Palm-sized, vibration-insensitive, and vacuum-free all-fiber-photonic module for 10⁻¹⁴-level stabilization of CW lasers and frequency combs

Ultra-stable single-wavelength lasers and optical frequency combs are critical to many fields that require extremely stable frequency references, such as optical lattice clocks,^1,2 gravitational wave detection,³ precision spectroscopy,^4,5 and redefinition of SI units.⁶ They can be also used to generate ultra-stable microwaves through optical frequency division (OFD),^7,8 which can improve the performance of various microwave photonic applications, including radio astronomy and radar systems.^9,10 In recent years, from earthquake detection¹¹ to field-deployed spectroscopy,¹² there has been a growing demand for more compact, robust, and portable ultra-stable laser systems operating in the non-laboratory environment.

There have been several approaches for realizing compact-size laser stabilization platforms, where most representative examples include compact ultra-low expansion (ULE) cavities,^13–17 integrated chip-scale resonators,^18,19 bulk dielectric whispering-gallery-mode (WGM) resonators,^20,21 stimulated Brillouin scattering (SBS),^22,23 and optical fiber delay-lines.^24–31 The lasers stabilized by compact vacuum-gap Fabry–Pérot (FP) cavities have recently been reported to reach 10⁻¹⁵-level frequency instability at an integration time of 0.1^13,14 and 0.01 s.¹⁶ While the platform provides ultra-low frequency noise stabilization, the system is generally highly complex and requires isolation from the environment using a high-vacuum system and multiple layers of thermal shields. In the case of compact WGM resonator-based laser stabilization, the state-of-the-art long-term frequency instability is on the order of 10⁻¹⁴ at 0.1 s when using MgF₂ with an ultra-high Q factor of 2 × 10⁹.²¹ Although the resonator itself offers a compact structure, laser coupling is complex due to its prismatic coupling system and is susceptible to environment perturbations, such as vibration, thermal drift, and acoustic noise, again requiring a bulky vibration isolation platform, thermal shields, and vacuum. While the integrated chip-scale resonators^18,19 do not require a vacuum system, the minimum frequency instability of the stabilized laser is limited to 10⁻¹³-level at near 0.01 s. Recently, the optical fiber-based SBS process has generated narrow linewidth optical signals^22,23 with a frequency instability of 10⁻¹³ at less than 0.1 s.

Alternatively, an optical fiber delay-line can be used to stabilize the laser using a self-heterodyne method.^24–29 Because the platform is a fully fiber optic system, the system is alignment-free and robust and consists of off-the-shelf fiber-coupled components. Moreover, the platform can be directly applied to the stabilization of not only CW lasers²⁴ but also mode-locked fiber laser combs^25–27 and Kerr micro-combs (from tens-GHz²⁸ to hundreds-GHz repetition rates²⁹). Recently, the repetition rate of Kerr frequency comb has been stabilized to the 10⁻¹³-level frequency instability at 0.4 s, where the packaging size was mostly limited by the size of the acousto-optic frequency shifter (AOFS).²⁸ Although the development of gyroscope fiber optic coil winding technology makes it possible to make a 1-km-long fiber spool compact in size (∼7-cm diameter), the necessity of modulators, such as AOFS, limited the overall size of the system. In this paper, we show how to stabilize a 1550-nm CW fiber laser as well as comb-lines of a self-referenced optical frequency comb to 10⁻¹⁴-level frequency instability without the use of a vacuum system using an all-fiber optical delay-line-based, modulator-free ring-resonator configuration, which is well suited for field applications outside of a laboratory environment. This configuration can offer a large Q factor (4.5 × 10⁹) using a 100-m-long polarization-maintaining (PM) fiber. While a fiber ring resonator based on the Pound-Drever-Hall (PDH) method has recently been demonstrated to stabilize a 1550-nm CW laser frequency,³⁰ in this work, the generation of an error signal was accomplished using a simpler balanced photodetection³¹ without the use of a modulator. This also allowed for the stabilized frequency noise level to reach the thermal noise limit of the 100-m-long fiber. Furthermore, in order to suppress the length fluctuation of the fiber delay due to external vibrations, the shape of the fiber spool mount is specially designed to have a vibration sensitivity of ∼10⁻¹⁰ (1/g) level. Finally, the optical setup was packaged in a palm-sized case and tested.

