1. Introduction

Ultra-stable lasers are today at the heart of several applications, from atomic clocks [1,2], gravitational wave detectors [3,4], microwave generation [5,6], and earthquake detection [7,8]. The highest frequency stability can be achieved by stabilizing commercial lasers to ultra-low expansion (ULE) Fabry-Perot optical cavities. Research in this field has made outstanding advances over the last three decades, with state-of-the-art cavity-stabilized lasers now delivering frequency stability at the level of parts in 10¹⁷ between 1 and 100 s [9,10]. Whilst these results are obtained in fixed laboratory settings, significant advances have been made in developing transportable cavities which deliver a fractional frequency stability in the low 10⁻¹⁵ level, with expected improvements to the 10⁻¹⁶ level by employing lower thermal noise mirrors [11]. An alternative laser stabilization technique, based on optical fiber delay lines [12], has been gaining attention in the last decade for its potential ability to fill the performance and cost gap between off-the-shelf narrow linewidth lasers and research-grade cavity-stabilized lasers. Indeed, several orders of magnitude separate the frequency stability performance between these two technological families, with narrow linewidth lasers (such as extended cavity diode and optical resonator-based lasers) delivering stabilities at the 10⁻⁹ - 10⁻¹⁰ level [13]. Thus, applications requiring better frequency stability than that delivered by integrated commercial and research-grade lasers [14], but not requiring the outstanding stability delivered by ULE cavity-based lasers, currently find a gap in available solutions. Whilst the highest frequency stability performance is likely to still be delivered by ULE cavity-based lasers for many years to come, lasers stabilized to fiber delay lines are a particularly attractive solution for ease of assembly, transportability and low cost. Indeed, in contrast with optical cavities, they do not require precise machining of glass, skilled optical alignment, and contacting of mirrors. Also, the material cost of fiber spool-based solutions is substantially lower.

Lasers stabilized to fiber-based delay lines were previously shown to reach a residual phase noise comparable to ultra-low expansion (ULE) glass cavity-stabilized lasers, once the laser frequency drift is removed. In the work by Jiang et al. [15] the drift was measured to be of the order of 1 kHz/s, primarily due to residual thermal fluctuations. In later works, the drift was reduced by improving the thermal isolation of the spool from the environment by employing several layers of thermal radiation shielding in a vacuum chamber. In a recent work by Huang et al. [16], the drift was reported to be as low as 5 Hz/s and further reduced to 0.1 Hz/s when the linear component of the drift was removed by adding a frequency offset within the stabilization scheme [15]. However, for the laser to be able to maintain this performance during continuous operation, this drift reduction approach can be used only if the drift is linear indefinitely or for a sufficient time between drift calibration against a reference of higher stability. In ULE cavities, the frequency drift has indeed been shown to be very linear over several months as it arises from material creep [17,18] and efficient drift compensation can be performed over these or even longer timescales, depending on the acceptable frequency error for each specific application. However, to date and to the best of our knowledge, the behavior of the drift of fiber delay line-based stabilized lasers has not been characterized for a sufficiently long time period. For example, the fractional frequency stability in [19] was characterized only up to 1000 s, which does not allow a conclusion to be made whether the demonstrated residual drift can be maintained over longer timescales, as required for practical use in the laboratory and/or the field.

In this work we experimentally investigate the evolution of the drift in a fiber delay line-based stabilized laser over several days. We aim to characterize the frequency drift once the fiber spool is placed in a suitably stable thermal environment and experimentally investigate the correlation between the spool temperature changes and the measured laser frequency drift. We stress that in this work we focus exclusively on the long-term (hours to days) performance. For this reason, no effort was made to optimize the short-term (<1 s) stability of the laser, which would likely require an anti-vibration isolation platform and/or spool design to minimize the acceleration sensitivity of the fiber to the environment [19], as these additional steps are outside the scope of this work.

