1. Introduction

A stable pulse train with high repetition rate is very essential for a high-speed OTDM system. An actively mode-locked fiber laser is ideal for generating a short pulse train with various bit rates. Recently, rational harmonic mode-locking techniques that generate pulse trains with high repetition rates have been reported [1, 2, 3]. When the repetition rate of the generated optical pulse train becomes an integer multiple of the RF drive frequency, the amplitudes among the pulses become varied and characterized by large fluctuations. To overcome this unevenness, several methods have been reported, including the use of another fiber laser with a nonlinear optical loop mirror (NOLM) [4] and an SOA loop mirror [5], nonlinear polarization rotation (NPR) [6], and optical feedback [7]. G. Zhu, et al. were able to show theoretically an equalized amplitude pulse train up to the fourth order rational harmonic mode-locking [8]. In a semiconductor-based ring laser, however, DC biasing the single electrode intensity modulator of an actively mode-locked fiber ring laser is commonly known to generate optical pulses at repetition rates that are twice as much as those of the RF drive frequency [9].

In this letter, We propose a simple method of equalizing pulse-amplitudes of rational harmonic mode-locked pulses in a semiconductor-based ring laser. Equalization can be easily achieved by using a dual-drive LiNbO3 Mach-Zehnder (MZ) modulator placed inside the ring laser itself and individually adjusting two voltages to the modulator. With this simple structure, amplitude-equalized pulse trains with more than two times the RF modulation frequency can be realized and will be demonstrated experimentally without introducing additional components or changes in structure.

2. Principle of pulse-amplitude equalization

The multiplication of repetition rate by rational harmonic mode-locking has been described in the literatures [1, 2, 3]. If the RF drive frequency (f_mod) is equal to a harmonic of the fundamental cavity frequency (f_cav), that is, f_mod=nf_cav (n is a positive integer), the nth-order harmonic mode-locking occurs, and the pulse repetition rate (f_rep) is the same as the RF drive frequency. That is f_rep=f_mod=nf_cav. To achieve rational harmonic mode-locking, the modulation frequency is slightly detuned from the harmonic mode-locking condition by f_cav/p. Thus f_mod=nf_cav ± f_cav/p, where p is a positive integer. The pulse train of the repetition rate at p times the RF drive frequency can then be obtained (f_rep=pf_mod). Figures 1(a) and 1(d) show the third (p=3) rational harmonic mode-locked pulse train as an example. The pulse repetition rate becomes three times the RF drive frequency (f_rep=3 f_mod, i.e., T_rep=T_mod/3) [7]. T_mod is the time interval of the modulation frequency for harmonic mode-locking. The pulses in solid line in Fig. 1(a) indicate the harmonic mode-locked pulses.

The amplitudes of the generated harmonic mode-locked pulses are determined by the transmission coefficients through the MZ modulator. Generally, the transmission curve of the modulator from input port to output port is defined as T_MZM(t)=I_out (t)/I_in(t), where I_in=|E_in(t)|², I_out=|E_out (t)|², and I_in(t) denotes the shape of the input optical pulse train at time t to the modulator. E_in and E_out are the input and output optical fields, respectively. The output field of the dual drive MZ modulator is given by

where γ is a scaling factor, between 0 to 1, that accounts for an asymmetric device, V_π the switching voltage, and v ₁(t) and v ₂(t) the voltages applied to the arms of the MZ modulator [10]. The scaling factor γ is less than one if the splitting/combining ratio of the MZ modulator is not exactly 50/50. This parameter, γ, is related to the optical extinction ratio δ, as γ=(√δ-1)/(√δ+1) [10]. The applied voltages to the two arms can be expressed as

where V_ac is a modulation amplitude, V _bias1 and V _bias2 the bias voltages applied to arm1 and arm2, ϕ ₁ and ϕ ₂ the phase of applied voltage to arm1 and arm2, respectively. Figure 2 shows the calculated values of the modulation amplitude, V_ac, in order to achieve the pulse-amplitude equalization for the third (p=3) and the fifth (p=5) rational harmonic mode-locking. When the phase difference between the applied voltages is π, |ϕ ₁-ϕ ₂|=π, small amount of modulation amplitude is sufficient to acquire pulse-amplitude equalization for the third (p=3) and the fifth (p=5) rational harmonic mode-locking cases. Pulse-amplitude equalization can be easily achieved in that condition.

