Extensive explorations are undertaken, for the first time, of the feasibility of utilizing quantum-dot semiconductor optical amplifier intensity modulators (QD-SOA-IMs) in cost-sensitive intensity-modulation and direct-detection (IMDD) passive optical network (PON) systems based on adaptively modulated optical orthogonal frequency division multiplexing (AMOOFDM). A theoretical QD-SOA-IM model is developed, based on which optimum QD-SOA-IM operating conditions are identified together with major physical mechanism considerably affecting the system performance. It is shown that, in comparison with previously reported SOA-IMs in similar transmission systems, QD-SOA-IMs cannot only considerably improve the AMOOFDM transmission performance but also broaden the dynamic range of optimum operating conditions. In particular, for achieving signal bit rates of >30Gb/s over >60km single mode fiber (SMF), QD-SOA-IMs offer a 10dB reduction in CW optical input powers injected into the modulators. In addition, QD-SOA-IMs can also be employed to compensate the chromatic dispersion effect.
© 2011 OSA
Quantum-dot semiconductor optical amplifiers (QD-SOAs) have demonstrated a large number of salient features for use in various application scenarios from all-optical signal processing to optical communications. Of those features, ultrafast gain recovery , large saturation power , patterning-free optical amplification , high operation speed [4–6], potential cost-effectiveness and the capability of being monolithically integrated with other optoelectronic devices, are the most important properties enabling their implementation in next-generation high-speed optical access networks. In particular, in cost-sensitive passive optical networks (PONs), QD-SOAs have been utilized in both downstream and upstream transmission to boost the optical signal power and improve the receiver sensitivity at the optical line terminal (OLT) side .
Recently, the feasibility of utilizing SOA intensity modulators (SOA-IMs) [8,9] and reflective SOA intensity modulators (RSOA-IMs)  to perform electrical-to-optical conversion of adaptively modulated optical orthogonal frequency division multiplexing (AMOOFDM) signals has been thoroughly investigated in intensity-modulation and direct-detection (IMDD) single-mode fiber (SMF)-based PON systems, as AMOOFDM offers a number of significant advantages including high spectral efficiency, inherent strong chromatic dispersion tolerance, full use of mature digital signal processing (DSP) and the capability of hybrid dynamic bandwidth allocation in both the time and frequency domains [11–15]. It has been shown [8–10] that SOA-IMs and RSOA-IMs not only facilitate cost-effective AMOOFDM transmitters but also enable colorless AMOOFDM transmissions in wavelength division multiplexing PONs (WDM-PONs). However, the previously published works [8–10] have indicated that, to maximize the achievable signal bit rate, optimum CW optical input powers as high as 20dBm to the SOA-IMs and RSOA-IMs are necessary, which may be too high for cost-effective practical implementation in PONs. Compared with SOAs/RSOAs, QD-SOAs have picosecond dynamic gain recovery speeds, implying that they can offer much higher modulation bandwidths. In addition, experimental demonstrations of record high penalty free QD-SOA output powers of 23dBm  suggest that desired linear intensity modulation operation is also feasible. Therefore, it is greatly advantageous if use can be made of QD-SOA intensity modulators (QD-SOA-IMs) in AMOOFDM transmitters for PON systems. However, as far as we are aware, no papers have been published to address such an important research topic.
In this paper, numerical simulations are undertaken, for the first time, to extensively explore the feasibility of utilizing QD-SOA-IMs in IMDD AMOOFDM PON systems. Here special effort is given to addressing the following technical challenges:
- • Development of a comprehensive theoretical QD-SOA-IM model by taking into account the effects of both quantum dots and wetting layer (WL).
- • Identification of key QD-SOA-IMs-associated physical mechanisms considerably affecting the AMOOFDM transmission performance.
- • Identification of optimum QD-SOA-IM operating conditions that correspond to the maximum AMOOFDM transmission performance.
