All Polarization Maintaining Brillouin Erbium-Doped Fiber Laser With Sub-kHz Linewidth Using Saturated Absorber and Self-Injection Feedback

A narrow-linewidth all-polarization-maintaining (PM) Brillouin erbium-doped fiber laser (BEFL) is proposed and demonstrated experimentally, which employs erbium-doped fiber (EDF) acting as both the linear gain and the Brillouin gain medium. In order to realize a single longitudinal mode (SLM) operation and a narrow linewidth fiber laser output, the saturable absorber (SA) and the optical self-injection feedback structure are employed in the BEFL for the first time. In this experiment, three sets of comparative experiments are conducted to demonstrate the effectiveness of the SA and the self-injection feedback structure. The experimental result shows that the SA structure can eliminate transient multimode phenomena and narrow the linewidth, and the self-injection feedback structure can act as an effective mode filter and a compound-cavity to make the intracavity mode purer. A stable SLM operation of the BEFL is verified by the delayed self-heterodyne system, which thanks to the adding of the SA and the self-injection feedback structure. The BEFL's wavelength stability detected by is less than 0.0045 nm over 14 hours. In addition, an ultra-narrow linewidth of approximately 224 Hz is obtained.

, [13], [14].However, the longer cavity length leads to the reduction of mode spacing, which makes it easy to achieve the mode hopping operation [15].
In recent years, the Brillouin fiber laser based on the stimulated Brillouin scattering (SBS) has attracted significant interest [16].At present, there are mainly three types of Brillouin gain medium fibers: the single-mode fiber [17], [18], the high nonlinear fiber [19] and the EDF [20], [21].Serving as the gain medium, the single-mode fiber has the characteristics of low price and stable excitation SBS.However, the length of the single-mode fiber usually requires several kilometers, which lead to mode hopping operation due to the short mode spacing in the cavity [17], [18].As a comparison, only a few meters of the high nonlinear fiber is requied to excite SBS, which can increase the mode spacing and reduce the phenomenon of the mode hopping.However, the power of the laser is too low due to the large loss coefficient of the high nonlinear fiber [19].Compared to the two types of optical fibers mentioned above, the EDF has been proposed as Brillouin gain medium in recent years, which can excite the SBS with a few mW power of the Brillouin pumped (BP).BEFL has the characteristics of low threshold and easy excitation [20].The output station of the BEFL strongly depends on the power of the BP.When the power of the BP exceeds the threshold of the SBS, stokes light resonates and amplifies in the cavity [20].Compared with other scattering effects, SBS has the characteristics of low threshold, high gain and narrow spectral width.Therefore, SBS can be applied in narrow-linewidth lasers.However, free running BEFL exhibit transient multimode phenomena, requiring additional filtering methods to achieve stable SLM operation.
In this article, we propose an all-PM BEFL based on the SA and the self-injection feedback structure, which is the first time proposed on our knowledge.The all-PM structure can suppress the interference of the environment and improve the practicability of the system [21].In the cavity, the SA serves as a dynamic Bragg grating to suppresses the transient multimode phenomenon and to achieve a stable SLM state.Moreover, the self-injection feedback structure is employed as an mode filter and and a compound-cavity to make the intracavity mode purer.As for the output performance of the BEFL, we achieved an all-PM SLM BEFL with a ultra-narrow linewidth of 224 Hz and an excellent wavelength stability of <4.5 pm.