 

Fig. 1. Timing diagrams for pulse-amplitude equalization. (a), (d) The input pulse train of the MZ modulator, (b), (e) transmission curve of the MZ modulator, and (c), (f) the output pulse train of the MZ modulator. [(a), (b), and (c)] are due to the small signal modulation (V_ac <V_π) and [(d), (e), and (f)] large signal modulation (V_ac >V_π).

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Therefore, we choose the phase difference of π for pulse-amplitude equalization with small modulation amplitude. In our case, ϕ ₁=0 and ϕ ₂=π. Then, the voltages are described as

where v_ac(t)=|V_ac|sin(2πf _mod t), $\overline{v_{\mathit{ac}}}\left(t\right)=\mid V_{\mathit{ac}}\mid \sin \left(2\pi f_{\mathit{mod}}t+\pi \right)$. The output optical pulse train derived from Eq. (1) is expressed as

Therefore, T_MZM(t) is given as

Figures 1(b) and 1(e) represent the transmission curves of the MZ modulator given by Eq. (5). As shown in Fig. 1(b), the third rational harmonic mode-locking pulses experience different transmission coefficients in the MZ modulator. This causes the pulse-amplitude variation. This pulse-amplitude fluctuation has been known to result from the interaction between circulating pulses and cavity loss modulation [3]. Equalization of pulse-amplitudes occurs only when the pulse gets the same transmission coefficient in the modulator [8]. The transmission curve of the modulator depends on the voltages applied to each arm of the MZ modulator. By adjusting the voltages applied to the modulator, i.e., bias voltages,V _bias1,V _bias2 and the modulation amplitude, V_ac, the shape of transmission curve can be changed from Fig. 1(b) to Fig. 1(e). Conventional rational harmonic mode-locked pulse is usually obtained by operating the modulator with the peak-to-peak amplitude of the applied voltage (V_ac) smaller than that of the switching voltage, V_π as shown in Fig. 1(c). On the contrary, by providing voltages larger than the switching voltage of the modulator, more minimum and maximum values of transmission curve can be generated in such a way that the rational harmonic mode-locked pulses experience almost the same transmission coefficient. This is to the case of similar in the single-drive modulator [8], but the freedom of adjusting is largely limited because only one voltage can be used to obtain the phase variation. Figure 1(e) is the result of large modulation (V_ac >V_π) with a dual control. In this case, transmission coefficients are almost equal to the mode-locked pulses arriving to the modulator and, as a result, pulse-amplitude equalization of the third (p=3) rational harmonic mode-locked pulse train is obtained (see Fig. 1(f)). The dash-and-dotted horizontal line is drawn for showing the same transmission coefficient met by the input optical pulses.

 

Fig. 2. Minimum modulation amplitude as a function of phase difference between the two applied signals for a pulse-amplitude equalization with mode-locking cases of p=3 and p=5.

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Fig. 3. Simulated pulse trains (solid line) and transmission curves (dotted line) for the third (p=3) rational harmonic mode-locking (a) without pulse-amplitude equalization (V _bias1=1.51V_π, V _bias2=1.51V_π and V_ac=0.86V_π) and (b) with pulse-amplitude equalization (V _bias1=1.30V_π, V _bias2=1.40V_π and V_ac=1.01V_π).

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Fig. 4. Simulated pulse trains (solid line) and transmission curves (dotted line) for the fifth (p=5) rational harmonic mode-locking (a) without pulse-amplitude equalization (V _bias1=1.50V_π, V _bias2=1.50V_π and V_ac=0.83V_π) and (b) with pulse-amplitude equalization (V _bias1=1.30V_π, V _bias2=1.72V_π and V_ac=1.12V_π).