- • Performance comparisons between QD-SOA-IMs and SOA-IMs to highlight the advantages of QD-SOA-IMs for use in IMDD AMOOFDM PON systems.
- • Exploration of the feasibility of effectively utilizing the QD-SOA-IMs-induced frequency chirp to improve the transmission performance of IMDD AMOOFDM PON systems.
Detailed numerical simulations show that, in comparison with SOA-IMs, QD-SOA-IMs cannot only considerably improve the AMOOFDM transmission performance but also significantly lower the required CW optical input powers by approximately 10dB for transmission distances of up to 140km. Whilst for transmission distances of <20km, the QD-SOA-IM enabled transmission performance is very similar to that corresponding to an ideal intensity modulator. In addition, simulations also show that use can be made of the QD-SOA-IM-induced frequency chirp to compensate for chromatic dispersion of standard SMFs.
2. Transmission system models
2.1 AMOOFDM transceivers and transmission systems
The considered transmission system is illustrated in Fig. 1 , which is composed of an AMOOFDM transmitter, a SMF link without in-line optical amplification and chromatic dispersion compensation, as well as an AMOOFDM receiver. The AMOOFDM transmitter comprises a transmitter electrical OFDM modem, a SOA-IM/QD-SOA-IM, a CW laser diode and a variable optical attenuator (VOA). The AMOOFDM receiver consists of a simple square-law photon detector and a receiver electrical OFDM modem.
As the operating principles of the AMOOFDM transceivers have been described in detail in [11, 13], therefore, the generation, transmission and recovery of an AMOOFDM signal is summarized as following:
- • In the electrical OFDM modem in the transmitter, each individual subcarrier having a fixed electrical power is independently assigned a signal modulation format that suites the system frequency response experienced by the subcarrier. The signal modulation format may vary from differential binary phase shift keying (DBPSK), differential quadrature phase shift keying (DQPSK), 8-quadrature amplitude modulation (QAM) and up to 256-QAM. Such adaptive modulation is performed via negotiations between the transmitter and the receiver.
- • To generate real-valued OFDM symbols, the inverse fast Fourier transform (IFFT) is applied to subcarriers conveying real user-data in the positive frequency bins, one zero-frequency subcarrier having a zero electrical power, and the aforementioned subcarriers’ complex conjugate counterparts that are arranged to satisfy the Hermitian symmetry. At the output of the IFFT operation, cyclic prefix is added in front of each OFDM symbol. After that, the digital electrical OFDM symbols are serialized and converted into an analog OFDM signal via a digital to analog convertor (DAC). After adding an optimum DC bias current to the OFDM modem-generated real-valued electrical OFDM signal, the combined signal is then used to directly modulate the optical power injected into the QD-SOA-IM and SOA-IM. A VOA is employed before the SMF to set the coupled optical power at a desired level.
- • At the receiver side, the AMOOFDM signal is converted back to the electrical domain by a square-law photon detector. The received data is finally recovered by applying an inverse DSP procedure of the transmitter in the electrical domain.
2.2 QD-SOA-IM model
Based on rate equations, a number of theoretical QD-SOA models governing the interactions between the carrier density and optical signal have been published to describe the input-output optical characteristics of QD-SOAs [5, 16–21].
In QD-SOAs, the wetting layer (WL) is a thin material layer, where QDs are grown. The WL layer acts as a free carrier reservoir, from which the carriers quickly transfer to the QDs where they will be available for stimulated recombination. The bias current is assumed to be directly injected into the WL. Strictly speaking, a typical energy band of a QD-SOA active layer consists of multiple energy states in the conduction and valence bands. Within a QD two energy states, i.e., the excited state (ES) and the ground state (GS), can be considered, this theoretical treatment is known as the 3-level rate equation model (3LREM) [16–18]. A 4LREM QD-SOA model  has also been developed, in which an additional energy level is introduced between the QDs and the WL.
