We propose a linearized optical single sideband Mach-Zehnder electro-optic modulator (MZ-EOM) for radio over fiber systems. This proposed modulator utilizes a dual-electrode MZ-EOM biased at quandrature, the two electrodes are fed with asymmetrical RF power through an 180° hybrid coupler and the two optical ports of MZ-EOM are bi-directionally injected by the same optical source, but with different optical power. Using such a modulator, third order nonlinear distortion is significantly suppressed and relative spurious free dynamic range is improved by 10 and 20 dB compared to dual-parallel linearized MZ-EOM and conventional MZ-EOM, respectively.
©2008 Optical Society of America
Subcarrier modulation (SCM) in optical fiber access systems has gained tremendous interest, because of its potential for cost reduction in cellular and broadband access networks. An analog photonic link requires a high degree of system linearity to reduce the impact of nonlinear distortion and achieve desired performance. Otherwise, nonlinear distortion will seriously degrade system performance. One introduction of system nonlinearity is due to the optical modulator in analog photonic systems. Specifically, the optical modulator has generally a nonlinear response, possibly inducing harmonic distortion (HD) and intermodulation distortion (IMD). Many techniques for reducing nonlinear distortion induced by the nonlinear response of the optical modulator have been investigated, such as the predistortion method , the adaptive pre-distortion method , the feed forward linearization technique  and balanced detection . However, these linearization techniques are all devised at the system level and make the system complicated. In other words, it is more desirable that linearization is realized at the component level. Indeed, linearized optical modulators were proposed and investigated. A linearized modulator, made with dual-parallel MZ-EOMs connected with two Y-junctions, was proposed . In this modulator, RF power feeding the two independent MZ-EOMs has a power splitting ratio of 1:γ 2, where γ>1 and constant. Also, the upper MZ-EOM is biased at positive quadrature and the lower MZ-EOM is biased at negative quadrature. Moreover, the Y-junction has a power splitting ratio of 1:γ 3. Because third-order IMD (3IMD) generated in dual MZ-EOMs are 180° out of phase from one another, 3IMD is suppressed along with a small cancellation of optical subcarrier power . This modulator is referred to as the dual-parallel MZ-EOM here. The main technical limitation of the dual-parallel MZ-EOM is that the two independent MZ-EOMs must be matched in optical transfer function and phase between the two independent MZ-EOMs, otherwise the suppression of nonlinear distortion will be seriously degraded. Intuitively it is very difficult for two independent MZ-EOMs to have the same frequency response and for phase imbalance between the two independent MZ-EOMs to be kept minimal. Therefore, it is difficult to realize a significant suppression of 3IMD practically. Later, an alternative linearized modulator using a single MZ-EOM within a Sagnac interferometer with polarization manipulation was proposed , in which optical double sideband (ODSB) modulation is obtained. It is well known that optical single sideband (OSSB) modulation for SCM is preferred for analog photonic systems to minimize the impact of fiber chromatic dispersion [7–10].
In this paper, we propose a linearized modulator, which utilizes a dual-electrode MZ-EOM to achieve OSSB SCM with 3IMD suppression and thus spurious free dynamic range (SFDR) is improved. We compare our proposed modulator with the dual-parallel MZ-EOM in the suppression of 3IMD and improvement of SFDR. In addition we also compare the SFDR performance using our proposed modulator to the conventional MZ-EOM.
