The 40-GHz rational harmonic mode-locking (RHML) and pulse-amplitude equalization of a semiconductor optical amplifier based fiber-ring laser (SOAFL) is demonstrated by the injection of a reshaped 10-GHz gain-switching FPLD pulse. A nonlinearly biased Mach-Zehnder modulator (MZM) is employed to detune the shape of the double-peak pulse before injecting the SOA, such that a pulse-amplitude equalized 4th-order RHML-SOAFL can be achieved by reshaping the SOA gain within one modulation period. An optical injection mode-locking model is constructed to simulate the compensation of uneven amplitudes between adjacent RHML pulse peaks before and after pulse-amplitude equalization. The indirect gain compensation technique greatly suppresses the clock amplitude jitter from 45% to 3.5% when achieving 4th-order RHML, and the amplitude fluctuation of sub-rational harmonic modulating envelope is attenuated by 45 dB. After pulse-amplitude equalization, the pulse width of the optical-injection RHML-SOAFL is 8 ps, which still obeys the trend predicted by the inverse square root of repetition rate. The phase noise contributed by the residual ASE noise of the RHML-SOAFL is significantly decreased from −84 to −90 dBc/Hz after initiating the pulse-amplitude equalization, corresponding to the timing jitter reduction from 0.5 to 0.28 ps.
© 2010 OSA
Actively mode-locking fiber lasers for generating picosecond pulse width at high repetition rate around 1550 nm have been developed for nearly two decades, which is one promising candidate of the key element for developing high-speed optical time-division-multiplexing (OTDM) network. The rational harmonic mode-locking (RHML) has recently emerged for extremely high-order frequency-multiplication of fiber laser pulse-train via gain-modulation at a frequency slightly offset from one longitudinal mode of laser. Most configurations employed an intra-cavity intensity modulator as the mode-locker to construct a RHML fiber ring, but the modulation bandwidth of the modulator generally limits the highest repetition rate of the mode-locked pulse-train at 10 GHz. Using a gain-switching FPLD pulse injection for optically mode-locking the fiber ring can effectively remove the need of broadband modulator. Previously, the external gain-modulation of both the semiconductor optical amplifier (SOA) and the erbium-doped fiber amplifier (EDFA) via optical pulse-train injection were demonstrated to obtain RHML up to 40 GHz [1,2]. Nevertheless, the RHML pulse-train suffers from a huge amplitude fluctuation between adjacent peaks, this is an inherent drawback occurred when the modulation frequency of RHML is not exactly coincident with the resonant frequency of laser cavity.
Recently, Yang et al.  have used a peak-equalized 5th-RHML pulse-train at repetition rate of 10 GHz to propose the RZ data-stream generation with a stabilized performance after long-term BER test. For a practical application in OTDM, the uneven RHML pulse carrier inevitably leads to a degraded return-to-zero (RZ) data-stream after external on-off keying operation, thus enlarging bit-error-rate (BER) due to the inaccurate decision of high- and low-level bits at receiving end. Therefore, both the equalization of adjacent peak amplitude and the reduction on RHML order of the laser become the concerned issues in the RHML laser system. To solve the problem of uneven pulse-amplitude, some groups proposed the parametric detuning of the intra-cavity MZM based mode-locker to overcome this disadvantage. Several approaches were successfully demonstrated by consecutively passing the RHML pulse-train forward and backward through a MZM, by using a dual-drive MZM configuration, or by employing the MZM biased at nonlinear region [4–6]. Some special configurations were also presented by using a feedback circulation within the SOAFL cavity , by establishing a polarization-maintaining laser resonator , or by adding a nonlinear optical loop mirror . Up to now, all these frameworks were designed to resolve the uneven pulse-amplitude problem occurred in the intra-cavity loss-modulation based systems, whereas the pulse-amplitude equalization technique for the optical injection based cross-gain modulation and rational harmonic mode-locking systems was seldom discussed.
In this work, we employ a 10-GHz gain-switching FPLD pulse-train with its waveform reshaped by a nonlinearly biased MZM to inject a semiconductor optical amplifier based fiber-ring laser (SOAFL) for 40-GHz RHML and pulse-amplitude equalization. In this approach, a traditional gain-switching FPLD pulse is reshaped into a double-peak pulse, which depletes and modulates the SOA gain to equalize the 4th-order RHML pulse-amplitude at repetition rate of 40 GHz. An optical injection mode-locking model is developed to numerically simulate the compensation of the depleted/reshaped gain of SOA set for the adjacent pulse peaks of the intra-cavity circulated RHML pulse-train before and after pulse-amplitude equalization. To judge the performances of the equalized RHML-SOAFL pulse-train, the RF spectra, the signal-to-noise suppression ratio, the clock amplitude jitter, the RHML pulse width, the single-sideband (SSB) phase noise, and the corresponding timing jitter are discussed.
