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Optical injection induced gain modulation of a semiconductor optical amplifier (SOA) is demonstrated to equalize the peak intensity of pulses generating from the rational-harmonic-mode-locking (RHML) SOA based fiberized semiconductor laser. This is achieved by adjusting the temporal shape of the injected optical signal generated from a Mach-Zehnder intensity modulator, in which the DC biased level exceeding Vπ and the electrical pulse amplitude of 1.5Vπ are concurrently employed. Numerical simulation on the injected optical signal profile and the SOA gain during the inverse-optical-pulse injection induced gain modulation process are also demonstrated. After a peculiar inverse-optical-pulse injection, each pulse in the 5th-order RHML pulse-train experiences different gain from temporally varied SOA gain profile, leading the pulse peak to equalize one another with a minimum standard deviation of 2.5% on the peak intensity variation. The optimized 5th-order RHML pulse exhibits a signal-to-noise suppression ratio of 20 dB and a reduced variation on temporal spacing from 11 to 4 ps. The clock amplitude jitter is compress from 35.3% to 7.3%, which is less than the limitation up to 10% for 5th order RHML generation.
©2009 Optical Society of America
1. Introduction
Fiber lasers generating ultra-short pulse at high-repetition-rate with sub-harmonic frequency source have emerged as a key component for the high-bit-rate optical time-division-multiplexing (OTDM) communication system. Active mode-locking of the fiber laser has become the leading technology lately due to its flexibility in repetition-rate control and wavelength detuning. However, the active harmonic mode-locking (HML) frequency is usually limited by the bandwidth of modulator, electronic components, and signal generator. To overcome these drawbacks, the rational-harmonic-mode-locking (RHML) technology has been investigated by applying low frequency synthesizer, then slightly detuning its frequency away from the harmonic longitudinal mode of the HML fiber laser to approach repetition-rate multiplication. Previously, Yoshida et al. and Lin et al. have individually proposed the generation of RHML pulse up to 200 GHz and 40th order [1, 2]. Zhu et al. further demonstrated the high-quality pulse-train up to 80 Gbit/s, which is doubling by injecting a 40-GHz RHML pulse-train into an external fiber loop mirror [3]. Later on, Zhao simulated that the RHML pulsewidth could be shortened with increasing RHML order [4]. Moreover, the wavelength tunable RHML fiber laser was also investigated by controlling the length of dispersion compensation fiber in the ring cavity and concurrently using Fabry-Perot semiconductor modulator as both the mode-locker and the tunable filter [5, 6]. However, the high-order RHML inevitably leads to an output pulse-train of inequivalent peak amplitudes, since the frequency-multiplied RHML pulses experiences different gain in fiber laser cavity when modulating by a slightly deviated HML frequency. The inequivalent pulse amplitude results in a serious problem and restricts the RHML fiber laser for versatile applications. Thus, several configurations were proposed to equalize the pulse amplitude, including the use of a semiconductor optical amplifier in a loop mirror [7], a nonlinear optical loop mirror [8], and a nonlinear polarization rotation [9]. In particular, some special frameworks proposed using both mode-locker and pulse-amplitude equalizer to generate high-order RHML without external configuration. For example, the RHML pulse amplitude equalization can be achieved by passing through a intensity modulator forward and backward consecutively [10], by using a dual-drive Mach-Zehnder modulator (MZM) [11], by injecting the pulse-train into a SOA ring cavity [12], or by using a nonlinear (negative) impulse modulation [13, 14]. Besides, Vlachos et al. demonstrated using an external optical pulse-train to inject a SOA fiber ring cavity for approaching 5-GHz HML and 40-GHz RHML pulses, while the concept to equalize pulse-intensity of RHML by optically cross-gain modulation was sketchily presented [15]. Creating a suitable gain shape of SOA should be the key point for equaling amplitude of RHML pulses, however, the principle of the peculiar gain modulation in time domain was not clearly mentioned. Later on, the similar technology was employed to further promote the repetition-rate of the all-polarization-maintaining SOA fiber laser to 50 GHz [16]. Recently, we have introduced a inverse-optical-pulse injected semiconductor optical amplifier (SOA) to overcome the traditional limitation on the modulation bandwidth of the SOA contact electrode, which gives rise to a 20th order RHML pulse-train generation based on the cross-gain modulation (XGM). The operation of the proposed technique relies strictly on the optically cross-gain modulation by injecting a CW light with periodic zero power dips into the SOA. In addition, the pulse quality of RHML was also investigated to show a limitation on RHML up to 7th order by weak gain depletion of SOA [17]. In this work, we demonstrate a peculiar gain modulation of SOA to equalize the mode-locking pulse amplitude of such a fiberized semiconductor laser (FSL) in RHML regime. This is approached by adjusting the profile of electrical comb and the biased point of MZM to form a peculiar inverse-optical-pulse for gain-modulating the SOA, such that each RHML pulse experiences different gain to equalize the intensity of pulse. The peculiar gain modulation process is also simulated to explain the relationship between the shapes of optical pulse and the SOA gain. To optimize pulse-amplitude equalization, the suppression ratio of the peak intensity to the noise level, and the precise confinement on the temporal spacing of the RHML pulse-train with corresponding clock amplitude jitter are discussed.
