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An intermodulation distortion suppression method based on the optical carrier band processing is demonstrated. A systematic analysis of the main optical spectrum contributors for the third-order intermodulation distortion in the nonlinear system is presented. Theoretical analysis shows that the third-order intermodulation distortion terms can cancel each other if a proper phase shifting is imposed to the optical carrier band. We experimentally demonstrate the approach with a two-tone test and a suppression of about 33 dB in the third-order intermodulation distortion is obtained. Experimental results show that an overall fundamental to third-order intermodulation distortion ratio of up to 64 dB is achieved and the link dynamic range is improved by 14.7 dB, compared with the conventional link without the proposed optical carrier band processing.
© 2013 Optical Society of America
1. Introduction
Due to its remarkable advantages such as high bandwidth and low cost, analog fiber-optic link has found widespread applications in antenna remoting, radio astronomy and other applications both in commercial and military markets [1–3]. An important figure of merit that is usually used to estimate the performance of the analog fiber-optic link is the spur-free dynamic range (SFDR), which is especially demanding for the challenging application such as military. The SFDR of the intensity-modulated fiber-optic link is susceptible to the nonlinear transmission characteristic of the intensity modulator. Harmonic and intermodulation products are serious especially when multiple radio frequency (RF) tones are applied to the modulator with high modulation index. For sub-octave systems, the harmonic distortions can easily be removed as they locate far away from the RF carriers, while the third-order intermodulation distortion (IMD3) components are the most pronounced to the fiber-optic link as they lie very close to the fundamental carriers and it is impossible to eliminate them simply by using RF filters [4]. To suppress the IMD3 components and improve the SFDR performance, numerous approaches have been demonstrated during the past years. Extended linearity can be achieved by using those proposed schemes, while either fabrication or controllability tolerance requirements of most of those designs may be difficult to meet. Techniques such as electronic pre-distortion [5] and feed-forward [6] are investigated to attain necessary distortions that can compensate the existing nonlinearity of the link. A linearization technique based on two parallel Mach-Zehnder modulators (MZMs) is demonstrated in [7], which builds two inverted photocurrents that can cancel the IMD3 but at the cost of increased complexity. Another linearized scheme consisting of two intensity MZMs in series is also proposed in [8]. The precise control of the RF power ratio is a problem that should be considered for the aforementioned linearized modulators with two MZMs either in series or parallel. Proposals using complex modulators such as dual parallel MZM (DPMZM) [9, 10], dual-electrode MZM (DEMZM), and dual-parallel polarization modulators (DPPOLM) are also reported to eliminate the IMD3 components that limit the linearity of the system [11, 12], but with additional complexity, unfortunately. The general design idea behind most of the aforementioned proposals is to introduce desired nonlinear distortions, which can be used to reduce the strength of the existing ones with the cost of increased system complexity [13]. We note that little attention has been paid to address the issue of IMD3 suppression by using direct optical processing except a few demonstrations up to now [13, 14].
In this letter, a novel linearization technique incorporating optical carrier band (OCB) processing is investigated, which can substantially reduce the IMD3 components and increase the SFDR of intensity-modulated directly-detected (IMDD) links. Rather than generate certain distortion to cancel the existing one, we analyze the main optical spectrum contributors of the IMD3 and suppress them directly by OCB processing in the nonlinear system. Parts of the beating products of the IMD3 are phase reversed and their amplitudes are modified to the desired value when a proper phase shift is imposed to the OCB. By this method, the IMD3 terms induced by the different optical spectrum contributors can cancel each other and the induced IMD3 is significantly suppressed. A fundamental to IMD3 ratio of more than 64 dB and an SFDR improvement of 14.7 dB is obtained. It is worth noting that the simplicity of the analog fiber-optic link is preserved, which is attractive for high SFDR analog fiber-optic link requiring reduced complexity.
