The wavelength dependent transmission performance of adaptively modulated optical OFDM (AMOOFDM) signals is investigated, for the first time, over optical amplification- and chromatic dispersion compensation-free IMDD SMF systems using semiconductor optical amplifiers (SOAs) as intensity modulators. A theoretical SOA model describing both optical gain saturation and gain spectral dynamics is developed, based on which optimum SOA operating conditions are identified for various wavelengths varying in a broad range of 1510nm–1590nm. Results show that, SOA intensity modulators operating at the identified optimum conditions enable the realization of colourless AMOOFDM transmitters within the aforementioned wavelength window. Such transmitters are capable of supporting >30Gb/s signal transmission over 60km SMFs.
©2009 Optical Society of America
Wavelength division multiplexed-passive optical networks (WDM-PONs)  have been widely considered as one of the strongest contenders for next generation access networks, as WDM-PONs are capable of offering a number of excellent features including, for example, enormous bandwidth, large split ratio, extended transmission reach, improved dynamic bandwidth allocation, aggregated traffic backhauling and simplified network architecture. A major stumbling block to widespread deployment of WDM-PONs is the high cost of WDM-PON equipment, since optical transmitters in customer optical network units (ONUs) require wavelengths being precisely aligned with specifically allocated WDM grid wavelengths. The conventional metropolitan or long-haul solution of utilizing wavelength specified lasers is, however, too expensive for such an application scenario, as a fundamental requisite of the solution is a large number of lasers of different wavelengths to implement in each individual customer base. This results in the extremely high inventory and maintenance cost.
To effectively reduce the WDM-PON equipment cost, a promising approach is to replace the wavelength referencing and control function from each ONU with a central wavelength supply from the central office [2,3]. An alternative approach is to use a tunable laser at each ONU. The first technical strategy can enhance the wavelength control functionality of WDM-PONs, and the second one makes economic sense because of the availability of commercial tunable semiconductor lasers at prices of a few hundred U.S. dollars. The major challenge in practical implementation of the aforementioned two strategies is, therefore, the provision of cost-effective colourless optical transmitters in ONUs to ensure that the uplink transmission performance is independent of the wavelengths assigned dynamically by central offices.
To realize colourless transmitters, a wide range of optical modulators have been proposed, including, for example, injection-locked Fabry-Perot lasers , reflective semiconductor optical amplifiers (SOAs)  and reflective electro-absorption modulators (EAMs) integrated with SOAs . Given the fact that the volumes of optical modulators required by WDM-PONs are potentially very high, it is considerably beneficial if use can be made of monolithically integrated semiconductor modulators to reduce significantly the installation and maintenance cost. In addition, such optical modulators also have other unique advantages such as small footprint and low power dissipation.
A recently proposed optical orthogonal frequency division multiplexed (OOFDM) signal modulation technique has attracted overwhelming research interest because of its strong inherent tolerance to chromatic dispersion, significant system flexibility, relatively high signal transmission capacity and potentially low system cost [5–8]. In particular, adaptively modulated OOFDM (AMOOFDM) has demonstrated great potential for providing a high speed, low-cost and robust solution for practical implementation in cost-sensitive application scenarios such as multi-mode fibre (MMF)-based local area networks (LANs) [5,9], single mode fibre (SMF)-based access and metropolitan area networks (MANs) [10–13], and long haul transmission systems .
It is greatly advantageous if the feasibility of employing SOAs as intensity modulators in AMOOFDM modems can be exploited for achieving colourless AMOOFDM transmitters for WDM-PONs. Our previous investigations have shown  that AMOOFDM modems using SOAs as intensity modulators are capable of supporting 30Gb/s transmission over 80km SMF in intensity modulation and direct detection (IMDD) links without optical amplification and chromatic dispersion compensation. In particular, the SOA-enabled transmission performance doubles that offered by directly modulated DFB lasers (DMLs) due to a considerable reduction in the intensity modulator-induced frequency chirp effect [11,13,14]. Based on a SOA that is not saturated strongly, a 10Gb/s AMOOFDM signal transmission over a 20km SMF has been demonstrated experimentally in an upstream link of a WDM-PON .
