Abstract

We propose and demonstrate a frequency multiplying optoelectronic oscillator with nonlinearly-coupled double loops based on two cascaded Mach–Zehnder modulators, to generate high frequency microwave signals using only low-frequency devices. We find the final oscillation modes are only determined by the length of the master oscillation loop. Frequency multiplying signals are generated via nonlinearly-coupled double loops, the output of one loop being used to modulate the other. In the experiments, microwave signals at 10 GHz with −121 dBc/Hz phase noise at 10 kHz offset and 20 GHz with −112.8 dBc/Hz phase noise at 10 kHz offset are generated. Meanwhile, their side-mode suppression ratios are also evaluated and the maximum ratio of 70 dB is obtained.

© 2013 Optical Society of America

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References

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  1. X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron.32(7), 1141–1149 (1996).
    [CrossRef]
  2. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” IEEE J. Opt. Soc.13(8), 1725–1734 (1996).
    [CrossRef]
  3. I. Ozdur, D. Mandridis, N. Hoghooghi, and P. J. Delfyett, “Low noise optically tunable opto-electronic oscillator with Fabry–Pérot Etalon,” J. Lightwave Technol.28(21), 3100–3106 (2010).
  4. S. L. Pan and J. P. Yao, “Multichannel optical signal processing in NRZ systems based on a frequency-doubling optoelectronic oscillator,” IEEE J. Sel. Top. Quantum Electron.16(5), 1460–1468 (2010).
    [CrossRef]
  5. L. Huo, Y. Dong, C. Lou, and Y. Gao, “Clock extraction using an opto-electronic oscillator from high-speed NRZ signal and NRZ-to-RZ format transformation,” IEEE Photon. Technol. Lett.15(7), 981–983 (2003).
    [CrossRef]
  6. Y. C. Chi, P. C. Peng, and G. R. Lin, “Clock-free RZ-BPSK data generation using self-starting optoelectronic oscillator,” J. Lightwave Technol.29(11), 1702–1707 (2011).
    [CrossRef]
  7. L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett.22(12), 857–859 (2010).
    [CrossRef]
  8. P. S. Devgan, M. W. Pruessner, V. J. Urick, and K. J. Williams, “Detecting low-power RF signals using a multimode optoelectronic oscillator and integrated optical filter,” IEEE Photon. Technol. Lett.22(3), 152–154 (2010).
    [CrossRef]
  9. D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
    [CrossRef]
  10. T. Sakamoto, T. Kawanishi, and M. Izutsu, “Optoelectronic oscillator using push-pull Mach–Zehnder modulator biased at point for optical two-tone signal generation,” in Conf. Lasers Electro-Optics (CLEO2005). (Tokyo, Japan., 2005), pp. 877–879.
  11. S. L. Pan and J. P. Yao, “A frequency-doubling optoelectronic oscillator using a polarization modulator,” IEEE Photon. Technol. Lett.21(13), 929–931 (2009).
    [CrossRef]
  12. W. Z. Li and J. P. Yao, “An optically tunable frequency-doubling optoelectronic oscillator incorporating a phase shifted fiber bragg grating based frequency-tunable photonic microwave filter,” Proc. MWP 2011, (Singapore, 2011) pp. 429–432.
    [CrossRef]
  13. L. X. Wang, N. H. Zhu, W. Li, and J. G. Liu, “A frequency-doubling optoelectronic oscillator based on a dual-parallel Mach-Zehnder modulator and a chirped fiber bragg grating,” IEEE Photon. Technol. Lett.23(22), 1688–1690 (2011).
    [CrossRef]
  14. D. Zhu, S. F. Liu, D. Ben, and S. Pan, “Frequency-Quadrupling optoelectronic oscillator for multichannel upconversion,” IEEE Photon. Technol. Lett.25(5), 426–429 (2013).
    [CrossRef]
  15. D. Zhu, S. L. Pan, and S. H. Cai, “High-Performance Photonic Microwave Downconverter Based on a Frequency-Doubling Optoelectronic Oscillator,” J. Lightwave Technol.30(18), 3036–3042 (2012).
    [CrossRef]
  16. M. Haji, L. P. Hou, A. E. Kelly, J. Akbar, J. H. Marsh, J. M. Arnold, and C. N. Ironside, “High frequency optoelectronic oscillators based on the optical feedback of semiconductor mode-locked laser diodes,” Opt. Express20(3), 3268–3274 (2012).
    [CrossRef] [PubMed]
  17. D. Eliyahu and L. Maleki, “Low phase noise and spurious level in multi-loop opto-electronic oscillators,” in proceeding of IEEE Conference on International Frequency Control Symposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum(Tempa, Florida, U.S.A, 2003), pp. 405–410.
    [CrossRef]
  18. R. M. Nguimdo, Y. K. Chembo, P. Colet, and L. Larger, “On the phase noise performance of nonlinear double-loop optoelectronic microwave oscillators,” IEEE J. Quantum Electron.48(11), 1415–1423 (2012).
    [CrossRef]
  19. Hewlett-Packard, “Phase noise characterization of microwave oscillators—frequency discriminator method,” product note 11729C–2 (Hewlett-Packard, Santa Clara, Calif.).