2. Operation principle
Before presenting the basic operation principle of the proposed approach, we firstly investigate the primary optical spectral contributors of the IMD3 for the conventional analog fiber-optic link by a two-tone analysis. The output optical carrier with its angular frequency of ωc, denoted as Ec, is modulated via the MZM in the IMDD link. A two-tone signal at the angular frequencies of ω1 and ω2 is used to drive the MZM. The envelope of the optical field at the output of the MZM can be expressed as
where φ is the direct current (DC) bias angle of the intensity MZM, and are the half-wave voltage of the MZM and the peak voltage of the input electrical two-tone signal, respectively.Applying the Bessel functions expression and ignoring the higher order harmonic and intermodulation terms, we can further express the envelope in Eq. (1) by
where is the modulation depth of the MZM. donates the nth order Bessel function of the first kind.The output optical field of the MZM is shown in Fig. 1(a), including the OCB, the 1st order optical upper/lower sideband (1-USB/1-LSB) and the 2nd order upper/lower sideband (2-USB/2-LSB). The higher optical sidebands are not shown in Fig. 1 as they are with negligible amplitude due to the small signal input. The OCB is composed of the optical carrier and the even-order nonlinear components. The 1-USB/1-LSB contains the fundamental and odd-order distortion components, while the 2-USB/2-LSB is composed of the even-order nonlinear components. The double-headed arrows in Fig. 1(a) mark the three main optical spectrum contributors to the IMD3 components. The output optical signal is then distributed to the photo-detector (PD) for the square law detection. The optical carrier and its sidebands are mixed, and the beating products of the fundamental and IMD3 components are shown in Fig. 1(b). There are three pairs of the main contributors for the IMD3. The beating of the optical carrier ωc and ωc + 2ω1,2-ω2,1 (ωc-2ω1,2 + ω2,1) generates IMD3 with detected photocurrent donates as I01’. The IMD3 induced by the 1-USB/1-LSB of ωc + ω1,2 (ωc-ω1,2) and 2nd sideband of ωc + 2ω2,1 (ωc-2ω2,1) is represented by I12. I0’1 is the photocurrent coefficient generated by the beating of the spectrum at the angle frequency of ωc + ω2,1-ω1,2 (ωc-ω2,1 + ω1,2) and ωc + ω1,2 (ωc-ω1,2). The sum of all the beating products of the aforementioned optical spectrum contributors builds the amplitude of the detected RF components.
Fig. 1 (a) The optical spectrum after the MZM ; (b) Detected RF spectrum in system without OCB processing; (c) Detected RF spectrum in system with the proposed OCB processing.
When the signal expressed in Eq. (2) is sent to a square law PD for detection, the generated photo-current containing the fundamental and IMD3 components can be mathematically given as
where is the responsivity of the PD, Po = Eo2 is used to represent the received optical power. By adopting small signal approximation, we can derive that I01’ = I12 = 2I0’1.As has been analyzed above, the induced IMD3s are all with the same sign and are constructively combined at the PD. By properly shifting the phase of the OCB by θ, the envelop of optical filed at the output of the MZM can then be given as
By taking the phase shifting of the OCB into consideration, we can mathematically evaluated the detected photocurrent including the fundamental and IMD3 components as
When square law detection is implemented, the phase shift of OCB can be mapped directly to the generated RF signals. It is obvious that the detected IMD3 can be completely suppressed in theory if the introduced phase shift meets the following expression
When a phase shift as given in Eq. (6) is imposed to the OCB, both the phase and amplitude conditions among the three main contributors of IMD3 are changed to the desired value. The photocurrent of I01’ and I0’1 are reversed to their opposite phase and their amplitude are attenuated to one-third of their original one. As a result, the IMD3 is completely removed in theory. A simulation based on two-tone signal is carried out. To show the performance improvement of the approach, the simulated fundamental to IMD3 ratio against the cosine of the phase shift of θ is shown in Fig. 2 when the modulation index is 0.35. We can conclude from Fig. 2 that the best fundamental to IMD3 ratio is obtained when cosθ = −0.33, which matches the formula derivation above very well. The suppression of the output IMD3 is achieved due to the cancellation of the different photocurrent of I01’, I12 and I0’1. According to Eq. (5), the amplitudes of the fundamental frequencies are also attenuated by about 4.8 dB when the phase shift is imposed to the OCB. The power penalty of the fundamental frequencies can be complemented by the additional optical input or light amplifier.
3. Experiment
A proof-of-concept experiment based on the OCB processing is constructed as shown in Fig. 3. A continues wave (CW) laser source (NKT Photonics) at wavelength of 1550.01 nm is applied as the optical carrier. The principal axis of the output light beam is aligned with that of the following standard MZM (Eospace 20 GHz MZM) by properly adjusting the polarization controller (PC) placed before the intensity modulator. The MZM is biased at the quadrature point. A bias control circuit (Mini-MBC-3) is adopted to stablely lock the working point of the MZM. Two signal generators (Angilent E8267D) are used to supply for the two-tone electrical drive signal at 18.00 GHz and 18.01 GHz. The two RF drive signals are power coupled by a RF combiner and works as a two-tone signal. The unbalanced insertion loss in the two different RF paths can be removed by properly calibrating the power levels of the two generators. The modulated signal is then introduced to the following OCB processor for the phase adjustment.
Fig. 3 Experimental arrangement for the IMD3 suppression in analog fiber-optic link employing OCB processing.