In this paper, making use of a significantly simplified but effective 2LREM QD-SOA model [19–21], a theoretical QD-SOA-IM model is developed, in which all the QDs in the SOA are assumed to be identical and uniform, and there exists only one confined energy level in the conduction and valence band of each QD. The intermediate (excited) state is replaced by calculating the carrier occupation probability near the band edge of the WL. The WL is populated by the injected current and serves as a reservoir of carriers, as illustrated in Fig. 2 . The 2LREM model is valid for cases where there exists a large population of carriers in the WL, which couples to discrete QDs on a picoseconds time scale, whilst at the same time the two carrier population levels undergo recombination processes, stimulated emission and pumping [19–21].
Similar to the treatments presented in [8–10], in developing the QD-SOA-IM model, various ultrafast intraband dynamic processes are ignored, which include carrier heating, spectral hole-burning, two-photon absorption and ultrafast nonlinear refraction. Such an assumption is justified because of the following two reasons: 1) The DACs/ADCs involved in the AMOOFDM transceivers have sampling rates of typically <20GS/s, which correspond to sampling time durations of >50ps. Such time durations are much longer than the intraband dynamic process response times of typically ~1ps. For a QD-SOA-IM subject to an optimum optical input power, the corresponding effective intraband carrier lifetime is approximately 30ps, which is even larger for practical optical input power conditions of <10dBm for QD-SOA-IMs. Therefore, the effective intraband carrier lifetime is far beyond the intraband dynamic process response times. 2) The optical gain saturation properties of the QD-SOA-IMs are mainly determined by the strong DC component of an optical signal propagating in the QD-SOA-IMs. For example, at the front facet of the QD-SOA-IMs, the modulated optical signals with noise-like waveforms have relatively small signal extinction ratios of approximately 1dB [8–10]. The above-mentioned two points indicate that it is sufficiently accurate to neglect the influence of the intraband dynamic process on the optical gain saturation characteristics of the QD-SOA-IMs for the transmission systems of interest of present paper.
Following the procedure in [8–10, 22,23], making the transformation with vg and T being the group velocity and the reduced time measured in a reference frame moving with the optical signal, respectively. z is the distance in longitudinal direction, i.e. z = 0 and L stands for the input and output facets of the QD-SOA-IM, and L is the length of the QD-SOA-IM active region. The optical field, A(z,T), can be written as20,21] and the above-mentioned assumptions, the temporal gain governing the dynamic characteristics of the QD-SOA-IM can be obtained:
The power and phase of the modulated optical signal at the output of the QD-SOA-IM are, therefore, given by:
Apart from intensity modulation, the QD-SOA-IM also imposes amplified spontaneous emission (ASE) noise onto the modulated optical signal. The total ASE power, PASE, can be calculated by Equations (5)-(9) are the final set of equations, which can be easily solved numerically when Gmax, Pin(T) and Фin(T) are known. After adding the ASE noises into Pout(T) and Фout(T), the final intensity modulated optical signal can be obtained.
2.3 Models for SMF and photon detector
A standard theoretical SMF model successfully used in [8–10, 13–15] is adopted here, in which the effects of loss, chromatic dispersion, and optical power dependence of the refractive index are included. The effect of phase modulation to amplitude modulation conversion noise is also incorporated upon photon detection in the receiver.
In the receiver, a square-law photon detector is utilized to detect the optical signals emerging from the transmission system. Shot noise and thermal noise are considered and their effects are simulated following procedures similar to those presented in .
2.4 Simulation parameters
In simulating the AMOOFDM signal, 64 subcarriers are used, of which 32 are in the positive frequency bins, and one that is close to the optical carrier frequency is assigned to have zero electrical power. The signal modulation formats taken on each subcarrier varies from DBPSK, DQPSK, and 8-QAM to 256-QAM. The DAC/ADC has a 12.5GS/s sampling rate, which gives rise to a signal bandwidth of 6.25GHz in the positive frequency bins and a bandwidth of each subcarrier of 195.3MHz. The cyclic prefix parameter that is defined in  is taken to be 25%, which gives a cyclic prefix length of 1.28ns within each OFDM symbol having total time duration of 6.4ns. The quantization bits of ADC/DAC and the signal clipping ratio are set to be 7-bits and 13dB, respectively, which are the optimum values identified in .
