1. Introduction

Phase stabilized, mode-locked lasers have only recently found their way to applications in optical frequency metrology [1]. By establishing a direct link to stable microwave clocks, self-referencing systems eliminate the need for complicated frequency chains and thereby greatly facilitate the precise determination of optical transition energies [2–4]. In the time domain, phase stabilization paves the way towards controlled waveform synthesis of few-cycle pulses, impacting the fields of extreme nonlinear optics and coherent control [5,6]. For an overview over the field of phase stabilization of ultrashort optical pulses, see [7].

Due to the high peak intensities required for the self-referencing detection of the carrier-envelope phase evolution, most experiments to date have been carried out with Ti:sapphire lasers. Despite their widespread and successful application in research laboratories, these sources suffer from several drawbacks, such as size, pump laser requirements, expense and the need for regular realignment. It is for these reasons, that Ti:sapphire lasers have rarely found use in real-world applications. On the other hand, all-fiber mode-locked lasers have the potential to circumvent all of these shortcomings. Based on direct pumping from fiber-coupled laser diodes and light propagation inside a waveguide, designs are more compact, less expensive and more stable than their free space counterparts. Moreover, the operation in the spectral window around 1.55 µm makes Er:fiber lasers compatible with a multitude of photonic devices developed for telecommunications technology.

Recently, it has been shown that the spectrum emitted by a mode-locked Er:fiber laser does indeed exhibit a comb structure [8]. The phase evolution was measured and could be stabilized via optical heterodyning with a Ti:sapphire laser [9]. However, the relatively low intensity currently available from Er:fiber lasers has so far prevented self-referencing stabilization.

Here, we present an amplified all-fiber laser system, optimized for the self-referenced measurement of the carrier-envelope phase evolution. Seed pulses are derived from a home-built, passively mode-locked Er:fiber laser [10]. The seed is temporally stretched in a standard telecom fiber with negative group velocity dispersion (GVD) before entering the amplifier. Owing to the positive GVD of the Er:fiber, the pulses shorten during amplification. By varying the length of the pre-chirping fiber, the peak intensity at the end of the amplifier can be accurately tuned. We achieve a significant broadening of the spectrum via self-phase modulation without pulse break-up. Due to the enhanced bandwidth, the pulses can be recompressed to a width below the Fourier limit of the seed spectrum.

The laser system on its own already bears great potential for further use in various fields of ultrafast science, such as coherent infrared generation and THz spectroscopy. In both cases, the central wavelength of 1.55 µm renders phase-matching constraints less severe as compared to Ti:sapphire lasers. Additional profits include low excess noise, simple handling and high reliability.

In order to prove the usefulness of our novel source, we demonstrate the generation of an octave-spanning supercontinuum inside a short piece (7 cm) of highly nonlinear fiber with reduced mode-field diameter. In principle, this bandwidth sets the basis for self-referencing detection of the carrier-envelope phase evolution [2–4]. However, it is a priori not clear, whether the coherent frequency comb from the mode-locked laser is maintained during amplification and continuum generation. Incoherent scattering processes and spontaneous emission might destroy the coherence.

Using an f-to-2f interferometer setup [3], we clearly detect carrier-envelope offset beats. This finding proves that decoherence is negligible for the short propagation distances realized in our design. Thereby, our measurements confirm that self-referenced detection of the phase evolution of ultrashort light pulses is feasible with an all-fiber optic laser system, eliminating several drawbacks related to free space Ti:sapphire technology.

2. Laser system

The Er:fiber ring laser providing the seed pulses for the amplifier is similar to the one reported by Tamura et al. [10]. It is pumped by two laser diode chips emitting at 980 nm. Mode-locking is initiated by correct adjustment of two polarization controller stages. The laser delivers 3 mW of fiber-coupled output power at a repetition rate of 67.4 MHz and a central wavelength of 1.55 µm.

