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• Abstract

SECTION 1

## INTRODUCTION

In this paper, a simple scheme based on a 2-Ch PM is proposed and experimentally demonstrated to compensate the dispersion-induced power fading. Based on the identical operation principle in [11], the dispersion compensation is obtained based on the complementary power fading function for the IM and PM link. However, in our scheme, rather than using two modulators and needing bias control for IM, only one 2-Ch PM without bias control is used to realize the IM and PM simultaneously. As well as the dispersion performance, the SFDR and the vector signal transmission performance are also investigated. The experiment results show that the dispersion effects are greatly mitigated for the RF signal with a bandwidth up to 18 GHz. Moreover, the system SFDR and vector signal transmission performance have been improved, especially at the valley frequency of the power fading function.

SECTION 2

## OPERATION PRINCIPLE

The schematic diagram of the proposed scheme is shown in Fig. 1. The linearly polarized optical carriers from laser diodes (LDs) are separately tuned to different polarization directions. Then, the optical carriers with different polarization directions are combined by a polarization-maintaining coupler (PMC) and sent to the 2-Ch PM driven by the RF signal. The 2-Ch PM developed by Versawave Technologies supports both transverse electric (TE) and transverse magnetic (TM) modes with opposite PM indexes, which is similar to the polarization modulator mentioned in [13] but without a polarizer at the input port. Then, the phase modulated signals are launched into the polarization selective element, which is composed of a polarization controller (PC3) and a polarizer. Thereafter, the modulated signal is transmitted over the standard single-mode fiber (SMF) to remote receiving and processing. We assume that the input optical carrier is aligned at $\theta$ relative to one principal axis ($y$-axis) of the 2-Ch PM. Then, the modulated optical signal can be expressed as TeX Source $$E (t) = E_{0}(\mathhat{y}\,\cos\theta\,e^{j\beta\,\sin\Omega\,t} + \mathhat{x}\,\sin\theta\,e^{-j\beta\,\sin\Omega\,t})e^{j\omega t}\eqno{\hbox{(1)}}$$ where $E_{0}$ and $\omega$ are the amplitude and angular frequency of the input optical field, $\beta = \pi V_{m}/V_{\pi}$ is the modulation depth relative to the amplitude $V_{m}$ of input microwave signal and the half-wave voltage $V_{\pi}$ of PM, and $\Omega$ is the microwave frequency. After the microwave signal is modulated on the optical carrier, the TM and TE fields are recombined at the output of polarization selective element. If the linear polarizer is set at angle $\alpha$ to the $y$-axis, the electric field after the polarizer is given by TeX Source $$E(t) = E_{0}(\cos\theta\,\cos\alpha\,e^{j\beta\,\sin\Omega\,t} + \sin\theta\,\sin\alpha\,e^{-j\beta\,\sin\Omega\,t})e^{j\omega t}.\eqno{\hbox{(2)}}$$ If $\theta = 45^{\circ}$ and $\alpha = 45^{\circ}$, the optical carrier on TE and TM modes are identically modulated by the RF signal. Thereafter, the two modes of modulated signals interfere in the polarization selective element and complete the PM-to-IM conversion. Thus, the IM of the RF signal is realized as TeX Source $$E_{\rm IM}(t) = {1 \over 2}E_{0}(e^{j\beta\,\sin\Omega\,t} + e^{-j\beta\,\sin\Omega\,t})e^{j\omega t} = E_{0}\, \cos(\beta\,\sin\Omega\,t)e^{j\omega t}.\eqno{\hbox{(3)}}$$ If $\theta = 90^{\circ}/0^{\circ}$ and $\alpha = 45^{\circ}$, only one mode of optical carrier is phase modulated by the RF signal. Therefore, no signal interferes in the polarization selective element, and the PM signal is finally obtained as TeX Source \eqalignno{\theta =&\, 90^{\circ}\quad E_{\rm PM}(t) = {\sqrt{2} \over 2}E_{0}e^{j\omega t - j\beta\,\sin\Omega\,t}\cr \theta =&\, 0^{\circ}\quad E_{\rm PM}(t) = {\sqrt{2} \over 2}E_{0}e^{j\omega t + j\beta\,\sin\Omega\,t}.&\hbox{(4)}} Consequently, in our scheme, if we separately set $\theta_{1}$ and $\theta_{2}$ as 45° and 90° with respect to the $y$-axis of the 2-Ch PM while keeping $\alpha = 45^{\circ}$, the PM and IM can be realized simultaneously.

Fig. 1. Schematic diagram of the proposed long-haul analog optical link for the mitigation of dispersion-induced power fading. LD: laser diode; PC: polarization controller; PMC: polarization-maintaining coupler; 2-Ch PM: 2-Ch phase modulator; SMF: single-mode fiber; PD: photodetector.

