Abstract

We present a bifrequency acousto-optic tunable filter (AOTF) for applications using polychromatic laser beams. The acousto-optic device is based on two successive anisotropic interactions in paratellurite: the first takes place with an acoustic shear wave tilted at 10° from the [110] axis, while the latter is provided by the acoustic shear wave propagating collinear to the [110] axis. It is then demonstrated that the sidelobes of the impulse response to optical wavelengths of such a bifrequency AOTF are greatly reduced. General expressions of operating frequencies, spectral bandwidths, and acoustic powers are derived. Numerical computations have been drawn for paratellurite. The bifrequency AOTF has been tested using a multiline beam radiated by an argon laser. According to the spectral power distribution of this polychromatic laser beam, the most critical configurations of wavelength filtration have been considered. Experimental results confirm the theoretical predictions.

© 2008 Optical Society of America

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References

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  1. C. D. Tran, “Acousto-optic devices: optical elements for spectroscopy,” Anal. Chem. 64, 971A-981A (1992).
    [CrossRef] [PubMed]
  2. L. Bei, G. I. Dennis, H. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis,” Prog. Quantum Electron. 28, 67-87 (2004).
    [CrossRef]
  3. V. B. Voloshinov, V. Ya. Molchanov, and J. C. Mosquera, “Spectral and polarization analysis of optical images by means of acousto-optics,” Opt. Laser Technol. 28, 119-127 (1996).
    [CrossRef]
  4. T. Yano and A. Watanabe, “Acoustooptic TeO2 tunable filter using far-off-axis anisotropic Bragg diffraction,” Appl. Opt. 15, 2250-2258 (1976).
    [CrossRef] [PubMed]
  5. J. E. B. Oliveira and E. L. Adler, “An analytical method for designing acousto-optical tunable filters,” Proc. IEEE Ultrason. Symp. 505-510 (1987).
  6. I. C. Chang, “Acousto-optic tunable filters,” Opt. Eng. 20, 824-829 (1981).
  7. P. A. Gass and J. R. Sambles, “Accurate design of a noncollinear acousto-optic tunable filter,” Opt. Lett. 16, 429-431(1991).
    [CrossRef] [PubMed]
  8. V. B. Voloshinov, “Close to collinear acousto-optic interaction in paratellurite,” Opt. Eng. 31, 2089-2094 (1992).
    [CrossRef]
  9. I. C. Chang, “Collinear beam acousto-optic tunable filter,” Electron. Lett. 28, 1255-1256 (1992).
    [CrossRef]
  10. J. Sapriel, D. Charissoux, V. Voloshinov, and V. Molchanov, “Tunable acoustooptic filters and equalizers for WDM applications,” J. Lightwave Technol. 20, 864-871 (2002).
    [CrossRef]
  11. J. C. Kastelik, M. G. Gazalet, and P. Boudy, “Cascaded TeO2 acousto-optic devices for high efficiency multifrequency modulation,” J. Appl. Phys. 83,, 674-678 (1998).
  12. M. Pommeray, J. C. Kastelik, M. G. Gazalet, and A. Kab, “Acousto-optic and electro-optic modulators for stereoscopic laser videoprojection,” Opt. Eng. 36, 957-963 (1997).
    [CrossRef]
  13. J. C. Kastelik, M. Pommeray, M. Slachciak, and M. G. Gazalet, “Optical modulation line for stereoscopic laser display”, Rev. Sci. Instrum. 76, 055106 (2005).
    [CrossRef]
  14. S. Dupont, J. C. Kastelik, and F. Causa, “Wide-band acousto-optic deflectors with high efficiency for visible range fringe projector pattern,” Rev. Sci. Instrum. 78, 105102(2007).
    [CrossRef] [PubMed]
  15. L. Denes, B. Kaminsky, and M. Gottlieb, “Image processing using AOTF,” Proc. SPIE 2962, 111-121 (1997).
    [CrossRef]
  16. V. I. Pustovoit, V. E. Pozhar, M. M. Mazur, V. N. Shornill, I. B. Kutuza, and A. V. Perchik, “Double-AOTF spectral imaging system,” Proc. SPIE 5953, 200-203 (2005).
  17. V. E. Pozhar and V. I. Pustovoit, “Long-path optical spectral AOTF-based gas analyzer,” Proc. SPIE 4574, 174-178(2001).
    [CrossRef]
  18. S. N. Antonov, “Acoustooptic nonpolar light controlling devices and polarization modulators based on paratellurite crystals,” Tech. Phys. 49, 1329-1334 (2004).
    [CrossRef]
  19. M. G. Gazalet, G. Waxin, J. M. Rouvaen, R. Torguet, and E. Bridoux, “Independent acoustooptic modulation of the two wavelengths of a bichromatic light beam,” Appl. Opt. 23, 676-681 (1984).
    [CrossRef]
  20. V. B. Voloshinov and D. D. Mishin, “Spectral resolution control of acousto-optical cells operating with collimated and divergent beams,” Proc. SPIE 2051, 378-385 (1993).
    [CrossRef]

