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We present a highly versatile approach to the application of femtosecond Er:fiber lasers in optical frequency metrology. Our concept relies on the implementation of two parallel amplifiers, seeded by a single master oscillator. With the comb spacing locked to a frequency of 100 MHz, we apply the output from the first amplifier to generate a feedback signal to achieve a simultaneous phase-lock for the comb offset frequency. The output of the independently configurable second amplifier enables precision frequency measurements in the visible and near-infrared. As a first application, we continuously measure the absolute frequency of a resonator-stabilized diode laser over a period of 88 hours.
©2004 Optical Society of America
1. Introduction
The field of optical frequency metrology has been revolutionized since frequency combs of femtosecond lasers have been exploited for measuring the frequency of optical transitions in atoms and ions [1,2]. A frequency comb emitted by such a device is fully determined by the laser repetition rate f rep, which represents the spacing of the comb lines, and the carrier-envelope-offset (CEO) frequency f CEO, which is defined as the comb’s offset from zero. Hence, optical frequencies may be precisely measured with the resulting “frequency ruler” [3]. As both f rep and f CEO are in the radio frequency regime, they may be detected and counted with use of standard electronics. Although the detection of f rep is rather effortless, the determination of f CEO is far more challenging. Usually, an octave-spanning spectrum has to be generated to resolve f CEO in an f-to-2f interferometer. Due to their high output power and ultrashort pulse duration, Ti:sapphire lasers were the first systems to allow for nonlinearly broadened spectra exceeding one optical octave and the detection of f CEO by employing microstructured optical fibers with extremely small core diameters (≤2 µm) for continuum generation [4]. These days, most femtosecond frequency combs are based on Ti:sapphire lasers. However, with these systems it is cumbersome to achieve continuous operation over several days or even weeks, which is one basic requirement for novel metrological devices such as optical atomic clocks [5].
Therefore, erbium-doped fiber lasers have strongly been investigated for their applicability to optical metrology in recent years. Although still exhibiting significantly more high-frequency phase noise than Ti:sapphire lasers, they may be preferable with regard to long-term applications. It is possible to sustain mode-locked operation for weeks, making them excellent candidates for routinely facilitated long-term metrology and permanently running optical clocks. Other advantages of using frequency combs based on Er:fiber lasers are cost-effectiveness and compact setup, as well as their wavelength around 1.55 µm. Matching the telecommunication bands, a time standard generated by such an optical clock may be broadcasted via existing terrestrial fiber transmission networks.
Last year, the development of an advanced Er:amplifier concept improved the obtainable output power and pulse duration to values allowing for the generation of an octave-spanning spectrum in a short piece of a dispersion-shifted highly nonlinear fiber (HNF) with a mode-field diameter of 3.7 µm. Most importantly, the generated spectrum still revealed the fundamental comb structure of the oscillator. Thus, self-referenced detection of the carrier-envelope offset frequency was demonstrated for the first time with use of a fiber-based laser system [6]. Since then, significant progress has been made in controlling and stabilizing f rep and f CEO of fiber lasers. It has been shown, for instance, that the pump power of the oscillator is one suitable control variable for both repetition rate and CEO [7–9]. Of course, two different control parameters have to be applied in order to stabilize both frequencies simultaneously. Recently, Washburn et al. demonstrated a fully phase-locked Er:fiber laser system employing a fiber stretcher to stabilize f rep and controlling f CEO by varying the pump power [10].
In this paper, we present an Er:fiber laser system which is reliable and versatile enough to allow for long-term applications in frequency metrology. A novel concept employing two parallel amplifier stages results in high flexibility to configure the system. The first branch is used to generate an octave-spanning spectrum and detect f CEO. The repetition rate of the laser and the CEO frequency are stabilized simultaneously by controlling the oscillator length and pump power, respectively [11]. As the signals of both branches are mutually phase-coherent, the second branch provides a stable, well-defined frequency comb to perform precise frequency measurements. Its output characteristics may be varied independently from the first branch, establishing a link to a wide range of different optical frequencies. In order to demonstrate the reliability of our setup, we have used the frequency-doubled comb of the fiber laser for a frequency measurement of a resonator-stabilized extended cavity diode laser (ECDL). This laser operates at the frequency of the intercombination line of the Ca transition at 455.986 THz.
Fig. 1. Schematic setup of the two-color Er:fiber laser system. Solid lines indicate propagation inside optical fiber, dashed lines stand for propagation in free space. CL, fiber-to-free-space coupling lenses; MTS, manual translation stage; PBS, polarizing beam splitter; λ/2 and λ/4, wave plates; LF, Lyot filter; FI, Faraday isolator; WDM, wavelength division multiplexer; HNF, highly nonlinear fiber; SHG, frequency doubling crystal; L, lenses; POL, polarizer; PD1, InGaAs photo diode; PD2, Si photo diode.
