1. Introduction

Stabilized laser systems are used as frequency references, realization of the definition of the meter [1], in cold atom trapping [2], or for calibration of optical components to name but a few. In such laser systems the frequency is usually stabilized to a precisely known reference which may be an atomic, ionic, or molecular transition. In the C-band the Bureau Internationale des Poids et Mesures (BIPM) commends the use of acetylene at a pressure of 3 ± 2 Pa as a reference [3, 4]. At such low pressures one often employs multi-pass cavities to increase the effective absorption length well beyond the cavity length, thus, enhancing the signal-to-noise ratio. The observed line widths of the relevant acetylene transitions in linear absorption measurements are inhomogeneously broadened and depend on the ambient temperature (Doppler broadening). In order to have access to the narrower homogeneous line widths, thus increasing the accuracy with which the absolute frequency can be determined, one often uses nonlinear saturation spectroscopy. For telecommunication applications it would be desirable to realize a robust all-fiber frequency standard which is compatible with commercial fiber components. Specifically, such an all-fiber system would require a fiber-based absorption cell, which became possible with the advent of hollow core photonic bandgap fibers (HCPCF) [5] and several applications of such cells were reported [6, 7, 8, 9]. A number of groups have demonstrated stabilization of a fiber laser in combination with bulk gas cells [10, 11, 12] and Knabe and coworkers have successfully stabilized a fiber laser with a gas-filled HCPCF [13], however, not in a all-fiber configuration. Here, we present an all-fiber version of a frequency-stabilized laser system operating in the C band. We examine three different methods to stabilize the laser frequency to the nonlinear saturation dip of the P15 acetylene transition.

2. Experimental

To stabilize a laser to an absorption line its intrinsic width must be narrower than the width of the absorption line. Such needs are ideally met by a ring cavity and the specific geometry used here is shown in Fig. 1(a). The cavity length is 4.4 m yielding to a mode spacing of 46.6 MHz. The active medium is a 1.5 m long erbium-doped fiber pumped by a 300 mW diode at a wavelength of 976 nm. To ensure unidirectional operation and to suppress parasitic back reflections the cavity contains two fiber-optic isolators. A polarization controller and a polarizer define the state of polarization. The 1% output coupler extracts a power of 0.7 mW. Several components guarantee single-mode operation. First, we use a tunable dielectric filter (DF) with a bandwidth of 37 GHz (0.3 nm) for a coarse wavelength selection between 1530 nm and 1570 nm. Second, we employ a tunable fiber Fabry-Perot (FFP) with a free spectral range of 75 GHz (0.6 nm) and a line width of 0.5 GHz (4 pm) for fine tuning. Coarse frequency tuning with the DF, as shown in Fig. 1(b), allows to select different absorption lines of acetylene. Once a suitable line is identified the DF remains fixed and fine tuning across this line is realized by a combination of different measures. First, the cavity length is varied with the piezo, whose maximum elongation is 30 μm. Second, the FFP is automatically tuned with a feedback loop by a proportional-integral-derivative (PID) controller such that its transmission maximum is locked to the cavity mode to prevent mode hops. To that end the cavity contains two additional 1% output couplers, one before and one after the FFP, and both signals are sent to a balanced photo receiver. Its output provides the feedback signal for stabilizing the FFP to the cavity mode. As a result we can fine tune the cavity mode mode-hop free within a frequency range of about 1.3 GHz, limited only by the piezo. The width of the cavity mode was measured to < 2 kHz and the ASE background is 65 dB below signal level.

 

Fig. 1 (a): Schematic of the ring laser; for details see text. (b): Spectral intensity as a function of wavelength for different settings of the bandpass filters within the cavity.

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An integral part of all stabilization experiments hereafter is a recently developed all-fiber gas cell; details may be found in reference [14]. Briefly, it consists of a 80 cm long, 19 cell HCPCF (NKT Photonics, HC19-1550-01) with a core diameter of (20 ± 2) μm filled with acetylene. At room temperature the inhomogeneous line width is 466 MHz. The homogeneous line width is determined by pressure, transit time, and power broadening. Pressure broadening values are between 5.6 MHz/mbar and 10.7 MHz/mbar [15]. Transit time broadening amounts to (21.6 ±2.2) MHz for the HCPCF used [16, 17]. That is, for pressures smaller than a few mbar transit time broadening is the dominating mechanism. We fill the HCPCF with approximately 2 mbar as a compromise between a strong enough absorption strength and a low enough pressure broadening. To obtain a sufficiently large feedback signal we use a laser power of 200 mW which further broadens the line by about a factor of 1.5. The resulting homogeneous line width is measured to (47 ± 2) MHz. Note that the pressure used is higher than the recommended value of 3 ± 2 Pa [4]. The HCPCF gas cell is connected to standard optical fibers with angled cleaves at 8 degrees resulting in return losses of 48 dB. Although very low, the return losses can result in an oscillatory background signal which may be as high as the nonlinear absorption signal.

