Inter-channel nonlinear crosstalk in analog phase-modulated wavelength-divisionmultiplexed systems

Hoon Kim; J. H. Lee; Ho-Chul Ji

doi:10.1364/OE.16.020687

1. Introduction

Transmission of radio-frequency (RF) signals over fiber using sub-carrier multiplexing (SCM) technology has a wide range of applications including common antenna TV (CATV), hybrid fiber-wireless, and analog true-time delay systems. Typically, those systems have exploited wavelength-division-multiplexing (WDM) technology to enhance the system capacity and to provide network flexibility. However, it has been shown that nonlinear optical crosstalk, such as stimulated Raman scattering (SRS), cross-phase modulation (XPM), and optical Kerr effect acting with polarization dependent loss (OKE-PDL), can degrade the system performance and limit the capacity and scalability [1]. This crosstalk can be problematic in some systems and thus a couple of methods have been proposed and demonstrated to cope with it [2]–[4]. However, all of them require bulky and/or expensive optical devices that might not be appropriate for cost-sensitive applications. In [2], for example, complementary modulation of two closely spaced optical twin carriers and balanced detection was used to suppress the crosstalk by 50 dB. Another way of coping with the problem is to utilize the dispersion management. In this case, however, the performance improvement is limited over narrow frequency bands (1–2 GHz) and it requires dispersion compensation modules at the transmitter and/or receiver, which also increases the system cost significantly [4].

In this paper, we report on the nonlinear crosstalk reduction of SCM WDM systems by using phase modulation. Thanks to the constant intensity of the signals at the output of the transmitter, inter-channel nonlinear crosstalk can be greatly suppressed in phase-modulated (PM) systems [5]. Our theoretical analysis together with two-channel experiment and simulation shows that the PM system can suppress the nonlinear crosstalk by up to 15 dB over a wide range of RF frequencies, compared to intensity-modulated (IM) systems. Analog polarization-modulated WDM systems where the transmitters emit constant-intensity signals are also known to be capable of producing low nonlinear crosstalk provided the channel spacing is large (e.g., >200 GHz) and the signal RF frequency is high (e.g., >1 GHz) [6]. However, these systems require sophisticated polarization control or tracking modules at the receiver, and might not be suitable for cost-sensitive applications.

Fig. 1. Schematic diagram of an analog phase-modulated wavelength- division-multiplexed system. LD: laser diode, Demod: demodulator, PD: photo-diode. WDM: wavelength division multiplexer/demultiplexer.

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Figure 1 shows the schematic diagram of an analog PM WDM system. Each wavelength channel is modulated with SCM signals by using a phase modulator. After being combined with a wavelength-division-multiplexer, the signals are transmitted to the receiver over fiber. At the receiver, the phase information impressed on each channel is converted into the intensity information by a demodulator. For demodulator, we can utilize an optical filter which has a steep slope at the channel wavelength. A wavelength-offset wavelength-division-demultiplexer can also take the place of numerous demodulators. In either case, the filter functions as a frequency-to-intensity converter not as a phase-to-intensity converter and consequently we might need an analog electronic conversion circuit at the transmitter or receiver which integrates the SCM signals, because the integral of frequency with respect to time corresponds to phase. However, if the bandwidth of each SCM signal is much less than its respective subcarrier frequency (i.e., for slowly varying amplitude and phase modulation), the conversion circuit puts out the same amplitude and phase information as the input signal and thus is not necessary [7], [8].

Fig. 2. Signal and crosstalk in two-channel analog phase-modulated systems. The pump channel is phase-modulated whereas the probe channel generates a continuous-wave, unmodulated signal.

