Abstract

In this paper, we introduce and analyze both experimentally and theoretically multiple-band frequency locking, which becomes possible in an acousto-optic (AO) system with optoelectronic feedback. This effect is observed in a system combining a collinear AO cell and positive electronic feedback. The feedback signal is formed with the optical heterodyning effect, which occurs at the AO cell output and takes place in the special regime of collinear AO diffraction. It is shown for the first time, to the best of our knowledge, that frequency locking is possible in this system when connecting an external RF generator not only in one band near the self-oscillation frequency, but in several bands. The existence of as many as nine frequency-locking bands is predicted. The number of frequency-locking bands and their widths depend on the feedback gain and RF generator signal magnitude.

© 2020 Optical Society of America

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    [Crossref]
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  5. J. Lamperski and P. Stepczak, “Application of UDWDM technology in FTTH networks,” Proc. SPIE 9816, 981611 (2015).
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    [Crossref]
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    [Crossref]
  28. M. F. Wehner, J. Chrostowski, and W. J. Mielniczuk, “Acousto-optic bistability with fluctuations,” Phys. Rev. A 29, 3218–3223 (1984).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  35. S. N. Mantsevich, V. I. Balakshy, and Y. I. Kuznetsov, “Acousto-optic collinear filter with optoelectronic feedback,” Appl. Phys. B 123, 101 (2017).
    [Crossref]
  36. S. N. Mantsevich and V. I. Balakshy, “Experimental examination of frequency locking effect in acousto-optic system,” Appl. Phys. B 124, 54 (2018).
    [Crossref]
  37. S. N. Mantsevich and V. I. Balakshy, “Examination of optoelectronic feedback effect on collinear acousto-optic filtration,” J. Opt. Soc. Am. B 35, 1030–1039 (2018).
    [Crossref]
  38. S. N. Mantsevich and V. I. Balakshy, “Collinear acousto-optic filtration with electronically adjustable transmission function,” IEEE Photon. J. 11, 7800315 (2019).
    [Crossref]
  39. S. N. Mantsevich and V. I. Balakshy, “Applications of frequency locking effect in acousto-optic systems for control of optical radiation composition,” J. Opt. Soc. Am. B 36, 728–735 (2019).
    [Crossref]
  40. S. E. Harris and R. W. Wallace, “Acoustooptic tunable filter,” J. Opt. Soc. Am. 59, 744–747 (1969).
    [Crossref]
  41. S. E. Harris, S. T. K. Nieh, and D. K. Winslow, “Electronically tunable acousto-optic filter,” Appl. Phys. Lett. 15, 325–326 (1969).
    [Crossref]
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    [Crossref]
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    [Crossref]
  44. Y. A. Zyuryukin, S. V. Zavarin, and A. N. Yulaev, “Characteristic features of wideband anisotropic light diffraction in lithium-niobate crystal by a longitudinal acoustic wave,” Opt. Spectrosc. 107, 152–156 (2009).
    [Crossref]
  45. V. I. Balakshy and S. N. Mantsevich, “Influence of light polarization on characteristics of a collinear acoustooptic diffraction,” Opt. Spectrosc. 106, 441–445 (2009).
    [Crossref]
  46. V. I. Balakshy and S. N. Mantsevich, “Acousto-optic collinear diffraction of arbitrarily polarized light,” Tech. Phys. 56, 1646–1651 (2011).
    [Crossref]
  47. V. I. Balakshy and S. N. Mantsevich, “Polarization effects at collinear acousto-optic interaction,” Opt. Laser Technol. 44, 893–898 (2012).
    [Crossref]

2019 (3)

S. N. Mantsevich, A. S. Voloshin, and K. B. Yushkov, “Optical-frequency-comb generation with collinear acousto-optic diffraction: theory and simulations,” Phys. Rev. A 100, 013829 (2019).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Collinear acousto-optic filtration with electronically adjustable transmission function,” IEEE Photon. J. 11, 7800315 (2019).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Applications of frequency locking effect in acousto-optic systems for control of optical radiation composition,” J. Opt. Soc. Am. B 36, 728–735 (2019).
[Crossref]

2018 (4)

H. Guillet de Chatellus, L. R. Cortés, C. Schnébelin, M. Bwebsitea, and J. Azaña, “Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics,” Nat. Commun. 9, 2438 (2018).
[Crossref]

V. Durán, C. Schnébelin, and H. Guillet de Chatellus, “Coherent multi-heterodyne spectroscopy using acousto-optic frequency combs,” Opt. Express 26, 13800–13809 (2018).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Experimental examination of frequency locking effect in acousto-optic system,” Appl. Phys. B 124, 54 (2018).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Examination of optoelectronic feedback effect on collinear acousto-optic filtration,” J. Opt. Soc. Am. B 35, 1030–1039 (2018).
[Crossref]

2017 (2)

