Reﬂective Semiconductor Optical Ampliﬁer Direct Modulation Capability Enhancement Using Birefringent Fiber Loop

: The feasibility of employing a birefringent ﬁber loop to enhance the performance of a directly modulated reﬂective semiconductor optical ampliﬁer is experimentally demonstrated for the ﬁrst time. The birefringent ﬁber loop acts as an optical ﬁlter of opposite slope than that of the reﬂective semiconductor optical ampliﬁer electro-optical response and counteracts the ﬁnite reﬂective semiconductor optical ampliﬁer modulation bandwidth of only 0.89 GHz. By proper adjustment of its detuning, the birefringent ﬁber loop tailors the spectral components that physically manifest due to the reﬂective semiconductor optical ampliﬁer dynamic perturbation subject to direct modulation in the saturated gain regime, and suppresses the pattern-dependent distortions in the time domain. In this manner, the birefringent ﬁber loop manages to signiﬁcantly improve the quality characteristics of the encoded signal at higher data rates than those enabled by the reﬂective semiconductor optical ampliﬁer limited modulation capability. Owing to the birefringent ﬁber loop, the reﬂective semiconductor optical ampliﬁer modulation range is extended to 4 Gb/s at the raw bit error rate of 1.0 × 10 − 9 , and to 11 Gb/s at the forward error correction limit of 3.8 × 10 − 3 . These results, which are unique against the evaluation criterion adopted in the ﬁrst case, and the modulation speed achieved with post-ﬁltering schemes in the second, highlight the beneﬁcial role that the birefringent ﬁber loop can play in supporting reﬂective semiconductor optical ampliﬁer operation for intensity ampliﬁcation and modulation purposes.


Introduction
Reflective semiconductor amplifiers (RSOAs) are special version of semiconductor optical amplifiers (SOAs) constructed with an anti-reflective coating on the front facet and a high reflectivity coating on the rear end [1]. This design modification in the active medium cavity conveniently allows an optical signal coming from one (forward) direction to have its intensity increased and at the same time its information content altered as it exits from the other (backward) direction without using additional fiber hardware and fiber connections. The RSOAs downstream amplification and upstream modulation dual functionality together with their capability of providing higher gain with lower injection currents, less polarization dependency, higher modulation linearity, lower noise figure and less temperature sensitivity than their conventional counterparts [2,3] has rendered these elements indispensable for the realization of modern access applications which critically rely on the manipulation of bidirectionally flowing data [4][5][6][7][8][9][10][11][12] and where wavelength-independent, i.e., color-less, operation is highly desired [13]. Still, the data rates that RSOAs can support in these applications are limited by the RSOAs slow direct (electrical) modulation speed, which in turn is constrained by RSOAs finite modulation bandwidth being as low as very few GHz according to evidence based on experimental measurements [14] and numerical simulations [15]. A promising solution, which owing to its clear concept, feasible implementation and passive nature has gained wide popularity across the research community, is to resort to frequency discrimination and equalization [16]. The idea is to properly tailor the spectrally broadened components of the data encoded signal at the RSOA output, which occur due to the dynamic modulation of the RSOA bias current and the subsequent perturbation of the RSOA gain. For this purpose, different optical notch filtering technologies, including a delay interferometer (DI) [17,18], a fiber Bragg grating (FBG) [19], an array waveguide grating (AWG) [20] and a microring resonator [21], have been proposed. Recently, we employed a birefringent fiber loop (BFL), either alone [22], in cascade with another BFL [23] or assisted by an optical bandpass filter (OBPF) [24], to a standard SOA configured as intensity modulator. However, applying this scheme to an RSOA is not a trivial task due to the RSOA double-pass structure, which inherently imposes a greater strain on its dynamic behavior [12,25], especially subject to a fast electrical excitation [26]. Thus in this paper, we experimentally demonstrate that using a BFL can significantly boost the direct modulation capability of an RSOA. Specifically, we verify that this enhancement can be achieved well over the RSOA nominal modulation bandwidth and up to a point which can satisfy at least the mid-term needs of the target applications RSOAs are destined to serve. To this end, the BFL proven potential to improve the RSOA direct modulation performance in combination with the BFL attractive features can favor the adoption of this passive module as an efficient and affordable alternative for enabling the unobstructed exploitation of RSOAs for intensity amplification and modulation purposes. Figure 1a depicts the block diagram