Photonic millimeter-wave generation from high-order frequency-multiplied optical pulse-train of Erbium-doped fiber laser (EDFL) harmonic mode-locked at repetition frequency of 1 GHz is demonstrated. A Fabry-Perot laser diode (FPLD) operated at below threshold condition is employed as an intra-cavity optical mode-locker, which is purely sinusoidal-wave-modulated at 1 GHz without any DC biased current in this experiment. The threshold modulating power of 18 dBm for the FPLD is observed for harmonic mode-locking the EDFL. The frequency-multiplication of EDFL pulse-train is implemented by detuning the modulating frequency of the FPLD. At highest repetition rate of 42 GHz, the peak power and pulseswidth of frequency-multiplied EDFL pulse-train are 140 mW and 2.7 ps, respectively.
© 2004 Optical Society of America
Generation of high-speed laser pulse-train is mandatory for applications in photonic millimeter-wave clock distribution [1–4] and ultrahigh-bit-rate fiber-optic time-division-multiplexed transmission , etc. The synchronized optoelectronic oscillators at frequencies up to 200 GHz based on mode-locked semiconductor lasers have been extensively investigated. Erbium-doped fiber lasers (EDFLs) using harmonic or rational harmonic mode-locking schemes have recently emerged as the promising sources to provide stable, nearly transform-limited, and picosecond pulse with low timing jitter [6–8]. Previously, versatile gain- or loss-modulation schemes for mode-locking EDFL at high repetition frequencies were reported [9–11]. Alternative approaches using such as the fiber dispersion, the intra-cavity fiber Fabry-Perot filtering, and the optical-pulse-injection and all-optical-modulation have also been demonstrated [12–14]. In particular, the mode-locked EDFL pulse-train can also be generated by using gain-switched laser-injection and fiber-dispersion-based repetition-rate multiplication processes [15, 16]. In this work, we demonstrate the generation of photonic millimeter-wave clock signals at frequency up to 42 GHz by multiplying the repetition frequency of a harmonic mode-locked EDFL at 1 GHz. This is implemented by using a purely sinusoidal-wave modulated Fabry-Perot laser diode (FPLD) as both the mode-locker and the frequency multiplier. The intra-cavity FPLD is operated at below threshold condition to obtain harmonic and rational harmonic mode-locking from the EDFL. The performances of the millimeter-wave clock from the 42th-order frequency-multiplied EDFL are characterized.
2. Principle and experimental
The FPLD mode-locked EDFL is shown in Fig. 1. A commercially available, bi-directionally pumped EDFA with maximum gain of 17 dB is connecting with a 1560-nm single-mode-fiber-pigtailed FPLD via a 50% optical coupler (OC) to construct an EDFL ring cavity.
Instead of using an optical circulator, the OC-link connects the sinusoidal-wave modulated FPLD and the EDFL, which not only facilitates the fine-tuning of the optical power injected into the FPLD but also makes the system more cost-effective (at a penalty of larger insertion loss). A 35% output of the EDFL is monitored. The total cavity length is about 50 m, which corresponds to a fundamental cavity frequency of around 4.48 MHz. The FPLD is in series with a 47-ohm resistor for maximum modulation depth, which exhibits threshold current and longitudinal mode spacing of 13 mA and 1.2 nm, respectively. To achieve pure sinusoidal-wave modulation instead of lasing, the DC driving current of the FPLD is set at zero mA, which is then modulated at 1 GHz using a RF synthesizer (ROHDE&SCHWARZ SML01) in connection with a power amplifier. The mode-locked EDFL pulses are monitored by a high-speed photodetector (New Focus 1014, f3dB=45 GHz) in connection with a digital sampling oscilloscope (HP 86100A+83484A, f3dB>50 GHz), and by an optical auto-correlator (Femtochrome, FR-103XL) with temporal resolution of 7 fs.
