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Abstract
We demonstrate a narrow-linewidth high-order-mode (HOM) Brillouin random fiber laser (BRFL) based on a long-period fiber grating (LPFG) and distributed Rayleigh random feedback in a half-open linear cavity. The single-mode operation of the laser radiation with sub-kilohertz linewidth is achieved thanks to distributed Brillouin amplification and Rayleigh scattering along kilometer-long single mode fibers whilst a few mode fiber-based LPFGs enable the transverse mode conversion among a broadband wavelength range. Meanwhile, a dynamic fiber grating (DFG) is embedded and incorporated to manipulate and purify the random modes, which hence suppresses the frequency drift resulting from random mode hopping. Consequently, the random laser emission with either high-order scalar or vector modes can be generated with a high laser efficiency of 25.5% and an ultra-narrow 3-dB linewidth of 230 Hz. Furthermore, the dependence of the laser efficiency and frequency stability on the gain fiber length are also experimentally investigated. It is believed that our approach could provide a promising platform for a wide range of applications such as coherent optical communication, high-resolution imaging, highly sensitive sensing, etc.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Over the past few decades, higher-order-mode (HOM) laser sources involving both scalar and vector modes have proven to be utilized as mode division multiplexing (MDM) for the extension of optical fiber communication capacity [1–3]. In particular, the cylindrical vector beams (CVBs) with the radial and azimuth polarization distributions [4] are intrinsically potential for diverse applications such as high-resolution imaging, optical tweezers [5,6], etc. Several spatial techniques have been successfully used to generate HOM lasers, such as spiral phase plates and spatial light modulators [7,8]. However, the high insertion loss and the large volume make the high efficiency and integration of space systems a challenging and sophisticated process. All-fiber lasers are superior alternatives arising from their simple structure and low-cost manufacture utilizing fiber-based mode converters, such as the long-period fiber grating (LPFG) [9], photonic lantern [10], acoustically induced fiber grating (AIFG) [11], and mode selective coupler (MSC) [12].
Fiber lasers based on the nonlinear gain of stimulated Brillouin scattering (SBS) along long-span fibers have been widely studied to generate highly coherent laser sources of coherent optical communication and optical fiber sensing systems, originating from their typical characteristics of coherent time extension and phase noise suppression in long fiber cavity [13–17]. Recently, attempts have been made to generate HOM Brillouin fiber lasers. Wang et al. demonstrated a HOM Brillouin fiber laser based on intramodal and intermodal SBS, taking advantage of the transverse mode selectivity between different linear-polarization (LP) modes of cascaded photonic lantern [18]. Heng et al. proposed an all-fiber Brillouin laser architecture using an MSC and realized transverse mode switching between LP01 and LP11 mode via a homemade optical switch [19]. Xu et al. reported a dynamic switching all-fiber erbium-doped Brillouin laser by cascading an AIFG and an MSC operating in the identical wavelength region [20]. Although all above-mentioned fiber laser structures based on highly accumulated Brillouin gain in long fiber cavity basically realize transverse mode switching between several HOMs or LP01 and HOM, the fixed laser cavity with inevitable multiple longitudinal modes usually restricts the performance (e.g., noise characteristics) of the HOM fiber lasers.
Compared to the conventional cavity-based fiber laser, random fiber lasers (RFLs) exhibit unique cavity mode elimination and flexible manipulation owing to distributed feedback mechanism, i.e., distributed backward Rayleigh scattering originating from the intrinsic refractive index inhomogeneities along silica fibers [21]. Thanks to such unique features, RFLs have been also demonstrated for potential in diverse applications such as random number generation, time-domain ghost imaging, and other fields [22–24]. Recently, some HOM-RFLs are reported. Du et al. first proposed an RFL realizing switchable spatial mode output via an offset splicing spot and a few-mode fiber Bragg grating (FM-FBG) [25], but the inserted element losses give rise to the low overall efficiency of 0.5% and high laser threshold of 1.8 W. Wang et al. demonstrated cylindrical vector beams based on randomly distributed feedback fiber laser using an MSC [26]. The RFL can generate low-speckle-contrast HOM light whilst the slope efficiency is 1.2% at LP01 output and 2.1% at HOM output. Ma et al. reported an RFL carrying orbital angular momentum (OAM) with a controllable topological charge, which can range from −50 to 50 using a spatial light modulator. The laser efficiency can reach 23% with a high threshold of 2.24 W [27]. A high-efficiency and narrow-linewidth HOM laser based on an all-fiber cavity is always desirable for practical demands in terms of high-capacity advanced coherent optical communication and ultra-sensitive sensing.
