Fiber lasers have been widely used in the fields of optical fiber communication, distributed optical fiber sensing, and optical spectrum analysis ^[1–3], where spectral purity is particularly important since it directly influences the resolution and accuracy of these applications. Mostly, spectral purity includes single-longitudinal-mode (SLM) selection and linewidth compression, and both of them have attracted more and more interest in recent research.

In order to realize SLM output, several approaches have been reported and demonstrated, such as short cavity ^[4,5], saturable absorber ^[6], twisted-mode element ^[7], and passive multiple ring cavities ^[8]. However, those conventional methods are usually influenced by the self-pulsation effect induced by interactions between doped ions in short-cavity configurations, dependence of modulation depth of the equivalent grating on pump power, and other negative factors, which leads to a linewidth broadening. Therefore, effective methods to compress linewidth are still needed. Recently, spontaneous/stimulated scattering effects in optical fibers offered an alternative method to compress the linewidth, in which the compression results were strongly dependent on the intrinsic linewidth of scattered light. Considering the intrinsic linewidth of stimulated thermal Rayleigh scattering (STRS) is on the order of kilohertz ^[9], STRS-based lasers have special potential in the area of ultranarrow fiber lasers. However, in optical fibers, the gain of stimulated Brillouin scattering (SBS) could be ∼1000 times larger than that of STRS, and increasing the power of the pump source would lead STRS to be entirely drowned in SBS, whose intrinsic linewidth is ∼10MHz. Up to now, the main methods to suppress SBS include particular structure designs of fibers ^[10], phase modulation ^[11], and distributed parameters modulation ^[12–14] (such as strain, temperature, and core radius along the fiber length). Among parameter modulation methods, periodic tapered fiber is an efficient way to suppress SBS to achieve STRS-based lasers. In this paper, an SLM fiber laser with ultranarrow linewidth is demonstrated in detail, wherein passive multiple cavities are utilized to select SLM, and periodic structures of tapered fiber are employed to suppress the SBS effect in single mode fiber (SMF). To design and optimize the tapered structures, a semi-quantitative estimation has been built to illuminate the mechanism of SBS suppression with the periodic tapered fiber.

As detailed in Section 1, SBS is one of the most dominant disturbances for STRS in optical fibers, and the suppression of SBS has therefore become a major issue for STRS-based fiber lasers. In this section, a semi-quantitative estimation has been established to demonstrate the principle of the SBS suppression method based on tapered fibers. In general, SBS is regarded as an inelastic entanglement between the photons and acoustic phonons, wherein the interaction between the incident and scattered photons would modulate the material properties profoundly through the electrostriction and thermal absorbtion, and eventually influence the evolution of phonons. Such a process could be described mathematically by a set of acousto-optic coupled equations with the assumptions of the slowly varying envelope approximation and undepleted pump ^[15]: where vStokes, vPump, PStokes, and PPump are the frequencies and optical power of Stokes and pump lights, respectively; α is the loss coefficient of the optical fiber; vB, wB, and g0 are the Brillouin frequency shift (BFS), full width at half maximum (FWHM), and peak gain of SBS gain spectrum (BGS), where g0 is mostly inversely proportional to vB and wB; Aao denotes the acousto-optic effective area of the fiber and could be approximately replaced by optical effective area Aeff in fibers with quasi-rectangular index profile.

In SBS progress, Eq. (1) has a well-defined initial condition: PStokes(vStokes,L)=PSeed(vStokes), which means the power of seed photons could be estimated by the Rayleigh–Jeans approximation PSeed(vStokes)≈2kTvStokes/vB; k and T are respectively Boltzmann’s constant and the fiber temperature; and revising constant 2 is given by polarization scrambling. Equation (1) can be considered as a Cauchy problem of a first order inhomogeneous differential equation, and its general solution could be expressed as where BGS can be generally written as

Equation (3) indicates the cumulative increase of the scattered light at a certain frequency vStokes and certain location z0. The total generated Stokes power at the exit end (z0=0) should especially be paid attention to, and it can be obtained through the integration over the whole spectrum:

It is worth indicating that PStokes cannot be described using an analytic expression because both Aeff and vB depend strongly on the radius of the fiber core. However, the dependences do not have definite mathematical expressions in tapered fibers with a very complex axial distribution as shown in Fig. 1. Based on Ref. ^[16], the relationship between a and vB in weakly guiding acoustic waveguides can be written as where Ji is the i-order Bessel function of the first kind; Ki is the i-order modified Bessel function of the second kind; Vphase=vB·λ/2n1 is the phase velocity of the phonons; VL1 and VL2 are the longitudinal acoustic velocities of core and cladding materials, respectively; n1 is the refractive index of the core.

