. We present a sub-85 fs self-starting stretched-pulse passively mode-locked Erbium-fiber oscillator in a sigma setup with tunable repetition rate. The sigma cavity included a movable mirror enabling a tunable pulse repetition rate variation of ±1 % from 55.3 MHz to 56.4 MHz with continuous, uninterrupted mode-locked operation and an output power around 14 mW. Based on the wide tuning range of the repetition rate the presented fiber oscillator is a suitable candidate for applications in femtosecond spectroscopy or precision metrology around 1.56 µm.
©2004 Optical Society of America
Passively mode-locked Erbium-fiber oscillators are efficient femtosecond (fs) laser sources in the telecommunication band around 1.56 µm, which allow the generation of ultra-short laser pulses with a duration down to 55 fs . Since these Erbium-fiber lasers are compact and reliable, they are appropriate candidates for fs-applications in fundamental and applied physics around 1.56 µm. By this, recently ultra-short pulsed Erbium-fiber based systems have been investigated and used for the generation of octave-broad supercontinua in nonlinear fibers [2–4]. Furthermore, the comb structure of the Erbium-fiber oscillator’s output spectrum was demonstrated by the measurement of the carrier-envelope-offset frequency [2,5–7]. Applications like frequency metrology require the control of two characteristic orthogonal parameters of the corresponding frequency comb, i.e. the repetition rate fRep and the carrier-envelope-offset-frequency fCEO . It has been demonstrated, that an internal fiber stretcher  or the pump power  are suitable control elements for adjusting the oscillator’s repetition rate. On the other hand, these control mechanisms show technical limitations like narrow control range and small servo bandwidth.
Furthermore, a tunable oscillator repetition rate is also necessary for experiments, which require two synchronized laser sources, e.g. pump-and-probe experiments [10,11]. Therefore, a control of at least one oscillator’s repetition rate is essential to achieve the synchronization.
In this paper, we report on a self-starting sub-85 fs diode-pumped stretched-pulse Erbium-fiber laser oscillator operating around 1.56 µm which was passively mode-locked by nonlinear polarization rotation [12,13]. The oscillator was tunable in its repetition rate by about 1.1 MHz (from 55.3 MHz to 56.4 MHz) with continuous, uninterrupted mode-locked operation. We observed only minor changes in the autocorrelation function and in the optical spectrum with tuning confirming stable mode-locked operation during the introduced cavity length changes.
2. Experimental setup
The schematic setup of the fiber oscillator system, which included a free-space section and a delay line for repetition rate tuning, is sketched in Fig. 1. The fiber-based part of the oscillator consisted of a normal 1.33 m long dispersive Erbium-doped fiber, which has a group-velocity dispersion (GVD) of ~-22 fs/(nm·m) at a wavelength of 1560 nm, and two anomalous dispersive fibers: SMF 1528 (GVD=~18 fs/(nm·m), length=0.89 m) and HI 1060 (GVD=~5.5 fs/(nm·m), length=1.31 m). Based on these fiber data the fiber part of the oscillator showed a normal total cavity dispersion of about -6 fs/nm at 1560 nm. The Erbium-fiber was pumped via a 980/1550 nm-coupler at 980 nm with a single mode fiber-coupled laser diode along the propagation direction of the oscillator pulses. A Faraday isolator ensured unidirectional operation and a polarization beam splitter (PBS 1) and two polarization controllers (PC) were applied for the passive mode-locking mechanism by nonlinear polarization rotation. For the transition from the fiber to the free-space part of the oscillator two long distance pigtailed fiber collimators were used. The free-space part was composed by a combination of two waveplates (one half-waveplate and one quarter-waveplate), a polarization beam splitter (PBS 2) and a movable mirror (MM). The resulting geometrical cavity is described and known as sigma configuration . In this presented work the linear part of the sigma setup provided easy, stable and reliable variation of the cavity length by moving the mirror with a translation stage and allowed subsequently tuning of the oscillator’s repetition rate. The free-space beam length could be adjusted with the mechanical translation stage by a travel range of 5.2 cm resulting in optical cavity length change of 10.4 cm. The translation stage position of 2.5 cm corresponded to the maximal free-space length, i. e. the minimal repetition rate and the position of -2.7 cm to the minimum length resulting in the maximal repetition rate. The adjustment of the free-space part was carried out around the central position of the translation stage, so that small unavoidable misalignment by moving the translation stage resulted only in small effects on the laser operation for different stage positions.
The oscillator’s repetition rate was analyzed with a fast InGaAs-photodetector and a radio frequency (RF) spectrum analyzer. The optical spectrum was detected with an optical spectrum analyzer and the autocorrelation function width, representing an upper limit for the pulse duration, was measured with a second order interferometric autocorrelator.
For a pump power of about 185 mW, a self-starting mode-locked operation was achieved for all positions of the translation stage and also sustained during cavity length changes. The repetition rate changed linearly with the position of the translation stage from 55.3 MHz to 56.4 MHz resulting in a relative change regarding to the central translation stage position of nearly ±1 %. The linear dependence and the slope of approximately -0.11 MHz per additional centimeter propagation distance corresponded to the expected value. A significant deviation of the expected linear repetition rate changes of the laser have to be taken into account, only if strong spectral changes are observed, which could lead to a different group velocity and accordingly an additional change in the repetition rate.
The average output power varied between 13.5 mW and 14.5 mW depending on the position of the translation stage, whereas the maximum was observed around the central position of the translation stage and the minimum at each of the end positions. This output power dependence on the translation stage position is a result of the fine adjustment of the free space section, since it was done around the central translation stage position, and of the distance-dependent coupling efficiency between the used pigtailed fiber collimators.
