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Abstract
A dual-ring parity-time (PT) symmetric Brillouin fiber laser (BFL) with an unbalanced polarization Mach-Zehnder interferometer (UP-MZI) is proposed and experimentally investigated. An UP-MZI consisting of optical coupler, polarization beam combiner (PBC) and two asymmetric length arms with 10 km and 100 m single-mode fiber, is used to achieve Vernier effect and PT symmetry. Due to the orthogonally polarized lights created in the PBC, the dual-ring PT symmetry BFL with an UP-MZI implements two unbalanced length feedback rings that are connected to one another, one long length ring with a Brillouin gain and the other short length ring with a loss of the same magnitude, to break a PT symmetric and maintain the Vernier effect. By contrast with existing PT symmetry BFL studies, this design does not require same lengths of the gain and loss loops, but can manipulate freely PT symmetry status in accordance with a rational scaling factor between them. Experimental results reveal that the 3-dB linewidth of dual-ring PT symmetry BFL with an UP-MZI is about 4.85 Hz with the threshold input power of 9.5 mW, in accordance with the 97 Hz measured linewidth at the -20 dB power point. Within 60 mins of the stability experiment, the power and frequency stability fluctuation are ±0.02 dB and ±0.137 kHz, respectively. Thanks to the two asymmetric ring lengths, the sidemode suppression ratio (SMSR) is optimized by 54 dB compared to that with the only long ring structure, 26 dB when using only the Vernier effect or 12 dB for existing PT symmetry BFL. This BFL design with single longitudinal mode and high SMSR output can be applied to high coherent communication and Brillouin-based microwave photonics systems with low phase noise.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Brillouin fiber lasers (BFLs) are widely used in fiber sensing [1–3], optical fiber communication [4–7] and other fields due to their advantages of narrow linewidth and low noise. Currently, the concept of Parity time (PT) symmetry has been widely used in physics for theoretical and experimental studies, especially in the field of nonlinear optics, where the availability of mode selection is a key feature of PT symmetry, which has been demonstrated in various oscillators [8–21], especially in BFL [22–24]. The PT symmetry BFLs consists of two coupled loops with the same geometry, one with gain and the other with loss. The PT symmetry is broken when the loop gain and loss are well matched and larger than the mutual coupling coefficient between the two mutual coupled loops. Due to the strong mode selectivity of PT symmetry, a narrow linewidth single-mode laser is achieved without a narrowband filter. The related studies of the PT symmetry BFLs are as follows. A PT symmetry BFL with a fiber Bragg grating (FBG) is proposed, which has a single longitudinal mode (SLM) narrow linewidth output [22]. The FBG is added to the fiber loop to realize the mutual coupling of the two loops, then by adjusting the polarization controllers (PCs), the loop gain and loss are the same, so as to achieve PT symmetry. In the fiber ring laser under a 8.02 km cavity length, the output SLM laser has a 3 dB linewidth of 368 Hz and a sidemode suppression ratio (SMSR) of about 33 dB. A PT symmetric Brillouin fiber laser (BFL) is realized through a dual-polarization cavity (DPC) and a single micro-ring resonator (MRR) [23], which has the characteristic of a narrow line width. The DPC composed of optical coupler, polarization beam combiner (PBC) and MRR, due to the reciprocity of optical in MMR, realizes two mutually coupled loops, and PT symmetry is accomplished by adjusting the PC to change the polarization state of the optical wave. The results with 3 dB linewidth of 11.95 Hz, threshold input power of 2.5 mW, SMSR of 40 dB and optical signal-to-noise ratio (OSNR) of 69 dB are realized. Recently, another SLM PT symmetry BFL was reported [24], it is realized based on the z-cut lithium niobate phase modulator (LN-PM) Sagnac loop. The PT symmetry is achieved based on the LN-PM Sagnac loop, and the LN-PM Sagnac loop is constituted by the LN-PM and two PCs. Meanwhile, the design uses the Pound-Drever-Hall frequency locking technology to improve the stability. This experiment achieves a PT symmetric BFL with a linewidth of 3.85 Hz, a maximal SMSR of 43 dB, and an OSNR of 65 dB. However, the above PT symmetric BFL requires two coupling loops of equal length, so it is difficult to improve the SMSR.
