Abstract

We report on the first building of an active spectral narrowing mechanism in a pulsed, multiline optical parametric oscillator (OPO) based on a novel aperiodically poled lithium niobate (APPLN) device constructed using the aperiodic optical superlattice technique. The APPLN device functions simultaneously in the system as a multi-channel optical parametric down converter (OPDC) and an electro-optic (EO) gain spectral filter working on the corresponding (multiple) signal bands. When the APPLN OPO was installed in a diode pumped Nd:YVO4 laser system, highly narrowed dual-wavelength signal lines (at 1540 and 1550 nm) were observed at the output of the system through EO control of the APPLN. Correspondingly, an enhancement of the power spectral density of the source by a factor of ~7.8 with respect to the system operated in passive mode was found.

© 2016 Optical Society of America

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References

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  1. M. Wirth, A. Fix, P. Mahnke, H. Schwarzer, F. Schrandt, and G. Ehret, “The airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performance,” Appl. Phys. B 96(1), 201–213 (2009).
    [Crossref]
  2. M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5-µm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett. 23(13), 1004–1006 (1998).
    [Crossref] [PubMed]
  3. K. Kawase, T. Hatanaka, H. Takahashi, K. Nakamura, T. Taniuchi, and H. Ito, “Tunable terahertz-wave generation from DAST crystal by dual signal-wave parametric oscillation of periodically poled lithium niobate,” Opt. Lett. 25(23), 1714–1716 (2000).
    [Crossref] [PubMed]
  4. C. L. Wang and C. L. Pan, “Tunable dual-wavelength operation of a diode array with an external grating-loaded cavity,” Appl. Phys. Lett. 64(23), 3089–3091 (1994).
    [Crossref]
  5. X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064- and 1074-nm dual-wavelength Nd:YAG laser using a Fabry–Perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1 (2014).
    [Crossref]
  6. T. M. J. Kendall, W. A. Clarkson, P. J. Hardmar, G. W. Ross, and D. C. Hanna, “Multiline optical parametric oscillators based on periodically poled lithium niobate,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2000), paper CMC2.
    [Crossref]
  7. Y. H. Chen, W. K. Chang, H. P. Chung, B. Z. Liu, C. H. Tseng, and J. W. Chang, “Tunable, pulsed multiline intracavity optical parametric oscillator using two-dimensional MgO: periodically poled lithium niobate-aperiodically poled lithium niobate,” Opt. Lett. 38(18), 3507–3509 (2013).
    [Crossref] [PubMed]
  8. J. Y. Lai, Y. J. Liu, H. Y. Wu, Y. H. Chen, and S. D. Yang, “Engineered multiwavelength conversion using nonperiodic optical superlattice optimized by genetic algorithm,” Opt. Express 18(5), 5328–5337 (2010).
    [Crossref] [PubMed]
  9. C. L. Chang, Y. H. Chen, C. H. Lin, and J. Y. Chang, “Monolithically integrated multi-wavelength filter and second harmonic generator in aperiodically poled lithium niobate,” Opt. Express 16(22), 18535–18544 (2008).
    [Crossref] [PubMed]
  10. S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. 15(6), 415–431 (1979).
    [Crossref]
  11. L. A. W. Gloster, I. T. McKinnie, Z. X. Jiang, T. A. King, J. M. Boon-Engering, W. E. van der Veer, and W. Hogervorst, “Narrow-band β-BaB2O4 optical parametric oscillator in a grazing-incidence configuration,” J. Opt. Soc. Am. B 12(11), 2117–2121 (1995).
    [Crossref]
  12. B. Jacobsson, M. Tiihonen, V. Pasiskevicius, and F. Laurell, “Narrowband bulk Bragg grating optical parametric oscillator,” Opt. Lett. 30(17), 2281–2283 (2005).
    [Crossref] [PubMed]
  13. C. H. Lin, Y. H. Chen, S. W. Lin, C. L. Chang, Y. C. Huang, and J. Y. Chang, “Electro-optic narrowband multi-wavelength filter in aperiodically poled lithium niobate,” Opt. Express 15(15), 9859–9866 (2007).
    [Crossref] [PubMed]
  14. J. W. Chang, H. F. Yau, H. P. Chung, W. K. Chang, and Y. H. Chen, “Characterization and analysis of finite-beam Bragg diffraction in a periodically poled lithium niobate electro-optic grating,” Appl. Opt. 53(24), 5312–5321 (2014).
    [Crossref] [PubMed]
  15. Y. H. Chen, J. W. Chang, C. H. Lin, W. K. Chang, N. Hsu, Y. Y. Lai, Q. H. Tseng, R. Geiss, T. Pertsch, and S. S. Yang, “Spectral narrowing and manipulation in an optical parametric oscillator using periodically poled lithium niobate electro-optic polarization-mode converters,” Opt. Lett. 36(12), 2345–2347 (2011).
    [Crossref] [PubMed]
  16. H. P. Chung, W. K. Chang, C. H. Tseng, R. Geiss, T. Pertsch, and Y. H. Chen, “Electro-Optically Spectrum Tailorable Intracavity Optical Parametric Oscillator,” Opt. Lett. 40(22), 5132–5135 (2015).
    [Crossref] [PubMed]
  17. B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
    [Crossref]
  18. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
    [Crossref] [PubMed]
  19. C. Y. Huang, C. H. Lin, Y. H. Chen, and Y. C. Huang, “Electro-optic Ti:PPLN waveguide as efficient optical wavelength filter and polarization mode converter,” Opt. Express 15(5), 2548–2554 (2007).
    [Crossref] [PubMed]

