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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 24 — Nov. 19, 2012
  • pp: 27163–27173
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Cancellation of photodiode-induced second harmonic distortion using single side band modulation from a dual parallel Mach-Zehnder

Preetpaul S. Devgan, Alexander S. Hastings, Vincent J. Urick, and Keith J. Williams  »View Author Affiliations


Optics Express, Vol. 20, Issue 24, pp. 27163-27173 (2012)
http://dx.doi.org/10.1364/OE.20.027163


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Abstract

We have theoretically and experimentally investigated using a dual parallel Mach-Zehnder modulator (DP-MZM) in an RF photonic link to cancel the second harmonic distortion due to the photodiode. Biasing the DP-MZM for single sideband modulation, the second harmonic generated by the DP-MZM can be set out of phase with the second harmonic generated at the photodiode. We measure the output intercept point of the second harmonic distortion of the link to be 55.3 dBm, which is an improvement of over 32 dB as compared to only the photodiode.

© 2012 OSA

1. Introduction

2. Theory of SSB DP-MZM operation for canceling photodiode-induced second order nonlinearity

2.1 Derivation of upper and lower sideband fields at fundamental and second harmonic RF frequency

Rewriting Eq. (4) with the definitions of ϕ1(t) and ϕ2(t) as given above and making use of the Jacobi Anger expansions eizcosθ=n=inJn(z)einθand eizsinθ=n=Jn(z)einθgives the following
Eout(t)=14[eiϕdc1(n=Jn(ϕrf1)einΩrft)1eiϕdc3+eiϕdc3eiϕdc2(n=inJn(ϕrf2)einΩrft)]Ein(t)
(5)
where Jm is an mth-order Bessel function. For this treatment we are going to focus on the carrier and the first and second upper and lower side bands. Using the identity Jn(z)=(1)nJn(z) the fields for the carrier and the two first and second RF harmonic sidebands can be written as
Ecarrier(t)=E¯ineiωot4[1eiϕdc3+eiϕdc1J0(ϕrf1)+eiϕdc3eiϕdc2J0(ϕrf2)],Eusb,fund(t)=E¯ineiωotiΩrft4[eiϕdc1J1(ϕrf1)+ieiϕdc3eiϕdc2J1(ϕrf2)],Elsb,fund(t)=E¯ineiωot+iΩrft4[eiϕdc1J1(ϕrf1)+ieiϕdc3eiϕdc2J1(ϕrf2)],Eusb,second(t)=E¯ineiωoti2Ωrft4[eiϕdc1J2(ϕrf1)eiϕdc3eiϕdc2J2(ϕrf2)],Elsb,second(t)=E¯ineiωot+i2Ωrft4[eiϕdc1J2(ϕrf1)eiϕdc3eiϕdc2J2(ϕrf2)],
(6)
whereEin(t)=E¯ineiωot. Setting ϕrf1 = ϕrf2, the upper fundamental optical sideband is nulled when ϕdc1 = π/2 + ϕdc2 + ϕ3. From Eq. (6), one can derive the optical power of the DC, fundamental and the second harmonic due to the DP-MZM by using the small signal approximation for the Bessel functions. However, for completeness, the DC, fundamental and second harmonic photocurrents generated at the photodiode are derived starting with Eq. (4) in the following section.

2.2 Derivation of DC, fundamental and second harmonic photocurrent from the output field of the DP-MZM

2.3 Taylor expansion of second harmonic photocurrent from incoming fundamental optical power

3. Experimental demonstration

4. Conclusion

References and links

1.

J. E. Roman, L. T. Nichols, K. J. Wiliams, R. D. Esman, G. C. Tavik, M. Livingston, and M. G. Parent, “Fiber-optic remoting of an ultrahigh dynamic range radar,” IEEE Trans. Microw. Theory Tech. 46(12), 2317–2323 (1998). [CrossRef]

2.

C. Chang, J. A. Cassaboom, and H. F. Taylor, “Fiber optic delay line devices for RF signal processing,” Electron. Lett. 13(22), 678–680 (1977). [CrossRef]

3.

R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. 54(2), 832–846 (2006). [CrossRef]

4.

P. S. Devgan, V. J. Urick, J. F. Diehl, and K. J. Williams, “Improvement in the phase noise of a 10 GHz optoelectronic oscillator using all-photonic gain,” J. Lightwave Technol. 27(15), 3189–3193 (2009). [CrossRef]

5.

L. Wang, N. Zhu, W. Li, and J. 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]

6.

W. Li, N. H. Zhu, and L. X. Wang, “Reconfigurable instantaneous frequency measurement system based on dual-parallel Mach–Zehnder Modulator,” IEEE Photon. J. 4(2), 427–436 (2012). [CrossRef]

7.