2. Experimental procedure

In our fiber spool design, we concentrated on reducing the potential contribution to the frequency drift from factors external to the fiber, such as time-dependent stresses induced by the different thermal expansion coefficients of a supporting drum and the fiber, the tension across multiple fiber layers, the viscoelastic effect of the fiber coating on the silica glass. We also aimed at reducing uneven thermal radiation experienced by the fiber spool. In order to reduce the potential drift contribution arising from stresses due to the drum-fiber interface and between different winding layers, we have chosen a design where the contact area between the fiber and its supporting structure is minimized. We initially wound the optical fiber on a collapsible drum of 50 mm in diameter, then the obtained spool was transferred onto the supporting cage structure shown in Fig. 1. Here, the structure has a slightly smaller diameter than the spool, so that no radial stress is imposed on the spool. The main mechanical stresses experienced by the spool are due to the weight of the spool itself on the supporting structure and possible residual stresses due to the winding process. The cage structure also contributes to maximizing uniformity of exposure of the fiber spool to thermal radiation, without shielding effects that would be present if a closed drum was used. The rods in contact with the fiber spool are made of PEEK material, a vacuum-compatible plastic with very low thermal conductivity of 0.26 W m⁻¹ K⁻¹ This was chosen to prevent heat transfer by conduction from the vacuum chamber walls to the optical fiber. In previous work it was shown that the phase response of the optical carrier in the fiber can exhibit non-linear behavior, with respect to temperature, due to the viscoelastic effects of the protective fiber acrylate coating [20]. In standard single-mode telecom fibers, such as the commonly used SMF-28e, the diameter of the coating and glass fiber is 250 µm and 125 µm, respectively. In order to minimize this effect and isolate the drift contributions from the silica fiber itself rather than the coating, we used a G.562 single-mode optical fiber (125 µm diameter) coated with a single 15 µm acrylate layer (coated fiber diameter of 155 µm), which was manufactured at the Optoelectronics Research Centre (ORC) at the University of Southampton. Whilst the single acrylate coating is more than 4 times thinner than in standard double-coated fibers, it still provides sufficient protection of the silica fiber for safe handling. The chosen loose winding solution and cage structure could potentially result in increased vibration sensitivity, which would lead to increase the short-term laser frequency instability, than a more traditional tight winding solution and full-body support. The loose winding is also a less suitable solution for transportation. However, we stress that the structure was designed with the sole intent of characterizing the nature and long-term behavior of the frequency drift and it is not intended for best vibration insensitivity and robustness during transportation. The spool was temperature-controlled in a vacuum chamber (120 mm long and 100 mm diameter), which in turn was placed into a temperature-controlled metal enclosure. The vacuum provides a dual function: first, it allows external fast thermal fluctuations to be low-pass filtered by removing heat transfer by conduction and convection, resulting in a thermal time constant of approximately 12 hours; Second, it removes the contribution to the drift arising from fiber sensitivity to changes in the atmospheric and acoustic pressure [21]. The vacuum chamber was initially evacuated with a turbo vacuum pump and then maintained at a pressure below 10⁻⁶ mbar (10⁻⁴Pa) using an ion pump for the duration of the tests. In order to further reduce the temperature variations experienced by the optical fiber spool in the vacuum chamber, two mirror-polished copper radiation shields were used. To further minimize stresses induced by the coating onto the silica fiber, we chose to operate the vacuum chamber at 66 °C. At this relatively high temperature the Young’s modulus of the used acrylate coating layer [22] is approximately 30 times lower than at room temperature, which is expected to reduce further the coating’s impact on the thermal properties of the fiber. The outer enclosure was stabilized at 40 °C, providing an intermediate step from the chamber and the room temperatures. The experiment was performed in a laboratory environment with air conditioning system maintaining the air temperature within +/- 0.5 °C.

 

Fig. 1. (a) Fiber spool-based delay line arrangement within the vacuum chamber environment. The optical fiber is loosely wound on a cage consisting of 8 PEEK rods mounted on an 8-spoke metal wheel on which a thermistor is mounted. Two thermal shields are placed between the fiber and the chamber wall to increase the time constant for thermal transfer. (b) Illustration of the loose winding arrangement on the cage-like fiber supporting structure. The fiber spool (orange) diameter is a few millimeters bigger than the supporting structure. A thin vacuum-compatible plastic sheet (blue) is inserted between the optical fiber and the PEEK rods to avoid sagging of the fiber between rods.

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Figure 2 shows the experimental setup we used in our tests, consisting of a Michelson interferometer in a vacuum chamber with a 1 km-long arm imbalance and the laser stabilization optics and electronics. The 1 km-long imbalance is achieved by double-passing a 500 m-long optical fiber spool. The chosen length was primarily dictated by the maximum available length from the thin-coated fiber draw at the ORC. However, it is also a good trade-off between achieving sufficient interferometer sensitivity (which increases with increasing length) and compactness of the spool, to more easily achieve uniform heat distribution across it. Indeed, this length has proven to be adequate for the experimental investigation of the long-term behavior of the frequency drift of a laser stabilized to the spool. In contrast with previous work by other groups [15,23], instead of an acousto-optical modulator (AOM) followed by a Faraday mirror on the long arm of the interferometer, we installed only a plain (non-polarization rotating) mirror, which was obtained by silver coating a cleaved fiber tip. We chose this arrangement to avoid the use of active components in the vacuum chamber as these might contribute to temperature gradients across the optical fiber by creating hot spots within the thermally insulated environment. We also chose to use a plain mirror instead of a fiber-pigtailed Faraday mirror, as these are usually constructed with free-space optics inside a small housing and could exhibit temperature-dependent phase changes. Whilst we expect this phase contribution to be smaller than that from the 500 m-long fiber spool, in order to confirm this assumption a measurement of the temperature sensitivity of the Faraday mirror, in a vacuum environment, would be required. Instead, we chose the easier approach of replacing the Faraday mirror with a plain mirror. In lasers stabilized to a fiber delay line, a Faraday mirror is usually inserted on both arms of the interferometer to maximize the fringe contrast (or beat note in a heterodyne arrangement) [24]. Changes in contrast are in fact converted into frequency errors by the laser feedback loop. However, our tests have shown that the temperature-induced polarization changes in an environment stabilized at the tens of mK-level can be neglected for the purpose of our experimental work. As we did not employ an AOM, we obtained interferometric fringes at the interferometer output (port 3 of circulator) instead of an RF beat as in previous works [16,23]. An erbium-doped fibre amplifier (EDFA) was used at port 3 of the circulator to increase the optical power available on the photodetector. The output of the photodiode was sent to a proportional-integral-derivative (PID) loop filter to control the laser frequency with an AOM at the laser output. An additional slow feedback loop maintains the AOM around its center frequency by adjusting the laser current. As changing the laser current also changes the laser output power, an optical intensity stabilizer (Thorlabs EVOA1550A) was inserted between the laser and the AOM. The feedback bandwidth of the fast and slow loops were 50 kHz and 1 Hz respectively. A low level of optical power was injected in the interferometer (10 µW) to minimize the potential impact of heat dissipation in the fiber due to propagation losses. Whilst these are expected to be low, the high level of thermal isolation provided by the vacuum environment could potentially result in non-negligible temperature changes in the fiber.