2. Proposed Linearized OSSB MZ-EOM
The proposed OSSB linearized MZ-EOM is shown in Fig. 1, which is comprised mainly of a dual electrode MZ-EOM, two optical circulators and a 3-dB optical combiner. It is seen that a CW light is injected bi-directionally into the two optical ports with a power splitting ratio of 1:γ 3. The two lights travel over the MZ-EOM bi-directionally and then the two outputs via optical circulators are combined with a 3-dB optical combiner. Transmitted RF signals are first divided into two parts and relatively phase-shift by π/2 from one another, then each passes through a 180° hybrid electrical coupler (HEC) and the two outputs of each hybrid coupler are inputs to the two RF input ports with a voltage splitting ratio of 1:γ. The lower branch of the MZ-EOM is biased at quandrature. Compared to the dual-parallel MZ-EOM, the disadvantage of this proposed modulator is that dual RF ports in each MZ electrode are required. It is obvious that optical field in each direction experiences two co- and two counter- propagating electric fields induced by the RF signals. When the optical field copropagates with the RF signal, optical modulation occurs just like in a normal MZ-EOM. However, it was shown that modulation efficiency is severely reduced when the optical field counter-propagates with the RF signal induced electric field for RFs above 2 GHz . Therefore, the counter-modulation response of MZ-EOM can be neglected for RFs of 2 GHz and beyond. Suppose that two RF signals with frequencies of Ω 1 and Ω 2, both larger than 2 GHz, drive the two HECs simultaneously. The two driving voltages for the upper and lower HECs can be written, in a normalized form, as Vu(t)=π[V 0 (sin(Ω 1 t)+sin(Ω 2 t))]/Vπ and Vl(t)=π[V 0 (cos(Ω 1 t)+cos(Ω 2 t))]/V π, where V 0 is the RF signal voltage magnitude and Vπ is the half wave switching voltage for the MZ-EOM. So the RF signals appearing at the two output ports are V u,180°(t)=-m(sin(Ω1 t)+sin(Ω2 t)) and Vu,γ(t)=γm(sin(Ω1 t)+sin(Ω2 t)) for the upper HEC and V l,180°(t)=-m(cos(Ω1 t)+cos(Ω2 t))-π/2, and V l,γ(t)=γm(cos(Ω1 t)+cos(Ω2 t))-π/2 for the lower HEC as shown in Fig. 1, where m=πV 0/Vπ is the modulation index. The output electric fields emitting from the left side optical port of the MZ-EOM just before reaching the MZ-EOM’s optical coupler is for the upper branch and for the lower branch, where ω is the angular optical frequency. Similarly, the output electric fields emitting from the right side optical port are given by for the upper branch and for the lower branch. ELeft and ERight are the output electric field amplitudes for the optical light applied to the left and right side optical ports of the MZ-EOM. The total output electric field at the output of the optical combiner is then given by,
Using the Jacobi-Anger expansion and considering first-order terms only, Eq. (1) can be expressed by,
where J 1( ) is the first order Bessel function. Note, that only the upper sideband exists as seen by the term in Eq. (2), hence OSSB. To verify the above theory, we modeled a radio over fiber (RoF) system using such a modulator driven by two RF signals at 10 and 12 GHz.
The simulated output optical spectrum is shown in Fig. 2 for a radio over fiber system using the proposed modulator with γ=1.9 for (a) and γ=2.8 for (b). It is observed that only the upper sideband of the two optical subcarrier components at 10 and 12 GHz exists, i.e. OSSB modulation, in addition to other distortion components. Also it is seen that two IMDs at 8 and 14 GHz in Fig. 2(a) are close to the two optical subcarriers. Thus, the two IMDs are detrimental to both the optical subcarriers. Therefore it is desirable that these IMDs are suppressed. We have set γ=1.9, i.e. a non-optimal value, so that in Fig. 2(a) CTB of -20.4 dBc is obtained. We then set γ=2.8, i.e. the optimal value, and Fig. 2(b) shows that the CTB of -39.2 dBc is obtained. This shows an improvement in CTB of approximately 19 dB is obtained. We must also note from Fig. 2(b) that we have approximately a 10 dB loss in RF subcarrier power due to linearization. The simulations were carried out with VPI TransmissionMaker 7.5.