Various mechanical perturbations, such as acoustic noise, vibration, and thermal drift coupled to the optical references, cause optical length fluctuations followed by the frequency fluctuation of the stabilized laser. To reduce the vibration-induced frequency noise, a passive vibration isolation platform or active vibration control³² can be used. However, such systems are generally bulky and heavy, which compromises the compactness and light weight of the optical fiber-based stabilization method. Therefore, there was previous research on the design and implementation of vibration-insensitive fiber spools,³³ which recently showed down to 8 × 10⁻¹¹ (1/g) vibration sensitivity for a 1-km-long single-mode fiber (SMF) delay-line,³⁴ where the vibration sensitivity of the mechanical length reference is defined as the length expansion ratio (dl/l) induced by vibration with unit acceleration of g.

To validate the optimization, we assessed the vibration sensitivity of the designed vibration-insensitive 100-m PM fiber spool. We applied vibration to the in-loop ring resonator shown in Fig. 3(a) and then measured the frequency noise of the stabilized laser using the out-of-loop frequency noise measurement setup depicted in Fig. 3(c). The measured frequency noise is converted to the length fluctuation spectrum, which is then divided by the vibration spectrum to obtain the vibration sensitivity spectrum. For comparison, we also measured the vibration sensitivity of two other 100-m PM fiber spools, which are wound on a 15-cm-diameter plastic spool and a miniaturized 26-mm-diameter aluminum spool. The measured vibration sensitivities of these spools are shown in Fig. 2(d). The vibration sensitivity of the optimized spool is shown as curve (i), which shows a flat spectrum along the broadband input vibration frequency from 30 to 500 Hz, with ∼10⁻¹⁰ (1/g) level [with a minimum value of 9.4 × 10⁻¹¹ (1/g)]. It is slightly higher than the simulation result, and the imperfect winding procedure and unequal vibration transmission from the bottom of the spool to the fiber appear to be the causes of the error. The vibration sensitivity of the typical plastic spool is shown as curve (ii) with a vibration sensitivity of 4 × 10⁻⁸ (1/g), which is ∼400 times higher than the designed vibration-insensitive spool. The miniaturized aluminum spool with a diameter of 26 mm (48 mm when including the wound fiber) and a height of 5 mm has a vibration sensitivity of 10⁻⁸ (1/g) [curve (iii) in Fig. 2(d)]. In addition, a vibration-insensitive 1-km single-mode fiber spool [that is used for the out-of-loop noise measurement; see Fig. 3(b)] is also designed in the same way to have a vibration sensitivity of 2.0 × 10⁻¹² (1/g) calculated from simulation in order to prevent the impact of vibrations when measuring the frequency noise. The vibration sensitivity of the spool is shown as curve (iv) in Fig. 2(d), with the level of under 10⁻¹⁰ (1/g) [with a minimum value of 3.9 × 10⁻¹¹ (1/g)]. Note that the slightly lower vibration sensitivity of the 1-km SMF spool compared to the 100-m PMF spool also comes from the imperfect winding procedure. Ideally, the vibration sensitivity may not be influenced by the fiber length, since it is primarily determined by the mechanical strain of the bulk fiber. While we modeled the optical fiber as a bulk fiber in the simulation, in reality, the fiber is wound layer by layer with epoxy to fix it. The amount of epoxy is not perfectly uniform, causing the difference in material property and dimension between simulation and experiment.