As an SOA has a wide spectral coverage of >100nm and its optical gain saturation characteristics vary significantly with SOA operating conditions and optical signal properties, detailed explorations of the wavelength dependent transmission performance of the AMOOFDM signals modulated using SOAs are, therefore, very crucial for evaluating the feasibility of utilizing SOAs to achieve colourless AMOOFDM transmitters for WDM-PONs. However, previous work reported in  was undertaken using a fixed wavelength of 1550nm only. Although the transmission performance of SOA modulated AMOOFDM signals for a few wavelengths have been presented in , very limited discussions have, however, been made. To address the important issue and to provide valuable insights for practical system designs, the present paper is a significant extension of the paper published previously , because, here, special attention is focused on exploring, for the first time, the wavelength dependent transmission performance of SOA modulated AMOOFDM signals, based on a comprehensive SOA model capable of describing wavelength dependent SOA characteristics. The focus of this paper is to investigate extensively, for the first time, the wavelength dependent transmission performance of AMOOFDM signals modulated by SOAs over IMDD SMF link without optical amplification and dispersion compensation. A theoretical SOA model describing both optical gain saturation and gain spectral characteristics is developed, based on which optimum SOA operating conditions are identified for various wavelengths within a broad range of 1510nm–1590nm. It is shown that SOA intensity modulators operating at the identified optimum operating conditions are capable of achieving colourless AMOOFDM transmitters. In addition, results also indicate that it is feasible to transmit >30Gb/s AMOOFDM signals over 60km SMFs.
2. Transmission system models
2.1 Transmission system and AMOOFDM models
In Fig. 1, the transmission system considered here is illustrated, which consists of a transmitter, an optical amplification- and chromatic dispersion compensation-free IMDD SMF link, a photodiode and a receiver. The transmitter is composed of an AMOOFDM modem [5,9,11,14,15], a tunable semiconductor laser, an SOA intensity modulator, an ideal optical filter and an optical attenuator. The generation, transmission and detection of the AMOOFDM signals are modeled following procedures similar to those reported in [5,9,11,14,15], in which approaches used to produce and detect real-valued electrical signals for arbitrary modulation formats are also presented. The major procedures associated with the transmitter are: symbol mapping, inverse fast Fourier transform (IFFT), cyclic prefix insertion, symbol serialization and Digital-to-Analog Conversion (DAC). The signal modulation format taken on each subcarrier varies from differential binary phase shift keying (DBPSK), differential quadrature phase shift keying (DQPSK), 8-quadratic amplitude modulation (QAM) to 256-QAM. The real-valued electrical signal emerging from the output of the AMOOFDM modem is up-shifted to ensure that each sample point has a positive value. The up-shifted electrical signal is then used to directly drive the SOA, whose optical gain alters with the electrical driving signal. Therefore, a continuous wave (CW) injected into the SOA provides an optical carrier wave, which is then modulated by the driving current in the SOA.
A tunable semiconductor laser is employed to provide a CW light source with the desired optical power and optical carrier wavelength. The DC bias current and the driving current are also adjusted appropriately to enable the SOA to operate at optimum operating conditions. Such adjustments may also alter the output power of the modulated optical signal. An optical filter is introduced to remove the SOA-induced optical noise outside the AMOOFDM signal band. An optical attenuator is also inserted at the input facet of the SMF link to fix the coupled optical power at a required level.
At the receiver end, the optical signal is detected using a photodiode. The data is finally recovered following an inverse procedure of the AMOOFDM modem in the transmitter.
2.2 SOA intensity modulator model
In developing the SOA intensity modulator model, various SOA intraband dynamic processes are not considered, which include carrier heating, spectral hole-burning, two-photon absorption and ultrafast nonlinear refraction . Such theoretical treatment holds well, because 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. Furthermore, as discussed in Section 3, the optical gain saturation properties of the SOA are mainly determined by a strong DC component of the optical signal propagating in the SOA. For example, at the output facet of the SOA, the modulated optical signal with a noise-like waveform with an approximated Gaussian probability density function has a relatively small signal extinction ratio of <2dB. It should be noted that, when extremely high CW optical input powers of >30dBm are injected into the SOA, the effective interband carrier lifetimes may approach towards regimes where the intraband effects also become important in determining the optical gain saturation characteristics of the SOA. However, as discussed in Section 4, such CW optical input powers are well above the optimum optical input power of 20dBm of interest of the present paper. For the SOA subject to the optimum optical input power, the corresponding effective interband carrier lifetime is approximately 50ps, which is far beyond the intraband dynamic process response times. The above analyses indicate that it is sufficiently accurate to neglect the influence of the intraband dynamic processes on the optical gain saturation characteristics of the SOAs. Moreover, the validity of the developed SOA intensity modulator model is also confirmed by agreement between theoretical results obtained here and experimental measurements reported in , as discussed in Section 4.