P. S. Devgan, V. J. Urick, and K. J. Williams, “Detection of low-power RF signals using a two laser multimode optoelectronic oscillator,” IEEE Photon. Technol. Lett. 24, 857–859 (2012).

8.

R. R. Hayes and D. L. Persechini, “Nonlinearity of p-i-n photodetectors,” IEEE Photon. Technol. Lett. 5(1), 70–72 (1993). [CrossRef]

9.

H. Jiang and P. K. L. Yu, “Equivalent circuit analysis of harmonic distortion in photodiodes,” IEEE Photon. Technol. Lett. 10(11), 1608–1610 (1998). [CrossRef]

10.

V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, and K. J. Williams, “Long-haul analog photonics,” J. Lightwave Technol. 29(8), 1182–1205 (2011). [CrossRef]

11.

D. M. Pozar, Microwave Engineering (Wiley, 1998)

12.

A. S. Hastings, D. A. Tulchinsky, and K. J. Williams, “Photodetector nonlinearities due to voltage-dependent responsivity,” IEEE Photon. Technol. Lett. 21(21), 1642–1644 (2009). [CrossRef]

13.

J. D. McKinney, D. E. Leaird, A. M. Weiner, and K. J. Williams, “Measurement of photodiode harmonic distortion using optical comb sources and high-resolution optical filtering,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2009), paper CWI5.

14.

A. S. Hastings, V. Urick, C. Sunderman, J. Diehl, J. McKinney, D. Tulchinsky, P. Devgan, and K. Williams, “Suppression of even-order photodiode nonlinearities in multioctave photonic links,” J. Lightwave Technol. 26(15), 2557–2562 (2008). [CrossRef]

15.

H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett. 31(21), 1848–1849 (1995). [CrossRef]

16.

G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron. 20(10), 1208–1216 (1984). [CrossRef]

17.

G. H. Smith, D. Novak, and Z. Ahmed, “Technique for optical SSB generation to overcome dispersion penalties in fibre-radio systems,” Electron. Lett. 33(1), 74–75 (1997). [CrossRef]

18.

B. Hraimel, X. Zhang, Y. Pei, K. Wu, T. Liu, T. Xu, and Q. Nie, “Optical single-sideband modulation with tunable optical carrier to sideband ratio in radio over fiber systems,” J. Lightwave Technol. 29(5), 775–781 (2011). [CrossRef]

19.

S. K. Korotky and R. M. de Ridder, “Dual parallel modulation schemes for low-distortion analog optical transmission,” IEEE J. Sel. Areas Comm. 8(7), 1377–1381 (1990). [CrossRef]

20.

G. Zhu, W. Liu, and H. Fetterman, “A broadband linearized coherent analog fiber-optic link employing dual parallel Mach–Zehnder Modulators,” IEEE Photon. Technol. Lett. 21(21), 1627–1629 (2009). [CrossRef]

21.

S. Li, X. Zheng, H. Zhang, and B. Zhou, “Highly linear radio-over-fiber system incorporating a single-drive dual-parallel Mach–Zehnder modulator,” IEEE Photon. Technol. Lett. 22(24), 1775–1777 (2010). [CrossRef]

22.

T. Kawanishi and M. Izutsu, “Linear single-sideband modulation for high-SNR wavelength conversion,” IEEE Photon. Technol. Lett. 16(6), 1534–1536 (2004). [CrossRef]

23.

S.-K. Kim, W. Liu, Q. Pei, L. R. Dalton, and H. R. Fetterman, “Nonlinear intermodulation distortion suppression in coherent analog fiber optic link using electro-optic polymeric dual parallel Mach-Zehnder modulator,” Opt. Express 19(8), 7865–7871 (2011). [CrossRef] [PubMed]

24.

K. J. Williams, R. D. Esman, and M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol. 14(1), 84–96 (1996). [CrossRef]

OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(060.4080) Fiber optics and optical communications : Modulation
(230.5170) Optical devices : Photodiodes
(060.5625) Fiber optics and optical communications : Radio frequency photonics

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 10, 2012
Revised Manuscript: August 24, 2012
Manuscript Accepted: October 19, 2012
Published: November 16, 2012

Citation
Preetpaul S. Devgan, Alexander S. Hastings, Vincent J. Urick, and Keith J. Williams, "Cancellation of photodiode-induced second harmonic distortion using single side band modulation from a dual parallel Mach-Zehnder," Opt. Express 20, 27163-27173 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-24-27163