When the modulated signal is transmitted over the SMF to remote receiving, chromatic dispersion causes each spectral component to experience different phase shifts depending on the fiber-link distance, modulation frequency, and the fiber-dispersion parameter, which results in a power degradation of the composite intensity and phase modulated RF signal separately as [4], [8], [14] TeX Source \eqalignno{P_{\rm IM}(f) = &\, A_{1}J_{0}^{2}(\beta)J_{1}^{2}(\beta)\,\cos^{2}\left({\pi\hbox{LD}\lambda_{1}^{2}f^{2} \over c}\right)&\hbox{(5)}\cr P_{\rm PM} (f) = &\, A_{2}J_{0}^{2}(\beta)J_{1}^{2}(\beta)\,\sin^{2}\left({\pi\hbox{LD}\lambda_{2}^{2}f^{2} \over c} \right)&\hbox{(6)}} where ${\rm J}_{\rm k}(\cdot)$ is the $k$th-order Bessel function of the first kind; $D$ denotes the fiber dispersion parameter in ps/nm/km; $L$ is the fiber transmission length; $c$ is the light velocity in vacuum; $\lambda_{1}$ and $\lambda_{2}$ are wavelengths of the two light waves, respectively; $f$ is the frequency of RF signal; and ${\rm A}_{1}$, ${\rm A}_{2}$ are the parameters related to the input optical power, link loss, and the optoelectronic conversion efficiency of PD. In our scheme, rather than using only one LD and separating it by a 1 × 2 optical coupler, the two different LDs are not only been used to provide two optical carriers, but also been used to eliminate the coherence of the two optical carriers. Thus, when two extremely low frequency-spaced lights are chosen, we can suppose that $\lambda_{1} \approx \lambda_{2} \approx \lambda$. From (5) and (6), we can be see that the fading effect leads to cosine-like fluctuation of the signal power, which means that the signals periodically disappear at the fading nodes related to the fiber length and microwave frequency. Moreover, if we adjust the power of the LDs to make the parameter $A_{1}$ equal to $A_{2}$, the sum of the intensity and phase modulated RF signal power can be tuned to a constant, which is independent of the fiber length and microwave frequency. Therefore, the dispersion compensation can be realized. Combined with the dispersion compensation principle, two-tone SFDR as a commonly used metric for RF link linearity, and vector signal transmission performance can be further studied.

SECTION 3

## EXPERIMENT RESULTS

To demonstrate the proposed scheme, an experiment has been performed based on the configuration shown in Fig. 1. Two tunable laser sources (NKT Photonics, YOKOGAWA AQ2202) are used to provide the optical carriers. The wavelengths are separately set as 1550.2 nm and 1550 nm, with extremely low frequency spacing. By aligning the PC1 and PC2, the two optical carriers can achieve proper polarization direction and be sent to the 2-Ch PM after the combination using a PMC. The SMF with length of 24.45 km is used to transmit the optical signal to the receiver terminal. The measurement of corresponding frequency response of this long-haul analog optical link is accomplished with a microwave vector network analyzer (VNA, R&S ZVA40) providing input frequency sweep to the modulator, with the photodetector output serving as the analyzer input. By adjusting the optical power appropriately as 10.7 dBm for IM and 16.6 dBm for PM, respectively, the measured frequency response before and after dispersion compensation are shown in Fig. 2. From Fig. 2(a), we can see that the RF power fades seriously around the frequencies of 10.2 and 17.5 GHz for the IM and PM link, respectively. The power faded even more than 60dB at the valley frequency comparing with the unfading frequency points. Owing to the proposed dispersion compensation link, Fig. 2(b) shows that the measured frequency response after dispersion compensation is quite flat and that the maximum power fluctuation is within approximately 6 dB. Therefore, the dispersion performance of this long-haul link is greatly improved by using the dispersion compensation scheme.

Fig. 2. Measured frequency response before (a) and after (b) the dispersion compensation. The inset presents a zoom-in view of the power fluctuation.

In order to further analyze the link feature, the two-tone test method is utilized to study the SFDR of this long-haul link. The input RF signal comprises two closely spaced and equal-amplitude RF tones from two microwave sources (Anritsu 68047C and 69347A), and the detected signal is monitored by a RF spectrum analyzer (R&S FSMR). We mainly analyzed the SFDR performance before and after the dispersion compensation at the selected two frequency points of 9.5 GHz and 17.5 GHz, as shown in Fig. 3. The upper lines with $\hbox{slope} = 1$ are the fundamental signal tone, while the lower lines are the third-order intermodulaion distortion (IMD3) power. The noise floor is approximately −160 dBm/Hz. The circles and stars are the measured values, while the solid lines are the calculated values. For the IM and dispersion compensated link with two-tone frequencies of 9.5 GHz and 9.51 GHz, the SFDR after the dispersion compensation improved 15.3 $\hbox{dB/Hz}^{2/3}$; meanwhile, the third-order output intercept point (OIP3) increased 23.3 dB, from $-49.8$ dBm to −26.5 dBm. For the PM link, at the frequency point of 17.5 GHz where the power is most severely deteriorated, it is clearly seen that the SFDR is reduced to 63 $\hbox{dB/Hz}^{2/3}$ for the dispersion-induced power fading. Thanks to the dispersion compensation scheme, the SFDR improved 24 $\hbox{dB/Hz}^{2/3}$ and the OIP3 also increased 35 dB.