The exclusion of the intraband dynamic processes simplifies significantly the comprehensive theoretical SOA model developed in . When a transformation of the coupled wave propagation equations  is made to the retarded reference frame, T = t−z/νg with t, z and νg being the time, the transmission distance and the group velocity, respectively, and when the optical field is defined as
with P(z,T) and ϕ(z,T) being the optical power and the optical phase, respectively, the output optical signal from the SOA is governed by
where the subscript i is referred to the wavelength λi. Pin,i(T) and ϕin,i(T) are the power and phase of the input optical signal. Pout,t(T) and ϕout,i(T) are the power and phase of the modulated output optical signal. hi(T) represents the integrated optical gain along the entire SOA length L.gi(z,T) is the saturated optical gain defined as gi(z,T) = Γai[N(T) − N 0i] with n(t) and N 0i being the carrier density and the carrier density at transparency, Γ is the confinement factor and ai is the differential gain. For a specific optical gain spectrum, gs,i(T) is the small-signal gain of the SOA at a fixed wavelength λi, which can be expressed as gs,i(T) = Γai N 0i[I(T)/I 0i−1] , here I(T) is the total injected electrical current including the DC bias current and the driving current, and I 0i is the transparency current. τc is the carrier lifetime. Esat,i = ħωiwd/Γai is the SOA saturation energy, where ωi, w and d are the optical signal frequency, the width and depth of the SOA active region, respectively. α is the linewidth enhancement factor. It can be seen from Eq.(4) that, α varies the phase of the modulated AMOOFDM signal only. Owing to direct detection in an IMDD link, such a phase variation does not affect the transmission performance of the SOA modulated signal. Therefore, the wavelength dependence of the α parameter is not considered in this paper. Eqs. (3)–(4) can be easily solved numerically when gs,i(T), pin,i(T) and ϕin,i(T) are made known.
In order to simulate the optical wavelength dependence of small-signal gain gs,i(T), a theoretical gain spectral model should be as realistic as possible without requiring too many parameters and easily calibrated against experimental measurements of an actual SOA. Here a widely used SOA optical gain spectral model is adopted . The wavelength- and injected current-dependent small-signal gain in dB, GdB,I (λi,T), can be expressed as
where GdB (λ max) is the small-signal peak gain corresponding to a wavelength λ max and a current Imax. In this paper, these parameters are treated as a reference point and their corresponding values are listed in Table 1 . GdB,I (λ max,T) is the small-signal gain at λ max for an injected current I(T) and satisfies
Therefore, GdB,I (λi,T) and GdB,I (λ max,T) are time-variant due to the injection of a time-dependent driving current I(T). ag (λi) and bg (λi) are the normalized small-signal gain coefficient and normalized differential gain, respectively. They are defined as ag (λi) ≣ gs,i (T) / g max (T, λmax) and bg (λi) ≣ ai /a(λ max), where g max(T, λ max) and a(λ max) are the small-signal gain and the differential gain at λ max, respectively. The spectral dependence of ag(λi) and bg (λi) can be written as 
Apart from performing intensity modulation, the SOA also imposes simultaneously ASE noise onto the modulated optical signal. The total ASE power PASE ,i at λi can be calculated by 
where Nf is the SOA noise figure, B 0 is the optical bandwidth and ħωi is the photon energy. In deriving Eq. (9), it is assumed that ASE noise does not affect the SOA gain dynamics. This assumption is valid because the saturated optical gain is typically small (<5dB) when the SOA operates in a deeply saturated gain region, as discussed in Section 3 and Section 4. In addition, the small saturated optical gain also gives rise to the negligible SOA self-saturation effect.
After adding the ASE noise into Pout,i (T) and ϕout,i (T) , by using Eq. (1), the modulated optical signal can be obtained. In the receiver, the transmitted optical signal is detected using a photodiode when a CW optical input wave is chosen in the transmitter.
2.3 Models for SMF and PIN detector
A SMF model successfully used in [10–11,14–15] is adopted here, in which the effects of loss, chromatic dispersion, and optical power dependence of refractive index are included. In particular, the wavelength dependence of fiber loss and chromatic dispersion is also considered to accommodate optical signals having wavelengths within a broad wavelength window. The effect of Kerr nonlinearity-induced phase noise to intensity noise conversion is incorporated upon photon detection in the receiver.
In the receiver, shot noise and thermal noise associated with the photodiode are considered. These effects are simulated following procedures similar to those presented in .