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The crosstalk mechanisms of two-channel analog PM systems are illustrated in Fig. 2. The pump channel is assumed to be phase-modulated by a sinusoidal signal whereas the probe channel to produce un-modulated, continuous-wave (CW) light to identify the crosstalk. When the signals propagate over dispersive optical fiber, the chromatic dispersion of fiber induces intensity fluctuations [9]. This PM-to-IM conversion occurs throughout transmission and induces crosstalk to other channels through SRS and optical Kerr effect. For example, the amplitude fluctuations of the pump channel induced by fiber dispersion are transferred to the probe channel through SRS. On the other hand, optical Kerr effect mediates the phase modulation of the probe channel and this phase crosstalk is converted into intensity crosstalk by fiber dispersion and the demodulator. The amplitude fluctuations of the pump channel also modulate the polarization of the probe channel through XPM. When followed by PDL elements, this polarization modulation manifests itself as intensity modulation. In this paper, the crosstalk, defined as the ratio of the power of the RF signal induced on the CW probe channel to the power of the RF signal on the modulated pump channel at the receiver when the channels have the same average optical power [1], can be expressed as

Crosstalk (dB) = 10 \log {\frac{RF power on probe channel}{RF power on pump channel}}

The rest of this paper is organized as follows. In Section 2, we theoretically analyze the inter-channel nonlinear crosstalk in analog PM WDM systems, including SRS and XPM. Experimental/simulation setup is described in Section 3 to compare the theoretical data with the measured and simulated ones. The results are also discussed in this section. Finally, this paper is summarized in Section 4.

2. Theoretical analysis

The electric field of the pump signal phase-modulated at an angular frequency of Ω can be expressed as

E_{p} (t) = E_{0, p} \exp j {ω_{p} t + A \sin (Ω t)} = E_{0, p} \sum_{m = - \infty}^{\infty} J_{m} (A) \exp j {ω_{p} t + m Ω t}

where E_0,p is the electric field amplitude at the output of the transmitter, t is time, ω_p is the angular frequency of the optical carrier, J_m is the Bessel function of the first kind of order m, and A is the phase modulation depth. The corresponding optical intensity propagating in dispersive and lossy optical fiber can be expressed as [8]

P_{p} (z, t) = P_{z, p} (1 + \sum_{m = 0}^{\infty} P_{m, p} (z) \cdot \sin {Ω (t - k' z)})

P_{m, p} (z) = 4 J_{m} (A) J_{m + 1} (A) \sin (\frac{2 m + 1}{2} Ω^{2} k ″ z)

where z is the transmission distance, k′ is the derivative of the propagation constant k with respect to the angular frequency ω evaluated at ω_p, and k″=d²k/dω² evaluated at ω_p. P_z,p is the optical power generated by E0,_p ·exp(-αz/2), where α is the fiber loss. In (3), only DC and fundamental components at the modulation frequency of Ω are considered.

2.1. PM-to-IM Conversion by Demodulation Filter and Fiber Dispersion

In this paper, we assume that the phase information is converted into intensity information at the receiver by a demodulation filter which has an intensity slope of T (dB/rad). When a phase modulated signal passes through the demodulation filter, the output electric field has amplitude variation proportional to 10^Δω·T/20, where Δω is the frequency deviation caused by phase modulation of the signals. Thus, the electric field of the phase-modulated pump signal after it passes through optical fiber and the demodulation filter can be expressed from (2) as

E_{p} (z, t) = E_{0, p} \exp (- \frac{α z}{2}) \sum_{m = - \infty}^{\infty} J_{m} (A) 10^{m Ω T ⁄ 20} \exp j {ω_{p} t + m Ω t - k_{m} z}

where k_m is the propagation constant of the m-th sideband and can be expanded to the second order as k_m=k_c+mΩk′+(mΩ)²k″/2, where k_c is the carrier propagation constant. Thus, the corresponding optical intensity of the electric field having the angular frequency Ω can be expressed as

P_{p} (z, t) = P_{z, p} [\sum_{m = - \infty}^{\infty} J_{m}^{2} (A) 10^{m Ω T ⁄ 10} - F \sin {Ω (t - k' z) + Ψ}]

where

F = 2 ∣ \sum_{m = - \infty}^{\infty} J_{m} (A) J_{m + 1} (A) 10^{\frac{(2 m + 1) Ω T}{20}} \exp j {\frac{- 2 m - 1}{2} Ω^{2} k ″ z} ∣

