1. Introduction

Fiber Optical Parametric Amplifiers (FOPA) provide signal amplification and idler wave generation based on four wave mixing (FWM) in an appropriately designed optical fiber [1]. Compared to the ubiquitous erbium doped fiber amplifier (EDFA), the FOPA response is ultrafast and not spectrally constrained to spectral coverage of electronic transition bands, but is fully defined by the dispersion properties of the waveguide. Indeed, based on the properties above, FOPAs have demonstrated record gains [2], record gain bandwidths [3,4] and have proven themselves as the most practical means of ultrafast all optical signal processing [5,6]. Two-pump FOPAs utilize the same FWM process as their single pump counterparts, however using two pump lasers positioned approximately symmetrically around the fiber zero-dispersion wavelength (ZDW) [7]. Through three FWM processes, two-pump FOPAs generate three idler waves in addition to the signal amplification, enabling significant flexibility in all optical signal processing. Additionally, this architecture enables higher gain and wider, more uniform gain bandwidth regions than those offered by one-pump FOPAs [7].

From a practical perspective, one of the fundamental limitations to the development of FOPAs is Stimulated Brillouin Scattering (SBS). The SBS is a non-linear optical phenomenon which sets a hard limit to the maximum amount of optical power that can be coupled into a waveguide [1]. For FOPA systems, this implies a strict limit to the pump power that can be delivered to the HNLF due to a generated backward propagating wave due to material properties. This input power is generally referred to as the SBS threshold and is defined for an effective interaction length L_eff, effective modal area A_eff and Brillouin gain parameter g₀ with Brillouin gain bandwidth and the incident pump linewidths Δν_B and Δν_p respectively as [8]:

Presently, there are two prominent strategies used to suppress SBS experimentally. The first technique seeks to increase the SBS threshold by manipulating the Brillouin bandwidth Δν_B and thus the peak gain, g₀. Alternatively, the second manipulates the incident laser linewidth Δν_p in order to minimize the spectral overlap between the incident laser and the Brillouin bandwidth, thus limiting the gain experienced by the back-reflection, a dependence clearly recognized in Eq. (1).

The typically used methods to broaden Δν_B include: introducing temperature gradients along the fiber [9], introducing longitudinal strains [10,11], and changing the dopant concentration in the fiber [12], all of which are methods of shifting the Brillouin frequency ν_B along the fiber length. These methods have demonstrated significant increases in the SBS threshold of up to 15 dBm [10] in the best case. These, termed passive, material methods for SBS suppression enjoy the distinct advantage of simplified subsequent FOPA implementation due to the lack of necessary additional components. However, more importantly, such implementations do induce a change in the dispersive properties of the fiber of interest, a fact that is generally undesirable in the FOPA implementation. In addition, the passive methods listed above, provide a smaller SBS threshold increase.

Alternatively, the active SBS suppression methods seek to instead broaden the linewidth of the incident light to reduce the coherent buildup of the generally narrow SBS bandwidth. This objective can be achieved by direct pump source frequency modulation, or by imparting (external) phase modulation, without introducing significant intensity modulation on the laser of concern [13]. In either case the laser is dithered in either phase or frequency by a controlling electrical waveform. Typical waveforms demonstrated for dithering include single or multiple harmonics [14,2], and pseudorandom bit sequences [15]. Linewidth broadening using phase modulation has been shown to be an extremely effective SBS suppression method with threshold increases of up to 22dB recorded using five combined sinusoidal tones up to 10GHz [2]. Such active methods provide a significant performance advantage over the passive methods of SBS suppression and are thus widely used, despite the additional complexity of implementation.

While active systems enjoy a performance advantage, they are not without their drawbacks. When used in a FOPA system operating under significant gain, the increased pump linewidth has been shown [16] to introduce signal gain fluctuation, thus introducing amplitude modulation on both the signal and the idler, thus degrading the signal quality factor (Q). Even more significantly, the phase modulation from the pump is transferred to the idler in FOPA systems. The excess idler broadening directly transfers to an increased penalty of the information modulated streams experiencing incomplete dispersion compensation [17] and/or filter dispersion. These considerations demonstrate the necessity of pump-dithering optimization, thus minimizing the above mentioned penalties, while maintaining the SBS threshold limit.

