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We have developed an optical frequency comb using a mode-locked fiber ring laser with an intra-cavity waveguide electro-optic modulator controlling the optical length in the laser cavity. The mode-locking is achieved with a simple ring configuration and a nonlinear polarization rotation mechanism. The beat note between the laser and a reference laser and the carrier envelope offset frequency of the comb were simultaneously phase locked with servo bandwidths of 1.3 MHz and 900 kHz, respectively. We observed an out-of-loop beat between two identical combs, and obtained a coherent δ-function peak with a signal to noise ratio of 70 dB/Hz.
©2012 Optical Society of America
1. Introduction
Optical frequency combs have made notable progress and are used not only for frequency metrology, but also for length measurement [1], thermal metrology [2], terahertz-wave generation [3], astronomy [4], environmental monitoring [5], medical diagnostics [6], and other applications. Recently, some groups have succeeded in reducing the comb linewidth and they have reported that the relative linewidths of all comb modes can achieve the millihertz level [7–11]. In particular, work on optical frequency standards, studies related to the possible next definition of the second, and dual-comb spectroscopy [12] have all begun to utilize the linewidth narrowing technique. Basically, the technique involves phase-locking a comb mode to an ultrastable CW laser with a narrow linewidth. However, to reduce the linewidth, the comb must have a broad servo bandwidth of 100 kHz or more to reduce the residual phase noise and realize a high-energy concentration in the coherent peak of the phase-locked spectrum, and also to ensure long-term operation. When a piezoelectric transducer (PZT) is used to control the cavity length of a mode-locked laser [7–10], the servo bandwidth is usually limited to a few tens of kilohertz. In addition, a large residual phase noise remains in the locking beat signal, and the energy concentration in the coherent peak is not high. Furthermore, locking with a narrow servo bandwidth lacks robustness and reliability and is easily broken by background noise. Although a high-speed PZT was utilized in a recent study [13], it was a somewhat special device. Some groups have employed an intracavity electro-optic modulator (EOM) with a servo bandwidth of more than 300 kHz for fast control of the cavity length [11, 14]. We have already demonstrated that such a comb has a narrow relative linewidth and a small phase noise of the comb modes [11]. Subsequently, a waveguide EOM (wg-EOM) has been employed to control the cavity length [15, 16] because it has high mechanical robustness, an extremely broad bandwidth of more than 1 MHz, and does not require a high operating voltage. In [15], a figure-eight configuration was employed to insert a wg-EOM with a polarization-maintaining pigtail into the mode-locked laser cavity. In this study, we have developed a mode-locked fiber laser with an intra-cavity wg-EOM in a simple ring cavity configuration, and utilized a nonlinear polarization rotation mechanism for mode-locking. We also describe the high-speed control of the comb provided by the mode-locked laser, where we carried out the simultaneous phase-locking of the carrier envelope offset (CEO) beat and the beat note with a reference laser, which is needed to reduce the relative linewidth of the comb. We then evaluated the out-of-loop beat observed using two almost identical comb systems.
2. Outline of a comb system using a high-speed servo controllable mode-locked fiber ring laser
Figure 1 shows a mode-locked fiber laser system with an intra-cavity wg-EOM and four output branches. The cavity design is based on that reported by Tamura et al. [17]. The gain medium, an erbium-doped fiber (EDF), is pumped backwards by a 1480-nm laser diode via a wavelength division multiplexing (WDM) coupler. The repetition rate is set at 43 MHz, which is favorable for starting the mode-locking operation and for broadening the comb spectrum with a highly nonlinear fiber (HNLF). An output coupler consumes 30% of the intra-cavity power, and the output power is approximately 4 mW. The pump power is typically 80 mW for the oscillator, and the spectral width Δλ is approximately 24 nm.
Fig. 1 Setup for a comb with a fiber-coupled waveguide EOM and four-branch configuration. Thick solid lines and curves represent optical fiber; O.I., optical isolator; O.C., output coupler; WDM, wavelength division multiplexing coupler; Q, quarter wave plate; H, half wave plate; P, polarizer; TEC, thermo-electric cooler; EDF, erbium-doped fiber; HNLF, highly nonlinear fiber; PPLN, periodically-poled lithium niobate; PD, photo diode.
An intra-cavity wg-EOM, namely a lithium-niobate-based phase modulator for 1.55 μm, is also inserted for fast control of the cavity length. The operating voltage (Vπ) is less than 5.0 V, and so a high-voltage amplifier is not required. The insertion loss and polarization extinction ratio are less than 5 dB and more than 20 dB, respectively. Wg-EOMs usually have a polarization-maintaining fiber (PMF) on the input side, which often makes it difficult to start the mode-locking utilizing a polarization-rotation mechanism. We attribute the difficulty in the mode-locking to back reflection at the spliced point between the SMF and PMF. Therefore, in this study, we employ a wg-EOM with SMFs on the input and output sides. However, it is still a question as to whether the mode-locking can be maintained whenever the voltage applied to the EOM is widely varied because the input polarization cannot be expected to be linear. For example, if the input is circularly polarized, the output is in a linear polarization state when Vπ is applied to the EOM. However, in practice the mode-locking remains stable at any operating voltage between –10 and 10 V. Therefore, we are able to use the mode-locked laser for the comb experiment.