In general, the length of the two mutually coupled resonators or loops of PT symmetry is the same [25,26], in the meantime, resonator or loop gain and loss are larger than mutual coupling coefficients between the two mutual coupled resonators or loops. Recently, the PT-reciprocal scaling (PTX) symmetry is proposed, which belongs to the PT symmetric system in the broad sense. In PTX, PT symmetry is achieved by a scaling factor between the gain and loss factors of the two resonators or loops, rather than requiring equality [27,28]. PTX is more free to operate and easier to select modes than PT symmetry. Similarly, compared to PT symmetry with two mutually coupled loops, the asymmetric dual loop PTX design reduces the number of resonant modes in the OEO and erbium-doped fiber laser (EDFL) due to the Vernier effect, so mode selection is easier to implement, at the same time, which not only does not sacrifice linewidth, but also improves the SMSR [29,30]. An optoelectronic oscillator (OEO) by combination of spectral Vernier effect and PT symmetry [29] with two mutually coupled loops of different lengths, and produces microwave signals with low noise and high SMSR. The spectral Vernier effect achieved with two mutually coupled loops of different lengths increases the effective free spectral range. Combined with PT symmetry, mode selection and SMSR are improved. For microwave signals at 10 GHz, combining the spectral Vernier effect and PT symmetry increases the SMSR to 67.68 dB, which is 11.20 dB or 26.05 dB higher than that when using spectral Vernier effect or PT symmetry alone, and the phase noise is as low as -124.5 dBc/Hz@10 kHz. Dual-loop PT symmetric Erbium-Doped-Fiber Laser (EDFL) with a rational loop length ratio is proposed [30], in which the lengths of the two coupling loops are different. The PT symmetry and Vernier effect can be fully utilized to improve the SMSR. In the experiment, a dual-loop EDFL with a 200/3 rational length ratio can output a SLM laser of 1555.88 nm, improve the SMSR to 53.2 dB and achieve a linewidth of sub-kHz.
In this paper, we propose and experimentally prove a dual-ring PT symmetric BFL with an unbalanced polarization Mach-Zehnder interferometer (UP-MZI). In contrast to the previous work [23], this system does not require equal gain and loss loop lengths. Partial local modes can still be aligned as long as the length ratio is a rational number, which will enhance the gain difference between the primary and side modes and facilitate mode selection. The Vernier effect is achieved by an UP-MZI consisting of two asymmetric length arms with 10 km and 100 m single-mode fibers (SMF) to increase the effective mode spacing. PT symmetry is achieved by regulating the PCs so that SBS gain of the long ring (LR) and loss of the short ring (SR) are balanced and larger than the mutual coupling coefficient of the dual mutual coupled ring. The combined effect of Vernier effect and PT symmetry can achieve stable SLM laser output and significantly improve the SMSR. The experimental evaluation of the laser is performed. Based on a 97 Hz linewidth measured at the -20 dB power point, the 3 dB linewidth of the dual-ring PT-symmetric BFL with an UP-MZI is about 4.85 Hz, with a threshold input power of 9.5 mW. Within 60 mins of the stability experiment, the power and frequency stability fluctuation of the dual-ring PT symmetry BFL with an UP-MZI are ±0.02 dB and ±0.137 kHz, respectively. Compared to only the LR structure, the SMSR of the dual-ring PT-symmetric structure is improved by 54 dB, by 26 dB compared to the Vernier effect only, and by 12 dB compared to the existing PT symmetric BFL.
2. Principle
The experimental setup of the proposed laser is shown in Fig. 1. The pump light supplied by the laser (NKT X15) with a central wavelength of 1549.95 nm is injected into the dual-ring BFL with an UP-MZI via PC1 and Cir1, where PC1 is used to regulate keep the same polarization between the Stokes wave and the pump and maintain maximum SBS gain. The UP-MZI consisting of optical coupler, PBC and two asymmetric length arms with 10 km and 100 m SMF, is used to achieve simultaneously Vernier effect and PT symmetry at the same time. The Stokes light generated by the stimulation circulates counterclockwise in two coupling rings with different lengths once the pump power surpass the SBS threshold. As illustrated in Fig. 1, Cir1, OC1, PBC, PC4, and OC2 are shared by both the LR and the SR. While, the LR with SBS gain is composed of Cir1, OC1, a 10 km SMF, PC2, PBC, PC4, and OC2. Similarly, the SR with loss is comprised of Cir1, OC1, a 100 m SMF, PC2, PBC, PC4, and OC2. In the ring configuration, the gain and loss are regulated by adjusting PC2 and PC3 in the UP-MZI, while PC4 is adjusted to ensure that the gain/loss of the two rings are larger than the mutual coupling coefficient between the SR and the LR. Only the 10 km SMF provides SBS effect gain because the pump optical power does not reach the SBS threshold of 100 m. Two co-propagating light waves achieve mutual coupling at the common part. The PT symmetry is broken when the ring gain and loss are of the same magnitude and larger than the mutual coupling coefficient between the SR and the LR, which greatly enhances the gain difference between the primary and side modes and facilitates mode selection, resulting in a single-mode laser output. Stokes light is split into two lights in OC2, with 90% still circulate counterclockwise within the dual-ring structure, and 10% being used as the output laser. The output laser is then split into two beams using a 50/50 OC3. One end of the OC3 is connected to an optical spectrum analyzer (OSA) to monitor the output laser's spectrum with a resolution of 0.01 nm, while the other end is input into an electrical spectrum analyzer (ESA) with a resolution of 1 Hz after beating frequency by a photodetector (PD). The ESA is used to analyze the output laser's frequency spectrum. For the system stability, a temperature controller system is added with 0.02 °C resolution.