2. Experimental setup
The SOA based FSL setup as shown in Fig. 1, which employs the anti-reflection coated SOA (QPhotonics, QSOA-1550) to provide a gain spectrum centered at 1535 nm with a spectral linewidth of 30-50 nm. The SOA is biased at 300 mA with its gain strongly modulated via an external inverse-optical-pulse injection. The inverse-optical-pulse is implemented by nonlinearly driving an external MZM with an electrical comb generator at 1 GHz. The output of the electrical comb seeded with a RF-synthesized sinusoidal wave after 40dB-gain amplification is slightly power-attenuated to obtain a linear transfer from MZM with Vπ of 4.5 V, while the MZM and the tunable laser were set at VDC = 3.2 V and 1555.8 nm, respectively. The MZM generated inverse-optical-pulse is connected with a set of optical intensity controller, consisting of an Erbium-doped fiber amplifier (EDFA) and an optical attenuator (OTTN). The optimized injection power of the inverse-optical-pulse for the RHML FSL is about 5 dBm. A polarization controller (PC) is required at the input port of SOA to release its polarization dependent gain difference of 3 dB.
Fig. 1 System setup. EAMP; electrical power amplifier; COMB: comb generator; EATTN: electrical attenuator; MZM: Mach-Zehnder modulator; EDFA: Erbium-doped fiber amplifier; OC: optical coupler; ISO: optical isolator; WDM: wavelength-division multiplexer; SOA: semiconductor optical amplifier; PC: polarization controller.
By detuning the polarization state and the repetition frequency of the inverse-optical-pulse for optimizing the gain-modulation depth and mode-locking power, the different RHML condition up to 20th order can be achieved. The Faraday isolator (ISO) is used to ensure the unidirectional propagation and prevent the intra-cavity power dissipation by the inverse-optical-comb circulated in the FSL cavity. An additional fiber-grating based wavelength-division multiplexing (WDM) filter is also used to avoid the regenerative amplification of inverse-optical-comb in the FSL. Moreover, there is a trade-off between the average power and pulsewidth of the RHML pulse as shown in Fig. 2.
Our experimental results reveals that the output RHML pulsewidth is inversely proportional to the intra-cavity feedback power. Figure 2 illustrates the variation of the pulsewidth and the intra-cavity peak power at different intra-cavity coupling ratio, while the mode-locking FSL pulsewidth is slightly shortened from 27 to 18 ps as the intra-cavity coupling ratio increases from 10% to 90%. This result can directly be attributed to the relationship between SOA gain and RHML pulsewidth, as described by [18]
where τp is the FWHM of the pulse, g 0 is the single-pass integrated gain, fm is the modulation frequency, and Δv is the homogeneous linewidth. As the intra-cavity coupling ratio increases, the SOA gain pumped by constant current is depleted by the inverse-optical-pulse schematically illustrated in Fig. 3(a), which exhibits almost constant power except an narrow window where the power instantaneously drops to zero. Such an injection completely depletes the net gain of SOA with an extremely large duty cycle in one modulation period, however, a transient gain left in the SOA due to the inverse-optical-pulse is sufficient to cause mode-locking of the SOA based fiber laser. According to the above equation, the pulsewidth becomes narrower with decreasing SOA gain, which has been confirmed by both the theoretical model and the experimental results. In our case, an output coupler (OC) with power-splitting ratio of 50% is selected to obtain pedestal-free RHML pulse from the FSL with relatively short pulsewidth and sufficient output power.