Figure 3(a) shows the schematic of the CW laser stabilization system based on the fiber ring resonator. A 1550-nm PM erbium-doped fiber laser (ETH-20-1550.12-PZ10B, Orbits Lightwave, Inc.) is used as the laser source. The laser output goes through an acousto-optic frequency shifter 1 (AOFS₁), which works as an extra-cavity fast frequency modulator. Then, the 50/50 coupler divides the laser output into two, of which one is applied to the ring resonator and the other is directly applied to one of the input ports of the balanced photodetector. Frequency noise for each environment is compared after the fiber reference, which includes a ring resonator and balancing ports, when put in a low-vacuum chamber (∼1-Torr pressure), an air-tight chamber, or an unsealed open chamber. The output of the balanced photodetector, which works as an error signal, is applied to two PI servos (LB-1005, New Focus for fast feedback and D2-125, Vescent for slow feedback) after being digitally low-pass- and high-pass-filtered. The outputs of each servo are then fed back to a voltage-controlled oscillator [VCO₁ in Fig. 3(a) that drives the AOFS₁] and a lead zirconate titanate (PZT) transducer for fast and slow frequency corrections, respectively.

Figure 3(b) shows the schematic using the identical ring-resonator setup to stabilize the comb-line noise of the self-referenced optical frequency comb. The nonlinear amplifying loop mirror-based erbium fiber frequency comb (FC1500-250-ULN, Menlo Systems GmbH), whose repetition rate is ∼250 MHz, is used as a comb source. The f_ceo of the comb is detected by built-in electronics and stabilized by home-built electronics using a 50 MHz signal generator locked to Rb clock. After the 1550-nm comb modes are filtered using the 0.7-nm bandwidth fiber Bragg grating (FBG) and then amplified by an erbium-doped fiber amplifier (EDFA), ∼6 mW optical signal is incident to the ring resonator, which is in an air-tight chamber. Note that the repetition rate and f_ceo of the optical frequency comb should be controlled carefully to get the enough amount of dip in the error signal, since the filtered optical signal is a pulse-like signal in the time domain and the period of the pulse should match well to the fiber delay. By careful control of f_rep and f_ceo, we could obtain a 10.8% dip in the error signal. When setting the operation point at the steepest slope point, the sensitivity slope was measured to be 9.4 μV/Hz, which was enough to obtain the fiber thermal noise-limited performance. The detected error signal from the balanced photodetector is applied to a single PI servo, where the output is fed back to the intra-cavity electro-optic modulator (EOM) in the mode-locked oscillator.

The stabilized CW laser and optical frequency comb are characterized in two ways: (i) the out-of-loop frequency noise measurement using a self-heterodyne method with a 1-km fiber delay-line [Fig. 3(c)]³⁵ and (ii) the Allan deviation measurement by the beat note detection [Fig. 3(d)]. For the self-heterodyne measurement, we built a Mach–Zehnder interferometer with a 1-km-long fiber delay and an AOFS in the long arm for an unbalanced self-heterodyne. To eliminate the impact of vibrations in the out-of-loop measurement, we employed the vibration-insensitive 1-km fiber spool with vibration sensitivity <10⁻¹⁰ (1/g) [of which the vibration sensitivity is shown by curve (iv) in Fig. 2(d)]. The interference signal is then photodetected and mixed with the output of VCO₂ (that drives AOFS₂) to shift the electric signal to the baseband and subsequently analyzed by a fast Fourier transform (FFT) spectrum analyzer (SR760, Stanford Research Systems). For the Allan deviation measurement, we built another independently stabilized CW laser and obtained the beat note at ∼920 and ∼90 MHz, respectively, with the first stabilized CW laser and stabilized comb. The frequency fluctuation of the beat note was sampled at 1 Hz rate with a frequency counter (SR620, Stanford Research Systems), and the frequency instability was evaluated by the overlapping Allan deviation (for >1 s averaging time).