Fig. 1. Experimental setup. NKT: the narrow linewidth fiber laser; PCs: polarization controllers; Cir: circulator; OC: optical coupler; SMF: single-mode fiber; PBC: polarization beam combiner; PD: photodetector; OSA: Optical Spectrum Analyzer; ESA: electrical spectrum analyzer.
2.1. Free spectral range
The Brillouin frequency shift ${f_B}$ is given by ${f_B} = ({2{\textrm{V}_A}/c} ){\mathrm{\nu }_P}$, where ${\textrm{V}_A}$ is the acoustic velocity in the SMF, c is the velocity of light, and ${\mathrm{\nu }_P}$ is the pump optical frequency. ${f_B}$ is about 10.735 GHz at the 1549.95 nm wavelength. The laser mode f can only oscillate at a frequency that simultaneously satisfies the LR and the SR resonance conditions [29,30].
where ${n_m}\,({m = L,S} )$ is the integer. The $FS{R_\textrm{L}}$ of the 10 km SMF LR and the $FS{R_\textrm{S}}$ of the 100 m SMF SR are: where ${L_m}\,({m = L,S} )$ is the ring length of LR and SR, $n = 1.468$ is the fiber effective index. The FSR of LR and SR are about 20 kHz and 2 MHz, respectively, due to the ring lengths of LR and SR being 10 km and 100 m, respectively.According to the Vernier effect, the effective FSR of the double-ring structure is the least common multiple of LR and SR, which is [31]:
where $\textrm{gcd}({{n_L},{n_S}} )$ is the greatest common divisor of ${n_L}$ and ${n_S}$, effective $FSR$ is 2 MHz which is determined by the length of the SR, as shown in Fig. 2 (a), (b) and (c).Fig. 2. The principle of the dual-ring PT symmetry BFL with an UP-MZI. (a) only the LR, (b) only the SR, (c) the dual-ring using only the Vernier effect without PT symmetry, and (d) dual-ring mode selection mechanism combining Vernier effect and PT symmetry.
2.2. Dual-ring PT symmetry with an UP-MZI
Just some of the resonant modes will be found at the same frequencies if the lengths of the two resonators are not equal and the FSR is 20 kHz and 2 MHz respectively. If this is the case, the resonant modes will be mutually linked at the same frequencies, and the coupled mode equations can then be rewritten as [29,30]
The mutual coupling coefficients k between the SR and the LR can be expressed as $k = Kz/{L_s}$, where K is the coupling coefficient of OC1 and z is the coupling length. Where ${A_p}$ and ${B_q}$ are the amplitudes of the $p$th and $q$th mode of the LR and SR, $\alpha $ is the angle between the linear polarization state of the two rings, p and q are integers that, respectively, represent the $p$th and $q$th modes propagating in the LR and SR. As the $p$-th mode in the LR and the $q$-th mode in the SR are at the equal frequency $\mathrm{\omega } = {\omega _p} = {\omega _q} = 2\pi pFS{R_L} = 2\pi qFS{R_S}$, p and q should satisfy the relationship of $p = a\cdot {n_L}/\textrm{gcd}({{n_L},{n_S}} )$, $q = a\cdot {n_S}/\textrm{gcd}({{n_L},{n_S}} )$, that is, ${g_{B\_{A_p}}} ={-} {g_{B\_{B_q}}} = {g_{B\_AB}}$, the system is PT symmetric, and the system's eigenfrequencies can be represented as follows [30]
Numerous resonant modes in the LR are contained within a resonant mode in the SR if the length of the LR is significantly longer than the SR, that is, $FS{R_L} \ll FS{R_S}$. The mutual coupling coefficients between the SR mode and the LR modes that are near to the SR mode in this situation can be viewed as constants since the resonant mode in the SR and those modes in the LR are mutually connected.