2. Experimental setup
The configuration of the RHML-SOAFL for obtaining a pulse-amplitude equalized RHML pulse-train at 40 GHz is shown in Fig. 1 . A RF amplifier with 35-dB gain is used to magnify the 10-GHz sinusoidal-wave for driving a traditional gain-switching FPLD via a bias-tee device. A MZM is driven by a 27dB-gain RF amplifier and a DC voltage to offset its bias point for nonlinear operation. A phase shifter controls dominates the relative time delay between the gain-switched FPLD pulse and the sinusoidal wave used to drive the MZM for deforming the double-peal pulse. An EDFA is added to amplify the reshaped double-peak pulse for amplifying the optical power up to 5 dBm. In the SOAFL cavity, the anti-reflection coated SOA (Q-photonics, QSOA-1550) biased at current of 300 mA is employed as the gain medium, which provides a gain spectrum with spectral linewidth of 30-50 nm centered at 1535 nm. The Faraday isolator (ISO) is used to ensure the unidirectional propagation, and an output coupler (OC) with power-splitting ratio of 50% is introduced to obtain pedestal-free RHML pulse-train with a shortened pulse width.
3. Results and discussions
3-1 Theoretical simulation
In general, the HML pulse-train only includes one pulse within a gain-modulation period, where the problem of gain variation existing in any point of the gain-modulation period needs not to be considered. Alternatively, the RHML pulse-train can only be implemented by detuning the modulation frequency from fm to fm + f0/p, where fm, f0, and p are defined as modulation frequency, longitudinal mode-spacing, and frequency multiplication order, respectively. For p-order RHML pulse-train with a repetition frequency of pfm + f0, the RHML generates p pulses per HML modulation period (with a pulse spacing of 1/p HML period). The p-order RHML pulse-train inevitably suffers from serious amplitude fluctuation, as each RHML pulse experiences different gain variation within harmonic mode-locking (HML) modulation period. Apparently, the adjacent RHML pulses intrinsically experience different gain each other in the SOAFL gain-modulated at a slightly deviated HML frequency. Such a gain difference results in an uneven peak-intensity for the RHML pulse-train, which becomes significant when increasing the RHML order. That is, a 10-GHz traditional pulse injection induced XGM effect only contributes to an optimized gain-profile for 10-GHz HML scheme, whereas the pth-order RHML pulse-train suffers a serious amplitude fluctuation from experiencing the uneven gain-profile set for HML condition, as shown in Fig. 2 . The uneven amplitudes of the RHML pulses induced by the experienced can be equalized if the gain-shape of SOA in time domain is further detuned as a function of time within the HML period.
For example, the gain reshaping in a SOAFL can be achieved by injecting the SOA with a double-peak pulse in one HML period. Detuning the relative intensity of such a double-peak pulse causes the temporal reassignment of the gain for each pth-order RHML pulse within the HML period, such that the pulse-amplitude equalization of RHML-SOAFL is approached by compensating the gain difference between adjacent RHML pulses, as shown in Fig. 3 . By modifying a theoretical model previously proposed to describe the propagation behavior of the HML pulse-train in a SOA fiber ring , we discuss the intra-cavity RHML pulse-train under the change on the externally injecting shape of the gain-switching FPLD pulse. The rate equation of the transient gain (g) is given by ∂g/∂τ = [(g-g0)/τc-gPout(τ)/Esat], where g0, τc, Εsat, Pout denote the small signal gain coefficient, carrier lifetime, saturation energy, and temporally varied output power, respectively. Assuming that the h(τ) = ∫g(z,τ)dz is the integrated gain at each point of the circulating pulse shape, the rate equation of the transient gain can be rewritten as
In general, the Pinj(τ) denotes the injected power of the gain-switched FPLD obtained at the output port of the MZM. The Figs. 3(a) and 4(a) plot the simulating results of the single- (traditional) and the double-peak (reshaped) gain-switching FPLD pulse-trains obtained by deforming the transfer function of the MZM, as shown in Eq. (2). The Pinj(τ) is rewritten as the intensity product of the gain-switching pulse and the modulated sinusoidal waveEq. (2) into Eq. (1), the integrated gain of SOAFL can be described as
