## Cancellation of photodiode-induced second harmonic distortion using single side band modulation from a dual parallel Mach-Zehnder |

Optics Express, Vol. 20, Issue 24, pp. 27163-27173 (2012)

http://dx.doi.org/10.1364/OE.20.027163

Acrobat PDF (1079 KB)

### 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

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]

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]

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]

_{2H}, OIP3

_{3H}), respectively. Work has been done to make photodiodes with better linearity, with reports of measured output intercept points of the second harmonic (OIP2

_{2H}) of 50 dBm [12

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]

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]

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]

_{2H}of 55.3 dBm for the link, which is an improvement of 32.3 when compared to the photodiode by itself.

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

_{dc1,2}and ϕ

_{rf1,2}, respectively. The overall MZM has a DC bias control to provide a phase shift between the two smaller MZMs, labeled as ϕ

_{dc3}. Note

_{π,dc}is the DC voltage required for π phase shift and V

_{π,rf}(Ω

_{rf}) is the RF voltage required for π phase shift at an RF angular frequency Ω

_{rf}. In order to generate SSB modulation, the incoming RF signal is split by a 90 degree hybrid and the two outputs are connected to each of the smaller MZMs. Following a previous analysis using a single MZM [10

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]

_{ο}is the angular frequency of the laser,

*κ*is a constant relating the average laser power

*P*to the field amplitude such that

_{laser}_{out1}from both MZMs is chosen as the output that propagates through the rest of the modulator. The lower MZM output is modified by the phase shift provided by ϕ

_{dc3}and then combined at the final Y-branch at the output of the DP-MZM, which is written asAgain choosing E

_{out1}, the total output field of the DP-MZM is written asBeginning with Eq. (4), two paths are followed to complete the theoretical analysis for this system. First, the fields for the carrier and the upper and lower side band will be derived in order to determine the bias relationship that will allow for single side band operation. Secondly, the photocurrent generated at the photodiode will be derived in order to determine the form of both the fundamental and second harmonic due to the DP-MZM. The second harmonic photocurrent from the photodiode nonlinearity is then derived using a Taylor expansion of the photodiode response to the fundamental optical power from the DP-MZM.

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

_{1}(t) and ϕ

_{2}(t) as given above and making use of the Jacobi Anger expansions

*J*is an m

_{m}^{th}-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

*ϕ*=

_{rf1}*ϕ*, the upper fundamental optical sideband is nulled when

_{rf2}*ϕ*= π/2 +

_{dc1}*ϕ*. 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.

_{dc2}+ ϕ_{3}### 2.2 Derivation of DC, fundamental and second harmonic photocurrent from the output field of the DP-MZM

_{MZM}is the optical insertion loss for the DP-MZM. Expanding ϕ

_{1,2}(t) gives the following

*ϕ*=

_{rf1}*ϕ*, and noting that the optical signal from the DP-MZM is passed through an optical amplifier before entering the photodiode, the generated photocurrent can be written as

_{rf2}*G*

_{o}is the optical gain from the EDFA after the DP-MZM output to the photodiode,

_{dc1,2,3}. In order to cancel the photodiode-induced second harmonic, we have to set the phase of the second harmonic photocurrent from the DP-MZM to be 180 degrees with relation to the second harmonic photocurrent generated from the photodiode by the fundamental optical power. In the next section the Taylor expansion for the photocurrent due to the fundamental power from the DP-MZM will be shown. Using the second harmonic photocurrent due to the Taylor expansion of the photodiode response and the second harmonic photocurrent due to the DP-MZM, one can show for a specific set of bias points, the two photocurrents can cancel.

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

*a*=

_{0}*I*= ℜ*

_{PD}(P_{dc})*P*, and

_{dc}*P*=

_{opt,in}*P*+

_{dc}*P*. Plugging in and looking at the photodiode-induced second harmonic term yieldsIn order to cancel the photodiode-induced second harmonic, the phase of the second harmonic photocurrent due to the DP-MZM in Eq. (12) will have to be 180° with respect to the photocurrent in Eq. (15). Using the SSB relationship as a limiting condition, one can do a scan of bias values to find the bias point that meets the cancellation condition. For example, when ϕ

_{Fund}(t)_{dc3}= 1.555π, ϕ

_{dc2}= 1.95π, and ϕ

_{dc1}= 2.005π, the second harmonic is out of phase with the photodiode induced second harmonic. Note this is not the only set of bias points that meet the SSB condition while also keeping the second harmonic of the photodiode out of phase with the second harmonic from the DP-MZM, as we will see later. In order to make the amplitude match for the best cancellation, the ϕ

_{dc3}can be tuned slightly while keeping the phase difference close to 180 degrees. We now can measure the second harmonic of the link to see if we are indeed cancelling second harmonic distortion due to the photodiode.

## 3. Experimental demonstration

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]

_{2H}) is 23.0 dBm and the output intercept point of the third harmonic (OIP3

_{3H}) is 17.6 dBm. Now the photodiode is used in the photonic link and the DP-MZM is biased to generate the SSB modulation. Starting with the three biases set to the operating points from above, the ϕ

_{dc3}and ϕ

_{dc1}are adjusted to match the amplitudes of the two second harmonics and to maintain the SSB operation. When the second harmonic is minimized at the output of the photodiode at a DC photocurrent of 8 mA, the optical carrier and sidebands are measured at the OSA and the results appear in Fig. 3(a) . The optical carrier and the lower optical side band are 7 GHz apart while the upper optical side band is suppressed. We then measure the second and third harmonic powers to determine the OIP2

_{2H}and the OIP3

_{3H}of the link. The results are shown in Fig. 3(b). We find that the OIP2

_{2H}of the link is 55.3 dBm, which is 32.3 dB higher than the photodiode’s measured nonlinear response. For this to occur we must be cancelling the photodiode induced nonlinearity with the second harmonic generated by the DP-MZM. The measured OIP3

_{3H}is 17.6 dBm, which matches the OIP3

_{3H}of the photodiode and means the link distortion is limited by the photodiode. We note that both the second and third harmonic cannot be cancelled equally at the same time. While one can set the bias condition to cancel the photodiode induced third harmonic nonlinearity, doing so will cause the OIP2

_{2H}to decrease and become a limiting factor for the link. In this demonstration we focus on cancelling the photodiode induced second harmonic with the caveat that in this case the photodiode is still the limiting component in the link for the OIP3

_{3H}.