For the stabilization of CW laser, when the laser is stabilized by the fiber ring resonator in a low-vacuum chamber (near 1 Torr), the frequency noise level is suppressed by 10⁴ times at a Fourier frequency of 100 Hz to 1 kHz [curve (ii) in Fig. 4] compared to the free-running frequency noise [curve (i) in Fig. 4]. In the Fourier frequency range of 10 Hz to 1 kHz, the stabilized frequency noise is limited by the thermal noise of the 100-m fiber delay, which results from thermal fluctuations of the fiber delay length.^36,37 A large peak near 10 kHz Fourier frequency is the control-loop resonance peak caused by the limited frequency modulation bandwidth of PZT-based actuator. As shown in curve (iii) in Fig. 4, the air-tight case also showed a very similar frequency noise level with the low-vacuum result, only slightly worse in the 1–10 Hz Fourier frequency range. The frequency noise level is increased by 10²–10⁴ times compared to the vacuum case below 1 kHz range [curve (iv) in Fig. 4] when the fiber resonator is placed in an unsealed case, which causes acoustic noise from laboratory fans and air conditioners to be coupled to the frequency noise. The integrated rms optical phase errors of vacuum and air-tight cases are 261 and 335 mrad, respectively, when integrated from 10 Hz to 100 kHz. Note that the BPD photodetection limit (shot noise limited) [curve (vi) in Fig. 4] is far below the thermal noise level, demonstrating that the system is not limited by the locking sensitivity of the resonator. The stabilized frequency noise level can reach the fiber thermal noise-limited performance without using the PDH method as well as the vacuum system.

The linewidth can be projected by the β-separation line method³⁸ from the measured frequency noise spectrum. The β-separation linewidth of the CW laser is reduced from 18 kHz (free-running) to 77.4 Hz (stabilized in low vacuum). For the air-tight case, the linewidth is reduced to 309.7 Hz (CW) and 526.8 Hz (comb), which is worse than the vacuum case due to the significantly worse frequency noise spectra below few Hz offset frequency range [see curves (ii) and (iii) in Fig. 4]. Note that, for our system, the fundamental limit in linewidth is 6.9 Hz, which is determined by the thermal noise of 100-m fiber.

Figure 5(a) shows the time trace of the beat frequency of two CW lasers, before and after the independent stabilization in an air-tight chamber. The frequency fluctuation (standard deviation) of the free-running lasers’ beat note is 7.4 MHz [curve (i) in Fig. 5(a)], while the frequency fluctuation of the beat note of the stabilized lasers is 97 kHz [curve (ii) in Fig. 5(a)] over 6 min. The time traces (i) and (ii) in Fig. 5(a) and the time trace for vacuum and an unsealed environment are converted to frequency instability using overlapping Allan deviation shown as shaded points in curves (i)–(iv) in Fig. 5(b). The frequency instability in air-tight and unsealed chambers diverges fast with a τ slope after 1 s due to the thermal drift. The air-tight chamber can partially block the convection, achieving around 100 times improvement compared to the case of unsealed chamber. The frequency instability in vacuum diverges with a τ^1/2 slope and improved three times at 1-s averaging time compared to that of air-tight case, since vacuum can efficiently block the air convection and the thermal drift is due to conduction through the contact of the chamber. To evaluate the frequency instability for <1 s averaging time, the Allan deviation is computed from the frequency noise curves (ii)–(iv) in Fig. 4(a) and marked with unshaded points in curves (ii)–(iv) in Fig. 5(b). The frequency instability minimally reaches 2.2 × 10⁻¹⁴ and 2.7 × 10⁻¹⁴ both at 0.03 s averaging time for vacuum and an air-tight environment, respectively.

