1. Introduction

The fs frequency comb has proven to be a powerful tool in both precision spectroscopy and ultrafast science. By providing a direct phase coherent link between optical and microwave frequencies it has dramatically simplified the measurement of optical frequencies while simultaneously enabling access to sub-cycle (i.e. attosecond) control and synchronization of optical fields. Its impact continues to grow in many areas of science and technology as new applications develop. Although originally demonstrated using bulk solid-state lasers, passively mode-locked fiber-based lasers have become a reliable source for generating fs frequency combs, with near turn-key operation and long term performance capability. Many demanding “high performance” applications necessitate minimal noise in the frequency comb structure, requiring narrow linewidth comb components with low phase noise at optical frequencies, and/or low jitter of the carrier-envelope phase in the time domain.

Passively mode-locked fiber lasers utilizing non-linear polarization evolution (NPE) or incorporating a fast semiconductor saturable absorber mirror (SESAM) have demonstrated free running carrier-envelope offset frequency (f_ceo) linewidths of ~10 kHz [1,2]. With active stabilization, the phase of f_ceo can be controlled with <1 rad rms error in these systems, enabling sub-Hz f_ceo linewidths with over 90% of the power in the optical carrier. Such systems represent current state-of-the-art performance in fiber based frequency combs. Fiber lasers based on these designs often require free-space sections in the oscillator and/or incorporate many polarization control components, making them less amenable to simple, inexpensive and robust all-fiber oscillator designs. Similar performance levels in a simplified all fiber design would be advantageous as the use and applications for the frequency comb continue to expand. A recent paper demonstrated that fs fiber lasers utilizing carbon nanotubes (CNTs) as a fast saturable absorber (SA) for mode-locking offer a convenient system capable of generating phase-stabilized frequency combs [3]. In that work, the free running f_ceo linewidth of ~600kHz indicates a large amount of noise intrinsic to the fiber laser system. With active stabilization, this noise can always be suppressed, but only by a finite amount ultimately determined by the feedback-loop bandwidth. In this paper, we investigate the performance of a fiber frequency comb based on a tapered-fiber CNT design (tf-CNT) [4]. We identify and minimize noise sources to show that these systems can operate with free-running f_ceo linewidths of only ~20 kHz with sub-radian phase control of f_ceo possible using active stabilization. An intra-cavity piezo-electric transducer with a bandwidth up to 20 kHz was also available as a fiber stretcher to control the laser cavity length for locking the laser repetition rate. In this paper, we focus our study solely on the noise sources and stabilization of f_ceo to show that the tf-CNT frequency comb offers low noise performance in a simple, compact, and robust design.

2. Experimental setup

A schematic diagram of the tf-CNT fs frequency comb is shown in Fig. 1 . The oscillator was provided by Kphotonics. The basic design is similar to that reported in [4]. An intracavity polarization controller (not shown in Fig. 1) is used to ensure a repeatable and stable polarization of the laser output. As the cavity contains no polarization sensitive components, the present system should be amenable to an all polarization-maintaining fiber design. We obtain ~3 mW of average power in the single pulsing regime at a repetition rate of 42 MHz. A typical spectrum for the final configuration is shown in the inset of Fig. 1. The output from the tf-CNT laser is sent through an inline fiber-coupled acousto-optic modulator (AOM) configured to transmit the first-order diffracted beam (< 2 dB loss). In this configuration, the modes of the frequency comb are equally shifted by exactly the AOM driving frequency (80 MHz ± 5%), enabling direct control of f_ceo external to the laser cavity without affecting the laser repetition rate. This approach enables high bandwidth feedback control with a simple servo design, not limited by details of the laser. Specifically, we are not limited by the erbium gain lifetime which is known to limit the feedback bandwidth to ~10’s kHz when using the pump laser power to control f_ceo [5,6]. No significant decrease of the laser spectral bandwidth was found in transmission, though slight distortion of the overall shape was observed. To minimize potential intensity modulation related to the radio frequency dependent diffraction efficiency of the AOM, we limited the range of f_ceo correction to < 1 MHz. Although an AOM has previously been used for directly controlling and stabilizing f_ceo in Ti:sapphire laser systems [7,8], it is particularly useful in fiber systems as it can help to increase the servo bandwidth and is, to the best of our knowledge, the first time one has been incorporated into an all fiber design. The pulse train transmitted through the AOM is amplified in a single stage amplifier to ~100 mW. We use a single mode fiber (SMF28) having anomalous dispersion to compress the pulses. A short segment (~5cm) of highly nonlinear fiber (HNLF) was spliced directly to the SMF28 compression fiber to generate the octave bandwidth needed for detection of f_ceo. The design of the amplifier, compression stage and supercontinuum generation was reported in Ref. [9]. Due to the stable mode-locking and all fiber design, we observe very broad and smooth supercontinuum at the output of the HNLF extending from about 1 μm to beyond 2 μm. In previous work, we have shown that this continuum can be reliably compressed to near the Fourier-transform limit to generate sub-20 fs pulses centered near 1300 nm [9], or as a convenient source of ~110 fs pulses centered near 1040 nm for efficient amplification in Yb gain fiber [10]. Here, we couple the output from the HNLF to free space for detection of f_ceo. The portion of the spectrum near 2 μm is phase-matched for second harmonic generation in a 1 cm long sample of periodically-poled lithium niobate (PPLN) which interferes with the original spectrum near 1 μm. An interference filter selects the overlapping portion of the “f” and “2f” spectra and the f_ceo beatnote is detected using a silicon avalanche photodiode. Due to the short length of the HNL fiber, no delay line or other spatial separation of the beam was necessary to temporally overlap the pulses selected from 1 μm and 2 μm spectral regions. We note this system can easily be integrated into a truly all guided design as demonstrated in [11] by using a commercially available fiber coupled PPLN sample.

