1. Introduction

Since the first demonstration of a Ti:Sapphire optical frequency comb (OFC) used as a link between microwave and optical frequencies [1], depending on the intended application, the focus in the design of OFCs has been placed on a single combination of aspects, such as spectral coverage, noise property, output power, or repetition frequency. Astronomy-related measurements, for example, employ frequency combs with high repetition rate, like those based on Kerr-lens mode-locked lasers that are in excess of 10 GHz [2,3]. Trace gas sensing in medical applications require the OFC to cover specific portions of the mid-infrared (mid-IR), as the difference frequency generation (DFG) and optical parametric oscillator frequency combs do [4,5]. With optical atomic clocks, high stability and broad spectral coverage of the visible and near-infrared (NIR) regions are essential, and these are the requirements the OFC reported in this paper was developed to fulfil.

The technology of optical clocks has dramatically improved in recent years [6,7]. With the ability to achieve an accuracy and a stability as low as 10⁻¹⁸, optical clocks have become more suitable in defining the second, than the current Cs microwave atomic clock. Optical lattice clocks especially have the potential to achieve high stability within a short integration time. Highly stable lattice clocks have been demonstrated using improved reference cavities [8] and atoms such as Sr, Yb and Hg, which can have their clock lasers centered at wavelengths of 698 nm, 1156 nm and 1063 nm, respectively, in the visible and NIR [9,10]. In particular, Sr clocks have been shown to achieve stabilities as low as 10⁻¹⁶ level at 1s [11,12] and that of the next generation optical clocks is expected to improve beyond 10⁻¹⁶ at 1 s. An OFC achieving comparable stability, i.e. low phase noise, and able to cover a spectral range sufficiently broad to include the different wavelengths of clock lasers, enables the study of optical clocks based on various atomic references and their comparison, which could lead to observing the time variation of a physical constant.

While Ti:Sapphire combs have been shown to provide uncertainties as low as 2.3 × 10⁻¹⁷ averaged over 1 s [13], such systems fail to operate over long periods of time in excess of a day, which proves problematic for many clock applications. On the other hand, fiber combs, while they have higher frequency noise than those of Ti:Sapphire combs, are less prone to misalignment and can sustain long term operation [14]. In addition to being more robust and more user friendly, fiber combs are more compact in size and more affordable than their Ti:Sapphire laser counterparts.

Typically, stabilization of the OFC is achieved via two phased-locked loops (PLLs) acting on each of the degrees of freedom, the offset and repetition frequencies. The larger noise component of fiber comb, than that of Ti:Sapphire comb, the broader the feedback is required to improve the overall stability. Fast feedback for phase stabilization of the repetition frequency has been achieved via the use of transducers, such as intra-cavity electro-optic modulators (EOMs) [15,16], and that for phase stabilization of the offset frequency has been carried out using current modulation of the pump laser diode (LD), acousto-optic modulators (AOMs) [16,17] and the other novel devices [18]. Thanks to these improvements, the feedback bandwidth of both PLLs have reached sub-MHz levels. The noise brought forth by both feedback loops, stemming from the detection system, the PLL electronics, and eventual cross-talk between the two, adds to the overall fiber comb noise, and a stability better than 10⁻¹⁶ over 1 s of average time has yet to be realized [15,19], as increasing the feedback bandwidth beyond the MHz-level is rather difficult. To reduce additional noise from the PLLs, one alternative is to passively stabilize the offset frequency via DFG. Though the process of DFG, the offset frequency cancels out, along with accompanying noise terms, and the phase stabilization of a frequency comb is simplified to a single PLL, which acts on the repetition frequency.

To date, few reports on adapting DFG combs for the examination of optical clocks can be found. Most relate to applications in the Mid-IR, since frequency conversion efficiencies producing near-IR wavelength are low. A notable paper is that of Zimmermann et al. [20], which describes a Ti:Sapphire based DFG comb centered at 946 nm. Although the resulting comb was narrowband and the spectral region was insufficient to allow further efficient amplification, this study lays the groundwork for the acquisition of stable modes via DFG. Krauss et al. applied this method to an Er:fiber laser which produced DFG pulsed that were simply amplified to higher average powers using a fiber amplifier, however, these were centered at 1.5 μm [21].

