1. Introduction

Optical frequency combs have become indispensable tools for precision frequency metrology [1–4]. Additionally, frequency combs have been applied to a number of other disciplines, such as attosecond physics, optical atomic clocks, and high fidelity microwave generation [4–10]. While frequency combs were initially developed using solid-state, mode-locked lasers, fiber-based frequency combs quickly became an attractive alternative due to their low cost, alignment free operation, and insensitivity to environmental perturbations [8,11]. Unfortunately, fiber-based frequency combs have historically suffered from worse phase noise performance as compared to their solid-state counterparts (see for example [12–14]). While sophisticated laser designs and electronic feedback systems have now greatly increased the achievable coherence of fiber-based frequency combs [15–21], a continued decrease in phase noise is beneficial for many applications. As an example, we require a frequency comb for coherence transfer and as an optical frequency reference for high precision studies of atomic hydrogen – applications that will benefit tremendously from increased coherence and stability.

A common way to improve the coherence of frequency combs is through increasingly fast frequency feedback loops [17–21]. However, many available frequency actuators often operate on a linear combination of the two degrees of freedom of the frequency comb – f_ceo and f_rep [22]. As a result, a fast f_ceo feedback loop can interfere with the f_rep loop, or vice-versa. Therefore, it is also attractive to investigate the origin of the noise and to suppress it at its source. It has been shown for erbium fiber frequency combs, the pump diode’s relative intensity noise (RIN) can be a major contributor to the laser’s phase noise, and reducing the pump diode RIN may result in improved phase noise performance [23,24]. Later, it was shown in two Ytterbium-based fiber frequency combs that there are other significant contributions to amplitude noise [25,26], which in turn couple to phase and frequency fluctuations [27]. Some of these other contributions include amplified spontaneous emission (ASE), fluctuations in cavity loss, vacuum field fluctuations entering through the output coupler, and gain medium dipole fluctuations [28]. For these Yb-systems, suppression of the comb RIN was shown to directly reduce the phase noise of an individual comb tooth [25] and of the f_ceo frequency itself [26]. Since the quantum noise sources in these systems were non-negligible, it was more effective to suppress on the amplitude noise of the frequency comb itself as, even in the limit of a perfectly quiet pump laser, the quantum noise sources would remain.

In this work, we apply an amplitude noise servo to a mode-locked, erbium-fiber frequency comb. Erbium-based frequency combs are of particular interest due to the wide availability and low cost of the telecom components necessary for their construction. While it may be expected that the long upper state lifetime of erbium, as compared to ytterbium, would greatly limit the bandwidth of the RIN servo, we demonstrate a 550 kHz bandwidth with a carefully designed feedback loop. Additionally, our results indicate that quantum noise sources contribute significantly to the amplitude noise of the comb. Due to the strong correlation of amplitude and phase noise in our frequency comb, we find that reducing the amplitude noise of the frequency comb simultaneously reduces the residual phase noise on the f_ceo frequency lock and a comb tooth near the center frequency of 1555 nm. These results show that a simple frequency comb design, with an amplitude noise (RIN) servo, can achieve near state-of-the-art phase noise performance for an erbium fiber frequency comb.

In contrast to previous applications of RIN servos for Yb:fiber frequency combs [23,24], the f_ceo phase lock and the RIN servo both actuate on the pump current simultaneously using a simple summation circuit. Our analysis of this composite lock shows that this scheme is advantageous as it effectively stabilizes the f_ceo lock and enables an increase in the feedback gain. This can be understood because, while RIN and the f_ceo are highly correlated, the RIN can generally be detected with much smaller line delays as compared with f_ceo since the latter usually requires amplification, spectral broadening, and extra signal conditioning. Therefore, by utilizing the RIN information for the highest feedback frequencies, the locking bandwidth can be extended. Employing this composite feedback technique results in 270 mrad and 44 mrad integrated phase noise on f_ceo and f_beat respectively. This result is competitive with other state of the art erbium fiber frequency combs. For example, the frequency comb in [20], which is based on a nonlinear amplifying loop mirror, has demonstrated integrated phase noise of 160 mrad and 130 mrad on f_ceo and f_beat respectively. Additionally, we believe this composite feedback technique could be used in conjunction with fast frequency actuators, such the loss modulation in [19,20], for even greater feedback gain and bandwidths than shown here. Therefore, we believe this demonstrates a generally useful strategy for improving f_ceo lock performance in fiber frequency combs.

