1. Introduction

All-optical signal processing is considered as one of the key aspect of future optical networks. All-optical conversion between different modulation formats is an important functionality for network transparency. There have been a number of reports on format conversions. However, most of them are between on-off keyed (OOK) signals. Although optical communication systems today primarily employ conventional OOK signals, recent studies have revealed that phase-shift keyed (PSK) signals exhibit particularly better performance than OOK signals for long-haul transmission. [1] However, OOK modulation formats are still attractive for metro and access networks. As a result, format conversion from OOK to PSK would be desirable at an intermediate node between a metro network and a long-haul backbone.

Semiconductor optical amplifiers (SOAs) in a Mach-Zehnder configuration [2] and a conventional SOA [3] have been used to achieve OOK to binary phase-shift keying (BPSK) conversion. Recently, gain transparent SOA (GT-SOA) has been recognized as a phasemodulation element other than conventional SOA [4]. Due to the advantage of avoiding unnecessary amplitude modulation in the transparent probe light, GT-SOA becomes a pure phase modulator that is controlled optically, which is a preferable feature in converting OOK to BPSK. While with the conventional SOA, wavelength conversion can’t be obtained and the extinction ratio (ER) of the input signal should be optimized to obtain phase difference of π and erase amplitude information at the same time. [3] The inherent 1.3µ m to 1.5µ m wavelength conversion with gain-transparent operation may be another advantage considering that the whole transmission window from 1.3–1.5µ m will be utilized in the future fiber communication networks. All-optical conversion between 1.3 µ m and 1.5 µ m spectral windows would be a critical technology to enhance flexibility at optical cross-connects and add/drop multiplexing nodes. The devices and technologies are more mature in the 1.3µ m window too. Although numerical investigation of GT-SOA in interferometric structures has been reported in literatures [5], the major concern is the switching window opened by a short switching pulse due to the phase difference introduced through the asymmetry of interferometer. Simulation and analysis of GT-SOA used as optical phase-modulator in PSK applications has not been seen in literatures, to the best of our knowledge. In this paper, numerical simulation of the phase modulation effect of GT-SOA is performed using a wideband dynamic model of GT-SOA and the quality of the converted BPSK signal is evaluated using the differential-phase-Q factor. Performance improvement with holding light injection is analyzed and non-return-to-zero (NRZ) and return-to-zero (RZ) modulation formats of the OOK signal is compared.

2. Modeling GT-SOA as optical phase-modulator

 

Fig. 1. schematic of OOK-to-BSPK format conversion involving gain-transparent SOA used as an optical phase-modulation.

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The configuration of OOK-to-BPSK converter based on GT-SOA is given in Fig. 1. The OOK signal @λ ₁ and CW (continuous wave) holding light @λ ₂ are combined with another CW probe light @λ ₃ and injected into a 1.3µ m SOA. The function of holding light injection will be discussed in section 4. In the gain-transparent operation of the SOA, 1 λ ₁ and λ ₂ are in the 1.3µ m wavelength region and λ ₃ is in the 1.5µ m wavelength region. As photon energy of the CW probe light is below the band-gap energy of the SOA, it will experience no gain based on the amplified stimulated emission and thus no noise from amplified spontaneous emission. Although this means that the CW probe light will not experience gain modulation introduced by the OOK signal, it still experiences a significant phase modulation due to the induced refractive index change, which is related to gain change by the famous Kramers-Kronig relation [6]. In this way, amplitude information @λ ₁ will be converted into phase information @λ ₃, which will be filtered out for differential demodulation and balanced detection.

In order to simulate the optical phase-modulation process physically, a dynamic model of GT-SOA is adopted, where broadband ASE, the longitudinal variation of carrier density and gain saturation induced phase-shift through Kramers-Kronig relation are all included. SOA is divided into small sections to account for the non-uniform carrier density distribution in the longitudinal direction and spectrum slicing is applied to account for the broadband ASE. The SOA is a 1.3µ m bulk material device with physical parameters given in table 1. The GTSOA is polarization independent and the reflectivity of end facets is both 0.

Table1. physical parameters of the SOA used in simulation

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2.1 Wave propagation equations for signal and ASE

In a moving coordinate, the time-domain wave propagation equations for the optical signal and ASE can be given by: ^[7]

Here we assume that the in-band OOK signal is traveling along forward direction. The subscript s, f and b denotes the in-band signal, the forward and backward traveling ASE respectively. ν_k is the frequency of the kth spectrum slice. ν ₁ and ν ₂ are the frequencies of OOK signal and holding light respectively. Γ is the confinement factor. α is the absorption loss.

