1. Introduction

A continuous growth in the aggregate data transfer rate, either by an increasing number of nodes, or high bandwidth-demanded applications (i.e. video), necessarily requires simultaneous increase in the data processing capacity (i.e. switching/routing) in the network back bone. Therefore, the reduction of the number of optical-to-electrical conversions is critical for the overall processing complexity and/or its size and dissipation. Furthermore, an all optical processor, or a combination of an optical pre-processor and a sub-rate electrical backplane certainly represents a powerful concept for circumventing the electrical processing speed and power consumption bottlenecks.

Optical parametric mixing has been established as the pre-processing architectures for the task at hand [1]. In fact, the parametric mixing has been successfully employed in high-gain high-bandwidth amplification, phase sensitive amplification, wavelength conversion, phase conjugation, multicasting, regeneration, switching, multiplexing, and sampling [1, 2]. The four-wave mixing (FWM) process in silica with its exponential gain and high efficiency, as well as the femtosecond response and phase preservation over a wide spectral range make the parametric mixing – based processes excellent candidates for a spectrally invariant, band translator technology extending from the visible to the IR regions [3]. Indeed, the parametric converters satisfy both important requirements critical for WDM applications: bit rate-, as well as modulation format-transparency.

The parametric converter architecture is rather simple: a pump wave mixes with an information-bearing signal to create its replica(s) (idler(s)) at a different wavelength(s), whereas the envelope of the created idler follows the signal waveform complex conjugate envelope, gated by a pump wave. Figure 1 shows the single pump parametric converter. In reality, however, multiple impairment mechanisms are involved in parametric mixing process and result in degradation of the signal to noise ratio (SNR) and an unwanted signal/idler distortion. For one, the pump fluctuations have been identified as a major source of such impairments [4–6]. These pump fluctuations originate from different sources such as: amplified spontaneous emission from optical amplifiers (ASE), random jitter, laser relative intensity noise (RIN) [7] and can be further enhanced by nonlinear mixing. When present, the pump noise is necessarily imprinted onto all waves involved in the parametric interactions. As a subclass of parametric processors, the wavelength converters based on highly nonlinear fibers (HNLF) are inherently susceptible to the pump-induced impairments [4, 7]. In practical terms, to obtain the transparent conversion over the bandwidth of several tens of nanometers in a typical HNLF-based mixer with the length of several tens of meters, relatively high pump powers exceeding hundreds of milliwatts are required. Such power can be achieved by using an optical amplifier which necessarily adds a finite level of ASE noise to the pump wave.

 

Fig. 1 Single pump parametric wavelength conversion.

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Recognizing these limitations, in this contribution we investigated the pump noise effect removal after the optical-to-electrical conversion is performed. The approach is motivated, in part, by ubiquitous use of digital signal processing in the modern communication links. We previously demonstrated the pump noise cancellation in analog application of the parametric sampling gates [8] based on synchronous detection of the idler and pump waves. In this work, we describe the same method in digital application to compensate the pump-noise transfer in the HNLF-based parametric converter. Consequently, we experimentally demonstrate a rigorously quantified 4 dB improvement in the wavelength conversion performance.

2. Noise cancellation algorithm

In the single pump parametric mixer and under the low parametric gain assumption, the idler intensity can be expressed as having a quadratic dependency on pump power [2] and can be approximated by,

In practice and for a typical converter design, the walk-off delay time between the pump and idler waves are negligible (i.e. ~0.1 ps) and result in a relatively strong correlation between the two waves at the mixers output. Indeed, in an efficient mixer, the pump and idler are travelling at almost the same speed inside the nonlinear medium, such that the unwanted instantaneous fluctuations of the pump wave are synchronously imprinted on the idler(s). In consequence, once the fluctuations of the pump are detected, they can be effectively subtracted from fluctuations of the idler. It ought to be pointed out, however, that the fact that the equalization is performed in the digital domain does limit the applicability of the technique and bounds it to a single conversion step. Nevertheless, the technique and the underlying concept do represent an important step in performance improvement of parametric devices.

