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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 20999–21009
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SFDR enhancement in analog photonic links by simultaneous compensation for dispersion and nonlinearity

Zhiyu Chen, Lianshan Yan, Wei Pan, Bin Luo, Xihua Zou, Yinghui Guo, Hengyun Jiang, and Tao Zhou  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 20999-21009 (2013)
http://dx.doi.org/10.1364/OE.21.020999


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Abstract

A method to improve the spurious-free dynamic range (SFDR) of analog photonic links has been proposed and experimentally demonstrated, which only consists of a phase modulator (PM), a polarizer and an optical filter. Such structure could compensate for the chromatic dispersion and the nonlinearity of the modulator simultaneously. In addition, by adjusting the states of polarization (SOPs) launching into the PM and the polarizer, the proposed scheme could also be reconfigured to mitigate the second harmonic nonlinearity induced by the photodetector. Experimental results show that the suppressions of the second-order and third-order intermodulation distortions (IMD2 & IMD3) are larger than 14-dB and 25.4-dB, respectively. Furthermore, the SFDR can achieve ~110-dB·Hz4/5 for 40-km fiber transmission, which is 26-dB higher than that of the link without compensation.

© 2013 OSA

1. Introduction

2. Principle and theoretical model of the proposed link

The schematic diagram of the proposed APL is shown in Fig. 1
Fig. 1 Schematic diagram of the proposed APL. PM: phase modulator; DSB: double sideband; OC: optical carrier.
. When a linearly polarized incident light is oriented at an angle of θ to one principal axis of the PM, two modes (TE and TM) with different electro-optic coefficient are generated along two principal axes. The normalized optical field at the output of the PM can be expressed as
E1=x^cosθexpj[ωct+γmsin(Ωt)]+y^sinθexpj[ωct+msin(Ωt)].
(1)
where ωc is the angular frequency of the optical carrier, γ is the electro-optic ratio, Ω is the microwave frequency, and m is the TM modulation depth, which is defined as
m=πV0Vπ.
(2)
where Vπ is the half-wave voltage of the phase modulator.

When the signal is sent to a polarizer with its principal axis oriented at angle of α to one principal axis of the PM, we obtain

E2=[cosαcosθexpjγmsin(Ωt)+sinαsinθexpjmsin(Ωt)]exp(jωct).
(3)

Applying the Jacobi-Anger expansion to Eq. (3), E2 can be rewritten as

E2=n=+[cosαcosθJn(γm)+sinαsinθJn(m)]expj(ωc+nΩ)t.
(4)

Afterwards, an optical bandpass filter is used to suppress one of sidebands. Here, the optical filter can be mathematically modeled by excluding those terms in Eq. (4) for which n<0. Finally, the optical field is detected by a square-law photodetecor with responsivity to produce a photocurrent, which is given by

i=lnl0,n0{cos2αcos2θJn(γm)Jl(γm)+cosαcosθsinαsinθJn(γm)Jl(m)+cosαcosθsinαsinθJl(γm)Jn(m)+sin2αsin2θJn(m)Jl(m)}expj(ln)Ωt.
(5)

To investigate the linearity of the modulator, we only consider the terms in Eq. (5) that are oscillating at the frequency of Ω. This is equivalent to the summation of the terms for which | l-n | = 1, i.e.

i|ω=Ω=l0,n=l+1{cos2αcos2θJl+1(γm)Jl(γm)+cosαcosθsinαsinθJl+1(γm)Jl(m)+cosαcosθsinαsinθJl(γm)Jl+1(m)+sin2αsin2θJl+1(m)Jl(m)}exp(jΩt)+L1,Ν=L1{cos2αcos2θJL1(γm)JL(γm)+cosαcosθsinαsinθJL1(γm)JL(m)+cosαcosθsinαsinθJL(γm)JL1(m)+sin2αsin2θJL1(m)JL(m)}exp(jΩt).
(6)

According to the restricted condition in Eq. (6), such expression can be rewritten as follows when l is set to be 0 and 1, while L equals to 1 and 2, respectively.

i|ω=Ω=2{cos2αcos2θJ1(γm)J0(γm)+cosαcosθsinαsinθJ1(γm)J0(m)+cosαcosθsinαsinθJ0(γm)J1(m)+sin2αsin2θJ1(m)J0(m)}cos(Ωt)+2{cos2αcos2θJ2(γm)J1(γm)+cosαcosθsinαsinθJ2(γm)J1(m)+cosαcosθsinαsinθJ1(γm)J2(m)+sin2αsin2θJ2(m)J1(m)}cos(Ωt).
(7)

