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Abstract
Strong scattering random media can localize light and extend photon lifetime through multiple scattering, which offers opportunities for stabilizing random lasers. Here, we demonstrate a frequency stabilized Brillouin random laser with high coherence enabled by photon localization in random fiber grating array (RFGA). Photon trapping is realized due to wave interference in multi-scattering Fabry–Pérot (FP) cavities between random fiber gratings enabling light localization to prolong photon lifetime. The formation of the high finesse peaks of RFGA suppresses multi-longitudinal modes, which offers single-mode operation at high pump power. The RFGA distributed feedback-based Brillouin random fiber laser (BRFL) maintains a small frequency drift with the pump laser (a phase-locked laser with a linewidth of 100 Hz) at 51 kHz/s for a total change of 620 kHz over 12 s. Note there is no locking between the two lasers, and the beat frequency is measured by the optical heterodyne method. The correlation coefficient change of the measured optical beat frequency is maintained at 4.5%. This indicates that the BRFL is capable of maintaining a small optical frequency difference with the phase-locked pump laser over 12 s thanks to the RFGA capable of trapping photons in the same path, which is a remarkable feature for a random fiber laser. Furthermore, we confirm the single-mode lasing with a long lifetime in the stabilizing BRFL by the replica symmetry behavior and ultralow intensity noise at high pump power. Our findings explore a new approach to stabilize the frequency of Brillouin random lasers passively without commonly used active phase locking laser themes, which makes a simple and cost-effective system.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Random lasers (RLs) with disordered scattering feedback media have attracted a great attention due to random lasing nature. Anderson localization, a phenomenon of light confinement in strong scattering random media, has been predicted and demonstrated in RLs [1–3]. Light can be confined in the regime of Anderson localization owing to wave interference in multiple-scattering random media. RLs with high quality factor and long lifetime based on the localization effect have been revealed [4,5]. Random lasing emission in high-dimensional RLs leads to multi-directionality [6]. Recent experiments have shown the reduced threshold and improved lasing efficiency in one dimensional RLs with strong scattering media [7,8]. However, a major challenge for these RLs is multi-mode lasing emission. Multiple lasing modes coexisting in the random system induce broad bandwidth on the order of nanometers and large frequency drift, even though the suppressed mode interaction in the localized regime of the multi-mode RLs is introduced by the reduced spatial overlap of modes [9].
Random fiber lasers (RFL) with transverse confinement imposed by fiber geometry have been demonstrated showing more stable lasing frequency and narrower linewidth [10,11] in comparison to RLs. Different from one-dimensional hollow-core fiber random lasers with filled dyes in air holes of the fiber as gain medium [12,13], the gain of RFLs with all-fiber configuration is based on stimulated Brillouin scattering (SBS) [14,15], stimulated Raman scattering (SRS) [16,17], and Erbium-doped fiber (EDF) [18,19]. The light localization in a random grating array in a single-mode fiber has been experimentally demonstrated by measuring the exponential decay of transmissivity along the disordered fiber gratings [20]. Later, EDF gain random lasers based on Bragg gratings via Anderson localization were demonstrated [21–24]. Due to multi-mode lasing emission and broad lasing linewidth of picometers (hundreds of MHz) in the EDF-based RFLs, however, they exhibit large frequency drift and short lifetime of nanoseconds, which impose limits for fiber sensor technologies and optical communications. Brillouin random fiber lasers (BRFL) with a linewidth of kHz have been demonstrated [25,26]. The narrower bandwidth of Brillouin gain (tens of MHz) than EDF gain enables fewer modes with smaller drift in the Brillouin random laser system. Light follows different paths without localization effect in Brillouin random laser systems with weak Rayleigh scattering (RS) random feedback media, leading to a short lifetime of milliseconds and large frequency drift of 10 MHz [27,28]. Random fiber grating (RFG) with large refractive index contrast as distributed feedback medium in BRFL have been investigated [29,30]. The weak multi-scattering of the RFG with random spatial periods of micrometers over several centimeters is not adequate to localize photons for a long time of seconds. Little is known about the characterizations of Brillouin random lasing emission in strong scattering random media. To understand limits in noise features of a Brillouin random laser system with the light localization effect, a strongly scattering disordered random fiber grating array (RFGA) as a distributed feedback of a BRFL is investigated in the current paper. The focus of this work is to characterize the BRFL with the strong scattering RFGA by detecting the lasing modes evolution, frequency drift, and intensity fluctuation.