It is found that the EDFL can be stably mode-locked with a large-signal modulated or gain-switched FPLD, in which the FPLD functions as both an optical mode-locker and a band-pass filter. The situation is completely different in our case since the sinusoidal-wave modulated FPLD (with RF power of 18 dBm) is not lasing (without sufficient DC and/or RF biasing) but in loss-modulation mode, as shown in Fig. 2. This has been confirmed since that the FPLD output is inconceivably small even after 21-dB optical amplification with an EDFA. The non-dc-current operation also excludes the possibility that gain-switching pulses generated from the FPLD, which could destroy the mode-locking mechanism of EDFL. Such a purely sinusoidal-wave modulated FPLD can thus be a cost-effective alternative to the conventional electro-optical intensity modulator for actively mode-locking the EDFLs. Subsequently, the perfect harmonic mode-locking of EDFL is achieved by adjusting the modulation frequency of the FPLD to precisely coincide with the harmonic frequency of the EDFL cavity, which leads to a completely symmetrical pulse shape output from the harmonic mode-locked EDFL. To achieve the frequency multiplication or rational harmonic mode-locking, the modulating frequency (fm) of the FPLD has to be detuned by fc/p apart from the harmonic frequency (nfc) of the EDFL, where fc is the fundamental EDFL cavity frequency, n and p are integers denoting the harmonic and rational harmonic orders of the EDFL, respectively. This leads to a frequency multiplied pulse-train with a repetition rate changing from (n+1/p)fc to (np+1)fc, which is exactly p times the detuned modulation frequency fm.
3. Results and discussion
The optimized FPLD mode-locking of the EDFL is obtained at a modulation power of 18 dBm, while the mode-locking pulsewidth and peak power of the EDFL are about 49 ps and 300 mW, respectively. The harmonic orders of the FPLD mode-locked EDFL is 228 (corresponding to frequency of 1.02 GHz). The harmonic mode-locking sustains when FPLD is driving with DC current of <1.5 mA and RF power of <21 dBm. The increasing in DC current of the FPLD inevitably results in the lasing of FPLD. This leads to the initiation of regenerative amplification process in the EDFL, while a secondary pulse-train grows behind the mode-locked pulse-train. As the FPLD changes from loss-modulation to gain-switching mode, the evolution between harmonic mode-locking and regenerative amplification mechanisms is observed in the EDFL. The secondary pulse is greatly amplified as the DC current of FPLD further increases to gain-switching threshold, which exhibit a very similar shape with that of the incident gain-switched FPLD pulse. Meanwhile, the mode-locked pulse intensity significantly decays due to the gain competition with the gain-switched FPLD pulse. The regenerative amplification process eventually suppresses the mode-locking mechanism due to gain competition effect. These observations corroborate the difficulty in harmonic mode-locking of EDFL using an optical-pulse-injection induced gain-modulation process.
The phenomenon of rational harmonic mode-locking is observed as the modulation frequency of FPLD detunes to match the equation fm=(n±1/p)fc, which results in the high-order frequency multiplication of the mode-locked EDFL pulse-train. The rational harmonic mode-locked pulse-trains with different p orders are shown in Fig. 3. For example, the modulation frequency for obtaining the second rational harmonic mode-locked EDFL pulse-train (n=228, p=2) is 1.017874 GHz, which is detuned from the perfectly harmonic mode-locking frequency by -2.253 MHz (approximately half of the longitudinal mode spacing of EDFL). As the rational harmonic mode-locking order extends to 10, the detuning frequency becomes only 448 kHz. The electrical spectra of the FPLD mode-locked and frequency-multiplied EDFL pulse-trains at repetition frequencies from 10 to 40 GHz is shown in Fig. 4. There are still lower harmonic components concurrently lasing with high-order frequency-multiplied pulses, which leads to an unequalized amplitude between adjacent EDFL pulses.
The highest rational harmonic mode-locking order of 42 is obtained by detuning the FPLD modulation frequency of about 106 kHz (see the inset of Fig. 5), however, the mode-locking pulse shape monitored by DSO is like a sinusoidal wave with relatively large DC offset. Such a poor extinction ratio of only 3 dB is mainly attributed to the limited bandwidth of the photodetector and the digital sampling oscilloscope. In frequency domain (see Fig. 6), it is understood that if the repetition frequency of harmonic mode-locked EDFL is up to 40 GHz, only the DC (f=0 Hz) and fundamental component (f=40 GHz) of the optical pulse can be accurately converted into an electrical signal, the high-order harmonics (f≥80 GHz) of the pulse are filtered out due to the finite bandwidth of the PD (see the inset of Fig. 6). To obtain a non-distorted pulse shape, the auto-correlation measurement is employed and a high-extinction-ratio EDFL pulse-train (dashed line in Fig. 7) can be observed. The peak and DC offset power of the rational harmonic mode-locked EDFL pulses at different repetition rates are plotted in Fig. 5. The average power of the mode-locked EDFL remains at 8.5 mW with tiny variation of <1%. The peak power is decreasing from 300 mW to 140 mW as the rational harmonic mode-locking frequency increases up to 42 GHz, while the DC offset power measured from the EDFL output has greatly increased from 2 to 7 mW.
