Orthogonal dual-soliton in a fiber microresonator for force sensing

doi:10.21203/rs.3.rs-1764315/v1

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Orthogonal dual-soliton in a fiber microresonator for force sensing

https://doi.org/10.21203/rs.3.rs-1764315/v1

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Soliton frequency combs generated in microresonators offer powerful tools for optical metrology, due to its high time-frequency resolution. Here, via exciting the intracavity Brillouin laser in a high Q monolithic fiber resonator, we generate a pair of orthogonal Kerr soliton combs, which share the same repetition (≈ 1 GHz) but different central wavelengths (≈ 10 GHz). Difference of their carrier-envelope-offset frequencies (Δf_ceo) is determined by the Brillouin-resonance overlap spectrally. We find that beat notes of the Δf_ceo is mechanically sensitive to external force, demonstrating a high sensitivity 0.3 kHz/µN, with a linear measurement range up to 7.3 mN. Leveraging the noise-filtering and lock-in heterodyne measurement, we obtain a detect limit down to 520 pN. This work reveals a novel paradigm of dual-soliton microcomb multiplexing pumped by one single laser, and combines the ultrahigh resolution dual-comb strategy and fiber sensor technology. It may open a way towards the realization of versatile and powerful microcomb based sensors with simple structure, which could be widely attractive in precision measurements such as high precision gyroscope, mechanical tracing, and material science examination.

Generated via pumping an optical microcavity with a resonant continuous-wave laser, dissipative Kerr soliton (DKS) [1] with large comb spacings and high coherence has led to continued enthusiasm since its advent, and spurred versatile advances in applications ranging from time-frequency synthesis [2, 3], coherent communication [4, 5], fast signal processing [6, 7], astronomical metrology [8, 9], high-resolution sensing [10, 11], to quantum information technology [12–14]. Especially, the dual comb generation, in both cavity-pairs [15] and single cavity [16, 17], offers a compact and powerful tool for fast spectroscopy and ranging [18–20]. This technique can illustrate broadband spectrum in the radio frequency, avoiding the utilization of large optical spectrometers with moving parts and limited optical bandwidth. Beat notes of the dual-combs also provide unique frequency standards for super-resolution heterodyne measurements [10, 11]. Besides generated in on-chip or whispering-gallery-mode microresonators [17, 21, 22], soliton microcombs can also be excited in high-Q fiber cavities [23–25], opening a platform for low-loss optical fiber system, which is the cornerstone of modern information network. But up to now, dual-soliton microcomb formation in a compact monolithic fiber cavity is still not obtained.

Here, we demonstrate orthogonal dual-soliton formation in a highly nonlinear silica fiber Fabry-Perot (F-P) monolithic resonator. By efficiently generating a Brillouin laser [26, 27] in the fiber resonator, we control both the pump laser and the Brillouin laser entering the red-detuning region of two orthogonally-polarized resonant modes, thus form two single DKS. Uniquely, this two orthogonal DKS share the same repetition rate (≈ 1.01 GHz) due to the coherent cross-phase-modulation [28], but they have different carrier-envelope frequencies in optical band, due to different pumping location. Moreover, we find that such Δf_ceo is dependent on the spectral overlap of the Brillouin gain band and a resonance, which is ultrasensitive to external force applied onto the F-P cavity. Therefore, by using the optoelectronic heterodyne scheme [28] with sub Hz resolution, we obtain a force sensor with detect limit down to 520 pN, while its maximum measurement range reaches 7.3 mN, innovating the performance of force sensor based on photonics.

Figure 1a shows the schematic concept of our orthogonally-polarized dual-soliton generation in a fiber F-P monolithic resonator, and the picture of the device. The fiber F-P resonator composes of a commercial highly-nonlinear-fiber section (≈ 10 cm long, core diameter ≈ 4 µm, nonlinear coefficient ≈ 10 W^− 1 km^− 1), and two side-coated Bragg mirrors (reflection ratio > 99.5% covering the C + L band). Fabrication and characterization of the F-P monolithic resonator is shown in methods. This geometry supports two orthogonal mode families (X and Y) transmitting along the fiber, due to its natural birefringence. The free-spectral-ranges of the orthogonal mode families could be a bit different (in kHz level), but the intracavity loss of the orthogonally-polarized modes is almost the same. As Fig. 1b plots, in ≈ 1550 nm band, the measured resonance linewidths in the X and the Y polarizations are 4.83 MHz and 6.03 MHz respectively (Lorentz fitting), corresponding to Q factors 4.0×10⁷ and 3.2×10⁷. Besides high Q factor, anomalous group velocity dispersion of the cavity is only ≈ − 3.2 fs²/mm for the X polarized mode and ≈ − 3.4 fs²/mm for the Y polarized mode around 1550 nm. These parameters enable us to generate DKS in the monolithic resonator by using a continuous-wave laser with single watt power.