2013 (1)

D. Zhu, S. F. Liu, D. Ben, and S. Pan, “Frequency-Quadrupling optoelectronic oscillator for multichannel upconversion,” IEEE Photon. Technol. Lett.25(5), 426–429 (2013).
[CrossRef]

2012 (3)

2011 (2)

L. X. Wang, N. H. Zhu, W. Li, and J. G. Liu, “A frequency-doubling optoelectronic oscillator based on a dual-parallel Mach-Zehnder modulator and a chirped fiber bragg grating,” IEEE Photon. Technol. Lett.23(22), 1688–1690 (2011).
[CrossRef]

Y. C. Chi, P. C. Peng, and G. R. Lin, “Clock-free RZ-BPSK data generation using self-starting optoelectronic oscillator,” J. Lightwave Technol.29(11), 1702–1707 (2011).
[CrossRef]

2010 (4)

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett.22(12), 857–859 (2010).
[CrossRef]

P. S. Devgan, M. W. Pruessner, V. J. Urick, and K. J. Williams, “Detecting low-power RF signals using a multimode optoelectronic oscillator and integrated optical filter,” IEEE Photon. Technol. Lett.22(3), 152–154 (2010).
[CrossRef]

I. Ozdur, D. Mandridis, N. Hoghooghi, and P. J. Delfyett, “Low noise optically tunable opto-electronic oscillator with Fabry–Pérot Etalon,” J. Lightwave Technol.28(21), 3100–3106 (2010).

S. L. Pan and J. P. Yao, “Multichannel optical signal processing in NRZ systems based on a frequency-doubling optoelectronic oscillator,” IEEE J. Sel. Top. Quantum Electron.16(5), 1460–1468 (2010).
[CrossRef]

2009 (1)

S. L. Pan and J. P. Yao, “A frequency-doubling optoelectronic oscillator using a polarization modulator,” IEEE Photon. Technol. Lett.21(13), 929–931 (2009).
[CrossRef]

2003 (1)

L. Huo, Y. Dong, C. Lou, and Y. Gao, “Clock extraction using an opto-electronic oscillator from high-speed NRZ signal and NRZ-to-RZ format transformation,” IEEE Photon. Technol. Lett.15(7), 981–983 (2003).
[CrossRef]

2002 (1)

D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
[CrossRef]

1996 (2)

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron.32(7), 1141–1149 (1996).
[CrossRef]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” IEEE J. Opt. Soc.13(8), 1725–1734 (1996).
[CrossRef]

Akbar, J.

Arnold, J. M.

Ben, D.