The setup of the single pass amplifier system is sketched in Fig. 1. After leaving the oscillator, the seed pulses are temporally stretched in a standard single-mode fiber with a GVD of β=-0.023 ps²/m. The amplifier itself is pumped from both sides by fiber-coupled pump diodes operating at 980 nm. Each laser chip provides 200 mW of output power. The fiber used for the amplifier is highly doped with Er³⁺ ions, giving rise to an unpumped attenuation of 80 dB/m at 1530 nm. This allows to limit the length of the gain medium to 2 m. Owing to the positive GVD of the Er:fiber (β=+0.057 ps²/m), the pre-chirped pulses shorten during amplification.

 

Fig. 1. Fiber optic stretched pulse amplifier system. WDM: Wavelength-division multiplexer.

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Figure 2 shows output spectra from the amplifier for various lengths l of the stretcher. For comparison, the seed spectrum from the oscillator is depicted in the inset of Fig. 2(a). Its lineshape is well described by a Gaussian with a full width at half maximum (FWHM) of 42 nm. In case of a long stretcher, the output spectrum is predominantly influenced by gain narrowing and the highly structured profile of the Er:laser transition reducing the bandwidth to 27 nm FWHM (Fig. 2(a)). For smaller amounts of pre-chirp (Figs. 2(b+c)), the pulses attain shorter durations inside the amplifier. Due to the small mode field diameter of the Er:fiber (4.2 µm), off-resonant nonlinear pulse shaping starts to prevail. Self-phase modulation counteracts the effect of gain narrowing and broadens the spectrum to beyond 100 nm for the shortest length of the stretcher (Fig. 2(c)).

To prevent the onset of excessive nonlinearities which would eventually lead to a breakup of the pulses [11], the light is coupled out from the fiber to free space immediately after the amplifier. Since the negative pre-chirp induced by the stretcher is not yet fully compensated for, an external pulse compression scheme has to be applied. To this end, we use a double-pass sequence with two silicon prisms, as depicted in Fig. 1. The role of the compressor is not to apply further negative group velocity dispersion to the pulses. We rather work with a short distance between the prism tips and a relatively long path through the material, which provides overall positive GVD. By introducing more or less Si into the light path, we can accurately fine tune the amount of positive chirp added to the pulses.

 

Fig. 2 (a-c). Output spectra from the Er:doped fiber amplifier for various lenghts l of the pre-chirping fiber. Inset: Seed spectrum derived from the mode-locked fiber ring laser.

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In order to minimize reflection losses at the silicon surfaces, the polarization is set horizontally with two waveplates in front of the compressor and the prisms are inserted under the Brewster angle. The average optical output power after the prism sequence is 110 mW.

The characteristics of the output pulses are determined via a second harmonic FROG measurement [12]. Results for a stretcher with a length of 120 cm are depicted in Fig. 3. As the reconstructed intensity trace clearly confirms (Fig. 3(b)), indeed no pulse break-up occurs inside the fiber. Although the spectrum obviously develops additional structure due to the combined action of amplification and nonlinearity (Fig. 3(a)), the major part of the energy is still contained in a single pulse with only small side peaks originating from uncompensated higher-order chirp. Furthermore, the data show that the pulse width is reduced to 65 fs after the compressor. This finding has to be contrasted with the lower limit for the input pulse duration of 85 fs calculated via Fourier transform of the spectrum in the inset of Fig. 2(a), assuming a flat phase relationship. Thus, the spectral broadening inside the amplifier enables us to achieve output pulses with a duration even shorter than the transform limit of the seed. The spectral phase of the amplified pulse remains flat to within π/2 over the entire bandwidth (Fig. 3(a)), indicating efficient compression with the prism sequence. The spectrum itself would allow for pulse durations of 55 fs, if the remaining higher-order phase distortions could be eliminated, e.g. by introducing a deformable mirror at the end of the compressor [13].