The right half of Fig. 1 shows four branches, some of which contain an erbium-doped fiber amplifier (EDFA) and HNLF for spectral broadening. The output power is equally distributed into the four branches, amplified by the EDFA, and broadened by the HNLF if necessary. The chirp of the optical pulses is optimally managed for effective amplification and spectral broadening [18]. The three branches employed in this study are used to detect a CEO beat, a beat note with a 1064-nm laser, and a beat note with another comb, respectively.
The frequencies of all the comb modes are stabilized when two of the comb modes are frequency-stabilized. In this study, we stabilize the carrier envelope offset frequency (fCEO) and the frequency of the comb mode at 1064 nm. We use a 1064 nm Nd:YAG laser stabilized to an ultrastable cavity as the 1064 nm reference. The fCEO and the beat frequency between the laser and the comb (fbeat) are individually phase-locked at 30 MHz.
3. High-speed servo control of fiber based frequency comb
In the early stages of work in this field, fiber-based frequency combs were considered noisy compared with Ti:sapphire laser-based frequency combs since the spectrum of the CEO beat was broad [19]. Some previous studies solved the linewidth problem by selecting the total dispersion of the laser cavity [20], and by increasing the servo bandwidth of the fCEO stabilization [21]. In addition, two high-speed servos (for example, fCEO and fbeat) are required simultaneously to reduce the linewidths of all the comb modes. One servo usually affects the other. Therefore, the broad servo bandwidth of fCEO locking often assists the simultaneous operation of the two phase-lock loops. In this section, we report fCEO and fbeat locking with a broad servo bandwidth.
3.1 Phase-locking of carrier envelope offset beat
Figure 2 shows the feedback control system of the fCEO schematically. The CEO beat was detected with an InGaAs photo detector at 1020 nm using a common path f-2f interferometer. The beat note was filtered and amplified at 30 MHz, and then frequency divided to 3 MHz. A double-balanced mixer was used to detect the phase difference between the signal and a hydrogen-maser-based microwave reference (3 MHz). The output of the mixer was added to the injection current of the pump laser as the feedback signal via a loop filter. To achieve a broad servo bandwidth, we undertook the following; (1) the feedback current signal was directly added to the cathode of the pumping laser diode without a bias-T; (2) we eliminated low-pass filters from the phase lock loop as far as we could; (3) we used a relatively broad bandpass filter (center: 30 MHz, 3dB bandwidth: 10 MHz) to ensure the bandwidth; (4) we optimized the parameter of the loop filter experimentally; and (5) we adjusted the intracavity polarization state to maximize the injection current sensitivity against the fCEO. In addition, in this experiment, a differential control was effective in increasing the bandwidth.
Fig. 2 PLL systems for fCEO, and beat note between the comb and a reference laser. Thick solid lines represent optical fiber, and a thin solid line represents a beam in space. Broken lines represent electric wire. PD, photo detector; BPF, electrical band pass filter; PPLN, periodically-poled lithium niobate.
Figure 3 shows an in-loop CEO beat and the spectral density of the residual phase noise. We obtained a coherent δ-function peak with a signal to noise ratio of 70 dB/Hz and a servo bandwidth of more than 900 kHz, which we estimated from the servo bumps in the in-loop spectrum and the spectral density of the phase noise. To the best of our knowledge, this is the broadest servo bandwidth for fCEO locking yet achieved when fbeat is simultaneously locked. The broad bandwidth also enables us to increase the proportional-integration corner frequency in the loop filter to 50 kHz, which indicates successful locking with a broad servo bandwidth. An unexpected bump appears at 600 kHz in the in-loop beat spectrum for simultaneous locking with an fbeat.
Fig. 3 (a) Spectrum and (b) spectral power density of phase noise of the in-loop CEO beat. RBW, resolution bandwidth.
As regards fCEO locking in rare-earth doped lasers, it has been a generally accepted opinion that the servo bandwidth is limited due to the long lifetime of the laser level in the gain medium [22]. We overcome the conventional limitation and consider it to be a sufficiently broad servo bandwidth for a narrow linewidth comb.
3.2 Phase-locking of beat note between comb and a cw laser using an intracavity, waveguide electro-optic modulator
PZTs have been used to control the cavity length of mode-locked lasers. However, the phase locking of a beat frequency with a reference laser (fbeat) using PZTs is often difficult because fbeat contains large and fast phase noise during free running operation, and in most cases their servo bandwidths are limited to less than a few tens of kHz. For phase locking with a broad servo bandwidth, it is possible to use a transducer with broad and flat frequency response characteristics. In this study, we employ an intracavity wg-EOM to control the cavity length (fbeat) [15, 16].
