1. Introduction

Multiwavelength fiber lasers (MWFLs) have aroused considerable interest due to their potential applications in optical fiber sensing, microwave photonics and dense wavelength division multiplexing (DWDM) systems over the past years. Various approaches and mechanisms have been proposed to obtain multiwavelength operation in a fiber laser, such as frequency- or phase-shifted feedback [1, 2], four-wave mixing [3, 4], nonlinear optical loop mirror (NOLM) [5–8], nonlinear polarization rotation [9, 10], semiconductor optical amplifier [11, 12], Raman amplifier [13, 14] and stimulated Brillouin scattering (SBS) [15–20]. Among these approaches, the MWFLs based on SBS or NOLM are particularly attractive for their simple configuration, narrow linewidth (by utilizing SBS effect) and flat output amplitude (by utilizing NOLM effect). However, the MWFLs based on SBS effect have large amplitude divergence between low- and high-order Stokes lines. These lasers also have inconvenient tunability for the output Stokes lines (such as varying the erbium-doped fiber (EDF) pump power to adjust their number) [15–18]. On the other hand, MWFLs based on NOLM have unsatisfied stability and linewidth during the process of multiwavelength operation [5]. Inspired by their respective problems, we propose the combination of NOLM and SBS effects to achieve nonlinear Brillouin optical loop mirror (NBOLM) in a MWFL. The output Stokes lines of this MWFL have narrow linewidth, adjustable flatness of amplitude, and simple tunability of number. Moreover, we derive a model based on the equations from models of MBEFL in [20–22] and NOLM in [23, 24] to explain the operation mechanism of the MWFL employing a NBOLM.

In this paper, we build up the NBOLM function by injecting a Brillouin pump (BP) light signal into a coil of single mode fiber (SMF) in the NOLM. Due to the SBS effect, the fiber laser can achieve extremely narrow linewidth and rigid multiwavelength channels spacing. At the same time, its NOLM effect acts as an amplitude-equalizer to optimize the output performance of Stokes lines and an intensity dependent loss to adjust the number of output Stokes lines in the fiber laser [5]. By considering the influence of SBS effect on nonlinear polarization evolution (NPE) in this NBOLM, we derive its power transmission equations of Stokes lines. Then, we combine these power transmission equations from NBOLM and rate and power propagation equations in EDF to build up a model for the MWFL employing a NBOLM. By utilizing this model, we numerically demonstrate how the number and amplitude flatness of output Stokes lines depend on input polarization state$A_s^{cw}$, quarter-wave plate (QWP) angle$\alpha$and EDF pump power$P_{EP}$. Thereafter, we experimentally validate the numerical results and these two results are well in agreement.

2. Theory and experimental setup of the MWFL employing a NBOLM

Figure 1 illustrates the proposed MWFL configuration. It consists of EDF, optical circulator, two optical couplers, WDM, 1480 pump laser diode, tunable laser source (TLS) and NBOLM. The NBOLM is formed by a highly twisted SMF, a quarter-wave plate, a polarization controller (PC), and a 3 dB optical coupler. The 15 m EDF pumped by the 1480 nm laser diode provides the linear gain. The 20 km highly twisted SMF in the NBOLM is used as Brillouin gain with effective cross section area of$50\mu m^2$. Circulator is used to ensure unidirectional propagation of the light signals and decreases the noise. The TLS acts as the BP light signal and injects into the cavity via the 20% port of Coupler (80/20). Measured results are extracted from the system by using a 90/10 coupler at one output port of the NBOLM. The 10% port of this coupler is connected to the OSA for monitoring the output spectrum. The 90% port output to a power meter for measuring the total power of all the Stokes lines.

 

Fig. 1 Schematic diagram of the proposed fiber laser.

