recovery. Data recovery. S/P & FFT. Fig. 8. The experimental configuration using CO-OFDM signal. The experimental .... Conf., Los Angeles, CA, USA, Mar. 2012 ...
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JLT.2016.2586944, Journal of Lightwave Technology
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REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < experiment by replacing the CW light with a CO-OFDM signal and verify that the RPN will occur in a practical transmission system. Finally, we use the measured transfer function to evaluate the transmission performance of a typical long-haul Raman amplified coherent optical communication system using 112 Gb/s PM-QPSK or 256 Gb/s PM-16QAM signal. II. THEORETICAL BACKGROUND The RPN is the phase noise caused by fiber nonlinearity. Through XPM effect, the phase of signal is modulated by Raman pumps. Such phase modulation is not a constant but a stochastic process since the Raman pump power has fluctuation. In [10], using scalar coupled amplitude equations and assuming non-depletion of pump, we derived the analytical expression of the Raman-induced phase shift generated within a single span: θ RPN = γ s (2 − f R )Ψ ± ( z, T ) (1) where
∫
+
Ψ= ( z, T ) ( z, T ) Ψ −=
z
0
∫
z
0
2
A (0, T + zd − z ′d ) exp(−α p z ′)dz ′ + p
(2)
2
Ap− ( L, T + zd − z ′d ) exp −α p ( L − z ′) dz ′
(3)
Here, γ s is the nonlinear parameter of signal, f R is the fractional Raman contribution, the plus and minus sign denote the co- and counter-pumping configurations respectively, z and T are the distance and reduced time (retarded reference frame) respectively, d is the walk-off parameter, α p is the attenuation of Raman pump, and Ap
2
is the pump power.
Based on harmonics analysis method, the phase fluctuation δθ RPN at a specific modulation frequency f and the corresponding RPN ( f ) = δθ
2 RPN
θ RPN
2
2
The reasons are twofold. First, according to the theory, the RPN generated by counter-pump will not cause non-negligible penalty to the system. This is because the cut-off frequency of the counter-pumping transfer function H RPN ( f )counter is below kHz, which is six order less than the typical baud-rate used in the current high speed coherent transmission systems. It means that the phase noise in this case can be effectively treated as a constant over quite a few symbols and can thus be easily removed by the carrier phase estimation (CPE) algorithm. Second, due to the low cut-off frequency feature, the counterpump induced phase modulation is slowly varied and is difficult to be measured since the phase variation will be submerged with other types of phase noise, such as laser phase noise, frequency-offset and white noise. III. EXPERIMENTAL MEASUREMENT In this section, we conducted an experiment to measure the RPN transfer function for co-pumping configuration. The RINto-RPN frequency response can be measured by applying a known amount of modulation on the Raman pump and detecting the resulting phase modulation on the received signal. By sweeping the modulation frequency, the transfer function can be obtained. In what follows, we will first describe the experimental set-up. Then, we will illustrate the modulation frequency response of the Raman pump diode used in the experiment. Next, we will discuss the signal model upon coherent reception and show the main steps of calculation. The final measurement result will be presented and compared with theoretical calculation in the last part. A. Experimental set-up
can be found [10],
where ⋅ denotes average. The RPN transfer functions for coand counter-pumping configurations are given by [11]: −α z −2α z α p2 RPN co ( f ) 1 − 2e cos ( 2π fd ) + e H = = RPN ( f ) co 2 RIN p ( f ) α p2 + (2π fd ) 2 (1 − e−α z ) p
p
(4)
p
RPN counter ( f ) 1 − 2e p cos ( 2π fd ) + e = RIN p ( f ) α p2 + (2π fd ) 2 α z
H = RPN ( f ) counter
2α p z
(e
α p2
αpz
)
−1
2
(5)
In [14], taking the consideration of polarization effect, the coefficient of the phase shift is changed from (2 − f R ) to 4 3 . However, the form of the transfer function remains the same. In pump depletion regime, the transfer function can be determined through numerical calculation [11]. Since the Raman pump RIN can be regarded as a stationary Gaussian stochastic process, consequently the RIN-induced RPN is also Gaussian distributed. Its statistical property depends on both the pump RIN and the transfer function. In practice, the pump RIN can be easily measured. Therefore, it is crucial to know the transfer function in order to predict the statistical property of RPN and develop efficient noise suppression techniques. In this paper, we will directly measure the RPN transfer function by applying a known amount of modulation on the Raman pump and detecting the resulting phase modulation on the received signal. Only co-pumping RPN transfer function is measured here.
Fig. 1. Experimental set-up.
The experimental set-up is depicted in Fig. 1. An external cavity laser (ECL) with ~50 kHz linewidth is split into two beams by a polarization-maintaining 3dB coupler. One beam is used as signal and is launched into 100 km standard single mode fiber (SSMF) link after passing through a variable optical attenuator (VOA). The input power is –6 dBm. The other beam is used as the local oscillator (LO) for self-homodyne detection and its power is 12 dBm. A depolarized Raman pump diode centered at 1457 nm is biased to produce 100 mW output on average. A small amount of sinusoidal modulation tone was applied to the CW driving current using an arbitrary function generator (AFG), and the frequency response of the pump laser was measured using a photodiode and an electrical spectrum analyzer (ESA). The measurement results will be shown in the next part. The Raman pump co-propagates with the signal along
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JLT.2016.2586944, Journal of Lightwave Technology
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REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT)
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