Two cascaded SOAs used as intensity modulators for adaptively modulated optical OFDM signals in optical access networks

Ali Hamié; Mohamad Hamzé; Haidar Taki; Layaly Makouk; Ammar Sharaiha; Ali Alaeddine; Ali Al Housseini; Elias Giacoumidis; J. M. Tang

doi:10.1364/OE.22.015763

1. Introduction

Optical orthogonal frequency division multiplexing (OOFDM) has been considered as one of the strongest contenders for improving the cost-effectiveness and flexibility of wavelength-division multiplexing passive optical networks (WDM-PONs) [1]. In particular, adaptively modulated OOFDM (AMOOFDM) can further enhance signal line rate, network flexibility and performance robustness [1]. On the other hand, the employment of semiconductor optical amplifiers (SOAs) and reflective SOAs (RSOAs) in customer optical network units (ONUs) has also been adopted as a promising solution for achieving cost-effective WDM-PONs [1]. Even though SOAs and RSOAs can be remotely seeded and guarantee adequate optical amplification over the whole C-band, direct modulation of SOAs/RSOAs is bandwidth-limited (typically around 1GHz) due to long carrier lifetime. An interesting but complex digital signal processing (DSP) approach with adaptive bit-and-power loading (BPL) OOFDM has been recently reported in [2] for 40Gb/s signal line rate by using a 1 GHz bandwidth RSOA over 26km of single-mode fiber (SMF) dual-feeder fiber direct-detected WDM-PON without chromatic dispersion (CD) compensation.

To improve transmission performance, the two cascaded semiconductor optical amplifiers in a counter-propagating configuration (TC-SOA-CC) has been proposed for all optical signal processing [3]. It was shown in [3] that the two cascaded SOAs have improved performance over the single SOA configuration. In particular, a measured extinction ratio (ER) up to 20dB was obtained for close contra-directional signal wavelengths and for a wide range of optical input powers. Based on this configuration, a number of various functions have been also proposed. For example, all optical switching [3] and logic NOR function [4] have been realized with a high extinction ratio (ER) ≥12dB over a wide range of wavelengths. The all-optical inverted and non-inverted wavelength conversions feasibility has also been demonstrated to deliver an ER≥7dB over a wide range of wavelengths [5]. All optical logic OR gate can be easily achieved with an ER≥7dB [6]. In addition, the theoretical and experimental static characterizations of the TC-SOA-CC were performed [3]. A deeper understanding of this configuration in the dynamic regime is provided in [7], where we have shown the frequency responses obtained at the TC-SOA-CC optical outputs and the evolution of the effective carrier lifetimes and the gains for each signal in each SOA. As the AMOOFDM have several advantages over other modulation techniques, concerning the CD tolerance, spectral efficiency, hybrid dynamic bandwidth allocation, and is less complex than adaptive BPL OOFDM [8–10], an electrical-to-optical conversion was performed. This conversion of AMOOFDM signals has been thoroughly investigated in intensity-modulation and direct-detection (IMDD) single-mode fiber (SMF)-based passive optical network (PON) systems. Previous research has demonstrated the potential of utilizing the SOA intensity modulators (SOA-IMs) [11], reflective SOA intensity modulators (RSOA-IMs) [12,13], and quantum dot SOA intensity modulators (QDSOA-IMs) [14]. It has been shown that these modulators not only facilitate the implementation of cost-effective AMOOFDM transceivers but also enable colorless AMOOFDM WDM operations [15].

In this paper, for the first time, we use the TC-SOA-CC as an intensity modulator (Fig. 1). In fact, in this configuration a feedback controls the evolution of the two SOA’s gain.

Fig. 1 Schematic view of a TC-SOA-CC with contra propagating signals.

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In static regime, the contra-directional input signals P_in,1 and P_in,2 are injected in SOA₁ and SOA₂, respectively. The two SOAs are directly connected. Two ports are coupled to SOA₁ and SOA₂, where the two others restitute the output powers P_out,1 and P_out,2. I_bias,1 and I_bias,2 are respectively the bias current of the SOA₁ and SOA₂. λ₁ and λ₂ are the wavelengths of the two injected optical powers. In fact, each SOA_i receives a total power P_tot,i which is the sum of two incident powers P_tot,i = P_in,i + P_out,j (j = 1,2, j ≠ i) where P_in,i(λ_i) is the input power and the SOA_j counterpropagating output power P_out,j = G_jP_in,j where G_j is the SOA_j gain. P_tot,i will be at a high level regardless of the input power due to the feedback between the two SOAs. So when one of the SOAs is used as an intensity modulator, in our setup SOA₂, its carrier lifetime will be reduced and thus we will have wide TC-SOA-CC electrical bandwidths in comparison to one SOA configuration. Moreover, compared with the SOA, the TC-SOA-CC has the advantage of more linear transfer function but with a lower gain-current slope.