2.4 Simulation parameters
In simulating the performance of AMOOFDM modems, parameters presented in  are adopted here: The total number of subcarriers is M=64, in which 32 subcarriers is in the positive frequency bins and used to carry original data, with one subcarrier close to the optical carrier frequency being dropped. Sampling rates of the DACs/ADCs are taken to be 12.5GS/s in both the transmitter and the receiver. The cyclic prefix parameter defined in  is 25%. The optimum 7-bits of quantization and 13dB signal clipping ratio are considered . The definition of signal clipping ratio is given in . The above-mentioned parameters give a signal bandwidth of 12.5/2 = 6.25GHz in the positive frequency bins, a bandwidth for each subcarrier of 6.25/32 ≈ 195.3MHz, and a cyclic prefix length of 1.28ns within each symbol having a total time duration of 6.4ns. In simulating the transmission performance of an entire fibre system, 1500 OFDM symbols are employed, which is oversampled to give a total number of sample points of 512488. For each set of conditions, 20 simulations are performed using different random data sequences. After averaging all bit error rates (BERs) corresponding to these simulations, a final BER is obtained.
The parameters used in simulating the SOA intensity modulator are representative for InGaAsP semiconductor materials [15,18], which are listed in Table 1. As discussed in Section 4, the modulation bandwidth of the SOA intensity modulator depends strongly upon SOA operating conditions. It has been shown  that, for optical input powers of <-10dBm, the SOA intensity modulator has a small modulation bandwidth of approximately 1GHz, and the bandwidth increases with increasing optical input power.
By attenuating/amplifying the modulated optical signal from the SOA, the optical power coupled into the SMF link is fixed at 6.3dBm. The choice of the coupled optical power enables us to compare fairly between results presented here and those reported in . The impact of noise associated with any amplifiers used to boost the signal power to 6.3dBm is neglected.
The simulation parameters for SMFs  and PIN detectors [11,22] are also given in Table 1. It should be noted that SMF attenuation and dispersion parameters are wavelength dependent. As an example, the attenuation and dispersion parameters are 0.22dB/km and 14.2ps/nm/km (0.22dB/km and 19.8ps/nm/km) at 1510nm (1590nm), whilst the corresponding parameters at 1550nm are 0.2dB/km and 17ps/nm/km.
3. SOA characteristics
To gain an in-depth understanding of simulation results presented in Section 4, in this section brief discussions are made of the wavelength dependent SOA optical gain properties. Figure 2 shows the SOA optical gain spectra for different bias currents and optical input powers. In obtaining Fig. 2, a 10GHz sinusoidal electrical driving current having a fixed peak-to-peak (PTP) value of 80mA is applied to the SOA to ensure that the SOA operating conditions considered here are similar to those adopted in other figures of the paper. Throughout this paper, the PTP, CPTP, of a driving current is defined as CPTP = C max − C min with C max (C min) being the maximum (minimum) current found within the entire driving current waveform considered. For an electrical OFDM signal having a clipping ratio of less than its corresponding optimum value identified in , we have , here ξ, is the clipping ratio and Pav is the average OFDM signal power.
Figure 2 shows that, for a specific optical input power, the SOA gain spectral peak shifts towards a long wavelength with decreasing bias current. This agrees very well with experimental measurements . In addition, as seen in Fig. 2, a rapid decline in bias current required at transparency with increasing CW wavelength also shows good agreement with results reported in . The above-mentioned behaviors confirm strongly the validity of the wavelength dependent SOA model developed here.
As expected, it can be seen in Fig. 2 that, the SOA gain spectra vary considerably with optical input power. For optical input powers of <10dBm, strong wavelength dependent SOA gain spectra occur, implying that the AMOOFDM transmission performance is sensitive to CW wavelength. Whilst for optical input powers of >10dBm, the SOA operates in a deeply saturated gain region, resulting in a flat gain spectrum with a significantly reduced optical gain. This indicates that a wavelength independence of the AMOOFDM transmission performance is expected over such operating conditions.
Given the central role of the characteristics of current versus SOA optical gain in determining the transmission performance of the SOA modulated AMOOFDM signals, in Fig. 3, the current-gain curves for different optical input powers are plotted for different CW wavelengths varying in a broad range of 1510nm–1590nm. It is shown that, for optical input powers of >10dBm, a linear current-gain lineshape occurs in the vicinity of the transparency bias current. As expected from Fig. 2, for a long CW wavelength, such a linear region broadens and simultaneously shifts towards a low bias current. This implies that, to maximize the transmission performance of the AMOOFDM signals, the SOA has to be set at a low bias current for a long CW wavelength. Outside the linear current-gain region, the modulated AMOOFDM signals suffer from the signal clipping effect [15,17]. To minimize the effect, it is necessary to optimize the PTP value of the driving current. Moreover, Fig. 3 also shows that, a long CW wavelength corresponds to a decreased slope of the current-gain curve, leading to a degraded extinction ratio of the modulated optical signals.
