1. Introduction

Optoelectronic oscillators (OEOs) generating microwave signals at high frequencies are important for a number of applications, such as communications, radar, and signal processing [1]. Typically, OEOs can generate low phase noise electrical and optical signals by storing the microwave energy in an optical delay line. However, conventional OEOs generally operate at frequencies below 10 GHz and are limited by bandwidth restrictions of the electrical components used [2]. This can be resolved by using frequency doubling techniques as shown in [3], although this requires additional elements such as electrical frequency dividers and optical amplifiers. Alternatively, semiconductor mode-locked laser diodes (MLLD) are relatively cheap and compact sources of ultra short (~1 ps), high intensity (> 10 mW), and high frequency optical pulses at repetition rates exceeding 100s of GHz [4,5]. Quantum well (QW) materials in particular are excellent platforms for fabricating MLLDs; however, their susceptibility to spontaneous emission noise and inter-cavity losses makes them prone to broad linewidths and therefore substantial phase noise [6]. At present, various methods are used to reduce the phase noise by synchronizing the pulses to an external radio frequency (RF) electrical clock via hybrid [7] or synchronous mode locking [8], although these require a high frequency electronic drive applied to the active optoelectronic device being used which can limit the maximum oscillation frequency.

Alternatively, a passive feedback technique known as regenerative mode locking can be employed to stabilize the pulse train by extracting the carriers via photodetection, to which high-Q RF filtering and amplification is applied to enhance the signal before it is fed back into the saturable absorber (SA) using a bias-T, along with a reverse bias voltage [9]. These RF components can be costly, and furthermore, are restricted to operate within finite frequency bands. Nevertheless there are a number of reports on all-optical regenerative feedback techniques that are less constrained by frequency limitations. In [10], K. Mergham, et al. proposed an all-optical noise reduction method based on external feedback into a 17 GHz quantum-dash MLLD. The stability of the laser was improved and a RF linewidth of 500 Hz was observed over a wide biasing range, although the use of an external fiber cavity produced additional RF resonances due to superfluous modal interactions, giving rise to large amplitude and phase fluctuations separated in frequency by a distance corresponding to the length of the external fiber cavity. These often occur in fiber based harmonic mode locking and are known as supermode noise resonances [11]. More recently, C. Lin, et al. [12] characterized the RF linewidth using a similar feedback system with a quantum-dot based passive MLLD operating at 5.1 GHz. A RF linewidth of 350 Hz was achieved using a dielectric coated fiber with high reflectivity to induce the feedback with precise matching of the external cavity length. From the experimental results it was evident that the signal feedback intensity was an important function which influenced the level of noise reduction. In both reports, relatively low feedback levels (−22 dBm and −36 dBm, respectively) were used to obtain sub-kHz RF linewidths. Furthermore, these optical feedback experiments employed costly quantum-dot and –dash based MLLDs, which are less noisy in general due to lower intracavity losses and a larger differential gain than in QW based lasers [13], leading to exceptionally low noise levels when feedback is applied. Similar extended cavity feedback arrangements can also be found in [14–20].

Whilst low RF linewidths are relatively easy to achieve using optical feedback techniques, the associated supermode noise resonances can influence the phase noise at the sidebands of the RF resonance peak and subsequently affect the timing jitter. There are a number of methods used to suppress the supermode noise, such as those used in harmonically mode-locked fiber lasers [21–24]. In this work, we present an alternative feedback technique to reduce the RF linewidth of a QW based MLLD using a dual optical feedback loop configuration for supermode noise suppression. Dual feedback loops have been extensively studied and demonstrated for the stabilization of supermode noise in optoelectronic oscillators and fiber ring lasers in particular [21,22,25–27]. An additional ‘composite cavity’ loop is used, of which the associated cavity modes coincide with the fundamental fiber cavity modes at large multiples of the free spectral range (FSR), thereby reducing the number of harmonic modes oscillating in the fiber cavity and lessening the mode beating effects [21,22]. Here, this technique is implemented for stabilizing MLLD feedback, and supermode noise levels are subsequently reduced to less than −100 dBm, and a timing jitter of 340 fs (10 kHz – 100 MHz) is achieved. We also investigate the effects of the RF linewidth reduction as a function of the feedback cavity length. It is known that the linewidth is reduced as the external feedback length increases since more of the optical energy is stored in the system. The feedback signal intensity is also a crucial parameter for optimizing the RF linewidth, as shown in previous reports [10,12], where a larger feedback ratio is needed for maximum effect on the linewidth reduction, although lower feedback levels are desirable for relaxing packaging conditions. The characterization of the feedback signal intensity is therefore presented using various external cavity lengths, and it is shown that the linewidth is reduced to sub-kHz using moderate feedback intensities (−26 dBm) and longer fiber lengths within the coherence length limit. Using the proposed feedback technique, a minimum measured RF linewidth of 192 Hz is achieved using a 66 m long dual loop external cavity at a 20 GHz pulse repetition rate, which is the lowest reported linewidth of any high frequency (>1 GHz) passively operating MLLD to date, making it useful for high frequency OEOs and other ultra-low noise applications.