To show the cancellation of 3IMD, we looked at the combined optical power. The optical power emitted from the left side optical port of the MZ-EOM just before reaching the left optical circulator is and optical power emitted from the right side optical port of the MZ-EOM just before reaching the right optical circulator is . The total combined optical power is given by, POut(t)=[PLeft(t)+PRight(t)]/2. Considering the above, we obtain the output optical power in detail as . Using the Taylor series approximation until the third term, we obtain the output optical power given by, . By simple mathematic manipulation, the expression for the output optical power is simplified into
where cubic terms are related to the third order nonlinear distortion, which can be approximately cancelled if the condition of PLeft/PRight=γ 3 is satisfied, where PLeft and PRight are the unmodulated optical power applied to the left and right optical ports of the MZ-EOM, respectively. Considering the condition of PRight=PLeft/γ 3, we obtain , where the average optical power for the optical carrier is and the optical subcarrier power for the RF signal is . This leads to a linearized modulation index of . The relationship for the linearized modulation index normalized with unlinearized modulation index is given by
Equation (4) shows that mlin/m is always less than unity for γ>1. This suggests that the suppression of 3IMD will also lead to a decrease of optical modulation index. In other words, the optical subcarrier power for the RF signal is also suppressed with the suppression of 3IMD. We used the linearized optical modulation index to express the real optical modulation index. It is seen that the linearized optical modulation index is decreased by a factor of γ(γ-1)(1-γ+γ 2) due to linearization, the same as in the parallel MZ-EOM . Figure 3(a) shows the simulated RF carrier electrical power and suppression of CTB with RF splitting voltage ratio γ. It is seen that the maximum RF carrier power is obtained at γ=1.9 and the maximum suppression of CTB is obtained at γ=2.8. Thus, the maximum RF carrier power and linearization are not obtained simultaneously. Figure 3(b) shows the ratio of mlin/m in percentage versus γ. It is obvious that with the increase of γ, the linearized optical modulation index approaches the unlinearized optical modulation index. This suggests that the proposed linearized MZ-EOM in Fig. 1 is equivalent to the conventional MZ-EOM if γ is very high, such as 10.
Only considering terms up to the third order, Eq. (3) represents the summation of the left and right modulated optical powers emitted from the MZ-EOM, where we assume an ideal MZ-EOM is used. If we consider the use of a non-ideal MZ-EOM, then a phase difference of Δφ between PLeft(t) and PRight(t) exists before the 3-dB optical combiner, which leads to a phase imbalance between the bi-directional transmissions of the MZ-EOM. The optical output power after the optical coupler is now given by,
where mlin=π(Vu(t)-Vl1(t))/Vπ is the linearized modulation index. Substituting the ideal condition for 3IMD cancellation of PRight=PLeft/γ 3 and normalizing with respect to PLeft in Eq. (5), then we obtain the normalized optical output power, , where the component proportional to mlin is the optical subcarrier power PRFsub for the RF signal, the component proportional to m 3 lin is the optical 3IMD power P3IMD and the final component is the optical carrier power Pcarrier. Considering square-law photo-detection, the normalized electrical power for the RF signal is and electrical power for the 3IMD is . To obtain the expression of SFDR, it is required to solve the Eq. for P 3IMD,elec,norm=noise floor, for mlin. Then the SFDR is obtained by the difference between PRF,elec,norm and the noise floor, where it will become a function of Δφ. Utilizing Mathematica 6.0 and solving noise floor, for mlin, we obtain one real solution, i.e. , which leads to the expression of SFDR related to Δφ,
If we let γ=2.8 and scale using PLeft=1 mW in Eq. (6), then SFDR [dB]=-10 log[2.352×10-6Δφ 2] is obtained. Figure 4(a) shows the SFDR versus Δφ for the proposed OSSB dual electrode MZ-EOM. It is seen that SFDR is considerably decreased with the increase of Δφ. Note, in theory as Δφ→0 the best linearization is achieved and at Δφ=π, no linearization is obtained at all, i.e. as the conventional MZ-EOM. If Δφ→0, the optical power from the bi-directional transmissions are added and 3IMD components are out of phase, such that the suppression of 3IMD is achieved. On the contrary, if the bi-directional optical transmissions have a phase shift of π from one other, then the components of 3IMD from the two transmissions are in phase and cannot be cancelled. Note Fig. 4(a) also applies to the dual-parallel MZ-EOM. Fig. 4(b) shows the SFDR versus γ for the proposed design and we see that the maximum SFDR occurs approximately at a voltage splitting ratio of γ=2.8 and drops off as it deviates from this optimal value. This suggests that the 3IMD suppression is sensitive to the phase imbalances between bi-directional transmissions and the voltage splitting ratio.