In this paper, a linear-cavity BRFL-generating HOM is experimentally demonstrated. A homemade LPFG is inserted in the cavity as a mode converter to achieve mode conversion from the fundamental Gaussian mode (LP01) to higher-order scalar (LP11) and vector (CVBs) mode. A dynamic fiber grating (DFG) is utilized to stabilize the laser frequency. The DFG is produced when the ion population distribution along erbium-doped fibers (EDFs) is modulated by two coherent counter-propagating standing waves [28]. Stokes frequency drift caused by the SBS process can be suppressed by the long-lifetime DFG, and the time dynamic of random laser is extended to milliseconds, which is beneficial to dramatically mitigating the mode jump [29]. As a result, the proposed BRFL can generate high-order modes with remarkable cavity mode elimination. The HOM-laser efficiency can reach 25.5% whilst a sub-kHz linewidth of 230 Hz is achieved. Furthermore, the impact of the SBS gain fiber lengths on the laser efficiency and frequency stability is experimentally investigated for further optimization.
2. Experimental setup
The experimental setup of the proposed HOM-BRFL based on a half-open linear cavity is illustrated in Fig. 1. A narrow-linewidth laser with a center wavelength of 1550 nm (SE15, LAMDA) was amplified by an erbium-doped fiber amplifier (EDFA) to serve as the Brillouin pump. Through an optical coupler (OC1, 3 dB), the pump light was launched into a single-mode fiber (SMF) which served as both Brillouin gain and a ‘random mirror’ providing random distributed feedback through Rayleigh scattering with a typical fiber loss of 0.2 dB/km at the wavelength of 1550 nm. An isolator (ISO1) is used to prevent scattered light from entering EDFA and damaging the instrument. By implementing another ISO2, the end face scattering at the end of the SMF is eliminated. The residual pump light is also dumped and will not interfere with Stokes light at the laser output port. As the pump power exceeded the SBS threshold, the Stokes light can be backward generated via the SBS interaction, which is then launched into the DFG composed of a 10 m-long off-the-shelf EDF (EDFC-980-HP, Coherent Inc.; the peak core absorption is 5.85 dB/m@1530 nm) and a polarization controller (PC1) used to adjust the polarization of the counter-propagating Stokes lights separated by the OC2 (3 dB). Note that, the DFG with unpumped EDF is mainly employed to purify the random lasing spectra by highly suppressing multiple random modes, benefiting the frequency-stabilized random laser radiation without serve mode hoping albeit with additional insertion loss [29]. With the assistance of the reflection from DFG, the spectrally purified Stokes light was recirculated through the OC2 and amplified via the SBS to form a complete lasing resonance above the threshold. The random laser from another port of the OC2 is converted into the HOM via an LPFG with pre-adjustment of the PC2 before being output. The converted HOM random laser radiation transmits and outputs along the FMF pigtail of the LPFG without severe distortion and non-ignorable loss, which can be captured and observed by a charge-coupled device (CCD) camera.
Here, the LPFG-based mode converter is written in the two-mode fiber (TMF) by using point-by-point exposure with a CO2 fusion splicer (LZM-100, AFL) [9]. The effective refractive index of the LP11 mode in TMF is calculated by the finite element method, and then the corresponding grating pitch is obtained according to the phase-matching conditions. By adjusting the exposure time and moving speed of the CO2 laser, periodic refractive index modulation can be formed within the grating region of about 4 mm and the insertion loss of about 1.2 dB in a piece of TMF without the coating layer. The mode conversion efficiency can be obtained by the power contrast between the fundamental mode and the converted HOM mode based on the transmission of the LPFG via the common approach with the SMF-TMF-SMF structure, as mentioned in Ref. [9].The mode conversion efficiency is adjusted by the power of the CO2 laser, which can reach as high as 98.4% via the SMF-TMF-SMF structure, as shown in Fig. 2. In particular, the LPFG is written around the dispersion turning-around point of the TMF, and exhibited the advantage of over 100 nm broad bandwidth, which indicate the potential of broadband wavelength tunning operation [9].
