1. Introduction

Wavelength-tunable high-repetition-rate optical pulse generation is essential for many applications such as high-speed optical communication systems and optical signal processing. Harmonically mode-locked fiber ring lasers (HML-FRLs) have proven to be able to generate wavelength-tunable short pulses with small timing jitter and gigahertz repetition rates [1–6].

Generally, the repetition rate of the HML-FRLs given by nf_cav is equal to the modulation frequency f_mod of the intracavity modulator, where n is an integer called harmonic order, and f_cav is the fundamental cavity frequency. Therefore, maximum repetition rate of the HML-FRLs is normally limited by the bandwidth of the intracavity modulator and the operating frequency range of the drive electronics. Recently, a scheme called the rational harmonic mode-locking has been proposed and demonstrated to generate pulses at high repetition rates by driving the laser at a frequency slightly offset from one of its harmonics [7–12]. In this technique, a pulse train with a repetition rate of (pn+1)f_cav can be generated when f_mod is set at (n+1/p)f_cav, where p is an integer called rational harmonic order. However, the pulse amplitude normally becomes uneven when p is greater than two. Uneven amplitudes create difficulties in the real application of these pulses. To solve the problem, a scheme based on semiconductor optical amplifier in a loop mirror has been reported [8]. But the system configuration is complicated. Other techniques based on nonlinear optical loop mirror [9,10] or nonlinear polarization rotation [11] have also been proposed to equalize the pulse amplitude. While in these structures, more fiber amplifier or long dispersion-shifted fiber is required to generate enough nonlinear effects in the fiber. For a simple scheme to equalize the pulse amplitude, modulator transmittance adjustment method has been proposed and demonstrated so far [12]. The principle is based on nonlinear modulation by adjusting the bias level and the modulation depth of the intracavity modulator.

Another important issue for the HML-FRLs is the range of the wavelength tunability. The HML-FRLs usually employ silica-based erbium-doped fibers (EDFs) as the gain media. Therefore, the wavelength tunability is normally limited to the conventional wavelength band (C-band). The gain profile of the silica-based EDFs can be shifted toward the longer wavelength band (L-band) [13], though careful optimization of the fiber length and the pump power is required. In addition, the typical cavity length of the HML-FRLs is 10-100 m, and the corresponding order of harmonics is 500-5000 for 10-GHz mode-locking. Such a long cavity length and a high harmonics order introduce the system vulnerability to external perturbation and intensity fluctuation known as supermode noise [2]. Several techniques to suppress the supermode noise have been proposed and demonstrated so far, such as insertion of an intracavity high finesse Fabry-Perot etalon [3], a semiconductor optical amplifier (SOA) [4,5], and a silica-based highly nonlinear dispersion-sifted fiber (HNL-DSF) [6]. However, the Fabry-Perot etalon is usable for only a single repetition frequency. On the other hand, use of the SOA is advantageous in that it is usable in any repetition frequency, does not elongate the cavity, and is applicable to multiwavelength fiber lasers. However, the SOA is an active element which causes additional noise and cost. With these respects, the use of self-phase modulation (SPM) in a silica-based highly nonlinear passive fiber element and spectral filtering by an optical bandpass filter (OBPF) is attractive techniques for noise suppression. In this method, higher intensity pulses are spectrally broadened by the SPM and then suffer higher loss through the OBPF. Therefore, fast intensity limiting is achieved, and the intensity fluctuation can be suppressed. The length of the silica-based HNL-DSF required for the stabilization, however, is reported at least several tens of meters. Employing such a long element in the ring cavity makes the laser system more sensitive to external perturbation.

Meanwhile, picosecond pulse sources consisting of a continuous-wave (CW) laser diode (LD), external modulators, and an OBPF have also been attracting attention recently [14,15]. In this scheme, optical frequency comb signal is generated from the external modulators, and then an optical pulse train is formed from the comb signal. The benefits of such pulse generators are compactness, straightforward configuration, high stability, and low timing jitter. However, the wavelength tunability is limited by that of the CW LD. In addition, maximum pulse repetition rate is also limited by the modulator bandwidth and the operating frequency range of the drive electronics.

In this paper, we report a wavelength-tunable short-cavity rational HML-FRL employing a 151-cm-long bismuth-oxide-based erbium-doped fiber (Bi-EDF) and a 250-cm-long bismuth-oxide-based highly nonlinear fiber (Bi-HNLF). Since the Bi-EDF has a wide gain bandwidth, continuous wavelength tuning covering both the C-band and the L-band can be achieved. The pulse-amplitude equalization can also be achieved by adjusting the bias level and the modulation depth of the intracavity modulator. The Bi-HNLF has an ultra-high nonlinear coefficient of 1100 W⁻¹km⁻¹, about 50-60 times higher figure than that of the conventional silica-based HNL-DSFs. Because of this feature, the length of the nonlinear fiber for effective suppression of the supermode noise is dramatically shortened; the total cavity length is as short as 10 m. Thus, stable and amplitude equalized pulses up to 40 GHz (p = 4) are successfully obtained for the entire wavelength tuning range.