In this paper, numerical simulations are undertaken, for the first time, to extensively explore the feasibility of utilizing TC-SOA-CC intensity modulators in IMDD AMOOFDM PON systems. Special effort is given to addressing the following technical challenges:

Development of a comprehensive theoretical TC-SOA-CC-IMs model where the SOA₁ acts as an amplifier and the SOA₂ behaves as an intensity modulator.
Identification of key TC-SOA-CC-IMs associated physical mechanisms considerably affecting the AMOOFDM transmission performance.
Identification of optimum TC-SOA-CC-IMs operating conditions that correspond to the maximum AMOOFDM transmission performance.
Performance comparisons between TC-SOA-CC-IMs and SOA-IMs to highlight the advantages of TC-SOA-CC-IMs for use in IMDD AMOOFDM PON systems.
Exploration of the feasibility of effectively utilizing the TC-SOA-CC-IMs -induced frequency chirp to improve the transmission performance of IMDD AMOOFDM PON systems.

2. Transmission system models

2.1 AMOOFDM transmission systems

The considered transmission system is illustrated in Fig. 2, which is composed of an AMOOFDM transmitter, a SMF link and an AMOOFDM receiver. This transmitter comprises an electrical OFDM modem [11–16], TC-SOA-CC-IMs, two CW laser diodes and a variable optical attenuator (VOA) or an EDFA to keep the input power to the SMF fixed. The major procedures associated with modeling the electrical AMOOFDM modems and transmission link are identical to those reported in [9,11–16].

Fig. 2 Transmission system with block diagrams of the AMOOFDM transmitter and receiver.

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2.2 TC-SOA-CC-based intensity modulator models

The schematic diagram of the TC-SOA-CC-IMs where the SOA₁ acts as an amplifier and the SOA₂ works as an intensity modulator is shown in Fig. 2. As explained before, each SOA receives two optical powers from its front facet and rear facet. The theoretical TC-SOA-CC model adopted here is an extension of the theoretical SOA intensity modulator models presented in [1,11,12] knowing that each SOA is subject to receive forward A⁺ and backward A^- propagating optical signals. Similar to the treatments presented in [1,11,12], in developing the TC-SOA-CC model, various ultrafast intraband dynamic processes are ignored, which include carrier heating, spectral hole-burning, two photon absorption and ultrafast nonlinear refraction [17]. Following the procedure in [1,11,12,18,19], when a transformation of the wave propagation equation is made to the retarded reference frame, $T = t - \frac{z}{v_{g}}$ with $t, z$ and $v_{g}$ being the time, the distance in longitudinal direction and the group velocity, respectively. The optical field is defined as

A_{i}^{\pm} (z, T) = \sqrt{P_{i}^{\pm} (z, T)} \exp [j φ_{i}^{\pm} (z, T)] (if i = 1, S O A_{1}; i f i = 2, S O A_{2}) .

With

P_{i}^{+} (z, T)

and

φ_{i}^{+} (z, T)

being the optical power and phase, respectively, at the forward direction of the input signal along SOA_i and

P_{i}^{-} (z, T)

and

φ_{i}^{-} (z, T)

being the optical power and phase, respectively, at the backward direction of the input signal along SOA_i. A set of equations which govern the propagation of the optical signal travelling through each SOA are obtained as follows:

\frac{\partial g_{i} (z, T)}{\partial T} = \frac{g_{0, i} - g_{i} (z, T)}{τ_{c, i}} - \frac{g_{i} (z, T)}{E_{s a t, i}} ({| A_{i}^{+} (z, T) |}^{2} + {| A_{i}^{-} (z, T) |}^{2}) .

\frac{\partial P_{i}^{\pm} (z, T)}{\partial z} = \pm g_{i} (z, T) P_{i}^{\pm} (z, T) .

\frac{\partial φ_{i}^{\pm} (z, T)}{\partial z} = \pm \frac{1}{2} α g_{i} (z, T) .

where

g_{i} (z, T)

is the optical gain defined as

g_{i} (z, T) = Γ_{i} a_{i} [N_{i} (T) - N_{0, i}] .