In this paper, we demonstrate a stabilizing Brillouin random laser with photon localization enabled by strong scattering RFGA. Light is localized in the RFGA due to wave interference in multi-scattering Fabry–Pérot (FP) cavities between random fiber grating pairs. Once a single longitudinal mode lasing is established in the BRFL via the high finesse filter formed between FP cavities at high pump power, a long-lived lasing mode of 12 s is achieved because the light is trapped in the multiple FP cavities. Note, there is no active phase-locking mechanism in the random laser. The established random mode maintains the lasing because the small frequency difference between multiple random modes from RFGA ensures lasing continuously under resonance condition, even though the thermal and acoustic effects induce slight laser frequency drift. The long-lived mode with a small correlation coefficient change of 4.5% and frequency change rate of 51 kHz/s over 12 s leads to the stabilized random lasing with a small frequency drift of 620 kHz. The correlation coefficient change remains constant with time in the RFGA-based BRFL, while it is varied significantly in other weak scattering feedback-based BRFLs, which confirms the frequency stabilized random laser with RFGA enabled by photon localization. The stabilizing BRFL shows replica symmetry behavior at high pump power and ultralow relative intensity noise, which is another indicator of single-mode lasing with a long lifetime.
2. Experimental section
2.1 Principle and simulation
RFGA provides distributed feedback for the Brillouin random fiber laser. RFGA is fabricated along a polarization-maintaining (PM) fiber by the plane-by-plane inscription method. The refractive index of the PM fiber is modulated spot by spot with random periods by the exposure of a femtosecond (fs)-IR pulse laser through the method [31]. A few dB loss is introduced in the RFGA during the inscription process. The parameters of RFGA, including the length of each grating and distance between two gratings, are characterized by optical frequency domain reflectometry (OFDR). There are 38 random gratings in the RFGA with a distance between two gratings of 15 cm $\pm$ a couple of millimeters and the length of each RFG is 5 mm. The intrinsic refractive index modulation spots in each 5 mm-long grating of the RFGA are around 9400. The refractive index modulation periods are randomly varied between 0.5180 µm and 0.5464 µm, corresponding to a broad backscattering wavelength range from 1500 nm to 1580 nm. Wave interference between multi-scattering grating pairs in the RFGA plays a key role in improving spatial trapping and lasing stability. The schematic of light propagation in the RFGA with increased pump power is plotted in Fig. 1(a). When light with low pump power transports in the RFGA, it can not pass through all the sub-gratings before it drops below the noise level due to scattering loss suggesting no wave interference between grating pairs. By increasing pump power, light propagates in one FP cavity formed between two gratings, where photons travel back and forward leading to the coherent interference of waves. The spectrum of the RFGA exhibits narrow linewidth with a high finesse $\mathcal {F}$. Light propagates in more FP cavities under higher pump power indicating a higher finesse $\mathcal {F}^\mathrm N$ contributed to the product of the finesse of N individual resonators with the same resonant frequency. Longitudinal lasing modes in the Brillouin gain region can be remarkably suppressed and a single longitudinal mode emission can be realized in the random laser system at high pump power due to the high finesse of the RFGA. The reflection spectra of the RFGAs with different numbers of random fiber gratings are simulated based on the transfer matrix method. The narrower spectral peaks owing to multiple scattering between gratings confirm the high finesse and quality factor of the RFGA (see Section 1 Figure S1 in the Supporting Information). Reflection and transmission spectra of the RFGA are measured by an optical spectrum analyzer (OSA) with a resolution of 5 MHz as shown in Fig. 1(b). The average transmission at the wavelength of 1550 nm is -20 dB corresponding to the transmittance of 0.01. The reflection spectrum presents a large number of peaks with narrow linewidth as expected. In a strongly scattering disordered medium, wave interference in multi-scattering paths leads to photon localization. The localization length $\xi$ is given by [8]
where $L$ is the RFGA length and $\langle T(L)\rangle$ is the average transmission of the RFGA. The localization length is $\xi =0.1 L$, well within the length limit of the RFGA. Wave interference in many FP cavities gives shorter localization length than the fiber length. Photons are confined in the RFGA when transported in the random laser, which leads to long-lived lasing modes. In addition, there are multiple random modes with small frequency differences due to the scattering paths with small difference, especially under high pump power, where more random modes are survived over the cavity loss. The random modes can be selected to compensate for the small frequency drift due to temperature and acoustic variations, leading to a long-lived modes without mode-hopping.