Figure 1c demonstrates the principle and process of the orthogonally-polarized dual-soliton generation. First, a tunable external cavity single-frequency laser is amplified by using an erbium doped fiber amplifier (EDFA) and then coupled into the F-P fiber monolithic resonator in the X polarization. With red-detuning the pumping laser, it enters a resonance (state 1). When the intracavity pumping laser power is high enough (threshold ≈ 130 mW), a Brillouin laser (BL) is excited in another resonance (Y polarization), at the frequency down-shifted from the pump laser, Δf_BL ≈ 10 GHz, majorly determined by the silica material. Continue to increase the pump red-detuning, in increased BL power could be high enough for Kerr comb formation. At state 2, we show the case that both the pumping laser and the BL are located at the blue-detuned region of their resonances. Although there could be combs generated already, none of them is a DKS. The continuous red-detuning of the pumping laser not only promotes the BL power, but also can push the BL more redly. At state 3, when both the pumping laser and the BL are in the red-detuned region of their resonances, dual DKS could appear. Supplementary Section S1 provides detailed theoretical analysis. In experiment, we measure the soliton evolutions in both polarization (Fig. 1d). By scanning the pumping laser (≈ 1550 nm) from blue to red with a speed 50 GHz/s, we observe the three aforementioned states. The measured results verify that the BL appears later (state 1), chaotic combs are generated in both X and Y polarization (state 2), and finally the orthogonally-polarized dual-soliton are generated (state 3). Soliton existence range of the dual-soliton is 2.5 MHz. In Fig. 1e, we plot the spectra of the orthogonally-polarized DKS. The beautiful sech² shape envelop solidly suggests the DKS formation. Central wavelengths of the X-polarized and Y-polarized soliton combs are 1549.969 nm and 1550.044 nm. 3-dB bandwidth of them is 2.38 THz and 2.4 THz, corresponding to a single pulse duration 132 fs and 131 fs, respectively. Around 1550 nm, birefringence of the two orthogonal-polarized modes is in 2×10^− 5 level, enabling free-spectral-range difference about 12 kHz. Detail measurements are shown in Supplementary Section S2. And we show the measured auto-correlation FROG maps in Supplementary Section S3. Since power of the BL is stronger than the pumping laser, the power of the Y-polarized soliton is 4 dB higher, reaching 0.12 mW.

Such dual-soliton co-generation offers rich beat notes in the radio frequency domain. In Fig. 2a, we schematically show that there would be two types of down-conversion beat notes when measuring the dual-DKS by using a photodetector. First, when soliton is generated intracavity, due to the soliton trapping[29–31] via XPM coupling in between, the two orthogonal combs share the same repetition frequency (f_rep). On the other hand, the pumping laser and the BL are located at two different central wavelengths, thus the two combs generated by them can have varied carrier-envelope-frequencies. Spectral distance of the pumping laser and the BL Δf_PB equals to 9×f_rep plus 269 MHz (Δf_ceo). Here the 269 MHz offset comes from the dislocation of the two orthogonal cavity modes. We measure the beat notes of them in Fig. 2b, by using a 10 GHz photodetector. First, we verify the self-beat notes of the X and Y polarized solitons via using a polarizing beam splitter, as the blue and red curves plots. One only sees the cascade beating lines with repetition 1.01 GHz, determined by the cavity length. Clean harmonic RF beat notes with signal-to-noise ratio (SNR) larger than 47 dB are observed. In synthetic measurement of the mixed polarization output, besides the f_rep notes, we also see strong Δf_ceo beating lines. The first Δf_ceo appears at 269 MHz, this number equals to the pump-BL frequency difference minus 9×f_rep. At the 9.1028 GHz, the strong beat note suggests the optical beating of the pumping laser and the BL. This result well meets the comb spectra measured in Fig. 1e. Figure 2c plots the temporal traces of the X and Y polarized solitons. Both of the pulses have the same repetition 0.99 ns.