The material gain per unit length at a given energy E=hν _k can be given as the difference between the stimulated emission and absorption rates (R_st and R_ab) between the conduction and valence bands: [9]

Where ε ₀ is the vacuum permittivity. m₀ is the free electron mass. c is the light speed in vacuum. n₂ is the refractive index of the active region. E_g is the band gap energy. M_b is the matrix element of bulk semiconductors. f_c(E_c) and f_v(E_v) are the Fermi-Dirac distribution for the conduction and valence bands respectively. While the spontaneous emission rate per unit volume per unit energy can be given by: [9]

Rsp in Eq. (4) should be multiplied by hΔν to translate the unit from J^-1m^-3s^-1 into m^-3s^-1, where Δν is the width of each spectrum slice. The total material gain and spontaneous emission should be summed up for heavy hole band and light hole band.

2.2 carrier density rate equation

The carrier density rate equation is given by: [7]

Where spontaneous emission exists in two orthogonal polarizations (TE and TM) and the inband signal is aligned to TE polarization. I is the injected current. e is the electron charge. V is the volume of the active region. τ is the carrier lifetime of the SOA. R_ASE(z,t) and R_sig(z,t) is the stimulated emission rate for ASE and in-band signal respectively.

2.3 Phase change equation

According to Eqs. (1), (2) and (5), the carrier density in the SOA will be modulated by the input power of the in-band OOK signal. Due to the dependence of refractive index on carrier density, the probe light in the transparency region of SOA will experience phase modulation. Although absorption coefficient at the transparent probe wavelength will also change due to free-carrier absorption, this change is very small and can be omitted just for simplicity, according to Ref. 5. The phase change in each SOA section for the transparent probe can be related to carrier density change by [5]:

Where N is the carrier density, N^st is stead-state value of the carrier density, α_N is the linewidth enhancement factor, Δz is the length of each SOA sub-section. Using the definition of linewidth enhancement factor ${\alpha }_N=\frac{4\pi }{\lambda }\frac{dn⁄dN}{dg⁄dN}$, the above equation can be transformed into:

The differential refractive index in each sub-section $\frac{dn}{dN}\approx \frac{\Delta n}{\Delta N}$ can be dynamically calculated from the differential gain $\frac{\mathit{dg}}{dN}\approx \frac{\Delta g}{\Delta N}$ using the Kramers-Kronig relation if the change of carrier density (ΔN) is very small. Thus, the dependence of $\frac{dg}{dN}$ and $\frac{dn}{dN}$ on carrier density can be included in our model, while $\frac{dg}{dN}$ and α_N are constant in Ref. 5. As the pulse width considered is quite long comparing to the characteristic time of the third-order nonlinear process in the SOA, temperature effect is neglect.

3. Differential-phase-Q of phase-modulated signal

OOK to BPSK format conversion process was simulated using the GT-SOA model given above. The GT-SOA used in our simulation is biased at 200mA to give a peak small signal chip gain of 34.0163dB at 1307nm. The optical signal at the input of the GT-SOA is an OOK signal with data rate of 10Gbit/s and centered at 1310nm. The peak power of the OOK signal is 15dBm and the extinction ratio is 9dB. The transparent probe light is at 1550nm. Figure 2 presents the waveform of input OOK signal, the phase of the converted BPSK signal and the waveform of the demodulated signal at destructive output port of delayed interferometer (DI). The data was assumed to be 1000,1100,1110,1111,0000 in a repetition mode. The RZ-like pulse observed in the demodulated signal originates from the temporal overlap of the rising/falling end of the original phase with the falling/rising end of the delayed phase (dash line in Fig. 2) of the converted signal. The encoding of the data signal is altered according to an XOR function between subsequent bits in the DI, but it can be addressed by a post processing in the receiver.

 

Fig. 2. Waveform of input OOK signal (a), the phase of the converted BPSK signal (b) and the waveform of demodulated signal at destructive output port of DI (c)

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Differential-phase-Q factor was introduced by Chris Xu et. al. to evaluate the quality of a phase-modulated signals for differential receivers[10]. They showed that this parameter is quite accurate although the definition is very simple. The differential-phase-Q was defined according to the differential phase, which is the phase difference between two sampling points separated by one bit period mapped to the range of-π/2 to 3π/2. It was defined as: [10]

Where σ_Δφ,0 and σ_Δφ,π are the standard deviation of differential-phase on 0 and π rails, respectively. In this paper, we will use the differential-phase-Q factor to estimate the quality of the phased-modulated signal obtained with GT-SOA.