4. Transmission performance of SOA modulated AMOOFDM signals
4.1 Wavelength dependent transmission performance
The wavelength dependence of AMOOFDM transmission performance is examined in Fig. 4. In simulating Fig. 4, the bias current, the PTP value of the driving current and the transmission distance are fixed at 100mA, 80mA and 60km, respectively. In numerical simulations throughout this paper, the signal line rate, Rsignal, is calculated using the formula given below:
where Ms = M/2 = 32 is the total number of data-carrying subcarriers in the positive frequency bins, Sk is the signal bit rate corresponding to the k-th subcarrier, nk is the total number of binary bits conveyed by the k-th subcarrier within one symbol period Tb, rs is the ADC/DAC sampling rate, and η is the cyclic prefix parameter .
The total channel BER, BERT, is defined as
where Enk is the total number of errors counted directly and Bitk is the total number of transmitted binary bits. Both Enk and Bitk are for the k-th subcarrier, whose subchannel BER, BERk is given by BERk = Enk /Bitk. For a specific subcarrier, the total number of bits processed for calculating BERk depends upon the signal modulation format taken on the subcarrier. For example, based on the simulation parameters given in Section 2.4, for 16-QAM, the total number of bits processed are 3.72×106, giving rise to a lowest BERk of 2.7×10-7. Based on BERT and BERk, the highest modulation format taken on each subcarrier within a symbol can be identified through negotiations between the transmitter and the receiver according to the frequency response of a given transmission link in an initial stage of establishing the link. Generally speaking, a high (low) modulation format is used on a subcarrier suffering a low (high) transmission loss. Any subcarrier suffering a very high transmission loss may be dropped completely if there are still a large number of errors occurred even when the lowest modulation format is employed. It is also worth addressing that, the signal line rate computed using Eq. (10) is only considered to be valid when the condition of BERT = 1.0×10-3 is satisfied. The signal modulation format taken on each subcarrier across the entire spectrum follows the link frequency response. For example, the transmission performance at 1550nm corresponding to the red curve shown in Fig. 4 is achieved by using 32-QAM on 4 subcarriers, 16-QAM on 8 subcarriers, 8-QAM on 16 subcarriers and DQPSK on 3 subcarriers.
Figure 4 shows that, under the SOA operating conditions specified above, the AMOOFDM transmission performance depends strongly upon the input optical signal properties including wavelengths and powers. As envisaged from the discussions in Fig. 2 and Fig. 3, for optical input powers of ≤10dBm, the signal line rate grows rapidly with increasing CW wavelength until 1570nm. A further increase in CW wavelength brings about an almost flattened signal line rate developing trend. Such wavelength dependent performance behaviors are consistent with experimental measurements . On the other hand, for optical input powers of >10dBm, the signal capacity differences for different CW wavelengths are reduced considerably, and an almost symmetric signal capacity lineshape occurs with respect to a CW wavelength of 1550nm. Moreover, for a fixed CW wavelength, the signal line rate increases with increasing optical input power for optical input powers of <20dBm, beyond this value, the achievable signal line rate drops sharply, which suggests the optimum optical input power is approximately 20dBm.
The physical mechanisms behind the above-mentioned transmission performance behaviors are the co-existed effects of SOA effective carrier lifetime and extinction ratio of the modulated signal . The SOA effective carrier lifetime, τe,i, is written as 
where P̄ is the average optical output power, A(iΔT) (A(jΔT)) is the i-th (j-th) signal sample, ΔT is the sampling duration, K 1 (K 2) is the number of samples satisfying A 2 ≥ P̄ (A 2 < P̄) within the entire AMOOFDM signal considered, and K 1 + K 2 is the total number of samples. The statistical definition of the SOA modulated AMOOFDM signal extinction ratio takes into account the fact that the time-domain signal waveform has an approximated Gaussian probability density function, According to the definition, the resulting signal extinction ratio value is a function of SOA operating conditions and OFDM signal properties including peak-to-average power ratio (PAPR) and PTPs of the driving currents .
As seen in Fig. 5, for optical input powers of ≤10dBm and CW wavelengths of <1570nm, both the SOA effective carrier lifetime and the modulated signal extinction ratio decrease quickly with increasing CW wavelength. A short effective carrier lifetime corresponds to a large SOA bandwidth, leading to the reduced frequency chirp effect and thus an improved transmission performance . Whilst a small signal extinction ratio increases the minimum optical signal-to-noise ratio (OSNR) required for achieving a specific transmission performance, resulting in a reduction in signal transmission capacity. Comparisons between Fig. 5 and Fig. 4 indicate that, under the aforementioned optical input power and CW wavelength range, the reduction in SOA effective carrier lifetime dominates the wavelength dependent AMOOFDM performance illustrated in Fig. 4.
