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Abstract
An Hz-magnitude ultra-narrow linewidth single-frequency Brillouin fiber laser (BFL) is proposed and experimentally demonstrated. The single frequency of the laser is selected by parity-time (PT) symmetry, which consists of a stimulated Brillouin scatter (SBS) gain path excited by a 24 km single-mode fiber (SMF) and an approximately equal length loss path tuned with a variable optical attenuator (VOA). These paths are coupled through a fiber Bragg grating (FBG) into a wavelength space. Accomplishing single-frequency oscillation involves the precise adjustment of polarization control (PC) and VOA to attain the PT broken phase. In the experiment, the linewidth of the proposed BFL is 9.58 Hz. The optical signal-to-noise ratio (OSNR) reached 78.89 dB, with wavelength and power fluctuations of less than 1pm and 0.02 dB within one hour. Furthermore, the wavelength can be tuned from 1549.9321 nm to 1550.2575 nm, with a linewidth fluctuation of 1.81 Hz. The relative intensity noise (RIN) is below -74 dB/Hz. The proposed ultra-narrow single-frequency BFL offers advantages such as cost-effectiveness, ease of control, high stability and excellent output characteristics, making it highly promising for the applications in the coherent detection.
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1. Introduction
Single frequency narrow linewidth fiber lasers have been widely used in Lidar [1], high-precision sensor measurement [2,3], microwave photon [4,5], high-capacity coherent optical communication [6] and optical hydrophone [7], characterizing by high brightness, compact structure, excellent monochromaticity and elevated coherence time. At room temperature, Er-doped fibers (EDF) exhibit uniform broadening characteristics, which causes significant mode competition, making it challenging to achieve a stable single-frequency laser output. In order to achieve single-frequency oscillation, numerous research efforts have proposed methods for mode selection. For instance, the short-cavity method represents one of the initial approaches to achieve effective single-frequency laser emission [8]. However, limited by cavity’s length, it is arduous to attain laser linewidth at the kilohertz level. The incorporation of ultra-narrowband filters, including high fitness Fabry-Perot resonators [9], constitutes an effective mean to achieve single-frequency laser output. Nonetheless, their structural complexity, manufacturing difficulties, and high cost remain noteworthy considerations. Employing cascaded multi-ring cavity to enhance free spectrum range (FSR) is a potential mean to realize single-frequency oscillation [10,11]. However, this method is relatively complex and tend to be more susceptible to environmental impacts, resulting in diminished stability. Furthermore, employing unsaturated absorption effects in non-pumped gain fiber [12] or novel two-dimensional materials [13] offer a viable approach to mode selection, but the output power is limited.
Recently, parity-time (PT) symmetry, originally proposed by Carl M. Bender, suggests that non-Hermitian Hamiliton could possess real eigenvalues [14], and the principle has been widely studied in mode selection. This characteristic of mode selection has been confirmed in the fields of optoelectronic oscillators (OEO) and lasers. Generally, mode selection based on PT symmetry can be categorized into five distinct methods: coupled micro-ring cavities, coupled waveguides, photonic crystal, polarization properties in waveguides and counter-propagating waves in Bragg gratings. In 2014, Liang Feng et al. introduced a single-frequency laser based on InGaAsP/InP micro-ring resonator that is independent of the gain spectrum bandwidth [15]. In 2017, Weilin Liu et al. proposed a PT-symmetric micro-ring laser composed of two mutually coupled active micro-resonators. This design achieved single-frequency oscillation with a sidemode suppression ratio exceeding 36 dB through electrical pumping [16]. In 2020, Zhiqiang Fan et al. presented a single longitudinal mode laser with a narrow linewidth of 433 Hz, achieving via integrated micro-ring resonators [17]. Micro-ring resonators offer high-quality factors, low thresholds, and integration ease. However, the fabrication is extremely intricate and cost-prohibitive. In 2012, Mohammad-Ali Miri et al. pioneered use of PT symmetry for achieving single-frequency lasers with semiconductor laser amplifiers [18]. In 2023, Zeqiu Liu et al. showed direct modulation single mode lasing by breaking PT symmetry employing two identical FP resonators [19]. Leveraging PT-symmetry in coupled waveguide semiconductor lasers enables high-power, high-side-mode-suppression-ratio outputs, albeit with greater manufacturing complexity and less adaptability compared to fiber lasers. In 2016, Kyoung-Ho Kim et al. has achieved single-amplifying lasing mode by coupled photonic-crystal lasers [20]. In 2022, Lingfang Wang et al. manipulated line-defect photonic crystal achieving single-mode laser with 0.056 nm linewidth [21]. This