Fig. 1. (a) Schematic of light propagation in the RFGA with increased pump power. Photons are localized in the RFGA due to wave interference between many FP cavities at high pump power. (b) Reflection and transmission spectra of RFGA. Multiple narrow peaks with high finesse confirm wave interference between FP cavities in the RFGA.
2.2 Experimental setup
The schematic of the BRFL setup is described in Fig. 2(a). A NKT laser with a linewidth of 100 Hz is used as the pump light, which power is controlled by an erbium-doped fiber amplifier (EDFA). The state of polarization of the pump light is aligned to the slow axis of a polarization beam splitter (PBS) by adjusting a polarization controller (PC). The pump light is injected into the Brillouin gain medium through polarization-maintaining (PM) circulator 1. A 2 km-long Panda-type PM fiber is used as the Brillouin gain medium. The pump light in the Brillouin gain medium stimulates backward Stokes light, which travels anticlockwise in the cavity after Rayleigh scattering provided by a PM random fiber grating array. The lasing output is sent to an OSA for spectrum analysis, an oscilloscope for temporal intensity dynamics analysis and an optical heterodyne system by combining the lasing output of the BRFL and the pump laser after a PM coupler for beat spectral evolution analysis. The beat spectra are detected by a high-speed photodetector with 20 GHz bandwidth and recorded by an electrical spectrum analyzer (ESA). The preserved state of polarization of light in the all PM random fiber laser system leads to a high degree of stability in linear polarization against external perturbations during its propagation, which is beneficial for the Brillouin random lasing with low intensity fluctuation and frequency drift. Furthermore, the PM gain fiber has a smaller effective mode field diameter of 6.48 µm than that of SMF (10.4 µm), which provides a higher Brillouin gain coefficient for the BRFL. More gain from the PM fiber ensures that multiple random modes can sustain the multiple cavity trips to increase the total effective length. This is important to maintain resonant laser condition under the temperature drift and acoustic disturbance from the environment by multiple random modes with small mode frequency differences. Figure 2(b) shows the output power of the BRFL based on RFGA as a function of pump power. At pump power above 7.2 mW, Rayleigh scattering from the RFGA provides the necessary back-scattered Stokes light to enable the gain in the random laser system higher than the loss in a round trip, which leads to laser oscillations. After the lasing threshold, output power linearly increases with pump power. A sharp peak with a red-shift of $\sim$10.34 GHz from the pump laser, corresponding to the Brillouin frequency shift in the slow axis of the PM fiber [32], appears on the output spectrum at the pump power above the threshold as shown in the inset of Fig. 2(b). The side peaks with small amplitudes are attributed by the side modes of the optical local oscillator inside the high-resolution OSA.
Fig. 2. (a) Schematic of the experimental setup for the BRFL based on RFGA. EDFA: erbium-doped fiber amplifier; PC: polarization controller; PBS: polarization beam splitter; RFGA: random fiber grating array; PM: polarization-maintaining. (b) The output power of BRFL as a function of pump power. Inset: optical spectrum with a sharp peak at the Brillouin resonant frequency of $\sim$10.34 GHz away from the pump laser.