Within the same optical input power range of ≤10dBm, for wavelengths of ≥ 1570nm the SOA effective carrier lifetime grows slowly with increasing CW wavelength, as shown in Fig. 5. Over this region, the signal extinction ratio curve becomes flat. Therefore, a slight degradation of the AMOOFDM transmission performance is observed in Fig. 4 for CW wavelengths of >1570nm. For optical input powers of ≤10dBm, the occurrence of a minimum SOA effective carrier lifetime at 1570nm can be explained by considering Eq. (12): a maximum SOA output optical power occurs in the vicinity of the CW wavelength of 1570nm. This can be understood by considering Fig. 2(a) and Fig. 2(b); On the other hand, the SOA saturation energy increases with increasing CW wavelength, as shown in Fig. 6, resulting from a long wavelength-induced reduction in differential gain. The co-existence of the above two physical processes underpins the occurrence of the minimum SOA effective carrier lifetime observed in Fig. 5.
It can also be seen from Fig. 5 that, for optical input powers of ≤10dBm, for a given CW wavelength, both the SOA effective carrier lifetime and the signal extinction ratio decrease with increasing optical input power. It is clear from the above discussions that, this gives rise to an increase in signal line rate with increasing optical input power, as shown in Fig. 4, which agrees very well with results presented in .
For optical input powers of >10dBm, the SOA operates in a strongly saturated optical gain region, the variations in both the SOA effective carrier lifetime and the signal extinction ratio reduce significantly across the entire wavelength window of 1510–1590nm. As a direct result, the transmission performance of the AMOOFDM signals is insensitive to CW wavelength, as shown in Fig. 4. The existence of a maximum transmission performance for 1550nm in Fig. 4, is mainly due to that the linear SMF loss is minimum at such a wavelength. However, a further increase in optical input power to >20dBm leads to an extremely small signal extinction ratio, which plays a dominant role in determining the AMOOFDM transmission performance. This gives rise to a degradation of the AMOOFDM transmission performance for optical input powers of >20dBm, as seen in Fig. 4.
4.2 Optimum SOA operating conditions for different wavelengths
The optimum SOA operating conditions for different CW wavelengths are explored in Fig. 7, where contour plots of signal line rate as a function of both optical input power and bias current are presented for different wavelengths varying in a wide range of 1510–1590nm. In computing this figure, the transmission distance is fixed at 60km and a driving current with a constant PTP value of 80mA is considered.
Figure 7 shows that, for a specific wavelength, there exists an optimum bias current and an optimum optical input power, corresponding to which a maximum signal line rate is obtained. Such bias current and optical input power dependence of the transmission performance agrees very well with that reported in , from which detailed explanations can also be found. From discussions in  and Section 4.1, it is clear that the SOA effective carrier lifetime effect and the signal extinction ratio effect are the major contributors to the evolution trends illustrated in Fig. 7.
It is very important to note in Fig. 7 that, the optimum SOA operating conditions are wavelength dependent, i.e., with increasing CW wavelength, the optimum SOA bias current decreases with the optimum optical input power remaining almost unchanged. For example, for 1510nm, the optimum bias current and the optimum optical input power are approximately 200mA and 20dBm, respectively; whilst for 1590nm the values of these two parameters are approximately 50mA and 20dBm. The impact of CW wavelength on the optimum SOA bias current can be explained by considering the fact that, a long CW wavelength shifts the linear region of the current-gain curve towards a low bias current, as shown in Fig. 3. On the other hand, the insensitivity of optimum optical input power to CW wavelength is a direct result of deeply saturated optical gain of the SOA. For such a case, several key factors are insensitive to CW wavelength, which include SOA optical gain, effective carrier lifetime and signal extinction ratio.
It is worth addressing, in particular, that by operating the SOA at optimum operating conditions corresponding to different wavelengths, a <3Gb/s variation in maximum achievable signal line rate is obtained across an entire wavelength range of 80nm, as shown in Fig. 7. This indicates that colourless AMOOFDM transmitters are achievable when different optimum SOA operating conditions are chosen corresponding to different CW wavelengths.