2. Experimental setup

Figure 1 shows a schematic of the experimental setup. The bismuth-based rational HML-FRL was composed of a Bi-EDF, pump LDs, wavelength-division multiplexed (WDM) couplers, optical isolators, a Bi-HNLF, an output coupler, an OBPF, a polarization controller (PC), a LiNbO₃ Mach-Zehnder intensity modulator (LN-MOD), a radio-frequency (RF) amplifier, and a synthesized microwave generator.

 

Fig. 1 Experimental setup for evaluating the performance of a rational harmonic mode-locked short-cavity fiber ring laser using a Bi-EDF and a Bi-HNLF.

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To achieve wide wavelength tunability, a 151-cm-long Bi-EDF was used as the gain medium [16,17]. Major specifications of the Bi-EDF were as follows: erbium concentration 3250 ppm; refractive index of the core at 1550 nm 2.03; that of the cladding 2.02; core diameter 5.1 μm; peak absorptions 90 dB/m at 980 nm, 130 dB/m at 1480 nm, and 210 dB/m at 1530 nm, respectively. Both ends of the Bi-EDF were fusion spliced to SiO₂ fibers. The fiber-to-fiber loss was 2.3 dB at 1310 nm. The Bi-EDF was bidirectionally pumped with two LDs. A 974-nm LD with an output power of 27.5 dBm was used for the forward pumping, and a 976-nm LD with an output power of 27.5 dBm was used for the backward pumping. Both pump beams were coupled in the ring cavity through WDM fiber couplers. Two optical isolators were used to realize unidirectional ring laser oscillation.

Sinewave signal from a synthesizer was amplified by an RF amplifier and then led to an LN-MOD. Rational harmonic mode-locking up to 40 GHz (p = 4) was achieved by manipulating f_mod of the LN-MOD with a step of 1 kHz in the range form 9.913228 GHz to 9.933847 GHz. The bandwidth, the insertion loss, and the extinction ratio of the LN-MOD were 12.5 GHz, 2.7 dB, and 25 dB, respectively. The pulse-amplitude equalization was also achieved by tuning the modulation parameters of the LN-MOD properly [12]; the bias level was adjusted in the range from 0.0 V to 4.0 V; the modulation depth was adjusted in the range from 2.5 V to 4.0 V. A PC was used to align the polarization state to that of the LN-MOD. Continuous wavelength tuning was achieved by changing the center wavelength of an OBPF, where we used two OBPFs (OBPF 1/2) alternatively; the OBPF 1 covering the C-band had a bandwidth of 1.0 nm and an insertion loss of about 1.5 dB; the OBPF 2 covering the L-band had a bandwidth of 1.0 nm and an insertion loss of about 1.7 dB.

To suppress the supermode noise, we used the SPM in a 250-cm-long Bi-HNLF [18,19] and the spectral filtering by the OBPF 1/2. The refractive indexes of the core and the cladding were 2.22 and 2.13 at 1550 nm, respectively. The core diameter was 1.72 μm, the effective core area being estimated as 3.3 μm². The nonlinear coefficient γ was as high as 1100 W⁻¹km⁻¹. This extremely high figure was attributed to high nonlinearity of the glass material and the small effective core area. The group-velocity dispersion (GVD) was –310 ps/nm/km at 1550 nm. Such a large normal GVD was mainly attributed to the material dispersion of the high refractive index glass. Both ends of the Bi-HNLF were fusion spliced to SiO₂ fibers, and the fiber-to-fiber loss was 6.0 dB at 1310 nm.

Optical power was coupled out of the ring cavity through a 9% output coupler. The output pulses were monitored by an optical power meter and an optical spectrum analyzer. The output pulses were also led to an intensity autocorrelator and a sampling oscilloscope with an electrical bandwidth of 63 GHz, after being pre-amplified by an erbium-doped fiber amplifier (EDFA). The full width at half-maximum T_FWHM of the output pulses was estimated from the autocorrelation traces. The total length of the ring cavity including all optical components was as short as 10 m, f_cav being estimated as about 20 MHz.

3. Experimental results and discussions

Figure 2 shows the average output power measured as a function of the center wavelength λ_c of the output pulses, where λ_c is continuously varied by tuning the OBPF 1/2. The wavelength tuning ranges are 1533-1615 nm (82 nm) for 10 GHz (p = 1), 1534-1613 nm (79 nm) for 20 GHz (p = 2), 1535-1608 nm (73 nm) for 30 GHz (p = 3), and 1537-1606 nm (69 nm) for 40 GHz (p = 4), respectively. Because of the wide gain bandwidth of the Bi-EDF, these wavelength tuning ranges cover both the C-band and the L-band. The wavelength dependence of the output power is attributed to the gain profile of the Bi-EDF. If we use the pump LDs with higher output power, the output power will be increased, and the wavelength tuning range will be broadened.

 

Fig. 2 Average output power versus the center wavelength.