Figure 2 also shows a schematic of the phase-locking for the beat note between the comb and the reference laser. The beat note was detected with an InGaAs photo detector at 1064 nm. The detected signal was filtered and amplified at 30 MHz, and mixed using a double-balanced mixer with a hydrogen maser based frequency reference (30 MHz). The output of the mixer was fed back via a loop filter as applied voltage to the intracavity wg-EOM.
With the fbeat locking, we made a similar effort to that employed for the above-mentioned fCEO locking. In our experiment, differential control enabled us to achieve a broad servo bandwidth exceeding 1 MHz although it is not needed to achieve locking.
Figure 4 shows the spectrum of an in-loop beat and the spectral density of the residual phase noise. We obtained a coherent δ-function peak with a signal to noise ratio of 75-80 dB/Hz and a servo bandwidth of 1.3 MHz reproducibly. The servo bandwidth was estimated from the frequency at the servo bumps. Unexpected bumps appear at around 600 kHz in the in-loop beat spectrum for simultaneous locking with an fCEO.
Fig. 4 (a) Spectrum and (b) spectral power density of phase noise of the in-loop beat between the comb and the 1064 nm reference laser. RBW, resolution bandwidth.
4. Evaluation of out-of-loop beat of two comb systems using mode-locked fiber lasers
In this section, we observe an out-of-loop beat between two independent combs with reference to a common laser to evaluate the relative performance of the comb. Figure 5 shows the experimental setup we used to observe out-of-loop beat signals, which is similar to that in our previous report [11]. The second comb has a delay line to tune the repetition rate so that it is identical to that of the first comb. The two combs were stabilized at a 60 MHz shifted frequency by setting both fCEO and fbeat at 30 MHz with opposite signs. We directly detected a 60 MHz beat note between two combs in the 1700 nm region.
Fig. 5 Experimental setup to observe an out-of-loop beat between two combs with reference to a common 1064 nm laser. The beat note between each comb and the reference laser, and each CEO beat is phase locked to a microwave reference. Out-of-loop beat is directly observed by adjusting the repetition rates so that they are identical. O.I., optical isolator; O.C., output coupler; WDM, wavelength division multiplexing coupler; Q, quarter wave plate; H, half wave plate; P, polarizer; TEC, thermo-electric cooler; EDF, erbium-doped fiber; LD, laser diode.
Figure 6 shows the spectrum, the spectral density of the phase noise, and the frequency stability of an out-of-loop beat. The signal to noise ratio of the coherent δ-function peak is 70 dB/Hz. The RMS phase is 0.34 rad, which is estimated by integrating the phase noise from 100 mHz to 2 MHz. Therefore, one comb’s RMS phase is estimated to be 0.24 rad, which corresponds to an energy concentration of approximately 94%. The residual phase noise is reduced, and the reliability of long-term operation is improved by the broad servo bandwidths of the intracavity wg-EOM. In addition, the relative frequency stability is 3 × 10−16 at an averaging time of 1 s, and is improved to 2-5 × 10−19 with an averaging time of approximately 70000 s, which is similar to our previous report [11] because it is limited by fiber noise that originates from the plural output branches of the comb systems.
Fig. 6 (a) Spectrum, (b) spectral density of phase noise and integrated RMS phase, (c) enlarged spectrum, and (d) frequency stability of the out-of-loop beat.
5. Conclusion
We developed a mode-locked fiber laser with an intra-cavity waveguide EOM for an optical frequency comb with a narrow linewidth. The laser has a simple ring cavity and is based on a nonlinear polarization rotation mechanism for mode locking. We attempted to increase the fCEO servo bandwidth. As a result, we achieved broad servo bandwidths for the fCEO and the fbeat simultaneously to narrow the relative linewidths of all the comb modes. Furthermore, we observed an out-of-loop beat between two identical comb systems to evaluate the performance of the combs.
This simple and robust laser with simultaneous and high-speed two phase locking offers high-performance and practicality, which could support applications requiring high precision and reliability such as optical clocks. In addition, it will become a mainstream high-speed-controllable optical frequency comb since it has a broad bandwidth, mechanical stability, a simple configuration, and commercially available components.
Acknowledgments
We are grateful to M. Onishi, T. Sasaki, T. Okuno and M. Hirano of Sumitomo Electronics Inc. for helpful discussions on optical fiber. We are also grateful to K. Kawasaki of Mitsutoyo Corp. for his help with system fabrication. This work is supported by the “Grant for Industrial Technology Research” program of the New Energy and Industrial Technology Development Organization (NEDO), and also by the “Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST)”.
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