3. Results
3.1 Lasing mode characterization and spectral evolution
The output lasing spectrum of the BRFL is measured using the heterodyne-based method. We count the number of modes according to the mode amplitude within 20 dB of the maximum value at each pump power. The number of modes as a function of pump power is plotted in Fig. 3(a). The sharply increased lasing modes with increased pump power below 9 mW indicate that more longitudinal modes above the noise floor are excited in the Brillouin gain bandwidth. However, the low finesse of the RFGA is not enough to suppress the lasing modes at the low pump power. Higher pump power enables wave interference in more FP cavities leading to increased finesse of the reflection spectrum of the RFGA. As a result, one mode is selected and other longitudinal modes are suppressed at the pump power above 20 mW. The variation in the number of lasing modes confirms the power-dependent light transportation in the RFGA as expected. Figure 3(b) shows several beat spectra at different pump powers. The bottom four spectra show multi-mode lasing emission with envelopes of quasi-Lorentzian shape, which suggests the lasing modes located at the high gain region of Brillouin bandwidth (20 MHz for the PM gain fiber). The longitudinal mode spacing of 0.1 MHz corresponds to the cavity length of around 2 km. The top spectrum shows a single longitudinal mode lasing with a high signal-to-noise ratio of 60 dB, which suggests the reduced frequency and intensity fluctuations of the random laser.
Fig. 3. (a) Number of modes of the BRFL as a function of pump power. Single longitudinal mode operation in the random system above 20 mW. (b) Beat spectra of the RFGA-based BRFL with different pump powers. Mode frequency of around 10.34 GHz corresponds to the Brillouin frequency shift in the slow axis of the PM gain fiber.
To illustrate photon trapping via time dependent frequency drift of the random laser with RFGA, we exploit the spectral evolution of the beat signal between the pump laser and the BRFL in a continuous time, which adds a new dimension to show the trapping time and frequency stability of lasing modes for a random laser. The beat spectra at different pump powers are monitored continuously over 15 s in a time interval of 15 ms, as shown in Figs. 4(a-c), in which the color bar represents the power of beat spectra. The frequency resolution of the beat spectrum is 10 kHz. The frequency of beat spectra is normalized to $f_{}-\left \langle f_{}\right \rangle$. The frequencies of the lasing modes over their lifetime at different pump powers are plotted in Fig. 4(d). The lifetime of the lasing mode is found to be prolonged to 12 s with increased pump power to 117 mW. When the light with higher pump power transports in the Brillouin random laser system, photons survive for a longer time due to localizing light in more multi-scattering FP cavities of the RFGA, which leads to a longer-lived lasing mode. It is found that the lasing mode at each pump power has a positive chirp over its lifetime as plotted in Fig. 4(d). The mode chirp can be understood through the mode-pulling effect in the stimulated Brillouin scattering process. Mode-pulling is induced by nonlinear phase shift as a result of strong dispersion in the narrow Brillouin gain. As a result, the Stokes lasing mode is pulled away from the Brillouin resonant frequency of the cold cavity by an amount during lasing operation [33–35]. The frequency change range of lasing modes depends on the Brillouin gain spectrum and the relative position between the gain peak and the lasing frequency. The same gain spectrum and small change of frequency separation between the Stokes signal and the pump light at different pump powers indicate that the lasing mode moves in a similar range. To prove the stabilization of the BRFL enabled by the RFGA distributed feedback, no external temperature insulation chamber is added to the system. The lasing mode with small difference in chirp rate over 12 s owing to the temperature variation. The sensitivity of Brillouin frequency shift is $\sim$1 MHz/$^{\circ }$C. The slight temperature change induces the small Brillouin peak shift. As a result, the different chirp rates over time under the same pump power are achieved as shown in Fig. 4(c). The same lasing mode is kept at around 5 s even with small disturbance because the random fiber laser has a stabilization mechanism enabled by random modes, which shows the self-stabilization ability of the random fiber laser with feedback of RFGA to ignore the small disturbance from environmental change. The frequency drift is 620 kHz over the lifetime of 12 s at the pump power of 117 mW. Compared with demonstrated BRFL based on the Erbium-doped fiber loop, which exhibits a mode-hopping free operation over 0.8 s with the frequency drift of 1.2 MHz owing to the photonic memory in EDF [36], the frequency drift of the long lifetime mode hopping free BRFL enabled by photon localization in RFGA ($\sim$40 kHz in 0.8 s) represents a factor of 30 improvement. Figure 4(e) shows that the frequency change rate of lasing modes decreases from 194 kHz/s to 51 kHz/s with increased pump powers from 20 mW to 117 mW. The decreased frequency drift rate is attributed by photon confinement in the specific random mode, which overcomes the loss from the RFGA in one trip as a seed to get the gain from the 2 km Brillouin gain