method does not sacrifice output power, threshold pump power, and linewidth to achieve single-frequency oscillation, but its specialized design adds complexity. Recently, optical polarimetric diversity for PT-symmetric mode selection has been verified, simplifying the system by implementing it between two subspaces in a single-space unit [22]. Our group has demonstrated sub-kHz linewidth single-frequency laser output based on polarimetric PT-symmetry [23,24]. Worthy of consideration, polarization characteristics are susceptible to disturbances, resulting in moderate stability. The counterpropagating transmission of Bragg gratings is a concise mode selection method leveraging PT symmetry. Moreover, utilizing fiber Bragg grating (FBG) as a coupler possesses the potential to incorporate two spatially separated cavities into a single wavelength space or facilitate specialized design considerations for the lengths of two spatially separated cavities. In 2022, Jianing Zhang et al. demonstrated a single-frequency laser output with 163 Hz linewidth. They utilized Bragg gratings in a ring cavity to explore the dynamic evolution of cavity eigenmodes around the exceptional point (EP) [25]. However, their experiment involves the use of an external magnetic field to adjust isolation, adding complexity to the system’s control. In 2023, Zheng Dai et al. demonstrated fiber Bragg grating as PT-symmetric coupling device to achieve a single-frequency laser with sub-kHz linewidth [26]. However, the article employs dual-loop with a precise loop length ratio, requiring meticulous design of the ring cavity lengths.
The Brillouin laser exhibits distinctive properties, allowing for a significant reduction in the linewidth of the pump laser by several orders of magnitude. In contrast to DFB lasers with external cavity feedback and the Vernier effect for linewidth compression, utilizing SBS easily allows for laser outputs with linewidth below 1 kHz [27]. In 2018, Sarat Gundavarapu et al. designed a sub-Hz level linewidth stimulated Brillouin laser integrated on a waveguide platform. This Brillouin laser process high integration capabilities and outstanding output characteristics [28]. However, the integrated laser is manufactured using wafer-level processes, incurring high production costs and a relatively intricate fabrication procedure. Additionally, the introduction of the Pound-Drever-Hall (PDH) system for frequency stabilization contributes to the system's increased complexity. Furthermore, the temperature variations resulting from heat dissipation of the highly integrated chip can impact the stability of the laser. In contrast, all-fiber structures exhibit advantages characterized by reduced manufacturing expenses and robust stability. Moreover, fibers possess a large mode field volume and effective optical mode area, enabling fiber Brillouin lasers to offer optimal spectral purity. The characteristics of PT-symmetric mode selection provide a valuable settlement in BFLs. Liuyuan Tao et al. has designed a BFL with a 300 Hz linewidth based on a PT-symmetric nonreciprocal Sagnac loop [29]. The BFL has achieved widely wavelength tuning over a range of 35 nm through current modulation of the seed laser. However, the addition of single-mode fiber (SMF) length in the Sagnac loop needs to match the SMF of stimulated Brillouin scattering, leading to an increase in the system's complexity and instability. Meanwhile, the paper lacks a comprehensive analysis of stable single-wavelength stability, leaving certain specific applications without sufficient reference. By utilizing micro-ring resonators (MRR) as a coupler to form a dual-polarization cavity, a PT-symmetric structure proposed by Y. Liu et al. is created to achieve a single-frequency laser output with a linewidth of 11.95 Hz in the BFL [30]. The laser exhibits a low oscillation threshold of 2.8 mW and narrow-linewidth. Nonetheless, the manufacturing process and cost of MRR are relatively high, and the excessive use of polarization controllers adds complexity and difficulty to system control. Zhenpeng Deng utilized a Bragg grating as PT-symmetric coupling device to demonstrate a single-mode BFL with 368 Hz linewidth [31]. Because the intense transmission light of the grating is used to construct a loss loop for the PT symmetric system, the Rayleigh scattering effect caused by the pump in the designed laser is challenging to eliminated. This manuscript has proposed the BFL based on PT-symmetric structure with FBG incorporate Brillouin scattering effect and transmission loss into an equivalent loop of approximately equal length. This configuration merges the gain and loss loops into an overlapping spatial loop, effectively creating a wavelength space, significantly reducing sensitivity to environmental disturbances. The proposed BFL exhibits simpler control mechanisms for mode selection, Hz- level linewidth, good spectral stability, and linewidth stability. Additionally, the more comprehensive testing and experimental analysis for BFL can provide a well reference value for its practical application.