Naturally, due to the relationship between the bandwidth of the electrical phase modulating signal, the bandwidth of the broadened pump, and the resulting broadening of the idler, it follows that the ideal electrical waveform ought to occupy the least spectral bandwidth possible. The current state of the art among the pump-dithering methods utilizes multiple, carefully selected, electrical sinusoidal frequencies generated by voltage controlled oscillators (VCO) to maximize the effectiveness of the SBS suppression [14]. The frequencies are selected to maximize the spectral broadening and power distribution. According to elementary Fourier analysis, the spectral distribution of a harmonic driven phase modulation exhibits Bessel-function of the first kind - distributed amplitudes of the frequency components in the phase modulated pump, where the second harmonic is significantly weaker than the zeroth and first orders. Thus, practically speaking, the frequency separation of the multiple tones used for SBS suppression corresponds to frequencies which are factors of three of each other [9,14]. While this method has been proven to be an efficient scheme for suppressing SBS, the optical bandwidth occupied by such waveforms is prohibitively large (25GHz for the current record) for systems requiring reliable information transfer. The excess optical bandwidth broadening in the above well-established methods is a consequence of the discrete nature of the modulation and the unused bandwidth between the spectral peaks.

In this contribution, we introduce and quantify two new electrical modulation schemes, poised to provide equal SBS suppression to the current standard relying on pure sinusoidal tones, however with significantly reduced linewidth broadening, consequently avoiding excess bandwidth beyond that required for a given increase of a certain Brillouin threshold.

2. Theoretical foundations

As noted in the introductory section, previously demonstrated pump dithering schemes were suboptimal in that the resulting bandwidth significantly surpassed the bandwidth necessary for the obtainable amount of SBS threshold increase. For instance in [2], an increase in threshold of 20 dB was obtained by effectively broadening the pump linewidth to as much as 25 GHz which is more than four times the bandwidth necessary for the obtained amount of SBS threshold increase, and originates from the (inherently) discrete spectrum of the harmonically driven phase modulation [14] with a low spectral filling ratio. It ought to be emphasized, however that strict comparisons between different experiments are not straight forward due to difference in fiber SBS properties that vary across fiber samples. Ideally (i.e. for the minimum bandwidth occupancy), the SBS suppressing pump should possess a uniform continuous spectrum across the occupied bandwidth for maximum suppression to bandwidth efficiency. In practice, it is easiest to satisfy the last requirement with frequency-varying waveforms, since the elementary Fourier analysis precludes continuous spectrum generation over a limited observation time [Bracewell]. Consequently, in this work the sought after requirement is achieved in two different ways: (i) using a deterministic waveform, namely the chirp; and (ii) random - noise-like waveforms, relying on an RF-noise source that will inherently achieve the desired functionality.

The most straightforward example of this is the linear sinusoidal chirp waveform defined as:

In Eq. (2), i is the imaginary unit, ν₀ is the initial frequency, and k represents the chirp rate or rate of frequency increase/decrease. However, the continuous linear chirp does not satisfy SBS threshold mitigation properties in that the consecutive frequencies must be separated by more than the SBS coherence bandwidth (20-50MHz). Furthermore, as a practical consideration, the switching time between the modulation frequencies should be shorter than the phonon lifetime, τ_p, in the HNLF for effective SBS suppression. This limitation thus prompts the implementation of a modified, discontinuous, precisely controlled frequency-hopped waveform which can easily be realized given current available electronics. Consequently, the first approach can be summarized as follows: By providing a discontinuous frequency-hopped chirp, the modulation frequency is swept discontinuously over a given range, abruptly switching to new frequencies at least 30 MHz away. The dwelling time of each frequency hop ought to be less than 10 ns, ensuring compliance with SBS mitigation properties.