Figure 2 illustrates the architecture of the equalization approach. The scheme relies on subtracting an appropriate correction term from the detected idler to reduce the idler excess noise imposed by the pump fluctuations. Since the idler noise is a result of the beating between the pump noise,$n_p(t)$, and the signal mean value, $\overline{S}(t)$, the pump noise predominantly contaminates the “1” bit intervals in the idler bit stream. Consequently, the correction signal is constructed from the product of the pump and idler waves, rather than from the pump alone in order to guarantee that the noise variance in the “0” bit periods is not increased by the correction signal. This fact is made clear in Fig. 2 that emphasized the absence of correction in logical “0” intervals

 

Fig. 2 Pump noise cancellation architecture.

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The equalization can also be mathematically described using the following relation,

In Eq. (3),$P(t)$and$\overline{P}(t)$are the instantaneous and averaged pump power respectively. A numerical factor$\alpha$can be obtained using a simple search algorithm minimizing the idler BER. In more detail, the proposed technique decorrelates the pump and idler by simultaneously detecting the pump and idler and removes the corresponding pump fluctuation from the idler. Figure 3 shows the pump/idler intensity scatterplot before and after the equalization. The correlation between the pump and idler is represented by the 45° tilt of the noise cloud in Fig. 3(a), implying a strong correlation between the two waves. The effect of the algorithm in removing the pump noise from the idler is represented by the absence of the noise cloud tilt in Fig. 3(b). Note that in the case of idler only detection (that with respect to the result shown in Fig. 3 is interpreted as the marginal distribution in the x-axis direction) the noise fluctuations are significantly diminished after the pump noise contribution subtraction, or, equivalently the decorrelation procedure. According to the simulation results, almost $20{\log }_{10}\left(\sigma /{\sigma }_{eq}\right)\approx 6$ dB improvement in idler SNR can be obtained using the proposed algorithm.

 

Fig. 3 Pump/Idler intensity scatterplot (a) before equalization and (b) after the equalization. (Any tilt in the noise cloud represents a correlation between the pump and idler.)

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With the aim of evaluating the performance of the method, a highly nonlinear fiber (HNLF) based parametric converter has been simulated utilizing a nonlinear Schrodinger equation solver software and the idler bit error rate (BER) have been calculated for different pump and signal OSNR. The parametric converter was designed to translate a 10 Gbps OOK signal over 20 nm of bandwidth. Figure 4(a) shows the obtained idler BER as a function of signal OSNR and different pump OSNR. In the case of the high pump OSNR the idler performance follows the back to back 10 Gbps OOK signaling performance represented by the black curve. The performance curve is characterized by the error floor characteristics for a low pump OSNR (blue curve) which is itself an indication of the minimum noise on the idler imposed by the pump. In contrast, after the equalization, the performance characteristic (red curve) reverts back close to the ideal performance. In effect, the equalized performance corresponds to the utilization of a pump characterized by a 5 dB better OSNR (green curve). Furthermore, the BER curve as a function of pump OSNR, before and after the equalization, has been calculated for different signal OSNRs. The difference between the required pump OSNR to achieve idler BER = 10⁻⁴, before and after the equalization is plotted in Fig. 4(b). The simulation results estimate approximately uniform 5 dB improvement in the required pump OSNR regardless of the signal OSNR (see Fig. 4(b)).

 

Fig. 4 Simulation results. (a) Idler BER for 10 Gbps OOK signaling as a function of signal OSNR and different pump OSNR. (The equalization scheme gains 5 dB in required pump OSNR.) (b) Pump OSNR improvement using the equalization algorithm as a function of signal OSNR.

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3. Experimental results

The experimental setup for the single pump parametric wavelength converter is shown in Fig. 5 . The optical frontend consists of the conventional pump and data modulated signal which enter a parametric interaction in the HNLF based mixer. Conversely, the electrical back plane, unlike the conventional single threshold receiver, is specifically designed for simultaneous capture and digitization of the pump and idler waves. A digital signal processing (DSP) unit applies the equalization algorithm to the quantized pump/idler to improve the idler quality.

