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 Optical Society of America
RF photonic links are currently used in microwave frequency applications such as antenna remoting , delay lines , signal processing , low phase noise RF generation [4,5] and frequency detection of RF signals [6,7]. Photonic techniques are preferred for performing these applications as they have broad instantaneous bandwidths, low loss and immunity to electromagnetic interference. The most common architecture for these links utilizes a Mach-Zehnder intensity modulator (MZM) to impose the RF signal onto the optical carrier. The MZM is used as it can be biased at quadrature in order to add no even-order distortion to the RF signal upon detection at a photodiode. However as the performance of these links increases, the photodiode-induced second order nonlinearity becomes a limiting factor. While traditional models have assumed that the photodiode acts as a linear device to recover the RF signal from the optical carrier upon which it was modulated, more in-depth studies have shown that this is not the case [8,9] and that the nonlinear photodiode will be limited by the second-order distortion . The nonlinearity of the photodiode is often measured by the output intercept point (OIPn), which is the output power at which the extrapolated power of the linear fundamental response and that of the n-th order distortion intersect [10,11]. In this particular case, we are interested in the second and third order harmonic distortions, which are described by the second and third order harmonic output intercept points (OIP22H, OIP33H), respectively. Work has been done to make photodiodes with better linearity, with reports of measured output intercept points of the second harmonic (OIP22H) of 50 dBm [12,13]. However these are non-commercial, specialty photodiodes and the measurements were limited to the 1-2 GHz frequency range. It is desirable to improve the nonlinear performance of commercially available photodiodes operating at higher frequencies. One method that had been shown to do this used a dual output MZM at quadrature bias with balanced detection to cancel the photodiode-induced second order nonlinearity in the HF frequency band . However phase matching two parallel links operating in the multi-gigahertz range and over long fiber lengths becomes a significant challenge. In addition, chromatic dispersion in long fiber links leads to additional problems such as RF fading  and added distortion  that need to be addressed.
Work has been shown with a modulator which incorporates two MZMs inside a third overall MZM structure known as the Dual Parallel Mach Zehnder Modulator (DP-MZM). This type of modulator allows for the generation of single sideband (SSB) modulated signals, which provides the advantage of overcoming penalties due to chromatic dispersion [17,18]. The use of two discrete MZMs in parallel has been previously investigated to linearize unwanted second and third order distortions due to the individual MZMs . Recent work has demonstrated high performance links using an integrated DP-MZM [20–22] and a coherent link with a polymeric DP-MZM . While these demonstrations have achieved high performance by cancelling the modulator nonlinearities, to the best of our knowledge, none have looked at cancelling the photodiode-induced second harmonic nonlinearities while maintaining SSB modulation.
We have designed a photonic link using a DP-MZM for single side band modulation that can cancel the photodiode-induced second harmonic distortion. A mathematical description shows the generated second harmonic from the DP-MZM is 180 degrees out of phase with the second harmonic generated by the photodiode nonlinearity. By doing this we measure an OIP22H 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
The photonic link using the DP-MZM appears in Fig. 1 . The output of the DP-MZM (JDSU Part No. 21101281-010, RF bandwidth of 20 GHz) is connected to an EDFA whose output goes to a 90/10 coupler. The 10% output is connected to an optical spectrum analyzer (OSA) to monitor the carrier and the SSB modulation while the 90% output is sent to the photodiode. The detected RF signal is measured with an electrical spectrum analyzer (ESA). The inset in Fig. 1 shows the schematic of the DP-MZM. Each of the smaller MZMs has a DC bias and an RF input to modulate the optical carrier, labeled as ϕdc1,2 and ϕrf1,2, respectively. The overall MZM has a DC bias control to provide a phase shift between the two smaller MZMs, labeled as ϕdc3. Note and , where Vπ,dc is the DC voltage required for π phase shift and Vπ,rf(Ωrf) is the RF voltage required for π phase shift at an RF angular frequency Ωrf. 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 , we start with the field at the input of the DP-MZM as, where ωο is the angular frequency of the laser, κ is a constant relating the average laser power Plaser to the field amplitude such that After the initial Y-branch split at the beginning of the DP-MZM the two resulting fields are and , with the former entering the upper MZM and the latter entering the lower MZM. The transfer matrices for each of the MZMs can be written asEq. (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
Rewriting Eq. (4) with the definitions of ϕ1(t) and ϕ2(t) as given above and making use of the Jacobi Anger expansions and gives the followingEq. (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
Taking the field in Eq. (4) and multiplying by its complex conjugate to get the optical power from the DP-MZM yieldsEq. (8) asEqs. (10a) and (10b) and then just looking at the DC, fundamental and second harmonic power, the following can be writtenEq. (12), the phase between the fundamental and the second harmonic can be adjusted by simply changing ϕdc1,2,3. 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
Re-writing Eq. (12) for the optical power of the fundamental in terms of a single sine function, we getEq. (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 ϕdc3 = 1.555π, ϕdc2 = 1.95π, and ϕdc1 = 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 ϕdc3 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
To begin, the nonlinearity of the 30μm diameter photodiode (Discovery DSC-30S) has to be measured. Using a three-laser heterodyne phase-locked loop setup , at an RF frequency of 7 GHz and a time-averaged photocurrent of approximately 8 mA, the second and third order nonlinearity is measured and shown in Fig. 2 . From these results, the output intercept point of the second harmonic (OIP22H) is 23.0 dBm and the output intercept point of the third harmonic (OIP33H) 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 ϕdc3 and ϕdc1 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 OIP22H and the OIP33H of the link. The results are shown in Fig. 3(b). We find that the OIP22H 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 OIP33H is 17.6 dBm, which matches the OIP33H 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 OIP22H 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 OIP33H.
As mentioned above there is more than one bias condition that will allow for second harmonic cancellation while maintaining the single side band requirement. Exploring different bias conditions, we find a second operating point where the nonlinearity is cancelled. In the second condition, the biases are set to ϕdc3 = 2π, ϕdc2 = 1.67π, and ϕdc1 = 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 OIP22H of the link is 40 dBm, which is again much higher than the photodiode’s OIP22H. 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.
As a final point of comparison, Fig. 5 shows the maximum RF power of the fundamental using SSB modulation for the link as compared to the RF power of the fundamental when the second harmonic is cancelled. The maximum RF power is −10.3 dBm which is 6.3 dB higher than in the case when the second harmonic is cancelled. However as shown in the inset of Fig. 5, the second harmonic RF power is −41 dBm, which gives a single point OIP22H 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 OIP22H.
A photonic link utilizing SSB modulation from a DP-MZM can cancel photodiode-induced second harmonic nonlinearities. While specialty photodiodes have been shown to have OIP22H of 50 dBm in the 1-2 GHz range [12,13], it is desirable to use cheaper, commercially available photodiodes at higher frequencies and get the same or better nonlinear performance. A theoretical analysis shows that by correctly setting the three bias points in the DP-MZM, the second harmonic from the DP-MZM can be set 180 degrees out of phase with the photodiode-induced second harmonic due to the incoming fundamental signal. A photonic link is then experimentally demonstrated with a measured OIP22H of 55.3 dBm. The OIP22H of the links is 32.3 dBm higher than the measured OIP22H 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 OIP22H of the link is 34.9 dB higher than in the maximum fundamental power condition. The improvement in OIP22H is due to the photodiode-induced second harmonic being canceled by the second harmonic from the DP-MZM. In addition, the measured OIP33H 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 OIP22H and OIP33H 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. 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]