A. Configuration of BEFL
The experimental setup of the all-PM SLM BEFL is illustrated in Fig. 1.The all-PM structure is adopted to guarantee the practicability of the system.The BP employed is a standard distributed feedback (DFB) laser with a maximum power of 15.5 dBm and a linewidth of approximately 3 kHz.After passing through an optical circulator (CIR1), the BP excites SBS in 4-m-long PM commercialized EDF.The EDF (EDF1, IXF-EDF-FGL-PM-L3) serves as the linear gain medium is pumped by the LD with the maximal power of 400 mW.When the power of the BP exceeds the threshold of SBS in the EDF, the power of the stokes light will increase significantly.After traversing the EDF, the BP is blocked by the isolator and the backward-propagating stokes light can be cycled amplification in the cavity.Since the Brillouin gain coefficient of EDF is too small, the total gain at stokes wavelength is less than the maximum linear gain of EDF.In addition, the wavelength of the laser is around 1530 nm due to the maximum gain wavelength of EDF is 1530 nm [20].The coarse filter structure can be constructed by using the CIR2 and the fiber Bragg grating (FBG).The center wavelength, reflectivity and 3-dB bandwidth of the PM FBG is 1549.41nm, 99.33% and 0.22 nm, respectively.The SA is utilized as an coarse filter structure to suppress the amplified stimulated emission (ASE) noise beyond the bandwidth.Because the gain of EDF can be approximately considered uniform in the bandwidth, the total gain superimposed at the stokes light wavelength is the largest.
To achieve SLM operation and improve the mode rejection ratio, we implemented a 2-m-long EDF (EDF, IXF-EDF-FGL-1480-PM) as the SA.When the power of the BP exceeds the threshold of the SBS, counterclockwise propagating stokes light is generated.The mode of the stokes light automatically matches with the resonant mode in the cavity.The self-injection feedback structure composed of optical coupler (OC2 and OC3), which has filtering function that make the intracavity mode purer.The laser output is extracted from the 90% port of the PM OC3 with a coupling ratio of 90:10.
The working principle of the BEFL is depicted in Fig. 2(a).The gain spectrum of EDFA is uneven and the maximum gain wavelength is the point a.When the power of the BP exceeds the threshold of the SBS, stokes light is generated at wavelength of the point b.Because the total gain at the point b is higher than the total gain at the point a, the output wavelength of the laser is the point b.However, when the central wavelength of the Brillouin gain spectrum significantly deviates from the maximum gain wavelength of the EDF, the gain at the point c is lower than that at the point a.Consequently, the laser initially oscillates at wavelength of the point a.Because of the uniform broadening property of the EDFA, the gain at wavelength of the point c is decreasing, making the laser unable to operate at wavelength of the point c.At this time, the laser is free running EDFLs [20].The reflection spectrum of the FBG used in the experiment shown in Fig. 2(b) displays a center wavelength of 1549.41 nm and a 3-dB bandwidth of 0.22 nm.The FBG functions as a reflection filter to complete the original wavelength selection and to reduce the potential longitudinal mode in the cavity.Thanks to the flat gain profile within the FBG, the gain is maximized at the wavelength of the stokes light [20].The gain spectral width of the SBS is about 20 MHz, it is usually necessary to ensure that the cavity length is less than 10 m.

B. Operation Principle of Reflective Saturated Absorber
The filtering bandwidth is an important performance indicator of saturated absorber structures, which is usually calculated using the transfer matrix method.The transfer function of the SA composed of Sagnac ring is solved by the transfer matrix [21], [22].As shown in Fig. 3, the derivation of the reflective saturable absorber (RSA) is partially different.Because the length of single-mode fiber is too short, the loss coefficient is ignored in the calculation.Where β L=n ω L/c=2πνnL/c is the increment of phase, L 1 and L 2 is the length of single-mode fiber, E in 1−1 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. is the first input light intensity, E in 1l−1 is the input SA light intensity, E t 2−1 is the output SA light intensity, E t 2l−1 is input FBG light intensity, Other light intensity symbols have similar meanings.Unlike Sagnac ring structure, the light intensity at both ends of the SA is not the same every time independently.The transmission function of the dynamic fiber grating (DFG) formed in SA changes.The DFG is first formed by a round trip of initial light intensity and incident light.Under the action of this grating, E t 2−1 and E b 2−1 will change, which will lead to the change of DFG and eventually become stable with the increase of the number of iterations.As the model of DFG, the transmission matrix expression of the uniform grating H grating (1) as follows: As the number of iterations of reflected light increases, the dynamic grating properties formed gradually stabilize.The transfer function is shown in (2).
Since each iteration only increases the order of the coefficient of F 12 F 22 , and F 12 is always less than F 22 .With the increase of the order, the coefficients becomes smaller and approaches zero.Furthermore, the approximate expression of the transfer function is as follows: The transfer functions of the RSA and the Sagnac ring of the SA are approximately the same.The longer the length of the SA, the narrower its filtering bandwidth.However, SA can increase the cavity length and reduce the mode spacing of the laser.To ensure the SLM of the laser, the bandwidth of the SA needs to be smaller than the mode spacing.In this experiment, the length of the SA was adopted as 2 m.Where Δn is the change of refraction index and the value is generally less than 3 × 10 −7 [23], [24], λ