3. Results

In the following we investigate three different stabilization schemes. In all cases the oscillator output is further amplified to a maximum power level of 200 mW. Specifically, we examine a classical pump-probe scheme with two counter-propagating beams, a reflected pump beam version of the latter, and the Pound-Drever-Hall scheme. The stabilized frequency is compared to an optical frequency comb (Menlo System FC1500) at METAS, which is referenced to a hydrogene maser. The comb measures absolute frequencies with an uncertainty of a few 100 Hz. To quantify the stability we extract the Allan deviation from the measured frequency versus time. The Allan deviation is compared to a theoretical estimate [18]

3.1. Pump-probe scheme

The pump-probe geometry is motivated by its frequently used free-space analogue and the experimental details are shown in Fig. 2(a). Approximately 90% of the laser beam is sent directly through the all-fiber gas cell and serve as a pump. The remaining 10% is injected into the gas cell from the opposite direction and serve as a probe. To suppress interferences between spurious pump reflections and probe light, the probe is frequency shifted by 40 MHz with an acousto-optic modulator (AOM). The AOM is powered by an RF generator which is stabilized to an atomic clock in order to exclude that the AOM limits the stability. Two circulators extract parts of the probe beam before and after the gas cell. The two signals are send to a balanced photo detector and its output goes to a lock-in and a PID controller. The PID controls the voltage of the intra-cavity piezo and stabilizes the cavity mode to the center of the saturation dip. The measured Allan deviation versus time is shown in Fig. 2(b). It reaches a value of 3 · 10⁻¹⁰ after about 1000 s. The measured mean frequency has an offset of (20.30 ± 0.05) MHz when compared to the reference [3]. While 20 MHz are due to the AOM, the remaining 300 kHz are typical for the system and are caused by fluctuations. Through imaging the transverse mode profile on a CCD we have noticed that slight variations of the polarization or the fiber position cause the mode profile inside the multimode HCPCF to change which then leads to frequency drifts and to an offset compared to the reference.

 

Fig. 2 (a) Pump-probe setup. (b) Allan deviation versus time (blue curve) and Eq. 1 with S/N = 90 (black curve). The laser was stabilized for 8400 s.

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3.2. Reflected pump scheme

In order to simplify the stabilization scheme the probe is replaced by the reflected pump [19]. Here this is realized by inserting a 50% reflective end connector, as shown in Fig. 3(a). Moreover, only a single circulator is needed to direct the light to the photo detector. In such configuration pump and probe have the same frequency. The measured Allan deviation (see Fig. 3(b) green curve) is only about a factor of two higher when compared to the previous scheme. While conceptually easier to realize this scheme introduces new sources of errors which are due to the cavity formed around the HCPCF. Even though the return losses at the first standard fiber HCPCF interface are 48 dB or less they are still sufficiently intense to cause an interference contribution to the signal which can be as strong as the nonlinear absorption signal itself. Figure 4 (red curve) shows the 1f error signal versus laser frequency and the oscillatory interference contributions.

 

Fig. 3 (a) Reflected pump setup. (b) Allan deviation versus of time [lenght of data record]: Without dithering and polarization scrambling (green curve)[1300 s]. With dithering only (red curve)[8000 s]. With dithering and polarization scrambling (blue curve)[1200 s]. Eq. 1 with S/N = 1700 (black curve).

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Fig. 4 The 1f error signal with (red curve) and without interferences (black curve).