3. Results and discussions
The spectrum of the proposed HOM-BRFL was measured by an optical spectrum analyzer (OSA) with a resolution of 0.02 nm, (AQ6370D, YOKOGAWA). The generated Stokes laser shows a wavelength up-shift of 0.082 nm with respect to its pump, corresponding to the Brillouin frequency shift at the wavelength of 1550 nm in silica fibers, as shown in Fig. 3(a). The high optical signal-to-noise ratio (OSNR) of ∼59.5 dB is also obtained. The two-lobe-shaped intensity output pattern, as, shown in the inset of Fig. 3(a), is observed by the CCD camera (C10633, HAMAMATSU), indicating that the generation of the LP11 mode via the LPFG. Figure 3(b) illustrates the laser efficiency and threshold power versus different fiber lengths in the proposed HOM-BRFLs. Results show that the output efficiency of the HOM random laser increases with the increased fiber length while undergoing a decline as the fiber length further increases beyond 7 km. The reason relies on that, when the length of SBS gain fiber rises from 2 km to 7 km, both the SBS gain and Rayleigh feedback obtained by Stokes light are increasingly improved, promoting the output efficiency of HOM random laser continuously increasing. However, since the pump consumption is not negligible in the BRFL with fiber lengths longer than 7 km, the Brillouin gain becomes saturated, resulting in a maximum HOM-laser efficiency of 25.5% at the optimal length of 7 km. With further increase of the fiber length up to 10 km, the growth trend of Rayleigh backscattering power gradually slows down due to non-negligible transmission loss, resulting in a significant decrease of HOM-laser efficiency to 18.7%. Consequently, there is a trade-off between the Rayleigh feedback strength and the Brillouin gain saturation in terms of the fiber length for optimal laser efficiency [30]. Moreover, the laser threshold drops gradually from 48.6 mW to 13.7 mW with the increase in fiber length, as shown in Fig. 3(b).
Fig. 3. (a) Spectrum of random laser output (the inset: output laser pattern) (b) laser efficiency and laser threshold power of the proposed HOM-BRFLs versus different fiber lengths.
The intensity profiles and interference patterns are monitored by the CCD camera to verify the spatial mode of the output laser. The LP11 mode can be degraded by four vector modes, including TE01, TM01, HE21odd, and HE21even by adjusting the PC2 to change the polarization state of the output light and eliminating the degeneracy of higher order modes. The OAM modes with the phase singularity and helical wavefront have a transformation relation among CVB modes. The odd mode and even mode of the same polarization state (for example, the LP11o,x and LP11e,x, where x represents the horizontal polarization) can be superposed to generate linear- polarization OAM mode via creating an extra phase difference of π/2 between the two modes [31]. Moreover, a polarizer is embedded between the output port and the CCD camera to verify the polarization distribution of the output beam. Spatial modes can be distinguished according to the different shapes filtered by the polarizer.
By rotating the polarizer, the two-lobe-shaped intensity patterns are parallel or perpendicular to the direction of the polarizer, as shown in Figs. 4(a) and 4(b), corresponding to the mode of TM01 or TE01, respectively. The wavefront of the OAM mode rotates around the phase singularity during transmission. After the plane Gaussian wave interferes with it, the polarity of the topological charge of OAM mode can be identified by the fork orientation of the interference fringe, and the number of forks implies the topological charge value. The pattern after the polarizer filtering in different directions changes alternately between light and dark, as depicted in Fig. 4(c), indicating the OAM mode is linearly polarized. Figure 4(d) shows the topological charge of generated OAM mode is -1.
Fig. 4. Near-field intensity distribution of (a) TM01, (b) TE01, (c) OAM mode, and (d) the interference of OAM mode and Gaussian modes, respectively. The arrows indicate the polarizer axis from 0° to 135° with a step of 45°.