 

Fig. 3. Intensity (black lines) and phase (blue lines) of the compressed pulses in the wavelength (a) and time domain (b) for a stretcher with a length of l=120 cm. Pulse characteristics are determined via second-harmonic FROG.

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3. Application: Supercontinuum generation and self-referencing detection of the carrier-envelope phase evolution

3.1 Background

It has been realized a long time ago, that the spectrum of periodically emitted ultrashort pulses from a mode-locked laser consists of a comb of discrete frequencies. The lines are equally spaced by the repetition rate f_rep of the laser and the entire comb is offset from zero by a frequency δ, which is determined (in the time domain) by the pulse-to-pulse phase shift. The position of each individual line is therefore exactly defined by the two frequencies f_rep and δ, which fall into the radio frequency (RF) regime. The repetition rate can be easily measured with a simple photodetector and locked to a precise microwave clock. In comparison to this, the detection of the offset frequency has been a daunting task. However, a scheme for the straightforward, so called self-referencing determination of δ was demonstrated recently [3,4]. The method involves generation of a broadband continuum covering more than one optical octave from femtosecond light pulses. This goal has been achieved in waveguides with low cross-sections and specially tailored GVD. When the second harmonic of the long-wavelength end of the spectrum is superimposed on the short-wavelength wing of the fundamental, a characteristic beat signal revealing the offset frequency δ is detected [2]. A direct control over δ is achieved by either varying the pump power of the laser, or by swiveling one of the resonators’s end mirrors.

Therefore, the key to efficient self-referencing detection of the carrier-envelope phase evolution is the generation of an octave-spanning continuum and its frequency doubling. It is of essential importance, that the coherent comb structure of the spectrum is preserved during these steps. Until now, the intensity required for driving these highly nonlinear processes could only be provided by Ti:sapphire sources or similar bulk lasers. Here, we demonstrate self-referencing detection of δ with our all-fiber laser system.

3.2 Experiment

The setup of the f-to-2f interferometer for self-referenced detection of the carrier-envelope phase evolution is depicted in Fig. 4. First, the 65 fs pulses from the compressor output are coupled into a polarization-maintaining highly nonlinear dispersion shifted fiber with a reduced mode field diameter of 3.7 µm. The zero-dispersion wavelength is situated close to 1.55 µm. Details of pulse evolution inside this type of fiber have been studied recently for lower intensities and much longer propagation distances [14]. In our case, a length of 7 cm suffices for the generation of an octave-spanning continuum. After the fiber, the emerging light is collimated and focussed into a 1 cm thick BBO nonlinear crystal. Due to the type I phase-matching geometry, the frequency doubled light is polarized perpendicular to the fundamental. A subsequent polarizing beam splitter separates the two components. The second harmonic is directed over a variable delay line, which allows to adjust the temporal overlap. Both parts are then superimposed spatially with the help of a second polarizing beam splitter, before they pass an interference filter and a polarizer. Finally, the optical power is detected with a Si avalanche photo diode. The signal is boosted in a low-noise pre-amplifier and fed into a RF spectrum analyzer.

Figure 5 shows the spectral content of the generated continuum. A prominent maximum occurs around 1160 nm and the spectrum stretches out to 850 nm on the short-wavelength side (black line). The existence of the broadband peak appears to be an interesting feature, since all of its energy is still contained in a single femtosecond pulse. We demonstrate efficient frequency doubling of this maximum into the visible. Resulting spectra for two different phase-matching angles Θ₁=22.3° and Θ₂=21.2° of a 10 mm BBO doubling crystal are displayed as gray lines in Fig. 5.

 

Fig. 4. f-to-2f interferometer setup for the detection of the carrier-envelope phase evolution. PM-HNDSF: polarization-maintaining highly nonlinear dispersion shifted fiber, BBO: nonlinear crystal, Θ: phase-matching angle, PBS: polarizing beams splitter, IF: interference filter, Pol.: polarizer, Si-APD: silicon avalanche photo diode.