Additionally, while an RF chirp being supplied to a phase modulator possesses a flat electrical spectrum, it must be noted that this will not produce a spectrally flat optical chirp due to the nonlinear nature of the transfer characteristic of the phase modulation [18]. The optical power, therefore, will not be uniformly distributed as desired, but will distribute in a suboptimal staircase pattern [18]. This limitation can be circumvented by manipulating the amplitude of the driving electrical waveform to be many times greater than the V_π voltage of the phase modulator. This straightforward technique effectively enhances the higher order tones by driving the phase modulator in an unconventional regime (i.e. driving with a 6 V_π voltage swing), thus realizing a flat optical spectrum as desired in a manner similar to that used with VCO tones and a saturated modulator driver [14].

Expanding upon the limitations of an RF sinusoidal chirp, an alternative waveform providing a flat electrical, and more importantly optical, spectrum is a random Gaussian white noise source [18,19]. An RF noise source presents a promising alternative since it avoids the frequency switching and phase modulator overdriving workarounds of a controlled chirp waveform by virtue of its random nature. This simplification poises the RF noise source as an attractive alternative SBS suppressing phase modulation waveform for investigation which will be demonstrated and quantified in detail in the following section.

3. The SBS threshold increase quantification

The standard experimental setup for measuring the SBS threshold is depicted in Fig. 1 . A tunable laser was used as the pump and fed into a Lithium Niobate phase modulator which was driven at V_π (except as indicated) by the electrical waveform configuration under test. The modulated pump signal was passed into a 1W EDFA booster followed by a variable optical attenuator (VOA) used to control the amount of incident power that was allowed into the fiber. The resulting signal was fed into the first port of a circulator which connected at the second port to a 200m piece of HNLF with a nonlinear coefficient [20] γ = 0.013 W⁻¹m⁻¹ following a 99/1 tap (omitted in Fig. 1) to monitor input power and terminated at a power meter to monitor the output power transmitted through the fiber. Finally, the third port of the circulator was connected to an additional power meter to monitor the backreflected power and detect the onset of the SBS.

 

Fig. 1 Experimental setup for SBS Threshold measurement. PC – Polarization controller, RF – Radio Frequency Tones, PM – Phase Modulator, EDFA – Erbium Doped Fiber Amplifier, VOA – Variable Optical Attenuator, SMR – Single Mode Fiber.

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The desired phase modulating waveforms were generated using their respective sources. The sinusoidal chirp waveforms were generated using a Direct Digital Synthesizer (DDS) with a maximum tunable range of DC – 400MHz for high phase stability and fast frequency switching times. Chirp patterns were programmed into the RAM of the DDS to produce frequency sweeps with bandwidths from as wide as 20MHz to 400MHz to as narrow as 300MHz to 400MHz and the results were compared to demonstrate the dependence of the SBS suppression on chirp bandwidth. To realize the frequency-hopped chirp, the DDS was separately programmed to switch frequencies in a discontinuous yet highly controlled manner operating at the most effective bandwidth as determined above. This alternative concept takes advantage of the DDS’s ability to discretely switch over large frequency spans and consists of splitting the effective 350MHz bandwidth into five discrete bins of 70MHz each with 208 frequencies per bin. The output frequency was then switched between bins systematically to maximize the spectral distance from the immediately preceding frequency. This same waveform was then amplified by a high power 29dBm electrical driver before feeding the phase modulator with waveforms at many levels greater than V_π to find the optimal drive voltage to maximum SBS suppression. Finally, a 1.5 GHz RF noise source was used in the same setup, filtered with a number of low pass filters ranging from 225MHz to 1.5GHz in order to investigate the RF noise bandwidth effect on the SBS suppression capability. Before presenting the results, it is worthwhile to mention that variation in SBS bandwidth in optical fibers are known to cause difficulty in strict results' reproducibility in different FOPAs.