Moreover, the peak amplitude of the adjacent pulses is still not equivalent at higher rational harmonic orders, which has previously been explained as the existence of unmatched lower rational harmonic components in the EDFL cavity . In addition, the oscillation and competition of independent supermodes with frequencies equivalent to the harmonics of the fundamental cavity mode could also lead to a strong fluctuation of the pulse amplitude. These can be simply overcome by inserting of an intra-cavity high-finesse Fabry-Perot filter with free spectral range exactly matching the repetition rate of the rational harmonic mode-locked EDFL pulses. As a result, the peak-amplitude equalized pulse-train is shown in Fig. 7 (solid line). The pulsewidth of rational harmonic mode-locked EDFL is reduced from 49 ps to 2.7 ps as the rational harmonic mode-locking order increases from 1 to 42 (see Fig. 8), which is found to be linearly proportional to the square root of the repetition frequency, (pfm)-1/2. It is known that as the modulation frequency detunes from that of the harmonic EDFL longitudinal mode, the pulse characteristics of the EDFL abruptly degrades. For example, the pulse shape of the harmonic mode-locked EDFL is significantly varied as the modulating frequency is detuned positively or negatively. The highest peak power is achieved at the exactly matched frequency (zero detuning) condition. The pulse reshaping effect is very sensitive to the detuning frequency even with a detuning step of 1 kHz. The peak amplitude of mode-locked EDFL pulse is gradually degraded and finally disappears with the increase of the detuning frequency. The maximum frequency detuning range is about 40 kHz.
The single side band (SSB) phase noise density and associated timing jitter of the rational harmonic mode-locked EDFL pulses are two important parameters for the photonic millimeter-wave clock signal generated from the FPLD mode-locked and frequency-multiplied EDFL. The fluctuation in cavity round-trip time usually occurs due to the thermally fluctuated optical path length, which could lead to a mismatch between the external modulation period and the cavity round-trip time and eventually degrade the mode-locking process. This is one of the principal phase noise sources in harmonic mode-locked EDFL without feedback control. For the harmonic mode-locked scheme, the SSB phase noise spectra of the corresponding pulses are shown in Fig. 9. At offset frequency of 1 kHz and higher, it is obviously that the uncorrelated SSB phase noise density for the FPLD mode-locked EDFL is relatively high since the FPLD has a larger amplified spontaneous emission noise when operated under loss-modulation scheme.
The FPLD mode-locked EDFL pulse has an SSB phase noise density less than -105 dBc/Hz at offset frequency larger than 1 kHz from the carrier. This corresponds to a timing jitter of 0.49 ps in the integral region from 10 Hz to 100 kHz. Note that the corresponding phase noise of the RF synthesizer is -122 dBc/Hz. Furthermore, the FPLD based frequency multiplier inevitably experiences an empirical law which confines the phase noise of conventional frequency multipliers. That is, the SSB phase of the rational harmonic mode-locked EDFL pulses would exhibit a 10▫log P2 increment for a given rational harmonic order P. Indeed, we have shown in Fig. 10 that the measured SSB phase noise density exhibits a linear relationship with the logarithmic repetition frequency, the noise density increases from - 105 dBc/Hz to -70 dBc/Hz as the rational harmonic mode-locking order increases from 1 to 42. This results in a nearly exponential rising in the associated timing jitter of EDFL pulses from 0.5 ps to 6 ps or larger. To improve the phase noise as well as the timing jitter performance at higher rational mode-locking orders, a regenerative mode-locking and/or a PZT-based feedback controlling schemes are required.
A rational harmonic mode-locked EDFL with repetition frequency up to 42 GHz and pulsewidth of 2.7 ps by using a purely loss-modulated FPLD as an optical mode-locker is demonstrated for the first time. Note that the FPLD is neither lasing nor gain-switching in contrast to conventional approaches. The harmonic mode-locking threshold of the EDFL is observed when the RF modulation power of FPLD is 18 dBm. The highest rational harmonic mode-locking order of 42 is achieved by slightly detuning the FPLD modulation frequency of 106 kHz. The millimeter-wave clock signal at 1 GHz generated from the FPLD mode-locked EDFL pulse exhibits SSB phase noise density of <-105 dBc/Hz and corresponding timing jitter of 0.5 ps. At clock frequency of 42 GHz, the phase noise density and jitter increases to - 70 dBc/Hz and 6 ps.
This work is supported by National Science Council of ROC under grants NSC92-2215-E-009-028 and NSC 93-2215-E-009-007.
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