1974).

Palosz, W.

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Growth of Hg2Cl2 and Hg2Br2 single crystals by physical vapor transport,” J. Cryst. Growth 310, 2457-2463 (2008).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Development of mercurous halide crystals for acousto-optic devices,” Proc. SPIE 666166610B (2007).
[CrossRef]

Pape, D.

A. Goutzoulis and D. Pape, Designing and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).

Pisarevskiy, Yu. V.

C. Barta, P. M. Sileverstova, N. A. Moiseeva, and Yu. V. Pisarevskiy, “Propagation of acoustic waves in crystals of univalent halides,” Krist. Tech. 15, 843-848(1980).
[CrossRef]

Pisarevsky, Y. V.

M. Silvestrova, C. Barta, G. Dobrshansky, L. Belyaev, and Y. V. Pisarevsky, “Acousto-optic properties of calomel crystal Hg2Cl2,” Sov. Phys. Crystallogr. 20, 649-651 (1975).

Rosch, W.

N. B. Singh, D. Suhre, N. Gupta, W. Rosch, and M. Gottlieb, “Performance of TAS cystal for AOTF iaging,” J. Cryst.Growth 225, 124-128 (2001).
[CrossRef]

Sileverstova, P. M.

C. Barta, P. M. Sileverstova, N. A. Moiseeva, and Yu. V. Pisarevskiy, “Propagation of acoustic waves in crystals of univalent halides,” Krist. Tech. 15, 843-848(1980).
[CrossRef]

Silvestrova, M.

M. Silvestrova, C. Barta, G. Dobrshansky, L. Belyaev, and Y. V. Pisarevsky, “Acousto-optic properties of calomel crystal Hg2Cl2,” Sov. Phys. Crystallogr. 20, 649-651 (1975).

Singh, N.

M. Gottlieb, A. Goutzoulis, and N. Singh, “High-performance acousto-optic materials: Hg2Cl2 and PbBr2,” Opt. Eng. 31, 2110-2117 (1992).
[CrossRef]

Singh, N. B.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

D. J. Knuteson, N. B. Singh, M. Gottlieb, D. Suhre, and N. Gupta, “Crystal growth, fabrication and design of mercurous bromide acousto-optic tunable filters,” Opt. Eng. 46, 064001 (2007).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

N. B. Singh, D. Suhre, N. Gupta, W. Rosch, and M. Gottlieb, “Performance of TAS cystal for AOTF iaging,” J. Cryst.Growth 225, 124-128 (2001).
[CrossRef]

N. B. Singh and R. Mazelsky, “Development of mercurous halides for acousto-optic devices,” Curr. Top. Cryst. Growth Res. 2, 435-444 (1995).

M. Gottlieb, A. P. Goutzoulis, and N. B. Singh, “Fabrication and characterization of mercurous chloride acoustooptic devices,” Appl. Opt. 26, 4681-4687 (1987).
[CrossRef] [PubMed]

N. B. Singh, M. Gottlieb, and A. Goutzoulis, “Devices made from vapor-phase grown mercurous chloride crystals,” J. Cryst. Growth 82, 274-278 (1987).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Soos, J.

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Growth of Hg2Cl2 and Hg2Br2 single crystals by physical vapor transport,” J. Cryst. Growth 310, 2457-2463 (2008).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Development of mercurous halide crystals for acousto-optic devices,” Proc. SPIE 666166610B (2007).
[CrossRef]

Stroud, R.

J. Xu and R. Stroud, Acousto-Optic Devices (Wiley, 1992).

Suhre, D.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

D. J. Knuteson, N. B. Singh, M. Gottlieb, D. Suhre, and N. Gupta, “Crystal growth, fabrication and design of mercurous bromide acousto-optic tunable filters,” Opt. Eng. 46, 064001 (2007).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

N. B. Singh, D. Suhre, N. Gupta, W. Rosch, and M. Gottlieb, “Performance of TAS cystal for AOTF iaging,” J. Cryst.Growth 225, 124-128 (2001).
[CrossRef]

D. Suhre and E. Villa, “Imaging spectroradiometer for the 8-12 μm region with 3 cm−1 passband acousto-optic tunable filter,” Appl. Opt. 37, 2340-2345 (1998).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Suhre, D. R.

Thomson, D.

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

Trivedi, S. B.

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Growth of Hg2Cl2 and Hg2Br2 single crystals by physical vapor transport,” J. Cryst. Growth 310, 2457-2463 (2008).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Development of mercurous halide crystals for acousto-optic devices,” Proc. SPIE 666166610B (2007).
[CrossRef]

Villa, E.

Voloshinov, V.

Voloshinov, V. B.

Wagner, B.

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

Xu, J.