D. Zhu, S. F. Liu, D. Ben, and S. Pan, “Frequency-Quadrupling optoelectronic oscillator for multichannel upconversion,” IEEE Photon. Technol. Lett.25(5), 426–429 (2013).
[CrossRef]

Cai, S. H.

Chang, D.

D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
[CrossRef]

Chembo, Y. K.

R. M. Nguimdo, Y. K. Chembo, P. Colet, and L. Larger, “On the phase noise performance of nonlinear double-loop optoelectronic microwave oscillators,” IEEE J. Quantum Electron.48(11), 1415–1423 (2012).
[CrossRef]

Chi, Y. C.

Y. C. Chi, P. C. Peng, and G. R. Lin, “Clock-free RZ-BPSK data generation using self-starting optoelectronic oscillator,” J. Lightwave Technol.29(11), 1702–1707 (2011).
[CrossRef]

Colet, P.

R. M. Nguimdo, Y. K. Chembo, P. Colet, and L. Larger, “On the phase noise performance of nonlinear double-loop optoelectronic microwave oscillators,” IEEE J. Quantum Electron.48(11), 1415–1423 (2012).
[CrossRef]

Delfyett, P. J.

Devgan, P. S.

P. S. Devgan, M. W. Pruessner, V. J. Urick, and K. J. Williams, “Detecting low-power RF signals using a multimode optoelectronic oscillator and integrated optical filter,” IEEE Photon. Technol. Lett.22(3), 152–154 (2010).
[CrossRef]

Dong, Y.

L. Huo, Y. Dong, C. Lou, and Y. Gao, “Clock extraction using an opto-electronic oscillator from high-speed NRZ signal and NRZ-to-RZ format transformation,” IEEE Photon. Technol. Lett.15(7), 981–983 (2003).
[CrossRef]

Erlig, H.

D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
[CrossRef]

Fetterman, H. R.

D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
[CrossRef]

Gao, Y.

L. Huo, Y. Dong, C. Lou, and Y. Gao, “Clock extraction using an opto-electronic oscillator from high-speed NRZ signal and NRZ-to-RZ format transformation,” IEEE Photon. Technol. Lett.15(7), 981–983 (2003).
[CrossRef]

Haji, M.

Hoghooghi, N.

Hou, L. P.

Huo, L.

L. Huo, Y. Dong, C. Lou, and Y. Gao, “Clock extraction using an opto-electronic oscillator from high-speed NRZ signal and NRZ-to-RZ format transformation,” IEEE Photon. Technol. Lett.15(7), 981–983 (2003).
[CrossRef]

Ironside, C. N.

Journet, B.

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett.22(12), 857–859 (2010).
[CrossRef]

Kelly, A. E.

Larger, L.

R. M. Nguimdo, Y. K. Chembo, P. Colet, and L. Larger, “On the phase noise performance of nonlinear double-loop optoelectronic microwave oscillators,” IEEE J. Quantum Electron.48(11), 1415–1423 (2012).
[CrossRef]

Li, W.

L. X. Wang, N. H. Zhu, W. Li, and J. G. Liu, “A frequency-doubling optoelectronic oscillator based on a dual-parallel Mach-Zehnder modulator and a chirped fiber bragg grating,” IEEE Photon. Technol. Lett.23(22), 1688–1690 (2011).
[CrossRef]

Li, W. Z.

W. Z. Li and J. P. Yao, “An optically tunable frequency-doubling optoelectronic oscillator incorporating a phase shifted fiber bragg grating based frequency-tunable photonic microwave filter,” Proc. MWP 2011, (Singapore, 2011) pp. 429–432.
[CrossRef]

Lin, G. R.

Y. C. Chi, P. C. Peng, and G. R. Lin, “Clock-free RZ-BPSK data generation using self-starting optoelectronic oscillator,” J. Lightwave Technol.29(11), 1702–1707 (2011).
[CrossRef]

Liu, J. G.