The OCB processor used in this paper is a waveshaper (Finisar 4000s) that can be considered as a filter bank which can finely and independently processing the different photonic spectrum bands. By properly setting the processing filter bandwidth and the respective band information of the waveshaper, both the phase and the amplitude of the spectral components in the respective band can be assigned with the desired value independently. A band-pass filter, whose center frequency is set to be in accordance with the optical carrier, is assigned with a 3-dB bandwidth of 18 GHz and is used to process the OCB in the proposed approach. The phase of the OCB is shifted by approximately acos(−0.33) as has been analyzed in the second part, while the amplitude and phase of the 1-SB and 2-SB are leaving unchanged. The managed optical spectrum is then imposed to the following PD (EM4, EM169-03), at which square law detection is implemented. The electrical output is analyzed by the following electrical signal analyzer (ESA, Agilent N9030A).
The link performance for both compensated and un-compensated versions is examined under a two-tone signal test. Figure 4 shows the measured electrical spectrum for both compensated and un-compensated cases when the RF power driving the MZM is 6 dBm. Due to the nonlinear characteristic of the intensity MZM, IMD3 components at frequencies of 17.99 GHz and 18.02 GHz are aroused when the input two-tone signals are at frequencies of 18.00 GHz and 18.01 GHz. By properly shifting the phase of the OCB, the three main IMD3 contributors attributing from the spectrum beating can approximately cancel each other. As a result, linearization of the link is achieved and the fundamental to IMD3 ratio is then stronglyenhanced. The additional power penalty attributing to the OCB processor is made up by the laser source, whose output power is about 4.8 dB higher than that of the system without compensation. As a result, the fundamental frequencies are with nearly identical levels. As can be seen in Fig. 4(b), a fundamental to IMD3 ratio of more than 64 dB is obtained for the OCB processing approach due to the effective IMD3 suppression, while the fundamental to IMD3 ratio is about 30 dB for links without compensation as shown in Fig. 4(a).
Fig. 4 Electrical spectra of the output fundamental signal and their IMD3s for (a) the conventional link without any processing in optical domain; (b) the proposed link with OCB processing.
By evenly varying the input RF power, both the fundamental and the IMD3 power are monitored by using the ESA. Figure 5 shows the measured fundamental and IMD3 power as a function of the input RF power for both cases with and without linearization. The measured noise floor that dominated by the shot noise is −160.5 dBm/Hz for both links. As can be seen in Fig. 5, by using the proposed approach, the SFDR of the link is increased from 99.6 to 114.3 dB in 1 Hz bandwidth. An improvement of more than 14.7 dB in the SFDR can be obtained as compared with conventional link without the OCB processing.
As a matter of fact, there are many spectrum contributors to the IMD3 components, which are introduced by the mixing of optical carrier and all the different sidebands. Only the three main contributors are considered in this paper, while the other contributors induced by the higher order optical sidebands are ignored due to their insignificant amplitude. When the OCB processor is properly adjusted, the IMD3 can be remarkably suppressed due to the cancellation of the different IMD3 contributors. Since a commercial waveshaper with low resolution of about 10 GHz is used as the OCB processor, the minimum RF carrier frequency is above 10 GHz. With a lower carrier frequency, the desired OCB phase shift, acos(−1/3), cannot be achieved correctly, resulting in a reduced or even failed IMD3 suppression. Note that only a fixed phase shift within a narrow band is required in this scheme. So the OCB processor can be achieved by other devices with lower cost and higher resolution, for example, a fine spatial light modulator [15] or integrated devices. It is more practical and economical to achieve linearized analog-photonic link when such kind of processors are incorporated in practical application. The proposed technique is suit for sub-octave analog fiber-optic link as the second order harmonic and inter-modulation distortions suppression are not considered in this proposed approach.
4. Conclusion
In summary, we comprehensively investigate the main optical spectrum contributors of the IMD3 components in IMDD based analog fiber-optic link. A linearized approach incorporating the OCB processing is proposed. The suppression of IMD3 is achieved by properly shifting the phase of the OCB. A proof-of-concept experiment is performed, which shows a 34 dB suppression of the IMD3 as compared with system without the OCB processor. The SFDR of the link is increased from 99.6 to 114.3 dB in 1 Hz bandwidth, which means an improvement of 14.7 dB in the SFDR. The suppression of the IMD3 is performed by direct processing in optical domain. Neither pre-distortion nor complex modulator combination is required to cancel the existing distortions. The simplicity of the scheme is then preserved. The proposed technique can be greatly promoted for analog optical links whose simplicity and preferable SFDR specification are especially demanding.
Acknowledgments
This work was supported in part by 973 Program (2012CB315705), National 863 Program (2011AA010306), NSFC Program (61271042, 61107058 and 61120106001), the Fundamental Research Funds for the Central Universities, and the Fund of State Key Laboratory of Information Photonics and Optical Communications.
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