As seen in Fig. 2(a) , the optimal RF chirp bandwidth for the HNLF used was from 50 MHz to 400 MHz for a total bandwidth of 350 MHz. The result is as expected since Δν_Β of HNLF is generally approximately 20-50 MHz, hence phase modulation at frequencies below this did not contribute significantly to increasing the SBS threshold. The HNLF used in the tests had a CW SBS threshold of 15 dBm, thus the use of the 350 MHz chirp represented an 11 dB threshold increase, approximately equivalent to the increase expected from three VCO tones. Comparing this to the expected threshold increase predicted by Eq. (1) of approximately 16 dB indicates inefficiency in the operation of the continuous linear chirp, restricting the system capabilities.

 

Fig. 2 (a) SBS threshold chirp bandwidth and (b) Drive voltage dependence with associated PM spectra. The insets show the corresponding qualitative optical spectra.

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The switching chirp waveform was also implemented spanning the bandwidth from 50MHz–400MHz. While no significant change in the spectral shape was observed, the application of the alternative frequency-hopped chirp resulted in a <1dB increase in the SBS threshold with respect to the CW case, [see Fig. 2(a)]. The observed behavior indicates that while waveform timing is a significant issue for SBS suppression with phase modulation, that a more stringent restriction is hindering the system performance.

As implied previously, the RF linear chirp with a V_π amplitude is a suboptimal driving signal for obtaining a flat chirped optical spectrum and in fact results in a stair-case-like optical spectrum [see inset in Fig. 2(a)]. For ideal SBS suppression the resulting modulated spectrum of the pump wave ought to be uniform across its span resulting in even power distribution across the entire pump linewidth. To overcome this obstacle, the phase modulator was overdriven many times above V_π. An example is depicted in Fig. 2(b), where it is shown that the staircase pattern associated with the DDS chirp has been smoothed out by enhancing the higher order harmonics while minimally broadening the FWHM linewidth of the pump to approximately 2.5GHz.

The same SBS measurement system was used to verify the effect that the increased level of spectral flatness had on the SBS threshold increase with the results shown in Fig. 2. From the data, it is clearly evident that the increased drive voltage (and thus increased spectral flatness) results in an incremental increase in the measured SBS threshold. In the best case, at a drive voltage of 19.77 V peak to peak (p-p) (approximately 6 times greater than the V_π of the modulator) we have an increase in SBS threshold of approximately 4 dB over the normally driven case. This corresponds to an increase of approximately 15 dB in SBS threshold over the CW case, which is comparable to the estimated value of 16 dB as predicted from Eq. (1). This increase demonstrates that overdriving the phase modulator in order to increase the effectiveness of the chirp for SBS suppression by phase modulation successfully addresses the issue of inefficiencies in efficient phase modulation using a chirped sinusoidal waveform.

An RF noise source generates a low-passed white (i.e. uniform) spectrum spanning a given bandwidth while at any given time instant, t, having random frequency, phase, and amplitude components. While the noise source produces a similar result as the chirp or controlled switching DDS, it must be noted that the extra degrees of freedom granted by changing the amplitude and phase combined with the random nature of the switching indeed sets the noise source apart from previous waveforms generated. To determine the effectiveness of a white noise source for SBS suppression, a noise source with output bandwidth from 10 MHz to 1.5 GHz was low pass filtered to control output bandwidth and used to drive a single phase modulator in the setup shown in Fig. 1. The phase modulated spectrum of the pump is shown in Fig. 3 and shows that the peak power has been significantly suppressed and that the pump linewidth has been broadened to a FWHM of approximately 6 GHz for a full 1.5 GHz noise source. When plugged into Eq. (1), this linewidth is estimated to yield an SBS threshold increase of approximately 20 dBm.

 

Fig. 3 Noise Source bandwidth effects on SBS threshold increase with associated optical spectrum.