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Figure 3 shows the autocorrelation traces of the output pulses at λ_c = 1575 nm. The T_FWHM of the output pulses are estimated as 14.3 ps for 10 GHz (p = 1), 10.4 ps for 20 GHz (p = 2), 7.7 ps for 30 GHz (p = 3), and 7.4 ps for 40 GHz (p = 4), respectively. Figure 4 shows T_FWHM measured as a function of λ_c. The T_FWHM are 13.6-15.3 ps for 10 GHz (p = 1), 9.1-10.8 ps for 20 GHz (p = 2), 7.4-8.0 ps for 30 GHz (p = 3), and 7.0-8.0 ps for 40 GHz (p = 4), respectively. Figure 5 shows the corresponding time-bandwidth product T_FWHMΔν of the output pulses measured as a function of λ_c. The T_FWHMΔν are 0.42-0.54 for 10 GHz (p = 1), 0.40-0.60 for 20 GHz (p = 2), 0.39-0.48 for 30 GHz (p = 3), and 0.33-0.47 for 40 GHz (p = 4), respectively. The T_FWHM increases due to the large GVD of the Bi-HNLF [18], and the output pulses become sech² pulses with small frequency chirp. If we use appropriate dispersion compensating fiber, the chirped output pulses will be compressed. On the other hand, for the 10-GHz (p = 1) system without the Bi-HNLF, the wavelength tuning range, T_FWHM, and T_FWHMΔν are 1533-1620 nm (87 nm), 9.6-11.0 ps, and 0.29-0.33, respectively. These results indicate that the output pulses are close to transform-limited sech² pulses.

 

Fig. 3 Autocorrelation traces at the center wavelength of 1575 nm.

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Fig. 4 Pulse width versus the center wavelength.

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Fig. 5 Time-bandwidth product versus the center wavelength.

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The sampling oscilloscope traces of the output pulses at λ_c = 1575 nm are shown in Fig. 6 . The bit intervals are 100 ps for 10 GHz (p = 1), 50 ps for 20 GHz (p = 2), 33.3 ps for 30 GHz (p = 3), and 25 ps for 40 GHz (p = 4), respectively. The pulse amplitude is equalized by adjusting the modulator transmittance function. However, the pulse amplitude at 30 GHz (p = 3) and 40 GHz (p = 4) is not completely equalized because the modulation parameters slightly deviate from the optimum values. We have to note that a precise match of the bias level and the modulation depth of the intracavity modulator is required to achieve complete amplitude equalization [12]. In our experimental results, the amplitude variation at 30 GHz (p = 3) and 40 GHz (p = 4) is about less than 10% over the entire wavelength tuning range. Because of the ultra-high nonlinearity of the short Bi-HNLF, the supermode noise is also suppressed effectively, and the pulse intensity is very stable. In contrast, Fig. 7 is a similar trace for the 10-GHz (p = 1) system without the Bi-HNLF. The sampling oscilloscope trace without the Bi-HNLF is very noisy because the supermode noise can no longer be reduced.

 

Fig. 6 Sampling oscilloscope traces at the center wavelength of 1575 nm.

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Fig. 7 Sampling oscilloscope trace at 1575 nm for the 10-GHz system without the Bi-HNLF.

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To discuss the noise quantitatively, we calculated the signal-to-noise ratio SNR_peak at the pulse intensity peak, where we measured the average and the standard deviation by using statistics function of the sampling oscilloscope. Figure 8 shows SNR_peak as a function of λ_c. The SNR_peak are 9.4-15.0 dB for 10 GHz (p = 1), 9.7-13.0 dB for 20 GHz (p = 2), 9.5-13.0 dB for 30 GHz (p = 3), and 10.2-12.4 dB for 40 GHz (p = 4), respectively. High SNR_peak is maintained over the entire wavelength tuning range. These results show effectiveness of the short Bi-HNLF as a wideband supermode noise suppressor.

 

Fig. 8 Signal-to-noise ratio at the pulse intensity peak versus the center wavelength.

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Finally, we discuss the long-term performance of the laser. Our experimental results show that this bismuth-based fiber laser can maintain stable operation of the rational harmonic mode-locking for at least 10 minutes over the entire wavelength tuning range. This is mainly determined by the temperature induced cavity length change and the temporal variation of the polarization state. Therefore, a temperature control of the laser cavity and the polarization-maintaining configuration are required to realize the long-term stability for wideband optical transmission and processing applications.

4. Conclusion

We have proposed and experimentally demonstrated a rational HML-FRL using a 151-cm-long Bi-EDF and a 250-cm-long Bi-HNLF. Continuous wavelength tunability covering both the C-band and the L-band has been achieved by utilizing the wide gain bandwidth of the Bi-EDF. The pulse-amplitude equalization has also been achieved by the modulator transmittance adjustment method. The supermode noise has been reduced sufficiently due to the ultra-high nonlinearity of the Bi-HNLF. The total length of the ring cavity including all optical components has been as short as 10 m. Thus, stable and amplitude equalized pulses from 10 GHz (p = 1) to 40 GHz (p = 4) have been successfully generated over the entire wavelength tuning range.