2007 (1)

S. Dupont, J. C. Kastelik, and F. Causa, “Wide-band acousto-optic deflectors with high efficiency for visible range fringe projector pattern,” Rev. Sci. Instrum. 78, 105102(2007).
[CrossRef] [PubMed]

2005 (2)

V. I. Pustovoit, V. E. Pozhar, M. M. Mazur, V. N. Shornill, I. B. Kutuza, and A. V. Perchik, “Double-AOTF spectral imaging system,” Proc. SPIE 5953, 200-203 (2005).

J. C. Kastelik, M. Pommeray, M. Slachciak, and M. G. Gazalet, “Optical modulation line for stereoscopic laser display”, Rev. Sci. Instrum. 76, 055106 (2005).
[CrossRef]

2004 (2)

S. N. Antonov, “Acoustooptic nonpolar light controlling devices and polarization modulators based on paratellurite crystals,” Tech. Phys. 49, 1329-1334 (2004).
[CrossRef]

L. Bei, G. I. Dennis, H. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis,” Prog. Quantum Electron. 28, 67-87 (2004).
[CrossRef]

2002 (1)

2001 (1)

V. E. Pozhar and V. I. Pustovoit, “Long-path optical spectral AOTF-based gas analyzer,” Proc. SPIE 4574, 174-178(2001).
[CrossRef]

1998 (1)

J. C. Kastelik, M. G. Gazalet, and P. Boudy, “Cascaded TeO2 acousto-optic devices for high efficiency multifrequency modulation,” J. Appl. Phys. 83,, 674-678 (1998).

1997 (2)

M. Pommeray, J. C. Kastelik, M. G. Gazalet, and A. Kab, “Acousto-optic and electro-optic modulators for stereoscopic laser videoprojection,” Opt. Eng. 36, 957-963 (1997).
[CrossRef]

L. Denes, B. Kaminsky, and M. Gottlieb, “Image processing using AOTF,” Proc. SPIE 2962, 111-121 (1997).
[CrossRef]

1996 (1)

V. B. Voloshinov, V. Ya. Molchanov, and J. C. Mosquera, “Spectral and polarization analysis of optical images by means of acousto-optics,” Opt. Laser Technol. 28, 119-127 (1996).
[CrossRef]

1993 (1)

V. B. Voloshinov and D. D. Mishin, “Spectral resolution control of acousto-optical cells operating with collimated and divergent beams,” Proc. SPIE 2051, 378-385 (1993).
[CrossRef]

1992 (3)

C. D. Tran, “Acousto-optic devices: optical elements for spectroscopy,” Anal. Chem. 64, 971A-981A (1992).
[CrossRef] [PubMed]

V. B. Voloshinov, “Close to collinear acousto-optic interaction in paratellurite,” Opt. Eng. 31, 2089-2094 (1992).
[CrossRef]

I. C. Chang, “Collinear beam acousto-optic tunable filter,” Electron. Lett. 28, 1255-1256 (1992).
[CrossRef]

1991 (1)

1987 (1)

J. E. B. Oliveira and E. L. Adler, “An analytical method for designing acousto-optical tunable filters,” Proc. IEEE Ultrason. Symp. 505-510 (1987).

1984 (1)

M. G. Gazalet, G. Waxin, J. M. Rouvaen, R. Torguet, and E. Bridoux, “Independent acoustooptic modulation of the two wavelengths of a bichromatic light beam,” Appl. Opt. 23, 676-681 (1984).
[CrossRef]

1981 (1)

I. C. Chang, “Acousto-optic tunable filters,” Opt. Eng. 20, 824-829 (1981).

1976 (1)

Adler, E. L.