Theoretically, the mixed electric field intensity of the high-order mode in the TMF can be expressed as the superposition of each frequency [32]. To calculate the purity of the generated OAM mode in terms of the mixed electric field, the coefficients of the mixed electric field expression can be obtained by analyzing the projection of the OAM light filtered by the polarizer. The azimuth distribution of the OAM mode amplitude can be represented by the gray value of the data ring in a radius (the inset) of the CCD photograph, as shown in Fig. 5(a). Figure 5(b) and its inset demonstrate the amplitude spectrum and phase spectrum of the fitted-data ring via the Fourier transform. The magnitude and phase value of the DC and the first two azimuth angles can determine the proportion of the OAM mode in the mixed expression. It should be noted that this method can only figure out the OAM mode with linear polarization (LP-OAM) and the calculation above is based on the wavelength of 1550 nm.
Fig. 5. (a) The azimuthal intensity distribution of the OAM mode, the grey-scale map (the inset) (b) amplitude spectrum and phase spectrum (the inset) of the data ring
Taking advantage of the broad-bandwidth LPFG, the HOM-BRFL can flexibly realize the tunable OAM-mode laser emission with a rather broadband working wavelength range. The dependence of the LP-OAM mode purity on the Stokes laser wavelength is depicted in Fig. 6. Results illustrated that the purities of LP-OAM mode over the detecting entire wavelength range from 1541 nm to 1560 nm are entirely well beyond 90% and the maximum reaches 98.2% at 1557.082 nm. The limitation of the tunning range currently relies on the working wavelength (1530-1560 nm) of the main fiber components, including the optical circulator, the optical coupler, the amplifier (e.g., EDFA), etc. Regarding the wide bandwidth of the used LPFG, the arbitrary working wavelength would be highly expected if broadband indispensable devices were utilized to conduct the laser structure. Note that, the fluctuation of the mode purity in terms of different wavelengths is less than 5.3%, which is associated with the inhomogeneous gain of the EDFA and the slight wavelength-dependent conversion efficiency of the LPFG from 1541 nm to 1560 nm.
The temporal waveforms of the laser output have been measured by a photodetector with a bandwidth of 350 MHz (PDB435C-AC) and an oscilloscope (OSC) (DSOS404A, KEYSIGHT), to explore the intensity dynamics and statistical characteristics of the random laser emission. For comparison, both of the intensity dynamics of the laser output at the pump power below and above the laser threshold are illustrated. Figures 7(a-1) and 7(a-2) show the temporal trace and its power density distribution of the random emission when the pump power is below the laser threshold, indicating the asymmetric distribution of the intensity at the output, which is caused by the Brillouin scattering without random lasing resonance. The phase portrait was reconstructed by a two-dimensional intensity plot of IN versus IN + 1 (N = 1, 2…) with a delay of one-step intervals, as illustrated in Fig. 7(a-3). SBS emission exhibits a chaotic behavior in phase portrait which originates from the thermal noise in optical fibers [33]. On the other hand, Fig. 7(b) illustrates the stable establishment of the random lasing oscillation above the laser threshold. Results show the probability distribution of the temporal intensity traces exhibiting an approximately Gaussian distribution and the confined cycle signature of the stable laser output indicating the more enhanced coherence of the successive temporal points in phase.
Fig. 7. Statistics of SBS emission below the laser threshold (the upper row) and (b) Brillouin random lasing above the laser threshold (the bottom row). (a-1) and (b-1) indicate temporal trace; (a-2) and (b-2) represent power density distribution; (a-3) and (b-3) show phase portrait. (Oscilloscope sampling rate: 10 MSa/s)
To characterize the linewidth of the HOM-BRFL, a delayed self-heterodyne interferometer (DSHI) based on the delay fiber of 100 km is utilized. The optical beat signal was visualized by an electrical spectrum analyzer (ESA) (FSV3000, ROHDE&SCHWARZ). As shown in Fig. 8(a), the proposed HOM-BRFL with the SBS fiber length of 10 km exhibits a 20-dB linewidth of 4.6 kHz, corresponding to the 3-dB linewidth of 230 Hz. In contrast, the 20-dB linewidth of the pump laser is also characterized as 303.5 kHz, whilst the corresponding 3-dB linewidth is 15.2 kHz. The comparison indicates the remarkable linewidth compression with two orders of magnitudes and demonstrates the linewidth-compression ability of the SBS and distributed Rayleigh scattering, which is beneficial to high-capacity and wide-coverage coherent communication systems [34]. Furthermore, the dependence of the laser linewidth on the gain fiber length is also investigated. The 3-dB linewidths of the HOM Stokes lasers based on different SBS gain fiber lengths are shown in Fig. 8(b). The variation of the linewidth can be theoretically calculated by the modified Stokes linewidth in terms of the effect of Rayleigh feedback for phase noise suppression [14]. The linewidth correction factor and the Brillouin linewidth are set as 2.27 and 20 MHz, respectively. The experimental result shows the 3-dB Stokes linewidth decreases obviously from 709 Hz to 230 Hz as the length of the fiber increases from 3.4 km to 10 km with the same pump light, which has a good agreement with the theoretical prediction.