S. N. Mantsevich, V. I. Balakshy, and Y. I. Kuznetsov, “Acousto-optic collinear filter with optoelectronic feedback,” Appl. Phys. B 123, 101 (2017).
[Crossref]

K. B. Yushkov, V. Y. Molchanov, A. V. Ovchinnikov, and O. V. Chefonov, “Acousto-optic replication of ultrashort laser pulses,” Phys. Rev. A 96, 043866 (2017).
[Crossref]

2016 (3)

2015 (2)

J. Lamperski and P. Stepczak, “Application of UDWDM technology in FTTH networks,” Proc. SPIE 9816, 981611 (2015).
[Crossref]

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

2014 (2)

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

V. Balakshy, Y. Kuznetsov, S. Mantsevich, and N. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

2012 (2)

P. Salzenstein, A. S. Trushin, and V. B. Voloshinov, “Laser stabilized by acousto-optic cells for optoelectronic oscillators,” Proc. SPIE 8428, 84281D (2012).
[Crossref]

V. I. Balakshy and S. N. Mantsevich, “Polarization effects at collinear acousto-optic interaction,” Opt. Laser Technol. 44, 893–898 (2012).
[Crossref]

2011 (2)

V. I. Balakshy and S. N. Mantsevich, “Acousto-optic collinear diffraction of arbitrarily polarized light,” Tech. Phys. 56, 1646–1651 (2011).
[Crossref]

M. R. Chatterjee and M. A. Al-Saedi, “Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback,” Opt. Eng. 50, 055002 (2011).
[Crossref]

2009 (3)

O. Gliko, W. E. Brownell, and P. Saggau, “Fast two-dimensional standing-wave total-internal-reflection fluorescence microscopy using acousto-optic deflectors,” Opt. Lett. 34, 836–838 (2009).
[Crossref]

Y. A. Zyuryukin, S. V. Zavarin, and A. N. Yulaev, “Characteristic features of wideband anisotropic light diffraction in lithium-niobate crystal by a longitudinal acoustic wave,” Opt. Spectrosc. 107, 152–156 (2009).
[Crossref]

V. I. Balakshy and S. N. Mantsevich, “Influence of light polarization on characteristics of a collinear acoustooptic diffraction,” Opt. Spectrosc. 106, 441–445 (2009).
[Crossref]

2004 (2)

V. I. Balakshy and I. M. Sinev, “Mode competition in an acousto-optic generator,” J. Opt. A 6, 469–474 (2004).
[Crossref]

V. I. Balakshy and I. M. Sinev, “Competition of modes in an optically heterodyned acoustooptic generator,” Quantum Electron. 34, 277–282 (2004).
[Crossref]

2002 (1)

H. Gnewuch and C. N. Pannell, “Monolithic bulk shear-wave acousto-optic tunable filter,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 1635–1640 (2002).
[Crossref]

2001 (1)

M. R. Chatterjee and E. Sonmez, “Overview of acousto-optic bistability, chaos, and logical applications,” Proc. SPIE 4514, 41–60 (2001).
[Crossref]

2000 (2)

1999 (2)

D. P. Baldwin, D. S. Zamzow, D. E. Eckels, and P. G. Miller, “AOTF-echelle spectrometer for air-ICP-AES continuous emission monitoring of heavy metals and actinides,” Proc. SPIE 3534, 478–486 (1999).
[Crossref]

V. I. Balakshy and A. V. Kazaryan, “Laser beam direction stabilization by means of Bragg diffraction,” Opt. Eng. 38, 1154–1159 (1999).
[Crossref]

1994 (1)

V. I. Balakshy, A. V. Kazaryan, and V. Y. Molchanov, “Deflectors with a feedback: new possibilities for image processing,” Proc. SPIE 2051, 672–677 (1994).
[Crossref]

1992 (2)

V. I. Balakshy, A. V. Kazaryan, V. Y. Molchanov, and H. Ming, “Bistable acousto-optic devices for optical information processing systems,” Proc. SPIE 1731, 303–312 (1992).
[Crossref]

M. R. Chatterjee and J.-J. Huang, “Demonstration of acousto-optic bistability and chaos by direct nonlinear circuit modeling,” Appl. Opt. 31, 2506–2517 (1992).
[Crossref]

1989 (1)

1984 (2)

R. Vallée, C. Delisle, and J. Chrostowski, “Noise versus chaos in acousto-optic bistability,” Phys. Rev. A 30, 336–342 (1984).
[Crossref]

M. F. Wehner, J. Chrostowski, and W. J. Mielniczuk, “Acousto-optic bistability with fluctuations,” Phys. Rev. A 29, 3218–3223 (1984).
[Crossref]

1982 (2)

J. Chrostowski, “Noisy bifurcations in acousto-optic bistability,” Phys. Rev. A 26, 3023–3025 (1982).
[Crossref]

J. Chrostowski and C. Delisle, “Bistable optical switching based on Bragg diffraction,” Opt. Commun. 41, 71–74 (1982).
[Crossref]

1974 (1)

A. E. Siegman and D. D. Kuizenga, “Active mode-coupling phenomena in pulsed and continuous lasers,” Opto-electronics 6, 43–66 (1974).
[Crossref]

1970 (1)

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

1969 (2)

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

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, “Electronically tunable acousto-optic filter,” Appl. Phys. Lett. 15, 325–326 (1969).
[Crossref]

1964 (1)

L. E. Hargrove, L. F. Richard, and M. A. Pollack, “Locking of He–Ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[Crossref]

Al-Saedi, M. A.