L. X. Wang, N. H. Zhu, W. Li, and J. G. Liu, “A frequency-doubling optoelectronic oscillator based on a dual-parallel Mach-Zehnder modulator and a chirped fiber bragg grating,” IEEE Photon. Technol. Lett.23(22), 1688–1690 (2011).
[CrossRef]

Liu, S. F.

D. Zhu, S. F. Liu, D. Ben, and S. Pan, “Frequency-Quadrupling optoelectronic oscillator for multichannel upconversion,” IEEE Photon. Technol. Lett.25(5), 426–429 (2013).
[CrossRef]

Lou, C.

L. Huo, Y. Dong, C. Lou, and Y. Gao, “Clock extraction using an opto-electronic oscillator from high-speed NRZ signal and NRZ-to-RZ format transformation,” IEEE Photon. Technol. Lett.15(7), 981–983 (2003).
[CrossRef]

Maleki, L.

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron.32(7), 1141–1149 (1996).
[CrossRef]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” IEEE J. Opt. Soc.13(8), 1725–1734 (1996).
[CrossRef]

Mandridis, D.

Marsh, J. H.

Nakatani, K.

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett.22(12), 857–859 (2010).
[CrossRef]

Nguimdo, R. M.

R. M. Nguimdo, Y. K. Chembo, P. Colet, and L. Larger, “On the phase noise performance of nonlinear double-loop optoelectronic microwave oscillators,” IEEE J. Quantum Electron.48(11), 1415–1423 (2012).
[CrossRef]

Nguyen, L. D.

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett.22(12), 857–859 (2010).
[CrossRef]

Oh, A. C.

D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
[CrossRef]

Ozdur, I.

Pan, S.

D. Zhu, S. F. Liu, D. Ben, and S. Pan, “Frequency-Quadrupling optoelectronic oscillator for multichannel upconversion,” IEEE Photon. Technol. Lett.25(5), 426–429 (2013).
[CrossRef]

Pan, S. L.

D. Zhu, S. L. Pan, and S. H. Cai, “High-Performance Photonic Microwave Downconverter Based on a Frequency-Doubling Optoelectronic Oscillator,” J. Lightwave Technol.30(18), 3036–3042 (2012).
[CrossRef]

S. L. Pan and J. P. Yao, “Multichannel optical signal processing in NRZ systems based on a frequency-doubling optoelectronic oscillator,” IEEE J. Sel. Top. Quantum Electron.16(5), 1460–1468 (2010).
[CrossRef]

S. L. Pan and J. P. Yao, “A frequency-doubling optoelectronic oscillator using a polarization modulator,” IEEE Photon. Technol. Lett.21(13), 929–931 (2009).
[CrossRef]

Peng, P. C.

Y. C. Chi, P. C. Peng, and G. R. Lin, “Clock-free RZ-BPSK data generation using self-starting optoelectronic oscillator,” J. Lightwave Technol.29(11), 1702–1707 (2011).
[CrossRef]

Pruessner, M. W.

P. S. Devgan, M. W. Pruessner, V. J. Urick, and K. J. Williams, “Detecting low-power RF signals using a multimode optoelectronic oscillator and integrated optical filter,” IEEE Photon. Technol. Lett.22(3), 152–154 (2010).
[CrossRef]

Steier, W. H.

D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
[CrossRef]

Urick, V. J.

P. S. Devgan, M. W. Pruessner, V. J. Urick, and K. J. Williams, “Detecting low-power RF signals using a multimode optoelectronic oscillator and integrated optical filter,” IEEE Photon. Technol. Lett.22(3), 152–154 (2010).
[CrossRef]

Wang, L. X.

L. X. Wang, N. H. Zhu, W. Li, and J. G. Liu, “A frequency-doubling optoelectronic oscillator based on a dual-parallel Mach-Zehnder modulator and a chirped fiber bragg grating,” IEEE Photon. Technol. Lett.23(22), 1688–1690 (2011).
[CrossRef]

Williams, K. J.

