A tapered silica photonic crystal fiber was designed and fabricated to generate more than one octave spanning supercontinuum (from 550 nm to 1400 nm at −30 dB level), by an input pulse of 40 fs 200 pJ directly from an Yb:fiber ring laser. The low pulse energy spectrum broadening are favorable to generate the high contrast fceo signals with low noise. The fceo signal with 40 dB signal-to-noise ratio was detected, which helps to build a compact real-world frequency comb.
© 2014 Optical Society of America
A carrier-envelope-offset (CEO)-locked Yb:fiber laser frequency comb covering visible and near infrared wavelength band with a compact, low-noise, and narrow-linewidth system can provide an efficient optical frequency ruler for a variety of applications, such as the optical coherence tomography, spectroscopy, and frequency metrology [1,2]. The noise issue is extremely important, considering that such a frequency comb is going to be used to transfer the optical to radio frequency while maintaining the optical stability. The total phase noise power spectral density in a frequency comb is calculated by simply sum up the phase noise from the intracavity noise and the extracavity noise [3, 4]. The intracavity noise sources inside the Yb:fiber laser oscillator, are the pump noise, environmental fluctuation resulted birefringence dispersion, length and loss fluctuations, and amplified spontaneous emission (ASE). The extracavity noise mainly consists of the amplitude and phase noise in the amplifier and excess noise amplification during supercontinuum (SC) generation in a photonic crystal fiber (PCF) [5–7]. The fiber amplifier may introduce extra amplitude noise in the amplification process and may cause frequency noise on the broadened frequency comb as a result of the amplitude-to-phase conversion . The SC generated in a PCF can also suffer from significant fluctuations in amplitude, which translates to a poor fceo signal-to-noise (S/N) ratio and can limit the utility . Previous work reveals that lower pulse energy leads to lower phase noise. If the SC can be generated by low-energy pulses from a simple laser oscillator, the extracavity noise can be greatly depressed, and robust fceo signals can be achieved. To our experience, the S/N ratio over 40 dB of the fceo can guarantee the long term work of the electronic locking system.
Furthermore, low-noise frequency combs with low pulse energy are especially useful for their high repetition rate (>10GHz) applications, such as high speed telecommunications  and high-precision calibration of astronomical spectrographs [10,11]. At present, mode-locked Yb fiber lasers have been achieved only around GHz repetition-rate at present [12–15]. Recently, the repetition rate of 0.75 GHz and 3GHz were separately achieved for mode-locked Yb:fiber lasers with ring and linear cavity configuration [14,15]. For these high repetition rate lasers with lower output pulse energy, the pulse energy required for octave spanning SC has to be reduced. Recently, octave spanning spectra were realized for mode-locked Yb:fiber lasers with the repetition rate from 300 to 500 MHz [16–18]. High-nonlinearity soft glass fibers [18–20] can reduce the required pulse energy to tens of pJ. With tapered silica PCFs, the pulse energy as low as 280 pJ was proven to be able to obtain octave spanning spectrum . The tapered fibers with two zero-dispersion wavelengths (ZDWs) are quite efficient to locate the supercontinuum peaks to specific wavelength regions , which is promising for frequency comb application. The down-tapering shape is also important to enhance the amount of blue-shifted light that could be explained with the concept of group acceleration matching [22, 23]. Even though these fibers were used to generate octave-spanning spectrum, no much work has been done to make it a laser frequency comb.
In this letter, we report our simulation and design of tapered PCFs with specified dispersions. A piece of optimized tapered silica photonic crystal fiber was then fabricated. More than one-octave-spanning SC (from 550 nm to 1400 nm at −30 dB level) was generated, by the injection of 40 fs pulses at 200 pJ, which were the direct output from a Yb:fiber ring laser oscillator. Consequently, fceo signals with >40 dB S/N ratio were detected by the standard f-to-2f technique. The simplified configuration without any power amplification system and spectrum broadening with such low pulse energy are regarded to contribute to the low extracavity noise, resulting in the robust fceo signals. By such a simplified structure, it is feasible to obtain a simple and easy-to-use optical frequency comb.