2. Laser configuration

Our frequency comb begins with a mode-locked, erbium fiber laser in a linear cavity arrangement, as shown in Fig. 1. Mode-locked operation is achieved via a commercial 2 ps lifetime, semiconductor saturable absorber (SA). The SA has a 15% modulation depth and 10% non-saturable loss. All optical fiber in the oscillator is anomalously dispersive with a round trip dispersion of ~-7000 fs², which promotes stable soliton mode-locking [29]. The oscillator is pumped with a 976 nm laser diode through an optically coated FC/PC connector coupled to an uncoated FC/PC connector. The coated connector has a reflectivity of 80% at 1550 nm but has high transmission at 976 nm. This cavity design was implemented for its simplicity. Such designs are compatible with all polarization maintaining fiber, and have demonstrated robust performance outside the laboratory [30].

 

Fig. 1 Schematic layout of laser system. SA, Semiconductor saturable absorber mirror; PZT, piezoelectric transducer; BW, Brewster Window; HWP, half wave plate; EDF, erbium doped fiber; OC, output coupler; WDM, wavelength division multiplexer; LD, 976 nm laser diode; PD, photodiode; RIN, relative intensity noise servo; Iso, optical isolator; HNLF, highly nonlinear fiber; CW, continuous wave, single mode laser; BPF, optical bandpass filter; PPLN, periodically-poled lithium niobate.

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Since the noise performance of mode-locked lasers is also correlated with the pulse duration [31,32], the cavity design favors broader spectral operation [33]. The fiber section of the cavity is 31 cm to minimize dispersion and reduce nonlinear phase shifts to prevent destabilization. The rest of the oscillator is free space to ensure appropriate SA saturation, resulting in a repetition rate of $\approx$ 115 MHz. The output of the laser is 10 mW with a spectral bandwidth of ≈16 nm, indicating a bandwidth-limited pulse duration of ~170 fs for a sech² distribution. We believe that the spectral output of this laser is currently limited by the lifetime of the SA [33].

The output of the oscillator is sent to an amplification stage for f_ceo detection. The amplifier is composed of erbium-doped fiber, which is pumped by a pair of 700 mW, 976 nm diodes in the forward and backward directions. After amplification, the average power is $\approx$ 270 mW, and the spectrum is broadened to 60 nm of bandwidth. The pulse train then enters a length of SMF-28 to recompress the pulse before 22 cm of highly nonlinear fiber (HNLF). An octave of bandwidth is achieved after the HNLF, spanning 960–2100 nm. The light is then guided to an f-to-2f interferometer, as shown in Fig. 1, for f_ceo detection. For f_ceo stabilization, the pump current is actuated.

3. RIN servo

In order to effectively suppress the comb’s relative intensity noise, RIN_comb, it is critical to first determine its origin. If RIN_comb is found to originate exclusively from pump diode intensity noise, RIN_pump, then reducing the pump noise would clearly be the most effective strategy. However, if other noise sources, such as ASE, also contribute significantly, then direct detection and suppression RIN_comb is more effective.

To determine the contribution of RIN_pump to RIN_comb, we first measured the amplitude response of the comb to pump diode fluctuations, $H\left(\omega \right)$ . The comb’s amplitude noise which is due to the pump diode fluctuations only, RIN’, can then be determined through.

While determining the amplitude noise of the pump diode, it was found that our particular pump diode operates in two distinct noise regimes, one much noisier than the other. We attribute the regime shift to the laser diode switching between multiple and single longitudinal mode operation. The regime shifts appears to occur randomly, and the pump diode is generally in the noisy regime. While the pump diode is only infrequently in the quiet regime, it is useful for determining what level the amplitude noise of the comb is due to quantum noise sources, as the pump diode noise contribution is less prominent. In the noisy regime, RIN_pump determines the noise up to $\approx$ 200 kHz, and in the quiet regime, $\approx$ 80 kHz. This performance is shown in Fig. 2(a) and Fig. 2(b).

 

Fig. 2 (a) RIN_comb vs RIN’, noisy regime. The dotted line (200 kHz) indicates end of pump limited intensity noise. (b) RIN_comb vs RIN’, quiet regime. The dotted line (80 kHz) indicates end of pump limited intensity noise. (c) Measured intensity noise for both quiet and noisy regimes, as well as with the RIN servo active. (d) f_ceo with the RIN servo on and off (421 and 811 mrad r.m.s. phase noise respectively).

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Since our results show that noise sources other than RIN_pump also significantly contribute to RIN_comb, our servo detects and reduces RIN_comb directly. As shown in Fig. 2(c), the servo actively suppresses the noise beyond the limit set by RIN_pump alone. The effect of the amplitude noise servo on f_ceo is shown in Fig. 2(d). Integrating from 10 Hz to 1.5 MHz, we measure 811 mrad integrated phase noise with the RIN servo off, and only 421 mrad with the servo active. This is an improvement of 51% to 84% power in the coherent spike in the f_ceo lock, indicating that amplitude noise and phase noise are highly correlated within the oscillator.