As shown in Fig. 2, a common mode of the LR and SR will experience frequency splitting when ${g_{B\_AB}}$<$k$, which indicates that the system is functioning in the unbroken PT symmetry domain with only Vernier effect. The PT symmetry broken condition is met for a pair of conjugate modes when ${g_{B\_AB}}$>$k$, one of which exhibits an SBS gain in the LR and the other an loss in the SR, while all other resonant modes are neutral in Fig. 2(d).
We calculate the SBS gain enhancement, also known as the gain contrast ratio, to measure the improvement in mode selection. It is defined as the gain difference ratio between a dual-ring PT symmetric BFL and a general BFL, provided by
2.3. Linewidth of dual-ring PT symmetry BFL with an UP-MZI
BFL with distinct narrow linewidth specialty can narrow pump light from wide linewidth to narrow linewidth of Brillouin lasing. Two methods are used to calculate the theoretical linewidth and linewidth limit of the double-ring PT-symmetric BFL with an UP-MZI.
A proportional relationship of linewidth between the pump light $\Delta {\nu _P}$ and the Brillouin lasing $\Delta f$ is expressed by [32]
A wide linewidth laser has generally a short length cavity, such as a He-Ne laser, a semiconductor laser, a fiber DBR laser, or a fiber DFB laser. The laser's maximum Schawlow-Towns linewidth is expressed by [33]
where $\Delta {\nu _c} = c{R_N}/2\pi {L_L}$ is the full width at half maximum (FWHM) of a passive LR resonant mode, ${R_N}$ is the net loss of the ring cavity, h is the Planck’s constant, and ${P_0}$ is the output power. For a λ=1549.95 nm fiber ring laser with a LR length of ${L_L}$=10 km, a net loss of ${R_N}$=0.45, and an output power ${P_0}$=0.34 mW, the linewidth limit is calculated to be $\Delta {f_{ST}}$=3.47 × 10−16 Hz, which is ultra-small.Based on the results of the theoretical linewidth prediction and linewidth limit calculation for the double-ring PT-symmetric BFL with an UP-MZI, it is shown that the theoretical linewidth is ultra-narrow. However, in practice, the actual line width of the BFL may be wider compared to the theoretical value due to the effects of system noise and unstable operation.
3. Results and discussion
3.1 Threshold measurement of dual-ring PT symmetry BFL with an UP-MZI
In accordance with the system structure in Fig. 1, we tested and analyzed the performance parameters of the dual-ring PT symmetry BFL with an UP-MZI as shown in Fig. 3. In the test, NKT was used as the pump light output with a central wavelength of 1549.95 nm and a linewidth of 100 Hz. The spectra of the mixture of pump and Stokes lights generated by the dual-ring PT symmetry BFL with an UP-MZI are shown in Fig. 3(a). It is shown in the study that the OSNR of the pump light can be significantly improved by the BFL from 52 dB to 71 dB. The threshold curves between the pump power and the dual-ring PT symmetric BFL with an UP-MZI output power is shown in Fig. 3(b). The pump and BFL power are measured at the NKT output and at the 10% port of OC2, respectively. Increasing the pump power in the range from 0 mW to 28 mW and observing the optical spectral change can obtain a threshold input power of 9.5 mW.
Fig. 3. Optical spectra of dual-ring PT symmetry BFL with an UP-MZI. (a) The measured optical spectrum of the Brillouin lasing produced at a pump wavelength of 1549.95 nm; (b) The power threshold curve between the pump and BFL output.
3.2 Electrical spectra of dual-ring PT symmetry BFL with an UP-MZI
Measured electrical spectra of beat signals at the PD output for different structures of BFLs with different measurement resolution bandwidths (RBWs) is shown in Fig. 4 at the fixed pumping wavelength of 1549.95 nm. When only the LR is turned on, due to the lack of mode selection, when the pump light exceeds the threshold, the multi-mode Stokes lasing is generated as shown in Fig. 4(a). When the dual-ring are closed, the gain and loss of the dual-ring is regulated to maintain unbalance by PC2 and PC3, resulting in the absence of PT symmetry and only valid Vernier effect. The observed the effective FSR in the spectral range from 100 kHz to 10 MHz is 1.8 MHz. The effective FSR is smaller than the theoretical FSR because the actual length of the SR is larger than 100 m, which becomes the least common multiple of $FS{R_L}$ and $FS{R_S}$ according to the Eq. (3) due to the Vernier effect, as shown in Fig. 4(b). The PC4 is optimized to balance the SBS gain and loss in both rings, while ensuring that the gain/loss ratio exceeds the mutual coupling coefficient. This leads to a broken PT symmetry, which enables the generation of a SLM laser output. The experimental results are presented in Fig. 4(c).