Differential-phase-Q factor of the converted BPSK signal at probe wavelength can be calculated from the differential-phase eye diagram at an optimal sampling instance. The results for different extinction ratios (ER) of the in-band OOK signal are shown in Fig. 3(a). The peak power of the OOK signal (P₁) is changed from 7dBm to 21dBm in the simulation. As an example, differential-phase eye diagrams and electrical eye diagrams after balanced detection @ P₁=15dBm for each curve are shown in the insets of Fig. 3(a). The electrical eye diagrams are obtained without considering the optical and electrical filtering effect for simplicity. Balancing calculation efficiency with calculation accuracy, we chose to use a pseudo-random data length of 2⁷-1 in the simulation.

The differential-phase-Q of the converted BPSK signal depends on two aspects. Firstly, the average phase difference between “0” and “1” at the transparent probe wavelength (φ ₀₁), which is induced by carrier density dynamics in the GT-SOA, should be near to π. Otherwise, the standard deviation of the differential-phase will be large, thus a low differential-phase-Q will be obtained. Secondly, the pattern effect in the induced phase-shift should be small. As pattern effect means different phase-shift for different “1s” or “0s”, large pattern effect apparently brings large standard deviation of the differential-phase. The summation of standard deviation of the phase-shift with respect to 0 and π (σ ₀₁=σ ₀+σ ₁) can be used to quantify the magnitude of pattern effect. φ ₀₁ and σ ₀₁ obtained at the optimal sampling instance for each case are plotted in Fig. 3(b), where the dash line in the left figure represents φ ₀₁=π. Generally speaking, φ ₀₁ is larger for OOK signal with higher ER. While for each specific ER, φ ₀₁ first increase due to the increase of P₁, then decrease due to gain saturation introduced by the average power of the OOK signal. The overall pattern effect is larger for larger ER, while it can be reduced by increasing the input power of the OOK signal, due to the reduction of effective carrier lifetime at high signal input powers. Figure 3(b) can be used to explain the differential-phase-Q obtained in Fig. 3(a).

When ER=7dB, carrier density modulation introduced by the OOK signal is small, and the large DC component helps to enhance recovery speed of SOA. So the overall pattern effect is small. However, the differential-phase-Q of the converted BPSK signal is quite low, as φ ₀₁ is far less than π. The largest Q value appears when φ ₀₁ is nearest to π. The results for ER=8dB is quite similar, but the Q value is higher because the overall average phase difference is nearer to π.

For the four ER values considered in our simulation, the overall phase difference is nearest to π when ER=9dB, which gives the highest differential-phase-Q. Pattern effect will be relatively large in this case, especially at low input powers of the OOK signal. So it will also have an impact on the obtained differential-phase-Q. When P₁ is in the range of 9~11dBm, φ ₀₁ reaches π. However, the differential-phase-Q has not reaches its maximum value due to the large pattern effect. The increase of differential-phase-Q continues, as a result of the reduced pattern effect, until φ ₀₁ reaches π again. After that, φ ₀₁ will be less than π and the differentialphase-Q will reduce with the increased input power of the OOK signal.

When ER=10dB, φ ₀₁ is larger than π in the power range considered, which also gives relatively low differential-phase-Q. Its maximum will appear at much higher input power of the OOK signal, where the average phase difference reaches π and the pattern effect is much lower.

 

Fig. 3. Differential-phase-Q of converted BPSK signal (a), average phase difference between “0” and “1” and pattern effect (b) of converted BPSK signal at the transparent probe wavelength for different ERs of the input OOK signal.

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From Fig. 3, it can be concluded that the quality of the converted BPSK signal obtained with GT-SOA depends on the ER and input power of the in-band OOK signal. An optimal range of the ER and input power exist for obtaining a high differential-phase-Q, where the overall average phase difference between “0” and “1” is relatively nearer to π. Large input power of the OOK signal is preferred to reduce the pattern effect.

4. Holding light injection

In OOK applications, holding light injection is often used as an effective method to reduce the pattern effect when the carrier lifetime of SOA is much longer than the bit period of the input data. In this section the function of holding light injection in the phase modulator based on GT-SOA will be clarified. In fact, on one hand, holding light injection will clamps the carrier density level and the overall average phase difference will reduce. On the other hand, it can enhance the recovery speed of SOA and the reduce pattern effect. Both effects are favorable for obtaining a high differential-phase-Q for a OOK signal with relatively high ER. Figure 4 shows the differential-phase-Q of the converted BPSK signal when holding light at 1290nm is applied. ER is 10dB and 13dB respectively in Figs. 4(a) and 4(b).