M. R. Chatterjee and M. A. Al-Saedi, “Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback,” Opt. Eng. 50, 055002 (2011).
[Crossref]

Azaña, J.

H. Guillet de Chatellus, L. R. Cortés, C. Schnébelin, M. Bwebsitea, and J. Azaña, “Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics,” Nat. Commun. 9, 2438 (2018).
[Crossref]

Balakshy, V.

V. Balakshy, Y. Kuznetsov, S. Mantsevich, and N. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

Balakshy, V. I.

S. N. Mantsevich and V. I. Balakshy, “Collinear acousto-optic filtration with electronically adjustable transmission function,” IEEE Photon. J. 11, 7800315 (2019).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Applications of frequency locking effect in acousto-optic systems for control of optical radiation composition,” J. Opt. Soc. Am. B 36, 728–735 (2019).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Examination of optoelectronic feedback effect on collinear acousto-optic filtration,” J. Opt. Soc. Am. B 35, 1030–1039 (2018).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Experimental examination of frequency locking effect in acousto-optic system,” Appl. Phys. B 124, 54 (2018).
[Crossref]

S. N. Mantsevich, V. I. Balakshy, and Y. I. Kuznetsov, “Acousto-optic collinear filter with optoelectronic feedback,” Appl. Phys. B 123, 101 (2017).
[Crossref]

V. I. Balakshy, Y. I. Kuznetsov, and S. N. Mantsevich, “Effect of optoelectronic feedback on the characteristics of acousto-optical collinear filtering,” Quantum Electron. 46, 181–184 (2016).
[Crossref]

V. I. Balakshy and S. N. Mantsevich, “Polarization effects at collinear acousto-optic interaction,” Opt. Laser Technol. 44, 893–898 (2012).
[Crossref]

V. I. Balakshy and S. N. Mantsevich, “Acousto-optic collinear diffraction of arbitrarily polarized light,” Tech. Phys. 56, 1646–1651 (2011).
[Crossref]

V. I. Balakshy and S. N. Mantsevich, “Influence of light polarization on characteristics of a collinear acoustooptic diffraction,” Opt. Spectrosc. 106, 441–445 (2009).
[Crossref]

V. I. Balakshy and I. M. Sinev, “Mode competition in an acousto-optic generator,” J. Opt. A 6, 469–474 (2004).
[Crossref]

V. I. Balakshy and I. M. Sinev, “Competition of modes in an optically heterodyned acoustooptic generator,” Quantum Electron. 34, 277–282 (2004).
[Crossref]

V. I. Balakshy and A. V. Kazaryan, “Laser beam direction stabilization by means of Bragg diffraction,” Opt. Eng. 38, 1154–1159 (1999).
[Crossref]

V. I. Balakshy, A. V. Kazaryan, and V. Y. Molchanov, “Deflectors with a feedback: new possibilities for image processing,” Proc. SPIE 2051, 672–677 (1994).
[Crossref]

V. I. Balakshy, A. V. Kazaryan, V. Y. Molchanov, and H. Ming, “Bistable acousto-optic devices for optical information processing systems,” Proc. SPIE 1731, 303–312 (1992).
[Crossref]

Baldwin, D. P.

D. P. Baldwin, D. S. Zamzow, D. E. Eckels, and P. G. Miller, “AOTF-echelle spectrometer for air-ICP-AES continuous emission monitoring of heavy metals and actinides,” Proc. SPIE 3534, 478–486 (1999).
[Crossref]

Brownell, W. E.

Bwebsitea, M.

H. Guillet de Chatellus, L. R. Cortés, C. Schnébelin, M. Bwebsitea, and J. Azaña, “Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics,” Nat. Commun. 9, 2438 (2018).
[Crossref]

Chatterjee, M. R.

M. R. Chatterjee and M. A. Al-Saedi, “Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback,” Opt. Eng. 50, 055002 (2011).
[Crossref]

M. R. Chatterjee and E. Sonmez, “Overview of acousto-optic bistability, chaos, and logical applications,” Proc. SPIE 4514, 41–60 (2001).
[Crossref]

M. R. Chatterjee and J.-J. Huang, “Demonstration of acousto-optic bistability and chaos by direct nonlinear circuit modeling,” Appl. Opt. 31, 2506–2517 (1992).
[Crossref]

Chefonov, O. V.

K. B. Yushkov, V. Y. Molchanov, A. V. Ovchinnikov, and O. V. Chefonov, “Acousto-optic replication of ultrashort laser pulses,” Phys. Rev. A 96, 043866 (2017).
[Crossref]

Cheng, Z.