Table 1 shows the parameters used in simulating the SOA-IM/QD-SOA-IM, SMF, and the photon detector. It should be noted that, for practical QD-SOAs, their α values may vary significantly from a value as low as α=0.1 in InAs QD lasers near the gain saturation regime  to a huge value as large as α=60 recently measured in InAs/InGaAs QD laser . Specific band structures also play a significant role in determining the α value [27–29]. In addition, α parameter is dependent upon injection current, photon energy and temperature . Considering the fact that a typical values of α ≈(2-7) can be considered , in this paper, α is set at 5 for both the SOA-IM and QD-SOA-IM.
3. Simulated transmission performance
3.1 Optical gain saturation characteristics
In order to gain an in-depth understanding of the effect of the QD-SOA-IM gain saturation on the AMOOFDM transmission performance, Fig. 3(a) is plotted to show the QD-SOA gain versus CW optical input power for different bias currents. It can be seen in Fig. 3(a) that the QD-SOA optical input saturation power increases significantly with increasing bias current. It can also be observed in Fig. 3(a) that, for optical input powers of <0dBm, the gain variation for bias current varying from 100mA to 300mA is almost independent of bias current. The physical mechanism behind such behavior is that the QD-SOA charge neutrality defined in  is assumed in the ground state only. In Fig. 3(b), comparisons of the gain versus bias current between the SOA and QD-SOA are presented for three optical input powers of 0dBm, 10dBm and 20dBm. As seen in Fig. 3(b), the QD-SOA reaches saturation much faster than the conventional SOA when an identical bias current is applied, this is due to the fact that the effective carrier lifetime of the QD-SOA is much smaller than that of the SOA. Generally speaking the QD-SOA modulation bandwidth is proportional to the inverse of the effective carrier lifetime. All the results shown in Fig. 3 agree well with those obtained in [16,19,21], indicating the validity of the developed QD-SOA-IM model in this paper.
In Fig. 4 (a) we see the normalized frequency response of the QD-SOA-IM for 0 dBm optical input power, and Fig. 4(b), (c), and (d) present the spectra of the modulated AMOOFDM signals at the output facet of the QD-SOA-IM subject to different CW optical input powers. It can be seen in Fig. 4 that the larger the CW optical input power to the QD-SOA-IM is, the wider the signal bandwidth is obtained due to reductions in both effective carrier lifetime and signal spectral distortion. Clearly, this leads to the improved transmission performance. At the same time, however, a large CW optical input power also brings about serious signal clipping due to the reduced slope of the gain – current curve, which can be seen in Fig. 3 (b).
3.2 Impact of bias current and optical input power
In Fig. 5 we see contour plots to demonstrate the achievable AMOOFDM transmission capacity of a 60km IMDD SMF transmission system for both the SOA-IM and the QD-SOA-IM as function of bias current and CW optical input power. The peak-to-peak (PTP) driving current is set to 80mA. In numerical simulations throughout this paper, the signal line rate is calculated using the expression:Eq. (10) is considered to be valid only when the condition of BERT < 1.0 × 10−3 is satisfied.
As seen from the contour plots in Fig. 5, in comparison with the SOA-IM, for both bias current and CW optical input power, the QD-SOA-IM has much broader variation ranges of optical input power and input bias current, over which higher signal bit rates are achievable. For example, to achieve signal bit rates of >30Gb/s, the SOA-IM requires a CW optical input power to vary in a 3dB range between 19dBm to 21dBm; whilst the QD-SOA-IM allows a CW optical input power to vary in a 20dB range between 10dBm and 30dBm. More importantly, to achieve maximized signal bit rates, the QD-SOA-IM allows the injection of CW input powers as low as 10dBm. Clearly, the QD-SOA-IM considerably extends the optical input power range, and subsequently improves the performance robustness of the PON systems.