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The results of the test sweeping output bandwidths of the noise source are displayed in Fig. 3. We note that even with a bandwidth as low as 225 MHZ, corresponding to a resulting pump spectrum FWHM of approximately 900 MHz, there is an observed SBS threshold increase of approximately 12.5 dB that is comparable to that offered by either three VCO tones or a typical DDS chirp and is in good agreement with the predicted value of 12.8 dB SBS threshold increase from Eq. (1). Furthermore, as the bandwidth of the noise source was increased the SBS threshold also increased following the theoretical trend described by Eq. (1). In the broadest case, 1.5 GHz, an SBS threshold increase of approximately 19 dB was observed, yet again in very close agreement to the 20 dB theoretical prediction. This increase allows for a pump launch power of 3 W into 200 m of HNLF and currently represents the highest attained SBS threshold increase to date, with a narrow-band modulation and a single phase modulator.

3. The effect of pump dithering on signal integrity

3.1 Signal integrity analysis: experimental setup

In the previous section the SBS threshold increase attributable to each proposed phase modulation system was quantified. In order to strictly evaluate the penalties associated with the idler broadening incurred under each method, bit error ratio (BER) measurements were taken for the most effective cases of each method including the current standard VCO generated sinusoidal waveform with constituent frequencies of 60MHz, 180MHz, 540MHz, and 1620MHz, a frequency-hopped chirp ranging from 50MHz to 400MHz, the same chirp waveform driving a phase modulator with 6V_π peak-to-peak amplitude, and an RF noise source of 1.5 GHz electrical bandwidth.

There were three primary constituents of the test system used: the transmitter (TX), the FOPA system, and the receiver (RX). The transmitter, shown in the first stage of Fig. 4 , was used to generate the input data signal for the amplifier as well as to impart a controlled level of noise in order to take meaningful BER measurements versus input optical signal to noise ratio (OSNR). The output of the transmitter thus represented the input signal for the FOPA, under conditions of varying input signal quality. A laser at 1552 nm was used as a signal modulated by an amplitude modulator with a 10 Gb/s 2³¹-1 pseudo-random bit sequence (PRBS) non-return to zero (NRZ) data, amplified by a low noise figure (NF) erbium doped fiber amplifier (EDFA) preamplifier, and passed through a variable optical attenuator (VOA) to control the signal level input into a 3dB coupler. An amplified stimulated emission (ASE) noise source was filtered by a 1 nm single cavity Fabry-Perot (FP) etalon filter, subsequently amplified by an EDFA preamplifier, and passed through a VOA enabled precise control of the injected noise level, and thus the system input OSNR variation. The EDFA output was filtered by a 1 nm single cavity FP etalon filter prior to coupling with the signal. The combined output of the 3 dB coupler was attenuated by yet another VOA allowing flexible control of the input level introduced into the two pump FOPA. The output of the TX block was tapped to measure the back to back BER and OSNR and the TX was shown to produce a BER at a reference level of 10⁻⁹, assumed henceforth, at an OSNR of 15.3dB.

 

Fig. 4 Transmitter (TX): PC - Polarization Controller, PRBS – Pseudo-random Bit Sequence Data, AM - Amplitude Modulator, EDFA - Erbium Doped Fiber Amplifier, VOA - Variable Optical Attenuator, OSA - Optical Spectrum Analyzer. Two pump FOPA: PC - Polarization Controller, RF – Radio Frequency Waveform, PM - Phase Modulator, EDFA - Erbium Doped Fiber Amplifier, WDM - Wavelength Division Multiplexer, OSA - Optical Spectrum Analyzer, HNLF – Highly Nonlinear Fiber. Reciever(RX). EDFA - Erbium Doped Fiber Amplifier, OSA - Optical Spectrum Analyzer, VOA - Variable Optical Attenuator, SMF - Single Mode Fiber