Cheung, S. K.

Chrostowski, J.

R. Vallée, C. Delisle, and J. Chrostowski, “Noise versus chaos in acousto-optic bistability,” Phys. Rev. A 30, 336–342 (1984).
[Crossref]

M. F. Wehner, J. Chrostowski, and W. J. Mielniczuk, “Acousto-optic bistability with fluctuations,” Phys. Rev. A 29, 3218–3223 (1984).
[Crossref]

J. Chrostowski, “Noisy bifurcations in acousto-optic bistability,” Phys. Rev. A 26, 3023–3025 (1982).
[Crossref]

J. Chrostowski and C. Delisle, “Bistable optical switching based on Bragg diffraction,” Opt. Commun. 41, 71–74 (1982).
[Crossref]

Cortés, L. R.

H. Guillet de Chatellus, L. R. Cortés, C. Schnébelin, M. Bwebsitea, and J. Azaña, “Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics,” Nat. Commun. 9, 2438 (2018).
[Crossref]

Cotton, R. J.

G. D. Reddy, R. J. Cotton, A. S. Tolias, and P. Saggau, Random-Access Multiphoton Microscopy for Fast Three-Dimensional Imaging (Springer International Publishing, 2015), pp. 455–472.

Dekemper, E.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Delisle, C.

R. Vallée, C. Delisle, and J. Chrostowski, “Noise versus chaos in acousto-optic bistability,” Phys. Rev. A 30, 336–342 (1984).
[Crossref]

J. Chrostowski and C. Delisle, “Bistable optical switching based on Bragg diffraction,” Opt. Commun. 41, 71–74 (1982).
[Crossref]

Durán, V.

Eckels, D. E.

D. P. Baldwin, D. S. Zamzow, D. E. Eckels, and P. G. Miller, “AOTF-echelle spectrometer for air-ICP-AES continuous emission monitoring of heavy metals and actinides,” Proc. SPIE 3534, 478–486 (1999).
[Crossref]

Elandaloussi, H.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Evdokimova, N.

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

Fedorova, A. A.

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

Feigelson, R. S.

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

Franssens, G.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Fussen, D.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Gliko, O.

Gnewuch, H.

H. Gnewuch and C. N. Pannell, “Monolithic bulk shear-wave acousto-optic tunable filter,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 1635–1640 (2002).
[Crossref]

Guillet de Chatellus, H.

H. Guillet de Chatellus, L. R. Cortés, C. Schnébelin, M. Bwebsitea, and J. Azaña, “Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics,” Nat. Commun. 9, 2438 (2018).
[Crossref]

V. Durán, C. Schnébelin, and H. Guillet de Chatellus, “Coherent multi-heterodyne spectroscopy using acousto-optic frequency combs,” Opt. Express 26, 13800–13809 (2018).
[Crossref]

Hargrove, L. E.

L. E. Hargrove, L. F. Richard, and M. A. Pollack, “Locking of He–Ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[Crossref]

Harris, S. E.

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

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

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, “Electronically tunable acousto-optic filter,” Appl. Phys. Lett. 15, 325–326 (1969).
[Crossref]

Huang, J.-J.

Huignard, J.-P.

Ivanov, A.

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

Kalinnikov, Y. K.

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

Kazaryan, A. V.

V. I. Balakshy and A. V. Kazaryan, “Laser beam direction stabilization by means of Bragg diffraction,” Opt. Eng. 38, 1154–1159 (1999).
[Crossref]

V. I. Balakshy, A. V. Kazaryan, and V. Y. Molchanov, “Deflectors with a feedback: new possibilities for image processing,” Proc. SPIE 2051, 672–677 (1994).
[Crossref]

V. I. Balakshy, A. V. Kazaryan, V. Y. Molchanov, and H. Ming, “Bistable acousto-optic devices for optical information processing systems,” Proc. SPIE 1731, 303–312 (1992).
[Crossref]

Kiselev, A. V.

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

Korablev, O. I.

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

Kuizenga, D. D.

A. E. Siegman and D. D. Kuizenga, “Active mode-coupling phenomena in pulsed and continuous lasers,” Opto-electronics 6, 43–66 (1974).
[Crossref]

Kuznetsov, Y.

V. Balakshy, Y. Kuznetsov, S. Mantsevich, and N. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

Kuznetsov, Y. I.

S. N. Mantsevich, V. I. Balakshy, and Y. I. Kuznetsov, “Acousto-optic collinear filter with optoelectronic feedback,” Appl. Phys. B 123, 101 (2017).
[Crossref]

V. I. Balakshy, Y. I. Kuznetsov, and S. N. Mantsevich, “Effect of optoelectronic feedback on the characteristics of acousto-optical collinear filtering,” Quantum Electron. 46, 181–184 (2016).
[Crossref]

Lamperski, J.