fiber. Such a process is repeated with more cycles because the mode survives for a longer time in the RFGA at higher pump power. As a result, the correlation coefficient has a smaller change (4.5%) at higher pump power as shown in Fig. 4(e). The role of slightly changed scattering length from RFGA over the fixed 2 km gain length is to maintain the resonance condition of random laser under slight temperature variation. Similar to phase-locked cavity change to be adaptable to the laser cavity length change from temperature, here we have many slight different random modes from the RFGA to be selected to match the temperature change simultaneously, rather than sequentially changed round trips with 2$\pi$ phase shift in phase-locked feedback cases, which takes a longer time to reach 2$\pi$ of constructive mode addition. At the beginning and end of each lasing mode (transient regimes), we observe mode-hopping with a frequency jump of hundreds of kHz. A short-time spectral evolution in the transient regime at the pump power of 117 mW is shown in Fig. 4(f). The mode hopping is because the lasing mode moves to the frequency at which Brillouin gain is not enough to support the lasing mode imposed by the mode-pulling effect. As a result, the random lasing process is rebuilt up and the lasing mode randomly hops to a favorable mode in the high gain position, where the random system can continue to single-mode lasing operation. We observe the multiple longitudinal modes at transient regimes as plotted in the inset of Fig. 4(f). Because of the reconstruction of lasing action at transient regimes, each longitudinal mode has an opportunity to be excited and multiple longitudinal modes suddenly appear in the gain bandwidth leading to an unstable laser system. The multi-mode emission indicates that the random laser approaches and recovers from transient regimes. The stabilization of the RFGA-based BRFL is not affected by the nonlinearities, such as four-wave mixing and cross phase modulation, owing to single longitudinal mode operation in the linearly polarized random system and the 40 dB lower reflected pump wave compared with the Stokes wave.
Fig. 4. Real-time spatio-temporal evolution of the BRFL based on RFGA at the pump power of (a) 20 mW; (b) 67 mW; (c) 117 mW. (d) Frequency of lasing modes over their lifetimes at different pump powers. The frequency axis is the relative value at 0.5 MHz per division. (e) Frequency change rate and normalized correlation coefficient change as a function of pump powers. The frequency change rates are evaluated by fitting the mode chirps shown in Fig. 4(d) with a linear function. Correlation coefficient is calculated between two neighboring traces over 15 s. (f) Close-up of Fig. 4(c) during the mode-hopping event. Inset: the multi-mode spectrum in the transient regime at 13.8 s.
To confirm the stabilized frequency in BRFL enabled by RFGA, two different distributed feedback fibers such as RS fiber and single RFG are investigated by replacing the RFGA in the BRFL. Spectral evolution of the BRFL based on 500 m-long RS fiber (PM fiber) at the pump power of 90 mW is measured as plotted in Fig. 5(a). We observe a lasing mode rapidly hops to another random mode on the order of milliseconds, even though a few modes survive for a longer time of 0.3 s as shown in Fig. 5(b). This is contributed by weak scattering in the 500 m-long RS fiber owing to the nonuniform density induced small refractive index fluctuation. Photons can not be trapped in the weak scattering distributed feedback fiber and escape promptly from the random laser system. As a result, the lifetime of lasing mode in the RS fiber-based BRFL is over 40 times shorter than that of the RFGA-based BRFL. Instead of the small frequency drift in RFGA-based random laser owing to the narrow filter effect and photon localization, lasing modes are randomly selected by the weak RS fiber and amplified in the high gain region of the Brillouin bandwidth in each round trip. The lasing mode drift over 10 s shows a Gaussian distribution in a frequency range of 6 MHz as plotted in Fig. 5(c). The Gaussian distribution of the frequency drift shows that the lasing RS-based system is a random process without mode trapping. Spectral evolution of 5 cm-long polarization-maintaining RFG-based BRFL is presented in Fig. 5(d) showing an unstable random lasing condition with several lasing modes. The lasing lifetime of the RFG-based BRFL is longer than that of RS-based BRFL due to higher refractive index modulation formed frozen scattering centers, which enables photons to be trapped for more time in the RFG compared with RS fiber. However, the weak multi-scattering of light between the sub-gratings of the RFG leads to low quality factor (see Section 1 Figure S2 in the Supporting Information). The lasing modes follow different scattering paths after certain time due to the broad linewidth peaks of the single RFG with weak localization, which leads to the fast mode hopping in a large frequency range of 4 MHz. The longest lifetime of a lasing mode is 1.2 s, as shown in Fig. 5(e). Compared with the single RFG as distributed feedback, the RFGA with 38 RFGs demonstrates 10 times longer lasing lifetime with a smaller frequency drift of 15.5%. The long lifetime in the BRFL based on RFGA is contributed by the light confinement in FP cavities, which acts as a seed for Brillouin lasing modes being