In Fig. 5 we also see that the optimum CW optical input powers are 20dBm for both the QD-SOA-IM and SOA-IM. For optical input powers less than the optimum CW optical power value, the degradation of the signal transmission capacity is due to the long effective carrier lifetime. This is seen clearly in Fig. 4, as a relatively small optical input power gives rise to a long effective carrier lifetime and thus a narrower modulation bandwidth. While for CW optical powers higher than the optimum value, the degradation is due to a decrease in signal extinction ratio. The signal extinction ratio is defined as :Fig. 6 we see the signal extinction ratio as a function of CW optical input power for the SOA-IM and QD-SOA-IM. In obtaining Fig. 6, a bias current of 100mA and a driving current PTP value of 80mA are adopted. It can be seen in the figure that the SOA-IM outperforms the QD-SOA-IM in signal extinction ratio for CW optical input powers less than 20dBm. This effect is examined once again in discussing results for long transmission distances (>100 km).
Now we discuss the bias current dynamic range. As shown in Fig. 5, the QD-SOA-IM also considerably broadens the bias current dynamic variation range, and both the SOA-IM and the QD-SOA-IM have similar optimum bias current values of 100mA. For bias currents larger than this optimum value, the reduction in signal line rate is due to the reduction in signal extinction ratio of the modulated signal and the increase in signal clipping effect; while for bias currents smaller than the optimum bias current range, the increase in effective carrier lifetime plays a dominant role in reducing the signal line rate.
3.3 Impact of driving current PTP
In addition to the CW optical input power and bias current, it is also important to study the influence of the driving current PTP on the AMOOFDM transmission performance. For QD-SOA-IMs and SOA-IMs, Fig. 7 and Fig. 8 show driving current PTP-dependent transmission performance for 10dBm and 20dBm optical input powers at various transmission distances. In obtaining Figs. 7 and 8, the bias current is set to be 100mA. It can be seen that, compared to the SOA-IM, the QD-SOA-IM always improves the AMOOFDM transmission performance over transmission distances of less than 120km. The optimum PTP value of the driving current is transmission-distance dependent: for transmission distances of <60km, the optimum PTP value is found to be 80mA.For transmission distances longer than 100km, the optimum PTP value is found to be 160mA. This can be explained by considering the fact that, after transmitting long distances (>100km), the significantly attenuated optical signal requires a high driving current PTP to achieve an acceptable BER. For PTPs larger than this optimum value, the reduction in signal line rate is due to the increased signal clipping effect due to the nonlinear gain current curve of the QD-SOA-IM, while for PTPs smaller than the optimum value, the reduction in signal capacity is due to the decrease in signal extinction ratio.
3.4 Optimized AMOOFDM transmission performance and physical limitations
Having identified the optimum QD-SOA-IM operating conditions including bias current, driving current PTP and CW optical input power, the maximum achievable signal bit rate of the AMOOFDM transmission system incorporating the QD-SOA-IMs is investigated in this section.
The numerical results are plotted in Fig. 9 and Fig. 10 , where the identified optimum QD-SOA-IM operating conditions are adopted, i.e., a bias current of 100mA, a driving current PTP of 80mA. Signal bit rate comparisons are also made in Fig. 9 between the QD-SOA-IM, the SOA-IM and an ideal intensity modulator (IM). In simulating the ideal IM, a simple square root operation is applied to the sum of the electrical driving current and dc bias current. It can be seen in Fig. 9 that, the QD-SOA-IM outperforms the SOA-IM in signal bit rate for all transmission distances of up to 140km. For transmission distances of 20km, the QD-SOA-IM offers signal bit rates almost identical to the ideal IM.