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Second harmonic generation with the same crystal also allows us to analyze the low frequency region of the spectrum using exclusively near-infrared detection. Varying the phase-matching angle Θ around 20.7°, we find a pronounced maximum at a wavelength of 1880 nm [14], corresponding to a second harmonic signal at 940 nm (see Fig. 5). At this wavelength, we observe an overlap between the fundamental and the frequency doubled spectrum. This finding proves that the bandwidth of the continuum exceeds one octave.

The RF spectrum of the photo current detected with the Si avalanche photo diode at the output port of the f-to-2f interferometer is depicted in Fig. 6. The phase-matching angle of the BBO is set to Θ₃=20.7°. A sharp maximum at 67.4 MHz indicates the repetition rate of our laser. In addition, we find clear satellite peaks at frequencies δ=5.4 MHz, f_rep-δ=62.0 MHz and f_rep+δ=72.8 MHz, revealing the offset of the frequency comb. Indeed, the appearance of the satellite peaks proves the conservation of a regular spectral comb structure, which was not clear a priori. We attribute the successful measurement of δ to the fact that the fiber propagation distance of the pulses is kept short for both, amplification and continuum generation. Obviously, the influence of incoherent processes such as amplified spontaneous emission, guided acoustic wave Brillouin scattering and spontaneous Raman scattering is negligible under our conditions.

 

Fig. 5. Supercontinuum generated inside the highly nonlinear fiber (black line) and its second harmonic (gray lines) for phase-matching angles of Θ₁=22.3°, Θ₂=21.2° and Θ₃=20.7°.

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Fig. 6. RF spectrum measured after the f-to-2f interferometer. Beat notes from the pulse-to-pulse phase slip appear at 5.4 MHz, 62.0 MHz and 72.8 MHz. The resolution is set to 250 kHz.

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Even though the optical power has decreased to 1 µW after the interference filter and the polarizer, the beat signals exhibit a signal-to-noise ratio of 30 dB at 250 kHz resolution bandwidth. The width of the carrier-envelope peaks is limited by the resolution of our RF spectrum analyzer. Due to the excellent stability of our all-fiber laser system, the positions of the peaks remain stable within 1 MHz over hours without external stabilization. On the other hand, δ is conveniently shifted to any desired value by adjusting the oscillator pump power. Active stabilization of δ appears to be straightforward under these circumstances.

4. Summary

In conclusion, we have provided a detailed presentation of a novel amplified all-fiber femtosecond laser system, based on a mode-locked fiber ring oscillator and a nonlinear single-pass amplifier. Profits of the technology include cost effectiveness, ease of use and high stability. We demonstrate simultaneous amplification and controlled spectral broadening inside a 2 m long Er:fiber, allowing us to shorten the output pulses to below the width of the seed. 110 mW of linearly polarized output power are obtained in 65 fs pulses at a repetition rate of 67 MHz, making our system a promising tool for a variety of applications of ultrafast optics.

The highly intense pulses are used to generate an octave-spanning supercontinuum within only 7 cm of a nonlinear fiber with reduced mode field diameter. Due to the short fiber propagation lengths, the coherent comb structure from the oscillator output is maintained during amplification and transferred to the continuum. This finding sets the basis for self-referencing measurements of the carrier-envelope phase evolution. With an f-to-2f interferometer setup, we detect characteristic beat notes revealing the pulse-to-pulse phase slip. The carrier-envelope beats in our approach exhibit narrow linewidths, low drift and high robustness, even without any measures to stabilize the laser. Including second harmonic generation of the high frequency region of the supercontinuum, we have demonstrated an extremely compact device to generate an optical comb between 540 nm and 1.9 µm. This wavelength interval spans a large part of the visible spectrum and all relevant telecommunication bands. As an example, our system might serve as an ultrastable and hands-off frequency divider in space-born all-optical atomic clocks.