Due to the stretched-pulse setup the intra-cavity propagating pulse was temporally stretched and compressed by group velocity dispersion (GVD) during one round trip. Since the position of the PBS 1 (output port) normally differs from the position of minimal pulse duration in the cavity, the extracted laser pulses typically have to be compressed outside the cavity for minimal pulse duration . As the pulses, that are generated in a stretched-pulse fiber laser, show mainly a linear pulse chirp , the chirp of the extracted pulses could be minimized by an appropriate composition of normal and anomalous dispersive fibers at the output port around the central translation stage position.
In Fig. 2 the corresponding optical spectra of the compressed laser pulses are shown for translation stage positions of -2.7 cm, 0.0 cm and 2.5 cm. The measured spectra of the compressed laser pulses spanned from 1500 nm up to 1660 nm and showed a modulated envelope. As the limited gain bandwidth of up to 35 nm of a standard Erbium-doped fiber  does not allow the generation of pulses with a spectral bandwidth of more than 100 nm as observed, nonlinear effects like self-phase modulation (SPM) and intra-pulse stimulated Raman-scattering (SRS) resulting in a self-frequency shift  influenced the pulse generation in the oscillator as well as the pulse propagation in the output port fiber. These effects (SPM and intra-pulse SRS) resulted in an energy redistribution of spectral parts leading to the modulation of the spectra and leading to the spectral width of 160 nm from 1500 nm up to 1660 nm.
It can be seen, that the output spectra for different translation stage positions were identical, except of the spectral peak around 1620 nm, which was less intense at the end positions of the translation stage in contrast to the spectrum at the central position of the translation stage. Comparable changes in the output spectrum and output power were observed for small misalignments of the free-space section during the laser operation at a fixed translation stage position. Similar spectral changes leading to a red-shifted central wavelength of the output spectrum by changing the pump power of an Erbium oscillator were also reported in reference . This power dependent behavior and the frequency difference of several THz between the peak around 1620 nm and the center of the remaining spectrum indicated, that the increase of the maximum around 1620 nm was generated by intra-pulse SRS induced self-frequency shifting . As the intra-cavity power and output power depended on the translation stage position, higher losses decreased the peak power of the propagating pulse and subsequently also the intensity of those parts of the spectrum generated by intra-pulse SRS at the end positions of the translation stage position.
In Fig. 3 the corresponding interferometric autocorrelation functions of the compressed pulses are shown for translation stage positions of -2.7 cm, 0.0 cm, and 2.5 cm. All autocorrelation function widths (FWHM) were 85 fs or less, which can be considered as an upper limit for the pulse duration. Taken into account the composition of the external fiber compressor, the fiber dispersion data and a minimal pulse duration of 85 fs at the output an internal cavity stretching factor (ratio between longest pulse to shortest pulse duration in the cavity) of up to 4 can be calculated. The residual oscillations in the wings of the autocorrelation functions can be attributed to the spectral shape: As the optical spectrum (frequency domain) and the electric pulse field analyzed by the autocorrelation function (time domain) can be transformed into each other by Fourier-transformation , the modulated shape of the output spectrum results in a modulated temporal pulse shape. Based on the spectrum at the central translation stage position (0.0 cm) the Fourier-transformed electric field and the related interferometric autocorrelation function were calculated assuming a spectral phase equal to zero over the whole spectrum. The resulting theoretical autocorrelation function is shown in Fig. 3(d) and it can be seen, that there exist comparable oscillations in the wings like they were observed experimentally.
Furthermore, the intensity autocorrelation functions were computed by averaging the interferometric autocorrelation function. By this, it was shown, that also the intensity autocorrelation widths (FWHM) were also less than 85 fs confirming the above mentioned upper pulse duration limit. For a precise ascertainment of the pulse duration, the measurement of the temporal and spectral pulse phase is required, which was not possible with the actually available detection setup.
The slight difference in the autocorrelation width of 5 fs between the central position and the end positions of the translation stage can be attributed to losses of the propagating pulse in the oscillator’s free-space part depending on misalignment losses at each of the translation stage positions. The losses resulted not only in different output powers, but also influenced the intra-cavity intensity-dependent dynamics of the periodically stretched and compressed intra-cavity pulses and, in consequence, the locations, where the pulse is maximally compressed (minimal intra-cavity pulse duration) and maximally stretched (maximal intra-cavity pulse duration). Since the chirp of the extracted pulses belongs to the intra-cavity locations of minimal pulse duration, a change of these locations results also in a modified compression capability of the extra-cavity compression fiber arrangement. Therefore, the fixed total dispersion of the output port’s fiber arrangement differed slightly from the optimum value at the end positions of the translation stage resulting in the observed slight increase of the pulse duration.
In summary we presented a stable, reliable passively mode-locked Erbium-fiber oscillator, which produced sub-85 fs laser pulses around 1.56 µm at a repetition rate of about 56 MHz. The oscillator was realized in a sigma setup in order to vary the repetition rate by changing only the length of the cavity. We achieved a tuning range from 55.3 MHz to 56.4 MHz corresponding to a maximum relative change of ±1 %. Therefore, the presented oscillator system is suitable for the synchronization with other pulsed laser sources or for improved applications in precision metrology like a stabilized frequency comb generator at 1.56 µm.
This research was partially supported by the Deutsche Forschungsgemeinschaft in the frame of SFB 407. We gratefully acknowledge the stimulating discussions with Harald R. Telle, Erik Benkler, and Nils Haverkamp from the Physikalisch-Technische Bundesanstalt (Braunschweig, Germany). We gratefully wish to thank the Institut für Physikalische Hochtechnologie (Jena, Germany) for the supply of the Erbium-doped fiber.
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