2015 (1)

2014 (2)

J. W. Chang, H. F. Yau, H. P. Chung, W. K. Chang, and Y. H. Chen, “Characterization and analysis of finite-beam Bragg diffraction in a periodically poled lithium niobate electro-optic grating,” Appl. Opt. 53(24), 5312–5321 (2014).
[Crossref] [PubMed]

X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064- and 1074-nm dual-wavelength Nd:YAG laser using a Fabry–Perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1 (2014).
[Crossref]

2013 (1)

2011 (1)

2010 (1)

2009 (1)

M. Wirth, A. Fix, P. Mahnke, H. Schwarzer, F. Schrandt, and G. Ehret, “The airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performance,” Appl. Phys. B 96(1), 201–213 (2009).
[Crossref]

2008 (1)

2007 (2)

2005 (1)

2000 (1)

1999 (1)

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[Crossref]

1998 (1)

1995 (1)

1994 (1)

C. L. Wang and C. L. Pan, “Tunable dual-wavelength operation of a diode array with an external grating-loaded cavity,” Appl. Phys. Lett. 64(23), 3089–3091 (1994).
[Crossref]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

1979 (1)

S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. 15(6), 415–431 (1979).
[Crossref]

Arbore, M. A.

Boon-Engering, J. M.

Brosnan, S. J.

S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. 15(6), 415–431 (1979).
[Crossref]

Bu, Y. K.

X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064- and 1074-nm dual-wavelength Nd:YAG laser using a Fabry–Perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1 (2014).
[Crossref]

Byer, R. L.

S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. 15(6), 415–431 (1979).
[Crossref]

Cai, G. X.

X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064- and 1074-nm dual-wavelength Nd:YAG laser using a Fabry–Perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1 (2014).
[Crossref]

Cai, Z. P.

X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064- and 1074-nm dual-wavelength Nd:YAG laser using a Fabry–Perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1 (2014).
[Crossref]

Chang, C. L.

Chang, J. W.

Chang, J. Y.

Chang, W. K.

Chen, L. J.

X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064- and 1074-nm dual-wavelength Nd:YAG laser using a Fabry–Perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1 (2014).
[Crossref]

Chen, Y. H.