J. Lamperski and P. Stepczak, “Application of UDWDM technology in FTTH networks,” Proc. SPIE 9816, 981611 (2015).
[Crossref]

Lassen, C.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Laude, V.

Mantsevich, S.

V. Balakshy, Y. Kuznetsov, S. Mantsevich, and N. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

Mantsevich, S. N.

S. N. Mantsevich and V. I. Balakshy, “Collinear acousto-optic filtration with electronically adjustable transmission function,” IEEE Photon. J. 11, 7800315 (2019).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Applications of frequency locking effect in acousto-optic systems for control of optical radiation composition,” J. Opt. Soc. Am. B 36, 728–735 (2019).
[Crossref]

S. N. Mantsevich, A. S. Voloshin, and K. B. Yushkov, “Optical-frequency-comb generation with collinear acousto-optic diffraction: theory and simulations,” Phys. Rev. A 100, 013829 (2019).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Experimental examination of frequency locking effect in acousto-optic system,” Appl. Phys. B 124, 54 (2018).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Examination of optoelectronic feedback effect on collinear acousto-optic filtration,” J. Opt. Soc. Am. B 35, 1030–1039 (2018).
[Crossref]

S. N. Mantsevich, V. I. Balakshy, and Y. I. Kuznetsov, “Acousto-optic collinear filter with optoelectronic feedback,” Appl. Phys. B 123, 101 (2017).
[Crossref]

V. I. Balakshy, Y. I. Kuznetsov, and S. N. Mantsevich, “Effect of optoelectronic feedback on the characteristics of acousto-optical collinear filtering,” Quantum Electron. 46, 181–184 (2016).
[Crossref]

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

V. I. Balakshy and S. N. Mantsevich, “Polarization effects at collinear acousto-optic interaction,” Opt. Laser Technol. 44, 893–898 (2012).
[Crossref]

V. I. Balakshy and S. N. Mantsevich, “Acousto-optic collinear diffraction of arbitrarily polarized light,” Tech. Phys. 56, 1646–1651 (2011).
[Crossref]

V. I. Balakshy and S. N. Mantsevich, “Influence of light polarization on characteristics of a collinear acoustooptic diffraction,” Opt. Spectrosc. 106, 441–445 (2009).
[Crossref]

Mateshvili, N.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Mielniczuk, W. J.

M. F. Wehner, J. Chrostowski, and W. J. Mielniczuk, “Acousto-optic bistability with fluctuations,” Phys. Rev. A 29, 3218–3223 (1984).
[Crossref]

Migus, A.

Miller, P. G.

D. P. Baldwin, D. S. Zamzow, D. E. Eckels, and P. G. Miller, “AOTF-echelle spectrometer for air-ICP-AES continuous emission monitoring of heavy metals and actinides,” Proc. SPIE 3534, 478–486 (1999).
[Crossref]

Ming, H.

V. I. Balakshy, A. V. Kazaryan, V. Y. Molchanov, and H. Ming, “Bistable acousto-optic devices for optical information processing systems,” Proc. SPIE 1731, 303–312 (1992).
[Crossref]

Molchanov, V. Y.

K. B. Yushkov, V. Y. Molchanov, A. V. Ovchinnikov, and O. V. Chefonov, “Acousto-optic replication of ultrashort laser pulses,” Phys. Rev. A 96, 043866 (2017).
[Crossref]

K. B. Yushkov, V. V. Romanov, G. S. Rogozhnikov, and V. Y. Molchanov, “70 Ghz arbitrary modulation of chirped laser pulses by means of acousto-optics,” Opt. Lett. 41, 5442–5445 (2016).
[Crossref]

V. I. Balakshy, A. V. Kazaryan, and V. Y. Molchanov, “Deflectors with a feedback: new possibilities for image processing,” Proc. SPIE 2051, 672–677 (1994).
[Crossref]

V. I. Balakshy, A. V. Kazaryan, V. Y. Molchanov, and H. Ming, “Bistable acousto-optic devices for optical information processing systems,” Proc. SPIE 1731, 303–312 (1992).
[Crossref]

Nieh, S. T. K.

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

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, “Electronically tunable acousto-optic filter,” Appl. Phys. Lett. 15, 325–326 (1969).
[Crossref]

Ovchinnikov, A. V.

K. B. Yushkov, V. Y. Molchanov, A. V. Ovchinnikov, and O. V. Chefonov, “Acousto-optic replication of ultrashort laser pulses,” Phys. Rev. A 96, 043866 (2017).
[Crossref]

Pannell, C. N.

H. Gnewuch and C. N. Pannell, “Monolithic bulk shear-wave acousto-optic tunable filter,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 1635–1640 (2002).
[Crossref]

Pieroux, D.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Polikarpova, N.

V. Balakshy, Y. Kuznetsov, S. Mantsevich, and N. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

Pollack, M. A.

L. E. Hargrove, L. F. Richard, and M. A. Pollack, “Locking of He–Ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[Crossref]

Poon, T.-C.