 

Fig. 2. Setup diagram. PS: power stabilizer, PC: polarization controller, M: mirror, PID: proportional-integral derivative filter, VCO: voltage-controlled oscillator, AOM: acousto-optic modulator, EDFA: erbium doped fiber amplifier; Filter: 100 GHz-wide optical filter. Optical paths in red, electrical paths in blue.

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In order to monitor the temperature of the fiber we placed a thermistor (Omega, 44032) on the fiber support structure (Fig. 1). We chose this location as placing the thermistor directly in contact with the fiber was not viable. Good thermal contact could not be ensured as the fiber layers rested loosely on the open frame support. The thermistor was connected to a 6 and ½ digit resistance meter and the measured resistance was logged with an analog-to-digital converter at 1 s intervals. In order to measure the frequency stability of the spool-stabilized laser, we compared it to a ULE-cavity stabilized reference laser of similar optical carrier frequency by combining the light from both lasers on a photodiode, producing a radio-frequency beat that we measured with a frequency counter (K + K). The fractional frequency instability of the reference laser is 6 × 10⁻¹⁷ from 1 s to 100 s integration time and its drift rate is below 20 mHz/s. In this case, because the drift arises from the ULE material creep and it is linear over very long timescales, the original drift of the ULE cavity can be reduced by a feed-forward correction. After liner drift compensation, the residual drift was below approximately 1 mHz/s.

3. Experimental results and discussions

The results of a 5 day-long measurement are shown in Fig. 3. In Fig. 3 (a), the frequency changes of the laser are shown (thick solid grey trace). By performing the ratio between the laser frequency changes and the fiber temperature readings, we obtain a temperature-to-frequency conversion value of 1.33 GHz/K (dashed red trace). This value is in good agreement with the expected value [12] of:

 

Fig. 3. Frequency deviation and frequency drift of the fiber spool-stabilized laser. (a): Frequency deviation over the course of 5 days (solid grey); Frequency deviation derived from the fiber temperature readings (dashed red); Residual frequency deviation after correcting the laser frequency from the temperature readings (solid blue). (b): Frequency drift of the fiber spool-stabilized laser before temperature-to-frequency correction (red); (c): Frequency drift of the fiber spool-stabilized laser after temperature-to-frequency correction; Residual frequency drift (grey) and filtered with an 2 h-long moving average (blue).

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4. Conclusions

We experimentally investigated, for the first time to the best of our knowledge, the long term drift of a laser stabilized to a fiber optical delay line in a vacuum environment over the course of 5 days and its correlation to the fiber temperature. In order to characterize the contribution to the measured drift of the silica fiber itself, rather than external factors, such as the fiber coating and the stresses induced by the fiber winding, we used a purposely fabricated thin coated optical fiber and a loose drum-less winding solution. We also reduced possible contributions from uneven thermal radiation exposure by using an open-frame fiber support. We showed that, when the fiber is maintained in a stable thermal environment (<20 mK-level over several days), the laser drift is highly correlated to the fiber temperature. Hence, a linear frequency compensation, suggested in previous works, cannot be used to reduce the drift. However, by exploiting the high frequency-temperature correlation, in our experiment we were able to calculate a suppression of the laser drift by a factor of 23, resulting in a residual drift below 16 Hz/s over 5 days. We anticipate that the drift could be reduced even further with improved temperature stabilization of the vacuum chamber, increasing the thermal time constant with a higher number of thermal shields, and by further improving the fiber temperature measurement with multiple thermistors and improved thermistor measurement devices. This work concentrated on identifying the origin and long-term behavior of the frequency drift of a laser locked to a delay line and our fiber support design choices were driven towards minimizing the contribution from any factor other than temperature. In an actual implementation of these techniques towards a portable and robust ultra-stable laser system, other design choices could be made to achieve increased robustness during transportation (tight windings rather than loose), longer time constants (solid body rather than cage-like fiber support), reduced sensitivity (vibration insensitive fiber support [26]) and improved thermal shielding and control so that the results presented in this paper can be also achieved in a non-laboratory environment.