With

N_{i} (T)

and

N_{0, i}

being the carrier density and the carrier density at transparency for each SOA, Γ_i is the confinement factor and a_i is the differential gain.

g_{0, i} (T)

is the small signal gain of the SOA_i, which can be expressed as:

g_{0, i} (T) = Γ_{i} a_{i} N_{0, i} [\frac{I_{i} (T)}{I_{0, i}} - 1] .

Here

I_{i} (T)

is the total injected current including the dc bias current and the driving current along SOA_i, and

I_{0, i}

is the current required at transparency.

τ_{c, i}

is the carrier lifetime.

E_{s a t, i} = \frac{ℏ ω_{0, i} w_{i} d_{i}}{Γ a}

is the SOA_i saturation energy with

ω_{0, i}

,

w_{i}

and

d_{i}

being the frequency of the optical signal, the width and depth of the SOA_i active region, respectively. α is the linewidth enhancement factor. By integrating (2)–(4) over the entire SOA_i cavity length L_i and simplifying the calculations by considering λ_{1 =} λ_2, the temporal gain governing the dynamic characteristics of the TC-SOA-CC-IM can be obtained:

\frac{\partial h_{1} (T)}{\partial T} = \frac{g_{0, 1} L_{1} - h_{1} (T)}{τ_{c, 1}} - \frac{P_{i n 1} (T) + P_{o u t 2} (T)}{E_{s a t, 1}} (\exp [h_{1} (T)] - 1) .

\frac{\partial h_{2} (T)}{\partial T} = \frac{g_{0, 2} L_{2} - h_{2} (T)}{τ_{c, 2}} - \frac{P_{i n 2} (T) + P_{o u t 1} (T)}{E_{s a t, 2}} (\exp [h_{2} (T)] - 1) .

where

h_{i} (T) = \int_{0}^{L_{i}} g_{i} (z, T) d z .

The power and phase of the modulated optical signals at the output of each SOA are, therefore, given by:

P_{o u t, i} (T) = P_{i n, i} (T) \exp [h_{i} (T)] .

φ_{o u t, i} (T) = φ_{i n, i} (T) - \frac{1}{2} α h_{i} (T) .

where

P_{i n, i} (T)

and

φ_{i n, i} (T)

are the power and phase of the optical input wave injected in SOA as shown in Fig. 1. Equations (6)-(9) can be easily solved numerically when I_i, P_in,i and φ_in,_i are made known. Apart from intensity modulation, each SOA also imposes amplified spontaneous emission (ASE) noise onto the modulated optical signal. The total ASE power, P_ASE,i, can be calculated by [20]

P_{A S E, i} = [N_{f, i} \exp (h_{i} (T)) - 1] B_{0, i} ℏ w_{0, i} .

where N_f,i is the noise figure, B_0,i and

ℏ w_{0, i}

are the optical bandwidth and the photon energy of SOAᵢ respectively and

G_{i} = \exp [h_{i} (T)]

.Under the optimum operating conditions identified in the paper, within the adopted 6.25GHz signal bandwidth region, the total ASE power for each SOA is approximately >30dB lower than the optical powers of both the injected CW beams and the modulated AMOOFDM signals. The exclusion of the effect of ASE noises on SOA gain saturation does not affect the accuracy of the results presented in the paper. For simplicity, such an effect is not considered in the theoretical model.

Equations (6)-(10) are the final set of equations, which are used in numerical simulations. After adding the ASE noises into P_out,i(T) and φ_out,i(T), the intensity modulated optical signal P_out,2 can be obtained. For the transmission system considered here, the validity of the TC-SOA-CC-IM model is verified by static results agreement between theoretical results obtained here and various experimental measurements at device level [3–6].

2.3 Models for SMF transmission link & photon detector used in simulations

In this paper, we have used the theoretical SMF model [9,11–16,21], where we have considered the effects of CD, loss, and optical power dependence on the refractive index. 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 stimulated following procedures similar to those presented in [22].

2.4 Simulation parameters

The total number of subcarriers used for the simulated AMOOFDM signal is M = 64 of which 31 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 for each subcarrier varies from DBPSK, DQPSK, and 8-QAM to 256-QAM. The sampling rate of the DAC/ADC is 12.5GS/s, giving rise to a signal bandwidth of 6.25GHz in the positive frequency bins, and also a 195.3MHz bandwidth for each subcarrier. The cyclic prefix parameter [16] is set to be 25%, which gives a cyclic prefix length of 1.28ns within each OFDM symbol having total time duration of 6.4ns. The signal clipping ratio and quantization bits are taken 13dB and 7-bits, respectively, which are the optimum values identified in [23]. The parameters used in simulating the TC-SOA-CC-IM/ SOA-IM, SMF, and the photon detector are shown in Table 1. For fair performance comparisons in simulating the performance of the TC-SOA-CC-IM/SOA-IMs, each SOA in the proposed configuration and the single SOA, have the same set of parameters.