3. Numerical results and analysis
To analyze the effectiveness of the proposed modulator, we simulated a radio over fiber system using a conventional MZ-EOM (OSSB), dual-parallel MZ-EOM (OSSB) similar to  and the proposed OSSB MZ-EOM with γ=2.8. We use a CW laser set to 1550 nm with a linewidth of 10 MHz and relative intensity noise (RIN) of -175 . The MZ-EOM has a half wave switching voltage of 5 V and an insertion loss of 6 dB for all the three modulators. The optical power injected into the modulator is kept the same. The link will carry three RF subcarriers at 9, 10 and 12 GHz. The 3IMD at 11 GHz is most detrimental to the center channel of 10 GHz. Therefore, we consider this as 3IMD suppression for the comparison. The PIN responsivity of 1.0 A/W and thermal noise of 10-12 A/√Hz are considered with a noise bandwidth of 3 GHz for each of the RF carriers. We consider two scenarios, a back to back system and a system with the use of 25 km of standard single mode fiber (SMF) to compare our proposed modulator with the other two modulators. The SMF has an attenuation of 0.2 dB/km and chromatic dispersion of 16 ps/nm-km. The simulation was carried out using VPI TransmissionMaker 7.5. The simulated RF carrier and 3IMD power versus the input RF power is shown in Fig. 5. Specifically, simulated SFDR in a back to back system using the proposed MZ-EOM, the dual-parallel MZ-EOM, and conventional MZ-EOM is shown in Fig. 5(a), (c) and (e); and correspondingly simulated SFDR in a system with the use of 25-km of SMF is shown in Figs. 5(b), 5(d) and 5(f). By comparing Figs. 5(a) and 5(c) with 5(e), it is seen that both linearized modulators introduce ~14% loss of RF carrier power compared to the conventional MZ-EOM.
For the back to back case, the proposed MZ-EOM, the dual-parallel MZ-EOM and the conventional MZ-EOM result in a SFDR of 83 dB·Hz 2/3 in Fig. 5(a), 73 dB·Hz 2/3 in Fig. 5(c) and 62.5 dB·Hz 2/3 in Fig. 5(e), respectively. Thus, for the back to back system the proposed MZ-EOM leads to a SFDR improvement of 10 dB and 20.5 dB over the dual-parallel and the conventional MZ-EOM, respectively. The physical reason for the 10 dB SFDR improvement in using this proposed linearized MZ-EOM compared to the dual-parallel linearized MZ-EOM is given as follows, because the proposed linearized OSSB MZ-EOM makes use of only one optical modulator. In other words, the proposed design does not have to deal with the different optical characteristics of two independent optical modulators. On the contrary, two different frequency responses for the two independent MZ-EOMs in the dual-parallel MZ-EOM degrade 3IMD suppression .
In the case where 25 km of SMF is used, the proposed MZ-EOM, the dual-parallel MZ-EOM and the conventional MZ-EOM result in a SFDR of 67.5 dB·Hz 2/3 in Fig. 5(b), 59.5 dB·Hz 2/3 in Fig. 5(d), and 47.5 dB·Hz 2/3 in Fig. 5(f). Therefore, for this case the proposed MZ-EOM leads to a SFDR improvement of 8 and 20 dB over the dual-parallel and the conventional MZ-EOM, respectively. The two tone test at RFs of 10 and 12 GHz was also simulated, where the linearized modulators showed a slight increase in SFDR of 1 and 1.5 dB for the back to back and 25 km of SMF cases, respectively. The conventional modulator showed an increase of 1.5 and 2.5 dB for the back to back and 25 km of SMF cases, respectively. Despite the increase in SFDR for the individual modulators, the relative improvement in SFDR remained basically the same for a light carrying two or three RF tones.
The suppression of IMD will improve bit error rate (BER). Here we consider an electrical ASK 2.48 Gb/s data signal carried by each RF carrier located 10 and 12 GHz. Fig. 6 shows the simulated BER for the link using the three modulators. The injected optical power is kept the same for all three modulators during the simulation, so that the average optical power injected into the SMF is the same. Furthermore, RF driving power is adjusted, such that the modulation index is the same for all three cases and then kept constant. So the modulated light injected into the SMF would have similar BER after the photo-detector, if no nonlinear distortion components are added by the respective modulator. We inserted an optical attenuator just before the photo-detector to vary the received optical power into the photo-detector for attaining BER. The improvement in BER for the proposed design is because of improved receiver sensitivity due to the suppression of 3IMD products. As shown in Fig. 6 it is found that the proposed MZ-EOM induces a receiver sensitivity improvement of 7 and 4.3 dB at BER=10-9, compared to the conventional MZ-EOM and the dual-parallel MZ-EOM, respectively.