of the directly modulated RSOA followed by a serially connected BFL. The purpose of directly modulating the RSOA is to imprint the digital information contained in an RF signal applied to the RSOA electrical interface on an optical signal that constantly drives the RSOA. However, the faster the digital content of the RF excitation modifies the RSOA bias current, the more the data equivalent bandwidth exceeds the RSOA nominal modulation bandwidth, B mod , which is finite [27], and hence the more is the process far from being ideal. As a consequence, the performance of the directly modulated RSOA becomes pattern-dependent and eventually unacceptable. Nevertheless, this performance limitation can be overcome and the RSOA be directly modulated at an extended data rate than that allowed by its limited modulation bandwidth by means of optical notch filtering. The goal pursued through the exploitation of this technique is to produce a filter characteristic which is the opposite to that of the RSOA, as shown in Figure 1b [28]. This equalizes the total frequency response and makes it independent of the electrical modulation frequency for a wider range than for the RSOA only. Moreover, by properly tailoring the frequency of occurrence of the repetitive lobes and the points of their extinction with respect to the spectral position of the encoded pulses, the spectral content of the latter can be acted upon by the filter's transmission according to their exact binary content [21,27]. In this manner, the impairments associated with these components due to the irregular RSOA gain variation by the electrical excitation are converted by the filter's slope into amplitude changes which cancel those after the RSOA [29]. Consequently, the uniformity between output pulses of same binary content and the distinction between output pulses of different binary content can be significantly enhanced. Thus the performance degradation of the encoded optical signal at the RSOA output can be sufficiently suppressed so that RSOAs can efficiently support the target applications both as external modulators and amplification elements. The desired spectral response of the compensating frequency discriminator can be technologically implemented in the polarization-based domain using a BFL, as described in the following.

Experiment
In order to run the experiments in a rational and self-consistent manner, we specified first the RSOA (CIP, model SOA-RL-OEC-1550, cf. photo in Figure 2a) driving conditions defined by the amount of the optical power and DC current, which is launched into, and biases, respectively, the RSOA.  For this purpose, we utilized as decision criterion the RSOA electrical modulation bandwidth on which we investigated the impact of these two parameters. The setup that we built to conduct the relevant measurement is depicted in Figure 3. The core module was an auto-calibrated vector network analyzer (VNA). The VNA provided an RF signal that was superimposed, via a bias-tee, on the RSOA DC bias, which was thus modulated within a frequency range of 10 MHz-12 GHz for fully capturing the RSOA electro-optical (E/O) response. The variations of the RSOA gain induced due to the modulation of the injection current were mapped on a continuous wave (CW) optical signal, which was emitted from a software-controlled laser source tuned around λ = 1560 nm and entered the RSOA through an optical circulator (OC). The RSOA encoded output was coupled back into the OC and passed through an optical bandpass filter (OBPF) to eliminate unwanted RSOA noise components. It was subsequently detected by a photodiode embedded inside the VNA and was converted again into electrical form, hence closing the circuit path established between the VNA electrical output and the VNA optical input port. In this manner, the VNA calculated the complex scattering parameter, S21, and produced from its squared modulus the RSOA E/O transfer function which, as shown in Figure 4a, had a low-pass characteristic. By controlling the RSOA DC bias, I bias , via a current source, and the CW optical power launched into the RSOA, P CW , with a variable optical attenuator (VOA), we further obtained the normalized E/O response for different values of these parameters, as shown in Figure 4b. From these curves we observed that increasing one parameter while keeping the other constant, and vice versa, was beneficial for the 3-dB electrical modulation bandwidth, B mod , which in either case was increased because of the reduction of the RSOA effective carrier lifetime [30,31]. According to this evidence, choosing P CW = −5 dBm and I bias = 70 mA results in B mod, RSOA = 0.89 GHz. The first choice caused the RSOA gain to drop by 5.4 dB from its unsaturated value, as shown in Figure 5a. Thus the RSOA was directly modulated under dynamically stressful conditions [32]. With the CW power going into the RSOA fixed to its set value, the second choice lied in the linear region of the gain-current curve shown in Figure 5b and hence made the RSOA amenable to direct modulation [33].