Table 1. SOA, SMF, and PIN Detector

View Table

It is worthy addressing the following two issues: a) the adoption of the 25% cyclic prefix is just for the purpose of comparing the obtained signal transmission performances with those reported in previously published works [1,11,12,15]. Depending upon the transmission distance, the cyclic prefix duration can be made adaptive [10]. In comparison with AMOOFDM having a fixed cyclic prefix of 25%, adaptive cyclic prefix cannot only improve the transmission capacity by approximately 30% for <80km SMF links with 1dB link loss margin enhancements, but also relax considerably the requirement on the intensity modulator bandwidths [10]. b) both experimental measurements [13] and numerical simulations [15] have shown that variations of signal wavelengths within the C-band do not considerably alter the signal transmission capacities presented in the following sections, even the extinction ratios of the modulated AMOOFDM signals decrease with increasing signal wavelength [15].

3. Simulated transmission performance

3.1 Static and dynamic characteristics of TC-SOA-CC

To understand and analyze all results that will be obtained later in dynamic simulations, it is important to study the optical gain characteristic effects of the TC-SOA-CC. Based on previous results [7], we have noticed that the evolutions of the effective carrier lifetimes τ_1,2 follow those of the gains G_1,2 of the SOA_1,2 respectively. Indeed, the carrier lifetime τ_i is inversely proportional to the total injected optical power P_tot,i in the SOA_i. Figure 3.a shows the evolution of gains G₁ of the SOA₁ and G₂ of the SOA₂ versus the input optical power P_in,1 at λ₁ = λ₂ = 1550nm and for two different values of P_in,2 of −15dBm and 10dBm.

We observe that in presence of a low power P_in,1, the signal P_in,2 profits from the high gain G₂ (unsaturated) allowing it to saturate the gain G₁ of the SOA₁. In this case, the power P_tot,1 is strong and therefore τ₁ is short. On the other hand the power P_tot,2 is weak and therefore τ₂ is long. By increasing P_in,1, the SOA₁ output optical power injected in the SOA₂ becomes important and saturates the gain G₂. This reduction in G₂ can induce an increase in G₁ by the counter-reaction process. In this situation, the power P_tot,1 is weak and therefore τ₁ is long. On the other hand, the power P_tot,2 is strong and therefore τ₂ is short. It is well known that the SOA₂ modulation bandwidth and its effective carrier lifetime τ₂ have an inverse relationship. Moreover, this behavior explains the positive gain variations of SOA₁ and the negative gain variation of SOA₁ obtained for a certain power range. This range shifts to high powers if P_in,2 increases. As in the TC-SOA-CC-IMs model, the SOA₂ works as an intensity modulator, we have shown the transfer function of the simulated gain G₂ versus P_in,1 for two configurations. The first one is done using the TC-SOA-CC configuration and the second is realized by using one of the two SOAs. Figure 3(b) shows the evolution of the relative gain versus the input optical power P_in,1 at λ₁ = λ₂ = 1550nm and for P_in,2 = −15dBm. The obtained results show that the SOA₂ gain nonlinearity is strongly accentuated in comparison with the transfer function using only one SOA. By varying P_in,1, the Gain G₂ steep slope is 20dB per 10dB (input range) for the TC-SOA-CC instead of 7.2dB for one SOA (Fig. 3(b)). These results in Fig. 3(a) and Fig. 3(b) are confirmed by agreement with the experimental measurements as presented in [3–7]. In addition, it can be easily found from Fig. 3(b) and the above explanations that, the TC-SOA-CC reaches its strongly saturated region using a lower input optical power much faster than the single SOA resulting in significantly reduced effective carrier lifetime τ₂ of SOA₂ and thus wide TC-SOA-CC bandwidths. Moreover, this leads to the improved transmission performance in comparison with single SOA at these lower optical input powers.

Fig. 3 (a) Gains G₁ and G₂ versus the input optical power P_in,1 with I_bias,1 = I_bias,2 = 280mA, (b) Relative gain G₂ versus the input optical power P_in,1 for TC-SOA-CC and for a single SOA with I_bias,1 = I_bias,2 = 280mA.