amplified before dropping to the noise level. In addition, the high finesse of the RFGA leads to the single-longitudinal mode operation within a small frequency range, while the random laser shows the multi-mode operation in the single RFG-based BRFL owing to the broadband filter effect. As a result, the BRFL based on RFGA with 38 RFGs is free of mode-hopping with single-mode operation over a long time. The small correlation coefficient change of 4.5% for the optical beat frequency between the BRFL and the phase-locked laser and the frequency change of 51 kHz/s indicate the potential of self-stabilization capability for the random fiber laser. The upper limit of the grating array number is the balance of the Brillouin gain and RFGA induced loss, which makes the seeded random modes above the lasing threshold level to ensure sustained random modes for low noise random laser operation. The multiple longitudinal modes with an amplitude of around -95 dBm in the RFG-based BRFL as shown in the inset of Fig. 5(e) is over 20 dB higher in comparison to the lasing emission in RFGA-based BRFL at high pump power. This confirms the broadband filter effect of the single RFG. The normalized correlation coefficient change in a step of 1 s over 10 s for RFGA, single RFG and RS fiber-based BRFLs is plotted in Fig. 5(f). The maintained correlation coefficient change over 10 s and small value in each time for the RFGA-based BRFL suggest the stabilized lasing frequency drift due to photon localization. The RS fiber-based BRFL without photon localization and single RFG-based BRFL with weak localization show the large correlation coefficient change with strong fluctuation over time as expected.
Fig. 5. (a) Real-time spatio-temporal evolution of the BRFL based on 500 m RS fiber at pump power of 90 mW. (b) Close-up of Fig. 5(a). (c) Histogram of frequency drift in the RS fiber. (d) Spectral evolution of the BRFL based on 5 cm RFG at pump power of 90 mW. (e) Close-up of Fig. 5(d). Inset: the lasing spectrum at 5.5 s. (f) Normalized correlation coefficient change for three distributed feedback fibers-based BRFLs in a step of 1s over 10 s. The correlation coefficients of the random laser with RFGA are calculated from the beginning of the long-lived lasing mode. The coefficient change in each time is calculated during 1 s.
3.2 Intensity fluctuation
The intensity dynamics and statistical features are investigated in the BRFL with RFGA. The intensity probability is identified with $\alpha$-stable Lévy distribution (see more details in the Supporting Information Section 2). The Lévy index $\alpha$ as a function of pump power is plotted in Fig. 6(a). There is a transition between statistical behaviors, from Gaussian distribution at the power below the threshold ($\alpha =2$ at 6 mW) to a Lévy distribution at the power around the threshold ($0<\alpha <2$ at 16 mW), and the intensity fluctuation is returned to Gaussian distribution at the power well above the threshold ($\alpha =2$ at 24 mW). Due to the thermal noise in the prelasing regime, Gaussian distribution at the power below the threshold is expected. The transition from the prelasing Gaussian distribution to the Lévy distribution is a signature of random lasing. The low finesse of the RFGA at the pump power near the threshold indicates multi-mode lasing operation as we discussed in Fig. 3. The strong coupling of longitudinal modes in the Brillouin gain bandwidth induces large energy exchange between Stokes photons and phonons, which increases the probability of extreme events. Thus the intensity fluctuation follows Lévy distribution. Unlike the prelasing Gaussian behavior for the power below the threshold, Gaussian behavior at the power well above the threshold indicates a random lasing process with coherent emission. Intensity change range of the BRFL as a function of pump power is shown in Fig. 6(b). By increasing the power above 24 mW, we observe the sharp decrease of intensity fluctuation, which is consistent with the statistical transition from Lévy regime to Gaussian regime, confirming a coherent single-mode lasing operation in the random system. Relative intensity noise (RIN) of the random laser system is characterized at different pump powers as shown in Fig. 6(c). At the pump power of 16 mW, the large RIN with high resonant noise peaks in the frequency range from 0.1 MHz to 1 MHz corresponding to inverse of round trip time of light in the laser shows the coupling of multiple longitudinal modes. High pump power enables one longitudinal lasing mode with high gain to overcome the loss via the RFGA formed high finesse filter. As a result, the number of longitudinal modes and spontaneous scattering from the gain medium are suppressed. The strong intensity fluctuation induced by modes competing for the available gain is alleviated. Thus, we observe the RIN of the random lasing emission operating at the pump power of 117 mW is around 100 dB lower than that at the pump power of 16 mW in the frequency range from 1 Hz to 1 MHz. The RIN of the commercial NKT laser is measured for comparison, which is around 10 dB lower than that of the Brillouin random laser with a pump power of 117 mW. The optimized RIN in the RFGA based BRFL is over 30 dB lower than that of BRFLs with 500 m RS fiber and 5 cm RFG as distributed feedback media (see the Supporting Information Section 3 for detailed discussion and direct comparison).