We characterize the Δf_ceo beat note more in details in Fig. 2d. In the free-running comb device, the absolute carrier envelope frequency of the X or the Y polarized soliton is unstable, due to the intrinsic drift of the pumping laser. Nevertheless, the absolute frequency of the BL also shifts with the pump. Thus, the Δf_ceo could be very stable, when the cavity is not disturbed. In Fig. 3, we will further explain this point. In the top panel of Fig. 2d, we zoom-in the first beat note of Δf_ceo in a 200 kHz wide window. It demonstrates a signal to noise ratio > 23 dB, with a resolution-limited bandwidth 27 Hz (3 Hz RBW, bottom panel). Such a narrow linewidth is benefit from the Brillouin narrowing effect [24], in which the BL narrowing factor is (1 + δ/Δ)². Here Δ = 6.03 MHz is the resonance linewidth while δ = 80 MHz is the Brillouin gain bandwidth. By using an ultrastable pumping laser (NKT E15, typical linewidth 100 Hz), the linewidth of the BL can reach 0.5 Hz in principle. In Fig. 2e, we demonstrated the measured single-sideband phase noises (SSB-PN) of the soliton beat notes. Typically, the phase noise of a soliton comb is determined by the pumping laser. The blue dots show the standard phase noise of our pump, the SSB-PN of the NKT E-15 is already very low, < -120 dBc/Hz @ 1 kHz. Thanks to the stabilization from the BL narrowing effect, the first FSR carrier (f_rep at 1.01 GHz) demonstrates considerably low SSB-PN at 1 MHz offset, i.e. -167 dBc/Hz. This number is 20 + dB higher than our previous study [24], because in the dual-soliton co-generation implementation, the pumping laser doesn’t work as an auxiliary laser for thermal stabilization. Besides, we show the SSB-PN of the first Δf_ceo beat note at 269 MHz, as the grey curve plots. It illustrates − 92 dBc/Hz @ 1 kHz, -118 dBc/Hz @ 10 kHz and − 140 kHz @ 1 MHz, averagely 7dB better than the SSB PN of the Δf_pump−BL at 9.28 GHz, due to the self-frequency shift [32]. Once locking the pumping laser via feedback loop, the result could be further optimized, but it now is still sufficient for high resolution sensing. We also note that for high precision sensing based on heterodyne scheme (see Fig. 4), the dual soliton formation is technically essential, since frequency of the Δf_ceo beat note at 269 MHz is much lower than the Δf_pump−BL beat at 9. 28 GHz, enabling further frequency down mixing via a highly-stable RF oscillator (typical SSB PN of a 9 GHz RF oscillator is higher than − 100 dBc/Hz @ 1MHz).

In Fig. 3, we investigate the property of the Δf_ceo of the orthogonal dual-soliton generated in our fiber monolithic resonator, and exam its unique potential for all-in-line fiber sensing. In Fig. 3a, we show the sensitive principle of the Δf_ceo schematically. Different from the pumping laser generated DKS, the f_ceo of the BL generated DKS is determined by the spectral location of the BL, which appears just at the largest overlapping point of the 9-FSR down-shifted resonance (orange shadow) and the Brillouin gain region (green shadow). When the fiber F-P monolithic resonator is influenced by external environment, e.g. force, both the birefringence of the resonator (f_rep of the Y polarized mode) and the Brillouin gain region offset (Δf_BL) could be changed. The latter is determined by Δf_BL = 2n_pv_A/λ_p, wherein n_p is the refractive index at pumping frequency, λ_p is the pumping wavelength, v_A is the acoustic velocity, which is determined by the material Young’s module, relative to stress [33]. Hence, when force is applied to the cavity, frequency of the pumping laser keeps unchanged, but frequency of the BL alters, therefore one can obtain a spectral shift of the Δf_ceo, in the high-resolution optoelectronic heterodyne measurement. More theoretical discussions and simulations are shown in Supplementary Section S1.