2. Experiments and results

The experimental setup is shown in Fig. 1(a) . A 20 GHz two-section MLLD, fabricated on a three-QW AlGaInAs/InP epitaxial structure was used for this experiment [28]. The output pulses of the laser were coupled into a lensed fiber which was fed through a circulator to minimize back reflections from component interfaces, as well as ensuring a unidirectional operation. A 3 dB fiber coupler was then used to split the output into two paths, one towards an optical delay line, and the other towards a dispersion shifted erbium doped fiber amplifier (EDFA) followed by a length of dispersion shifted fiber (DSF) (for maximizing the fiber loop length, without severely compromising the dispersion) before being recombined via a second 3 dB fiber coupler. Due to the large fiber losses resulting from the different core size between the single mode fiber (SMF) and DSF, the EDFA pump was required to operate with high gain (>15 dB) to compensate for the fiber losses. The signal was then fed into an optical attenuator before being coupled back into the SA end of the MLLD cavity for direct pulse modulation. A polarization controller was positioned to ensure the injected signal was TE polarized in order to promote better carrier coupling effects in the compressively strained QWs. The additional output of the 3 dB coupler was used for subsequent signal and spectral analysis. The total length of the inner fiber loop was ~22 m, and the outer fiber loop was ~66 m, of which ~48 m was dispersion shifted (via the EDFA, attenuator, and an additional length of DSF), resulting in a total dispersion of approximately 200 fs/nm.

 

Fig. 1 (a) Experimental configuration of the dual optical feedback loop. (circ.: optical circulator, atten.: optical attenuator), and (b) schematic diagram representing the alignment of modes in outer loop, inner loop, MLLD, and resulting output.

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The laser was passively mode-locked when the gain section was forward biased with 83 mA and the SA section was reverse biased with 2.9 V (at which the threshold current was 50 mA). The resulting output as viewed on a RF spectrum analyzer (R&S® FSV40) via a high speed photodetector (u²t Photonics XPDV2020R) matched up to 50 GHz is shown in Fig. 2(a) (red trace). The 3 dB linewidth was 155 kHz with a single-side-band (SSB) phase noise of −77 dBc/Hz at a 1 MHz offset. The corresponding root mean square (RMS) timing jitter can be calculated by integrating the SSB phase noise, which is shown in Fig. 2(b), and was calculated as 4.7 ps (integrated from 10 kHz – 100 MHz). Figure 2(c) shows the output of the optical feedback loop with an uncorrelated composite cavity length, (i.e. the modes associated with the inner loop were not aligned to the modes of the outer loop). When the composite cavity length was optimized using the variable optical delay line, such that every third mode of outer fiber loop was overlapped with a mode of the inner fiber loop i.e. ~22 m (see Fig. 1(b)), the peak power of the supermodes were reduced to less than −100 dBm (Fig. 2(d)). The subsequent linewidth of the signal at the output of the fiber loop is also shown in Fig. 2(a) (blue trace) for a comparison, with the MLLD operating under the same conditions as when passively mode-locked. The linewidth was reduced to as little as 192 Hz, with a SSB phase noise of −113 dBc/Hz at an offset of 1 MHz, and the integrated RMS jitter was calculated as 340 fs (integrated from 10 kHz – 100 MHz). When the outer and inner loop modes were misaligned, the linewidth was increased to 490 Hz. A comparison of the optical spectra and pulse width for the free-running laser (red) and with aligned feedback (blue) is shown in Figs. 3(a) and 3(b), respectively. The 3 dB bandwidth of the free running MLLD was 6.2 nm, and the pulse width was 0.9 ps. Due to the chromatic dispersion of the fiber loop, other than the DSF, the 3 dB bandwidth at the output of the optical feedback loop was 5.9 nm, and the pulse width was 2.1 ps. The pulses in both instances were free from Q-switching instabilities and pedestal modulation. The average output power coupled out of the free running MLLD was 1 dBm, and the feedback intensity was −26 dBm, assuming a lensed fiber coupling efficiency of 50% [28]. The output power of the oscillator was −8.5 dBm, measured at the output port of the 3 dB coupler.

 

Fig. 2 (a) RF spectrum of MLLD signal with aligned feedback (blue trace) and free running (red trace). (inset: 40 GHz RF span, free from Q-switching instabilities), (b) corresponding SSB phase noise, (c) the misaligned composite cavity length resulting in large supermode noise resonances, and (d) optimized (aligned) composite cavity length resulting in supermode noise suppression. (RF spectra were measured using 20 Hz resolution bandwidth and 10 Hz video bandwidth).

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Fig. 3 (a) Optical spectrum of MLLD with aligned feedback (blue trace) and free running (red trace), and (b) corresponding autocorrelation traces measured using second harmonic generation autocorrelator.