_{dc3}= 2π, ϕ

_{dc2}= 1.67π, and ϕ

_{dc1}= 2.17π and then tuned to minimize the second harmonic while maintaining the SSB modulation. Plugging these points into Eq. (12) does show that the second harmonics are out of phase and will cancel. A single point measurement shows that the OIP2

_{2H}of the link is 40 dBm, which is again much higher than the photodiode’s OIP2

_{2H}. However we see that measured output RF power of the fundamental is 10.7 dB lower in this case than in the previous case, as seen in Fig. 4 . The improvement in the RF output power can be seen in the optical spectrum which is shown as an inset of Fig. 4. Here the sideband is about 11.2 dB lower than in the previous case. This matches closely with the measured RF gain difference.

_{2H}of 20.4 dBm. Thus the link trades 6 dB of RF power at the fundamental for an increase of over 34 dB in the OIP2

_{2H}.

## 4. Conclusion

_{2H}of 50 dBm in the 1-2 GHz range [12

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]

_{2H}of 55.3 dBm. The OIP2

_{2H}of the links is 32.3 dBm higher than the measured OIP2

_{2H}of the photodiode by itself (23.0 dBm). The fundamental power of the link is 6.3 dB lower than the maximum RF fundamental power, but the OIP2

_{2H}of the link is 34.9 dB higher than in the maximum fundamental power condition. The improvement in OIP2

_{2H}is due to the photodiode-induced second harmonic being canceled by the second harmonic from the DP-MZM. In addition, the measured OIP3

_{3H}of the link is 17.6 dBm, which is limited by the photodiode’s nonlinearity. Another set of bias points can be found that also cancel the second harmonic nonlinearity. However the RF fundamental power is 10.7 dB lower than in the first case. The improvement in the RF output power is shown to match the difference in sideband-to-carrier power ratio for the two different bias conditions. The link can take advantage of SSB modulation to bypass chromatic dispersion penalties while also cancelling the second harmonic generated by the photodiode, without the need for balanced photodiodes. Such a system is useful for long-haul multioctave microwave links. While the photodiode-induced second and third harmonic nonlinearity cannot be simultaneously canceled at a single bias point, an optimization algorithm can be used to find a bias point that can partially cancel both nonlinearities at a single bias point. Future work can attempt to address this issue and compare the trade-offs with improving both OIP2

_{2H}and OIP3

_{3H}versus just one or the other.

## 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. |

2. | C. Chang, J. A. Cassaboom, and H. F. Taylor, “Fiber optic delay line devices for RF signal processing,” Electron. Lett. |

3. | R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech. |

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. |

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. |

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. |

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. |

8. | R. R. Hayes and D. L. Persechini, “Nonlinearity of p-i-n photodetectors,” IEEE Photon. Technol. Lett. |

9. | H. Jiang and P. K. L. Yu, “Equivalent circuit analysis of harmonic distortion in photodiodes,” IEEE Photon. Technol. Lett. |

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. |

11. | D. M. Pozar, |

12. | A. S. Hastings, D. A. Tulchinsky, and K. J. Williams, “Photodetector nonlinearities due to voltage-dependent responsivity,” IEEE Photon. Technol. Lett. |

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 |

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. |

15. | H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett. |

16. | G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron. |

17. | G. H. Smith, D. Novak, and Z. Ahmed, “Technique for optical SSB generation to overcome dispersion penalties in fibre-radio systems,” Electron. Lett. |

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. |

19. | S. K. Korotky and R. M. de Ridder, “Dual parallel modulation schemes for low-distortion analog optical transmission,” IEEE J. Sel. Areas Comm. |

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. | 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. | T. Kawanishi and M. Izutsu, “Linear single-sideband modulation for high-SNR wavelength conversion,” IEEE Photon. Technol. Lett. |

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 |

24. | K. J. Williams, R. D. Esman, and M. Dagenais, “Nonlinearities in p-i-n microwave photodetectors,” J. Lightwave Technol. |

**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

- 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]
- 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]
- R. A. Minasian, “Photonic signal processing of microwave signals,” IEEE Trans. Microw. Theory Tech.54(2), 832–846 (2006). [CrossRef]
- 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]
- 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]
- 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]
- 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).
- R. R. Hayes and D. L. Persechini, “Nonlinearity of p-i-n photodetectors,” IEEE Photon. Technol. Lett.5(1), 70–72 (1993). [CrossRef]
- 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]
- 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]
- D. M. Pozar, Microwave Engineering (Wiley, 1998)
- 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]
- 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.
- 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]
- H. Schmuck, “Comparison of optical millimeter-wave system concepts with regard to chromatic dispersion,” Electron. Lett.31(21), 1848–1849 (1995). [CrossRef]
- G. J. Meslener, “Chromatic dispersion induced distortion of modulated monochromatic light employing direct detection,” IEEE J. Quantum Electron.20(10), 1208–1216 (1984). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- T. Kawanishi and M. Izutsu, “Linear single-sideband modulation for high-SNR wavelength conversion,” IEEE Photon. Technol. Lett.16(6), 1534–1536 (2004). [CrossRef]
- 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]
- 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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