2. Description of the two-color mode-locked Er:fiber laser system
A scheme of the two-branch fiber laser is sketched in Fig. 1. The Er:fiber oscillator is a stretched-pulse ring resonator employing nonlinear polarization rotation as mode-locking mechanism [12]. The increased repetition rate of the laser of 100 MHz improves the performance in metrological experiments owing to a higher value of optical power per comb line. It further simplifies the demands on the pre-determination of the mode-number m. One of the two fiber-to-free-space coupling lenses (CL) of the oscillator is fixed to a piezo ring actuator for stabilizing f rep. The second coupling lens is mounted on a manual translation stage (MTS) to allow for coarse adjustment of the repetition rate. The total range of that stage is 16 mm, corresponding to approximately 0.5 MHz in variation of f rep. Mode-locked operation is not influenced during manual adjustment. 20% of the circulating power (approximately 8 mW) is coupled out of the ring and equally distributed to two parallel amplifiers. In both cases, we rely on the amplifier concept developed and described in detail in Ref. 6.
The first amplifier, in the following referred to as “stabilization branch”, has been designed to provide maximum power and minimum pulse duration to generate the octave-spanning spectrum required for the detection of f CEO. This amplifier is pumped by two 980 nm pump diodes with a total cw-power of 850 mW. It delivers an average output power of 200 mW, corresponding to pulse energies of 2.0 nJ at a center wavelength of 1550 nm. The spectral bandwidth (FWHM) amounts to 60 nm. Subsequently, the fiber output is compressed in a free-space silicon prism sequence to a minimum pulse duration of 85 fs, measured via second-harmonic generation FROG [13] (see Fig. 2). The material passage through the silicon prisms may be varied to optimize the spectrum exiting the following HNF [14]. We employ 8 cm of the same fiber which is used in Refs. 6 and 14. It is a single-mode fiber with a reduced mode-field diameter of 3.7 µm and a zero dispersion wavelength of 1.52 µm. The output continuum covers a wavelength range from 920 nm to more than 2 µm, hence exceeding the required optical octave. An f-to-2f interferometer is used for self-referenced detection of f CEO. A sequence of SF10 prisms spatially separates the two selected components at 930 nm and 1860 nm, respectively. After being reflected by separate end mirrors, these components pass back through the prism sequence. Temporal overlap is adjusted by moving one mirror with respect to the other. Afterwards, the long-wave component at λ=1860 nm is frequency-doubled in a 10-mm-thick BBO crystal. A fast silicon photo diode detects the beat signal at f CEO. This frequency, corresponding to the comb offset, is stabilized by controlling the pump power of the oscillator. The detected CEO beat is shown in Fig. 3. The 3-dB-bandwidth of the signal is 330 kHz for both free-running and stabilized CEO frequency, well comparable to results obtained by other groups [10,11]. Compared to Ti:sapphire laser systems, the beat note is comparatively broadband due to the known phenomenon of high-frequency phase noise in fiber-based systems. As we will show later, that issue is not precarious for the application presented in this paper.
Fig. 2. (a) Spectrum and (b) temporal pulse profile of the compressed pulses from the first amplifier branch (black lines). The corresponding phases are depicted in blue. The relatively flat spectral phase indicates an almost transform-limited pulse. These results were obtained using frequency-resolved optical gating.
Fig. 3. Detected comb offset recorded with an rf spectrum analyzer with a resolution bandwidth of 100 kHz and a video bandwidth of 10 kHz (black). The 3-dB-bandwidth of the Lorentzian fit (red) amounts to 330 kHz.
The second, parallel amplifier branch is built up similarly to the first one. As both amplifier branches are seeded by the same oscillator, the second amplifier delivers a stable frequency comb at its output as soon as the repetition rate and offset frequency are stabilized via the first arm. The presented two-branch setup provides maximum flexibility for the experiment due to the fact that, despite the shared master oscillator, the two branches are independent from each other. The second “application branch” may even be modified or rebuilt arbitrarily, if necessary, without affecting the first “stabilization branch”. In the current layout, the amplifier is pumped by 480 mW from a single 980 nm pump diode and delivers a maximum of 140 mW of average output power. Another piece of HNF is used for frequency broadening. The HNF is directly spliced to the amplifier output (prism sequence has been omitted) to decrease noise from air fluctuations. The broadened and tunable spectrum ranging from 1200 nm to 1800 nm is then coupled out into free-space and 85 mW of average power are available. By varying the pump power of the amplifier, the spectrum may be tuned for maximum power in a specific spectral range. The comb can then be used to directly measure frequencies in the near infrared. Also, frequency measurements in the range between 600 nm and 900 nm may be performed with sufficient signal-to-noise ratio after frequency-doubling in a nonlinear crystal. Therefore, this configuration allows the coverage of a broad spectral range that also includes several highly stable optical standards, whose clock transitions is usually below 1 µm.