J. E. B. Oliveira and E. L. Adler, “An analytical method for designing acousto-optical tunable filters,” Proc. IEEE Ultrason. Symp. 505-510 (1987).

Antonov, S. N.

S. N. Antonov, “Acoustooptic nonpolar light controlling devices and polarization modulators based on paratellurite crystals,” Tech. Phys. 49, 1329-1334 (2004).
[CrossRef]

Bei, L.

L. Bei, G. I. Dennis, H. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis,” Prog. Quantum Electron. 28, 67-87 (2004).
[CrossRef]

Boudy, P.

J. C. Kastelik, M. G. Gazalet, and P. Boudy, “Cascaded TeO2 acousto-optic devices for high efficiency multifrequency modulation,” J. Appl. Phys. 83,, 674-678 (1998).

Bridoux, E.

M. G. Gazalet, G. Waxin, J. M. Rouvaen, R. Torguet, and E. Bridoux, “Independent acoustooptic modulation of the two wavelengths of a bichromatic light beam,” Appl. Opt. 23, 676-681 (1984).
[CrossRef]

Carnahan, J. W.

L. Bei, G. I. Dennis, H. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis,” Prog. Quantum Electron. 28, 67-87 (2004).
[CrossRef]

Causa, F.

S. Dupont, J. C. Kastelik, and F. Causa, “Wide-band acousto-optic deflectors with high efficiency for visible range fringe projector pattern,” Rev. Sci. Instrum. 78, 105102(2007).
[CrossRef] [PubMed]

Chang, I. C.

I. C. Chang, “Collinear beam acousto-optic tunable filter,” Electron. Lett. 28, 1255-1256 (1992).
[CrossRef]

I. C. Chang, “Acousto-optic tunable filters,” Opt. Eng. 20, 824-829 (1981).

Charissoux, D.

Denes, L.

L. Denes, B. Kaminsky, and M. Gottlieb, “Image processing using AOTF,” Proc. SPIE 2962, 111-121 (1997).
[CrossRef]

Dennis, G. I.

L. Bei, G. I. Dennis, H. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis,” Prog. Quantum Electron. 28, 67-87 (2004).
[CrossRef]

Dupont, S.

S. Dupont, J. C. Kastelik, and F. Causa, “Wide-band acousto-optic deflectors with high efficiency for visible range fringe projector pattern,” Rev. Sci. Instrum. 78, 105102(2007).
[CrossRef] [PubMed]

Gass, P. A.

Gazalet, M. G.

J. C. Kastelik, M. Pommeray, M. Slachciak, and M. G. Gazalet, “Optical modulation line for stereoscopic laser display”, Rev. Sci. Instrum. 76, 055106 (2005).
[CrossRef]

J. C. Kastelik, M. G. Gazalet, and P. Boudy, “Cascaded TeO2 acousto-optic devices for high efficiency multifrequency modulation,” J. Appl. Phys. 83,, 674-678 (1998).

M. Pommeray, J. C. Kastelik, M. G. Gazalet, and A. Kab, “Acousto-optic and electro-optic modulators for stereoscopic laser videoprojection,” Opt. Eng. 36, 957-963 (1997).
[CrossRef]

M. G. Gazalet, G. Waxin, J. M. Rouvaen, R. Torguet, and E. Bridoux, “Independent acoustooptic modulation of the two wavelengths of a bichromatic light beam,” Appl. Opt. 23, 676-681 (1984).
[CrossRef]

Gottlieb, M.

L. Denes, B. Kaminsky, and M. Gottlieb, “Image processing using AOTF,” Proc. SPIE 2962, 111-121 (1997).
[CrossRef]

Kab, A.

M. Pommeray, J. C. Kastelik, M. G. Gazalet, and A. Kab, “Acousto-optic and electro-optic modulators for stereoscopic laser videoprojection,” Opt. Eng. 36, 957-963 (1997).
[CrossRef]

Kaminsky, B.

L. Denes, B. Kaminsky, and M. Gottlieb, “Image processing using AOTF,” Proc. SPIE 2962, 111-121 (1997).
[CrossRef]

Kastelik, J. C.