Expanding Eq. (7) to the third-order in m yields by using the Taylor series (i.e. J0(x) = 1-(x/2)2, J1(x) = [x-(x/2)3]/2 and J2(x) = (x/2)2/2), the photocurrent i can be simplified as

i|ω=Ω={cos2αcos2θ[1(γm/2)2][γm(γm/2)3]+cosαcosθsinαsinθ[1(m/2)2][γm(γm/2)3]+cosαcosθsinαsinθ[1(γm/2)2][m(m/2)3]+sin2αsin2θ[1(m/2)2][m(m/2)3]}cosΩt+{cos2αcos2θ[γm(γm/2)3](γm)2/8+cosαcosθsinαsinθ[m(m/2)3](γm)2/8+cosαcosθsinαsinθ[γm(γm/2)3]m2/8+sin2αsin2θ[m(m/2)3]m2/8}cosΩt.
(8)

The nonlinearity of the modulator only depends on the cubic term in Eq. (8), thus

i3th={cos2αcos2θ(γm)3/4+sin2αsin2θm3/4+cosαcosθsinαsinθ[γ3+γ2+γ+1](m/2)3}.
(9)

From Eq. (9), the term proportional to m3 corresponds to the main distortion. The third-order intermodulation distortion is associated with the nonlinear transfer function of the modulator. According to the [13

13. M. H. Huang, J. B. Fu, and S. L. Pan, “Linearized analog photonic links based on a dual-parallel polarization modulator,” Opt. Lett. 37(11), 1823–1825 (2012). [CrossRef] [PubMed]

], we assume that the electro-optic ratio γ is 1/3. Thus, the contribution to the signal distortion can be eliminated (i.e. i3th = 0) by appropriately adjusting the two incident polarization angles (α&θ), which leads to the following linearization conditions:

tan(α)tan(θ)=0.0542ortan(α)tan(θ)=0.6868.
(10)

Apparently, these equations do not have a unique solution for α and θ, which indicates that the linearization condition can be easily achieved. Among all the solutions for α and θ, there is one optimal one that maximizes the component proportional to m (fundamental component) while canceling the components proportional to m3 (third-order components). Therefore, we could try to obtain the optimal solution for the proposed link.

According to the Eqs. (8) and (10), the time-averaged converted electrical output power at Ω through an impedance Zout can be expressed as

Pout=(i|ω=Ω)2Zout=12Zout2[γmcos2αcos2θ+(γm+m)cosαcosθsinαsinθ+msin2αsin2θ]2.
(11)

In addition, using Eq. (2), the time-averaged input microwave power at frequency of Ω through an impedance Zin is given by

Pin=12Zin(mVππ)2.
(12)

G=PoutPin=ZinZout(πVπ)2[γ+(γ+1)tanαtanθ+tan2αtan2θ]2(tan2α+1)(tan2θ+1).
(13)

Therefore, the gain is maximized for the condition of tan2(α) = tan2(θ). In addition, combining Eq. (10) with Eq. (13), one optimal solution is obtained as

α=θ=0.692rad.
(14)

As a result, the nonlinearity of the modulator is compensated by adjusting the polarization angles launched into the PM and the polarizer. Meanwhile, the CD-induced power fading can also be canceled because of the SSB modulation in the proposed link.

The above theoretical derivation can be described by a physical explanation as shown in the inset of Fig. 1. Since the orthogonal TE and TM fields have different modulation depths inside the phase modulator, they will carry different amounts of IMD3 at the output of the PM. By properly selecting the SOPs launching into the PM and the polarizer (i.e. α & θ), and tuning the centre wavelength and bandwidth of the optical filter, the combined IMD3 components can be cancelled each other at the output polarizer. Therefore, we obtain the APL with high linearization.

i|ω=2Ω=l0,n=l+2{cos2αcos2θJl+2(γm)Jl(γm)+cosαcosθsinαsinθJl+2(γm)Jl(m)+cosαcosθsinαsinθJl(γm)Jl+2(m)+sin2αsin2θJl+2(m)Jl(m)}exp(jΩt)+L2,Ν=L2{cos2αcos2θJL2(γm)JL(γm)+cosαcosθsinαsinθJL2(γm)JL(m)+cosαcosθsinαsinθJL(γm)JL2(m)+sin2αsin2θJL2(m)JL(m)}exp(jΩt).
(15)