In this paper, we propose and demonstrate a sub-Hz ultra narrow linewidth single-frequency BFL in a spatial space. PT symmetry is composed of the gain path formed by SBS and the loss path based on a variable optical attenuator (VOA) and coupled through a FBG. The gain and loss can be achieved by finely tuning the polarization controller (PC) and VOA to achieve the PT-symmetric phase to PT-broken phase transition for single frequency oscillation. In the experiment, the spectral OSNR has improved 26.56 dB. The wavelength and power fluctuations are less than 1 pm and 0.02 dB within 1 hour, demonstrating an excellent stability of the proposed laser. Particularly, the linewidth of the proposed laser is 9.58 Hz, and the wavelength is within the tuning range of 1549.9321 nm to 1550.2575 nm with a linewidth float of 1.81 Hz. The proposed BFL based on PT-symmetric structure with coupling the gain and loss loops using a FBG into a wavelength space has the characteristics of easy tuning for single-frequency output, Hz- level linewidth, good spectral stability, and linewidth stability. It can promise broad applications in the field of coherent Lidar and precise detection of gravitational waves.
2. Principle
The experiment setup of proposed BFL is shown in Fig. 1. A seed laser (Connet, CoSF-D-ER-M-1550-PM-FA) with fixed 1 kHz linewidth is employed to pump source injection at one end of the 3 dB optical coupler (OC). An Er-doped fiber amplification (EDFA), comprised of a 980 nm pump and a segment of erbium-doped fiber, is used to supply the requisite energy for SBS oscillation. For loss loop, light transmission occurs sequentially through 24 km single-mode fiber (SMF), an optical isolator (ISO), VOA, then transmitted via the FBG and Cir2 to OC1. In the meantime, ISO and Cir2 ensures unidirectional propagation in the loop and mitigates the impact of pump laser Rayleigh scattering. The VOA is employed to control the intensity of loss. The gain loop originates from Stokes light stimulated by SBS when the pump light surpasses the SBS threshold. The Stokes light pass through a PC, then it is reflected by the FBG to OC1. The PC is used to control the gain coefficient due to the polarization dependence of SBS. Therefore, precise adjustment of VOA and PC enables the realization of PT symmetry. The output laser emanates from the 10% beam splitter port of OC2 and is concurrently monitored by both optical spectrum analyzer (OSA) and electric spectrum analyzer (ESA). An acousto-optic modulator (AOM) with 100 MHz shift is used to filter low-frequency noise and make the observation easy. Meanwhile, a filter is utilized to eliminate interference from high-frequency noise exceeding 140 MHz. When the gain and loss coefficients exceed the coupling coefficient which is determined by the reflectance of FBG, the PT-symmetric phase is converted to PT-broken phase, and a single-frequency is selected to oscillate in the laser.
Fig. 1. Experiment structure of the proposed PT-symmetric fiber laser. OC: optical coupler; WDM: 1550/980 nm wavelength division multiplexer; EDF: erbium-doped fiber; Cir: optical circulator; SMF: single-mode fiber; ISO: optical isolator; VOA: variable optical attenuator; FBG: fiber Bragg grating; PC: polarization controller; OSA: optical spectrum analyzer; PD: photodetector; AOM: acousto-optic modulator; EA: electronic amplification; ESA: electrical spectrum analyzer.