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References

  1. J. E. Roman, L. T. Nichols, K. J. Wiliams, R. D. Esman, G. C. Tavik, M. Livingston, and M. G. Parent, “Fiber-optic remoting of an ultrahigh dynamic range radar,” IEEE Trans. Microw. Theory Tech.46(12), 2317–2323 (1998). [CrossRef]
  2. C. Chang, J. A. Cassaboom, and H. F. Taylor, “Fiber optic delay line devices for RF signal processing,” Electron. Lett.13(22), 678–680 (1977). [CrossRef]
  3. R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech.54(2), 832–846 (2006). [CrossRef]
  4. P. S. Devgan, V. J. Urick, J. F. Diehl, and K. J. Williams, “Improvement in the phase noise of a 10 GHz optoelectronic oscillator using all-photonic gain,” J. Lightwave Technol.27(15), 3189–3193 (2009). [CrossRef]
  5. L. Wang, N. Zhu, W. Li, and J. 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]
  6. W. Li, N. H. Zhu, and L. X. Wang, “Reconfigurable instantaneous frequency measurement system based on dual-parallel Mach–Zehnder Modulator,” IEEE Photon. J.4(2), 427–436 (2012). [CrossRef]
  7. P. S. Devgan, V. J. Urick, and K. J. Williams, “Detection of low-power RF signals using a two laser multimode optoelectronic oscillator,” IEEE Photon. Technol. Lett.24, 857–859 (2012).
  8. R. R. Hayes and D. L. Persechini, “Nonlinearity of p-i-n photodetectors,” IEEE Photon. Technol. Lett.5(1), 70–72 (1993). [CrossRef]
  9. H. Jiang and P. K. L. Yu, “Equivalent circuit analysis of harmonic distortion in photodiodes,” IEEE Photon. Technol. Lett.10(11), 1608–1610 (1998). [CrossRef]
  10. V. J. Urick, F. Bucholtz, J. D. McKinney, P. S. Devgan, A. L. Campillo, J. L. Dexter, and K. J. Williams, “Long-haul analog photonics,” J. Lightwave Technol.29(8), 1182–1205 (2011). [CrossRef]
  11. D. M. Pozar, Microwave Engineering (Wiley, 1998)
  12. A. S. Hastings, D. A. Tulchinsky, and K. J. Williams, “Photodetector nonlinearities due to voltage-dependent responsivity,” IEEE Photon. Technol. Lett.21(21), 1642–1644 (2009). [CrossRef]
  13. J. D. McKinney, D. E. Leaird, A. M. Weiner, and K. J. Williams, “Measurement of photodiode harmonic distortion using optical comb sources and high-resolution optical filtering,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2009), paper CWI5.
  14. A. S. Hastings, V. Urick, C. Sunderman, J. Diehl, J. McKinney, D. Tulchinsky, P. Devgan, and K. Williams, “Suppression of even-order photodiode nonlinearities in multioctave photonic links,” J. Lightwave Technol.26(15), 2557–2562 (2008). [CrossRef]
  15. H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett.31(21), 1848–1849 (1995). [CrossRef]
  16. G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron.20(10), 1208–1216 (1984). [CrossRef]
  17. G. H. Smith, D. Novak, and Z. Ahmed, “Technique for optical SSB generation to overcome dispersion penalties in fibre-radio systems,” Electron. Lett.33(1), 74–75 (1997). [CrossRef]
  18. B. Hraimel, X. Zhang, Y. Pei, K. Wu, T. Liu, T. Xu, and Q. Nie, “Optical single-sideband modulation with tunable optical carrier to sideband ratio in radio over fiber systems,” J. Lightwave Technol.29(5), 775–781 (2011). [CrossRef]
  19. S. K. Korotky and R. M. de Ridder, “Dual parallel modulation schemes for low-distortion analog optical transmission,” IEEE J. Sel. Areas Comm.8(7), 1377–1381 (1990). [CrossRef]
  20. G. Zhu, W. Liu, and H. Fetterman, “A broadband linearized coherent analog fiber-optic link employing dual parallel Mach–Zehnder Modulators,” IEEE Photon. Technol. Lett.21(21), 1627–1629 (2009). [CrossRef]
  21. S. Li, X. Zheng, H. Zhang, and B. Zhou, “Highly linear radio-over-fiber system incorporating a single-drive dual-parallel Mach–Zehnder modulator,” IEEE Photon. Technol. Lett.22(24), 1775–1777 (2010). [CrossRef]
  22. T. Kawanishi and M. Izutsu, “Linear single-sideband modulation for high-SNR wavelength conversion,” IEEE Photon. Technol. Lett.16(6), 1534–1536 (2004). [CrossRef]
  23. S.-K. Kim, W. Liu, Q. Pei, L. R. Dalton, and H. R. Fetterman, “Nonlinear intermodulation distortion suppression in coherent analog fiber optic link using electro-optic polymeric dual parallel Mach-Zehnder modulator,” Opt. Express19(8), 7865–7871 (2011). [CrossRef] [PubMed]
  24. K. J. Williams, R. D. Esman, and M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol.14(1), 84–96 (1996). [CrossRef]

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