P. S. Devgan, M. W. Pruessner, V. J. Urick, and K. J. Williams, “Detecting low-power RF signals using a multimode optoelectronic oscillator and integrated optical filter,” IEEE Photon. Technol. Lett.22(3), 152–154 (2010).
[CrossRef]

Yao, J. P.

S. L. Pan and J. P. Yao, “Multichannel optical signal processing in NRZ systems based on a frequency-doubling optoelectronic oscillator,” IEEE J. Sel. Top. Quantum Electron.16(5), 1460–1468 (2010).
[CrossRef]

S. L. Pan and J. P. Yao, “A frequency-doubling optoelectronic oscillator using a polarization modulator,” IEEE Photon. Technol. Lett.21(13), 929–931 (2009).
[CrossRef]

W. Z. Li and J. P. Yao, “An optically tunable frequency-doubling optoelectronic oscillator incorporating a phase shifted fiber bragg grating based frequency-tunable photonic microwave filter,” Proc. MWP 2011, (Singapore, 2011) pp. 429–432.
[CrossRef]

Yao, X. S.

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron.32(7), 1141–1149 (1996).
[CrossRef]

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” IEEE J. Opt. Soc.13(8), 1725–1734 (1996).
[CrossRef]

Zhang, C.

D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
[CrossRef]

Zhang, H.

D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
[CrossRef]

Zhu, D.

D. Zhu, S. F. Liu, D. Ben, and S. Pan, “Frequency-Quadrupling optoelectronic oscillator for multichannel upconversion,” IEEE Photon. Technol. Lett.25(5), 426–429 (2013).
[CrossRef]

D. Zhu, S. L. Pan, and S. H. Cai, “High-Performance Photonic Microwave Downconverter Based on a Frequency-Doubling Optoelectronic Oscillator,” J. Lightwave Technol.30(18), 3036–3042 (2012).
[CrossRef]

Zhu, N. H.

L. X. Wang, N. H. Zhu, W. Li, and J. G. Liu, “A frequency-doubling optoelectronic oscillator based on a dual-parallel Mach-Zehnder modulator and a chirped fiber bragg grating,” IEEE Photon. Technol. Lett.23(22), 1688–1690 (2011).
[CrossRef]

IEEE J. Opt. Soc. (1)

X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” IEEE J. Opt. Soc.13(8), 1725–1734 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. M. Nguimdo, Y. K. Chembo, P. Colet, and L. Larger, “On the phase noise performance of nonlinear double-loop optoelectronic microwave oscillators,” IEEE J. Quantum Electron.48(11), 1415–1423 (2012).
[CrossRef]

X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron.32(7), 1141–1149 (1996).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. L. Pan and J. P. Yao, “Multichannel optical signal processing in NRZ systems based on a frequency-doubling optoelectronic oscillator,” IEEE J. Sel. Top. Quantum Electron.16(5), 1460–1468 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (7)

L. Huo, Y. Dong, C. Lou, and Y. Gao, “Clock extraction using an opto-electronic oscillator from high-speed NRZ signal and NRZ-to-RZ format transformation,” IEEE Photon. Technol. Lett.15(7), 981–983 (2003).
[CrossRef]

L. D. Nguyen, K. Nakatani, and B. Journet, “Refractive index measurement by using an optoelectronic oscillator,” IEEE Photon. Technol. Lett.22(12), 857–859 (2010).
[CrossRef]

P. S. Devgan, M. W. Pruessner, V. J. Urick, and K. J. Williams, “Detecting low-power RF signals using a multimode optoelectronic oscillator and integrated optical filter,” IEEE Photon. Technol. Lett.22(3), 152–154 (2010).
[CrossRef]

D. Chang, H. R. Fetterman, H. Erlig, H. Zhang, A. C. Oh, C. Zhang, and W. H. Steier, “39-GHz optoelectronic oscillator using broad-band polymer electrooptic modulator,” IEEE Photon. Technol. Lett.14(2), 191–193 (2002).
[CrossRef]