2.1. Gain based on the SBS
When the pump light travels through to the SMF and exceeds the Brillouin threshold, it generates frequency-down shifted Stokes light. The Brillouin frequency shift fB is given by ${f_B} = 2{n_p}{\textrm{v}_A}/{\mathrm{\lambda }_P}$, where np is the effective refractive index at the pump wavelength λp, vA is the acoustic velocity in the medium. When the center wavelength is at 1550.0026 nm, fb is approximately 11.28 GHz. The Brillouin gain spectrum with Lorentzian shape can be formulated as:
where gp is the Brillouin gain peak, ΔfB represents the Brillouin gain bandwidth, approximately 10 MHz. The effective fiber length of the system is 24 km. From the formula $FSR = c/{n_p}L$, the FSR is about 8.514 kHz. Thus, within the SBS gain bandwidth, there are over 1000 oscillating modes.Due to the inherent polarization dependency of SBS [32], the gain coefficient can be controlled by manipulating the PC. The efficiency of SBS can be expressed with the following formula:
where $\hat{s} = ({{s_1},{s_2},{s_3}} )$ and $\hat{p} = ({{p_1},{p_2},{p_3}} )$ represent the unit vectors of the Stokes wave and pump wave on the Poincare sphere, respectively. When the pump light and Stokes light exhibit parallel polarization and orthogonal polarization, the ηSBS are $1 - s_3^2$ and $s_3^2$, respectively. Birefringence fluctuations cause changes in polarization state, leading to stochastic variations in the parameter s3, thereby affecting the polarization efficiency [33].2.2. PT symmetry
A PT-symmetric system is established by coupling the Stokes light (serving as gain) and pump light (acting as loss) through uniform FBG with nearly identical lengths in two rings. In [34], the mode coupling equation for PT symmetry can be mathematically expressed as:
In gain and loss loops, by initially coarse adjusting the VOA, followed by fine-tuning the PC, it is possible to achieve that gain coefficient equals the loss coefficient. This means gan = -gbn = gn. Thus, the eigenfrequency is resolved as:
According to Eq. (5), as the coupling coefficient exceeds gain coefficient, the eigenfrequency bifurcate into two real values, which indicates energy conservation. This situation is defined as PT symmetric phase, shown in Fig. 2(a). When coupling coefficient is less than gain coefficient, the real components of eigenvalues collapse, while the imaginary components of eigenvalues bifurcate. This situation is defined as PT broken phase, characterized by one eigenstate experiencing amplification, while the other experiences attenuation. Fig. 2(b) depicts the evolution of the PT broken phase. When coupling coefficient is equivalent to gain coefficient, the situation is defined as exceptional point (EP). Meanwhile, the transition from PT-symmetric phase to PT broken phase can incite numerous phenomena.
Fig. 2. Evolution of the real (a) and imaginary (b) parts of eigenfrequencies as they vary with the ratios of kn to gn.
An essential feature of the PT-symmetry broken phase is the capability to enhance gain contrast. In conventional laser source, the gain contrast is defined as ${g_{max}} = {g_0} - {g_1}$. Wherein, g0 is the gain of center mode, while g1 corresponds to the gain of adjacent modes. In PT symmetry, the gain contrast is redefined as ${g_{\textrm{max}\_PT}} = \sqrt {g_0^2 - g_1^2} $. Obviously, the gain contrast is improved in PT symmetry. The improved ratio can be formed as:
Based on Eq. (6), it is evident that G consistently exceeds 1. Consequently, the central mode surpasses the threshold initially, achieving single-frequency oscillation. Fig. 3(a) and (b) depict the mode oscillation in BFL under conditions of without PT symmetry and with PT symmetry mode selection. When the PT symmetry system is absent, a multitude of modes within the Brillouin gain spectrum exceed the oscillation threshold. When the BFL in the PT broken phase, within the gain spectrum, only the mode at the center frequency exceeds the threshold, resulting in single-mode oscillation.
Fig. 3. The mode selection principle of the proposed BFL. (a) Multi-mode oscillation in the absence of PT symmetry. (b) Single mode oscillation with PT broken phase.
3. Experiment results and discussion
The schematic diagram of proposed BFL assisted with PT-symmetric is shown in Fig. 1. The laser’s output characteristics were experimented on a optical platform at room temperature of 24 °C. The seed laser achieved a settled output power of 10 mW with a fixed linewidth of 1 kHz. The center wavelength of FBG is 1549.988 nm and its 3 dB bandwidth is 0.3 nm.