When ER=10dB, without holding light, the differential-phase-Q is near 6 when P₁ ranges from 7 to 19dBm (see Fig. 3). When ER=13dB, it can be predicted from Fig. 3 that the differential-phase-Q obtained in the input power range considered will be very low without holding light due to the excess average phase difference and large pattern effect. However, with holding light of moderate input powers, the differential-phase-Q can be improved in both cases (see Fig. 4). Lower input power of the holding light is needed for a OOK signal with lower ER, due to the larger DC component in the OOK signal, which also clamps the carrier density level and functions as a holding light. In the simulation, for ER = 10dB, holding light with input power of -5, -12 and -9dBm is considered, while for ER=13dB, holding light with input power of 0, 3 and 6dBm is considered.

 

Fig. 4. Differential-phase-Q of converted BPSK signal at the transparent probe wavelength with holding light injection.

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We can also use average phase difference (φ ₀₁) and pattern effect (σ ₀₁) to explain the results obtained in Figs. 4(a) and 4(b). Figures 5(a) and 5(b) shows φ ₀₁ and σ ₀₁ as a function of P1 for input OOK signal with ER of 10dB and 13dB respectively.

Figure 5(a) shows that the holding light reduces pattern effect only when the input power of the OOK signal is relatively low, while at higher input powers, the effect of the DC component in the OOK signal dominates, and the reduction of pattern effect with increased input power of the OOK signal is almost the same for the three input powers of the holding light. The results are quite reasonable as the input power of the holding light is rather low in this case. On the other hand, φ ₀₁ is reduced by holding light injection. The higher the input power of the holding light, the smaller 01 φ ₀₁ obtained. So, it can be concluded that: 1) holding light injection can be used only when the ER of the input OOK signal is relatively high and the overall average phase difference is larger than π; 2) the input power of the holding light should not be too large, otherwise the overall average phase difference will be much lower than π. In Fig. 5(a), at low input powers of the OOK signal, φ ₀₁ is farer away from π when the input power of the holding light increases from -15 to -9dBm, while it is closer to π at high input powers, due to the cross of φ ₀₁ curve with φ ₀₁=π line. Accordingly, when P₁ is less than 11dBm, the higher the input power of the holding light, the lower the differential-phase-Q obtained, while for P1 greater than 13dBm, higher input power of the holding light result in higher differential-phase-Q. The major function of holding light is reducing overall average phase difference and make it close to π. The input power of the holding light is too small to have an obvious impact on the pattern effect. The high differential-phase-Q obtained at high input powers of the OOK signal can be attributed to both the low σ ₀₁ and φ ₀₁ that is near to π.

Similar reduction of overall average phase difference with higher input power of the holding light can also be seen in Fig. 5(b) with ER=13dB, but the slope of each curve and the change of φ ₀₁ due to the input power change of the holding light are much larger than in Fig. 5(a). As a result of the high ER of the OOK signal, σ ₀₁ increases with the increased input power of the OOK signal first, and then decreases when the DC component of the input OOK signal is large enough to clamp the carrier density level in the SOA, which is very different from the case of a relatively low ER. The overall pattern effect is much smaller with larger input power of the holding light. The differential-phase-Q obtained in Fig. 4(b) can also be well explained by Fig. 5(b), except that Fig. 5(b) predicts that the maximum differentialphase-Q in the case of P_h=0dBm and P_h=3dBm will be obtained when P₁ is about 11dBm and 13dBm respectively, while in Fig. 4(b), it is obtained actually at P₁=13dBm and P₁=15dBm respectively. We think that this small disagreement should be attributed to the statistic error in the differential phase, which comes from the non-Gaussian distribution of the samples. It can be both predicted from Fig. 5(b) and Fig. 4(b) that even higher differential-phase-Q can be obtained at much higher input power level of the OOK signal, which is beyond the power range considered in our simulation. In the case of ER=13dB, although the power of the holding light is large enough to reduce the pattern effect obviously and make a contribution to the improvement of differential-phase-Q, the major effect of this holding light is still the reduction of overall average phase difference. The reduced pattern effect can be seen as a byproduct, which is responsible for a much higher differential-phase-Q obtained with higher input power of the holding light.

As the major function of holding light is to reduce the overall phase difference, assist light at the short-wavelength band-edge can not be used in a PM based on GT-SOA, which is preferred in GT-SOA-based switches. In fact, the wavelength of the holding light near the material gain peak is preferred in our case, considering that the input power of the holding light needed would be lower. Besides, as we can’t count on the holding light to reduce the pattern effect, the carrier lifetime of the GT-SOA should not be too longer than the bit period of the data.