Fig. 8. Linewidth measurement (a) Spectra of self-heterodyne beat signals (the inset: the zooming of the beat signals of the HOM-BRFL); (b) laser linewidth dependence on the SBS gain fiber length (ESA sweeping time: 19 ms).
The real-time frequency drift of the HOM-BRFL was characterized by the frequency shift of beat signals between the random laser emission and the stable pump laser. The short-lifetime (∼10 ns) acoustic-optical coupling in SBS processes will inevitably introduce external thermal or mechanical disturbances associated with Stokes frequency drift into BRFL, leading to additional intensity noise and mode hopping. To address this issue, the long-lifetime DFG with the order of milliseconds can be used to alleviate the Stokes frequency drift [29]. The frequency fluctuations with different SBS-gain-fiber lengths are recorded at the same laser output power, as plotted in Fig. 9. Here, the frequency drift of every 2 milliseconds within a time window of 1 second (the inset) was collected by the ESA. The maximum frequency drift range of the HOM Stokes is 0.90 MHz and the minimum is 0.53 MHz whilst the standard deviation, as a statistical parameter, is 0.21 and 0.13, respectively. The results are comparable to that of previous frequency-stabilizing works and show better stability than the original BRFL [24]. It is believed that DFG plays the same role in random mode purification based on different SBS-gain-fiber lengths, which solves the problem that the longer-span fiber is more susceptible to external disturbance in the original BRFL [30].
Fig. 9. Frequency jitter of the HOM-BRFL versus the SBS gain fiber lengths. The inset represents real-time frequency drift with a time step of 2 ms within 1.0 s.
It should be pointed out that the HOM output characteristics (such as the HOM orders) in this scenario, are determined by the used LPFG, which will limit its application in MDM, to some extent. All-few-mode-fiber structure and other mode converters are superior alternatives arising from the higher purity and higher order of HOM. For example, the photon lantern [18] can realize up to six-order mode division multiplexing and demultiplexing and the AIFG can change the working wavelength and HOM orders flexibly by adjusting the frequency of the RF source [11]. For further improvement of the laser efficiency, diverse schemes with enhanced random feedback can be utilized, instead of the intrinsic weak Rayleigh scattering along conventional SMFs, such as specialty optical fibers with enhanced Rayleigh coefficient [35] and random fiber gratings with artificially introduced inhomogeneity [36,37]. Moreover, specialty optical fibers with higher Brillouin gain coefficient (e.g., highly nonlinear fibers) are also expected to allow the laser efficiency enhancement of the BRFL.
4. Conclusions
To summarize, a HOM-BRFL by utilizing a broadband LPFG and randomly distributed Rayleigh scattering has been proposed and experimentally demonstrated, providing 98.2% purity of LP-OAM mode and 25.5% laser efficiency of LP11 with cavity mode elimination. By controlling the polarization state of the RFL, high-purity azimuth-polarized and radial-polarized beams were also obtained. Thanks to the combined effect of the SBS and Rayleigh feedback on the compression of linewidth, the excellent 3-dB linewidth of 230 Hz was achieved. Moreover, laser properties like intensity dynamics and frequency jitters were systematically characterized. With further emphasis on higher-order spatial mode based on all-fiber laser, this new class of high-efficiency and narrow-linewidth lasers shows potential in various fields such as distributed long-haul coherent communication and optical fiber sensing systems.
Funding
National Natural Science Foundation of China (62275146, 61905138, 62275148); Science and Technology Commission of Shanghai Municipality (20ZR1420800, SKLSFO2022-05); State Key Laboratory of Advanced Optical Communication Systems and Networks (2022GZKF004); Jiangsu Province's Industry Outlook and Key Core Technologies - Key Projects (BE2022055-4); Shanghai Professional Technology Platform (19DZ2294000); 111 Project (D20031).
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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