 

Fig. 1 Schematic layout of tapered fiber CNT based fiber frequency comb. OC: output coupler; AOM: acousto-optic modulator; WDM: wavelength division multiplexer; EDF: erbium-doped fiber; HNLF: highly nonlinear fiber; f-2f: nonlinear interferometer for detection of the carrier envelope offset frequency. Inset shows output spectrum of laser before the broadening in the HNLF.

Download Full Size | PDF

3. Characterization and stabilization of f_ceo

By observing the free-running linewidth of f_ceo, one can assess the level of noise perturbing the evolution of carrier-envelope offset phase. Noise contributions arise from both external environmental perturbations as well as from more fundamental quantum limitations in the mode-locking process [12,13]. In previous work, it has been shown that excess amplitude modulation (AM) noise from the pump laser can be a dominant source of instability and broadening of the f_ceo linewidth in both solid-state and fiber laser systems [5,6,14,15]. In fiber lasers pumped by fiber Bragg-grating (FBG) stabilized diodes, the AM noise can be attributed primarily to noise in the diode laser power supply [6]. We have observed this coupling of AM to phase noise in the free running linewidth of the tf-CNT fiber laser. The residual intensity noise (RIN) from the pump diode can be reduced when operated at higher powers in combination with appropriate optical attenuation before the fiber laser. This effect is due to the decreased fractional amplitude fluctuations of the current supply when operating the diode laser at higher currents. Figure 2(a) shows the measured free-running linewidth of f_ceo as a function of the diode current when using a FBG pump diode. The pump power incident on the tf-CNT fiber oscillator was kept fixed at each point using optical attenuation. The free-running f_ceo linewidth was determined at each point using a Lorentzian fit to the data. Our results are in good qualitative agreement with those in [6], where the observed free-running f_ceo linewidth is reduced to below the 100 kHz level simply by minimizing the RIN from the pump diode in this way. In general, we have found a large variation in current noise from the power supplies of different models and manufacturers.

 

Fig. 2 (a) Measured linewidth of f_ceo versus current to pump laser diode. Optical power was attenuated at each data point to maintain a constant pump power. (b) Measured f_ceo beatnote for two different laser cavity configurations producing laser spectral bandwidths of 12 nm and 30 nm (full-width at half maximum). The resolution bandwidth (RBW) for each was 100 kHz. VBW: video bandwidth.

Download Full Size | PDF

The original laser used to obtain the data shown in Fig. 2(a) had a FWHM spectral bandwidth of ~12-15 nm. By minimizing the pump laser RIN, we were able to observe free-running f_ceo linewidths <100 kHz (FWHM) similar to that shown by the black solid curve in Fig. 2(b). Further reduction of the f_ceo linewidth for this laser was not possible with isolation from external perturbations alone. The laser cavity was modified to produce a broader spectral bandwidth by reducing the net cavity group-delay dispersion (GDD) and utilizing a SA with increased modulation depth. A typical spectrum of ~30 nm FWHM is shown in the inset of Fig. 1. Only recently has similar broad bandwidth performance been obtained with CNT based mode-locked fiber lasers utilizing stretched-pulse dispersion compensation designs [16,17]. These changes to the fundamental properties of the laser resulted in a greatly improved free-running f_ceo linewidth, particularly in the wings as shown by the dotted (red) curve in Fig. 2(b). It is known that quantum limitations to the timing jitter and phase noise can sensitively depend on parameters such as the intra-cavity pulse evolution, spectral bandwidth and cavity dispersion [12,13,18,19]. A more systematic investigation on the dependence of timing and optical phase noise in this laser system for different oscillator configurations will be the focus of future work.