The gain modulation in time domain is a key factor to approach the pulse-amplitude equalization, which is based on injecting the SOA with the peculiar inverse-optical-pulse generating from the different profile of electrical comb and the biased point of MZM. In general case, to arrive the perfect mode-locking condition, the electrical comb is driven by the optimum modulation power (about -8 dBm) and biased at the rising edge of MZM to form the inverse-optical-pulse, which provides the maximum depletion window and modulation depth. We overthrow the traditional conditions to meet the demand of pulse-amplitude equalization by using a non-symmetrical electrical comb to drive the MZM and the DC biased voltage at the falling edge of its transfer function (see Fig. 3(b)). Such an offset electrical pulse voltage crosses over the linear and nonlinear regions of MZM transfer function, providing a peculiar inverse-optical-pulse, which owns relatively narrow gain-depletion-window identical to the inverse-optical-pulse with a non-constant upper power level, as shown in Fig. 3(a). The deformation of electrical comb required to equalize the RHML pulse amplitude also depends on the power of sinusoidal wave used to trigger the electrical comb, as shown in Fig. 3(c). The optimal output of the electrical comb triggered at sinusoidal-wave power of -15 dBm looks like an inverse Gaussian shape. By choosing a triggered condition beyond the best one to form a non-symmetrical electrical comb profile shown in Fig. 3(c), such that a peculiar inverse-optical-pulse shown in Fig. 3(d) is generated to differentiate the gain for the each circulated RHML pulse within the FSL.
3. Results and discussions
3.1 Simulation on optical-injection induced gain-profile reshaping in SOA
In order to achieve RHML operation, the modulation frequency of the RF synthesizer is detuned to satisfy the equation of fm=(n±1/p)f0, where fm, f0, n, p denote the modulation frequency of RF synthesizer, the longitudinal mode spacing in cavity of laser, the harmonic and rational harmonic mode-locking orders, respectively. In more detail, the modulation frequency is slightly deviated from the harmonics of the cavity round-trip frequency, n*f0, by an amount of f0/p (p is an integer number). High-order RHML can only be achieved with severely control on the detuned frequency amount, providing a stable pulse-train repeated at multiplied frequency of p*fm. In comparison with the general SOA mode-locking fiber laser at HML condition, the gain profile optimized for HML is unsuitable for RHML to equal the pulse-amplitude. Hence, the detuning on SOA gain shape in time domain is necessary for equalizing the pulse-amplitude by matching the gain profile with the RHML pulse-train envelope. To obtain the optimized optical injection shape for modulating the SOA gain profile during RHML operation, we have created the model to simulate the optically cross-gain-modulated pulse-trains without and with pulse-amplitude equalization, as shown in Fig. 4. The injected profile of the electrical comb and the biased voltage of MZM will determine the waveform of the peculiar inverse-optical-pulse or the inverse-optical-pulse to inject the SOA fiber ring via XGM effect. Fig. 4(a) simulated the waveforms of the electrical comb with the ideally inverse Gaussian shape and the non-symmetrical electrical comb, which are formatted by the correlation of Gaussian and exponential decay functions under the different biased points of the MZM and the modulation intensity. Theoretically, and the output waveforms of the inverse-optical-pulse and peculiar inverse-optical-pulse also can be numerically modeled via the modified transfer equation of the MZM, as described below.
Fig. 3 (a) Illustration of the inverse-optical-pulse and the peculiar inverse-optical-pulse generated by MZM. (b) The transmission curve of MZM. (c) The variations of electrical comb with different driving intensity. (d) The profile of actual-optical -pulse with pulse-amplitude equalization.
where Vπ denotes the switching-off voltage required for the MZM, VDC is the DC biased voltage of MZM, Vin is the peak amplitude of the electrical comb, τ 0 is the electrical comb pulsewidth, t0 is the repetition period of the electrical comb, Iin is the intensity of the tunable laser input, and the Iout denotes the transmission intensity of the MZM. The Eq. (2) shows the normal inverse-optical-pulse obtained by driving the MZM with an ideally inverse Gaussian waveform in general case. For pulse-amplitude equalization, a peculiar inverse-optical-pulse generated by driving the MZM with the same Gaussian waveform of larger amplitude crossing over the nonlinear region of the MZM transfer function, and biasing the MZM with a changed DC offset voltage near the nonlinear region is mandatory. In particular, the gain-recovery process of the SOA is also considered by adding an exponential decay function to cross-correlate with a non-symmetrical comb function, where U(τ) is the Heaviside unit step function defined as U(τ)=1 for τ≥0 and U(τ)=0 for τ<0.