Another influence caused by the tapered structure is the variation of the optical effective area. In a step-index SMF, the optical effective area can be estimated by Marcuse’s equation: where V(z)=NA·2πa(z)/λ; the numerical aperture (NA) is typically 0.12 in Corning SMF 28e fibers. Equation (6) is effective only if the fundamental mode is definitely guided by the fiber; nevertheless, the light will leak out to the air once the mode field has expanded to the air–cladding boundary. Thus, Aeff reaches its maximum when the taper waist reaches the core-mode cutoff point ∼1.84μm, which corresponds to a waist diameter of ∼56μm in Corning SMF28e fibers ^[17].

Figure 2(a) shows the numerical solutions of Eqs. (5) and (6) with common parameters of SMF (VL1=5492m/s, VL2=6054m/s, n1=1.4677). It is clear that both BFS (orange line) and Aeff (blue line) change a lot according to the variation of the radius of the fiber core, and SBS therefore gets a suppression in tapered fibers since the nonuniformly distributed BFS will restrain the global modulation caused by the incident and scattered photonics. So far, a mathematical model to describe the SBS spatial optical power evolution in a well-defined tapered fiber has been built by substituting Eqs. (5) and (6) into Eqs. (3) and (4).

According to Burns’s parabolic model, the length ratio of the waist region to the transition region could be regarded as a function of the waist diameter ^[18], so that in a fixed-length segment of tapered fiber, the SBS suppression effect is relevant to only two independent variables: waist diameter w and duty ratio rtaper=ltaper/Ltaper. Figures 2(b) and 2(c) show the BGS versus different w and rtaper, respectively. It is clear that both the reduction of w and the increase of rtaper would decrease the amplitude of BGS, which means that SBS can be effectively suppressed in this way. Additionally, it can be seen from the comparison of Figs. 2(c) and 2(e) that BGS gain seems to be more alternative to rtaper than w, and the inflection points of the curves are (75 μm, 0.58) and (0.08, 0.12), respectively. Thus, two major findings can be achieved: (1) BGS cannot be unlimitedly reduced when decreasing w, and it would lead to a great loss because of the leaky mode. So the optimal w is ∼75μm. (2) Increasing rtaper could effectively suppress SBS, and SBS is almost completely suppressed when rtaper>0.08.

Figure 3(a) shows the experimental setup to verify the validity of the SBS suppression method proposed in Section 2. A 110-m-long segment of fiber under test (FUT) is pumped by a tunable laser (TLS, Yenista Tunics-Reference, with 500-kHz linewidth) and an erbium-doped fiber amplifier (EDFA, Opeak EDFA-C-PM-CW-MB, with maximum gain of 30 dB). Via the first and second ports of the optical circulator, the pump light enters FUT, where the stimulated scattering would occur once the pump power reaches the threshold. Then, the backward-scattered light would emit from the third port of the optical circulator and be monitored by an optical spectrum analyzer (OSA, Anristu MS9740A with an FMHW resolution of 30 pm and a readout resolution of 1 pm) and an optical power meter (OPM). A variable optical attenuator (VOA) is used to restrict the power into the OSA.

It could be found from the OSA that, whether in conventional SMF or tapered fiber, the power spectra of backward-scattered light would split into two power peaks with central wavelengths of 1549.998 nm (contributed by Rayleigh scattering) and 1550.081 nm (contributed by SBS and BFS at ∼10.375GHz). By integrating these power peaks, the total optical power of Rayleigh and Brillouin scattering can be obtained.

To make a further verification of the proposed SBS suppression method, several tapered fibers with different rtaper and w were fabricated and employed as FUTs in experiments (owing to the limitation of equipment in our laboratory, tapered fibers with rtaper≤0.02 are available). As indicated in Figs. 3(b)–3(e), the experimental data points show clear downward trends as the rtaper increases. It could be found from the comparison among these figures that decreasing the waists of tapers is also conducive to SBS suppression, but further decreasing the waist would not yield a proportional benefit, especially when w≤75μm. Meanwhile, more points with big error are observed when the waist diameter decreases to 60 μm as a result of the leak of the fundamental mode. Synthesizing the effects of SBS suppression, tapers with rtaper=0.02 and w=75μm are considered most practical. Figure 3(f) shows the power spectra of backward-scattered light in conventional SMFs (orange line) and tapered fibers with rtaper=0.02 and w=75μm (gray line) under the same condition, and a 1.84 dB decrease of total generated Stokes power is achieved in such a tapered fiber, which is close to the theoretical value of 2.37 dB.