Ψ = \arg [2 j \sum_{m = - \infty}^{\infty} J_{m} (A) J_{m + 1} (A) \cdot 10^{\frac{(2 m + 1) Ω T}{20}} \exp j {\frac{- 2 m - 1}{2} Ω^{2} k^{″} z}]

In (6), the first term is the DC component and the second is the fundamental component. Thus, F, expressed in (7), is the RF power on the pump channel at the receiver and will be used for the calculation of crosstalk defined in (1).

2.2. Stimulated Raman Scattering

Assuming no depletion of the pump channel, the optical power of the probe channel with SRS crosstalk can be written as [1]

P_{s} (z, u_{s}) = P_{s} (0, u_{s}) \exp (- α z) [1 + \frac{g_{12}}{A_{eff}} \int_{0}^{z} P_{p} (z', u_{s} + \frac{z'}{v_{s}}) d z']

where g ₁₂ is the Raman gain coefficient, A_eff is the effective area of fiber, and ν_s is the group velocity of the probe channel. Here, variables (z, t) are changed into (z, u_s), where u_s=t-z/ν_s. Using (3), the above equation can be expressed as

P_{s} (z, u_{s}) = P_{s} (0, u_{s}) \exp (- α z) [1 + \frac{ρ_{srs} g_{12} P_{0, p}}{A_{eff}} {L_{eff} - B \sin (Ω u_{s} + Θ_{srs})}]

where ρ_srs is the effective polarization overlap factor, P_0,p is the optical power generated by E0,p, L_eff={1-exp(-αz)}/α is the effective length of the fiber, and B and Θ_srs are shown below, where ν_p is the group velocity of the pump channel.

B = \frac{2 \sqrt{{(\sum_{m = - \infty}^{\infty} J_{m} (A) J_{m + 1} (A) {\frac{X_{m} \sin (X_{m} z) e^{α z} - α \cos (X_{m} z) e^{- α z} + α}{α^{2} + X_{m}^{2}}})}^{2}}}{+ {(\sum_{m = - \infty}^{\infty} J_{m} (A) J_{m + 1} (A) {\frac{X_{m} \cos (X_{m} z) e^{- α z} + α \sin (X_{m} z) e^{- α z} - X_{m}}{α^{2} + X_{m}^{2}}})}^{2}}

Then, the SRS-induced crosstalk can be expressed as

{Crosstalk}_{SRS} \approx 20 \cdot \log [\frac{ρ_{srs} g_{12} P_{0, p} B}{A_{eff} F}]

2.3. Cross-Phase Modulation

In XPM, the intensity modulation generated by PM-to-IM conversion by fiber dispersion induces a phase modulation on all neighboring channels through optical Kerr effect. The nonlinear phase induced on the probe channel, neglecting the power depletion or distortion of the pump channel, can be expressed as [1]

Φ_{s} (z, u_{s}) = \frac{4 π n_{2}}{λ A_{eff}} \int_{0}^{z} P_{p} (z' u_{s} + \frac{z'}{v_{s}}) d z'

where n₂ is the nonlinear refractive index of the fiber, λ is the wavelength, and B and Θ_srs are the same as in (11).

In analog PM systems, PM-to-IM conversion occurs through the demodulator at the receiver and fiber dispersion, as shown in Fig. 2. We first calculate the contribution from the demodulator. When the probe signal with the nonlinear phase shift of (13) passes through a demodulator having a slope of T, the electric field of the phase-modulated signals at the output of the demodulator can be expressed as

E_{s} (t) = E_{0, s} \sum_{m = - \infty}^{\infty} J_{m} (Φ_{s, AC}) \cdot 10^{\frac{m Ω T}{20}} \exp j {ω_{s} t + Φ_{s, DC} + m Ω t + m Θ_{srs}}

where ω_s is the carrier angular frequency of the probe channel. Then, the optical intensity of the signals at the receiver can be written as

P_{s} (t) = P_{s} (0, u_{s}) \exp (- α z) \times

Here, the DC (the first term) and the fundamental frequency (the second term) components are only considered.