According to Eq. (3), the circulating RHML pulse-train, the external injection gain-switching FPLD pulse, the gain-profile of SOAFL, and the output RHML pulse-train without and with pulse-amplitude equalization can be numerically simulated, as shown in Fig. 3. During simulation, the carrier recovery of the SOA is assumed to be much faster than the arrival of the externally injected pulse, and the circulating RHML pulse-train experiences a time-varying gain profile in the SOAFL. Such an assumption is necessary when injecting with a double-peak pulse instead of a single-peak one. Not only the modulation depth but also the shape of the injected double-peak FPLD pulse is detuned to approach the pulse-amplitude equalization. The original results of the RHML pulse-train with unequal peak amplitudes obtained under conventional HML modulating condition are shown in Fig. 2. Our simulations elucidate when the gain of SOA in time domain is detuned to a shape shown in Fig. 3(b), the original RHML pulse with a lower peak-intensity obtains more gain, whereas the RHML pulse of higher peak-intensity is compressed by lower SOA gain at the same time in each period. All of the RHML pulses within one HML period experiences different gain at corresponding time to equalize their peak amplitudes eventually [see Fig. 3(c)].
3-2 Experimental demonstration
To experimentally flatten the RHML pulse-train with uneven peak amplitudes, we further employ a nonlinearly biased MZM to deform the relative amplitude and shape of the double-peak pulse before injection. The reshaped SOA gain profile eventually fits the requested gain for each RHML pulse to approach the pulse-amplitude equalization. With the operating principle illustrating in Fig. 4, we detune the DC bias of the MZM from linear (point A) to nonlinear (point B) region, such that a deformed sinusoidal-wave can be created when biasing at condition (B), whose winding profundity is affected by the modulation depth of the electrical sinusoidal-wave and the DC bias added to a MZM as shown in Fig. 4.
The Fig. 5(a) experimentally monitors the normal and deformed sinusoidal-wave waveforms obtained at DC biased voltage of 3 and 5.5 V corresponding to 0.67 Vπ and 1.2Vπ, respectively. When passing the 10-GHz gain-switching FPLD pulse through such a MZM, the deformed transfer function splits the single-peak pulse into a reshaped double-peak pulse, and the phase controller is used in detuning the intensity ratio of the double-peak pulse for matching the different order RHML pulse-train. Furthermore, a 10 GHz gain-switching FPLD pulse with broadened pulse width will be beneficial to build up a double-peak pulse shape. The Fig. 5(b) shows the traditional (single-peak) and reshaped double-peak gain-switching FPLD pulses with a pulse width of 35 ps, which are subsequently employed to inject the SOA fiber ring for initiating RHML pulse-trains without and with pulse-amplitude equalization.
The Figs. 6 and 7 show the sampling traces of 20 and 30 GHz RHML pulse-train without and with pulse-amplitude equalization, indicating that the uneven RHML pulse-amplitude is effectively improved when the DC voltage transfers the MZM output to nonlinear region. The trade-off between MZM bias and phase shift is easily observed when approaching the peak-amplitude equalization. If the MZM bias is controlled within 5%, the peak-equalized RHML-SOAFL can maintain a relatively stable peak-amplitude equalized output. When increasing the RHML order, the uneven RHML pulse-train deviates from the gain profile of HML by their slightly offset frequency, such that the peak intensity of HML pulse-train is often stronger than the RHML pulse during the gain competition. Besides, the gradually attenuated modulation depth also contributes a DC level to decrease the pulse/DC amplitude ratio when the residual SOA gain cannot be eliminated. Therefore, the primary/secondary peak intensity ratio and optical power of the double-peak gain-switching FPLD pulse are detuned to balance the gain difference between HML and RHML and to erase the DC level, respectively.