4. Composite error signal phase locking

The results shown in Fig. 2(d) were obtained by optimizing the f_ceo frequency lock, and then engaging the RIN servo. As shown in the figure, the RIN servo clearly increases the coherence of the f_ceo lock. However, at Fourier frequencies between 10 kHz and 100 kHz, there is an increase of noise with the RIN servo engaged. This is an artifact of the feedback scheme since the RIN servo and the frequency lock both modulate the same degree of freedom (the pump current). Therefore, the two may interfere when the gain of both feedback loops are comparable. This suggests that improved performance can be obtained by adjusting the gain and corners of these two loops in concert.

To optimize the performance, we consider the RIN servo and the f_ceo frequency lock together as a single composite feedback loop. This feedback loop has an error signal in which both the detected RIN and the f_ceo error contribute. We analyze a simple model of this composite lock, pictorially depicted in Fig. 3(a). The detected RIN is conditioned with an ideal proportional amplifier and the frequency error is conditioned by a proportional-integral amplifier. Then, the signals are summed, and fed to the pump diode. The laser oscillator responds as a low pass filter, so an additional low pass term is applied to both the RIN servo and frequency lock. In Fig. 3(b) and Fig. 3(c), the gain and phase response of the modeled feedback loops are plotted, including the composite transfer function. The total transfer function is dominated by the RIN signal at frequencies above 40 kHz, so the phase margin at unity gain is determined entirely by the RIN information. This is advantageous due to the smaller phase delays of the RIN servo. Therefore, when compared with a feedback loop based only on the f_ceo, signal, the gain of the composite loop can be increased. Optimizing the composite lock as shown in Fig. 3 results in the stabilized f_ceo as shown in Fig. 4(a).

 

Fig. 3 (a) Schematic of RIN servo and fceo Frequency lock model. Δt, 50 ns line delay; PD, Photodetector; Syn., digital frequency synthesizer; PI, Proportional-Integral Amplifier; δt, 10 ns line delay; P, Proportional amplifier; LD, pump laser diode; Oscillator, laser oscillator. Dashed lines delineate subsystems of the system (feedback loops and the laser oscillator). (b) Model amplitude response of the frequency lock, RIN servo, and composite signal (c) Model phase response of the frequency lock, RIN servo, and composite signal showing the increased phase margin obtained by utilizing the RIN information.

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Fig. 4 (a) Final measured in-loop RF spectrum of fceo (1 kHz RBW) (b) Measured Inloop RF spectra of fbeat with composite lock on and off (1 kHz RBW).

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Integrating from 10 Hz to 1.5 MHz, the total integrated phase noise is 270 mrad with 93% of the power in the coherent peak, which is a significant improvement over the performanceshown in Fig. 2(d).

While utilization of this composite locking technique ultimately produces a more robust f_ceo frequency lock, it should not be forgotten that it also has the net effect of reducing RIN_comb, which is anticipated to also reduce the phase noise across the comb structure. We tested this by simultaneously phase locking a single comb mode to a homebuilt, cw-laser at 1550 nm. The homebuilt cw-laser is estimated to have a linewidth less than 20 kHz, and has a power output of 2 mW. The phase lock is achieved via actuation of two intracavity PZT’s; one for fast feedback with a smaller modulation depth, and another with a large modulation depth for slow drifts. The effect of the composite lock on the beat frequency, f_beat, between the single comb mode and the cw laser is shown in Fig. 4(b). The integrated phase noise on f_beatdrops from 166 mrad to 44 mrad by activating the composite lock. Since the phase noise of both the degrees of freedom of the comb, f_ceo and f_beat, are reduced, this result indicates that the coherence of the entire comb structure is increased by utilizing the composite feedback loop.

5. Conclusion

To summarize, we have achieved highly coherent phase locks on both of the frequency comb’s degrees of freedom. Amplitude noise suppression in the comb results in substantially improved coherence of the comb, indicating that there is a strong correlation between amplitude and phase fluctuations. Also, we have shown that reduction of pump diode fluctuations alone is ultimately less effective than directly suppressing the comb RIN. Because phase noise and amplitude noise are highly correlated, a composite feedback scheme allows for a large locking bandwidth of 550 kHz on f_ceo without fast frequency actuators, leveraging the minimal line delay in RIN detection. This simple feedback scheme should be compatible with other mode-locking mechanisms, e.g. non-linear polarization rotation or Sagnac loop initiated mode-locking [17,18], indicating that this technique could further improve the coherence of many other optical frequency combs.