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The FOPA, depicted in stage 2 of Fig. 4, consisted of one pump laser at 1539 nm which was phase modulated by the current modulation system under test, amplified by a high power EDFA booster, filtered by a 2 nm double cavity FP etalon filter to reject the excess noise around the pump, and combined into a wavelength division multiplexer (WDM). The second pump was generated at 1580 nm, similarly passed through a phase modulator driven by the waveform system under test, amplified by a high power EDFA with maximum output power of 3W, and filtered by a 1nm double cavity FP etalon filter before being combined into the WDM. Polarization controllers were included at the inputs to the phase modulators, the EDFAs, and the WDM in order to ensure proper polarization alignment of the pump lasers in the FOPA system. The modulation systems were each precisely tuned in order to offer the maximum SBS suppression efficiency as previously determined. The output from the WDM was coupled with the signal in the 90% port of a 10/90 power coupler while the signal was coupled into a polarization controller prior to the 10% port. The combined pumps were fed into the first port of a circulator, whose second port was connected to a spool of HNLF, whereas the third port was used for SBS monitoring on a high resolution OSA. The HNLF used was 175 m long and had a zero dispersion wavelength λ₀ = 1562 nm with a nonlinearity coefficient [20], γ = 0.016 W⁻¹m⁻¹ and an SBS threshold of approximately 15 dBm; the output of which was fed into the input of the receiver block.

The receiver, depicted in stage 3 of Fig. 4, stripped the high power pumps from the output of the HNLF using two FP etalons (a 2 nm wide double cavity and a 5 nm wide double cavity). The resulting filtered idler power was then measured and passed through a low NF EDFA preamplifier to prevent detector thermal noise from affecting the BER measurements. The idler was then passed through a final detector 0.6 nm single cavity FP etalon, attenuated by a VOA, then passed through 10 km of SMF for performance characterization after dispersion, or run directly into the photodetector for tests in the absence of propagation. The OSNR for each test was measured by tapping the system output immediately before the detector filter in order to account for the FOPA noise introduced as well as the EDFA when it was used.

The performance quantification of each of the pump dithering methods (VCO tones, frequency hopped chirp and RF noise source) was performed both with and without subsequent propagation through a dispersive line. The deliberate dispersion accrual was used in order to exacerbate the effects of pump dithering onto generated idlers by inducing phase to amplitude modulation (PM/AM) conversion. Furthermore, each of the two settings above was evaluated for the cases of (i) near transparency - thus availing performance evaluation under similar inherent FOPA noise figure conditions; and (ii) maximum attainable gain achieved for each of the three pump dithering methods used. The adopted methodology is required due to the inherent NF FOPA properties [21] including pump(s) to signal and idler noise and relative intensity noise transfer. Finally, the objective of the investigation was performance evaluation in a configuration in which pump counter-phasing [1,15] was not implemented.

3.2 Signal integrity analysis: results and discussion

For the near transparency tests, the pump powers into the fiber were set to 250mW resulting in a conversion efficiency of −5dB on an input signal of −10dBm. The results of the tests run without gain are shown in Fig. 5(a) . All of the BER curves of this section are accompanied by the best case example eye diagram. In the case without propagation, all of the phase modulation techniques demonstrate similar signal integrity penalties, actually demonstrating slight OSNR improvements of about 0.3dB with respect to the back to back case. The slight performance improvement with respect to back-to-back is due to the inherent polarization sensitivity of FOPAs, whereas only the pump(s)-co-polarized noise in the signal band gets frequency converted to the idler band, thus rendering the noise-noise beating in the orthogonal polarization negligible, resulting in the BER diminution for low OSNRs. The results observed were consistent with expectations since the only source of PM to AM conversion due to the induced broadening without propagation would have been from the filters in the system. The unusual penalty experienced by the 6V_π driven phase modulator case is attributable to the unwanted polarization modulation (PolM) caused by the extreme driving conditions (19V peak-to-peak), whereby the particular phase modulators used, induce polarization rotation in addition to the phase modulation of the optical field, resulting in gain modulation of the polarization sensitive FOPA.

 

Fig. 5 (a) Bit Error Rate curves for back to back versus the DDS chirp, VCO tones, noise source, and the overdriven DDS Chirp with no gain. Inset – DDS Chirp example eye diagram. (b) Bit error rate curves for back to back versus the DDS chirp, VCO tones, noise source, and the overdriven DDS Chirp with no gain after passing through 10 km of SMF. Inset - DDS Chirp example eye diagram.