The optimized 30-GHz RHML pulse-train with pulse-amplitude equalization is shown in Fig. 7(b). The auto-correlation traces of 4th-order RHML pulse-train without and with pulse-amplitude equalization are observed and shown in Fig. 8 , in which the temporal spacing of 25 ps between RHML peaks corresponds to 40 GHz repetition rate, and the pulse width of 40 GHz RHML pulse-train obtained with Gaussian fitting is 8 ps. The Fig. 9 shows the optical spectra of the un-equalized and equalized 4th-order RHML-SOAFL with a mode-spacing of 0.315 nm corresponding to a repetition rate of 40 GHz. In addition, the longitudinal modes of the equalized 4th-order RHML pulse-train present a better extinction ratio than that of un-equalized RHML pulse-train. At higher RHML orders, the competition between mode-locking and continuous-wave (CW) lasing make the dominant mechanism interchanged due to the attenuated pulse-shortening force with increasing RHML order . The decreasing modulation depth inevitably occurs to degrade RHML and result in a large residual SOA gain for CW lasing accompanied with a high-level DC component observed at time domain.
Alternatively, the un-equalized peak-intensity of RHML pulse-train can be attributed to the superposition of various HML pulse-trains. Although the selection of specific longitudinal modes-by RHML accomplishes frequency multiplication, the modulation of SOA at nearly HML frequency has lead to an uneven pulse-amplitude on the pulse-train. By analyzing the un-equalized RHML pulse in frequency domain via Fourier transform, the RF spectrum clearly resolves the sub-harmonic and rational harmonic frequencies composed within the RHML pulse-train. With a high-speed photodetector (Newfocus 1014, f3dB = 45 GHz) and a RF spectrum analyzer (HP 8565E, f = 50 GHz), it is observed that the higher order RHML without pulse-amplitude equalization will carry lower harmonic frequencies. The upper part of Fig. 10 depicts the difficulty in approaching desired 4th-order RHML condition since the lower order RHML frequency components at 10, 20, and 30 GHz is hardly suppressed without using pulse-amplitude equalization technique.
In contrast, the temporal reshaping on SOA gain effectively causes the pulse-amplitude equalization to suppress the residual modulation on the envelope of pulse-train. When a purely 4th-order RHML is achieved under pulse-amplitude equalization, not only the lower order RHML frequencies entirely diminish but also the signal-to-noise suppression ratio greatly enhances from 19 to 45 dB, as shown in Fig. 11 . The uneven pulse-amplitude observed in time domain is referred to the competition of RHML at different orders, which generates multi-frequency components corresponding to the RHML orders in frequency domain, thus leading to the fluctuated amplitude envelope of RHML pulse-train. The quality of pulse-amplitude equalization can be evaluated either by determining the spectral intensity ratio of the high/low RHML order components from the microwave spectrum in frequency domain, or by measuring the clock amplitude jitter (CAJ) between adjacent pulse peaks from the sampling RHML pulse train in time domain. In contrast to the microwave spectral analysis, the CAJ method monitors the degree of the peak-to-peak amplitude fluctuation caused by RHML by defining the CAJ = (σ/M) × 100% as a ratio of the standard deviation (σ) to the mean value (M) of the intensity histogram at each peak of the RHML pulse-train [7,12].
Without peak-amplitude equalization, the CAJ value is enlarged from 11.7% to 45% as the repetition rate increases from 20 to 40 GHz, since lower RHML component usually associates with the pulse-train when increasing RHML order. With pulse-amplitude equalization, the CAJ greatly decreases to 1.54% and 3.5% for the SOAFL operated at second and fourth RHML orders. Such a CAJ has already below the criterion of 10% set for obtaining less fluctuated pulse-train, as shown in Fig. 12 . Beyond 4th-order RHML operation, the continuous-wave lasing mechanism turns to dominate and the RHML mechanism is relatively hard to survive under competition. Not only the on/off extinction ratio of the high-order RHML pulse is greatly attenuated, but also the RHML pulse-train will exceed a huge amplitude-fluctuation with CAJ exceeding 60%. With the analysis via an auto-correlator (FR-103XL), the Fig. 13 shows the reduction of the RHML pulse width from 19.5 to 8 ps achieved by increasing the RHML frequency from 10 to 40 GHz, and a linear relationship between RHML pulse width and the inverse square of repletion rate is confirmed to follow a numerical model with recursive equation in frequency domain given as Eq. (4) in time domain, while the pulse width is decreased with increasing modulation depth, decreasing gain, and enlarging modulation frequency. The a(t) is expressed by a(t) = A(20.5π/τ)exp(-t2/2τ 2) with t = (2g/σ)1/4/[2πfmΩg]0.5.