S. Dupont, J. C. Kastelik, and F. Causa, “Wide-band acousto-optic deflectors with high efficiency for visible range fringe projector pattern,” Rev. Sci. Instrum. 78, 105102(2007).
[CrossRef] [PubMed]

J. C. Kastelik, M. Pommeray, M. Slachciak, and M. G. Gazalet, “Optical modulation line for stereoscopic laser display”, Rev. Sci. Instrum. 76, 055106 (2005).
[CrossRef]

J. C. Kastelik, M. G. Gazalet, and P. Boudy, “Cascaded TeO2 acousto-optic devices for high efficiency multifrequency modulation,” J. Appl. Phys. 83,, 674-678 (1998).

M. Pommeray, J. C. Kastelik, M. G. Gazalet, and A. Kab, “Acousto-optic and electro-optic modulators for stereoscopic laser videoprojection,” Opt. Eng. 36, 957-963 (1997).
[CrossRef]

Kutuza, I. B.

V. I. Pustovoit, V. E. Pozhar, M. M. Mazur, V. N. Shornill, I. B. Kutuza, and A. V. Perchik, “Double-AOTF spectral imaging system,” Proc. SPIE 5953, 200-203 (2005).

Mazur, M. M.

V. I. Pustovoit, V. E. Pozhar, M. M. Mazur, V. N. Shornill, I. B. Kutuza, and A. V. Perchik, “Double-AOTF spectral imaging system,” Proc. SPIE 5953, 200-203 (2005).

Miller, H.

L. Bei, G. I. Dennis, H. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis,” Prog. Quantum Electron. 28, 67-87 (2004).
[CrossRef]

Mishin, D. D.

V. B. Voloshinov and D. D. Mishin, “Spectral resolution control of acousto-optical cells operating with collimated and divergent beams,” Proc. SPIE 2051, 378-385 (1993).
[CrossRef]

Molchanov, V.

Mosquera, J. C.

V. B. Voloshinov, V. Ya. Molchanov, and J. C. Mosquera, “Spectral and polarization analysis of optical images by means of acousto-optics,” Opt. Laser Technol. 28, 119-127 (1996).
[CrossRef]

Oliveira, J. E. B.

J. E. B. Oliveira and E. L. Adler, “An analytical method for designing acousto-optical tunable filters,” Proc. IEEE Ultrason. Symp. 505-510 (1987).

Pommeray, M.

J. C. Kastelik, M. Pommeray, M. Slachciak, and M. G. Gazalet, “Optical modulation line for stereoscopic laser display”, Rev. Sci. Instrum. 76, 055106 (2005).
[CrossRef]

M. Pommeray, J. C. Kastelik, M. G. Gazalet, and A. Kab, “Acousto-optic and electro-optic modulators for stereoscopic laser videoprojection,” Opt. Eng. 36, 957-963 (1997).
[CrossRef]

Pozhar, V. E.

V. I. Pustovoit, V. E. Pozhar, M. M. Mazur, V. N. Shornill, I. B. Kutuza, and A. V. Perchik, “Double-AOTF spectral imaging system,” Proc. SPIE 5953, 200-203 (2005).

V. E. Pozhar and V. I. Pustovoit, “Long-path optical spectral AOTF-based gas analyzer,” Proc. SPIE 4574, 174-178(2001).
[CrossRef]

Pustovoit, V. I.

V. I. Pustovoit, V. E. Pozhar, M. M. Mazur, V. N. Shornill, I. B. Kutuza, and A. V. Perchik, “Double-AOTF spectral imaging system,” Proc. SPIE 5953, 200-203 (2005).

V. E. Pozhar and V. I. Pustovoit, “Long-path optical spectral AOTF-based gas analyzer,” Proc. SPIE 4574, 174-178(2001).
[CrossRef]

Rouvaen, J. M.

M. G. Gazalet, G. Waxin, J. M. Rouvaen, R. Torguet, and E. Bridoux, “Independent acoustooptic modulation of the two wavelengths of a bichromatic light beam,” Appl. Opt. 23, 676-681 (1984).
[CrossRef]

Sambles, J. R.

Sapriel, J.

Shornill, V. N.

V. I. Pustovoit, V. E. Pozhar, M. M. Mazur, V. N. Shornill, I. B. Kutuza, and A. V. Perchik, “Double-AOTF spectral imaging system,” Proc. SPIE 5953, 200-203 (2005).

Slachciak, M.

J. C. Kastelik, M. Pommeray, M. Slachciak, and M. G. Gazalet, “Optical modulation line for stereoscopic laser display”, Rev. Sci. Instrum. 76, 055106 (2005).
[CrossRef]

Spaine, T. W.