 

Fig. 5 Correlation measurement and mitigation topology: LD: Laser Diode, MZM: Mach-Zehnder Modulator, A: Amplifier, N: ASE noise source, PC: Polarization Controller, PPG: Programmable Pattern Generator, WDM: Wavelength Division Multiplex filters, VOA: Variable Optical Attenuator, HNLF: Highly Nonlinear Fiber, OLPF: Optical Filter, τ1,2: optical delay lines, ELPF: Electrical Filter, PD: receiver, ADC: Analog to Digital Converter. DSP: Digital Signal Processor.

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The signal was generated by a laser diode (LD₁) centered at 1569.2 nm and modulated using on-off keying (OOK) format in a Mach-Zehnder modulator (MZM₁). The modulator was driven by electrical 10 Gbps non-return to zero (NRZ) pattern. The pump (LD₂), centered at 1579.5 nm, used a second modulator (MZM₂) driven by a 5 GHz clock source operated in the carrier suppressed regime, in order to guarantee the effective suppression of Brillouin scattering, thus availing the experimental condition which focuses on the pump noise induced degradations. After amplification, pump and signal were combined and launched into a parametric mixer constructed using a 40 m-long HNLF with nonlinear coefficient of 25 W⁻¹km⁻¹ and zero dispersion wavelength of 1579 nm, and dispersion slope of 0.018 ps/nm²/km. The average signal and pump optical powers at the input of the HNLF were set to 18 dBm and 30 dBm, respectively. To precisely control the pump OSNR, the pump was coupled with an external noise source (N) followed by the variable optical attenuator. Optical flat top filters with 1 nm bandwidth were used for multiplexing and separating the signal, pump, and idler waves. The pump and idler were aligned in time using optical delay lines (τ₁ and τ₂) guaranteeing a synchronous acquisition of the waveforms. Then, the separated waves were detected by two independent receivers with 10 GHz bandwidth, sampled, and digitized using a real time oscilloscope operating at 50 GS/s with 5 effective number of bits (ENOB). Finally, the sampled waveforms were passed to a post-processing unit to measure the performance of the scheme. In all measurements, the signal OSNR was held constant at 25 dB.

Figure 6(a) and 6(b) show the experimental results measured in two regimes corresponding to different pump OSNRs. Specifically, in the case of low pump OSNR (< 20 dB), the idler bit errors were counted, ensuring the 10% statistical confidence. The sampling time and decision threshold were estimated using numerical optimization minimizing the BER. It is clearly seen from Fig. 6(a) that the adoption of the proposed algorithm provides a 4 dB improvement in the receiver performance. In contrast, the idler BER estimation corresponding to the pump OSNRs higher than 20 dB, combined with numerical off-line post-processing, requires excessive acquisition times. In the latter case, instead of the rigorous BER metric, the quality factor Q was estimated from the 2¹⁵ bits of the captured idler and equalized idler as,

 

Fig. 6 Experimental results. (a) Measured BER of 10 Gbps OOK signaling converted over 20nm by a single pump parametric mixer. The red dashed line represents the detected idler BER as a function of pump OSNR. The blue solid line is the equalized idler BER using the noise correlation between the pump and idler. (The signal OSNR was fixed at 25 dB). (b) Measured idler Q² factor at 10 GHz noise bandwidth before (dashed) and after (solid) equalization using the pump and idler correlation property.

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4. Conclusion

We have introduced a new technique for the performance improvement of the optical parametric wavelength converters. Typically, any impairment associated with the pump in paramedic converters, results in quality degradation of the converted signal (i.e. idler). In the proposed technique, in contrast to the standard conversion setting, both idler and pump waves are synchronously detected and digitized. Then, the pump intensity fluctuations are used to compensate for the pump-induced (i.e. correlated) fluctuations in the idler in the digital domain. A 4 dB improvement in receiver performance was experimentally demonstrated for a fiber-based converter. The technique bears significant implications to the construction of parametric devices, since it for the first time allows applications of lower-grade pump oscillators in wavelength converters. Furthermore, the proposed method can be generalized for other parametric devices.