J. Xu and R. Stroud, Acousto-Optic Devices (Wiley, 1992).

Appl. Opt. (9)

V. B. Voloshinov and N. Gupta, “Investigation of magnesium fluoride crystals for imaging acousto-optic tunable filter applications,” Appl. Opt. 45, 3127-3135 (2006).
[CrossRef] [PubMed]

V. Voloshinov and N. Gupta, “Ultraviolet/visible imaging acousto-optic tunable filters in KDP,” Appl. Opt. 43, 3901-3909 (2004).
[CrossRef] [PubMed]

N. Gupta and V. Voloshinov, “Hyperspectral imager from ultraviolet to visible using KDP AOTF,” Appl. Opt. 43, 2752-2759 (2004).
[CrossRef] [PubMed]

D. R. Suhre and N. Gupta, “Acousto-optic tunable filter sidelobe analysis and reduction using telecentric confocal optics,” Appl. Opt. 44, 5797-5801 (2005).
[CrossRef] [PubMed]

D. R. Suhre, L. J. Denes, and N. Gupta, “Telecentric confocal optics for aberration correction of acousto-optic tunable filters,” Appl. Opt. 43, 1255-1260 (2004).
[CrossRef] [PubMed]

N. Gupta and D. R. Suhre, “AOTF imaging spectrometer with full Stokes polarimetric capability,” Appl. Opt. 46, 2632-2037(2007).
[CrossRef] [PubMed]

N. Gupta and V. B. Voloshinov, “Development and characterization of two-transducer imaging acousto-optic tunable filters with extended tuning range,” Appl. Opt. 46, 1081-1088 (2007).
[CrossRef] [PubMed]

D. Suhre and E. Villa, “Imaging spectroradiometer for the 8-12 μm region with 3 cm−1 passband acousto-optic tunable filter,” Appl. Opt. 37, 2340-2345 (1998).
[CrossRef]

M. Gottlieb, A. P. Goutzoulis, and N. B. Singh, “Fabrication and characterization of mercurous chloride acoustooptic devices,” Appl. Opt. 26, 4681-4687 (1987).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

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

Curr. Top. Cryst. Growth Res. (1)

N. B. Singh and R. Mazelsky, “Development of mercurous halides for acousto-optic devices,” Curr. Top. Cryst. Growth Res. 2, 435-444 (1995).

Int. J. High Speed Electron. Syst. (1)

N. Gupta, “Hyperspectral and polarization imaging with double-transducer AOTF for wide spectral band coverage,” Int. J. High Speed Electron. Syst. 17, 845-855 (2007).
[CrossRef]

J. Cryst. Growth (2)

N. B. Singh, M. Gottlieb, and A. Goutzoulis, “Devices made from vapor-phase grown mercurous chloride crystals,” J. Cryst. Growth 82, 274-278 (1987).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Growth of Hg2Cl2 and Hg2Br2 single crystals by physical vapor transport,” J. Cryst. Growth 310, 2457-2463 (2008).
[CrossRef]

J. Cryst.Growth (1)

N. B. Singh, D. Suhre, N. Gupta, W. Rosch, and M. Gottlieb, “Performance of TAS cystal for AOTF iaging,” J. Cryst.Growth 225, 124-128 (2001).
[CrossRef]

J. Opt. A (1)

V. B. Voloshinov, V. I. Balakshy, L. A. Kulakova, and N. Gupta, “Acousto-optic properties of tellurium that are useful in anisotropic diffraction,” J. Opt. A 10, 095002 (2008).
[CrossRef]

Krist. Tech. (1)

C. Barta, P. M. Sileverstova, N. A. Moiseeva, and Yu. V. Pisarevskiy, “Propagation of acoustic waves in crystals of univalent halides,” Krist. Tech. 15, 843-848(1980).
[CrossRef]

Opt. Eng. (6)

N. B. Singh, D. Kahler, D. J. Knuteson, M. Gottlieb, D. Suhre, A. Berghmans, B. Wagner, J. Hedrick, T. Karr, and J. J. Hawkins, “Operational characteristics of a long-wavelength IR multispectral imager based on an acousto-optic tunable filter,” Opt. Eng. 47, 013201 (2008).
[CrossRef]

D. J. Knuteson, N. B. Singh, M. Gottlieb, D. Suhre, and N. Gupta, “Crystal growth, fabrication and design of mercurous bromide acousto-optic tunable filters,” Opt. Eng. 46, 064001 (2007).
[CrossRef]

A. P. Goutzoulis and M. Gottlieb, “Characteristics and design of mercurous halide Bragg cells for optical signal processing,” Opt. Eng. 27, 157-163 (1988).