H. P. Chung, W. K. Chang, C. H. Tseng, R. Geiss, T. Pertsch, and Y. H. Chen, “Electro-Optically Spectrum Tailorable Intracavity Optical Parametric Oscillator,” Opt. Lett. 40(22), 5132–5135 (2015).
[Crossref] [PubMed]

J. W. Chang, H. F. Yau, H. P. Chung, W. K. Chang, and Y. H. Chen, “Characterization and analysis of finite-beam Bragg diffraction in a periodically poled lithium niobate electro-optic grating,” Appl. Opt. 53(24), 5312–5321 (2014).
[Crossref] [PubMed]

Y. H. Chen, W. K. Chang, H. P. Chung, B. Z. Liu, C. H. Tseng, and J. W. Chang, “Tunable, pulsed multiline intracavity optical parametric oscillator using two-dimensional MgO: periodically poled lithium niobate-aperiodically poled lithium niobate,” Opt. Lett. 38(18), 3507–3509 (2013).
[Crossref] [PubMed]

Y. H. Chen, J. W. Chang, C. H. Lin, W. K. Chang, N. Hsu, Y. Y. Lai, Q. H. Tseng, R. Geiss, T. Pertsch, and S. S. Yang, “Spectral narrowing and manipulation in an optical parametric oscillator using periodically poled lithium niobate electro-optic polarization-mode converters,” Opt. Lett. 36(12), 2345–2347 (2011).
[Crossref] [PubMed]

J. Y. Lai, Y. J. Liu, H. Y. Wu, Y. H. Chen, and S. D. Yang, “Engineered multiwavelength conversion using nonperiodic optical superlattice optimized by genetic algorithm,” Opt. Express 18(5), 5328–5337 (2010).
[Crossref] [PubMed]

C. L. Chang, Y. H. Chen, C. H. Lin, and J. Y. Chang, “Monolithically integrated multi-wavelength filter and second harmonic generator in aperiodically poled lithium niobate,” Opt. Express 16(22), 18535–18544 (2008).
[Crossref] [PubMed]

C. H. Lin, Y. H. Chen, S. W. Lin, C. L. Chang, Y. C. Huang, and J. Y. Chang, “Electro-optic narrowband multi-wavelength filter in aperiodically poled lithium niobate,” Opt. Express 15(15), 9859–9866 (2007).
[Crossref] [PubMed]

C. Y. Huang, C. H. Lin, Y. H. Chen, and Y. C. Huang, “Electro-optic Ti:PPLN waveguide as efficient optical wavelength filter and polarization mode converter,” Opt. Express 15(5), 2548–2554 (2007).
[Crossref] [PubMed]

Chou, M. H.

Chung, H. P.

Dong, B. Z.

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[Crossref]

Ehret, G.

M. Wirth, A. Fix, P. Mahnke, H. Schwarzer, F. Schrandt, and G. Ehret, “The airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performance,” Appl. Phys. B 96(1), 201–213 (2009).
[Crossref]

Fejer, M. M.

Fix, A.

M. Wirth, A. Fix, P. Mahnke, H. Schwarzer, F. Schrandt, and G. Ehret, “The airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performance,” Appl. Phys. B 96(1), 201–213 (2009).
[Crossref]

Geiss, R.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Gloster, L. A. W.

Gu, B. Y.

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[Crossref]

Hatanaka, T.

Hauden, J.

Hogervorst, W.

Hsu, N.

Huang, C. Y.

Huang, Y. C.

Ito, H.

Jacobsson, B.

Jiang, Z. X.

Kawase, K.

King, T. A.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Lai, J. Y.

Lai, Y. Y.

Laurell, F.

Lin, C. H.

Lin, S. W.

Liu, B. Z.

Liu, Y. J.

Mahnke, P.

M. Wirth, A. Fix, P. Mahnke, H. Schwarzer, F. Schrandt, and G. Ehret, “The airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performance,” Appl. Phys. B 96(1), 201–213 (2009).
[Crossref]

McKinnie, I. T.

Nakamura, K.

Pan, C. L.

C. L. Wang and C. L. Pan, “Tunable dual-wavelength operation of a diode array with an external grating-loaded cavity,” Appl. Phys. Lett. 64(23), 3089–3091 (1994).
[Crossref]

Pasiskevicius, V.

Pertsch, T.

Schrandt, F.