3.1. Optical spectrum property
When the power of seed laser is fixed at 10 mW, the relationship between output power of the laser and the pump power are shown in Fig. 4(a). The threshold oscillator power is 28 mW shown in the Fig. 4(b). When the threshold is exceeded, the relationship of output power and pump power of Stokes light can be expressed by the linear equation as: y = 0.01965x-0.506. The optical spectra of seed laser and the Stokes light are monitored by an OSA. As illustrated in Fig 4 (c), when the center wavelength of the seed laser is 1550.0026 nm, the corresponding center wavelength of Stokes light is measured at 1550.0858 nm. During the manufacturing process of the commercial seed laser, a filter has been introduced at the central wavelength to suppress side modes. However, due to minor technical errors in the manufacturing process, the filter range exhibits a short-wavelength shift relative to the central wavelength, resulting in a portion of the spectrum in the right half exceeding the coverage of the filter. Consequently, the seed laser’s spectrum presents an asymmetric state. In the proposed BFL, due to the narrow range of the Brillouin gain spectrum, the relatively stable trend observed in the right half of the spectrum in the seed laser has been effectively filtered out with the center wavelength shifted to the central region of the Brillouin gain spectrum. But the left half of the spectrum is still affected by the seed laser. Hence, the spectra of the seed laser and BFL exhibit asymmetry. In comparison to the seed laser, the OSNR has improved from 52.33 dB to 78.89 dB. The stability of the laser over a period of 1 hour at 6-minute intervals is tested. Figure 5 depicts the wavelength and power fluctuations during test period. The wavelength exhibited fluctuations of less than 1 pm within one hour, while the power experienced fluctuations of less than 0.02 dB within the same time period. It is worth noting that the observed power fluctuations are primarily attributed to the long-term thermal effects of the seed laser.
Fig. 4. Laser threshold and optical spectrum property. (a)The relationship between pump power and output power when the seed laser is 10 mW. (b) The seed spectrum with a center of 1550.0026 nm and Stokes light spectrum with a center wavelength of 1550.0858 nm.
Fig. 5. The stability of Stokes light over 1 hour at 6 minutes interval. (a) The spectra stability of Stokes light (b) The wavelength and power fluctuation of Stokes light during the test period.
3.2. Spectral property
To mitigate the interference of low and high-frequency noise, we employed an AOM with 100 MHz frequency shift and an electronic filter with a cutoff frequency below 140 MHz. Fig. 6 shows the frequency spectra detected by PD under various measurement range and resolution. As shown in Fig 6(a) and (b), the frequency signals are recorded in the range of 20 MHz with 10 kHz resolution. Figure 6(a) indicates that the BFL is multi-mode oscillator. Figure 6(b) shows the PT broken phase can be achieved by tuning VOA and PC to realize single-frequency oscillation. The frequency spectra recorded for 2 MHz detection range with 910 Hz resolution and 100 kHz detection range with 10 Hz resolution are depicted in Fig. 6(c)-(d) and (e)-(f), respectively. In Fig. 6(e), the detected FSR is 8.4 kHz, which complies with the theoretical value. Figure 6(f) shows the single-frequency oscillation with 54.77 dB SNR. Compared with PT unbroken, the SNR has improved by 30.32 dB, proving that PT symmetry system has the capability of mode selection. The stability measurement of the single-frequency spectra over one hour is conducted. As illustrated in Fig. 7, the result shows a stable single-frequency laser output in PT broken phase.
Fig. 6. Measurements of frequency spectra of PT-broken and PT-unbroken phases in different span and resolution through an AOM frequency shift. (a)(b) Detection range: 20 MHz, resolution bandwidth (RBW): 10 kHz. (c)(d) Detection range: 2 MHz, RBW: 910 Hz. (e)(f) Detection range: 100 kHz, RBW: 910 Hz.