Nonetheless, the numerical model needs to be slightly modified for evaluating the p-order RHML case since the external modulation frequency is detuned to fm = (n + 1/p)f0, and the (n + 1/p) is not integer to result in the completely coupled longitudinal modes of the fiber ring length set for HML condition. We need to consider the equivalent cavity length as pL, such that the RHML longitudinal modes are able to couple in the HML fiber ring. In RHML case, each pulse in the p-order RHML pulse-train must propagate p times before obtaining sufficient gain, and there are (np + 1) pulse travels around the fiber ring with cavity length of pL. Therefore, the function still meets the p-order RHML condition, and the pulse width is proportional to fm −1/2 when the SOA gain and modulation depth is fixed. Furthermore, the single-sideband (SSB) phase noise and the corresponding timing jitter are demonstrated to characterize the stability of such a RHML-SOAFL output in both frequency and time domain. The phase noise components disperse the power of a frequency carrier, resulting in an amplitude perturbation in sideband of the 40-GHz frequency carrier.
Due to the insufficient gain depletion induced incomplete mode-locking in SOAFL at higher RHML orders, a residual ASE of SOA may persistently circulate in the fiber ring to contribute additional phase noise. The ASE can be greatly attenuated by injecting the double-peak gain-switched FPLD pulse to temporally deplete and reshape the SOA gain profile. Hence, the uncorrelated phase noise (usually at offset frequency larger than 100 kHz) contributed by residual ASE noise of the RHML-SOAFL is observed to decrease from −84 to −90 dBc/Hz after pulse-amplitude equalization, as shown in Fig. 14 . Due to the finite bandwidth of the optical receiver and the sampling oscilloscope which can only resolve a sinusoidal-wave like shape of the 40-GHz RHML-SOAFL pulse-train (the higher frequency components are cutting off by the finite bandwidth), the corresponding timing jitter (σJ) is calculated by integrating the SSB phase noise density L(f) at 40-GHz repetition-rate (fR) using σJ = [2∫L(f)df]0.5/2πfR, within an integration range between 100 Hz and 1 MHz offset from carrier. The timing jitter decreases from 0.5 to 0.28 ps after pulse-amplitude equalization, providing a more stable RHML-SOAFL pulse-train at repetition frequency of 40 GHz, as shown in Fig. 15 . With such a dual-peak optical pulse injection RHML technology, the results show a greatly enhanced carrier-to-noise ratio with lower amplitude fluctuation after pulse-amplitude equalization. These improvements will be beneficial for enhancing the Q factor and the BER performance of OTDM data transmission with the RHML pulse carrier.
By using the reshaped 10-GHz gain-switching FPLD double-peak pulse to reconstruct the gain profile of SOA in time domain, the 4th-order RHML-SOAFL is demonstrated for achieving 40-GHz RHML pulse-train with optimized performance of pulse-amplitude equalization. A traditional 10-GHz gain-switching FPLD pulse is transferred into the double-peak gain-switching FPLD pulse by using a MZM biased at nonlinear region before injecting the RHML-SOAFL. The numerical simulation indicates the optimized gain shape of SOA that is depleted and reshaped to compromise the difference between the intra-cavity circulating RHML pulses. Such a gain-switched FPLD pulse injection induces an indirect gain compensation to effectively balance the gain difference and amplitude fluctuation of 4th-order RHML pulse-train. After pulse-amplitude equalization, the clock amplitude jitter has a great reduction from 45% to 3.5%. The intra-cavity circulated RHML pulse-train greatly suppresses the amplitude fluctuation of its sub-harmonic modulating envelope by 45 dB, and the optimized RHML-SOAFL pulse width of 8 ps fitted by Gaussian function still obeys the trend predicted by the inverse square root of repetition rate. The uncorrelated phase noise contributed by the residual ASE noise of the RHML-SOAFL is significantly decreased from −84 to −90 dBc/Hz after initiating the pulse-amplitude equalization, which leads to a timing jitter reducing from 0.5 to 0.28 ps and provides a more stable 4th-order RHML-SOAFL pulse-train. By simply reshaping a gain-switched laser diode pulse at 10 GHz, our proposed scheme concurrently solves the problem of large amplitude noise accompanied with adjacent pulses obtained at fourth RHML order, providing an amplitude-equalization pulse-train repeated at 40 GHz to meet the demand of being a perfect RZ pulsed carrier for its future application in OTDM network.
This work is supported by the National Science Council of Republic of China under grants NSC 97-ET-7-002-007-ET, NSC 97-2221-E-110-019, and NSC-98-2622-E-002-023-CC3.
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