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To improve the stability we dither the cavity length as demonstrated by Ahtee et al. [10]. Experimentally, we mount a piezo on the HCPCF and vary its voltage at a frequency of 0.8 kHz. The voltage scan range is chosen such that the associated change in fiber length is between zero and an integer multiple of nλ, where λ is the oscillator wavelength and n the refractive index, otherwise the interference contributions do not average to zero. This measure reduces the interference contributions to the signal (black curve in Fig. 4) and we find that the S/N ratio (red curve in Fig. 3) increases by almost two orders of magnitude. However, the Allan deviation does not improve over time. The reason is the poor single-mode behavior of the HCPCF and the dependence of the error signal on the environmental conditions. As the mode distribution changes the background signal varies and causes the frequency to fluctuate. To further improve the stability we have introduced a polarization scrambler before the fiber amplifier. This leads to a somewhat lower S/N ratio (see Fig. 3(b) blue curve), however, the Allan deviation improves over time to the lowest value obtained, i.e. 4.4 · 10⁻¹¹ at 100 s.

3.3. Pound-Drever-Hall scheme

The last stabilization scheme investigated is the Pound-Drever-Hall scheme [20] as seen in Fig. 4(a). An electro-optic modulator (EOM) is inserted before the fiber amplifier, modulating the phase of the laser mode with a frequency of 21 MHz. The modulated beam double passes the absorption cell, which is the same as for the reflected pump sceme, and is analyzed by an AC coupled photo detector. Its signal is amplified, demodulated, and filtered with a bandpass before it serves as an error signal for the PID. The Pound-Drever-Hall scheme is interesting because it requires no frequency modulation and part of the laser radiation can be extracted before the EOM to be used for calibration purposes. Figure 4(b) shows the Allan deviation as a function of time and the minimum value at 1000 s is 1.5 · 10⁻¹⁰.

 

Fig. 5 (a) Pound-Drever-Hall setup. (b) Allan deviation versus time (blue curve) and Eq. 1 with S/N = 180 (black curve). The laser was stabilized for 7200 s

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3.4. Comparison and conclusions

Table 1 summarizes the results for the three different schemes and compares them to those of two relevant publications. Without any additional measures we find that the S/N ratios are similar for all three schemes. While the lowest S/N of 40 is found for the reflected pump, the highest S/N of 180 is obtained for the Pound-Drever-Hall scheme. Further, the S/N ratio is limited by interferences from the absorption cell, the poor single-mode behavior of the HCPCF, and the small but noneligible birefringence. Interferences can be mostly eliminated by dithering the HCPCF length. Consequently, the S/N ratio improves by almost two orders of magnitude (from 40 to 1700) and is similar to the values reported in references [10, 13]. Although we applied this measure only to the reflected pump scheme, it should be applicable to all three schemes. In the same way dithering the cavity length eliminates interferences, polarization scrambling should reduce the fluctuations due to the birefringence of the HCPCF. However, we find that dithering and polarization scrambling does not further improve the S/N ratio, it rather has the adverse effect.

Table 1. Comparison

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When comparing the Allan deviations versus time we find a similar behavior for all three schemes. The deviations from an ideal $1/\sqrt{\tau }$ dependence are largely due to the poor single-mode behavior of the HCPCF. While dithering does increase the S/N ratio it does not lead to a better Allan deviation. Changes in polarization, temperature variations, and mechanical vibrations result in fluctuations of the mode profile and cause frequency drifts. With polarization scrambling some of these fluctuations can be reduced and the Allan deviation decreases with time. Comparing the best results, i.e. the reflected pump scheme with dithering and polarization scrambling, to those of two relevant reports in the literature reveals that the S/N ratios are similar, however, the Allan deviations reached after 100 s differ quite substantially. We attribute this to the different homogeneous line width (see Eq. 1). Ahtee et al. use a bulk absorption cell [10] and a homogeneous linewidth as low as 1.9 MHz, Knabe et al. a Kagome-type HCPCF [13] and a homogeneous line width of 8 MHz, and in our work the line width is (47 ± 2) MHz. Consequently, the Allan deviations after 100 s should scale roughly like 2:8:50 which agrees, within a factor of 2, with the measurements.

In summary, we demonstrated the first all-fiber stabilized laser system that uses sub-Doppler spectroscopy. The minimum Allan deviation after 100 s was measured to 4.4 · 10⁻¹¹ and is limited mostly by the homogeneous linewidth of the P15 acetylene transition in the 20 μm core diameter HCPCF. To improve the S/N ratio and to further decrease the Allan deviation a truly single-mode HCPCF with a larger core diameter would be required.