Figure 8 examines the impact of driving current PTP on the maximum achievable AMOOFDM transmission performance for different wavelengths. In obtaining Fig. 8, the identified optimum optical input powers and bias currents are adopted for each individual wavelength selected. The transmission distance is taken to be 60km. It is very interesting to note from Fig. 8 that an optimum PTP value of 80mA exists for all CW wavelengths varying between 1510nm and 1590nm. The occurrence of the wavelength independent optimum PTP is due to the co-existed effects of signal clipping and signal extinction ratio. For a given CW wavelength, a high (small) PTP value leads to a strong (weak) signal clipping effect and a large (small) signal extinction ratio. A long CW wavelength considerably broadens the linear current-gain region, thus giving the reduced signal clipping effect. On the other hand, a long CW wavelength also decreases the slope of the linear current-gain curve, thus giving a reduced signal extinction ratio. The first effect offsets the second one, an almost wavelength independent optimum PTP value is observed in Fig. 8.
4.3. Capacity versus reach performance under optimum SOA operating conditions
It is clear from the discussions in Section 4.2 that the optimization of SOA operating conditions enables the realization of colourless AMOOFDM transmitters. Based on the identified optimum operating conditions for different CW wavelengths, the maximum achievable AMOOFDM transmission capacity versus reach performance is plotted in Fig. 9. Within a broad wavelength region of 1510–1590nm, an almost wavelength insensitive AMOOFDM transmission performance is obtainable for transmission distances of up to 150km. In particular, the SOA-enabled colourless transmitter is capable of supporting >30Gb/s signal transmission over 60km SMFs. It should be pointed out that the worst transmission performance at 1590nm is mainly due to the long wavelength-induced strong chromatic dispersion effect.
It is also worth addressing that the transmission performance of the colourless transmitters is very robust to variations in SOA parameters such as saturation energy and SOA length.
This strengthens further the technical basement of employing optimized SOA intensity modulators to achieve colourless AMOOFDM transmitters for WDM-PONs.
The wavelength dependent transmission performance of SOA modulated AMOOFDM signals has been investigated, for the first time, over IMDD SMF links without optical amplification and chromatic dispersion compensation. A theoretical SOA model describing optical gain saturation and gain spectral characteristics has been developed, based on which optimum SOA operating conditions have been identified for different wavelengths varying in a broad range of 1510nm–1590nm. Numerical simulation results have shown that, within the entire wavelength window, the SOA intensity modulators operating at the identified optimum conditions enable the realization of colourless AMOOFDM transmitters. In addition, it is also shown that the colourless AMOOFDM transmitters are capable of supporting >30Gb/s transmission over 60km SMFs.
It is worth mentioning that, the optimum optical input power identified in this paper is much higher than the typical output power of a commercially available tunable laser. To effectively reduce the optimum power, use may be made of two techniques including, for example, 1) employment of several CW optical waves at different wavelengths; 2) replacing conventional SOAs with quantum-dot SOAs. Detailed investigations of the feasibility of these approaches are currently being undertaken, and results will be reported elsewhere in due course.
This work was partly supported by the European Community’s Seventh Framework Programme (FP7/2007-2013) within the project ICT ALPHA under grant agreement n° 212 352, in part by the U.K. Engineering and Physics Sciences Research Council under Grant EP/D036976, and in part by The Royal Society Brian Mercer Feasibility Award. The work of J.L. Wei was also supported by the School of Electronic Engineering and the Bangor University.
The authors would like to thank Dr. Y. H. Hong and Dr. I. Pierce of Bangor University for their comments on the work.
References and links
1. K. Grobe and J.-P. Elbers, “PON in adolescence: from TDMA to WDM-PON,” IEEE Commun. Mag. 46, 26–34 (2008). [CrossRef]
2. P. Healey, P. Townsend, C. Ford, L. Johnston, P. Townley, I. Lealman, L. Rivers, S. Perrin, and R. Moore, “Spectral slicing WDM-PON using wavelength-seeded reflective SOAs,” Electron. Lett. 37, 1181–1182 (2001). [CrossRef]
3. K. Iwatsuki, J.-I. Kani, H. Suzuki, and M. Fujiwara, “Access and metro networks based on WDM technologies,” J. Lightwave Technol. 22, 2623–2630 (2004). [CrossRef]
4. E. K. MacHale, G. Talli, P. D. Townsend, A. Borghesani, I. Lealman, D. G. Moodie, and D. W. Smith, “Extended-reach PON employing 10Gb/s integrated reflective EAM-SOA,” in European Conference on Optical Communication (ECOC), (Brussels, Belgium, 2008), paper Th.2.F.1.