2. Tapered fiber design
Figure 1 shows the simulated spectrum broadening of 40 fs, 200 pJ pulses from 10-cm-long uniform fibers. The d/Λ ratios of the simulated fibers are kept at 0.53, while the pitches for these fibers vary from 1 μm to 2.5 μm. These parameters are based on one commercial PCF (Yangtze SCF-01, marked as Fiber I in this paper), which has a pitch of 3.1 μm and d/Λ ratio of 0.53. The commercial software of Fiberdesk was used for these calculations, which is based on solving the extended nonlinear Schrödinger equation (NLSE) by the split-step Fourier transform method . This software was also used to calculate the dispersion for above fibers, shown in Fig. 2. The black curve in Fig. 2(a) indicates the ZDW for PCFs with different pitches from 1 μm to 3.5 μm while d/Λ ratio is fixed to 0.53. The inner part of this curve is the anomalous region and the surroundings are normal dispersion ones. Fiber I, II, and III are marked in the curve. The dispersion curves for those fibers are shown in Figs. 2(b)–2(d), respectively.
Fiber I has one ZDW (1018 nm, shown in Fig. 2(b)) at the wavelength region from 500nm to 1700 nm. With the pitch decreasing, the ZDW was blue-shifted, until double ZDWs appear at the pitch smaller than 1.7 μm. At this stage, no obvious octave spanning spectrum broadening happens, shown in Fig. 1. With the further pitch decreasing, the dual ZDWs continue to blue shift, and the pulse spectra were extended broadly to long wavelength region. Meanwhile, obvious soliton fission and soliton self-frequency red-shift occur, and dispersive waves are generated at the short wavelength, generating octave spanning spectra. When the pitch is decreased smaller than 1.06 μm (Fiber III), ZDW disappears, and the dispersions become all normal, and the soliton mechanism of pulse propagation stops, no octave spanning spectrum was observed any more. In view of the beating signal using f-to-2f interference technique, we consider that the optimal choices of fiber pitches fall in the region of 1.15-1.2 μm with two peaks at 600 nm (2f) and 1200 nm (f) wavelength bands.
Such a fiber structure can be obtained just by tapering Fiber I. As the original fiber, Fiber I was tapered to have the pitch of 1.18 μm (Fiber II, with two ZDW at 788 nm and 1062 nm), while the d/Λ ratio of 0.53 was maintained. It is regarded that the short untapered input section and taper transition region (within 4-5 cm) do not significantly affect the temporal shape of the pulse at the start of the tapered section.
3. Experimental results
The optical setup of our Yb:fiber laser frequency comb is shown in Fig. 3(a). The laser oscillator is a dispersion managed mode-locked Yb:fiber ring laser. The free-space section contained a bulk faraday rotator, wavelength plates, two polarization beam splitters, and a pair of 1000 lines/mm transmission gratings for dispersion compensation. The total dispersion of this cavity is adjusted to be near zero to suppress the intracavity noise [24,25]. The repetition rate is 98.4 MHz. With the pump power of 350 mW, the output power of the oscillator was 92 mW. By a pair of gratings outside the cavity, the output pulse was dechirped to 40 fs (Gauss profile assumed) with the remaining power of 60 mW, shown in Figs. 3(b) and 3(c). 20 mW of this power is rejected from a PBS as the output of frequency comb while the other 40 mW is for the SCG.
The flame-brush technique was used to taper Fiber I down to our desired pitch. All other geometry was kept well during the tapering. The shape of the final tapered PCF is given in the left part of Fig. 4. The uniform taper waist is 10 cm long with the pitch of 1.18 μm. The corresponding nonlinearity coefficient is increased from 11 W−1km−1 to 81 W−1km−1. The untapered section and the taper transition part are separately 2 cm and 3 cm long at both ends, shown in Fig. 4. 40 fs 200 pJ pulses were launched into this taper by a lens, with the launch efficiency of about 50%. The generated SC spectrum is shown in Fig. 4(a), and the signals at the wavelength of 610nm and 1220 nm were selected for self reference fceo signal beating.
