A low-noise fiber frequency comb is demonstrated to improve the frequency accuracy and linewidth by suppressing the phase noise caused by the nonlinear self-phase modulation as well as the amplified spontaneous emission within the Er-doped fiber amplifier. The linewidth of the carrier-envelop-offset signal measures less than 1.9 mHz and the frequency stability well follows the reference Rb clock. This achievement will facilitate the use of the fiber frequency comb for industrial applications to precision near-infrared spectroscopy, frequency calibration, optical clocks and length metrology.
©2009 Optical Society of America
The frequency comb of femtosecond pulse lasers permits optical frequency measurement to be made traceable to the microwave frequency standard [1,2]. Ti:Sapphire femtosecond lasers provide a frequency comb being excellent in both the frequency stability and linewidth, but their practical use is limited particularly outside the laboratory environment by several reasons such as bulkiness, alignment complexity and external optical pumping. Fiber femtosecond lasers are now available, making rapid progress to compete with Ti:Sapphire counterparts by making the most of their intrinsic advantages of size, robustness and reliability . Stabilizing the frequency comb with reference to a radiofrequency time standard requires detecting two collective parameters; the pulse repetition rate (frep) and the carrier-envelope-offset frequency (fceo). Unlike frep that can be measured simply using a photodetector, fceo has to be extracted through a sequence of elaborate procedures; pulse power amplification, supercontinuum generation, frequency doubling and f-2f interference.
For fiber lasers, Nicholson et al. first demonstrated an all-fiber supercontinuum in which a negative-dispersion fiber was used to increase the amplification gain for subsequent spectral broadening with a hybrid highly nonlinear fiber . Positive pre-chirping was also tried using a single-mode fiber for the pulse power amplification with an Er-doped fiber to detect fceo with an S/N ratio of 30 dB . Special nonlinear-broadening fibers such as photonic crystal fibers and UV-exposed fibers were tested to obtain broader spectra [6,7]. Washburn et al. extracted fceo using a minimal length of nonlinear fiber to suppress phase noise with a standard deviation of 57 mHz at a gate time of 1 s . The common-path f-2f interferometer was proposed to detect fceo with an S/N ratio higher than 40 dB [9,10].
In addition to the generation and detection of fceo, more work is necessary to improve the frequency stability and linewidth of the generated fiber comb to be comparable to those of the crystal-based comb. McFerran et al. worked to eliminate pump-induced frequency jitters in order to obtain a sub-hertz fceo signal . And Schibli et al. attempted to reduce the phase noise generated in the amplitude-to-phase noise conversion during amplification, achieving a mHz linewidth for the fceo signal in an Yb-doped fiber system . In continuation of these efforts to improve the fiber-based comb, in this paper we present a fiber-based scheme of dispersion control with the aim of minimizing the phase noise within the amplification stage. This dispersion control reduces the peak power within the fiber amplifier using negative chirp, allowing the linewidth of the fceo signal to reach 1.9 mHz which is the narrowest yet reported with the Er-doped fiber laser to our knowledge.
2. Low-noise fiber frequency comb
Figure 1 shows the optical layout configured in this study to generate a low-noise frequency comb from an Er-doped fiber oscillator. This oscillator (C-Fiber, Menlosystems GmbH) is set to provide pulses of 100 fs duration at a 100 MHz repetition rate with an average power of 18 mW. The oscillator pulses are negatively pre-chirped using a dispersion-compensating fiber (DCF, 6801-LLWBDK, OFS) prior to amplification, and then delivered to an Er-doped fiber amplifier (Er80-8/125, LIEKKI) that was specially selected as it yields positive chirp during amplification. This serial combination of the negative pre-chirp with the positive chirp of the fiber amplifier is intended not only for overall dispersion compensation but also to maintain a desired level of negative chirp all through the fiber amplifier. This enables reduction of the peak pulse power by widening the pulse duration, thereby minimizing the nonlinear amplitude-to-phase noise as well as the spectral broadening generated within the fiber amplifier. An amplification gain of 15 dB is attained by dual pumping using a pair of laser diodes, which permits obtaining an octave-spanning supercontinuum through a highly nonlinear fiber (HNLF, Menlosystems GmbH). Isolators are located at the inlet and outlet of the fiber amplifier to reduce the amplified spontaneous emission (ASE) induced by Fresnel reflections occurring at the fiber end facets.
The f-2f interferometer configured in this study to extract fceo is of common-path type. The longer wavelength portion near 2.06 µm of the generated supercontinuum is frequency-doubled using a periodically poled lithium niobate (PPLN, Crystal Technology) and then overlapped with the original shorter wavelength portion around 1.03 µm. The resulting interference signal of fceo is detected using a high-sensitive photodetector (FPD310, Menlosystems GmbH) through an optical band-pass filter of a 10 nm bandwidth to reduce the background noise. To compensate for the time delay between the spectral portions at 1.03 and 2.06 µm wavelengths, a single-mode fiber (SMF-28, Corning) of 20 cm length is added between the HNLF fiber and the f-2f interferometer. Finally, the detected fceo signal is phase-locked to a Rb clock by controlling the diode laser pump current of the fiber oscillator. At the same time, to complete the whole stabilization process of the frequency comb, the frep signal is also phase-locked to the same Rb clock by adjusting the cavity length of the fiber oscillator using a PZT microactuator.