S. L. Pan and J. P. Yao, “A frequency-doubling optoelectronic oscillator using a polarization modulator,” IEEE Photon. Technol. Lett.21(13), 929–931 (2009).
[CrossRef]

L. X. Wang, N. H. Zhu, W. Li, and J. G. Liu, “A frequency-doubling optoelectronic oscillator based on a dual-parallel Mach-Zehnder modulator and a chirped fiber bragg grating,” IEEE Photon. Technol. Lett.23(22), 1688–1690 (2011).
[CrossRef]

D. Zhu, S. F. Liu, D. Ben, and S. Pan, “Frequency-Quadrupling optoelectronic oscillator for multichannel upconversion,” IEEE Photon. Technol. Lett.25(5), 426–429 (2013).
[CrossRef]

J. Lightwave Technol. (3)

Opt. Express (1)

Other (4)

D. Eliyahu and L. Maleki, “Low phase noise and spurious level in multi-loop opto-electronic oscillators,” in proceeding of IEEE Conference on International Frequency Control Symposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum(Tempa, Florida, U.S.A, 2003), pp. 405–410.
[CrossRef]

W. Z. Li and J. P. Yao, “An optically tunable frequency-doubling optoelectronic oscillator incorporating a phase shifted fiber bragg grating based frequency-tunable photonic microwave filter,” Proc. MWP 2011, (Singapore, 2011) pp. 429–432.
[CrossRef]

Hewlett-Packard, “Phase noise characterization of microwave oscillators—frequency discriminator method,” product note 11729C–2 (Hewlett-Packard, Santa Clara, Calif.).

T. Sakamoto, T. Kawanishi, and M. Izutsu, “Optoelectronic oscillator using push-pull Mach–Zehnder modulator biased at point for optical two-tone signal generation,” in Conf. Lasers Electro-Optics (CLEO2005). (Tokyo, Japan., 2005), pp. 877–879.

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Figures (5)

Fig. 1
Fig. 1

The experimental setup of FM-OEO scheme. (MZM, Mach–Zehnder modulator; OC, optical coupler; EC, electrical coupler; PC, polarization controller; EDFA, Erbium doped fiber amplifier; OVDL, optical variable delay line; PD, photodetector; EA, electrical amplifier; EBPF, electrical bandpass filter; ESA, electrical spectrum analyzer).

Fig. 2
Fig. 2

Electrical spectrum of the FM-OEO. Span = 30MHz. (a) OVDL1with τ O V D L 1 =0ps ; (b) OVDL1 with τ O V D L 1 =10ps ; (c) OVDL2 with τ O V D L 2 =0ps ; (d) OVDL2 with τ O V D L 2 =10ps .

Fig. 3
Fig. 3

(a) Electrical spectrum of the FM-OEO. (b) Electrical spectrum of the conventional dual-loop OEO.

Fig. 4
Fig. 4

Electrical spectrum of fundamental-frequency and frequency-doubled microwave signals.

Fig. 5
Fig. 5

Phase noise spectrum of the (a) single-loop OEO measured at 10 GHz, (b) double-loop OEO measured at 10 GHz, (c) FM-OEO measured at 10 GHz and, (d) FM-OEO measured at 20 GHz.

Equations (14)