Fig. 4. Test results displayed on the electrical spectra for different structures of the BFL with different measurement RBWs. Measured spectrum of RF beat frequency signal from the BFL with (a) only the long-ring, RBW: 6.5 kHz, (b) only the dual-ring using only Vernier effect without PT Symmetric, RBW: 6.5 kHz and (c) the dual-ring with Vernier effect and PT symmetric, RBW: 6.5 kHz. Zoom-in view of the spectrum in the range of 100 kHz to 300 kHz (d) only the long-ring, RBW: 100 Hz, (e) dual-ring using only Vernier effect, RBW: 100 Hz and (f) optimized SMSR combining Vernier effect and PT symmetry of the dual-ring. Zoom-in view of the spectrum in the range of 1.5 MHz to 2.1 MHz (g) only long-ring, RBW: 100 Hz, (h) dual-ring using only Vernier effect, RBW: 100 Hz and (i) optimized SMSR combining Vernier effect and PT symmetric in contrast to that with Vernier effect only.
Figure 4(d) and (e) present a magnified spectrum view of the closed only 10 km LR and the closed double ring structure, respectively, within the frequency range of 100 kHz to 300 kHz. The mode spacing of both structures is 21 kHz, which corresponds to a 10 km LR. By comparing Fig. 4(d) and Fig. 4(e), it is observed that the sidemodes of the dual-ring BFL exhibits a somewhat suppressed SBS gain, with an improved SMSR of 17 dB, as a result of the Vernier effect when compared to the long-ring BFL. However, the laser still operates in a multi-mode regime. The dual-ring were maintained in a closed state, and their gain and loss were balanced by adjusting and controlling the PCs. The gain/loss was adjusted to exceed the mutual coupling coefficient of the dual mutual coupled rings, thereby breaking the PT symmetry and enabling the realization of SLM laser output. Due to the combined effect of Vernier effect and PT symmetry, the SMSR is substantially increased, as demonstrated in Fig. 4(f), with an optimized SMSR of 54 dB and 26 dB compared to that of Fig. 4(d) and (e).
Figure 4(g) and (h) present an expanded spectrum view of the closed only 10 km LR and the closed double ring structure, respectively, within the frequency range of 1.5 MHz to 2.1 MHz at 1.8 MHz center frequency corresponding to the effective FSR of the dual-ring structure. As a result of the Vernier effect, the sidemodes are effectively suppressed, yet the BFL remains in multimode operation. Moreover, the ring gain of the 1.8 MHz sidemode is enhanced due to mode competition while the ring gain of the other sidemodes are suppressed, as illustrated in Fig. 4(h). Figure 4(i) depicts the spectrum with the combined effect of PT symmetry and Vernier effect in the frequency range of 1.5 MHz to 2.1 MHz. The optimized SMSR reaches 60 dB at 1.8 MHz frequency compared to that with the Vernier effect only.
3.3 Linewidth and stability measurement of dual-ring PT symmetry BFL with an UP-MZI
In order to measure the linewidth of the BFL, we reconstructed another measurement setup which is shown in Fig. 5. The pump light is emitted from the NKT port and subsequently split into two paths upon entering the OC1. In the upper branch, another BFL consists of 90/10 OC2, 10 km SMF and Cir2. The pump light is introduced into a 10 km SMF via Cir2. Upon exceeding the SBS threshold, stokes light is generated and undergoes multiple counterclockwise round trips within a ring cavity, leading to periodic resonance. The laser from the upper branch is output through the 10% port of OC4 and the output laser from the double-ring PT symmetric BFL with an UP-MZI in the lower branch enters the OC5 for mixing, and the mixed light enters the PD for beat frequency. Finally, we directly observe the linewidth of the laser using ESA. The electrical spectrum measured by ESA is shown in Fig. 6(a). According to Eq. (7), the theoretical linewidth of the dual-ring PT symmetric BFL can be computed as 10−5 Hz, which significantly surpasses the 1 Hz resolution accuracy of the ESA. The measured linewidth at -20 dB power point is 97 Hz, while the corresponding 3-dB linewidth is 4.85 Hz. The measured linewidth being greater than the theoretical value may be attributed to the influence of system noise and unstable operations.