C. Self-Injection Feedback Structure
The SA structure ensures that the laser has a stable SLM status and narrow the linewidth [25].The self-injected feedback structure has filtering function, which can make the mode in the cavity purer [26], [27].The self-injection feedback structure is illustrated in Fig. 4. The light is divided into two parts by the OC1.One of the components resonates and amplifies within the main cavity, following the 1 to 2 to 3 direction.The other components passes through the OC3, where 90% of the light is output and 10% of the light is injected into the cavity along the 5 direction.On the one hand, long cavity length increases the transmission life of laser.On the other hand, more proportion of light can be guided back into the cavity, thus this structure has a higher Q value and narrower transmission bandwidth [27].The longer the length of the self-injection feedback structure, the better its feedback effect.However, the self-injection feedback structure also plays a role as compound-cavity, which affects the mode spacing of the laser [28].Increasing the feedback length will result in a decrease in the mode spacing of the laser, which in turn affects the SLM of the laser.Therefore, the self-injection feedback structure did not adopt a long feedback length in the experiment.

A. BEFL Without SA and Self-Injection Feedback Structure
This section discusses the characteristics of the BEFL without the SA and the self-injection feedback structure.As shown in Fig. 1, the SA, OC2 and OC3 components have been omitted and the laser is output from the 50% port of the OC1.When the power of the BP is zero, the laser is a free running EDFLs.Fig. 5(a) shows the results of the laser wavelength using a.The wavelength of the laser is 1549.426nm, and the OSNR is 72.5 dB without the BP.However, the 0.02 nm resolution of the spectrometer limits ability to accurately determine the state of the laser.Fig. 5(b) shows the SLM state of the laser using the beat frequency method.It is worth noting that the output of the laser is multimode with a mode spacing of 32.5 MHz and the cavity length is 6.7 m.The multimode phenomenon arises from the existence of multiple resonant modes within the bandwidth of the FBG.The output state of the BEFL depends on the power of the BP and the 980 nm pump light.When the power of the BP is lower than the threshold of the SBS, the intracavity resonant light and the BP seize the gain of the EDF.Since the power of the BP is too small, the output of the laser is mainly the intracavity resonant light.When the power of the BP exceeds the threshold of SBS, the stokes light is generated in the EDF.The stokes light is rapidly amplified to seize most of the EDF gains and inhibit the generation and amplification of the other modes.As the power of the BP increases, it emerges as the dominant factor in the gain competition, leading to a gradual reduction in the power of the stokes light.The output of the laser is Rayleigh scattering of the BP and the wavelength of the BP is 1549.290nm in the experiment.
As depicted in Figs.5(b) and 6(a), the laser is an multimode EDFLs without the BP.When power of the BP increases to 10.13 dBm, stokes light obtain dominant advantage in the gain competition.However, when the power of the BP increases to 15.5 dBm, the output of the BEFL is BP-induced Rayleigh scattering light.This is because excessive BP snatch most of the gain of EDF, making the net gain of stokes light and intracavity resonant light less than zero.The wavelength of the stokes light and Rayleigh scattering light are 1549.384nm and 1549.290nm, and the Brillouin frequency shift is 0.094 nm.The cavity length of the BEFL is about 6.7 m, and the corresponding mode spacing is 32.5 MHz.The minimum resolution of the spectrometer is 0.02 nm, corresponding to 2.5 GHz.Therefore, the SLM of the BEFL cannot be observed from the spectrometer.SLM of the BEFL is measured by the delayed self heterodyne method and the results are shown in Fig. 6(b).BEFL can achieve a Through 500 statistical analyses of the laser beat frequency, 21 multimode phenomena were observed.However, the BEFL with the SA structure can achieve a stable SLM status for a long time.
The linewidth of the BEFL is measured by the delayed self heterodyne method as shown in Fig. 7(a) [29], [30].The light of the BEFL is divided into two parts by 50:50 OC.One part is sent through acousto-optic modulator with frequency downshift of 80 MHz and the other part is sent into a 79.8 km delay fiber.The light of two parts beat frequency through the coupler.The optical signal is converted into electrical signal by the PD for observation on the spectrometer.Theoretically, thousands of kilometers of the delay fiber are needed to accurately obtain the linewidth of the BEFL, which is impossible because of the serious 1 f noise and excessive attenuation loss.To reduce the measurement error, Lorentz fitting is usually used for the measurement data [14].As shown in Fig. 7(b), the 20-dB bandwidth of the BEFL is measured to be 17.9 kHz.Thus, the corresponding linewidth of the proposed fiber laser can be estimated to be 900 Hz.SBS can reduce linewidth of the laser to certain extent, but it cannot be  infinitely reduced.Further reducing the linewidth of the BEFL require some additional measures [19].