Figure 4(b) illustrates the normal and peculiar inverse-optical-pulse waveforms for modulating the SOA gain profile in time domain, which result in different gain profiles of SOA in time domain, as shown in Fig. 4(c). As a result, the peculiar inverse-optical-pulse effectively modulates the SOA gain profile to compensate the amplitude difference of the consecutive RHML pulses within one HML repetition period, as shown in Fig. 4(d). In comparison with two different kinds of optical pulse-trains, the normal inverse-optical-pulse induces typical Gaussian gain profile of SOA, which is unable to offer sufficient gain to support the frequency-multiplied RHML pulses generated within the HML pulse period to equalize pulse-amplitude. On the contrary, the injection of a peculiar inverse-optical-pulse into the SOA effectively detunes the gain profile to individually compensate the gain for each RHML pulse temporally. The difference of RHML pulse amplitude is relatively small at low-order RHML condition, the residual gain of SOA between adjacent peaks shown in Fig. 4(c) must be increased to equalize the pulse-amplitude of RHML. Concurrently, the biased voltage of MZM and the intensity of non-symmetrical electrical comb should be decreased, in order to obtain the peculiar inverse-optical-pulse shape with minor radian variation in the equation of the MZM transfer function. At higher order RHML condition, the electrical comb used to drive the MZM must be more asymmetric with larger secondary peak and prolonged trailing edge to assist the peal-amplitude equalization of RHML pulses.
3.2 Pulse-amplitude equalization of the RHML-FSL
In 3rd-order RHML case, the MZM is originally biased at VDC = 0.7Vand the peak voltage of the electrical comb is attenuated by 3 dB. Each pulse peak of the 3rd-order RHML pulse-train will suffer different gain to result in severely inequivalent pulse-amplitude if we use a perfect inverse-optical-comb injection into the FSL, as shown in Fig. 5(a). According to the our simulation in previous section, the biased point of the MZM is extended to the falling part of its transfer function with corresponding VDC=1.4~1.5Vπ (Vbias = 6.5 V), while the peak amplitude of the electrical comb is remaining as large as 6.5 V to equalize the pulse-amplitude of 3rd-order RHML, as shown in Fig. 5(b). However, a pedestal will exist on the low-order RHML-FSL pulse-train due to the incomplete gain depletion of SOA resulted from the insufficient power of the injected inverse-optical-pulse. The pedestal of the pulse-train shown in Fig. 5(b) is mainly attributed to the residual gain of SOA, which cannot be diminished from the RHML pulse-train with increasing order. Hence, we must increase the injecting power or decrease SOA gain in order to suppress the pedestal, as the RHML pulses between the HML pulses is unable to absorb the residual gain of SOA.
Figure 6 depicts the corresponding RF spectra of the 3rd-order RHML without and with pulse-amplitude equalization, the harmonic frequency components at 1, 2, and 4 GHz accompany with the 3-GHz main peak when the peak amplitude of RHML pulse-train is inequivalent, which can partially be referred to the mismatch between the driving frequency and the cavity resonant frequency. Alternatively, the harmonic frequencies generation in frequency domain results from a low-frequency envelope modulation on the RHML pulse-amplitude in time domain. Fig. 6(b) gives a direct evidence for the success of RHML pulse-amplitude equalization since the unwanted frequency components induced by HML and low-completely diminish. The signal-to-noise ratio is about 20 dB by using the peculiar inverse-optical-pulse to optically modulate the SOA gain. In addition, the 5th-order RHML pulse-trains without and with pulse-amplitude equalization are also shown in Fig. 7. The amplitude fluctuation of high-order RHML becomes more seriously without modulating the gain profile of the SOA with an inverse-optical-pulse, as shown in Fig. 7(a). That is, the capability of a common FSL for a high-order RHML is weaker than for a low-order RHML, and more harmonic frequency components other than the desired RHML one appear to corroborate the incomplete mode-locking process, as shown in Fig. 8(a). Consequently, the competition of low-order harmonic frequencies and the frequency of the desired RHML order is the major factor to cause the huge pulse-amplitude difference in time domain. After the pulse-amplitude equalization of 5th-order RHML, only a single-frequency peak is observed at 5 GHz with a corresponding signal-to-noise ratio of 17 dB.
Fig. 4. (a) Simulated profile of the electrical comb without (dash line) and with (solid line) pulse-amplitude equalization. (b) Simulated profiles of the inverse-optical-pulse (dash line) and peculiar inverse-optical-pulse (solid line). (c) Simulated gain profiles of SOA ring cavity without (dash line) and with (solid line) pulse-amplitude equalization. (d) Simulated inequivalent (dash line) and equivalent (solid line) pulse-amplitude of RHML via optical gain shaping method.
Fig. 5. The 3rd order RHML trace monitored on digital sampling oscilloscope (a) without (b) with pulse-amplitude equalization.