Fig. 3. Received versus input RF power for IM and dispersion compensated link with two-tone frequencies of 9.5 GHz and 9.51 GHz (a), PM and dispersion compensated link with two-tone frequencies of 17.5 GHz and 17.51 GHz (b).

Fig. 4 plots the measured electrical spectrum for the PM and dispersion compensated link with two tone frequencies of 17.5 GHz and 17.51 GHz. Compared with the PM link, the fundamental carrier increased 33.4 dB, while the IMD3 improved 25.8 dB after the dispersion compensation. Theoretically, the compensation link introduced 33.4 dB link gain will increase the IMD3 by 100.2 dB. Thus, the compensation link gives an effective suppression of IMD3 by 74.4 dB and an improvement of SFDR by 24.8 $\hbox{dB/Hz}^{2/3}$, which is in good agreement with the results in Fig. 3(b) that the SFDR is improved by 24 $\hbox{dB/Hz}^{2/3}$. The SFDR as a function of frequency before and after the dispersion compensation is shown in Fig. 5. It is clearly seen that, for the IM, PM, and dispersion compensated links, the SFDR at the frequency up to 18 GHz is well consistent with the link frequency response shown in Fig. 2. Moreover, the compensation scheme improves the SFDR especially at the valley of the frequency response and keeps the link SFDR at the high level between 85–90 $\hbox{dB/Hz}^{2/3}$, with improved RF link linearity.

Fig. 4. Spectrum analyzer traces for two-tone IMD3 test for PM and dispersion compensated link with two-tone frequencies of 17.5 GHz and 17.51 GHz.
Fig. 5. SFDR as a function of frequency before and after the dispersion compensation.

The potential of this long-haul analog optical link for vector signal transmission has also been verified. The 2-Ch PM is driven by a 10-KSym/s quadrature phase-shift keying signal at different carrier frequencies from a vector signal generator (VSG, Agilent, E8267D). At the receiving end, the detected signal is analyzed by Agilent VSA software in a spectrum analyzer for down-conversion and digital demodulation. A comparison of constellation diagram and error-vector magnitude (EVM) performances before and after the dispersion compensation link is made and shown in Fig. 6. Since the RF power fades seriously around the frequencies of 10.2 and 17.5 GHz for the IM and PM link, respectively, the constellation diagram is heavily distorted, and it cannot be clearly separated into four phase states, as shown in Fig. 6(a) and (c); meanwhile, the EVM is very high at 36.599% and 41.237%. Fortunately, by using the proposed dispersion compensation scheme, it is clearly seen that the quality of the constellation diagram is greatly improved and the EVM values are separately decreased to 17.282% and 17.614%. The similar results at center frequency of 5GHz are obtained in Fig. 6(e)(g). Since the power fading is not obviously at this frequency, the difference of the constellation diagram and EVM performances before and after the dispersion compensation link is relatively small, which coincides with the results in Figs. 2 and 5. From all above analysis, we can see that the proposed dispersion mitigation scheme not only increased the system SFDR but improved the vector signal transmission performance as well. Of course, since no amplifier is used in this long-haul link, the received signal powers are small and the overall EVM values are relatively high for the decreased signal to noise ratio, but this does not affect the demonstration that the system performance is improved due to the dispersion mitigation scheme.

Fig. 6. EVM performance before the dispersion compensation for IM at center frequency 10.2 GHz (a), PM at center frequency 17.5 GHz, PM, IM at center frequency 5 GHz (e), (f), and after the dispersion compensation at corresponding center frequency (b), (d), (g).
SECTION 4

## CONCLUSION

In conclusion, a novel approach for broadband dispersion compensation is proposed and experimentally demonstrated. The simultaneous optical PM and IM are implemented using a 2-Ch PM in conjunction with an optical polarizer. Thanks to the complementary power fading function for the PM and IM, the broadband and long reach dispersion compensation is implemented. The experiment results with mitigated power fading for the RF signal bandwidth up to 18 GHz over 24.45-km SMF transmission, the improved system SFDR and vector signal transmission performance indicate the feasibility of the dispersion compensation scheme in long-haul analog optical link.

## Footnotes

Corresponding author: K. Xu (e-mail: xukun@bupt.edu.cn).

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