Having defined the RSOA operating point, the setup of Figure 3 was modified by directly modulating the RSOA with a 2 10 − 1 bit-long non return-to-zero (NRZ) data from the pulse pattern generator (PPG) of a bit error rate tester (BERT) ( Figure 6). When this signal was applied to the 50 Ω RSOA impedance, it offset the RSOA DC current by ±10 mA. The RSOA output was connected to a BFL (cf. photo in Figure 2b), which was implemented using a 3 dB (50:50) polarization maintaining (PM) fused coupler, an intraloop polarization controller (PC) and a segment of polarization maintaining fiber (PMF) with birefringence B ≈ 3.3 × 10 −4 in the C-band. The total PMF length, L ≈ 8.5 m, resulted in the periodic comb-like transfer function shown in Figure 7a, which comprised of maxima (peaks) and minima (notches) repeated every ≈0.87 nm (Figure 7b), equal to the BFL free spectral range (FSR = λ 2 /BL). Setting the PC to generate a rotation of 90 • to beams coming from both loop directions [34] optimized the amplitude difference between peaks and notches, or the peak-to-notch contrast ratio (PNCR), to 22 dB (Figure 7c). To enhance stability against environmental perturbations by affordable means, the whole construction was enclosed inside a box, which was placed on a marbled base. In this manner, the peaks and notches could retain their spectral position without drifting for a duration that conveniently allowed taking the target measurements. In order to quantitatively assess this possibility, we observed with the help of the OSA the change in the BFL response notches' position with time. This change can be incurred due to random environmental perturbations, such as daily temperature variations or air currents from laboratory staff movements. In fact, according to a calculation conducted for the BFL and input signal parameters values in our experiment and for a typical temperature-dependent birefringence coefficient of −7 × 10 −8 /K, a drift in temperature of more than ∼1.3 • C only can cause a notch shift beyond half the BFL FSR [35], which is the range within a notch is allowed to lie to mitigate the pattern effects induced in the RSOA [27]. Thus we found that the notches' displacement due to reasons like the aforementioned ones was of the order of +0.1 nm for ∼12 min, as it can be observed in Figure 8a. This is better perceived using the experimental data derived for the notch shift in time and displaying with simulation assistance the BFL transfer function at different time instants (Figure 8b). Consequently, this interval provided enough margin to perform the experiment and obtain valid and repeatable results while scanning the relative spectral offset between carrier and notches with sufficient degree of resolution. After the permissible window closed, it was necessary to compensate for the inevitable notches' shift, and the more practical way of doing this was by fine adjusting the carrier position against the notch being closer to its longer sideband. As in our case a notch shifts with temperature at a rate of ∼0.33 nm/ • C, confining this shift to the bounds specified above would require to keep the temperature deviations within ±0.3 • C, which in turn could be achieved with a thermoelectric cooler (TEC) [36]. The corresponding slot for measurements can be significantly extended in a more compact and flexible manner by constructing the BFL using a PM photonic crystal fiber (PCF) [35], which exhibits a notable temperature-insensitivity, in place of the conventional PMF, and an electrically, instead of manually, actuated PC with endless control of polarization [36]. Finally, the BFL was followed by a booster erbium doped fiber amplified (EDFA) to compensate for insertion losses of ≈10 dB and guarantee the same level of received power at the diagnostic equipments so as to ensure a fair comparison between measurements with and without the BFL.

Results
Since the BFL filtering efficiency is critically determined by the detuning [23], ∆λ, which is defined as the difference between the CW seeding wavelength and the wavelength of the nearest notch in the BFL response, we investigated the impact of this parameter on the operation of the scheme by assessing first the performance against the error probability (EP). This metric was calculated through [37] EP = 1 2 erfc(Q/ √ 2), where erfc(x) is the error function and Q = |µ 1 −µ 0 | σ 1 +σ 0 is the Q-factor, where µ 1, 0 and σ 1, 0 are the mean and standard deviation of the peak power of the encoded marks ('1') and spaces ('0') whose values are extracted from the levels of the corresponding histograms. These in turn are obtained from the photodetected voltage samples that are recorded and stored by a digital communications analyzer (DCA).