We have proposed an OSSB dual electrode MZ-EOM that suppresses third order nonlinear distortion. It was shown that OSSB modulation with linearization is obtained. We have compared the proposed modulator to the dual-parallel MZ-EOM and conventional MZ-EOM. It is found that a relative SFDR improvement of 10 and 20 dB is achieved in comparison to the dual-parallel MZ-EOM and the conventional MZ-EOM, respectively. Compared to the dual-parallel MZ-EOM, the advantage of this proposed modulator is that only one MZ-EOM is used and thus suppression of 3IMD is improved. This is because the effects of two independent frequency responses due to the dual MZ-EOMs are removed and phase imbalance between the bi-directional transmissions can be maintained minimal in our proposed modulator. On the contrary it is very difficult to obtain a minimal phase imbalance between two independent MZ-EOMs in the dual-parallel MZ-EOM. The disadvantage of this proposed linearized modulator is that dual RF ports in each electrode of MZ-EOM are required.
References and links
1. L. Roselli, V. Borgioni, F. Zepparelli, F. Ambrosi, M. Comez, P. Faccin, and A. Casini, “Analog laser predistortion for multiservice radio over fiber system,” J. Lightwave Technol. 21, 1211–1223 (2003). [CrossRef]
2. R. Sadhwani and B. Jalali, “Adaptive CMOS predistortion linearizer for fiber-optic links,” J. Lightwave Technol. 21, 3180–3193 (2003). [CrossRef]
3. S. Mathai, F. Cappelluti, T. Jung, D. Novak, R. Waterhouse, D. Sivco, A. Cho, G. Ghione, and M. Wu, “Experimental demonstration of a balanced electro-absorption modulated microwave photonic link,” IEEE Trans. Microwave Theory Tech. 49, 1956–1961 (2001). [CrossRef]
4. B. Masella and X. Zhang, “A novel single wavelength balanced system for radio over fiber links,” IEEE Photon. Technol Lett. 18, 301–303 (2006). [CrossRef]
5. J. Brooks, G. Maurer, and R. Becker, “Implementation and evaluation of a dual parallel linearization system for AM-SCM video transmission,” J. Lightwave Technol. 11, 34–41 (1993). [CrossRef]
6. A. Loayssa, M. Alonso, D. Benito, and M. Garde, “Linearization of electrooptic modulators at millimeter-wave frequencies,” IEEE Lasers and Electro-Optics Society (LEOS) Annual Meeting 1, 275–276 (1999).
7. T. 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, 2052 – 2058 (2006). [CrossRef]
8. C. Lim, M. Attygalle, A. Nirmalathas, D. Novak, and R. Waterhouse, “Analysis of optical carrier-to-sideband ratio for improving transmission performance in fiber-radio,” IEEE Trans. Microwave Theory Tech. 54, 2181–2187 (2006). [CrossRef]
9. M. T. Zhou, A. B. Sharma, Z. H. Shao, and M. Fujise, “Optical single-sideband modulation at 60 GHz using electro-absorption modulators,” IEEE topic meeting on Microwave Photonics121–124 (2005). [CrossRef]
10. S. Mathai, F. Cappelluti, T. Jung, D. Novak, R. B. Waterhouse, D. Sivco, A. Y. Cho, G. Ghione, and M. C. Wu, “Experimental demonstration of a balanced electroabsorption modulated microwave photonics link,” IEEE Trans. Microwave Theory Tech. 49, 1956–1961 (2001). [CrossRef]
11. A. Loayssa, C. Lim, A. Nirmalathas, and D. Benito, “Design and performance of the bidirectional optical single-sideband modulator,” J. Lightwave Technol. 21, 1071–1082 (2003). [CrossRef]