Next, we calculate the optical intensity of XPM crosstalk converted by fiber dispersion. For small nonlinear phase modulation of (13), the optical power variation caused by fiber dispersion as functions of z and t is given as [1]

P_{s} (z, u_{s}) = P_{s} (0, u_{s}) \exp (- α z) [1 - k ″ \frac{\partial^{2}}{\partial u_{s}^{2}} \int_{0}^{z} Φ_{s} (z', u_{s}) d z']

Substituting from (13) and (16), the output power can be given by

P_{s} (z, u_{s}) = P_{s} (0, u_{s}) \exp (- α z) [1 + Ω^{2} k ″ \frac{8 π ρ_{xpm} n_{2} P_{0} S}{λ A_{eff}} \sin (Ω u_{s} + Θ_{P - I})]

where ρ_xpm is the polarization overlap factor for XPM, and S and Θ_P-I are shown as

S = \sum_{m = - \infty}^{\infty} J_{m} (A) J_{m + 1} (A) \frac{\sqrt{{1 - e^{- α z} \cos (X_{m} z) - α z}^{2} + {e^{- α z} \sin (X_{m} z) - X_{m} z}^{2}}}{α^{2} + X_{m}^{2}}

In general, both (15) and (17) contribute the XPM crosstalk. However, when the fiber dispersion is not large and the slope of the demodulation filter is steep, the PM-to-IM conversion by the demodulation filter dominates. In this case, the XPM crosstalk can be expressed using (6) and (15) as

{Crosstalk}_{XPM} \approx 20 \cdot \log [\frac{2}{F} \sum_{m = - \infty}^{\infty} J_{m} (Φ_{s, AC}) J_{m + 1} (Φ_{s, AC}) 10^{\frac{(2 m + 1) Ω T}{20}}]

3. Experiment/simulation and discussion

Fig. 3. Experimental setup. EDFA: Erbium-doped fiber amplifier, LD: laser diode, PD: photo detector.

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We compare the theoretical analysis with experiment and numerical simulation. Figure 3 shows the experimental setup. A laser diode operating at 1550.9 nm was used as a pump channel and modulated with a LiNbO3 phase modulator driven by a frequency sweeper. The phase modulation depth is 0.24π. The modulated pump signal at λ_pump was sent to a low-speed polarization scrambler to make the polarization-dependent nonlinear optical phenomena deterministic regardless of polarization rotation along the fiber. For a probe channel, a tunable laser diode at λ_probe was used. The two channels were multiplexed by using a 3-dB coupler and transmitted along standard single-mode fiber (SSMF). The fiber launch power was 7 dBm/channel. At the end of the transmission fiber, we placed an optical filter to demodulate the PM signal and to filter out the pump channel. The filter was detuned by 17 GHz from λ_probe to exploit the steep filter skirt as a demodulator. At this detuning condition, the slope of the filter was measured to be 0.4 dB/GHz. The rejection ratio of the filter was better than 50 dB when the wavelength separation between the two channels was larger than 2 nm. Thus, the linear crosstalk was suppressed less than 100 dB [10]. The PDL of this filter was measured to be 0.15 dB. After photo-detection, the signal was amplified and its RF power was measured with an RF spectrum analyzer.

Table 1. THE PARAMETERS USED FOR THEORETICAL CALCULATIONS

View Table

Fig. 4. Crosstalk versus modulation frequency when [fiber length, wavelength spacing (λ_probe- λ_pump)] is (a) [11.9 km, -5.4 nm], (b) [25.4 km, -5.4 nm], (c) [11.9 km, 2.0 nm], (d) [25.4 km, 2.0 nm], (e) [11.9 km, 10.0 nm], and (f) [25.4 km, 10 nm]. Owing to the overlap with the total crosstalk of the PM system, the XPM crosstalk for the PM system [orange curve denoted by PM (XPM)] is barely discernible in all the figures.