The BFL detuning was practically achieved by fine tuning the CW laser wavelength relative to the adjacent notch's fixed position so that the former was spectrally located on the left-hand side of the latter. This resulted in negative detuning values and made the BFL filter transmission decrease as the wavelength increased, which is necessary [32] in order to suppress the longer-wavelength, i.e., red-shifted, spectral components induced on the encoded signal due to the self-phase modulation (SPM) effect that physically accompanies the RSOA direct modulation [38]. Equivalently, the BFL exhibited in the frequency domain a high-pass filter characteristic which counteracted that of the RSOA so that the combined response could become independent of the electrical modulation frequency for a wider range than for the RSOA only [28]. Figure 9 shows that the EP could be kept below 10 −9 for a RSOA direct modulation speed extended up to 4 Gb/s for ∆λ = −0.05 nm. The feasibility of this extension was supported by Figure 10, which depicts the measured E/O response of the RSOA-BFL combination. It can be seen that compared to Figure 4a, the connection of the BFL after the RSOA shifted the electrical modulation bandwidth of the latter to ∼3 GHz. This value exceeded the NRZ coding pulses bandwidth, which by definition equals half the repetition data rate [39], as well as the minimum bandwidth required for optimized signal reception, which equals 2/3 times the data repetition rate [40]. The specified detuning value implies that the CW optical signal and BFL notch should be very closely spaced apart at the expense of very delicate experimental handling. In contrast, without the BFL, i.e., for ∆λ = −0.45 nm ∼ FSR/2, it was not possible to directly modulate the RSOA at any of the checked data rates shown in Figure 9. These results were further supported by raw BER measurements obtained from the BERT error analyzer and depicted in Figure 11 for data rates between 3 Gb/s and 4 Gb/s. Figure 11. Raw BER measurements versus data rate for BFL detuning ∆λ = −0.05 nm. The dashed line indicates the limit for acceptable EP at 1 × 10 −9 .

RS OA + B F L
The lower bound of the displayed data rates was dictated by the fact that below 3 Gb/s, the analyzer did not find any mistakes so the measured BER was zero. In other words, the BER was so low that the analyzer needed very long time to count mistakes. Similarly, for data rates over 4 Gb/s, the analyzer had a synchronization loss since the received data could not be synchronized with the clock of the PPG. It is noteworthy that although the limit for acceptable EP, EP = 1 × 10 −9 , which is the standard requirement in digital communication systems [39], is several orders of magnitude tighter than that employed in other filtering schemes proposed to enable faster RSOA direct modulation by NRZ data [17][18][19], still the BFL managed to successfully confront this ultimate challenge. Since the RSOA nominal modulation bandwidth can be broadened by taking into account, and intervening on, factors such as the dimension [41], optical confinement [42], packaging [43], impedance matching [44] and transport effects [45] of the active device, it can be realized that there is further margin for increasing the RSOA direct modulation speed by means of the BFL. In this direction, the BFL potential was also verified in the time domain and the results are compiled and presented in Figure 12. These include encoded pulse waveforms for a representative 25 bit-long segment of 1100111101010010100011100 and eye diagrams for 2 10 − 1 PRBS. As it can be seen, the uniformity of pulses at the RSOA output at 1 Gb/s (Figure 12a) was not preserved at 4 Gb/s (Figure 12b), since pulses suffered from pattern-dependent peak-to-peak amplitude fluctuations. This distortion was translated into a poor quality of the eye diagram at 4 Gb/s (Figure 12e) versus 1 Gb/s (Figure 12d), as indicated by the narrow opening at the center and the dispersed histograms' content. The deteriorated outcome of the single directly modulated RSOA could be considerably improved by the properly detuned BFL, which compensated for the pulse amplitude wandering (Figure 12c) and restored the eye's opening and histograms' form ( Figure 12f). These improvements were quantified by the significant reduction of the amplitude difference (AD) of the marks [46], from the inadmissible AD ≈ 1.55 dB for the RSOA only, down to the more than acceptable [47] AD ≈ 0.34 dB thanks to the BFL, as well as by the increase of the eye opening (EO) [39], from EO RSOA ≈ 46.68% to EO BFL ≈ 70.02%. Moreover, in Figure 13a it is observed that the RSOA spectrum is broadened towards the longer sideband, i.e., it is red-shifted. The spectrum retains its form at the output of the BFL at transparency, i.e., for ∆λ = 0 nm, since then the BFL does not act as notch filter on the red-shifted RSOA spectral components (Figure 13b). In this case, the spectrum is identical to that at the BFL input, or equivalently at the output of the OBPF right after the RSOA. In Figure 13c it can be observed instead that the corresponding spectrum becomes more symmetric at the output of the BFL, which has been detuned by ∆λ = −0.05 nm to