5. J. M. Tang, P. M. Lane, and K. A. Shore, “High speed transmission of adaptively modulated optical OFDM signals over multimode fibers using directly modulated DFBs,” J. Lightwave Technol. 24, 429–441 (2006). [CrossRef]
7. M. Schuster, S. Randel, C.A. Bunge, S. C. J. Lee, F. Breyer, B. Spinnler, and K. Petermann, “Spectrally efficient compatible single-sideband modulation for OFDM transmission with direct detection,” IEEE Photon. Technol. Lett. 20, 670–672 (2008). [CrossRef]
8. B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol. 26, 196–203 (2008). [CrossRef]
9. X. Q. Jin, J. M. Tang, P. S. Spencer, and K. A. Shore, “Optimization of adaptively modulated optical OFDM modems for multimode fiber-based local area networks,” J. Opt. Netw. 7, 198–214 (2008). [CrossRef]
10. X. Zheng, J.L. Wei, and J.M. Tang, “Transmission performance of adaptively modulated optical OFDM modems using subcarrier modulation over SMF IMDD links for access and metropolitan area networks,” Opt. Express 16, 20427–20440 (2008), http://www.opticsinfobase.org/abstract.cfm?uri=oe-16-25-20427. [CrossRef] [PubMed]
11. J. M. Tang and K. A. Shore, “30 Gb/s signal transmission over 40-km directly modulated DFB-laser-based single-mode-fibre links without optical amplification and dispersion compensation,” J. Lightwave Technol. 24, 2318–2327 (2006). [CrossRef]
12. B.J.C. Schmidt, Z. Zan, L.B. Du, and A.J. Lowery, “100 Gbit/s transmission using single-band direct-detection optical OFDM,” Optical Fibre Communication/National Fibre Optic Engineers Conference (OFC/NFOEC), (OSA, 2009), Paper PDPC3.
13. T. N. Duong, N. Genay, B. Charbonnier, P. Urvoas, P. Chanclou, and A. Pizzinat, “Experimental demonstration of 10Gbit/s transmission over 110km SMF by direct modulation of 2 GHz bandwidth DFB laser using discrete multi-tone modulation for passive optical network,” Optical Fibre Communication/National Fibre Optic Engineers Conference (OFC/NFOEC), (OSA, 2008), Paper NMB3.
14. J. L. Wei, X. Q. Jin, and J. M. Tang, “The influence of directly modulated DFB lasers on the transmission performance of carrier suppressed single sideband optical OFDM signals over IMDD SMF systems,” J. Lightwave Technol. (accepted for publication).
15. J. L. Wei, A. Hamié, R. P. Giddings, and J. M. Tang, “Semiconductor optical amplifier-enabled intensity modulation of adaptively modulated optical OFDM signals in SMF-based IMDD systems,” J. Lightwave Technol. (accepted for publication).
16. T. Duong, N. Genay, P. Chanclou, B. Charbonnier, A. Pizzinat, and R. Brenot, “Experimental demonstration of 10 Gbit/s for upstream transmission by remote modulation of 1 GHz RSOA using Adaptively Modulated Optical OFDM for WDM-PON single fiber architecture,” in European Conference on Optical Communication (ECOC), (Brussels, Belgium, 2008), PD paper Th.3.F.1. [CrossRef]
17. J. M. Tang and K. A. Shore, “Strong picosecond optical pulse propagation in semiconductor optical amplifiers at transparency,” IEEE J. Quantum Electron. 34, 1263–1269 (1998). [CrossRef]
18. K. Obermann, S. Kindt, D. Breuer, and K. Petermann, “Performance analysis of wavelength converters based on cross-gain modulation in semiconductor-optical amplifiers,” J. Lightwave Technol. 16, 78–85 (1998). [CrossRef]
19. N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989). [CrossRef]
20. G. P. Agrawal, Fibre-Optic Communication Systems, (Wiley, 1997).
21. J. M. Tang and K. A. Shore, “Maximizing the transmission performance of adaptively modulated optical OFDM signals in multimode-fiber links by optimizing analog-to-digital converters,” J. Lightwave Technol. 25, 787–798 (2007). [CrossRef]
22. P. Fay, W. Wohlmuth, A. Mahajan, C. Caneau, S. Chandrasekhar, and I. Adesida, “Low-noise performance of monolithically integrated 12-Gb/s p-i-n/HEMT photoreceiver for long-wavelength transmission systems,” IEEE Photon. Technol. Lett. 10, 713–715 (1998). [CrossRef]
23. S.-L. Lee, “Analytical formula of wavelength-dependent transparent current and its implications for designing wavelength sensors and WDM lasers,” IEEE J. Quantum Electron. 7, 201–209 (2001). [CrossRef]
24. R. Gutiérrez-Castrejón, L. Schares, L. Occhi, and G. Guekos, “Modeling and measurement of longitudinal gain dynamics in saturated semiconductor optical amplifiers of different length,” IEEE J. Quantum Electron. 36, 1476–1484 (2000). [CrossRef]