The slowly drifting f_ceo beatnote typically exhibits a ≈20 kHz linewidth. A >35dB signal-to-noise ratio (SNR) is observed with a RBW of 100 kHz (see Fig. 4(a) ). Instabilities or fluctuations in the background noise floor due to Q-switching or noise in the continuum generation process were not present. The offset frequency was phase locked to a RF local oscillator (LO) using a division of 10 to enable more robust locking. The f_ceo could be directly stabilized to the LO by controlling the pump laser power through the current controller, in combination with a feed-forward circuit to provide an increased feedback loop bandwidth of 100 kHz. However, using the AOM to control f_ceo in parallel extended the loop bandwidth to 300 kHz. The phase locked f_ceo is shown in Fig. 3(b) . The servo bumps at 300 kHz from the center frequency are evident in the figure. The inset shows an instrument resolution limited linewidth of ~1 Hz, indicating the offset frequency is phase coherent with the LO for long observations times. The total integrated power within the coherent spike is calculated to be ~94%.

 

Fig. 4 (a) Measurement of in-loop spectral density of phase fluctuations with an integrated value of 0.8 rad. Inset shows in-loop error signal of residual phase fluctuations versus time. (b) Allan deviation measurement of f_ceo indicating frequency fluctuations relative to the local oscillator. The 1/τ dependence is expected when comparing 2 phase coherent signals. Also shown is the measurement noise floor of the detection system (open squares). Dashed line is a guide for the eye showing the 1/τ dependence.

Download Full Size | PDF

 

Fig. 3 (a) Free-running linewidth of f_ceo measured with an electronic spectrum analyzer and 300 Hz video resolution bandwidth. Larger signal at ~42 MHz corresponds to the fundamental repetition rate of the laser. (b) Stabilized carrier envelope offset frequency recorded with 1kHz video resolution bandwidth. Inset shows resolution bandwidth limited 1 Hz linewidth. RBW: resolution bandwidth.

Download Full Size | PDF

The phase noise power spectrum becomes a more meaningful measure of the noise present in f_ceo once the measured linewidth is reduced below the resolution of the spectrum analyzer. The measured in-loop phase noise of the stabilized f_ceo is shown in Fig. 4(a), with the phase fluctuations from the error signal for a 10 s time interval shown in the inset. The in-loop integrated phase noise from 10 Hz to 400 kHz is 0.8 rad. The long-term phase stability of the laser is demonstrated in the Allan deviation measurement shown in Fig. 4(b) for up to 100 s averaging timescales. It is important to note that the frequency counter used for this measurement was phase locked to the LO to which f_ceo was locked. The noise floor was measured by directly connecting the LO (8.6 MHz) to the counter and measuring the fractional frequency instability. The 1/τ dependence is as expected when comparing two phase coherent sources. Measurement of the fractional frequency instability of f_ceo (measured at 86 MHz) gives nearly identical results, indicating that there is no measurable excess frequency instability introduced when f_ceo is phase locked to the LO and verifying that the signals remain phase coherent for these time scales. The right hand side of the graph shows the measured frequency fluctuations for f_ceo. The laser was able to maintain phase lock for time scales up to several hours, primarily limited by the dynamic range of the feedback control system.

4. Summary

In summary, we have shown that the tf-CNT fs fiber laser can be utilized to generate a low noise, high performance frequency comb in a simple all fiber oscillator design. We investigated sources of noise and optimized the system to provide a stable and narrow free running offset frequency linewidth (~20 kHz), amenable to tight phase locking with active stabilization. The integrated and low cost design will provide an attractive alternative for fiber based fs frequency combs. Compared to other fiber laser designs based on CNT’s, the tapered fiber design may enable higher powers due to the increased damaged threshold. This can aid in future designs generating higher power and higher repetition rate all-fiber frequency combs.