Reddy, G. D.

G. D. Reddy, R. J. Cotton, A. S. Tolias, and P. Saggau, Random-Access Multiphoton Microscopy for Fast Three-Dimensional Imaging (Springer International Publishing, 2015), pp. 455–472.

Richard, L. F.

L. E. Hargrove, L. F. Richard, and M. A. Pollack, “Locking of He–Ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[Crossref]

Rogozhnikov, G. S.

Romanov, V. V.

Saggau, P.

O. Gliko, W. E. Brownell, and P. Saggau, “Fast two-dimensional standing-wave total-internal-reflection fluorescence microscopy using acousto-optic deflectors,” Opt. Lett. 34, 836–838 (2009).
[Crossref]

G. D. Reddy, R. J. Cotton, A. S. Tolias, and P. Saggau, Random-Access Multiphoton Microscopy for Fast Three-Dimensional Imaging (Springer International Publishing, 2015), pp. 455–472.

Salzenstein, P.

P. Salzenstein, A. S. Trushin, and V. B. Voloshinov, “Laser stabilized by acousto-optic cells for optoelectronic oscillators,” Proc. SPIE 8428, 84281D (2012).
[Crossref]

Schnébelin, C.

V. Durán, C. Schnébelin, and H. Guillet de Chatellus, “Coherent multi-heterodyne spectroscopy using acousto-optic frequency combs,” Opt. Express 26, 13800–13809 (2018).
[Crossref]

H. Guillet de Chatellus, L. R. Cortés, C. Schnébelin, M. Bwebsitea, and J. Azaña, “Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics,” Nat. Commun. 9, 2438 (2018).
[Crossref]

Shapkin, A. A.

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

Siegman, A. E.

A. E. Siegman and D. D. Kuizenga, “Active mode-coupling phenomena in pulsed and continuous lasers,” Opto-electronics 6, 43–66 (1974).
[Crossref]

Sinev, I. M.

V. I. Balakshy and I. M. Sinev, “Mode competition in an acousto-optic generator,” J. Opt. A 6, 469–474 (2004).
[Crossref]

V. I. Balakshy and I. M. Sinev, “Competition of modes in an optically heterodyned acoustooptic generator,” Quantum Electron. 34, 277–282 (2004).
[Crossref]

Sonmez, E.

M. R. Chatterjee and E. Sonmez, “Overview of acousto-optic bistability, chaos, and logical applications,” Proc. SPIE 4514, 41–60 (2001).
[Crossref]

Spielmann, C.

Stepczak, P.

J. Lamperski and P. Stepczak, “Application of UDWDM technology in FTTH networks,” Proc. SPIE 9816, 981611 (2015).
[Crossref]

Stroud, R.

J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).

Tolias, A. S.

G. D. Reddy, R. J. Cotton, A. S. Tolias, and P. Saggau, Random-Access Multiphoton Microscopy for Fast Three-Dimensional Imaging (Springer International Publishing, 2015), pp. 455–472.

Tournois, P.

Trushin, A. S.

P. Salzenstein, A. S. Trushin, and V. B. Voloshinov, “Laser stabilized by acousto-optic cells for optoelectronic oscillators,” Proc. SPIE 8428, 84281D (2012).
[Crossref]

Vahala, K.

Vallée, R.

R. Vallée, C. Delisle, and J. Chrostowski, “Noise versus chaos in acousto-optic bistability,” Phys. Rev. A 30, 336–342 (1984).
[Crossref]

Van Opstal, B.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Vanhamel, J.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Vanhellemont, F.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Verluise, F.

Voloshin, A. S.

S. N. Mantsevich, A. S. Voloshin, and K. B. Yushkov, “Optical-frequency-comb generation with collinear acousto-optic diffraction: theory and simulations,” Phys. Rev. A 100, 013829 (2019).
[Crossref]

Voloshinov, V.

E. Dekemper, D. Fussen, B. Van Opstal, J. Vanhamel, D. Pieroux, F. Vanhellemont, N. Mateshvili, G. Franssens, V. Voloshinov, C. Lassen, and H. Elandaloussi, “ALTIUS: a spaceborne AOTF-based UV-VISNIR hyperspectral imager for atmospheric remote sensing,” Proc. SPIE 9241, 92410L (2014).
[Crossref]

Voloshinov, V. B.

P. Salzenstein, A. S. Trushin, and V. B. Voloshinov, “Laser stabilized by acousto-optic cells for optoelectronic oscillators,” Proc. SPIE 8428, 84281D (2012).
[Crossref]

Vyazovetsky, N. A.

O. I. Korablev, A. Ivanov, A. A. Fedorova, Y. K. Kalinnikov, A. A. Shapkin, S. N. Mantsevich, N. A. Vyazovetsky, N. Evdokimova, and A. V. Kiselev, “Development of a mast or robotic arm-mounted infrared AOTF spectrometer for surface Moon and Mars probes,” Proc. SPIE 9608, 960807 (2015).
[Crossref]

Wallace, R. W.