Figure 3b shows our experimental setup, using the dual-soliton device to detect force. The orthogonal dual-soliton is generated by using an amplified continuous-wave pumping laser, whose polarization is carefully tuned via a fiber polarization controller (FPC), for maximizing the energy coupling in the X polarization. Both the cavity and the pumping laser are thermally stabilized by using a thermo electric cooler (TEC), for suppressing the cross-interference caused by temperature drift. The dual-soliton is mixed and detected by using a balanced photodetector with both low noise and high transfer gain. Then the Δf_ceo is monitored by using electrical spectrum analyzer (ESA). For achieving higher sensitivity, the shift of Δf_ceo is further down-mixed with a microwave generator (MWG) and tested by using the lock-in amplification scheme (see Fig. 4). In the sensing implementation, external force is applied on the fiber F-P monolithic resonator via a rigid mechanical mount. A combined-levers based microprobe with minimum tuning scale 10 nN is used to calibrate the force. Figure 3c demonstrates the force sensing result spectrally. When increasing the force from 0 to 5.88 mN, we observe the Δf_ceo shifts by 1641 kHz. Determined by the specific resonance-Brillouin overlapping situations in different cavity samples, the spectral shift of the Δf_ceo commonly positive. The correlation of the force and the frequency shift of the Δf_ceo is well linear in this case, demonstrating a sensitivity 0.3 kHz/µN. Referring the RF linewidth limited spectral resolution 27 Hz, one can sense < 90 nN force by just monitoring the radio frequency shift. Due to the limited soliton existence range of the Y-polarized DKS (2.5 MHz), measurement range of the dual-soliton sensor is 7.3 mN. Such a number is considerably large for an ultrasensitive force meter. Figure 3d plots the linear response of our comb sensor for force detection. When increasing force from 0 to 7.33 mN, the Δf_ceo signal shift linearly increases from 0 to 2210 kHz. Generally in such a large measurement range, the coefficient of linearity R² approaching 1. More in details, for the 0 ~ 12 µN region, the linearity coefficient R² is 0.9885, while for the 7200 ~ 7330 µN region, R² is 0.9699.

To explore the detect limit of the dual-soliton sensor device, we measured the Δf_ceo shift induced intensity alteration via the lock-in heterodyne scheme. By using a tunable microwave signal with high purity, we mix the Δf_ceo beat note further down to f_M =100 kHz, in this step the information of Δf_ceo could be amplified once. The down-mixed signal is shown in Fig. 4a. We find that the down-mixed signal has several noise peaks, with frequency offsets in range of 300 Hz to 1 kHz, due to slow thermal instability even there have been TEC already. Leveraging an electrical band-pass filter with pass-band 200 Hz, these noises could be isolated out. The lock-in amplifier boosts the intensity at f_M over 40 dB [28]. As Fig. 4b illustrates, when a very small force applied to the fiber monolithic resonator, the change of Δf_ceo would also shift the f_M to f_M’. As a result, the intensity at the original f_M decreases. Such a decrement is considerably amplified and observable in an oscilloscope. In experiment, we can get a maximum output 4.34 V from the lock-in amplifier, corresponding to a transfer of frequency shift to intensity 321.5 mV/Hz (or 96.5 mV/nN). Top panel of Fig. 4c plots the output trace of the lock-in amplifier when the dual-soliton device is statically standing. Intensity uncertainty of this trace is ± 50 mV. Approximately, we estimate that the nano-force detect limit could approach 520 pN. Bottom panel shows the case we repeatedly add 30 nN on the monolithic resonator, verifying the ultrahigh sensitivity and demonstrating good recoverability of our dual-soliton fiber sensor. In Fig. 4d, we show the repeatedly measured results. In ten independent measurements using the same microcomb device, we obtain highly consistent results. The detect limit is in a range of 0.48 to 1.92 nN, while the measurement range keeps 3.1 to 7.3 mN. Typically, the dual-soliton sensor suggests a sensing performance 10⁷, which is orders higher than a conventional fiber or electrical force detector.