For the stabilization of the self-referenced optical frequency comb in an air-tight environment, the frequency noise level is maximally suppressed by 10⁶ times compared to the free-running comb-line noise level [curve (i) in Fig. 6]. The level reaches the fiber thermal-noise limited level in the Fourier frequency range of 10 Hz to 1 kHz [curve (ii) in Fig. 6]. The noise level is identical for the CW laser and the comb-line for a Fourier frequency of less than 1 kHz, meaning that they both follow the length stability of the fiber reference. However, for the comb, the 10–20 kHz peak for PZT control is not observed since the comb is stabilized using only the EOM. The locking bandwidth of the feedback is formed near 300 kHz, which is limited by the PI corner of the servo. The integrated rms optical phase error of the system is 380 mrad when integrated from 10 Hz to 100 kHz.

Figure 7(a) shows the time trace of the beat frequency between the 1550-nm comb-line and the CW laser, before and after the stabilization of comb-line in an air-tight chamber where the CW laser stays stabilized. The frequency fluctuation of the beat frequency is 5.8 MHz [curve (i) in Fig. 7(a)] and 25 kHz [curve (ii) in Fig. 7(a)] for free-running and stabilized combs, respectively. Similar to Fig. 6(a), the shaded points in curves (i) and (ii) are calculated from the time trace of beat note in curves (i) and (ii) in Fig. 7(a) and the unshaded points in curve (ii) are converted from the frequency noise data curve (ii) in Fig. 6. Curve (iii) is the same as curve (iii) in Fig. 5(b) for comparison. The minimum frequency instability for the stabilized comb-line is 2.6 × 10⁻¹⁴ at 0.01 s, which is similar to that of the stabilized CW laser. We can conclude that both CW laser and optical frequency comb can follow the stability of the fiber reference.

Finally, we packaged the fiber ring-resonator module in a compact enclosure and examined its mechanical robustness against external vibrations. As shown in Fig. 8(a), the setup is packaged with off-the-shelf optical components (two optical couplers and an optical isolator) and an optical fiber spool in an air-tight aluminum case with a dimension of 92 × 62 × 30 mm³. We also packaged the fiber ring-resonator with a miniaturized 100-m-long PM fiber spool made of aluminum with 26-mm diameter (48-mm diameter including fiber), 5-mm height, 9-ml volume, and ∼10⁻⁸ vibration sensitivity [curve (iii) in Fig. 2(d)]. The spool and other optical components are packaged in an air-tight aluminum case with a dimension of 112 × 72 × 12 mm³ [Fig. 8(b)].

To test the impact of external vibrations, we applied vibrations to the packaged module with a vibration-insensitive spool [Fig. 8(a)], which stabilized the CW laser, using the shaker (The Modal Shop, 2100E11) with a broadband (30 Hz–1 kHz) vibration spectrum up to 10⁻⁵ (g²/Hz). The operation of the locking system is monitored by measuring the in-loop error signal as shown in Fig. 9(a). When vibration is applied, the locking is maintained well, thanks to the low vibration sensitivity of the spool but with a slightly worse error signal. Compared to the measured frequency noise without vibrations [curve (ii) in Fig. 9(c)], the frequency noise becomes worse when the vibration level is increasing with the level plotted in Fig. 9(b). The frequency noise levels [curve (iii) in Fig. 9(c)] are measured when the vibration level of the corresponding color in Fig. 9(b) is applied. The measured frequency noise with vibration can be easily estimated by multiplying the measured vibration sensitivity [curve (i) in Fig. 2(d)] by the measured vibration spectrum [curve (iii) in Fig. 9(b)]. Note that when vibration is applied with a level of ∼10⁻⁵ (g²/Hz), the frequency noise of the stabilized laser is comparable to that of the free-running laser, which means that the vibration level lower than ∼10⁻⁵ (g²/Hz) should be applied to the system in order to take advantage from the stabilization system.