Wehner, M. F.

M. F. Wehner, J. Chrostowski, and W. J. Mielniczuk, “Acousto-optic bistability with fluctuations,” Phys. Rev. A 29, 3218–3223 (1984).
[Crossref]

Winslow, D. K.

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, “Electronically tunable acousto-optic filter,” Appl. Phys. Lett. 15, 325–326 (1969).
[Crossref]

Xu, J.

J. Xu and R. Stroud, Acousto-Optic Devices: Principles, Design, and Applications (Wiley, 1992).

Yang, K. Y.

Yang, Q.-F.

Yi, X.

Yulaev, A. N.

Y. A. Zyuryukin, S. V. Zavarin, and A. N. Yulaev, “Characteristic features of wideband anisotropic light diffraction in lithium-niobate crystal by a longitudinal acoustic wave,” Opt. Spectrosc. 107, 152–156 (2009).
[Crossref]

Yushkov, K. B.

S. N. Mantsevich, A. S. Voloshin, and K. B. Yushkov, “Optical-frequency-comb generation with collinear acousto-optic diffraction: theory and simulations,” Phys. Rev. A 100, 013829 (2019).
[Crossref]

K. B. Yushkov, V. Y. Molchanov, A. V. Ovchinnikov, and O. V. Chefonov, “Acousto-optic replication of ultrashort laser pulses,” Phys. Rev. A 96, 043866 (2017).
[Crossref]

K. B. Yushkov, V. V. Romanov, G. S. Rogozhnikov, and V. Y. Molchanov, “70 Ghz arbitrary modulation of chirped laser pulses by means of acousto-optics,” Opt. Lett. 41, 5442–5445 (2016).
[Crossref]

Zamzow, D. S.

D. P. Baldwin, D. S. Zamzow, D. E. Eckels, and P. G. Miller, “AOTF-echelle spectrometer for air-ICP-AES continuous emission monitoring of heavy metals and actinides,” Proc. SPIE 3534, 478–486 (1999).
[Crossref]

Zavarin, S. V.

Y. A. Zyuryukin, S. V. Zavarin, and A. N. Yulaev, “Characteristic features of wideband anisotropic light diffraction in lithium-niobate crystal by a longitudinal acoustic wave,” Opt. Spectrosc. 107, 152–156 (2009).
[Crossref]

Zyuryukin, Y. A.

Y. A. Zyuryukin, S. V. Zavarin, and A. N. Yulaev, “Characteristic features of wideband anisotropic light diffraction in lithium-niobate crystal by a longitudinal acoustic wave,” Opt. Spectrosc. 107, 152–156 (2009).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (2)

S. N. Mantsevich, V. I. Balakshy, and Y. I. Kuznetsov, “Acousto-optic collinear filter with optoelectronic feedback,” Appl. Phys. B 123, 101 (2017).
[Crossref]

S. N. Mantsevich and V. I. Balakshy, “Experimental examination of frequency locking effect in acousto-optic system,” Appl. Phys. B 124, 54 (2018).
[Crossref]

Appl. Phys. Lett. (3)

S. E. Harris, S. T. K. Nieh, and D. K. Winslow, “Electronically tunable acousto-optic filter,” Appl. Phys. Lett. 15, 325–326 (1969).
[Crossref]

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

L. E. Hargrove, L. F. Richard, and M. A. Pollack, “Locking of He–Ne laser modes induced by synchronous intracavity modulation,” Appl. Phys. Lett. 5, 4–5 (1964).
[Crossref]

IEEE Photon. J. (1)

S. N. Mantsevich and V. I. Balakshy, “Collinear acousto-optic filtration with electronically adjustable transmission function,” IEEE Photon. J. 11, 7800315 (2019).
[Crossref]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

H. Gnewuch and C. N. Pannell, “Monolithic bulk shear-wave acousto-optic tunable filter,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 1635–1640 (2002).
[Crossref]

J. Opt. A (1)

V. I. Balakshy and I. M. Sinev, “Mode competition in an acousto-optic generator,” J. Opt. A 6, 469–474 (2004).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (3)

Nat. Commun. (1)

H. Guillet de Chatellus, L. R. Cortés, C. Schnébelin, M. Bwebsitea, and J. Azaña, “Reconfigurable photonic generation of broadband chirped waveforms using a single CW laser and low-frequency electronics,” Nat. Commun. 9, 2438 (2018).
[Crossref]

Opt. Commun. (1)

J. Chrostowski and C. Delisle, “Bistable optical switching based on Bragg diffraction,” Opt. Commun. 41, 71–74 (1982).
[Crossref]

Opt. Eng. (2)

V. I. Balakshy and A. V. Kazaryan, “Laser beam direction stabilization by means of Bragg diffraction,” Opt. Eng. 38, 1154–1159 (1999).
[Crossref]