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Firstly, to exploit the model of MWFL based on a NBOLM, we shall further develop the lump model proposed in [20], which consists of coupled wave equations of SBS for SMF and rate and propagation equations for EDF. However, the SMF of this MWFL is in a NBOLM which provides SBS effect and NPE effect (the QWP provides different nonlinear evolutions through the polarisation difference in the power-symmetric structure) simultaneously. These two effects can interplay with each other in the NBOLM. Therefore, instead of being described by coupled wave equations of SBS solely, the SMF in the NBOLM is described by the coupled wave equations for SBS process [21, 22] and NPE [23, 24]:

Equations (1)-(4) indicate that the power $P_{Bp\_n}^{cw/ccw}(z)$varies with distance of the highly twisted SMF due to the SBS effect. To achieve the transfer matrix for Eqs. (3) and (4), we divide the highly twisted SMF into t spans ($t=10000$in the numerical simulation) as shown in Fig. 2. The initial input power $P_{in\_1}$(from the TLS) is divided into clockwise light signal with power$P_{Bp\_1}^{cw}$ and counterclockwise light signal with power$P_{Bp\_1}^{ccw}$ by the 3 dB coupler. These two signals input in the 1st SMF span with powers $P_{Bp\_1,1}^{cw}$ and $P_{Bp\_1,1}^{ccw}$ to generate the corresponding 1-order Stokes line with powers $P_{S\_1,1}^{cw}$ and$P_{S\_1,1}^{ccw}$. Although the directions of $P_{Bp\_1,1}^{cw}$ and$P_{S\_1,1}^{cw}$are in opposite direction, we take the same superscripts for simplicity (the same applies to the other Stokes lines). Then the 2nd SMF span with input powers $P_{Bp\_1,2}^{cw}$ and$P_{Bp\_1,2}^{ccw}$ generates the corresponding Stokes lines respectively with powers $P_{S\_1,2}^{cw}$ and$P_{S\_1,2}^{ccw}$, and so on. Lastly, at the 10000th SMF span, the generated $cw$($P_{S\_1,10000}^{cw}$) and $ccw$($P_{S\_1,10000}^{ccw}$) 1-order Stokes lines are coupled in the 3 dB coupler. This coupled 1-order Stokes line outputs from port 1 of the 3 dB coupler and is amplified by the EDF, then inputs into the NBOLM again as the next round-trip initial power$P_{in\_1}$. This round-trip process repeats till the MWFL is in a steady state and there is no power variation for the Stokes lines. During this round-trip process, $P_{Bp\_n}^{cw/ccw}(z)$in each fiber span (a small length$\Delta l$) is regarded asa fixed parameter. Therefore, Eqs. (3) and (4) can be solved by a integration technique similarly as in [24]. From the derivation based on Eqs. (3) and (4), we can write down the transfer matrix of one highly twisted SMF span for the (n-1)- order Stokes line as:

 

Fig. 2 Operation mechanism scheme of the NBOLM.

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3. Numerical results and discussion

We perform series of numerical simulations by the proposed model in Section 2. The parameters for rate and propagation equations described in [20] are $g_B=3\times {10}^{-12}m/W$, $h=6.63\times {10}^{-34}J\cdot s$, $N=3\times {10}^{25}/m^3$(the total Er³⁺ ion density in the EDF),${\tau }_{21}={10}^{-2}$s, $N_{2\_initial}={10}^{10}/m^3$(the initial second energy state population density in the EDF), $\Delta \nu =5\times {10}^{10}Hz$, ${\xi }_{pe}=0$, ${\xi }_{pa}=3.28\times {10}^{-25}{m}^2$, $c=3\times {10}^{8}m/s$.${\xi }_{se}$ and ${\xi }_{sa}$ of different frequency (wavelength) are achieved by curve fitting method. The other chosen parameters are$L_{EDF}=15m$, $L_{SMF}=20km$(the long SMF provides a low SBS threshold and more obvious nonlinearity effect for this fiber laser),$A_{eff}=50\mu m^2$(EDF and twisted SMF fiber),$n=1.45$, $q=6$turn/m,$h0=0.14$, $L_b=15m$,${\tilde{n}}_2=3.2\times {10}^{-20}$and ${\lambda }_{EP}=1480nm$.$P_{s\_1}^{cw/ccw}(L_{SMF})$is a very small quantity of the SBS noise ($\approx 6\times {10}^{-9}$W) for seeding each Stokes line at the other end of the SMF. The total cavity loss is$F_{Loss}=16dB$ which is fairly large because the experimental configuration using many fiber connectors, a long SMF and NOLM structure induces extra loss. The Stokes lines circulate in the round-trips as governed by the rate and propagation equations, SBS Eqs. (1) and (2), and power transmission Eq. (9). By utilizing Eq. (11), the steady state of this fiber laser can be determined.