Then, experiments are conducted to identify the component of Rayleigh power peak. STRS and spontaneous Rayleigh scattering (SponRS) cannot be directly distinguished by an OSA with a spectral resolution of 30 pm because they have nearly same frequencies and narrow linewidths (∼100kHz for SponRS and ∼1kHz for STRS). However, STRS and SponRS have linear and nonlinear responses, respectively, to the incident optical power ^[19]. If STRS occupies the domain part in backward scattering when the input optical power exceeds the threshold power, the power response curve should be nonlinear. So STRS and SponRS could be differentiated by drawing the response curve of the scattering optical power to incident optical power. As shown in Fig. 4, when the incident optical power increases, scattered optical power responds nonlinearly and has a threshold of 60–65 mW; therefore, there is evidence to believe STRS occurs when the optical power in the cavity is over 60–65 mW, and it would be the domain part in backward scattering.

Finally, an STRS-based fiber laser is built to further examine the performances of the tapered fiber. It is shown in Fig. 5 that the proposed laser could be simply divided into three parts: first, a fundamental multilongitudinal-mode (MLM) ring-cavity laser consisting of a 980 nm pump laser, 980/1550 nm wavelength division multiplexer (WDM), 80-cm erbium-doped fiber (EDF, Liekki Er110), fiber Bragg grating (FBG), optical circulator 1 and 90:10 coupler; second, a linewidth compression device employed to generate STRS and compress the linewidth consisting of optical circulator 2 and tapered fiber; and finally, an SLM selection device consisting of secondary cavities 1 and 2 (with cavity lengths of 0.3 and 0.5 m, respectively) made by optical couplers.

While the laser works, the scattered light will have million-time transition trips in the ring cavity during the fluorescence relaxation time of erbium ions (∼ms), which would eventually create an ultrahigh gain contrast ratio between Rayleigh scattering and SBS, and compress the linewidth. During the experiment, an OPM is used to monitor the output power of the laser, and according to the value of the OPM and the coupling ratio of the coupler, the optical power in the ring cavity is ∼75mW, exceeding the threshold of STRS. So STRS would occupy the domain part in backward scattering whose gain spectrum is much narrower. Thus the tapered fiber has the potential to compress the linewidth of the fiber laser.

A self-heterodyne detection method is utilized to measure the spectrum of the STRS-based laser and, as shown in Figs. 6(a) and 6(b), MLM output with 32-MHz free spectral range and SLM output are respectively observed when secondary cavities are excluded or included in the lasers. The Voigt fitting method is also employed in our experiment to mitigate the influences caused by long delayed fiber; more details can be found in Ref. ^[20]. It is shown in Figs. 6(c) and 6(d) that the measured linewidth of the laser operating in SLM is ∼200Hz, much narrower than the 9.5 kHz achieved without an SRTS-based linewidth compression device.

In this paper, an SBS suppression method using periodic tapered fibers is proposed, and a semi-quantitative estimation is built to illuminate the mechanism of suppressing SBS and to be a guide to design an STRS-based linewidth compression device. Experimental results of BGS/total generated Stokes power verify theoretical estimations of the SBS suppression method. Based on this theory, an optimized design of a 110-m-long segment of tapered fiber with w=75μm and rtaper=0.02 is achieved, and total generated Stokes power declines by 1.84 dB in comparison to that in a conventional SMF, which agrees with theoretical estimations and simulations of ∼2.37dB. Due to a large ratio of fluorescence relaxation time of erbium ions to a single transition time of scattered light in the ring cavity, SBS could be effectively suppressed and linewidth compression effect of STRS could be realized. Finally, an STRS-based SLM ring-cavity fiber laser is developed wherein multiple passive cavities and periodic structures of tapered fiber are respectively utilized to select SLM and compress linewidth, and its linewidth is experimentally verified to be downward from 9.5 kHz to 200 Hz through a self-heterodyne detection and Voigt fitting method.