Fig. 6. The measurement results of linewidth of dual-ring PT symmetric BFL with an UP-MZI. (a) linewidth measurement results of the dual-ring PT symmetric BFL (b) the pump linewidth result of normalized power spectrum S for 5 km delay fiber length; (c) the linewidth result of normalized power spectrum S of the dual-ring PT symmetry BFL with an UP-MZI for 25 km delay fiber length.
One of the heterodyne methods [22,34] for linewidth measurement is to use two independent lasers with the same pump source to generate a beat frequency, which allows for testing of laser linewidth. In our proposed scheme for linewidth measurement, the resulting power spectrum exhibits a Voigt line pattern due to the inability to effectively eliminate optical coherence within the cavity. In addition, we employed the method of the contrast ratio difference of the second peak and second trough (CDSPST) of the coherent envelope, as described in Refs. [35], to determine the laser linewidth. The linewidths of the pump laser and dual-ring PT symmetric BFL with an UP-MZI were measured using delay fiber lengths of 5 km and 25 km, respectively. The measurement results are shown in Fig. 6(b) and (c). The pump laser linewidth measured values of the CDSPST in the test experiment were 19 dB, as shown in Fig. 6(b). This indicates that the laser linewidth is estimated to be less than 150 Hz. The testing results of the BFL are shown in Fig. 6(c). The CDSPST value was measured to be 21 dB, indicating that the BFL linewidth is estimated to be less than 10 Hz. This result is consistent with the previously measured linewidth 3-dB of 4.85 Hz.
According to previously reported [36–38], The frequency dragging effect and the temperature effect are the main effects for the stability of the dual-ring PT symmetry BFL with an UP-MZI. One the one hand, the mode hoping $FS{R_{mode - hopping}}$ in one FSR due to the frequency dragging effect is
Fig. 7. (a) Stokes peak power fluctuations and (b) frequency drift of the mode were monitored every 4 minutes for 1 hour.
Table 1. Performance comparison of PT symmetry-based oscillators
4. Conclusion
In a word, we propose and experimentally prove a dual-ring PT symmetric BFL with an UP-MZI. To achieve PT symmetry and Vernier effect, an UP-MZI made up of a 50/50 OC, a PBC and two asymmetric length arms with 10 km and 100 m SMF is used. In the UP-MZI, two beams of stokes light split by PBC are passed the two arms respectively, one of which experiences SBS gain through PC2, 10 km SMF, OC1 and the other loss through the PC3, 100 m SMF, OC1, respectively. PC2 and PC3 are used to regulate the SBS gain and loss of the dual-ring to maintain the valid Vernier effect with or without PT symmetry. When the SBS gain and loss optimized by the PC4 is balanced to exceed the mutual coupling coefficient, a SLM BFL laser output with narrow linewidth is generated. The 3-dB linewidth of the dual-ring PT symmetry BFL with an UP-MZI is 4.85 Hz, in accordance with the 97 Hz measured linewidth at the -20 dB power point, with the threshold input power of 9.5 mW. Within 60 mins of the stability experiment, the power and frequency stability fluctuation of the dual-ring PT symmetry BFL with an UP-MZI are ±0.02 dB and ±0.137 kHz, respectively. Due to the of Vernier effect and PT symmetry, the SMSR is substantially increased by 54 dB, 26 dB and 12 dB compared to that of only LR ring, only Vernier effect and existing PT symmetry BFL. Thanks to narrower linewidth and high SMSR advantage, this design has potential application fields, such as Brillouin-based microwave photonics with low phase noise, high sensitivity fiber sensing, and high-resolution coherent optical communication.
Funding
National Key Research and Development Program of China (2019YFF0301802); Key Research and Development (R&D) Projects of Shanxi Province (201903D121124); Central Guidance on Local Science and Technology Development Fund of Shanxi Province (YDZJSX2022B005); Shanxi Scholarship Council of China (501100003398) (2020-112); Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2020L0268); Fundamental Re-search Program of Shanxi Province (20210302124390, 20210302124558, 202203021223005); Graduate Innovation Project of Shanxi Province (2022Y629); Foundation of Shanxi Province Key Laboratory of Quantum Sensing and Precision Measurement (201905D121001004); Technology Project of the North University of China under Grant (20221840, 20221842).
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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