1. Introduction

The integration of microstructured fibers with femtosecond laser systems have led to tremendous advances in the field of optical frequency metrology [1–3] initiated by the first demonstration of a self-referenced frequency comb with a Ti:Sapphire based laser system in 2000 [1]. However, Ti:Sapphire systems suffer when it comes to portability as they require frequent re-adjustments, are not very compact, and involve considerable expense owing to their large pump requirements. After its first demonstration by Washburn et al. [4], self-referenced Er-fiber laser frequency combs have emerged as relatively inexpensive, more compact counterparts, which offer the added advantages of low power consumption, longterm operation and compatibility with existing optical fiber-based technology [4–7]. Recently it has been shown that fiber laser frequency combs can provide both excellent long term stability with demonstrated relative Allan standard deviations of 2·10^-17 [8] and excellent short term stability indicated by sub-Hertz relative linewidths and timing jitter of the order of 1fs [9]. Fiber laser frequency combs are therefore suitable tools for highly demanding applications such as optical frequency synthesis, optical clocks and low phase noise RF generation.

In the last few years, there has been increasing focus on several emerging optical standards such as Hg⁺, Al⁺ single ions and neutral Yb optical lattice, which provide narrow natural linewidth optical transitions (at 281.5nm, 267nm and 578.4nm respectively) suitable for optical clock applications [10]. All those transitions have sub-harmonics in the spectral region around 1µm (1.126µm, 1.068µm, and 1.157µm respectively) allowing narrow linewidth Yb-fiber laser technology to be used as probe (“clock”) lasers [10]. For the transfer of the optical clock signal within the optical spectral region or to generate an RF clock output, a frequency comb covering the spectral region around 1µm is required and Yb femtosecond laser frequency combs immediately come to mind. Here Yb-fiber laser techology is particularly attractive since it allows the construction of ultra-compact femtosecond oscillators [11] and very efficient, power scalable amplifiers, using the concepts of cladding pumping and chirped pulse amplification [12]. However it remains to be shown that those power scaling concepts can be applied without introducing prohibitively large amounts of phase noise, for example, caused by AM-PM conversion in fiber amplifiers.

Frequency comb stabilization requires carrier envelope phase slip detection, for example by the f-to-2f self-referencing technique [1,13] which uses a heterodyne beat between the frequency doubled low frequency wing of the output comb and the high frequency wing at twice the frequency. This technique needs a full octave of optical output spectrum which can not be directly generated from a femtosecond fiber system. Previous demonstrations of self-referenced setups have involved a range of nonlinear devices for spectral broadening such as highly nonlinear dispersion-shifted fibers [4–9], ordinary photonic crystal fibers [1,3], and crystals [14]. Here we use a dispersion micromanaged (DMM) holey fiber [15,16] in order to generate efficient, low noise spectral components primarily at 523nm.

Supercontinuum generation is a phenomenon that is a consequence of several, highly complicated processes related to the fission of higher order solitons [17] and there needs to be a careful control over the various aspects contributing to it in order to obtain the desired spectral characteristics. DMM devices are essentially holey fibers (HFs) whose dispersion and nonlinearity are engineered on a millimeter or sub-millimeter scale by manipulating the physical profile of the fiber. This methodology offers controllable bandwidth and generates low noise anti-Stokes radiation (ASR) pulses tunable to anywhere within the visible region of the spectrum. These anti-Stokes pulses are a consequence of phase-matching between the dispersive wave and the soliton leading to energy leakage and resulting in Cherenkov radiation which appears on the shorter wavelength side of the spectrum. DMM devices are capable of generating highly coherent, low-noise ASR pulses and a careful selection of the length as well as the core size variation of the holey fiber can provide us with the required ASR wavelength. Compared to conventional continuum generation, dispersion micromanaging results in significantly lower noise characteristics, as the process of soliton fission is terminated before additional processes enter, causing accumulation of excess noise [15,18,19]. Fluctuations in intensity are often the main limiting factor for precision applications. The process of extreme broadening in microstructured fibers is a highly nonlinear process, and previous experiments have shown that noise resulting from the conversion of amplitude fluctuations to phase fluctuations inside the fiber can corrupt the CEO phase [20] and thus, the DMM fiber has been integrated with the self-referencing setup for high SNR CEO phase detection.