M. Wirth, A. Fix, P. Mahnke, H. Schwarzer, F. Schrandt, and G. Ehret, “The airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performance,” Appl. Phys. B 96(1), 201–213 (2009).
[Crossref]

Schwarzer, H.

M. Wirth, A. Fix, P. Mahnke, H. Schwarzer, F. Schrandt, and G. Ehret, “The airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performance,” Appl. Phys. B 96(1), 201–213 (2009).
[Crossref]

Takahashi, H.

Taniuchi, T.

Tiihonen, M.

Tseng, C. H.

Tseng, Q. H.

van der Veer, W. E.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Wang, C. L.

C. L. Wang and C. L. Pan, “Tunable dual-wavelength operation of a diode array with an external grating-loaded cavity,” Appl. Phys. Lett. 64(23), 3089–3091 (1994).
[Crossref]

Wang, X. Z.

X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064- and 1074-nm dual-wavelength Nd:YAG laser using a Fabry–Perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1 (2014).
[Crossref]

Wang, Z. F.

X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064- and 1074-nm dual-wavelength Nd:YAG laser using a Fabry–Perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1 (2014).
[Crossref]

Wirth, M.

M. Wirth, A. Fix, P. Mahnke, H. Schwarzer, F. Schrandt, and G. Ehret, “The airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performance,” Appl. Phys. B 96(1), 201–213 (2009).
[Crossref]

Wu, H. Y.

Yang, G. Z.

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[Crossref]

Yang, S. D.

Yang, S. S.

Yau, H. F.

Zhang, Y.

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

M. Wirth, A. Fix, P. Mahnke, H. Schwarzer, F. Schrandt, and G. Ehret, “The airborne multi-wavelength water vapor differential absorption lidar WALES: system design and performance,” Appl. Phys. B 96(1), 201–213 (2009).
[Crossref]

Appl. Phys. Lett. (2)

C. L. Wang and C. L. Pan, “Tunable dual-wavelength operation of a diode array with an external grating-loaded cavity,” Appl. Phys. Lett. 64(23), 3089–3091 (1994).
[Crossref]

B. Y. Gu, B. Z. Dong, Y. Zhang, and G. Z. Yang, “Enhanced harmonic generation in aperiodic optical superlattices,” Appl. Phys. Lett. 75(15), 2175–2177 (1999).
[Crossref]

IEEE J. Quantum Electron. (1)

S. J. Brosnan and R. L. Byer, “Optical parametric oscillator threshold and linewidth studies,” IEEE J. Quantum Electron. 15(6), 415–431 (1979).
[Crossref]

IEEE Photonics J. (1)

X. Z. Wang, Z. F. Wang, Y. K. Bu, L. J. Chen, G. X. Cai, and Z. P. Cai, “A 1064- and 1074-nm dual-wavelength Nd:YAG laser using a Fabry–Perot band-pass filter as output mirror,” IEEE Photonics J. 6(4), 1 (2014).
[Crossref]

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

Opt. Express (4)

Opt. Lett. (6)

Y. H. Chen, W. K. Chang, H. P. Chung, B. Z. Liu, C. H. Tseng, and J. W. Chang, “Tunable, pulsed multiline intracavity optical parametric oscillator using two-dimensional MgO: periodically poled lithium niobate-aperiodically poled lithium niobate,” Opt. Lett. 38(18), 3507–3509 (2013).
[Crossref] [PubMed]

Y. H. Chen, J. W. Chang, C. H. Lin, W. K. Chang, N. Hsu, Y. Y. Lai, Q. H. Tseng, R. Geiss, T. Pertsch, and S. S. Yang, “Spectral narrowing and manipulation in an optical parametric oscillator using periodically poled lithium niobate electro-optic polarization-mode converters,” Opt. Lett. 36(12), 2345–2347 (2011).
[Crossref] [PubMed]

H. P. Chung, W. K. Chang, C. H. Tseng, R. Geiss, T. Pertsch, and Y. H. Chen, “Electro-Optically Spectrum Tailorable Intracavity Optical Parametric Oscillator,” Opt. Lett. 40(22), 5132–5135 (2015).
[Crossref] [PubMed]