 

Fig. 5. Average phase difference between “0” and “1” and pattern effect of converted BPSK signal at the transparent probe wavelength with holding light injection. (a) ER=10dB, (b) ER=13dB

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5. Different modulation formats

In this section, the differential-phase-Q of the converted BPSK signal for input OOK signals in NRZ, 67%RZ (CS-RZ), 50%RZ, and 33%RZ modulation format will be compared. Firstly, The data was assumed to be 1000,1100,1110,1111,0000 in a repetition mode. The peak power of the OOK signal is 15dBm and the extinction ratio is 13dB. The CW holding light is at 1290nm and the input power is 3dBm. The waveform of the input OOK signal and the phase-shift at the transparent probe wavelength is plotted in Fig. 6. It should be noted that the converted signal for RZ input data is not a RZ-BPSK signal. As the intensity is constant and the phase is only somewhat RZ-like, it can still be seen as NRZ-BPSK. A clock signal should be used as probe if real RZ-BPSK signal is needed. It is very interesting that the pattern effect is much smaller when the input OOK signal is in RZ format, which can results in higher differential-phase-Q. The origin of the reduced pattern effect is two sided: first, the carrier density has more time to recovery when RZ data is used; second, the energy of RZ pulse (for the same peak power) is lower, which makes the carrier density recover more easily.

 

Fig. 6. Normalized input power and phase-shift at the transparent probe wavelength with holding light injection.

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The differential-phase-Q of the converted BPSK signal for different modulation formats of the input OOK signal is shown in Fig. 7(a), where the differential-phase and electrical eye diagrams of the best result obtained for each case are also given as insets. The differentialphase-Q of the converted BPSK signal for NRZ input data is low, ~8dB as shown in Fig. 7(a), and its electrical eye diagram is not clear. But it should be noted that the differential-phase-Q can be improved by optimizing ER or the combination of holding light and data signal input power, according to the results given in the previous sections. Figure 7(a) shows that the differential-phase-Q can also be improved by using optimized modulation format of the input data signal. It can be clearly seen that RZ OOK signal can give higher differential-phase-Q and more clear eye diagrams than NRZ OOK signal, especially when the duty cycle of the RZ OOK signal is shorter.

 

Fig. 7. Differential-phase-Q (a), average phase difference and pattern effect (b) of converted BPSK signal at the transparent probe wavelength for different modulation format of the OOK signal.

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For RZ OOK signal with duty cycle of 67% and 50%, the improvement in differentialphase-Q results from the reduced pattern effect and the improvement is in the low power region (P₁<15dBm). In fact, as shown in Fig. 7(b), φ ₀₁ for RZ OOK signal with duty cycle of 67% and 50% is larger than the case of NRZ OOK signal at high input powers, which can result in a lower differential-phase-Q. The reason can be attributed to the lower average power of RZ OOK signal and thus lower saturation level of SOA. While For RZ OOK signal with duty cycle of 33%, the improvement also results from the reduction in φ ₀₁, which can be clearly seen in Fig. 7(b). As a result, the improvement is in the high power region. The origin of the reduction of φ ₀₁ for 33% RZ pulse is the inadequate pulse energy that cannot produce the same carrier density change as other modulation formats. The larger input power of the OOK signal needed for maximum differential-phase-Q (in the power range considered) can also be attributed to the same origin. The lower pattern effect level with RZ modulation format showed in Fig. 7(b) agrees with the waveforms given in Fig. 6.

It is worth noting that, although only the case with 13dB ER of the input OOK signal and 3dBm input power of the holding light is considered, the improvement in differential-phase-Q with RZ-formatted OOK signal would be a general result.

6 Conclusions

We have investigated the performance of GT-SOA used as phase-modulator in OOK-to-BPSK modulation format conversion. The results show that an optimal range of the ER and input power of the OOK signal exist for obtaining a high differential-phase-Q of converted BPSK signal, where the overall average phase difference between “0” and “1” is nearest to π. The input power of the OOK signal should also be relatively large to reduce the pattern effect. For OOK signals with relatively high ER, holding light injection can be used to improve the performance. It is found that the major function of the CW holding light is to reduce the overall average phase difference between “0” and “1” and makes it near to π, although the holding light also reduce the pattern effect at the same time and bring additional benefit to the quality of converted BPSK signal. It is also found that RZ modulated OOK signal can give better results than NRZ modulated signal, due to the smaller pattern effect and average phase difference that might be nearer to π.