In Fig. 10 we see that, up to 120km, the performances supported by the QD-SOA-IMs are much better than those supported by the SOA-IMs for CW optical input powers of 10dBm and 20dBm. This indicates that the QD-SOA-IMs are capable of supporting signal line rates higher than those corresponding to the SOA-IMs by using 10dB lower optical input powers. In addition, Fig. 10 also shows that the QD-SOA-IMs subject to 5dBm optical input powers can achieve better transmission performance than the SOA-IMs subject to 10dBm input optical powers for transmission distances of <60km. For optical input powers of <5dBm, the superiority of the SOA-IMs over the QD-SOA-IMs for longer transmission distances is due to the fact that the QD-SOA-IMs have gain-current curves with flat slopes (Fig. 3(b)), leading to severe signal clippings and lower signal extinction ratio as seen in Fig. 6.To demonstrate the QD-SOA-IM-induced strong signal clipping effect, as stated above, Fig. 11 is plotted to compare the waveforms of the QD-SOA-IM- and ideal IM- modulated AMOOFDM signals for input optical power of 10dBm. In Fig. 11 we see that both upper and lower peaks of the QD-SOA-IM modulated waveforms are clipped compared to those corresponding to an ideal IM. The strong clipping effect associated with the QD-SOA-IM leads to severe degradation in the signal quality. In particular, the signal clipping effect is more important for long transmission distances.
3.5 Impact of negative frequency chirp
It is well known that a SOA-IM imposes negative frequency chirps on the modulated optical signals , this still holds well for the QD-SOA-IM. The negative frequency chirp originates due to the fact that the variations of the SOA/QD-SOA gain and corresponding signal phase always have opposite signs in the optical domain. For the cases of interest of the present paper, the “electrically modulated” optical signals also simultaneously affect the SOA/QD-SOA gains, as explicitly expressed in Eqs. (5-6), thus resulting in the occurrence of the negative frequency chirp effect, regardless of the employed optical or electrical driving approaches.
The negative frequency chirp effect can be used to mitigate the positive fibre chromatic dispersion effect, as shown in Fig. 12 . As expected, the fiber dispersion compensation effect is more pronounced for long transmission distances, and the QD-SOA-IMs have much stronger dispersion compensation capability compared to SOA-IMs. As square-law photon detection cannot preserve perfectly the chromatic dispersion-induced optical phase shift in the electrical domain, better dispersion compensation can reduce the phase variation, thus leading to the improved AMOOFDM transmission performance.
Extensive explorations have been undertaken, for the first time, of the feasibility of utilizing QD-SOA-IMs in IMDD SMF-based AMOOFDM transmission systems for applications in next generation PONs. Taking into account the QD and WL effects, a theoretical QD-SOA-IM model has been developed, based on which optimum QD-SOA-IM operating conditions have been identified together with major physical factors considerably affecting the system performance. It has been shown that, in comparison with previously reported SOA-IMs, QD-SOA-IMs cannot only considerably improve the AMOOFDM transmission performance but also broaden the optimum operating condition ranges. In particular, for achieving signal bit rates of >30Gb/s over >60km SMFs, QD-SOA-IMs allows a 10dB reduction in CW optical input powers injected into the modulator. In addition, QD-SOA-IMs can also be used to compensate the chromatic dispersion effect. Results have also shown that signal clipping and small signal extinction ratio play dominant roles in determining the maximum achievable AMOOFDM transmission performance. These results show the potential of using QD-SOA-IMs in future PON systems.
The work of J.M.Tang was supported by the PIANO+ under the European Commission’s (EC’s) ERA-NET Plus scheme within the project OCEAN under grant agreement number 620029. The work of M. Hamzeh was supported by the RESO laboratory at the Ecole Nationale d’Ingénieurs de Brest (ENIB) and the Arts Sciences & Technology University in Lebanon (AUL).
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