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

V 1 (t)= V b1 + V RF1 sin( ω m t )
E 1 ( t )= 1 2 E 0 exp( j ω 0 t )+ 1 2 E 0 exp( j ω 0 t )exp[ j π V π1 V 1 ( t ) ]
E 1 (t) E 0 2 { J 0 ( β 1 )exp(j ω 0 t)+ J 1 ( β 1 )exp[ j( ω 0 + ω m )t ]+ J 1 ( β 1 )exp[ j( ω 0 ω m )t ] }
V 2 ( t )={ R 2 G A2 2 E 0 2 J 0 ( β 1 ) J 1 ( β 1 )exp[ j( ω m t+ ω m τ 2 ) ]+ R 2 G A2 4 E 0 2 J 1 ( β 1 ) J 1 ( β 1 )exp[ j( 2 ω m t+2 ω m τ 2 ) ] }
  E 2 (t)= 1 4 E 1 ( t )+ 1 4 E 1 ( t )exp{ j π V π2 V b2 + j π 2 V π2 R 2 G A2 E 0 2 J 0 ( β 1 ) J 1 ( β 1 )exp[ j( ω m t+ ω m τ 2 ) ]+ j π 4 V π2 R 2 G A2 E 0 2 J 1 ( β 1 ) J 1 ( β 1 )exp[ j( 2 ω m t+2 ω m τ 2 ) ] }
E 3 ( t ) R 1 E 0 2 4 { [ J 0 ( β 1 ) J 0 ( β 2 )+ J 0 ( β 1 ) J 0 ( β 3 ) ]exp(j ω m t) +[ J 0 ( β 1 ) J 1 ( β 2 )+ J 0 ( β 1 ) J 1 ( β 3 ) ]exp[ j ω m ( t+ τ 2 ) ] +[ J 1 ( β 1 ) J 1 ( β 2 )+ J 1 ( β 1 ) J 1 ( β 3 ) ]exp[ j2 ω m ( t+ τ 2 ) ] +[ J 0 ( β 1 ) J 0 ( β 2 )+ J 0 ( β 1 ) J 1 ( β 2 ) ]exp[ j3 ω m ( t+ τ 2 ) ] +[ J 0 ( β 1 ) J 0 ( β 3 )+ J 0 ( β 1 ) J 1 ( β 3 ) ]exp[ j4 ω m ( t+ τ 2 ) ] }
E 3 ( t ) R 1 E 0 2 4 { [ J 0 ( β 1 ) J 0 ( β 2 )+ J 0 ( β 1 ) J 0 ( β 3 ) ]exp(j ω m t) +[ J 0 ( β 1 ) J 1 ( β 2 )+ J 0 ( β 1 ) J 1 ( β 3 ) ]exp[ j ω m ( t+ τ 2 ) ] } = R 1 E 0 2 4 { [ J 0 ( β 1 ) J 0 ( β 2 )+ J 0 ( β 1 ) J 0 ( β 3 ) ] +[ J 0 ( β 1 ) J 1 ( β 2 )+ J 0 ( β 1 ) J 1 ( β 3 ) ]exp( j ω m τ 2 ) }exp(j ω m t)
E 3 ( t )exp[ j ω m ( t+n τ 1 ) ] n=0 { G A1 R 1 E 0 2 4 [ J 0 ( β 1 ) J 0 ( β 2 )+ J 0 ( β 1 ) J 0 ( β 3 ) + J 0 ( β 1 ) J 1 ( β 2 )exp( j ω m τ 2 ) + J 0 ( β 1 ) J 1 ( β 3 )exp( j ω m τ 2 ) ] } n =exp(j ω m t) n=0 [ G e ( ω m ) ] n exp( j ω m n τ 1 )
G e ( ω m )={ G A1 R 1 E 0 2 4 [ J 0 ( β 1 ) J 0 ( β 2 )+ J 0 ( β 1 ) J 0 ( β 3 )+ J 0 ( β 1 ) J 1 ( β 2 )exp( j ω m τ 2 )+ J 0 ( β 1 ) J 1 ( β 3 )exp( j ω m τ 2 ) ] }
E 3 ( t ) exp(j ω m t) 1 G e ( ω m )exp( j ω m τ 1 )
P( ω m ,t ) | E 3 ( t ) | 2 2R = 1 2R[ 1+ G e 2 ( ω m )2 G e ( ω m )cos( ω m τ 1 ) ]
ω m τ=2kπ, k=0,1,2,3,...,
ω m = 2kπ τ 1
Δω ω = Δf f = Δτ τ

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