Fig. 6. Measured RF spectra of 3rd order RHML pulse train from RHML-FSL (a) without (b) with pulse-amplitude equalization.
Fig. 7. The 5th order RHML trace monitored on digital sampling oscilloscope (a) without (b) with pulse-amplitude equalization.
Fig. 8. Measured RF spectra of 5th order RHML pulse train from RHML-FSL (a) without (b) with pulse-amplitude equalization.
Furthermore, the timing error on the neighboring RHML pulses spacing of 200 ps for the 5th-order RHML pulse-train without pulse-amplitude equalization is up to 11 ps, this phenomenon also echo the competition of the RHML and HML frequency components in the FSL. With pulse-amplitude equalization, the related timing error can be greatly decreased from 11 to 4 ps, corresponding to a reduction on percentage error from 4% to 0.02 % as shown in Fig. 9. The index of the percentage error is an alternative way to scope the timing error of pulses at different RHML orders. Without peak-amplitude equalization, the perturbations on the percentage error is substantially enlarged from ±2% to ±4% when operating the FSL from 3rd-order to 5th-order RHML, whereas the percentage errors can almost be controlled within 1% variation after peak-amplitude equalization, indicating that the RHML pulse-train is guide to desired repetition rate without timing error.
At last, the clock amplitude jitter (CAJ) is characterized to judge the equalization quality of the RHML pulse amplitude, which is defined as the ratio of the standard deviation (σ) to the mean value (M) of the intensity histogram at the peak intensity of pulse [12, 19], as given by CAJ = (d/M)×100%. As shown in Fig. 10, the CAJ value is usually below 10 % under pulse-amplitude equalization, whereas it greatly exceeds 20 % if the condition of pulse-amplitude equalization substantially collapses. For example, the CAJ of the 2nd-order RHML pulse-train is about 21.8% without pulse-amplitude equalization, which is significantly suppressed to 1.0 % with pulse-amplitude-equalization. As the RHML order increase up to 5th-order, the CAJ after pulse-amplitude equalization is degraded from 1.0 % to 7.3 %, and the compressing ratio of CAJ value is also decreasing from 20 to 5 as the RHML order increases. During the RHML-FSL operation, the reduction on the modulation depth of the inverse-optical-pulse is mandatory to facilitate high-order RHML. It is also observed that the gain modulation depth somewhat affects the CAJ and the adjacent pulse-amplitude variation. In comparison with the 3rd and 5th-order RHML pulse-trains, the difference between the standard deviation on CAJ is finite, however, the deviation can be enlarged twice when reducing the modulation depth. Hence, the high-order RHML requires stronger gain modulation to achieve the lower CAJ at constant SOA gain. The CAJ of the FSL pulse-train at RHML order >5 is difficult to be suppressed within 10% via the peculiar inverse-optical-pulse modulation, and the induced pulse-amplitude equalization will gradually be degraded with increasing RHML order.
Fig. 9. The percentage error of pulse-repetition period without and with pulse-amplitude equalization.
Fig. 10. Clock amplitude jitter versus RHML order for the FSL without and with pulse-amplitude equalization.
5. Conclusion
In conclusion, we have demonstrated a new scheme of gain-profile modulating for the pulse-amplitude equalization of the optical-injection RHML-FSL. By detuning the shape of the injected optical pulse via a Mach-Zehnder intensity modulator to modulate the SOA gain profile during RHML operation, and the actual experimental results are in good agreement with the numerical simulate, and we also create the optical injection model to explain the relationship between the curve of optical pulse and the gain profile of SOA based on the time-domain analysis. Using the peculiar inverse-optical-pulse injected the FSL, the RHML pulse experiences different gain from the temporally varied gain profile of the SOA to equalize the pulse-amplitude. To quantify the performances before the 5th-order RHML, the signal-to-noise suppression ratio is suppressed to about 20 dB, the timing error of the pulse spacing can be greatly improved from 11 to 4 ps corresponding to the percentage error decreased from 4% to 0.02 %, and the CAJ after pulse-amplitude equalization is degraded from 1.0 % to 7.3 % below the threshold limitation of 10%.
Acknowledgments
The authors thank the National Science Council of Republic of China for financially supporting this research under grants NSC97-2221-E-002-055, NSC 97-ET-7-002-007-ET and NSC 97-2221-E-110-019. The authors also appreciate Prof. Wood-Hi Cheng’s helpful discussion. Mr. Yu-Chan Lin is a part-time research assistant in the Lab. of fiber laser communication and Si nanophotonics at National Taiwan University.
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