When l = 0 and L = 2, the above equation is expanded as follows by using the Taylor series:

i|ω=2Ω={cos2αcos2θ[1(γm/2)2](γm/2)2+cosαcosθsinαsinθ[1(γm/2)2](m/2)2+cosαcosθsinαsinθ[1(m/2)2](γm/2)2+sin2αsin2θ[1(m/2)2](m/2)2}cos2Ωt.
(16)

Ignoring the higher order components, the second harmonic distortion can be simplified as

i|ω=2Ω={cos2αcos2θ(γm/2)2+cosαcosθsinαsinθ(m/2)2+cosαcosθsinαsinθ(γm/2)2+sin2αsin2θ(m/2)2}cos2Ωt.
(17)

The second-order intermodulation distortion is associated with the nonlinear transfer function of the PD. Such distortion can be eliminated (i.e. i2th = 0) by also adjusting the polarization angles αandθ, which leads to the conditions:

tan(α)tan(θ)=γ2ortan(α)tan(θ)=1.
(18)

3. Experimental setup and results

To verify the proposed scheme, we build the experimental setup as shown in Fig. 3
Fig. 3 Experimental setup for the proposed APL. PC: polarization controller; PM: phase modulator; EDFA: erbium-doped fiber amplifier; SMF: single-mode fiber; VNA: vector network analyzer; ESA: electrical spectrum analyzer.
. It only consists of two polarization controllers (PCs), a PM, a polarizer and an optical filter. Firstly, a laser at 1550-nm with the power of 8-dBm is modulated by the PM, driven by a sinusoidal RF signal with a certain frequency. The incident light could be divided into two orthogonal polarizations inside the phase modulator, named as TM mode and TE mode. The splitting ratio of two modes depends on the SOP of the incident light, which is controlled by PC1. After the RF signal is modulated on to the two polarizations, TE and TM fields are combined at the output of polarizer through PC2. Here, the principal axis of polarizer is adjusted to be α with respect to that of PM by PC2. Subsequently an optical filter with a 0.8-nm bandwidth and an erbium-doped fiber amplifier (EDFA) are used to achieve the SSB modulation and compensate for the signal loss during the transmission along the SMF, respectively. After 40-km SMF transmission, the signal is detected by a photodetector (PD, HP 11982A) with the 3-dB bandwidth of 15-GHz. Finally, the frequency response of the APL is measured by the vector network analyzer (VNA, HP 8720D), whose RF output power is set to be 0-dBm, and the SFDR is measured by the electrical spectrum analyzer (ESA, HP 8593E).

4. Conclusion

Acknowledgments

This research is supported by the National Basic Research Program of China (2012CB315704), the Natural Science Foundation of China (No. 61275068, 61111140390), the Key Grant Project of Chinese Ministry of Education under Grant 313049, the 2013 Doctoral Innovation funds of Southwest Jiaotong University and the Fundamental Research Funds for the Central Universities.

References and links

1.

A. Seeds and K. J. Williams, “Microwave photonics,” J. Lightwave Technol. 24(12), 4628–4641 (2006). [CrossRef]

2.

J. P. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]

3.

Z. Y. Chen, L. S. Yan, J. Ye, W. Pan, B. Luo, X. H. Zou, Y. H. Guo, and H. Y. Jiang, “Pre-distortion compensation of dispersion in APL based on DSB modulation,” IEEE Photon. Technol. Lett. 25(12), 1129–1132 (2013). [CrossRef]

4.

A. Agarwal, T. Banwell, P. Toliver, and T. K. Woodward, “Predistortion compensation of nonlinearities in channelized RF photonic links using a dual-port optical modulator,” IEEE Photon. Technol. Lett. 23(1), 24–26 (2011). [CrossRef]

5.

G. Q. Zhang, X. P. Zheng, S. Y. Li, H. Y. Zhang, and B. K. Zhou, “Postcompensation for nonlinearity of Mach-Zehnder modulator in radio-over-fiber system based on second-order optical sideband processing,” Opt. Lett. 37(5), 806–808 (2012). [CrossRef] [PubMed]

6.

E. I. Ackerman, “Broad-band linearization of a Mach-Zehnder electrooptic modulator,” IEEE Trans. Microw. Theory Tech. 47(12), 2271–2279 (1999). [CrossRef]

7.

T. S. Cho and K. Kim, “Effect of third-order intermodulation on radio-over-fiber systems by a dual-electrode Mach–Zehnder modulator with ODSB and OSSB signals,” J. Lightwave Technol. 24(5), 2052–2058 (2006). [CrossRef]

8.