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Given the central role of the electrical current-induced SOA₂ optical gain variation in determining the quality of the modulated AMOOFDM signals, Fig. 4 is plotted to show the gain G₂ as a function of bias current I_bias,2 for different values of P_in,1 and P_in,2 using TC-SOA-CC. It can be seen from Fig. 4 that, to obtain a desired linear current-gain slope, the bias current I_bias,2 must be set at 50mA for a wide range of P_in,1 and P_in,2. From the discussions, it is easy to understand that a sharp gain-current slope gives a high extinction ratio of the modulated AMOOFDM signal. On the other hand, and in order to make a comparison between both configurations, Fig. 4(d) shows the gain G₂ versus the bias current I_bias,2 for TC-SOA-CC and gain G versus I_bias for the single SOA. It can be seen from this figure that compared with the SOA, the TC-SOA-CC has a lower gain-current slope which decreases the extinction ratio of the AMOOFDM signals but has the advantage of a more linear transfer function.

Fig. 4 Optical gain G₂ of SOA₂ versus I_bias,2 with I_bias,1 = 280mA. (a) P_in,2 = −10dBm, (b) P_in,2 = 10dBm, (c) P_in,2 = 20dBm, (d) P_in,1 = 10dBm.

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Figure 5(a) shows P_tot,2 for the TC-SOA-CC and P_out,SOA for the single SOA as function of input optical power P_in,1 for several values of P_in,2 using the same bias current I_bias = I_bias,2 = 50mA, and I_bias,1 = 280mA, the figure shows that we have an almost high input power to SOA₂ regardless of the input powers used for SOA₁ or SOA₂. Moreover, P_tot,2 is always higher than P_out using single SOA for all values of input optical power, this high power will cause the effective carrier lifetime of SOA₂ τ_{2(TC-SOA-CC-IM)} to be always smaller than the effective carrier lifetime of the single SOA τ_(SOA-IM) for all values of P_in,1 and P_in,2. Figure 5(b) shows the ratio of the effective carrier lifetime of SOA₂ using TC-SOA-CC-IM over the dynamic effective carrier lifetime of the SOA-IM with I_bias,1 = 280mA and I_bias = I_bias,2 = 50mA. Here, the effective carrier lifetime for the single SOA can be calculated as given in [11], for SOA₂ of the TC-SOA-CC-IM, it can be derived from Eq. (7)

\frac{1}{τ_{2}} = \frac{1}{τ_{c}} (1 + \frac{G_{2} (P_{i n, 2} + P_{o u t, 1})}{P_{s a t, 2}}) .

For the SOA-IM

Fig. 5 (a) P_tot,2 and P_out,_SOA as function of input optical power P_in,1 for several values of and P_in,2, (b) the ratio of τ_{e2(TC-SOA-CC-IM)}/τ_e(SOA-IM) as function of P_in,1 for several values of P_in,2.

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\frac{1}{τ} = \frac{1}{τ_{c}} (1 + \frac{G \times P_{i n}}{P_{s a t}}) .

As can be seen from Fig. 5(b), the ratio of τ₂/τ is shown for a wide range of input optical powers, we have a smaller effective carrier lifetime for the TC-SOA-CC in comparison with the single SOA, and this difference explains the higher signal capacities that we will see using the TC-SOA-CC-IM.

3.2 Impact of bias current and optical input power on the AMOOFDM transmission performance

The previously discussed results in the static study suggest that the improved transmission performance is possible using the TC-SOA-CC-IM in comparison with the single SOA over the IMDD-SMF system based on AMOOFDM. Therefore, the OFDM electrical driving current is injected in the SOA₂ in addition to the biasing current I_bias,2, and the output optical signal P_out,2 produced from SOA₂ is considered to be the output modulated AMOOFDM signal that enters the optical fiber. In numerical simulations, throughout this paper, the signal line rate is calculated using the same expression reported in [9,11–15]:

R_{s i g n a l} = \sum_{k = 2}^{M_{s}} S_{k} = \frac{\sum_{k = 2}^{M_{s}} n_{k}}{T_{b}} = \frac{f_{s} \sum_{k = 2}^{M_{s}} n_{k}}{2 M_{s} (1 + η)} .