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To validate the principle of the proposed pulse-amplitude equalization, amplitude equalization of rational harmonic mode-locked pulse was simulated (Fig. 3 and Fig. 4) using Eq. (4) and (5). It was helpful in determining the optimum bias level and modulation depth for getting the equalized pulse train. In the next section, the theoretical analysis is experimentally verified up to the fifth (p=5) rational harmonic mode-locking.

 

Fig. 5. Experimental setup. PC: polarization controller; PPG: pulse pattern generator; SOA: semiconductor optical amplifier; OTDL: optical tunable delay line; ATT: RF attenuator.

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3. Experiments and results

3.1. Experimental setup

To demonstrate pulse-amplitude equalization in a rational harmonic mode-locked semiconductor fiber ring laser, the experimental setup depicted in Fig. 5 was built. The rational harmonic mode-locked semiconductor fiber ring laser was composed of a semiconductor optical amplifier (SOA), an optical tunable delay line (OTDL), a polarization controller (PC), an isolator, and a dual-electrode LiNbO₃ MZ type modulator. The modulator, which has 10Gb/s bandwidth, switching voltage of ~5V, and insertion loss of 6dB, is connected to a high-speed differential driver. An RF clock from the pulse pattern generator (PPG) was applied to the differential driver (Anritsu A3HD2106), which gives the differential outputs with π phase difference to each other but the same amplitude. Then, V _bias1 and V _bias2 are controlled individually. The SOA (Alcatel 1901) is a polarization-insensitive type (0.6dB typically) with low tensile bulk separate confinement heterostructure, and its gain and cavity length are 25dB and 1000µm, respectively. It has a carrier lifetime of ~320ps. It was driven at the operating bias current of 95.7mA. The cavity length was estimated to be 22.31m, corresponding to a fundamental frequency of ~8.96MHz. The output pulse train from the rational harmonic mode-locked fiber laser was measured using a 3dB coupler. It was electrically converted by a high-speed photodiode with a 26GHz bandwidth and a 12ps full-width half maximum (FWHM) impulse response. The converted electrical signal was measured directly using an RF spectrum analyzer without a low-noise RF preamplifier.

3.2. Third rational harmonic mode-locking (p=3)

Conventional active mode-locking was obtained at 1560nm at a modulation frequency of 2.48832GHz (~277th harmonics), driven by the pulse pattern generator. By slightly detuning the RF drive frequency from the mode-locking frequency by f_cav/p with an integer p, the pth rational harmonic mode-locked optical pulse train was obtained from the rational harmonic mode-locked semiconductor fiber laser [7]. Based on this relationship, the third rational harmonic mode-locking (p=3) was observed at the modulation frequency of 2.490840GHz detuned from 2.48832GHz by f_cav/3. This produces a pulse train with a repetition rate that is three times the RF drive frequency (~7.42GHz) as shown in Fig. 6(a). Two arms of the dual-electrode modulator were equally biased at 7.558V (V _bias1,V _bias2≅1.51V_π) from the condition acquired analytically in Section 2. Modulation amplitude of 4.335V (V_ac=0.86V) was also determined from the analytical condition, V_ac=0.86V. The RF spectrum for Fig. 6(a) is shown in Fig. 7(a). The frequency scale is 1GHz/div, and the amplitude scale is 2dB/div. The main peak indicates the frequency component at the pulse repetition rate, i.e., ~7.42GHz. There are also other frequency components in the RF spectrum. When the rational harmonic mode-locked pulse has a triple repetition rate, the peak amplitude repeats every three pulses. By controlling the applied voltages to each arm of the dual-electrode modulator, pulse-amplitude equalization was obtained. From the amplitude equalization conditions described in Section 2, the applied bias voltages and the modulation peak were extracted as V _bias1=1.30V_π, V _bias2=1.40V_π and V_ac=1.01V_π. The bias voltages and the modulation amplitude were then tuned around those values. One of the arms was biased with a voltage of 6.240V (V _bias1≅1.25V_π) and the other at 7.128V (V _bias2≅1.43V_π). In addition, the amplitude of the drive signals applied to two arms was increased from 4.335V (V_ac≅0.86V_π) to 5.097V (V_ac≅1.02V_π). A slight deviation of the experimental voltage values from the simulation results are mainly resulted from the minor tuning by fiber polarization control in order to obtain the best equalized pulse amplitude. Figure 6(b) shows that the pulse-amplitudes can be equalized using the unbalanced dual-drive Mach-Zehnder modulator. Figure 7(b) is the RF spectrum for Fig. 6(b), showing that all other frequency components except the 7.42GHz component were effectively suppressed. This verifies that the amplitude-equalized pulse train has a pure 7.42GHz frequency component that corresponds to the pulse repetition frequency. The suppression ratio of the signal power at 7.42GHz to the noise power level (other frequency components) appeared to be about 16dB without using any low-noise amplifiers after the high-speed photo detector. As shown in Fig. 6 and Fig. 7, the proposed method equalizes the uneven pulse-amplitude effectively while keeping the pulse repetition rate at three times the RF drive frequency.