B. BEFL With SA Structure
A 2-m SA was employed in the experimental structure.Fig. 8(a) displays the spectrum of the laser without BP.The wavelength of the laser is 1549.432nm and the OSNR is 66 dB.As shown in Fig. 8(b), the output state of the laser transitions from EDFLs to BEFL with the BP power increases.When the power of the BP is too high, the stokes light cannot obtain sufficient gain to maintain resonance.Therefore, the output of the laser is Rayleigh scattering light from the BP.Fig. 9(a) illustrates the utilization of the delayed autoheterodyne method for monitoring the beat frequency, with no occurrence of multimode phenomena observed during the monitoring process.In addition, The outcomes of 500 frequency scans demonstrate that they have consistently remained in a SLM state.This indicates that adding the SA can solve the problem of transient multimode phenomenon.Moreover, wavelength stability is also an important index for evaluating the performance of the laser.The wavelength measurement results of the BEFL using a wavemeter are shown in Fig. 9(b).In 17 hours, the wavelength fluctuation of the BEFL is less than 1.6 pm.It is proved that the BEFL with the SA have a good wavelength stability.
As shown in Fig. 10, the 20-dB bandwidth of the BEFL is measured to be 9.75 kHz.Therefore, 490 Hz can be considered conservative characterization of the laser linewidth.The BEFL with the SA has a good linewidth performance and achieves a sub-kilohertz output.