M. R. Chatterjee and M. A. Al-Saedi, “Examination of chaotic signal encryption and recovery for secure communication using hybrid acousto-optic feedback,” Opt. Eng. 50, 055002 (2011).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (2)

V. I. Balakshy and S. N. Mantsevich, “Polarization effects at collinear acousto-optic interaction,” Opt. Laser Technol. 44, 893–898 (2012).
[Crossref]

V. Balakshy, Y. Kuznetsov, S. Mantsevich, and N. Polikarpova, “Dynamic processes in an acousto-optic laser beam intensity stabilization system,” Opt. Laser Technol. 62, 89–94 (2014).
[Crossref]

Opt. Lett. (4)

Opt. Spectrosc. (2)

Y. A. Zyuryukin, S. V. Zavarin, and A. N. Yulaev, “Characteristic features of wideband anisotropic light diffraction in lithium-niobate crystal by a longitudinal acoustic wave,” Opt. Spectrosc. 107, 152–156 (2009).
[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. Principal scheme of the examined system.
Fig. 2.
Fig. 2. Oscillogram of ${I_1}$ component transmission function for collinear AO diffraction.
Fig. 3.
Fig. 3. Simulation of ${I_1}$ component transmission function for collinear AO diffraction.
Fig. 4.
Fig. 4. Oscillogram of RF signal beatings CH1 (yellow curve) and signal optical beam intensity modulation CH2 (violet curve).
Fig. 5.
Fig. 5. (a) Theoretical and (b) experimental dependences of threshold gain value on normalized incident light intensity.
Fig. 6.
Fig. 6. Simulated frequency-locking bands for various feedback gain $\kappa$ values.
Fig. 7.
Fig. 7. Simulated ${I_1}$ component transmission functions for AO diffraction at ${f_g}$ acoustic wave for various ${\Gamma_{g0}}$ magnitudes.
Fig. 8.
Fig. 8. Experimentally measured frequency-locking bands obtained for various gain values $\kappa$.
Fig. 9.
Fig. 9. AO cell ${I_1}$ transmission functions obtained for various RF generator signal magnitudes ${U_{g0}}$; the feedback is turned off.
Fig. 10.
Fig. 10. Signal optical beam photodetector signal oscillograms illustrating (a) single-band frequency locking and (b) three bands of frequency locking.

Equations (20)

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f c ( λ ) = V λ | n e n o | ,
{ E 0 Y = E i cos α ( cos A 2 j R 2 s i n c A 2 π ) exp [ j ( ω t k o l + R 2 ) ] ; E + 1 Z = E i cos α Γ 2 s i n c A 2 π exp { j [ ( ω + Ω ) t k e l R 2 + Φ ] } ; E 0 Z = E i sin α ( cos A 2 + j R 2 s i n c A 2 π ) exp [ j ( ω t k e l R 2 ) ] ; E 1 Y = E i sin α Γ 2 s i n c A 2 π exp { j [ ( ω Ω ) t k o l + R 2 Φ ] } ,
I d = | ( E 0 Y + E 1 Y ) cos β + ( E 0 Z + E + 1 Z ) sin β | 2 .
I d = I 0 + I 1 cos ( Ω t + ϕ + Φ ) + I 2 cos ( 2 Ω t + ϕ + 2 Φ ) ,
I d = I 0 + I 1 cos ( Ω t + ϕ + Φ ) ,
tan ϕ = A R cot A 2 .
I 0 = I i Γ 2 4 s i n c 2 ( A 2 π ) ,
I 1 ( t ) = I i Γ 4 s i n c ( A 2 π ) 4 cos 2 ( A 2 ) + R 2 s i n c 2 ( A 2 π ) × cos ( Ω t + ϕ + Φ ) .
I d g ( t ) = I i ϑ [ 1 2 + T g ] × cos ( Ω g t + ϕ g + Φ g ) ,
T g = Γ g 4 s i n c ( A g 2 π ) 4 cos 2 ( A g 2 ) + R g 2 s i n c 2 ( A g 2 π ) .
U g ( t ) = I i ϑ σ T g cos ( Ω g t + ϕ g + Φ g ) ,
I d c ( t ) = ( I i I d g ) ϑ Γ c 2 s i n c ( Γ c 2 π ) cos ( Γ c 2 ) × cos ( Ω c t + ϕ c + Φ c ) ,
U c ( t ) = σ I d c ( t ) .
U ( t ) = U g 0 cos ( Ω g t ) + κ U g cos ( Ω g t + ϕ g + Φ g + χ ) + κ U c cos ( Ω c t + ϕ c + Φ c + χ ) ,
tan Φ g = σ κ ϑ I i T g U g 0 + σ κ ϑ I i T g R g .
tan Φ c = tan ( Φ c + ϕ c + χ ) R c ,
Γ = γ U ,
Γ c = σ κ γ ϑ I i 2 sin Γ c .
κ = 2 σ γ ϑ I i .
κ = 2 σ γ ϑ ( I i I d g ) .