where M_s = 32 is the number of all data-carrying subcarriers in the positive frequency bins, S_k denotes the signal bit rate corresponding to the k-th subcarrier, n_k is the total number of binary bits taken by the k-th subcarrier within one symbol period T_b, f_s is the sampling speed of the ADC/DAC, and

η

is the cyclic prefix parameter. The total channel bit error rate (BER), BER_T is expressed as:

B E R_{T} = \frac{\sum_{k = 2}^{M_{s}} E n_{k}}{\sum_{k = 2}^{M_{s}} B i t_{k}} .

where En_k is the total number of the detected errors and Bit_k is the total number of transmitted binary bits. Both En_k and Bit_k correspond to the k-th subcarrier, whose sub-channel BER, BER_k is given by BER_k = En_k/Bit_k. Based on BER_T and BER_k, the maximum modulation format assigned for each subcarrier within a symbol can be identified through negotiations between the transmitter and the receiver. Note that the signal transmission capacity calculated using Eq. (14) is considered to be valid only when the condition of BER_T<1.0 × 10⁻³ is satisfied.

Figure 6 shows contour plots to demonstrate the achievable AMOOFDM transmission capacity of a 60km IMDD SMF transmission system for both the TC-SOA-CC-IM and the single SOA-IM. The peak-to-peak (PTP) driving current is set to 80mA and λ₁ = λ₂ = 1550nm. Figure 6(a) shows the contour plot as function of P_in,1 and P_in,2 and Fig. 6(b) shows the contour plot as function of optical input power and bias current for the single SOA. As seen from the contour plots in Fig. 6, the TC-SOA-CC-IM in comparison with the SOA-IM has much broader variation ranges of optical input power, over which higher signal line rates are achievable. It can be seen, to achieve signal bit rates of almost 30Gb/s, the SOA-IM requires a CW optical input power to vary in a 3 dB range between 19dBm to 21dBm, whilst the TC-SOA-CC-IM allows a CW P_in,2 to vary in a 20dB range between 0dBm and 20dBm with P_in,1 having a value between 5dBm and 20dBm which is the input of the amplifier SOA₁.

Fig. 6 Contour plot of signal line rate. (a) TC-SOA-CC-IM with I_bias,1 = 280mA and I_bias,2 = 50mA. (c) Single SOA-IM.

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3.3 Signal line rate versus the input optical power P_in,1 and bias current I_bias,1

In addition, to the impact of the bias current I_bias,2 of the SOA₂, it is also important to study the influence of the input optical power and bias current of the amplifier SOA₁ on the AMOOFDM transmission performance of a 60km IMDD SMF transmission system for both the TC-SOA-CC-IM and the single SOA-IM. Figure 7 shows the signal line rate versus the input optical power P_in,1 for several values of the bias current I_bias,1 (50, 150, 200 and 280mA) and for P_in,2 = 0dBm (Fig. 7(a)), P_in,2 = 10dBm (Fig. 7(b)) and 20dBm (Fig. 7(c)). The driving current peak-to-peak (PTP) is set to be 80mA and λ₁ = λ₂ = 1550nm. In all what follows, the bias current I_bias,2 = 50mA for the TC-SOA-CC and I_bias = 50mA for the single SOA. Based on previous results [11], the maximum signal rate using single SOA is achieved at I_bias = 100mA, so it will always be shown to make a reasonable comparison. From Fig. 7(a)-(b), it can be seen that increasing I_bias,1 from 50mA till 280mA and P_in,1 from −10dBm till 20dBm improves the AMOOFDM transmission performance for both configurations. And we can also notice that for this wide range of I_bias,1, and P_in,1, the TC-SOA-CC-IM compared with the SOA-IM will end up producing a considerable improvement of the transmission performance. For instance, at low input optical power P_in,1 = P_in,2 = 0dBm, using the TC-SOA-CC-IM, we can benefit of almost 70% increase in signal line rate. Under the strongly saturated optical gain region, P_in,1 = 20dBm, the quality of the modulated AMOOFDM are similar.

Fig. 7 Signal line rate of TC-SOA-CC-IM and SOA-IM as a function of the input optical power P_in,1. (a) P_in,2 = 0dBm, (b) P_in,2 = 10dBm, (c) P_in,2 = 20dBm.