2. Setup of the experiment

The experiment was based on an Ytterbium (Yb)-fiber in-line oscillator [11] as shown in Fig. 1. A saturable absorber with a sub-picosecond lifetime was employed for mode-locking the laser at a repetition rate of 90MHz. The intra-cavity dispersion was compensated by a chirped fiber Bragg grating (FBG) to a value close to zero. We used an intracavity piezo-electric tube-based fiber stretcher to control the repetition rate of the laser. A single mode fiber with anomalous third order dispersion was employed to stretch the pulse train from the oscillator to ~20 ps. The pulse train was amplified at the full repetition rate using a 700 µm² mode field area polarization maintaining double clad Yb fiber which was end-pumped by up to 5 fibercombined 915nm single emitter diode lasers. We choose to pump the broad Yb-absorption band at 915nm instead the narrow, higher absorbance 975nm band in order to minimize output amplitude noise related to emitter temperature or mode-hop related pump-wavelength shifts. The mode-quality of the amplified signal was measured to be M²≈1.2. Due to pulse stretching and large amplifier mode field area the non-linear phase acquired in the amplification process (B-integral) was less than 0.1π. The pulses could be re-compressed using fused-silica transmission gratings to 120 to 150 fs at average powers up to 1.4W. Fig. 1b shows an autocorrelation trace of the re-compressed laser output. As reported in a previous publication [21], the linewidth of the individual comb lines of the system was determined to be smaller than 1 KHz by analyzing the spectral noise density of the error signal when locking the laser to a stable high finesse cavity.

 

Fig. 1. (a) Experimental set-up. SA: saturable absorber; PZT: piezo actuator; FBG: fiber-Bragg grating; ISO: isolator; PBS: polarizing beam splitter; DMM PCF: dispersion micromanaged photonic crystal fiber; LBO: Lithium triborate; BS: beam-splitter. (b) Autocorrelation measurement of the compressed laser output. For comparison a 117fs FWHM sech² function is shown.

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Fig. 2. (a) Dispersion profiles for the dispersion micromanaged holey fiber’s (DMM HF) initial and final core diameters of 3.3µm and 2.7µm respectively. (b) Spectrum generated by launching ~7 nJ, 130fs pulses into the 18mm long DMM HF. For qualitative comparison a spectrum generated in a 25 mm non-tapered HF as well as the launched laser spectrum is shown.

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For self-referenced f-to-2f CEO detection we used the second harmonic of the Yb-laser system and spectrally overlapped a 10nm wide spectral slice of the continuum output from a DMM device. Our self-referencing setup was based on a Mach-Zehnder configuration with a 7mm long, non-critically phase-matched type-I LBO crystal in one arm and a DMM holey fiber in the other with the modified dispersion profile (Fig. 2a). The LBO crystal was maintained at a temperature of 173°C. The splitting ratio for the two interferometer arms was set to generate in the first arm roughly 20mW of frequency-doubled radiation at 523nm. In the other interferometer arm about 600mW of the pump was coupled into the DMM corresponding to ~7nJ pulse energy. A broad output extending from 400nm to nearly 1300nm was obtained with an isolated anti-Stokes feature centered at around 530nm with a bandwidth of ~22nm as shown in Fig. 2b. The spectral shape of the continuum and the threshold energy for onset of continuum generation was found to be dependent on the orientation of the polarization axis of the linearly polarized launched pulse, most likely due to unintentional birefringence of the DMM device. The DMM device consisted of an 18mm long commercially available holey fiber (Crystal Fibre A/S) with an initial core diameter of 3.3µm which was tapered down to 2.7µm using an in-house CO₂-laser based tapering rig. The DMM was fabricated with appropriate parameters, such as the pulling speed of the fiber and the output power of the laser heat source, so as to maintain the adiabaticity of the structure. The fiber initially had a zero dispersion wavelength (ZDWL) at 880nm, i.e., at a core diameter of 3.3 µm. At the final core diameter of 2.7 µm, the zero dispersion wavelength had shifted to around 800nm in accordance with the eigenvalue equation for fibers [22]. The Cherenkov radiation phasematching condition [16], which depends on the center wavelength of the soliton, the nonlinearity of the structure, and the ZDWL, will now shift to the shorter wavelength side and hence yields an ASR feature centered at ~530nm. A narrow-band interference filter (bandwidth=10nm) was placed at the output of the DMM to spectrally filter out radiation at 520nm. The outputs from the two arms of the interferometer were then combined using a beam splitter. A delay line in one interferometer arm was used to introduce an appropriate delay to ensure temporal overlap of the two beams at the detector. The combined beam was then focused onto a Si PIN diode after passing a single mode optical fiber, which ensured a spatial overlap of the two beams and the CEO related beat signal could be observed. To stabilize f _CEO a mixing product of f _rep and f _CEO centered at 125 MHz was bandpass filtered (5.5MHz bandwidth), amplified and phase-locked to a stable RF reference using a digital phase detector and an analog PID-type feedback loop for controlling the oscillator pump diode current [23]. A frequency division by 16 was implemented after rectifying the signal in a comparator input stage to expand the locking range [3].