 

Fig. 6. Measured optical pulse trains from the third (p=3) rational harmonic mode-locked semiconductor fiber ring laser (a) without and (b) with pulse-amplitude equalization.

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Fig. 7. RF spectra of the optical pulse trains from the third (p=3) rational harmonic modelocked semiconductor fiber ring laser. (a) Without and (b) with pulse-amplitude equalization.

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Fig. 8. Measured optical pulse trains from the fifth (p=5) rational harmonic mode-locked semiconductor fiber ring laser (a) without and (b) with pulse-amplitude equalization.

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3.3. Fifth rational harmonic mode-locking (p=5)

The fifth rational harmonic mode-locking (p=5) was derived from the modulation frequency at 2.491609GHz by detuning from 2.48832GHz by f_cav/5. Figure 8 shows the amplitude-equalized and -unequalized pulse trains in the fifth rational harmonic mode-locked semiconductor fiber laser. Figure 8(a) was obtained when the dual arms of the modulator were biased at the same voltage of 7.509V (V _bias1,V _bias2≅1.50V_π) and equipped with the same amplitude signals of 4.14V (V_ac≅0.83V_π). The bias voltages of the two arms of the modulator were changed separately. One of the arms was biased at 6.855V (V _bias1≅1.37V_π) and the other at 7.998V (V _bias2≅1.60V_π). With an increase in the amplitudes of the drive signals applied to each arm from 4.14V (V_ac≅0.83V_π) to 5.263V (V_ac≅1.05V_π), the pulse-amplitudes were equalized. Figure 9 represents the RF spectrum of Fig. 8. The frequency scale is 1.5GHz/div, and the amplitude scale is 2dB/div. The main peak indicates the pulse repetition rate at about 12.34GHz. Three frequency components exist in Fig. 9(a). As shown in Fig. 9(b), the proposed pulse-amplitude equalization method suppressed the unwanted frequency components in the frequency domain. The suppression ratio of the 12.34GHz component power level to the noise power level is about 12dB. This result verifies that the proposed method effectively equalizes the uneven amplitudes of the fifth rational harmonic mode-locked pulse.

 

Fig. 9. RF spectra of the optical pulse trains from the fifth (p=5) rational harmonic mode-locked semiconductor fiber ring laser. (a) Without and (b) with pulse-amplitude equalization.

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4. Conclusion

We have proposed and successfully demonstrated a novel pulse-amplitude equalization method using an unbalanced dual-drive LiNbO₃ Mach-Zehnder modulator. The dual-drive modulator was used as a mode-locker and a pulse-amplitude equalizer in a rational harmonic mode-locked semiconductor fiber ring laser. The experimental results were consistent with the theoretical analysis. This is believed to be the simplest one in the pulse-amplitude equalization methods of higher order (>2) rational harmonic mode-locking. Only, the equalized rational harmonic order can be limited by the available amplitudes of the applying voltages. This can be utilized as a short optical pulse source with high repetition rate as required in high-speed OTDM systems.