L. Bei, G. I. Dennis, H. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis,” Prog. Quantum Electron. 28, 67-87 (2004).
[CrossRef]

Torguet, R.

M. G. Gazalet, G. Waxin, J. M. Rouvaen, R. Torguet, and E. Bridoux, “Independent acoustooptic modulation of the two wavelengths of a bichromatic light beam,” Appl. Opt. 23, 676-681 (1984).
[CrossRef]

Tran, C. D.

C. D. Tran, “Acousto-optic devices: optical elements for spectroscopy,” Anal. Chem. 64, 971A-981A (1992).
[CrossRef] [PubMed]

Voloshinov, V.

Voloshinov, V. B.

V. B. Voloshinov, V. Ya. Molchanov, and J. C. Mosquera, “Spectral and polarization analysis of optical images by means of acousto-optics,” Opt. Laser Technol. 28, 119-127 (1996).
[CrossRef]

V. B. Voloshinov and D. D. Mishin, “Spectral resolution control of acousto-optical cells operating with collimated and divergent beams,” Proc. SPIE 2051, 378-385 (1993).
[CrossRef]

V. B. Voloshinov, “Close to collinear acousto-optic interaction in paratellurite,” Opt. Eng. 31, 2089-2094 (1992).
[CrossRef]

Watanabe, A.

Yano, T.

Anal. Chem. (1)

C. D. Tran, “Acousto-optic devices: optical elements for spectroscopy,” Anal. Chem. 64, 971A-981A (1992).
[CrossRef] [PubMed]

Appl. Opt. (2)

T. Yano and A. Watanabe, “Acoustooptic TeO2 tunable filter using far-off-axis anisotropic Bragg diffraction,” Appl. Opt. 15, 2250-2258 (1976).
[CrossRef] [PubMed]

M. G. Gazalet, G. Waxin, J. M. Rouvaen, R. Torguet, and E. Bridoux, “Independent acoustooptic modulation of the two wavelengths of a bichromatic light beam,” Appl. Opt. 23, 676-681 (1984).
[CrossRef]

Electron. Lett. (1)

I. C. Chang, “Collinear beam acousto-optic tunable filter,” Electron. Lett. 28, 1255-1256 (1992).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Eng. (3)

M. Pommeray, J. C. Kastelik, M. G. Gazalet, and A. Kab, “Acousto-optic and electro-optic modulators for stereoscopic laser videoprojection,” Opt. Eng. 36, 957-963 (1997).
[CrossRef]

I. C. Chang, “Acousto-optic tunable filters,” Opt. Eng. 20, 824-829 (1981).

V. B. Voloshinov, “Close to collinear acousto-optic interaction in paratellurite,” Opt. Eng. 31, 2089-2094 (1992).
[CrossRef]

Opt. Laser Technol. (1)

V. B. Voloshinov, V. Ya. Molchanov, and J. C. Mosquera, “Spectral and polarization analysis of optical images by means of acousto-optics,” Opt. Laser Technol. 28, 119-127 (1996).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE Ultrason. Symp. (1)

J. E. B. Oliveira and E. L. Adler, “An analytical method for designing acousto-optical tunable filters,” Proc. IEEE Ultrason. Symp. 505-510 (1987).

Proc. SPIE (4)

L. Denes, B. Kaminsky, and M. Gottlieb, “Image processing using AOTF,” Proc. SPIE 2962, 111-121 (1997).
[CrossRef]

V. I. Pustovoit, V. E. Pozhar, M. M. Mazur, V. N. Shornill, I. B. Kutuza, and A. V. Perchik, “Double-AOTF spectral imaging system,” Proc. SPIE 5953, 200-203 (2005).

V. E. Pozhar and V. I. Pustovoit, “Long-path optical spectral AOTF-based gas analyzer,” Proc. SPIE 4574, 174-178(2001).
[CrossRef]

V. B. Voloshinov and D. D. Mishin, “Spectral resolution control of acousto-optical cells operating with collimated and divergent beams,” Proc. SPIE 2051, 378-385 (1993).
[CrossRef]

Prog. Quantum Electron. (1)

L. Bei, G. I. Dennis, H. Miller, T. W. Spaine, and J. W. Carnahan, “Acousto-optic tunable filters: fundamentals and applications as applied to chemical analysis,” Prog. Quantum Electron. 28, 67-87 (2004).
[CrossRef]

Rev. Sci. Instrum. (2)