Figure 3 demonstrates how the calculated number of output Stokes lines depends on the EDF pump power $P_{EP}$ when $P_{Bp\_1}=3mW$and${\lambda }_{Bp\_1}=1558.42nm$. Due to the free-running oscillation center wavelength of this fiber laser is around 1558.5 nm, we choose the BP wavelength around 1558.5 nm to obtain more output Stokes lines. It is noticed that the center wavelength is decided by Er³⁺ concentration, cavity loss and EDF length. In Fig. 3(a), the EDF pump power$P_{EP}$is taken to be 35 mW, below the laser threshold (about 62 mW for$\alpha ={120}^o$and$A_s^{cw}=0.36$) for outputting Stokes line. In such case, Stokes line is not expected. When $P_{EP}$ increases to 126 mW which is in excess of the cavity loss and satisfies the lasing condition of a fiber laser, 6 Stokes lines occur with a channel spacing of 0.08 nm as shown in Fig. 3(b). Similarly, further increasing $P_{EP}$ to 265 mW and 348 mW as depicted in Figs. 3(c) and 3(d), 13 and 16 Stokes lines are generated, still with a constant spacing 0.08 nm, respectively. As a result, the number of output Stokes lines increases with$P_{EP}$ in this MWFL based on a NBOLM. This is because that a high $P_{EP}$ provides a large amount of excited Er³⁺ ions for Stokes lines in the EDF. More Stokes lines acquire these excited Er³⁺ ions, and exceed the cavity loss and come out from this fiber laser.

 

Fig. 3 Numerical simulation spectra for different$P_{EP}$: (a)$P_{EP}=35mW$, (b)$P_{EP}=126mW$, (c)$P_{EP}=265mW$, (d)$P_{EP}=348mW$.

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It is noticed that the output power of every Stokes lines in this fiber laser are very low (usually below −30dBm in the numerical results or the following experimental results). This is because we use a very long SMF, many connectors and 10% power extracted from the system by a 90/10 coupler. The large enough amplified BP light signal passes through the SMF and generates Stokes lines. The power of the residual BP light signal and the Stokes lines is around the SBS threshold of the SMF (several dBm SBS threshold for 20km SMF) after the SBS effect. This is because if these powers larger than the SBS threshold, the extra power can transfer to the other Stokes line or generate a new one. These Stokes lines decrease to about −20dBm at the input port of the 90/10 coupler due the loss of the components ($\approx$7dB for SMF, $\approx$3$\sim$8dB for NOLM structure, $\approx$7dB for connectors and other components). Thereafter, due to the 10% port of the 90/10 coupler, the output power is about −30dBm. The ASE of EDF and the spontaneous Brillouin scattering in the SMF are ignored due to the large cavity loss.

To clearly explain the mechanism of the input polarization state$A_s^{cw}$and QWP angle$\alpha$on the number and amplitude of output Stokes lines, we calculate the reflection of NBOLM which varies with the input power as shown in Fig. 4. As seen in Fig. 4(a), as$\alpha$increase from ${126}^o$to${132}^o$with a fixed$A_s^{cw}=0.21$, the reflection of NBOLM decreases (from dotted line to dashed line). Specially, when we increase $A_s^{cw}$from 0.18 to 0.21 with a fixed$\alpha ={132}^o$, the slope of the reflection lines grows slightly (from solid line to dashed line). However, when we vary $A_s^{cw}$and$\alpha$simultaneously, the reflection of the NBOLM and its slopes change in a relative larger amount as shown in Fig. 4(b).

 

Fig. 4 Calculated reflection of the NBOLM for different $A_s^{cw}$and$\alpha$: (a) varied $A_s^{cw}$or$\alpha$, (b) varying $A_s^{cw}$and$\alpha$simultaneously.