G. E. Betts, “Linearized modulator for suboctave-bandpass optical analog links,” IEEE Trans. Microw. Theory Tech. 42(12), 2642–2649 (1994). [CrossRef]

9.

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]

10.

Q. Lv, K. Xu, Y. T. Dai, Y. Li, J. Wu, and J. T. Lin, “I/Q intensity-demodulation analog photonic link based on polarization modulator,” Opt. Lett. 36(23), 4602–4604 (2011). [CrossRef] [PubMed]

11.

C. Lim, A. Nirmalathas, K.-L. Lee, D. Novak, and R. Waterhouse, “Intermodulation distortion improvement for fiber–radio applications incorporating OSSB+C modulation in an optical integrated-access environment,” J. Lightwave Technol. 25(6), 1602–1612 (2007). [CrossRef]

12.

B. Masella, B. Hraimel, and X. Zhang, “Enhanced spurious-free dynamic range using mixed polarization in optical single sideband Mach-Zehnder modulator,” J. Lightwave Technol. 27(15), 3034–3041 (2009). [CrossRef]

13.

M. H. Huang, J. B. Fu, and S. L. Pan, “Linearized analog photonic links based on a dual-parallel polarization modulator,” Opt. Lett. 37(11), 1823–1825 (2012). [CrossRef] [PubMed]

14.

T. R. Clark and M. L. Dennis, “Coherent optical phase-modulation link,” IEEE Photon. Technol. Lett. 19(16), 1206–1208 (2007). [CrossRef]

15.

B. M. Haas and T. E. Murphy, “A simple, linearized, phase-modulated analog optical transmission system,” IEEE Photon. Technol. Lett. 19(10), 729–731 (2007). [CrossRef]

16.

V. J. Urick, F. Bucholtz, P. S. Devgan, J. D. McKinney, and K. J. Williams, “Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” Trans. Micro. Theo. Tech. 55(9), 1978–1985 (2007). [CrossRef]

17.

L. M. Johnson and H. V. Roussell, “Reduction intermodulation distortion in interferometric optical modulators,” Opt. Lett. 13(10), 928–930 (1988). [CrossRef] [PubMed]

18.

A. Ramaswamy, L. A. Johansson, J. Klamkin, H.-F. Chou, C. Sheldon, M. J. Rodwell, L. A. Coldren, and J. E. Bowers, “Integrated coherent receivers for high-linearity microwave photonic links,” J. Lightwave Technol. 26(1), 209–216 (2008). [CrossRef]

19.

V. R. Pagán, B. M. Haas, and T. E. Murphy, “Linearized electrooptic microwave downconversion using phase modulation and optical filtering,” Opt. Express 19(2), 883–895 (2011). [CrossRef] [PubMed]

20.

P. Li, L. S. Yan, T. Zhou, W. Li, Z. Y. Chen, W. Pan, and B. Luo, “Improvement of linearity in phase-modulated analog photonic link,” Opt. Lett. 38(14), 2391–2393 (2013). [CrossRef] [PubMed]

21.

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]

22.

P. S. Devgan, A. S. Hastings, V. J. Urick, and K. J. Williams, “Cancellation of photodiode-induced second harmonic distortion using single side band modulation from a dual parallel Mach-Zehnder,” Opt. Express 20(24), 27163–27173 (2012). [CrossRef] [PubMed]

OCIS Codes
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems
(060.5060) Fiber optics and optical communications : Phase modulation
(350.4010) Other areas of optics : Microwaves

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: June 18, 2013
Revised Manuscript: August 20, 2013
Manuscript Accepted: August 22, 2013
Published: August 30, 2013

Citation
Zhiyu Chen, Lianshan Yan, Wei Pan, Bin Luo, Xihua Zou, Yinghui Guo, Hengyun Jiang, and Tao Zhou, "SFDR enhancement in analog photonic links by simultaneous compensation for dispersion and nonlinearity," Opt. Express 21, 20999-21009 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20999