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The results from propagating the same generated idlers through 10 km SMF are shown in Fig. 5(b). In this case, the results reveal the effect of the phase modulation bandwidth on the signal integrity after significant propagation and, thus, 160 ps/nm of accumulated dispersion. As demonstrated in Fig. 5(a), the DDS chirp experienced a 0.2 dB penalty as a result of the propagation relative to the FOPA output case and no penalty at the 10⁻⁹ BER level with respect to the back to back measurement. The noise source driven PM exhibited a penalty of 0.4 dB in the case without propagation (and 0.3 dB with respect to back to back). The over-driven DDS chirp system had the same performance as the case with no propagation and a 0.4 dB penalty relative to the back to back case. Finally the penalty associated with VCO tone based dithering amounted to a 1.6 dB penalty from the FOPA output case and a penalty of 1.3 dB from the back to back case. The obtained results clearly demonstrate the importance of the dithering signal frequency occupancy. The idler broadening introduced by the phase modulation in the case of no gain represents a negligible effect on the BER even after accumulating 160 ps/nm worth of dispersion for most cases. The exception is the PM based on the VCO tones which exhibited non-negligible penalties relative to the other cases due to the proportionally wider bandwidth occupied by this PM approach.

The results for the cases with gain are presented in Fig. 6(a) and 6(b) for the near transparency and propagation cases respectively. The resulting signal degradation in these cases was exacerbated by the gain introduced in the FOPA. For the VCO tones, the maximum allowed pump power was 900 mW, approximately 14.5 dB above the SBS threshold of the fiber used producing a conversion efficiency of 18.5dB on an input of −10 dBm. The DDS maximum pump power was 750 mW, a 14 dB increase of the SBS threshold, producing a conversion efficiency of 15 dB. The overdriven DDS supported pump powers up to 900 mW, equivalent to the VCO tones, producing a conversion efficiency of 17 dB. Finally, the noise source supported pump powers as high as 1.5 W, approximately 17 dB above the SBS threshold, producing a conversion efficiency of 38 dB on an input signal of −23 dBm. The results without propagation correspond to those expected. Relative to the case of operation near transparency, the overdriven DDS exhibited similar performance again affected by the PolM addressed previously. The RF noise source shows a 0.3 dB penalty from the transparency case and a 0.2 dB penalty from the back to back case. The DDS chirp demonstrated an increase of 0.2 dB from the transparency case and introduced almost no penalty relative to the back to back case. On the other hand, the VCO tones demonstrated the least penalty, maintaining an OSNR increase of about 0.1 dB with respect to back to back, about 0.2 dB of penalty from the transparency case. This marginal improvement relative to the other cases can be attributed to the smaller system gain experienced in the VCO modulation case.

 

Fig. 6 (a) Bit error rate curves with gain for back to back versus the DDS chirp (G = 15 dB), VCO tones (G = 18.5 dB), noise source (G = 38 dB), and the overdriven DDS Chirp (G = 18.5 dB). Inset – DDS Chirp example eye diagram. (b) Bit error rate curves with gain for back to back versus the DDS chirp (G = 15dB), VCO tones (G = 18.5dB), noise source (G = 38 dB), and the overdriven DDS Chirp (G = 18.5 dB) after propagation through 10 km of SMF. Inset – DDS Chirp example eye diagram.

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After 10 km SMF propagation, the penalties follow the same tendency observed in the transparency case, this time, however, with increased severity. The penalties for the different systems relative to back to back were 0.3 dB for the DDS chirp, 0.6 dB for the overdriven DDS chirp, 0.8 dB for the RF noise source, and 1.5 dB for the VCO tones. These quantified degradations correspond to penalties of 0.3 dB for the DDS chirp, 0.3 dB for the overdriven DDS chirp, 0.6 dB for the RF noise source, and 2.0 dB for the VCO tones. The results are in excellent accord with the prediction previously stated regarding the dependence of BER degradation as a result of the idler linewidth broadening due to pump dithering. An overview of the results obtained is summarized in Table 1 .