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Figure 5 shows the numerical calculated impact of input polarization state $A_s^{cw}$and the QWP angle $\alpha$on the number of output Stokes lines for$P_{Bp\_1}=3mW$,${\lambda }_{Bp\_1}=1557.92nm$ and$P_{EP}=181mW$. In Figs. 5(a) and 5(b), taking $\alpha ={132}^o$and$A_s^{cw}=0.21$, we achieve 2 Stokes lines. By decreasing $A_s^{cw}$to$0.18$, there is 3 Stokes lines occur in this fiber laser. As seen in Figs. 5(c) and 5(d), we take $\alpha ={129}^o$and$\alpha ={126}^o$for$A_s^{cw}=0.21$, 5 and 7 Stokes lines can emerge, respectively. The reason is that the decrease of $A_s^{cw}$or $\alpha$can increase the reflection of the Stokes lines as shown in Fig. 4(a). It means that more power of the Stokes lines are reflected back into the cavity. In such case, the total cavity loss of the Stokes lines decreases. Therefore, more Stokes lines have power exceeding the threshold of the fiber laser and lasing out. Noticed that the variation of $A_s^{cw}$ changes the reflection of NBOLM slightly, and the increase of number for output Stokes lines is not obvious.

 

Fig. 5 Numerical simulation spectra for different $A_s^{cw}$or$\alpha$: (a)$A_s^{cw}=0.21,\alpha ={132}^o$, (b)$A_s^{cw}=0.18,\alpha ={132}^o$, (c)$A_s^{cw}=0.21,\alpha ={129}^o$, (d)$A_s^{cw}=0.21,\alpha ={126}^o$.

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Figure 6 depicts the calculated influence of the input polarization state$A_s^{cw}$and the QWP angle $\alpha$on the amplitude flatness of Stokes lines for$P_{Bp\_1}=3mW$,${\lambda }_{Bp\_1}=1558.42nm$ and$P_{EP}=181mW$. It is seen that the largest amplitude divergence of the Stokes lines (15 channels) is almost 18 dB for$\alpha ={119}^o,A_s^{cw}=0.16$. Slightly varying PC and the QWP angle to a position of $\alpha ={123}^o$and$A_s^{cw}=0.22$, the amplitude variation of the Stokes lines (11 channels) decrease to 2 dB, as depicted in Fig. 6(b). This is because the slope of reflection line changes with varying both $A_s^{cw}$and$\alpha$ as shown in Fig. 4(b). By finely adjusting $A_s^{cw}$and$\alpha$, the net gain of more Stokes lines are approximately equal. Therefore, the amplitudes of these Stokes lines become nearly the same.

 

Fig. 6 Numerical simulation spectra for varying$A_s^{cw}$and$\alpha$simultaneously: (a)$\alpha ={119}^o,A_s^{cw}=0.16$, (b)$\alpha ={123}^o,A_s^{cw}=0.22$.

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4. Experimental validation

The numerical calculated impacts$P_{EP}$, $A_s^{cw}$and $\alpha$on the number and amplitude of output Stokes lines are validated by our experimental results. Figure 7 demonstrates that the number of output Stokes lines vary with$P_{EP}$. Same as the previously calculated results (seen in Fig. 3), the number of output Stokes lines increases with$P_{EP}$ for${\lambda }_{Bp\_1}=1558.42nm$, $P_{Bp\_1}=3mW$and $\alpha ={120}^o$(a fixed$A_s^{cw}$). When$P_{EP}=35mW$, there is only one channel lasing (BP light signal with no Stokes line). Increasing $P_{EP}$ to$126mW$, we achieve 6 Stokes lines with a fixed spacing 0.08 nm as shown in Fig. 7(b). As we gradually increase $P_{EP}$to $265mW$and$348mW$, respectively, 11 [seen in Fig. 7(c)] and 16 Stokes lines [seen in Fig. 7(d)] occur in the fiber laser, all with a constant spacing 0.08 nm. It is noticed that the number of output Stokes lines in this work (around 16) is much lower than the number in [27]. The main reason is that we use many connectors and the long SMF induce a large cavity loss.

 

Fig. 7 Experimental output spectra for different$P_{EP}$: (a)$P_{EP}=35mW$, (b)$P_{EP}=126mW$, (c)$P_{EP}=265mW$, (d)$P_{EP}=348mW$.