Fig. 6. (a) $\alpha$ value as a function of pump power. An initial Gaussian regime ($\alpha =2$) is followed by Lévy regime ($0<\alpha <2$), and Gaussian regime ($\alpha =2$) is recovered at high pump power due to power-dependent modes in the random laser. (b) Intensity change range versus pump power. (c) RIN comparison at different pump powers.
We consider the replica symmetry or replica symmetry breaking determined by the distribution of Parisi overlap parameter to demonstrate the characterization of intensity fluctuation in the BRFL with RFGA. Parisi overlap parameter $q$ is given by [37–39]
Fig. 7. Histograms of $q$ values of the BRFL at the pump power of (a) 6.0 mW; (b) 11.3 mW; (c) 16 mW; (d) 117 mW; (e) $|q_{\rm max}|$ value as a function of pump power. (f) Histograms of $q$ values without RFGA.
4. Conclusion
In summary, we have demonstrated a stabilizing Brillouin random laser system with a long-lived lasing mode enabled by photon localization in RFGA. More FP cavities in the RFGA at higher pump power lead to higher finesse. As a result, multiple longitudinal modes are suppressed. More strikingly, wave interference in the multi-scattering FP cavities indicates the light localization, which leads to photon trapping in the RFGA based random laser. We have shown that the random laser supports a long-lived lasing mode of 12 s in the BRFL at high pump power. The long lifetime of the localized lasing mode leads to the small frequency shift of 620 kHz over 12 s indicating the stabilized frequency of the RFGA-based random laser with photon localization. We confirm the stabilizing BRFL with the light localizing RFGA feedback by comparing it with the feedback of RS fiber and RFG commonly used in random fiber lasers. Two feedback-based BRFLs exhibit unstable lasing modes with faster mode hopping in larger frequency range and larger correlation coefficient change with stronger fluctuation owing to no light localization in the weak scattering RS fiber and weak light localization in the weak multi-scattering RFG. The photon trapping induced long-lived modes and stabilized frequency in the random laser is equivalent to good locking condition in phase locked laser. The key for the nearly constant lasing frequency is that minor changed cavity length due to the temperature or acoustic wave can always find a "matched length" among many random modes with small spatial separation over long cavity length at given time. Hence the "seeded photons" sustained lasing condition, i.e. long lifetime is achieved. The stabilizing BRFL enabled by RFGA also gives rise to an low intensity noise and replica symmetry behavior at high pump power. Our contribution helps to understand mode propagation and noise properties in localized photons in Brillouin fiber lasers with random distributed feedback and constitutes an important step towards the design of frequency stabilized random fiber lasers with high coherence and low noise without the need for active feedback and locking on the laser cavity.
Funding
China Scholarship Council; Natural Sciences and Engineering Research Council of Canada (06071-RGPIN-2015); Canada Research Chairs (75-67138).
Acknowledgement
We thank Dr. Zichao Zhou for useful discussion on the simulation of random fiber grating array.
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.
Supplemental document
See Supplement 1 for supporting content.
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