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In Fig. 7c, and for a wide range of P_in,1 varying between −10dBm and 20dBm, increasing I_bias,1 will result with a flat AMOOFDM transmission performance for the TC-SOA-CC-IM which is always greater than what’s reached with a single SOA. This is because the superiority of the signal line rate for the TC-SOA-CC-IM at P_in,2 = 20dBm (Fig. 7(c)) compared with that obtained at P_in,2 = 10dBm (Fig. 7(b)) is due to the decrease of the effective carrier lifetime when you increase the power P_in,2 and to the increase of the linear gain-current curve as shown in Fig. 4(d). For instance, at P_in,1 = −10dBm and P_in,2 = 20dBm, we can boost the signal line rate with almost 115% which will be more than twice the transmission performance offered by single SOA. This enhancement in system capacity is due to the lower effective carrier lifetime of SOA₂ in comparison with the one SOA configuration for a big range of P_in,1 as we have seen in Fig. 4.

3.4 Signal line rate versus transmission distance

Having identified the optimum TC-SOA-CC-IM operating conditions including bias current, driving current PTP and CW input optical powers, the maximum achievable signal line rate of the AMOOFDM transmission system incorporating TC-SOA-CC-IM is investigated in this section. The numerical results are plotted in Fig. 8 where I_bias,2 = 50 mA, I_bias,1 = 280 mA, I_bias = 50mA for the single SOA, the input optical power of the SOA₁ amplifier is P_in,1 = 10dBm and a driving current PTP of 80mA is used. For different input optical powers 0 and 10dBm (i.e P_in,2 for TC-SOA-CC), we have made a comparison between the performances of the TC-SOA-CC-IM with that of the single SOA-IM.

Fig. 8 Signal transmission capacity versus reach performance of AMOOFDM signal for various transmission systems.

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As shown in Fig. 8, the TC-SOA-CC-IM outperforms the SOA-IM in signal line rate for distances less than 120km. Very similar to those observed in the directly modulated lasers (DML)/SOA/RSOA/QDSOA-based SMF IMDD transmission system [11,12,14,16], for the TC-SOA-CC-IM, Fig. 8 shows a CD-dominant performance region and a link loss-dominant performance region for transmission distances of less than 100km and greater than 100km, respectively. Over the first performance region, as expected from discussions in [16], significant performance differences are revealed among the intensity modulators, whilst their performance differences are abated considerably over the second performance region. In particular such an enhancement is more pronounced over the CD dominant performance region. For instance, at P_in,2 = 0dBm and 60km SMF, the TC-SOA-CC-IM supports approximately the double of the transmission performance corresponding to the SOA-IM. Figure 8 shows that, up to 120km, the performances supported by the TC-SOA-CC-IM for CW input optical power 0dBm are much better than those supported by the SOA-IM for 10dBm. This indicates that the TC-SOA-CC-IM is capable of supporting signal line rates higher than those corresponding to the SOA-IM by using 10dB lower input optical powers. Figure 8 also shows that the TC-SOA-IM offers signal line rate almost identical for the two injected optical input powers P_in,2 = 0 and 10dBm. For longer transmission distances higher than 120km, the superiority of the SOA-IM over the TC-SOA-CC-IM is due to the fact that the TC-SOA-CC has gain-current curves with lower slopes (Fig. 4(d)) compared to single SOA, leading to lower signal ER as explained in 3.1, and thus higher signal degradation for the link loss dominant performance region.

To demonstrate the TC-SOA-CC-IM induced low ER for long transmission distance, Fig. 9 is plotted to compare the waveforms of the TC-SOA-CC-IM, SOA-IM and ideal-IM modulated AMOOFDM signals. The numerical results are plotted with I_bias,2 = 50mA, I_bias,1 = 280mA, P_in,1 = P_in,2 = 10dBm, a driving current PTP of 80mA and for the SOA-IM the bias current and the input optical power are to be set to I_bias = 50mA and P_in = 10dBm, respectively. Figure 9 shows that the TC-SOA-CC-IM modulated waveform is attenuated compared to those corresponding to SOA and ideal intensity modulators. The ER associated with the TC-SOA-CC-IM leads to severe degradation in the signal quality and in particular for long transmission distance.

Fig. 9 Normalized AMOOFDM signal waveforms generated by a TC-SOA-CC-IM, single SOA-IM and ideal-IM.