Here, we present a comparison of our work’s performance and key characteristics with other compact CW laser stabilization platforms as shown in Fig. 10 and Table I. The comparison is mainly made with compact Fabry–Pérot cavities,^15–17 integrated chip-scale resonators,^18,19 bulk dielectric resonators,²⁰ and optical fiber-based SBS.²³ As shown in Fig. 10, our frequency noise power spectral density (PSD) and Allan deviation results are among the best; only the recent compact ULE Fabry–Pérot cavity with active temperature control within a high vacuum (10⁻⁵ Pa) chamber environment¹⁶ has a better result. Please note that our method does not necessitate active temperature control and a high vacuum environment, and it can still attain 10⁻¹⁴-level instability within 0.1 s.

The size, weight, and power consumption (SWaP) is another important metric for assessing different stabilization methods. Because different systems have vastly different operating conditions, making a fair, direct comparison is difficult. For this reason, instead of making a direct SWaP comparison between different systems, we made a comparison based on other metrics using available information. Table I shows the input signal coupling, volume/size of the reference part, and the necessity of vacuum chamber and active temperature control for each method, which are the important aspects of SWaP and the practical usability outside a laboratory environment. This table shows the cons and pros of each method in terms of size/weight and mechanical robustness. For example, while the compact Fabry–Pérot cavity’s volume itself is small with a good stability performance even below 10⁻¹⁴, it is alignment sensitive (due to free-space coupling) and often requires high vacuum and temperature control. The integrated chips can provide the smallest volume and size, but the performance is often limited to the 10⁻¹³ level. Our method can provide the 10⁻¹⁴-level instability from a mechanically robust all-fiber coupling, relatively small volume, and without vacuum or active temperature control. While we used table-top equipment for the PI servo and the balanced photodetector in this study, they can be replaced by circuit board-based components (e.g., Koheron PI200 and PD10B). Assuming the use of such circuit board-based components in conjunction with our fiber-based reference unit [as shown in Fig. 8(a)], the total stabilization system can be implemented with a fairly low SWaP (<300 ml volume, <300 g weight, and ∼3 W electric power consumption) for stabilizing CW lasers and frequency combs with 10⁻¹⁴-level instability.

In summary, we have demonstrated a simple, compact, and alignment-free laser stabilization module based on an all-fiber ring-resonator and balanced photodetection, which is highly suitable for the field applications outside a laboratory environment. The optical frequency noise of a 1550-nm CW laser and comb-lines of the self-referenced optical frequency comb is stabilized to the thermal-noise-limit of the used fiber delay, which resulted in the minimum frequency instability of 2.7 × 10⁻¹⁴ and 2.6 × 10⁻¹⁴ within 0.03-s and 0.01-s averaging time for the CW laser and comb, respectively. This stabilization system requires an air-tight atmosphere to accomplish thermal noise-limited performance; a vacuum environment is not required. We could further reduce the vibration-induced frequency noise by designing a vibration-insensitive spool with ∼10⁻¹⁰ (1/g)-level vibration sensitivity. The fiber optic part could be packaged in a palm-sized aluminum case using either a vibration insensitive spool or an ultracompact 9-ml spool. The performance of stabilization can be further enhanced by increasing the fiber delay length and/or lowering the loss of the fiber ring resonator.

This work was supported by the National Research Council of Science and Technology (NST) of Korea (Grant No. CAP22061-000), Institute for Information and Communications Technology Promotion (IITP) of Korea (Grant No. RS-2023-00223497), and National Research Foundation (NRF) of Korea (Grant Nos. 2021R1A2B5B03001407 and 2021R1A5A1032937).

I.J., C.A., W.J., and J.K.: Korea Advanced Institute of Science and Technology (P).

Igju Jeon: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Changmin Ahn: Conceptualization (equal); Formal analysis (equal); Investigation (equal). Chankyu Kim: Methodology (equal). Seongmin Park: Writing – review & editing (equal). Wonju Jeon: Formal analysis (equal); Methodology (equal). Lingze Duan: Formal analysis (equal). Jungwon Kim: Conceptualization (equal); Formal analysis (equal); Funding acquisition (lead); Project administration (lead); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.