3.3. Linewidth property
According to Fig. 6(f), the linewidth is estimated less than 100 Hz. Therefore, the traditional delayed self-heterodyne method, which requires delay lines of thousands of kilometers, is not applicable. In [36,37], a method based on contrast difference with the second peak and second trough (CDSPST) of the coherent envelope and length of delay lines is proposed, enabling the measurement of sub-hertz-level ultra-narrow linewidths. Due to the decreased accuracy at low power difference (ΔS) and the masking of high ΔS by ESA noise, the range for ΔS should be chosen within the range of 10 dB to 30 dB. We have emulated the relationship between the length of delaying fiber and ΔS in the range of 15 to 30 dB when the linewidth is 10 Hz. As shown in Fig. 8(a), when the ΔS is 21.6 dB, the corresponding length of delay fiber is 81 km. Fig. 8(b) depicts the linewidth measurement result using CDSPST method with 80 km delay fiber. The measured ΔS is 21.65 dB corresponding the calibrated real value of ΔS is 21.87 dB. With the CDSPST method, the linewidth of the proposed SBS PT-symmetric fiber laser is measured to be 9.58 Hz. Due to the environment disturbances and unavoidable 1/f noise [38], the actual linewidth is even lower.
Fig. 8. (a) The relationship between delay line length and power difference within a 10 Hz linewidth, in the simulated CDSPST method. (b) The output linewidth measured by CDSPST method.
3.4. Wavelength tuning property
The Stokes light is generated due to the SBS of the pump laser. The output wavelength can be controlled by simultaneously adjusting the pump laser and stretching the FBG to change passband range. The experimental setup employed a commercial laser capable of wavelength tuning within the range of 1549.85 nm to 1550.15 nm. The correspondent Stokes light output spectrum with the wavelength tunable laser is depicted in Fig. 9. The measured output wavelength can be tuned from 1549.9321 nm to 1550.2575 nm. Theoretically, utilizing a broader tunable seed laser in conjunction with a tunable FBG enables a wider range of output wavelength tuning. During wavelength tuning, the measured linewidth fluctuation is 1.81 Hz, as shown in Fig. 10. The fluctuation is caused by the disturbance of environment and thermal noise.
3.5 RINs property
The RINs of proposed PT symmetry BFL, a commercial seed laser and noise floor of the detection system are measured using the direct detection method with a PD (Thorlabs, PDB465C) and an ESA with a frequency range from 0 to 10 MHz and a RBW of 10 Hz. Both the output power of PT symmetry BFL and seed laser are 0.4 mW. The measurement spectrum of the RINs is depicted in Fig. 11. The detection noise floor is primarily attributed to the electronic noise of the PD and ESA and interference of environment. For seed laser, a relaxation oscillation frequency peak is observed at 0.3 MHz with an intensity of -90 dB/Hz. The RIN of proposed PT symmetry BFL is below than -74 dB/Hz, and no additional noise components are observed.
Fig. 11. RINs measured for PT symmetry BFL, commercial seed laser and detection noise floor in 0-10 MHz with RBW of 10 Hz for ESA.
4. Conclusion
We have proposed and experimentally demonstrated an all-fiber sub-10 Hz ultra-narrow linewidth single frequency fiber laser based on SBS and PT symmetric system with FBG as coupling element. The mode selection is realized by a PT symmetry system which consists of a gain path of the SBS and an attenuation path of the VOA coupled with an FBG. The single frequency laser output is realized by tuning the PC and VOA, which enables PT-symmetric phase conversion to PT-broken phase. The threshold power is 28 mW when the output power of seed laser is 10 mW. The OSNR of the proposed BFL reaches 78.89 dB with power and wavelength fluctuations of less than 0.02 dB and 1 pm within one hour. The linewidth is measured to be 9.58 Hz with a fluctuation of 1.8 Hz by the CDSPST method, when the wavelength is tuned from 1549.9321 nm to 1550.2575 nm. The RIN is measured below than -74 dB/Hz without additional noise. The proposed BFL has outstanding advantages including easy tuning for single-frequency output, Hz- level linewidth, and superior spectral and linewidth stability, which enables potential applications in Lidar and high precision measurement.
Funding
Youth Innovation Technology Project of Higher School in Shandong Province (2022KJ044); Natural Science Foundation of Shandong Province (ZR2023MF071); National Natural Science Foundation of China (62075007, U2006217); Laoshan Laboratory Science and Technology Innovation Projects (LSKJ20221202).
Disclosures
The authors declare no conflicts of interest
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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