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3.5 Impact of negative frequency chirp

OOFDM has strong resilience to CD in both coherent and IMDD transmission systems. In addition to that, the CD compensation approach can further improve the AMOOFDM transmission performance in IMDD transmission systems as explained in [12] regarding the impact of the presence of the square law-photon detector. It is well known that an SOA-IM imposes negative frequency chirps on the modulated optical signals [11,14], and as in our configuration the SOA₂ plays the role of intensity modulator then this still holds well for the TC-SOA-CC-IM. In this paper, the electrically modulated optical signals affect the gain G₁ and G₂ as explicitly expressed in Eqs. (6-7), thus resulting in the occurrence of the negative frequency chirp effect, regardless of the employed optical input powers or electrical driving approaches. To demonstrate the effectiveness of the aforementioned CD compensation approach for the SOA/TC-SOA-CC intensity modulated AMOOFDM signals in IMDD standard SMF transmission systems, in Fig. 10 performance comparisons are made for the cases of including and excluding fiber CD. The numerical results are plotted in Fig. 10 where I_bias,2 = 50mA, I_bias,1 = 280mA, P_in,1 = P_in,2 = 10dBm and a driving current PTP of 80mA is used. For the single SOA-IM the bias current and the input optical power are to be set to I_bias = 50mA and P_in = 10dBm, respectively. As it can be seen from Fig. 10, for long transmission distances, an improved transmission performance for the case of including fiber chromatic dispersion for the two intensity modulators is seen, and the TC-SOA-CC-IM have much stronger dispersion compensation capability compared to SOA-IM.

Fig. 10 Signal line rate versus reach performance for the cases of including and excluding the CD.

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In addition the use of TC-SOA-CC-IM is more effective regarding the capability to benefit from dispersion compensation for short distances starting at 60km SMF, whilst for the SOA-IM starting at 90km. It should be pointed out that, the SOA/TC-SOA-CC negative frequency chirp is a function of operating conditions, suggesting that such dispersion compensation technique is dynamically controllable.

4. Conclusion and perspectives

In this work, we have theoretically and numerically investigate of the use of TC-SOA-CC-IM for the transmission performance IMDD SMF-based AMOOFDM signals. It has been shown that the TC-SOA-CC-IM in comparison with the SOA-IM has much broader variation range of optical input power, over which higher signal line rates are achievable. In addition, the TC-SOA-CC-IM is capable of supporting signal line rates higher than corresponding to the SOA-IM by using lower input optical powers, and it is also shown that at low input optical power, we can increase the signal line rate up to 115% which will be more than twice the transmission performance offered by single SOA. For transmission distances up to 120km, the performance supported by the TC-SOA-CC-IM for CW input optical power 0dBm is higher than that supported by the SOA-IM for 10dBm optical input power. For long transmission distances, the TC-SOA-CC-IM has much stronger CD compensation capability compared to the SOA-IM. In addition the TC-SOA-CC-IM is more robust to CD compensation for shorter distances starting at 60km SMF, whilst for the SOA-IM starting at 90km. These results demonstrate the potential of using the TC-SOA-CC-IM in future optical access networks utilizing AMOOFDM for high signal capacities and long transmission distances. For future work, it is interesting to study the potential of the TC-SOA-CC to achieve non inverted wavelength conversion of an AMOOFDM signal with high efficiency since the all-optical inverted and non-inverted wavelength conversions feasibility has been demonstrated using TC-SOA-CC delivering an ER≥7dB over a wide range of wavelengths [5].

Acknowledgments

This work is supported by Center of research in information technology and communication (CRITC) at Arts Sciences & Technology University in Lebanon (AUL) and the Ecole Nationale d’Ingénieurs de Brest (ENIB), LAB-STIC MOM.

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SOA
Parameter	Value
Cavity Length	300 μm
Width of Active Region	1.5 µm [15]
Depth of Active Region	0.27 µm
Carrier Lifetime SOA	0.3 ns [25]
Confinement Factor (SOA)	0.35
Differential Gain	3 × 10⁻²⁰m² [26]
Linewidth enhancement factor	5 [27]
Group Velocity	8.43 × 10⁷m/s [16]
Optical Frequency	1550 nm
Carrier density at transparency	1.05 × 10²⁴m⁻³ [26]
Noise Figure	8 dB
SMF
Parameter	Value
Effective area	80 µm² [14]
Dispersion	17.0ps/nm/km [14]
Dispersion Slope	0.07ps/nm/nm/km [14]
Dispersion Wavelength	1550nm [14]
Loss	0.2dB/km [14]
Kerr Coefficient	2.35 × 10⁻²⁰m²/W [14]
PIN-DETECTOR
Parameter	Value
Quantum Efficiency	0.8 [14]
Noise Current Density	8pA/√Hz [24]

Two cascaded SOAs used as intensity modulators for adaptively modulated optical OFDM signals in optical access networks

Abstract

1. Introduction