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References

  1. A. Seeds and K. J. Williams, “Microwave photonics,” J. Lightwave Technol.24(12), 4628–4641 (2006). [CrossRef]
  2. J. P. Yao, “Microwave photonics,” J. Lightwave Technol.27(3), 314–335 (2009). [CrossRef]
  3. Z. Y. Chen, L. S. Yan, J. Ye, W. Pan, B. Luo, X. H. Zou, Y. H. Guo, and H. Y. Jiang, “Pre-distortion compensation of dispersion in APL based on DSB modulation,” IEEE Photon. Technol. Lett.25(12), 1129–1132 (2013). [CrossRef]
  4. A. Agarwal, T. Banwell, P. Toliver, and T. K. Woodward, “Predistortion compensation of nonlinearities in channelized RF photonic links using a dual-port optical modulator,” IEEE Photon. Technol. Lett.23(1), 24–26 (2011). [CrossRef]
  5. G. Q. Zhang, X. P. Zheng, S. Y. Li, H. Y. Zhang, and B. K. Zhou, “Postcompensation for nonlinearity of Mach-Zehnder modulator in radio-over-fiber system based on second-order optical sideband processing,” Opt. Lett.37(5), 806–808 (2012). [CrossRef] [PubMed]
  6. E. I. Ackerman, “Broad-band linearization of a Mach-Zehnder electrooptic modulator,” IEEE Trans. Microw. Theory Tech.47(12), 2271–2279 (1999). [CrossRef]
  7. T. S. Cho and K. Kim, “Effect of third-order intermodulation on radio-over-fiber systems by a dual-electrode Mach–Zehnder modulator with ODSB and OSSB signals,” J. Lightwave Technol.24(5), 2052–2058 (2006). [CrossRef]
  8. G. E. Betts, “Linearized modulator for suboctave-bandpass optical analog links,” IEEE Trans. Microw. Theory Tech.42(12), 2642–2649 (1994). [CrossRef]
  9. 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]
  10. Q. Lv, K. Xu, Y. T. Dai, Y. Li, J. Wu, and J. T. Lin, “I/Q intensity-demodulation analog photonic link based on polarization modulator,” Opt. Lett.36(23), 4602–4604 (2011). [CrossRef] [PubMed]
  11. C. Lim, A. Nirmalathas, K.-L. Lee, D. Novak, and R. Waterhouse, “Intermodulation distortion improvement for fiber–radio applications incorporating OSSB+C modulation in an optical integrated-access environment,” J. Lightwave Technol.25(6), 1602–1612 (2007). [CrossRef]
  12. B. Masella, B. Hraimel, and X. Zhang, “Enhanced spurious-free dynamic range using mixed polarization in optical single sideband Mach-Zehnder modulator,” J. Lightwave Technol.27(15), 3034–3041 (2009). [CrossRef]
  13. M. H. Huang, J. B. Fu, and S. L. Pan, “Linearized analog photonic links based on a dual-parallel polarization modulator,” Opt. Lett.37(11), 1823–1825 (2012). [CrossRef] [PubMed]
  14. T. R. Clark and M. L. Dennis, “Coherent optical phase-modulation link,” IEEE Photon. Technol. Lett.19(16), 1206–1208 (2007). [CrossRef]
  15. B. M. Haas and T. E. Murphy, “A simple, linearized, phase-modulated analog optical transmission system,” IEEE Photon. Technol. Lett.19(10), 729–731 (2007). [CrossRef]
  16. V. J. Urick, F. Bucholtz, P. S. Devgan, J. D. McKinney, and K. J. Williams, “Phase modulation with interferometric detection as an alternative to intensity modulation with direct detection for analog-photonic links,” Trans. Micro. Theo. Tech.55(9), 1978–1985 (2007). [CrossRef]
  17. L. M. Johnson and H. V. Roussell, “Reduction intermodulation distortion in interferometric optical modulators,” Opt. Lett.13(10), 928–930 (1988). [CrossRef] [PubMed]
  18. A. Ramaswamy, L. A. Johansson, J. Klamkin, H.-F. Chou, C. Sheldon, M. J. Rodwell, L. A. Coldren, and J. E. Bowers, “Integrated coherent receivers for high-linearity microwave photonic links,” J. Lightwave Technol.26(1), 209–216 (2008). [CrossRef]
  19. V. R. Pagán, B. M. Haas, and T. E. Murphy, “Linearized electrooptic microwave downconversion using phase modulation and optical filtering,” Opt. Express19(2), 883–895 (2011). [CrossRef] [PubMed]
  20. P. Li, L. S. Yan, T. Zhou, W. Li, Z. Y. Chen, W. Pan, and B. Luo, “Improvement of linearity in phase-modulated analog photonic link,” Opt. Lett.38(14), 2391–2393 (2013). [CrossRef] [PubMed]
  21. 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]
  22. P. S. Devgan, A. S. Hastings, V. J. Urick, and K. J. Williams, “Cancellation of photodiode-induced second harmonic distortion using single side band modulation from a dual parallel Mach-Zehnder,” Opt. Express20(24), 27163–27173 (2012). [CrossRef] [PubMed]

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