B. Jacobsson, M. Tiihonen, V. Pasiskevicius, and F. Laurell, “Narrowband bulk Bragg grating optical parametric oscillator,” Opt. Lett. 30(17), 2281–2283 (2005).
[Crossref] [PubMed]

M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5-µm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett. 23(13), 1004–1006 (1998).
[Crossref] [PubMed]

K. Kawase, T. Hatanaka, H. Takahashi, K. Nakamura, T. Taniuchi, and H. Ito, “Tunable terahertz-wave generation from DAST crystal by dual signal-wave parametric oscillation of periodically poled lithium niobate,” Opt. Lett. 25(23), 1714–1716 (2000).
[Crossref] [PubMed]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220(4598), 671–680 (1983).
[Crossref] [PubMed]

Other (1)

T. M. J. Kendall, W. A. Clarkson, P. J. Hardmar, G. W. Ross, and D. C. Hanna, “Multiline optical parametric oscillators based on periodically poled lithium niobate,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2000), paper CMC2.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Fourier spectrum of the calculated domain structure in LiNbO3. Two and four target spatial frequencies, required for phase-matching the 1064-nm pumped 1540/3442 and 1550/3393 nm signal/idler OPG processes and for phase-matching the corresponding EO polarization-mode conversion processes at 40°C, respectively, are resolved. The inset schematically shows a section of the domain structure.
Fig. 2
Fig. 2 (a) Calculated single-pass e-wave transmission spectrum at Ey = 150 V/mm and OPO signal spectrum based on 7 cavity roundtrips for signal buildup at Ey = 0 V/mm when an e-polarized wave with a flat spectrum over 1520-1560 nm and a 6 MW/cm2 e-polarized wave at 1064 nm are incident at the APPLN, respectively. (b) Calculated output signal spectra from an IOPO constructed using the APPLN device at Ey = 0 V/mm (red line) and 150 V/mm (blue line) at 40°C. (c) and (d) Simulated output spectra of the IOPO under the EO control (at Ey = 150 V/mm) at the 1540 and 1550 nm signal bands, respectively, for several different operating temperatures.
Fig. 3
Fig. 3 (a) Fourier analysis of an APPLN calculated for a three spectral-peak (1530, 1540, and 1550 nm) system. (b) Calculated IOPO signal spectrum based on the APPLN at Ey = 200 V/mm under intracavity 1064-nm pump intensity of 6 MW/cm2 and 11 cavity roundtrips for signal buildup.
Fig. 4
Fig. 4 Schematic arrangement of an EO spectral-line controlled/narrowed, multiline OPO achieved using the constructed APPLN device in a diode-pumped, EO Q-switched Nd:YVO4 laser. The inset shows an image of a portion of the HF-etched + z surface of the APPLN crystal.
Fig. 5
Fig. 5 (a) Measured normalized IOPG (black line) and IOPO (red line) signal spectra when the system shown in Fig. 4 was pumped at ~5 W diode power. (b) Measured signal spectra of the IOPO when the APPLN device is applied with Ey = 0 V/mm (red line) and 150 V/mm (blue line). (c) and (d) Expansion of signal spectrum from Fig. 5(b) at the 1540 and 1550 nm bands for the IOPO under EO control, respectively.
Fig. 6
Fig. 6 Measured temporal behavior of the IOPO output. Left: peak-to-peak intensity fluctuation. Right: a typical signal pulse shape.

Equations (1)

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OF={( α=1 M | η op,0 ( λ s,α ) η op ( λ s,α ) | w op ( λ s,α ) )+ γ op (max[ η op ( λ 1 ),..., η op ( λ M )] min[ η op ( λ 1 ),..., η op ( λ M )])+( β=1 N | η eo,0 ( λ β ) η eo ( λ β ) | w eo ( λ β ))+ γ eo (max[ η eo ( λ 1 ),..., η eo ( λ N )]min[ η eo ( λ 1 ),..., η eo ( λ N )])},

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