In this paper, we report the demonstration of a 1-μm wavelength region DFG fiber OFC, which has a sufficiently broad spectrum that includes the wavelengths of optical clocks based on various atomic references. Pulses from a mode-locked Yb:fiber laser were amplified by a Yb-doped fiber amplifier (YDFA) in order to efficiently seed a photonic crystal fiber (PCF) for supercontinuum generation. The spectrum obtained spanned from 580 to 1500 nm and the modes centered around the wavelengths of 610 and 1430 nm were used in the DFG process to produce 0.1 mW average power of offset-frequency-free pulses centered around 1060 nm. This primary DFG comb was further spectrally broadened after amplification by a series of YDFAs and supercontinuum generation using a PCF, yielding a final offset-free comb ranging from 690 mm to 1300 nm with an average power of several hundred mW. To demonstrate the simplicity of stabilizing the DFG comb, a single comb mode was phase locked to an ultra-low expansion (ULE) glass cavity stabilized continuous-wave (CW) laser.

2. Difference frequency generation from supercontinuum of Yb: fiber laser

A schematic diagram of the experimental setup of the offset-free broadband DFG comb is shown in Fig. 1. The 100-MHz OFC was based on a nonlinear polarization rotation mode-locked Yb:fiber oscillator which operated in the zero dispersion regime so as to ensure lowest relative intensity noise [22]. After amplification by a non-polarization-maintaining (PM) YDFA and dispersion compensation by a grating pair, the pulses had a duration of 80-100 fs and an average power of 1 W. A supercontinuum was generated from these pulses by using a non-PM commercially available PCF with a zero-dispersion wavelength at 945 nm. The broadband optical spectrum is shown in Fig. 2(a). A dichroic mirror was used to divide the supercontinuum into a visible side and a NIR side. Temporal overlap of the two pulses was adjusted via a moveable right angle prism placed in the visible side. Each optical path contained spectral filters to remove the 1 μm component from the fundamental pulses in order to distinguish them from a DFG output. Spatial overlap of the two beams was realized by using a combination of lenses placed in the NIR side, which compensated chromatic aberrations and matched the beam profiles of one to the other. The visible and NIR pulses were combined together upon a second dichroic mirror and were focused into a nonlinear crystal, periodically-poled magnesium oxide-doped stoichiometric lithium tantalate (PPMgSLT) fan-out nonlinear crystal for DFG. The pulses, centered at wavelengths of 610 nm and 1430 nm, as indicated by the red and green vertical bands respectively in Fig. 2(a), led to the generation of NIR light centered at 1060 nm, as shown by the optical spectrum of Fig. 2(b). The DFG process resulted in an average power of 0.1 mW, which was fifty times greater than that produced by the Ti:Sapphire DFG centered at 900 nm which employed a similar optical configuration [23]. Thanks to the fan-out structure of the nonlinear crystal, the resulting DFG spectrum could be tuned over 1000 nm to 1100 nm.

 

Fig. 1 Schematic diagram of the experimental configuration of the broadband offset-free DFG comb and the heterodyne beat signal generation between a single comb mode and a CW laser. The diagram can be divided into four color-coded sections. The first one, enclosed in a blue square, corresponds to the DFG process between the visible 610 nm and NIR 1430 nm pulses. The second part, included in the yellow delimited area, corresponds to further amplification and pulse compression of the DFG comb. The third section, which is within the purple square, pertains to the spectral broadening of the amplified DFG comb. And finally, the part demarcated by the orange square corresponds to the generation of a heterodyne beat signal between an ULE cavity stabilized CW laser and a single DFG comb mode for full phase stabilization.

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Fig. 2 (a) Optical spectra of the supercontinuum generated after PCF 1. The red and green spectra represent the visible and NIR region used in the DFG process. (b) Optical spectrum of the DFG comb centered at 1060 nm.

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3. Amplification and spectrum broadening of DFG comb

An advantage of generating an OFC around the 1 μm region is the suitability for simple amplification with a YDFA. Seed powers as low as those produced in the DFG process were sufficient for efficient amplification without the introduction of damaging amounts of amplified spontaneous emission (ASE) in the output. In addition, the DFG spectrum was tuned to be centered at 1060 nm, as shown in Fig. 2(b), so as to separate the amplified DFG signal from the ASE, which was centered at 1030 nm, via a long pass filter with a cut-on wavelength at 1050 nm. After a three-stage of non-PM YDFA, more than 1 W of the average power was obtained and the ASE level was at most a few percent. To compensate the dispersion introduced by the fiber amplifiers, a grating pair was used and a pulse duration of 135 fs was measured by second-harmonic-generation frequency-resolved optical gating (SHG-FROG), as shown in Fig. 3(a). Finally, amplified DFG comb was spectrally broadened using a PCF2. The spectrum spanned from 690 nm to 1300 nm as shown in Fig. 3(b), covering various clock-laser wavelengths, including those based on Sr (698 nm) and Hg (1063 nm).