3. Stabilization of repetition rate and carrier-envelope-offset frequency
The oscillator repetition rate of 100 MHz is detected by a fast InGaAs photo diode (PD1) at the rejection port of the polarizing beam splitter (PBS) (see Fig. 1). In order to reduce the high demands on detecting the phase noise of the repetition rate and to increase the short-time resolution, we detect the 114th harmonic (11.4 GHz) of this signal (see Fig. 4). It is down-converted to 350 kHz by mixing with a microwave oscillator referenced to a hydrogen maser. After low-pass filtering, this intermediate frequency signal is used to phase-stabilize the repetition rate. Additionally, it is phase-coherently tracked by use of a harmonic tracking filter (VCO) with a locking bandwidth of 1 MHz (tracking the 128th harmonic). Thus, the output of the VCO represents the 128×114th harmonic of the repetition frequency. Its purpose is to enhance the resolution of our counting system to a value better than 10-13 s-1.
As mentioned earlier, the CEO beat is detected by a silicon photo diode (PD2) at the end of the f-to-2f interferometer. Its frequency is tracked by a VCO with a tracking band of 1.5 MHz and stabilized to a 30-MHz-reference signal by controlling the pump power of the Er:fiber oscillator. The bandwidth of the digital phase-locked loop (PLL) is adjusted by means of digital pre-scalers, resulting in a standard deviation of the CEO frequency of σ CEO=1.4 Hz. The corresponding standard deviation for the repetition frequency is σ rep=1.3 mHz. It has been shown by Telle et al. [15] that for absolute frequency measurements — which is the application presented here — the fs-laser can be regarded as transfer oscillator. Under these conditions the fluctuations of the CEO as well as the repetition rate do not enter into the final result. Therefore, we have not tried to further improve the bandwidth of the lock, but rather concentrated on optimizing it for long-term operation.
The combination of a VCO as tracking filter together with the use of a digital PLL allows us to optimize the phase traceability and the long-term stabilization independently. The VCO loop is optimized for high tracking bandwidth of the beat signal, while the digital PLL with its pre-scalers assures that the beat signals remain within the range of our fixed frequency filters. We found that dividing the CEO signal by a factor of 16 gives the best result for long-term applications. Cycle-slip-free operation of the PLL tracking filter was ensured by monitoring its loop error signal and a veto signal on the digital PLL.
All beat frequencies are additionally counted by use of totalizing counters with interleaved sampling, zero dead-time and common gate. The plots in Fig. 5 show the recorded locked frequencies with respect to the reference frequency f 0, which is 100 003 087 Hz for the repetition rate and 30 000 000 Hz for the CEO beat, respectively. Here, the recording was intentionally interrupted after 10 000 seconds. Later results will show that also longer periods are achieved.
Fig. 4. Scheme of the electronics used for locking the repetition rate. PD1 is the photo diode detecting the repetition rate. LP, low-pass filter; PS, power splitter. An analogous stabilization scheme is also used for the CEO frequency.
Fig. 5. (a) Recorded frequency of the phase-locked repetition rate at 100 003 087 Hz and (b) the simultaneously phase-locked carrier-envelope-offset beat at 30 000 000 Hz for a period of measurement of 10 000 seconds.
4. Long-term measurement of an optical frequency at 455.986 THz
Table 1. Technical data of the extended cavity diode laser (ECDL)
As a first application we measure the frequency of a diode laser stabilized to an external high finesse cavity. It is operating at 455.986 THz (corresponding to a wavelength of 657.46 nm) [16]. The key data of this laser are summarized in Table 1. Owing to its ultra-narrow linewidth and its extremely small drift due to the multi-stage thermal and seismic isolation, the source is perfectly suited for this demonstration. The setup of the experiment is sketched in Fig. 6. The beam from the ECDL (red dashed line) is superimposed on the frequency comb beam from the second branch of our Er:fiber laser system (black). A lithium tri-borate (LBO) crystal generates the second harmonic of the wavelength components of the comb spectrum between 1300 nm and 1380 nm (violet). The first order diffraction of a grating is used for selecting the desired spectral range around 657 nm. A silicon detector collects the rf beat signal between the doubled femtosecond frequency comb and the cw-diode laser. Additionally, a spectrometer may be placed in the direction of the zero order reflection of the grating to directly observe and optimize spectral overlap.