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Figure 8 shows the experimental results that the number of Stokes lines depends on $A_s^{cw}$and $\alpha$individually with${\lambda }_{Bp\_1}=1557.92nm$,$P_{Bp\_1}=3mW$ and $P_{EP}=181mW$(similar to the numerical results in Fig. 5). As shown in Figs. 8(a) and 8(b), the Stokes lines increase from 2 to 3 by only adjusting the PC from state 1 to state 2 with$\alpha ={132}^o$. Similarly, the Stokes lines increase from 5 to 6 by solely decreasing $\alpha$ from ${129}^o$to ${126}^o$with a fixed$A_s^{cw}$. We note that the number of output Stokes lines make a little bit change by varying the PC state $A_s^{cw}$(the PC state is varied by adjusting the polarization controller and denotes with PC state 1 and 2 for different states$A_s^{cw}$). However, the variation of $\alpha$change the number of output Stokes lines obviously. These are mainly resulted from the difference of the reflection variation from the NBOLM as shown in Fig. 4(a)

 

Fig. 8 Experimental output spectra for different $A_s^{cw}$or$\alpha$: (a) PC state 1 and (b) PC state 2 for$\alpha ={132}^o$, (c)$\alpha ={129}^o$and (d)$\alpha ={126}^o$for unvaried $A_s^{cw}$.

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Furthermore, as we adjust both the PC state $A_s^{cw}$and QWP angle$\alpha$finely, the amplitude flatness of the Stokes lines can be improved as shown in Fig. 9 (similar to numerical result in Fig. 6). When $\alpha ={122}^o$ and $A_s^{cw}$in PC state 1, there are 5 Stokes lines in 3 dB power range as seen in Fig. 9(a). However, when $\alpha ={120}^o$and slightly adjusting PC to state 2, there are 11 Stokes lines in 3 dB power range as shown in Fig. 9(b). However, the total number of outputStokes lines mostly increase when $\alpha$decreases (PC state can increases or decreases several output Stokes lines, but its effect is more weak than$\alpha$) as shown in Fig. 9 (11 Stokes lines for$\alpha ={122}^o$, 16 Stokes lines for$\alpha ={120}^o$in experimental results) and in Fig. 6 (10 Stokes lines for$\alpha ={123}^o$, 14 Stokes lines for$\alpha ={119}^o$in numerical results). This is because$\alpha$affects the reflection ratio more obviously and the input polarization state mainly affects the slope of the reflect lines. Due to the inaccuracy of manual adjustment of $A_s^{cw}$and$\alpha$, it is difficult to achieve suitable positions of $A_s^{cw}$and $\alpha$for a better amplitude flatness as predicted by the numerical results.

 

Fig. 9 Experimental output spectra for varying$A_s^{cw}$and$\alpha$simultaneously: (a) PC state 1 with$\alpha ={122}^o$, (b) PC state 2 with$\alpha ={120}^o$.

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The power stability of this MWFL is also observed when$\alpha ={122}^o$, $A_s^{cw}$in PC state 1,${\lambda }_{Bp\_1}=1558.42nm$, $P_{Bp\_1}=3mW$and$P_{EP}=348mW$[seen in Fig. 9(a)]. We scanned the output spectra every six minutes in an hour and found that the output power of the Stokes lines is very stable except the last output Stokes line in the spectra. The peak power variations of line 1-11 are all within$\pm 0.12dB$, as shown in Fig. 10. However the peak power of line 12 varies a little bitter, even sometimes hops with a next Stokes line (not included in Fig. 10 for its large instability). This is because the EDF gain for line 12 is under the saturation level. Therefore, the variation of EDF gain for this line results in its unstable peak power. When this power is sometimes beyond the threshold, the next Stokes line occurs.

 

Fig. 10 Experimental peak power stability of the Stokes lines and Bp.

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5. Conclusion

We have developed a model for the MWFL employing a NBOLM. It has ingredients of coupled wave equations of nonlinear polarization evolution and SBS process, rate and propagation equations. This theoretical model successfully explains the influences of EDF pump power$P_{EP}$, input polarization state $A_s^{cw}$and QWP angle $\alpha$on the number and amplitude flatness of output Stokes lines in this fiber laser. We can find an optimum$P_{EP}$, $A_s^{cw}$and $\alpha$ to improve the output performance of the MWFL. Alternatively, we have experimentally validated the theoretical predictions and measured the output power stability of the Stokes lines. The results from experimental observations compare favorably with the theoretical predictions. This MWFL with easily controlling number and flat amplitude of Stokes lines may be useful to facilitate the potential application of multiwavelength optical source in DWDM optical communication system.