M. Gottlieb, A. Goutzoulis, and N. Singh, “High-performance acousto-optic materials: Hg2Cl2 and PbBr2,” Opt. Eng. 31, 2110-2117 (1992).
[CrossRef]

N. Gupta, D. R. Suhre, and M. Gottlieb, “LWIR spectral imager with an 8 cm−1 passband acousto-optic tunable filter,” Opt. Eng. 44094601 (2005).
[CrossRef]

N. Gupta, R. Dahmani, and S. Choy, “Acousto-optic tunable filter based visible-to-near-infrared spectropolarimetric imager,” Opt. Eng. 41, 1033-1038 (2002).
[CrossRef]

Opt. Lett. (1)

Proc SPIE (1)

N. Gupta, “Acousto-optic tunable filters for Infrared Imaging,” Proc SPIE 5953, 59530O (2005).

Proc. SPIE (4)

N. Gupta, “Hyperspectral imager development at Army Research Laboratory,” Proc. SPIE 6940, 69401P (2008).
[CrossRef]

V. B. Voloshinov and N. Gupta, “Acousto-optic imaging in the mid-infrared region of the spectrum,” Proc. SPIE 3900, 62-73(1999).
[CrossRef]

J. Kim, S. B. Trivedi, J. Soos, N. Gupta, and W. Palosz, “Development of mercurous halide crystals for acousto-optic devices,” Proc. SPIE 666166610B (2007).
[CrossRef]

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Thomson, D. Kahler, B. Wagner, J. Hawkins, and M. Fitelson, “Design and fabrication of mercurous bromide acousto-optic tunable filters,” Proc. SPIE 588158810E (2005).
[CrossRef]

Sov. Phys. Crystallogr. (1)

M. Silvestrova, C. Barta, G. Dobrshansky, L. Belyaev, and Y. V. Pisarevsky, “Acousto-optic properties of calomel crystal Hg2Cl2,” Sov. Phys. Crystallogr. 20, 649-651 (1975).

Other (6)

D. J. Knuteson, N. B. Singh, N. Gupta, M. Gottlieb, D. Suhre, A. Berghmans, D. Kahler, B. Wagner, C. Lears, and J. J. Hawkins, “Performance of crystals; operational characteristics of mercurous bromide crystals for acousto-optic applications,” inProceedings of the XIII International Workshop on Physics of Semiconductor Devices, Section H, Vol. II (Allied Publishers, 2005), pp. 1184-1189.

A. Goutzoulis and D. Pape, Designing and Fabrication of Acousto-Optic Devices (Marcel Dekker, 1994).

J. Xu and R. Stroud, Acousto-Optic Devices (Wiley, 1992).

B. A. Auld, Acoustic Fields and Waves in Solids (Wiley, 1973), Vol. 1.

J. F. Nye, Physical Properties of Crystals (Masson, 1974).

N. Gupta, “Development of agile wide spectral range hyperspectral/polarization imagers,” in Photonic Applications Systems Technologies Conference PhAST (Optical Society of America, 2005), paper PThA3.

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Figures (4)

Fig. 1
Fig. 1

(a) Photograph of packaged AO cell and (b) schematic drawing of the AO device inside the package.

Fig. 2
Fig. 2

Experimental setup for AO device characterization.

Fig. 3
Fig. 3

Photograph of the experimental setup for AO device characterization.

Fig. 4
Fig. 4

Diffraction efficiency as a function of applied rf power.

Equations (15)

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

θ m ± m λ 0 n Λ ,
θ 1 = ± λ 0 Λ .
V = λ 0 f / θ 1 .
Q = 2 π λ 0 L n Λ 2 cos θ 0 ,
V L x = c 11 ρ , V L z = c 33 ρ , V S x 1 = c 44 ρ , V S x 2 = c 66 ρ , V S z = c 44 ρ .
V L z θ = A ± ( B 2 + C ) 2 ρ ,
V z = ( c 66 sin 2 θ + c 44 cos 2 θ ) ρ .
M 2 = n 6 p eff 2 ρ V 3 ,
Δ B i = p i j S j , i , j = 1 , 2 , , 6.
[ p 11 p 12 p 13 0 0 0 p 12 p 11 p 13 0 0 0 p 31 p 31 p 33 0 0 0 0 0 0 p 44 0 0 0 0 0 0 p 44 0 0 0 0 0 0 p 66 ] .
[ 1 n o 2 + ( p 11 sin 2 θ + p 13 cos 2 θ ) S 0 ] x 2 + [ 1 n o 2 + ( p 12 sin 2 θ + p 13 cos 2 θ ) S 0 ] y 2 + [ 1 n e 2 + ( p 31 sin 2 θ + p 33 cos 2 θ ) S 0 ] z 2 + ( 2 p 44 S 0 sin 2 θ ) x z = 1 .
[ 1 n o 2 + ( p 11 sin 2 θ + p 13 cos 2 θ ) S 0 ] x 2 + [ 1 n e 2 + ( p 31 sin 2 θ + p 33 cos 2 θ ) S 0 ] z 2 + ( 2 p 44 S 0 sin 2 θ ) x z = 1.
p eff x = ( p 11 sin 2 θ + p 13 cos 2 θ ) ,
p eff z = ( p 31 sin 2 θ + p 33 cos 2 θ ) .
η π 2 M 2 P a L 2 λ 0 2 H cos 2 θ 0 ,

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