Fig. 6. Experimental setup for measuring the frequency of a resonator-stabilized ECDL by employing the phase-locked comb from the second amplifier branch of the fiber laser. CL, out-coupling lens; DM, dichroic mirror; BC, beam combiner; LBO, lithium borate crystal; G, grating.
Fig. 7. Measured difference of the ECDL frequency to an arbitrarily chosen offset frequency f offset over a period of 88 hours.
Fig. 8. Allan standard deviation of the measured frequency f ECDL. The integration time is as high as 30 000 seconds. For long integration times the Allan deviation rises with τ +1, which is typical for a drifting laser cavity.
As a first result, we were able to precisely trace the small temporal drift of the diode laser cavity. The beat frequency f x between the doubled frequency comb of the fiber laser and the ECDL has been tracked with an additional VCO with a tracking bandwidth of 1.3 MHz. Recording f rep, f CEO and f x simultaneously in the way described above, the absolute frequency of the measured laser line is calculated by f ECDL=m f rep+2 f CEO+f x. The correctness of the signs and the factor m=4 559 719 has been ensured before starting the experiment by varying the repetition frequency and the CEO frequency [17]. The measurement has been recorded over almost 88 hours without interruption at a rate of one data point per second. For a total number of 316304 data points the standard deviation of the CEO frequency amounts to σ CEO=2.2 Hz. For the repetition frequency (measured at 1459 GHz) it amounts to σ rep=0.8 Hz (σ rep=54 µHz at 100 MHz). These values correspond to a stability of 9.6×10-15 for f CEO and 5.4×10-13 for frep relative to f ECDL. The difference between the measured frequency f ECDL and an arbitrary offset frequency f offset=455 986 078 494 150 Hz is plotted in Fig. 7. The deviation of a few hundreds of kilohertz from the reference is due to cavity drift and manual readjustment since the last absolute frequency measurement of the calcium frequency standard, which was performed approximately one year ago. Fig. 8 shows the corresponding Allan standard deviation up to an integration time of 30 000 seconds. The plot is typical for a measurement of a drifting laser cavity. The initial instability of the presented measurement was 6.2×10-13 in one second, a factor of three higher than our H-Maser reference (2×10-13).
The short time stability has meanwhile been improved to the level given by that of the low frequency reference. As a consequence of these measurements, we conclude that the relative phase fluctuations of both femtosecond amplifiers over a measurement interval of 1 second are below the noise level of the hydrogen maser.
5. Summary and outlook
In conclusion, we have presented a novel design of a mode-locked Er:fiber laser system consisting of a stabilized ring resonator at a high repetition rate of 100 MHz and two parallel and coherent amplifier branches. The high-power first branch is used to detect and stabilize the carrier-envelope-offset frequency (“stabilization branch”). When the laser is completely phase-locked, the second amplifier provides a stable frequency comb. Depending on the desired application, this branch may be flexibly configured with respect to output power, spectrum and pulse duration. The fundamental comb structure and the first amplifier branch are in no way affected. In the present configuration the “application branch” provides a wide range of spectral components in order to perform measurements at various frequencies. Here, an LBO crystal is also used to generate frequency-doubled light around 657 nm.
As a first application for this system, we measure the frequency of a resonator-stabilized extended cavity diode laser exhibiting extremely low drift and narrow linewidth. An uninterrupted measurement over almost 88 hours is recorded to demonstrate the excellent long-term stability of the fiber laser compared to conventional solid-state laser systems [18,19]. To the best of our knowledge, the presented result reveals the longest continuous measurement of an optical frequency with use of a femtosecond comb. The experiment also shows that the phase noise of the fiber laser system is not a critical issue in terms of frequency metrology. The measured laser line at 455.986 THz is used to interrogate the intercombination line of the Calcium optical standard at PTB, i.e. the presented laser system should also enable a precise determination of the frequency of the 40Ca 3P1-1S0 transition. Compared to measurements performed with an intricate frequency chain [20] or a Ti:sapphire laser system [18,21], this fiber-based frequency comb allows for easier operation and longer measurement time. The reported system is therefore an important step towards a user-friendly, flexible, compact, and reliable laboratory tool for precision measurements of optical frequencies. Also, optical clocks operating uninterruptedly over weeks based on this concept may be feasible now.
Acknowledgments
We wish to thank A. Laubereau for his support during construction of the laser system. This work is supported by a grant from the Ministry of Science, Research and the Arts of Baden-Württemberg.
References and links
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