 

Fig. 3 (a) SHG-FROG measurements of the amplified DFG comb. A Gaussian curve was fitted to the measured trace and a FWHM of 135 fs was obtained. (b) Optical spectrum of the DFG supercontinuum spanning from 690 to 1300 nm (−20 dB). The spectrum is sufficiently wide that it includes the wavelength of clock lasers, namely Sr and Hg.

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4. Phase stabilization of DFG comb

To confirm the usability of the reported comb for optical clock applications, the DFG comb stabilized against an optical reference. As the offset frequency cancelled out in the DFG process, full phase stabilization was carried out through a single degree of freedom, the repetition frequency. The optical reference was provided by a CW laser centered at 1053 nm and stabilized to an ULE glass cavity. A heterodyne beat signal between the amplified DFG comb, extracted after the first of the three-stage YDFA, and the CW laser was obtained by using a balanced detector. As shown in Fig. 4(a), the signal to noise ratio (S/N) of the free-running beat signal obtained was approximately 30 dB at 100-kHz resolution bandwidth (RBW). In order to reach an S/N of 30 dB, the YDFA seed power was maximized and PCF used for first supercontinuum generation (PCF1) was chosen such as to minimize decoherence effects. Initially, a PCF with a length of 1 m was used, but no beat signal between the DFG comb and the CW laser could be detected. This was most likely due to a decoherence process occurring along the length of the PCF. Neely et al. reported on a similar situation in the development of a mid-IR comb [24]. First order coherence is strongly related to OFC aspects, such as input pulse duration, as well as PCF parameters, namely length, dispersion and nonlinear coefficient [25]. Reducing the PCF1 length to approximately 10 cm led to achieving a 30-dB beat signal S/N. The obtained S/N was not limited shot noise. The optimized fiber coupler, narrow-band pass filter, and the shorter PCF would improve the S/N. It would realize desired stability for the next generation optical clocks. A coherent peak of 30-dB S/N was obtained during phase stabilization, as shown by the RF spectrum of Fig. 4(b) acquired with a RBW of 1 kHz, which corresponds to the phase noise approximately 0.5 rad integrated from 1 kHz to 1.5 MHz. The PLL feedback was carried out on the current of the oscillator pump LD. Typically, pump current modulation is used to stabilize the offset frequency, since a change in the pump current results in a change in the fiber gain, which modifies the relative phase and group velocities, thus altering the offset frequency, and produces a small net cavity length change, thus varying the repetition rate. As the offset frequency, and any of its fluctuations, were cancelled out through the DFG process, pump current modulation was available to use in the stabilization of the repetition rate. This is an added advantage for establishing a simple feedback loop, since the more traditional approach of controlling the repetition frequency through modifications made to the cavity length via high bandwidth transducers, such as EOMs, is more involved and more complex. While control of the repetition frequency through pump current modulation oversaw the fast varying fluctuations, for long term operation, it was necessary to compensate the slow varying drifts in the cavity length, and this was carried out by feedback to a piezo-mounted mirror. Figure 4(c) shows the values of the repetition frequency as measured by a frequency counter at a 1 s gate time over a continuous period of an hour. There were no cycle slips and the repetition frequency was maintained within 1.4 mHz (standard deviation). This value of stability was limited by the microwave Rb clock used for the reference of the frequency counter and could be improved by employing more stable reference sources, such as hydrogen masers.

 

Fig. 4 Measurements of the beat signal created between an ultra-stable CW laser centered at 1053 nm and one DFG comb mode. RF spectra of (a) the free-running beat signal at 100-kHz RBW and (b) the phase stabilized beat signal at 1-kHz RBW averaged over 20 times. (c) Frequency counter values of the repetition frequency during phase-locking and over a period of an hour. Gate time was set 1 s, and the measurement was limited by the Rb reference.

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5. Conclusion

Through the DFG process, an offset-free broadband Yb:fiber OFC was achieved. The primary DFG comb was centered at 1060 nm and yielded sufficient average output powers for further amplification using YDFAs. The amplified and spectrally broadened DFG comb, spanned over 690 nm to 1300 nm, a range that includes the wavelengths of clock lasers, such as those based on Sr and Hg. As the offset frequency cancelled out in the DFG process, a full stabilization of the comb was carried out via the control of the repetition frequency alone. This was achieved by phase-locking a heterodyne beat signal between an ultra-stable CW laser and a DFG comb mode. Thus, the developed DFG comb has the potential to achieve high stability, sufficient for the study of the next generation of optical clocks.