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For comparison purpose, we also measured the crosstalk of the IM system. In this case, the phase modulator was replaced with a LiNbO₃ Mach-Zehnder modulator biased at a quadrature point. The center wavelength of the optical filter at the receiver was aligned to λ_probe.

The setup for numerical simulation is the same as Fig. 3. However, since the simulator we used (Photoss) cannot properly handle polarization scrambling we set the input polarization of the two channels to be linear and parallel. To take into account the polarization scrambling effect in our simulation results, we reduced the crosstalk magnitude by -20·log(2/3)≅3.52 dB because when the polarization scrambling is applied to the system the polarization overlap factor is reduced to 2/3 for XPM. This adjustment will induce an error of ~2.5 dB for SRS crosstalk because the polarization overlap factor for SRS is 1/2 rather than 2/3 in the presence of polarization scrambling. However, as will be shown below, in our experimental conditions, XPM is dominant over SRS and the simulation results match well with experimental and theoretical results.

Figure 4 shows the measured and numerically simulated crosstalk of the analog PM WDM system together with theoretical values as a function of pump modulation frequency when the fiber lengths are 11.9 and 25.4 km. For comparison, the crosstalk of the analog IM WDM system is also plotted together with the theoretical curves reported in [1]. The parameters used for the simulation and the calculation of theoretical curves are listed in Table I. The measurement and simulation data agree well with the theoretical curves. One distinctive feature of the inter-channel nonlinear crosstalk of the PM WDM system is that the nonlinear crosstalk is very small near DC frequencies, which is quite high in IM systems and can be problematic for some applications such as analog CATV and hybrid WDM systems [1], [11]. As illustrated in Fig. 2, for the nonlinear crosstalk to be induced in the probe channel, amplitude fluctuations of the pump channel should first arise from PM-to-IM conversion by fiber dispersion. However, since the amplitude fluctuations induced by fiber dispersion is proportional to the product of the accumulated dispersion and modulation frequency, the crosstalk is small at low modulation frequencies. Another thing that should be noted in Fig. 4 is that XPM dominates over nearly all the frequency range in the PM WDM system (Owing to the overlap with the total crosstalk of the PM system, the XPM crosstalk for the PM system [orange curves denoted by PM (XPM)] is barely discernible in the figures). This is very different from IM WDM systems where SRS crosstalk dominates over XPM at low frequencies but XPM becomes a major source of crosstalk as the modulation frequency increases at the wavelength spacing of Fig. 4 [1]. A quantitative explanation for the dominance of XPM in PM systems is as follows: In IM systems, the SRS crosstalk has low-pass- filter-like characteristics due to the walk-off between WDM channels. The same effect occurs also in PM systems. However, the PM-to-IM conversion by fiber dispersion has high-pass- filter-like characteristics, which, in turn, cancel the walk-off effects and make the SRS crosstalk have low dependence on modulation frequency. This also makes the SRS crosstalk low compared to that in the IM system. For example, at a wavelength spacing of 10 nm in Fig. 4(f), the SRS crosstalk level for the IM system are -72.8 dBm at 500 MHz, respectively, which are >20 dB higher than that of the PM system. On the other hand, XPM crosstalk in PM systems has high-pass-filter-like characteristics, just like in IM systems. Thus, except for near DC frequencies (where the crosstalk power is too small to be measured for the PM system in Fig. 4), the SRS crosstalk level was lower than the XPM crosstalk level. Moreover, our theoretical analysis shows that PM WDM systems have smaller XPM crosstalk than IM WDM systems. Thus, both the measurement and theoretical curves in Fig. 4 shows that, except for a special case where SRS crosstalk cancels out XPM in the IM system [i.e., at around 1 GHz in Fig. 4(a)], the crosstalk of the analog PM WDM system is 0–15 dB lower than that of the IM system throughout the measured frequency range. The results of Fig. 4 show the superior suppression of inter-channel nonlinear crosstalk of the PM SCM system to IM SCM system as well as the dominance of XPM for the PM SCM system for given conditions.