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From general oscillator theory it is known that as the length of the delay is increased, so too is the Q-factor of the oscillator, which reduces the RF linewidth accordingly. This effect was studied by interchanging the DSF lengths in this experiment to provide a comparison of the RF linewidth using 28.5 m, 39.9 m, 51.1 m, and 66 m long fiber loop cavities. To ensure the intensity was uniform across all measurements, the inner composite cavity loop was disconnected and the signal intensities were matched at −26 dBm at the interface between the attenuator and lensed fiber. The results are plotted in Fig. 4(a) . The narrowest linewidth (432 Hz) was acquired using a 66 m long fiber, whereas the widest linewidth (3.628 kHz) was measured using a 28.5 m long fiber. These results are consistent with the model in [29], which supports that the linewidth is proportional to 1/L (where L is the fiber length).

 

Fig. 4 (a) Main: RF spectra of MLLD signal with feedback using different fiber lengths. Inset: RF linewidth vs. inverse feedback loop length (1/L) measured with a feedback signal intensity of −26 dBm (black squares); corresponding linear fit (red), (b) RF linewidth values of MLLD with feedback as a function of the feedback signal intensity plotted in a logarithmic scale for different fiber lengths (listed in figure). Inset: RF linewidth vs. feedback intensity plotted in a linear scale for 66 m long fiber loop.

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Furthermore, it is evident that as the feedback power was reduced the RF linewidth was widened. Figure 4(b) shows the relationship between feedback power and linewidth. The lowest RF linewidths were obtained at the maximum feedback value, which was limited to −26 dBm in these experiments. As the feedback intensity was reduced, the linewidth was gradually increased to ~6 kHz until the feedback intensity fell below ~-40 dBm, at which point the linewidth increase was more sudden and tended towards that of the MLLD without feedback, indicating the lowest intensity required to sufficiently reduce the linewidth. This is consistent with the results obtained in [10] and [16]. At feedback levels below −34 dBm, some discrepancies were observed in the 1/L trend, which are due to the feedback intensities approaching their lower limit.

Recent reports have shown however that using higher feedback intensities can also have a detrimental effect on the linewidth and stability of the feedback system [19,30]. This may be due to the coherence collapse regime [31], which is the dominating influence of spontaneous emission in the system by fluctuations stimulated by the loss of coherence. This severely degrades the mode locking performance by disturbing the phase locking relation between the longitudinal modes. Therefore, to address this issue and find the upper limit of feedback intensity a similar experiment was carried out using only a 20 m long outer loop fiber consisting of SMF and a dispersion shifted EDFA to attain more feedback power. Using this configuration it was found that by applying feedback intensities up to 3 dBm would maintain an adequate linewidth reduction (<10 kHz) via optical feedback. However, applying intensities >3 dBm would cause severe instabilities. The linewidth was dramatically increased and the supermode noise spurs were spread further in frequency, separated by a distance corresponding to the fiber length (i.e. ~10 MHz), by a span of ~2 GHz around the pulse repetition frequency with each spur at the same intensity resembling a RF frequency comb. This may have been due to the greater overlap of modes in the FSR caused by an increase in both the laser and EDFA gain, giving rise to additional beat tones across the RF band as a result of operating in the coherence collapse regime, although a further investigation is required in order to fully understand this behavior. On observation of the signal on a SHG intensity autocorrelator, it was shown that the pulse quality had deteriorated and a large pedestal modulation (>50%) was observed.

During these experiments it was observed that the long term stability of the proposed system was compromised by mechanical and thermal instabilities in the fiber causing small changes in the optical path length, and thus frequency, over time. Since no cavity length stabilization mechanism was in place, the supermode noise suppression via the composite cavity was established only for a few minutes until retuning of the inner loop cavity length was required. This will become increasingly problematic when using longer lengths of fiber; although, the use of a dynamic differential feedback mechanism as shown in [21] and [32], may be used to counteract the path length changes and greatly improve the stability of the system. Moreover, the high EDFA pump gain would have increased the level of noise in the system due to amplified spontaneous emission, and it is therefore assumed that the RF linewidth and phase noise may be reduced further by reducing the losses associated with the fiber mismatch so that a reduction of the EDFA gain can be accommodated.

3. Conclusions

To summarize, an alternative method for reducing the phase noise and RF linewidth of a passively operating MLLD using an optical dual loop feedback delay line has been proposed and demonstrated. A composite cavity loop, based on those proposed and studied in [21,22,25–27] was incorporated into the experimental setup to reduce the effects of supermode noise and further reduce the timing jitter. Using the proposed technique, we have acquired an extremely low RF linewidth of 192 Hz and a low RMS jitter at 340 fs (integrated from 10 kHz – 100 MHz) using a 20 GHz QW-based MLLD. The acquired RF linewidth is the narrowest reported to date for any high frequency passive MLLD operating above 1 GHz (to the best of the authors’ knowledge), making this system promising for the development of compact, high frequency, low cost and low noise OEOs.