As a technological challenge, Nano force measurement is widely investigated for diverse applications ranging from material engineering to biological analysis [34]. In optics, high precision force sensing systems could be based on versatile methods such as opto-mechanics [35, 36], interferometry in micro-nano photonic structures [37], nonlinear scattering [38], optical frequency-domain reflectometry [39], and photonic forces [40–42]. The resolution and dynamic range of different force measurement schemes are reported in Fig. 5. Typically for every technology there is a compromise between resolution and dynamic range. Moreover, operation of the state-of-the-art force sensors with fN level sensitivity commonly have some practical limitations. For instance, opto-mechanical sensors often require cryogenic temperatures and in vacuum, while optical force sensors like tweezers and nanowires can only detect photon endogenous force meanwhile need ultra-clean or opto-fluidic environment. Our work owes unique merits both from optical fiber structures such as high flexibility, good compactness, immunity to electromagnetic, and from dual-comb metrology such as high resolution down to Hz level and optical spectrum analyzer free measurement.

In summary, we generate a pair of co-locked dissipative Kerr solitons in one single fiber monolithic resonator, by stimulating an intracavity Brillouin laser. The two soliton combs are polarization orthogonal, share the same repetition (≈ 1 GHz) but different central wavelengths (≈ 10 GHz), due to the Brillouin offset. As a result, we obtain stable dual-soliton beat notes presenting their carrier-envelope-offset in microwave. We find such carrier-envelope-offset signals are determined by the overlapping of Brillouin gain region and the resonance of the two orthogonal modes, thus they are mechanically sensitive to external force, demonstrating both extremely high sensitivity (detect limit 520 pN) and large linear measurement range (up to 7.3 mN). This work inspires novel physical mechanism of dual-soliton co-generation and multiplexing, demonstrates new scheme for dual-comb control, and open a way for high performance microcomb based optical fiber sensors.

Theoretical analysis of the dual DKS generation. In the orthogonal polarizations, a pair of dissipative Kerr solitons were generated, by using the pumping laser and its stimulated Brillouin laser 10 GHz away. The red-detuning of the pumping laser pushed the Brillouin laser from blue to red, thus both of them entered the soliton region. The comb evolution met the well-known Lugiato-Lefever Equation (LLE). Since the orthogonal mode families had similar free-spectral-ranges, the dual solitons oscillate in the same repletion frequency, but they had different central wavelengths.

Device fabrication and characterization. The highly-nonlinear-fiber (HNLF, NL-1550-POS, YOFC) with nonlinear coefficient over 10 /W/km and attenuation below 1.5 dB/km was carefully cut. Before coating the side mirrors, both fiber ends were mounted in ceramic ferrules and finely polished. Each Bragg mirror is formed by a ten-layer Ta₂O₅ / SiO₂ hybrid film, by using the ion assisted deposition. Broadband transmission from 1540 nm to 1560 nm, and single resonance are measured by using a widely tunable laser (Santec TSL-710).

Sensing implementation. The dual soliton microcomb device was fixed in a metal mount, in a scale of 8×2×1 cm³. Pumping laser was launched into the fiber monolithic resonator from one side (input port), while the comb outputs were measured in the other side (output port) all in line. The cover of this mount is mechanically flexible, precalibrated by using screws. External force was applied by using a three-stage manipulator, which could be precisely tuned on a micro motion stage. For better ensuring the stability when adding the force, the comb sensor device was also encapsulated in a temperature controlled and air-flow isolated box.

Acknowledgments

The authors acknowledge support from the National Science Foundation of China (61975025, U2130106), the National Key Research and Development Program (2021YFB2800602), and the Key project of Zhejiang Laboratory (2020KFY00562).

Conflict of interest. The authors declare that they have no conflict of interest.

Author contributions. B.Y. led this research, Y.R. and S.Z. led the groups. K.J. and Z.X. led the device fabrication. C.Q. and B.Y. led the experiment. C.Q. J.D. and T.T. performed the optical experiments. B.C. and Y.G. contributed to the heterodyne technique. B.Y., Z.X. and S.W.H. performed the physical analysis and numerical simulations. All authors processed and analyzed the results. B.Y., C.Q., Z.X. and Y.R. prepared the manuscript.

Data availability. The data that support the plots and maps within this paper and other findings of this study are accessible online, and more detailed data are available from the corresponding authors upon reasonable request.

Supplemental document. See Supplementary Information in www.nature.com.

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