Figure 5 shows the calculated crosstalk as a function of wavelength spacing (=λ_probe-λ_pump) at 100 MHz and 2.5 GHz. Also plotted are simulation data. In this plot, the fiber length is 25 km. For the calculation of SRS crosstalk, the Raman gain coefficient is assumed to be proportional to the wavelength spacing with its gain slope of 5×10^-15 m/W/THz. The input polarizations of the two channels are also assumed to be linear and parallel. The plots show that PM WDM systems outperform IM WDM systems in terms of the suppression of nonlinear crosstalk for most of the wavelength spacing except <-25 nm in Fig. 5(b). This is because in this range SRS cancels XPM in the IM system. When the wavelength spacing is negative (i.e., the probe channel is located at a shorter wavelength than the pump channel), SRS crosstalk is nearly out of phase with the XPM crosstalk and consequently they add destructively [1]. For PM systems, on the other hand, SRS leads XPM crosstalk by 90° in phase for positive wavelength spacing but lags XPM crosstalk by 90° for negative wavelength spacing [see (10) and (15)]. Thus, the amplitude of the total crosstalk (i.e., SRS+XPM) is symmetric around λ_probe-λ_pump=0, and neither constructive nor destructive addition of the crosstalk from SRS and XPM can happen. The figure also shows that XPM dominates over SRS when wavelength spacing is small but SRS contributes strongly for large wavelength spacing. For example, at 100 MHz, SRS crosstalk is dominant over XPM in the PM system for wavelength spacing of >3 nm. However, the crossover wavelength of SRS and XPM is increased to 16 nm at 500 MHz due to the walk-off between channels.

Fig. 5. Crosstalk as a function of wavelength spacing (λ_probe-λ_pump) at (a) 100 MHz and (b) 2.5 GHz. Fiber length is 25 km and PDL effects are neglected. The input polarizations of the two channels are assumed to be linear and parallel. Owing to the overlap with the total crosstalk of the PM system, the XPM crosstalk for the PM system is barely discernible in (b).

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Fig. 6. Calculated and numerically simulated crosstalk versus the fiber length of SSMF when [modulation frequency, wavelength spacing] is (a) [100 MHz, 2 nm], (b) [2.5 GHz, 2 nm], (c) [100 MHz, 10 nm], and (d) [2.5 GHz, 10 nm]. CD: chromatic dispersion, demod: demodulator. The input polarizations of the two channels are assumed to be linear and parallel. Owing to the overlap with the total crosstalk of the PM system, the SRS crosstalk for the PM system is barely discernible in (c).

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The calculated nonlinear crosstalk for PM and IM systems is plotted as a function of fiber length in Fig. 6. Also plotted are simulation data to show the validity of theoretical analysis. As shown in Fig. 2, in analog PM systems, PM-to-IM conversion occurs through both the demodulator at the receiver and fiber dispersion. We separate these two components in Fig. 6 to show the contribution of each component to XPM. Since XPM-to-IM conversion by fiber dispersion increases with accumulated fiber dispersion, it becomes the dominant source of crosstalk for fiber length of >60 km in Fig. 6(b). The two XPM crosstalk contributors (i.e., one by PM-to-IM conversion by fiber dispersion and the other by PM-to-IM conversion by demodulator) have different phases and thus they can add destructively, depending upon the accumulated dispersion. This can be seen clearly in Fig. 6(b) for a fiber length of 61 km.