A Michelson type f-to-2f interferometer was used to previously compensate the delay between the two wavelengths. A 5 × 7 × 0.5 mm fan-out Mn:PPLN was used for SHG and was tuned to efficiently double 1220 nm. The combined f and 2f beams were focused on to a Si avalanche photodiode (APD) with a filter of 10 nm band-pass-width, and more than 40 dB fceo signal was recorded, shown in Fig. 5.
It is seen from Fig. 4(a) that the simulated spectrum covers more than one octave spanning spectrum (550 nm to 1400 nm) at the level of −30 dB, and the experimentally recorded SC agrees well with the simulated spectrum. The two strong peaks at the wavelength bands of 610 nm and 1220 nm are favorable for the indispensable f-to-2f self-reference technique for the stabilization of fceo.
The spectrum broadening process is explained as follows. Once entering the taper transition section, pump pulse experiences a symmetric broadening as a result of self-phase modulation (SPM). After propagating 2 cm in the transition part, the large anomalous dispersion contributes to the soliton fission and soliton Raman-self-frequency-shift. At the same time, the dispersive waves occur and continuously shift to shorter wavelength, because of the varying phase-matching conditions in the taper transition section. In the first 1 cm length of the uniform taper waist, SPM causes spectrum broadened quickly from 700 nm to 1400 nm. One obvious sidelobe appears near 1250 nm in the normal dispersion region. The others exhibit soliton features, such as soliton fission, between the two ZDWs (788nm and 1062nm). Meanwhile, dispersion waves are generated at visible wavelength around 600 nm. Finally, the obvious peaks around 610 nm (2f) and 1220 nm (f) are formed, which is ideal for self reference beating technique in our system.
To study the coherence of the SC in the fiber, phenomenological white noise was added to the input pulse in simulation to analysis the coherence of the output SC . After propagating 10 cm in Fiber II (the same structure as the uniform taper waist in this paper), good coherence was obtained at almost all the extended wavelength band from 550 nm to 1400nm with a input pulse of 40 fs and 200 pJ (soliton order N~13) (shown in Fig. 6(a)). As the pulse width was increased from 40 fs to 80 fs, while the same peak power was maintained (soliton order N~26), the coherence become worse in Fig. 6(b), though a similar SC spectrum was obtained. When the nonlinear fiber length is extended from 10 cm to 20 cm, the coherence was also deteriorated, shown in Fig. 6(c)). Furthermore, Fig. 6(d) shows that superfluous pulse energy (soliton order N~16) also degrades SC coherence. A lower soliton order contributes a lower SC noise. These simulation results prove that a shorter pulse width, a lower pulse energy, and a shorter nonlinear fiber, are always necessary for good coherence in coherent supercontinuum generation.
A fiber amplifier may introduce extra amplitude noise in the amplification process and may result in frequency noise on the broadened frequency comb as a result of the amplitude-to-phase conversion. Therefore, the absence of the power amplifier is also a must for a low extracavity noise. In addition, the direct generation of the supercontinuum also helps to simplify the comb.
By designing and fabricating a tapered fiber, we have demonstrated octave spanning supercontinuum generated by 40 fs, 200 pJ pulses directly from a simple femtosecond Yb:fiber laser oscillator. The low pulse energy spectrum broadening results in robust fceo >40 dB. This result implies that it is possible to access octave-spanning spectrum at a higher repetition rate (GHz) for frequency combs by their relatively low pulse energy. The direct generation of high fceo signal makes the Yb:fiber laser comb comparable to solid-state lasers and offers the potential for building up compact and real-world fiber laser frequency combs.
This work was partially supported by the National Science and Technology Supporting Program of China (2012BAI08B00), Nature Science Foundation of China (10974006, 11027404, and 61177047), the International Science & Technology Cooperation Program of China (2012DFG11470), and National key Science Instruments R&D Program (2012YQ140005).
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