In order to stabilize the second degree of freedom of the comb, an intermode beat signal at the 28^th harmonic of the repetition frequency around 2.55 GHz was phase-locked to a second stable RF synthesizer using a double-balanced mixer as a phase detector and the intracavity fiber stretcher as feedback control element.

3. Results and conclusions

As shown in Figs. 3(a) the free running CEO-related beat signal could be observed with ~30 dB SNR at a RF spectrum analyzer set to 100 kHz resolution bandwidth. The SNR of the beat signal was maximized by adjusting the polarization of the input pulse to the DMM and the splitting ratio of the interferometer at the polarizing beam splitter using two half wave plates. The free running beat signal could be fitted with a 250 kHz FWHM Lorentzian line shape (Fig 3b). The line width is most likely limited by relative intensity noise of the 976nm grating stabilized telecom pump diode for the oscillator [23]

 

Fig. 3. a) Free running beat signal. b) Mixing product of f _CEO and f _rep at 125 MHz (phase locked with low gain). c) At higher gain phase locked operation a coherent peak (instrument limited bandwidth) as well as 60Hz pick-off can be observed.

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Fig 4. Frequency counter measurement of f _CEO (a) and f _rep (b). The low frequency oscillatory noise is correlated and might be related to cross talk or various environmental noise sources.

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Both f _r and f _CEO could be simultaneously phase-locked via RF synthesizers to a stable RF rubidium clock reference. The frequency of the optical comb lines f _o,n is then stabilized to f _o,n=n * f _r + f _CEO, where n is a large integer [1–3]. After closing the phase-locked loop for f _CEO the CEO-related beat signal collapsed to a coherent spike with instrument limited 1 Hz bandwidth (Fig3c), a first indication that Yb-comb technology is suitable for low noise optical frequency synthesis [9]. Fig 4 shows a frequency counter measurement of f _CEO (in loop) and f _r (out of loop) over 20 minutes. With the counter gate time set to 10s we measured an instability of 1.6mHz rms and 0.5mHz rms on the 125MHz and ~90MHz signals for f _CEO and f _r respectively. We note that an out-of loop characterization of the phase-locked f _CEO is necessary to confirm our results. However since the frequency noise of the comb-lines is governed by intracavity noise sources [24], we do not expect significantly different results for our in-loop characterization.

The oscillations on the traces shown in Fig. 3 as well as the 60 Hz sidebands of the phase locked f _CEO signal in Fig 3c) are possible caused by imperfections in the locking electronics as well as mechanical vibrations and could be removed by improvements in locking electronics and mechanical isolation. Mechanical drift of the free space fiber coupling to the DMM device required occasional re-alignment, limiting the unattended operation of the fully stabilized system to about 30 minutes.

In conclusion, we have experimentally demonstrated for the first time to our knowledge, a fully phase locked frequency comb centered at the 1 µm spectral region, using a Yb-fiber based laser system which is spectrally broadened by a DMM device. Furthermore we proved that carrier-envelope offset phase control is compatible with the power scalable cladding pumped chirped pulse amplification scheme. This will allow scaling of the average output power of fiber frequency comb lasers well beyond the few-watt limit of bulk Ti:Sapphire oscillator based comb systems. The concept of dispersion micromanagement has been integrated for the first time with a standard self-referencing scheme for self-referenced CEO phase slip detection. We expect that based on Yb-fiber technology frequency combs with GHz repetition rates at improved long-term stability with average powers of more than 10W can be realized. High power Yb-frequency combs will be an important tool for future frequency comb technology in the vacuum ultraviolet (VUV) and extreme ultraviolet (XUV) spectral regions using high harmonic generation within a passive enhancement cavity [25,26].