suitably tailor the red-shifted spectral components. Unlike previous works, showing encoded pattern profiles and introducing appropriate indices, such as the AD, is indispensable in order to fully demonstrate and characterize the extent of distortion and amelioration undergone by the encoded signal after the stand-alone RSOA and applied notch filter (BFL in our case), respectively. To this aim, we also tested the BFL capability to allow transmission of the encoded signal over fiber. This required to specify the net gain of the RSOA and BFL combination, G net , which is an important metric of the performance of post-filtering (R)SOA pattern-dependence combating [32]. This quantity is defined as G net (dB) = G avg, RSOA (dB) −G ar (dB), where G avg, RSOA is the average gain provided by the directly modulated RSOA and G ar is the amplification reduction suffered by the encoded signal due to the BFL filtering action. Therefore, the calculation of G net required the knowledge of G avg, RSOA and G ar , which were found as follows. First, for NRZ encoding, G avg, RSOA = G CW , where G CW = 8.99 dB is the RSOA CW gain derived from Figure 5. Second, G ar was extracted by measuring the mean value of the high level, V mean, 1 , and of the low level V mean, 0 , voltages, which were photodetected by the PD and recorded by the DCA, and taking their median, V med = (V mean, 1 + V mean, 0 )/2. This value was then compared between the BFL outputs for the case that the BFL was detuned by ∆λ = −0.05 nm and for the case that the BFL was detuned at transparency, ∆λ = 0 nm, which was equivalent to the RSOA output with BFL insertion losses compensated [32]. In this manner, we obtained G ar (dB) = 20 log |V med, BFL (∆λ=−0.05 nm) /V med, BFL (∆λ=0 nm) | = 4.13 dB. Therefore, G net (dB) = 8.99 − 4.13 = 4.86 dB, which would permit propagation of the RSOA directly modulated 4 Gb/s data over approximately 20 Km of standard single-mode fiber (SSMF) without dispersion compensation. Based on this evidence, we placed an available spool of 21.35 Km SSMF after the booster EDFA, whose output power accounted for the fiber's losses. The results taken from the transmission experiment conducted under these settings showed that the form of the eye diagram was close to that when the BFL was not followed by the specific fiber spool. This is indeed verified by comparing Figure 14 to Figure 12f. Therefore the BFL could be employed in real fiber optic distribution and access fiber networks which exploit RSOAs as external modulators [1]. The previous results clearly demonstrated and confirmed that owing to the BFL it is possible to considerably increase the RSOA direct modulation speed. Given the analogous degree of extension of the nominal RSOA modulation bandwidth by other optical filtering schemes [20], we proceeded to investigate to what extent we could exploit this fact while ensuring an acceptable performance. For this purpose, we employed as evaluation criterion the EP that can be tolerated when forward error correction (FEC) is applied, EP FEC . This is the metric against which the performance of directly modulated RSOAs assisted by photonic filtering schemes is commonly assessed [17][18][19]. Figure 15 shows that the BFL allowed EP FEC to be kept below the 3.8 × 10 −3 threshold [48] up to 11 Gb/s. This corresponds to a higher optical filter's efficiency, which is defined as the ratio between the RSOA extended modulation speed to the RSOA modulation bandwidth, than previously reported [17][18][19]. Moreover, Figure 16 shows that the EP FEC was minimized for an optimum detuning of ∆λ = −0.05 nm. This corroborates the observation and conclusion that in order to maximize the RSOA E/O bandwidth enhancement the CW signal should lie in the vicinity, and in the shorter wavelength side, of the BFL transfer function's nearest notch. Physically this helped suppress more efficiently ( Figure 17c) the spectral components of the encoded signal, which were shifted to longer wavelengths (appearing as 'knee' in Figure 17b) with respect to the original CW signal's optical spectrum (Figure 17a) due to SPM inside the RSOA. To this end, the temporal profile attributes of the RSOA direct modulation outcome benefited from the properly detuned BFL, since the encoded pulse pattern form, which right after the RSOA was severely impaired (Figure 18a), was significantly improved (Figure 18b), while the corresponding eye diagram, which also suffered great distortion (Figure 18c), became open and symmetric (Figure 18d).

Conclusions
In conclusion, we demonstrated through experimental work and results that a BFL can enhance the direct modulation capability of a RSOA whose modulation bandwidth is inherently limited. In this context, we showed that a properly detuned BFL allows the RSOA to produce an encoded signal of improved quality characteristics at an extended data range, which is of the order of 4 Gb/s and 11 Gb/s when the raw BER and the FEC-assisted BER is adopted as performance criterion, respectively. This fact, together with the BFL distinctive features, suggests that the BFL can constitute a viable post-filtering option for help employing RSOAs as intensity modulators in relevant applications.