C. BEFL With the SA and the Self-Injection Feedback Structure
By adding the self-injection feedback structure to BEFL and the structure is shown in Fig. 1.The self-injecting feedback Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.structure has filtering function that makes the intracavity mode purer.Meanwhile, the self-feedback structure also serves as a composite cavity.However, in order to ensure the stable output of the BEFL, it is crucial to match the wavelength of the stokes light with the peak position of the gain spectrum.Regrettably, the selfinjection feedback structure and the length of the main cavity are influenced by environmental factors.Consequently, aligning the maximum position of the net gain inside the cavity is difficult.In the experiment, we adjust the wavelength of the BP instead of modify the length of the self-injecting feedback structure.However, due to the influence of environment and temperature on the self-injecting feedback structure, EDFLs exhibits mode hopping phenomenon.The wavelength measurement results of the EDFLs are shown in Fig. 11(a), it can be seen that there are many mode hopping states and the maximum wavelength jump is approximately 0.1 nm.As shown in Fig. 11(b), the wavelength and power of the BP is 1549.304nm and 7.5 dBm.Consequently, the generation of the SBS occurred in the EDF, yielding a stokes light wavelength of 1549.396nm and a Brillouin frequency shift of 0.92 nm.At this point, the OSNR of the BEFL is 71 dB.In addition, under a 980 nm pump with the power of 120 mW, the output of the BEFL varies with BP as shown in Fig. 12(a).When the power of the BP is below 3.14 dBm, BP cannot excite the SBS and the output of the laser is EDFLs.Within the power range of 3.14 dBm to 8.32 dBm, SBS was generated in EDF, causing resonation and amplification of the stokes light within the cavity.However, as the power of the BP increases, BP gradually seizes the gain of the EDF, resulting in a reduction in the net gain of the stokes light.Once the power of the BP exceeds 8.32 dBm, BP captures most of the gain, resulting in a significant decrease in the power of the stokes light.As shown in Fig. 12(b), the linewidth of the laser measured by the delayed autoheterodyne method is 224 Hz.This indicates that self-injection feedback structure can reduce the noise of the laser, resulting in better linewidth performance of the laser.
It is worth noting that the wavelength of the BP no longer corresponds to 1549.290 nm.Therefore, the output wavelength of the BEFL has changed.This is primarily attributed to selfinjection feedback structure.As a result, the original wavelength of the stokes light may not align with the resonance wavelength of both the main cavity and the self-injection feedback   structure, leading to unstable output of the laser.In order to reduce experimental complexity, adjusting the wavelength of the BP instead of adjusting the length of the self-injection feedback structure.As shown in Fig. 13(a), the state diagrams of the stokes light wavelength were tested under different BP powers.The figure shows that when adjusting the wavelength of the stokes light to 1549.396 nm and 1549.420nm, several occurrences of mode hopping were observed over a 14 hours monitoring period.When the wavelength of the stokes light is 1549.402nm, the output wavelength of the laser is relatively stable.The wavelength fluctuation is less than 4.5 pm within 14 hours of detection.This indicates that the wavelength of the BP plays a crucial role in the stability of the laser output.Furthermore, the self-injecting feedback structure has a filtering function, but the added complexity of the system degrades the wavelength stability.This is mainly because the length of the self-injection feedback structure composed of fibers changes with temperature and vibration, which leads to jitter in the net gain of stokes light and cannot effectively suppress other modes in the cavity.Therefore, using physically stable structures can further improve wavelength stability performance.However, it is worth sacrificing wavelength stability appropriately to obtain narrower linewidth for BEFL.The results of the output power of the BEFL are shown in Fig. 13(b).Within 3.5 hours, the power fluctuation of the laser is less than 0.435 mW, indicating that the entire laser has good power performance.The main parameters of the three structures are shown in Table I.SA ensures the SLM operation of the laser and has the effect of narrowing the linewidth.The feedback structure has a filtering effect, making the intracavity mode more pure.

IV. CONCLUSION
In conclusion, an all-PM BEFL with the SA and the selfinjection feedback structure has been proposed and demonstrated.The effectiveness of the SA and the self-injection feedback structure are compared and analyzed based on the free-running BEFL.The experimental result proves that the SA structure can eliminate multimode phenomena and narrow the linewidth, while the self-injecting feedback structure can filter out the mode in the cavity effectively.Finally, the maximum fluctuation of the all-PM BEFL wavelength is 4.5 pm within 14 hours, and the linewidth of the BEFL is 224 Hz.It is worth noticing that the whole BEFL is exposed to the air environment without encapsulation, temperature control and other vibration isolation.Therefore, the stability and robustness of the BEFL can be further improved after the BEFL being packaged and vibration isolated.

Fig. 5 .
Fig. 5. (a) Spectrogram of free running EDFLs without the SA, self-injection feedback structure and BP.(b) spectrogram diagram of free EDFLs.

Fig. 6 .
Fig. 6.(a) Spectrogram of the different BP under 120 mw pump.(b) BEFL beat frequency state without the SA and the self-injection feedback structure.

Fig. 7 .
Fig. 7. (a) System architecture of delayed self heterodyne systems.(b) Linewidth measurement diagram of the BEFL without the SA and the selfinjection feedback structure.

Fig. 8 .
Fig. 8. (a) Spectrogram of EDFLs with the SA without the BP.(b) Spectrogram of the different BP under 120 mw pump.

Fig. 9 .
Fig. 9. (a) BEFL beat frequency state with the SA structure.(b) Wavelength test diagram of BEFL with the SA.

Fig. 11 .
Fig. 11.(a) Wavelength measurement diagram with the SA and the selfinjection feedback structure without BP.(b) Spectrogram of BEFL under BP injection.

Fig. 13 .
Fig. 13.(a) Wavelength diagram of the BEFL under the different BP wavelengths (b) Output power diagram of the BEFL under 7.5 dBm BP and 120 mw pump.

TABLE I PERFORMANCE
TABLE FOR THREE TYPES OF LASER STRUCTURES