3. Suppression of phase noise by dispersion control
Figure 2 illustrates how dispersion is controlled in the apparatus of Fig.1. In the first place, for the sake of comparison, Fig. 2(a) depicts a previous scheme of the authors in which a single-mode fiber was used to deliver the oscillator output pulses to an Er-doped fiber amplifier (Er20-4/125, LIKKEI). In this case, the single-mode fiber usually yields positive chirp, so the chosen fiber amplifier has a 4 µm core diameter to provide negative chirp for overall dispersion compensation. However, the problem with this previous scheme is that the zero dispersion point located within the fiber amplifier causes a rapid rise in the peak pulse power, resulting in severe amplitude-to-phase noise conversion and spectral broadening by self-phase modulation. On the other hand, the current scheme shown in Fig. 2(b) adopts a dispersion-compensating fiber of large negative chirp along with the fiber amplifier of a relatively large 8 µm core diameter producing positive chirp. This combination enables elimination of the zero dispersion point within the fiber amplifier, thereby reducing the nonlinear phase noise and spectral broadening. This advantage is successfully verified in the output spectrum of the amplified pulses measured at the exit of the fiber amplifier as shown in Fig. 2(c). No significant spectral broadening is observed for the scheme of Fig. 2(b), but this not the case for that of Fig. 2(a).
The net dispersion has to be reduced to zero at the inlet of the HNLF fiber, which is accomplished by adjusting the overall length of the single-mode fiber installed to connect the fiber amplifier and the HNLF fiber via the wavelength-division multiplexer (WDM). This make the pulse duration become short with the peak pulse energy being concentrated for effective generation of an octave-spanning supercontinuum. The spectral broadening in the fiber amplifier affects the power coupling efficiency of the WDM as its transmission bandwidth is confined within the wavelength range of ±10 nm about 1550 nm. The broadened spectrum of the EDF amplifier of 4 µm diameter used in Fig. 2(a) suffers considerable power loss, requiring more pumping power to compensate for the coupling loss.
The spontaneous emission in the Er-doped fiber amplifier produces a small amount of stray light which undergoes Fresnel reflections at splicing points. Subsequent amplification of this continuously reflected light disturbs efficient seed signal amplification and even increases the unwanted background noise. To prevent this, optical fiber isolators are located at both the end facets of the fiber amplifier. Fig. 3 shows the amplified spontaneous emission (ASE) of the Er-doped fiber with and without proper isolation of Fresnel reflections. The total amount of ASE at 1560 nm wavelength is well suppressed by the isolators by a factor of 30 dB. The resulting spectrum shows the same distribution as that of the typical emission spectrum of Erbium as illustrate at the inset in Fig. 3(b). The pump power required for supercontinuum generation is consequently much lowered after the suppression of the ASE. Less pumping also decreases the pump-induced phase noise in the Er-doped fiber amplifier. Besides, the use of isolators helps avoid occasional damages of the pump diodes caused by partial reflection of the amplified pulses.
The fceo signal extracted from the f-2f interferometer is phase-locked to a Rb reference clock with an offset of 30 MHz through an rf electronics and a large bandwidth servo. The low amplitude-to-phase noise conversion achieved in our dispersion-control scheme enables reduction of free-running fast jitters of the extracted fceo signal to less than 100 kHz in its full width half maximum. Besides, the electrical disturbance on the fceo signal caused by the environmental and pump noise is measured less than a few tens of kHz. All these low-frequency phase noises are effectively suppressed by stabilizing fceo using a pumping current servo (LB1005, Precision Photonics) with a large bandwidth of 10 MHz. During stabilization, the fceo signal is precisely monitored using an rf spectrum analyzer (E4440A, Agilent) as shown in Fig. 4(a). The measurement result clearly shows that the spectral power of fceo is concentrated on the centered coherent peak that builds on the top of a relatively broad noise pedestal spreading over a range of ±60 kHz. The measured linewidth of the coherent peak is resolution-limited to 0.75 Hz. The linewidth can be more precisely measured with a fast Fourier transform (FFT) analyzer . Here, the super-heterodyne technique was used along with a 30.0001 MHz reference signal so that fceo was down converted to 100 Hz. The result shown in Fig. 4(b) reveals the resolution-limited linewidth less than 1.9 mHz.
Finally, the temporal stability of the fceo signal was examined using an rf frequency counter (53131A, Agilent), whose result is presented in Fig. 5. Drift during a day is found ~5 MHz without stabilization, but it reduces to 2.14×10-3 Hz in standard deviation with stabilization. Long-term stability is also found excellent as the phase-locking of the comb usually lasts for more than a week in the laboratory environment.
The fiber frequency comb system developed in this study offers an instrument-limited narrow linewidth and frequency stability, which are comparable to those of the Ti:sapphire frequency comb. The phase noise within the Er-fiber amplifier is successfully suppressed by controlling the net dispersion in the gain medium using a dispersion-compensating fiber. The resulting linewidth of the carrier-envelop-offset signal measures less than 1.9 mHz and the frequency stability well follows the reference Rb clock. This achievement will facilitate the use of the fiber frequency comb for industrial applications to precision spectroscopy, frequency calibration, optical clocks and length metrology.
The authors thank K. Minoshima, H. Inaba and H. Takahashi in NMIJ/AIST for fruitful discussions. This research was supported by the Creative Research Initiative program and the National Space Laboratory program funded by the Korea Science and Engineering Foundation.
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