It is interesting to note that crosstalk components in PM system fluctuate over fiber length even after the effective length of fiber, L _eff. In unamplified transmission systems, fiber nonlinearities occur mostly within L _eff from the transmitter. Thus, roughly speaking, nonlinear crosstalk components build up until L _eff and then level off after that. The nonlinear crosstalk components in PM system also follow this behavior. As expressed in (6), however, due to the walk-off between the probe and pump channels the RF power on the pump channel oscillates as fiber dispersion accumulates and thus the crosstalk defined in (1) fluctuates.

4. Conclusion

We have presented an analytic expression for inter-channel nonlinear crosstalk in analog PM WDM systems and compared it with two-channel experiment. Due to constant optical intensity of the output of the optical transmitter, the PM system has lower SRS and XPM crosstalk than the IM systems. Especially, the PM system is very effective in suppressing SRS, which are <-90 dB in our experimental conditions even at low frequencies (<1 GHz). Thus, except for some cases where nonlinear crosstalk components cancel out each other in the IM systems, the total crosstalk of the PM system is smaller than that of the IM system. For example, the suppression of nonlinear crosstalk for PM system is >15 dB compared to IM system when wavelength spacing (λ_probe-λ_pump) is >5 nm. Thus, we believe the PM WDM systems can be used for analog CATV systems, radio-over-fiber systems, and clock distribution systems where inter-channel nonlinear crosstalk can limit the system performance.

References and links

1. M. R. Phillips and D. M. Ott, “Crosstalk due to optical fiber nonlinearities in WDM CATV lightwave systems,” J. Lightwave Technol. 17, 1782–1792 (1999). [CrossRef]

2. K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, “50-dB nonlinear crosstalk suppression in a WDM analog fiber system by complementary modulation and balanced detection,” J. Lightwave Technol. 21, 500–505 (2003). [CrossRef]

3. J. Chen, H. Kim, and Y. C. Chung, “Inter-channel interference in multispan WDM transmissions around perfect dispersion-compensated region,” Opt. Commun. 213, 367–371 (2002). [CrossRef]

4. A. L. Campillo, E. E. Funk, D. A. Tulchinsky, J. L. Dexter, and K. J. Williams, “Phase performance of an eight-channel wavelength-division- multiplexed analog-delay line,” J. Lightwave Technol. 22, 440–447 (2004). [CrossRef]

5. H. Kim, H. C. Ji, and J. H. Lee, “Nonlinear optical crosstalk in analog phase-modulated wavelengthdivision-multiplexed systems,” in Proc. OFC 2008, paper JThA69 (2008).

6. A. L. Campillo, “Interchannel nonlinear crosstalk in analog polarization modulated WDM systems,” J. Lightwave Technol. 24, 1186–1193 (2006). [CrossRef]

7. H. Kim, “EML-based optical single sideband transmitter,” IEEE Photon. Technol. Lett. 20, 243–245 (2008). [CrossRef]

8. H.-C. Ji, H. Kim, and Y. C. Chung, “Full-duplex radio-over-fiber system using phase-modulated downlink and intensity-modulated uplink,” to appear in IEEE Photon. Technol. Lett. (2008)

9. A. R. Chraplyvy, R. W. Tkach, L. L. Buhl, and R. C. Alferness, “Phase modulation to amplitude modulation conversion of CW laser light in optical fibers,” Electron. Lett. 22, 409–410 (1986). [CrossRef]

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Parameter		Value
Fiber loss	α	0.2 dB/km
Mode effective area	A_eff	80 µm²
Dispersion coefficient		16.5 ps/nm/km
Nonlinear refractive index	n₂	2.6×10^-20 m²/W

Inter-channel nonlinear crosstalk in analog phase-modulated wavelength-divisionmultiplexed systems

Abstract

1. Introduction

2. Theoretical analysis

2.1. PM-to-IM Conversion by Demodulation Filter and Fiber Dispersion

2.2. Stimulated Raman Scattering

2.3. Cross-Phase Modulation

3. Experiment/simulation and discussion

4. Conclusion

References and links

Cited By

Figures (6)

Tables (1)

Equations (25)

Optics Express