Table 1. Results summary

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It is important to note that while the maximum recorded pump power allowable into the fiber under the 1.5 GHz noise source modulation was 1.5 W, this value was limited by coupling losses in the experimental setup which amounted to as much as 3 dB from the high power boosting EDFA output to the input of the HNLF and the maximum output power limit of the L-Band EDFA of 3 W. Finally, it ought to be emphasized that all tests have been performed on the converted idler waves, which are directly affected by pumps' phase modulation. The performance of the signal, on the other hand, is essentially independent of the pumps' phase modulation method used. The pumps' counter-phasing, which was not attempted in this study, will be a subject of a future investigation.

The results of our investigation successfully demonstrate that the signal integrity penalties associated with imparting phase modulation onto the pump of a FOPA system are indeed directly related to the FWHM bandwidth of the pump broadening. We also note that, when exposed to dispersion, the penalty particularly of the VCO tones system increases substantially. This observation is attributed to the random variation of the VCO phases resulting in an additional broadening of the optical spectrum which, in turn, is translated to an elevated penalty upon propagation through a dispersive line. This broadening is absent for the DDS modulation since it has well defined and preserved phases. Additionally, it is significant to note that by decreasing the bandwidth and increasing the efficiency of the phase modulation for SBS suppression, we have demonstrated up to 38 dB of conversion efficiency gain with an OSNR penalty of 0.8 dB from back to back, which is the smallest recorded two-pump FOPA penalty to date for such high gain.

5. Conclusion

Two novel, bandwidth-efficient electrical signals were investigated as alternative driving waveforms for SBS suppression by phase modulation in fiber optic parametric amplifiers: an RF frequency-hopped chirp and an RF noise source. Firstly, the proposed waveforms demonstrated considerable increases in measured SBS threshold. An SBS threshold increase of 11 dB was recorded for a 350 MHz bandwidth frequency-hopped chirp, a 15 dB for an overdriven 350 MHz frequency hopped chirp, and 19 dB for a 1.5 GHz RF noise source, compared to the current record of 22 dB increase with five VCO tones (highest tone at 10GHz, and employing two phase modulators). Noting that the measurements presented were done using a single phase modulator and with an emphasis on minimum occupied bandwidth, we have successfully demonstrated the largest SBS threshold increase for a given bandwidth to date.

The performance quantification by means of BER measurements at 10 Gb/s for each proposed SBS suppression system as well as a typical VCO system in both minimal and high gain FOPA systems were also presented for the first time in a comparative manner. The results fully confirmed the previous conjecture that the pump dithering bandwidth directly correlates to the degradation of the idler quality. The reference measurement of the VCO system provided a maximum gain of 18.5 dB with an OSNR penalty of 1.5 dB with respect to back to back after 160 ps/nm of dispersion. In contrast, the DDS chirp operating with 15 dB conversion efficiency experienced virtually no measureable penalty versus the case with no gain, even after propagating through 10 km of SMF, which was undertaken with an objective of deliberate exacerbation of PM/AM transfer and the associated performance deterioration. This resulted in an overall OSNR penalty of only 0.3 dB from back to back, indicating that the 350 MHz bandwidth of the chirp used was sufficiently small to minimize the signal integrity penalty in this system. A further SBS threshold, corresponding to the 18.5 dB gain, was achieved by a frequency-hopped chirp overdriven to 6Vπ peak-to-peak magnitude re-emphasizing the fact that the minimized pump-dithering bandwidth plays a pivotal role in signal integrity conservation in pump phase modulated FOPAs. However an excess penalty of 0.3 dB was observed in this case which is attributed to polarization modulation caused by the excessive driving of the phase modulator in this case. Finally, the highest gain measured using the two pump FOPA system was attained using a 1.5GHz noise source providing 38 dB conversion efficiency gain with a penalty of only 0.8 dB after propagating through 10 km of SMF, which is the smallest penalty in a two pump FOPA of comparable gain recorded to date, thus paving the way to practical realizations of high gain FOPAs capable of preserving information integrity.