J. C. Kastelik, M. Pommeray, M. Slachciak, and M. G. Gazalet, “Optical modulation line for stereoscopic laser display”, Rev. Sci. Instrum. 76, 055106 (2005).
[CrossRef]

S. Dupont, J. C. Kastelik, and F. Causa, “Wide-band acousto-optic deflectors with high efficiency for visible range fringe projector pattern,” Rev. Sci. Instrum. 78, 105102(2007).
[CrossRef] [PubMed]

Tech. Phys. (1)

S. N. Antonov, “Acoustooptic nonpolar light controlling devices and polarization modulators based on paratellurite crystals,” Tech. Phys. 49, 1329-1334 (2004).
[CrossRef]

Other (1)

J. C. Kastelik, M. G. Gazalet, and P. Boudy, “Cascaded TeO2 acousto-optic devices for high efficiency multifrequency modulation,” J. Appl. Phys. 83,, 674-678 (1998).

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Figures (11)

Fig. 1
Fig. 1

Operating principle of the bifrequency AOTF.

Fig. 2
Fig. 2

Wave vector diagrams of the bifrequency interaction interaction Te O 2 .

Fig. 3
Fig. 3

Wave vector diagram with momentum mismatch.

Fig. 4
Fig. 4

Design of the bifrequency AOTF.

Fig. 5
Fig. 5

Diffraction efficiency versus phase mismatch.

Fig. 6
Fig. 6

Diffraction efficiency. Central wavelength λ c = 476.5 nm .

Fig. 7
Fig. 7

Diffraction efficiency. Central wavelength λ c = 488 nm .

Fig. 8
Fig. 8

Experimental result of diffraction efficiency for a single interaction. Central wavelength λ c = 488 nm .

Fig. 9
Fig. 9

Diffraction efficiency. Central wavelength λ c = 496.5 nm .

Fig. 10
Fig. 10

Experimental result of diffraction efficiency for a single interaction. Central wavelength λ c = 496.5 nm .

Fig. 11
Fig. 11

Experimental result of diffraction efficiency for the two successive interactions. Central wavelength λ c = 496.5 nm .

Tables (3)

Tables Icon

Table 1 Relevant Parameters of the Bifrequency AOTF

Tables Icon

Table 2 Spectral Power Distribution for the Argon Laser

Tables Icon

Table 3 Experimental Results

Equations (19)

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

k do = k ie + K 1 .
k ie = 2 π λ n ie , k do = 2 π λ n o ,
n ie = n o n e ( n o 2 sin 2 ( θ Be + θ a ) + n e 2 cos 2 ( θ Be + θ a ) ) 1 / 2 ,
k de = k do K 2 = k ie + K 1 K 2 .
k de = 2 π λ n de ,
n de = n o n e ( n o 2 sin 2 θ de + n e 2 cos 2 θ de ) 1 / 2
f 1 = v 1 λ [ n i e sin θ Be ( n o 2 n ie 2 cos 2 θ Be ) 1 / 2 ] ,
f 2 = v 2 λ [ n de sin θ de ( n o 2 n de 2 cos 2 θ de ) 1 / 2 ] .
k i 0 + Δ K i k i 0 = K 0 + Δ K K 0 .
Δ k i k i 0 = Δ λ λ 0 = Δ K K 0 = Δ f f 0 .
η = P P 0 sin 2 [ π 2 ( P P 0 + ( Δ Φ π ) 2 ) 1 / 2 ] P P 0 + ( Δ Φ π ) 2 ,
λ 0 Δ λ = f L cos ψ 0.8 v [ v n i sin θ B λ 0 f v n i cos ( ψ θ B ) λ 0 f sin ψ ] ,
λ 0 Δ λ = f L 0.8 v [ v n i sin θ B λ 0 f v n i cos θ B ] .
ψ = arctan [ ( 2 C 44 C 11 C 12 ) tan θ a ] θ a .
P 0 = λ 0 2 2 M 2 H L [ cos ( ψ θ B ) cos ψ ] 2 ,
M 2 = n i 3 n d 3 p eff 2 ρ v 3 ,
ρ v 2 = ( C 11 C 12 2 ) cos 2 θ a + C 44 sin 2 θ a .
p eff = ( p 11 p 12 2 ) cos ( θ B + θ a ) cos θ a + p 44 sin ( θ B + θ a ) sin θ a .
D = 10 log I c I s ,

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