Orthogonal polarization switchable lasing based on axial polarization pulling of SBS in polarization-maintaining fiber

Chunhua Wang; Yali Zhang; Gang Liu; Jingjing Zhao; Juan Zhang; Liang Chen; Xiaoyi Bao

doi:10.1364/OE.26.028385

1. Introduction

In addition to polarization evolution induced by random birefringence in practical single mode fibers (SMFs), the nonlinear polarization interactions between pump and signal lights in parametric amplification [1–4], stimulated Raman scattering (SRS) [5–8], and stimulated Brillouin scattering (SBS) [7–10] attract research interests because of their application potential. Among these nonlinear polarization effects, the SBS polarization pulling, featuring with the low requirement on pump power and extraordinary narrow gain bandwidth, has applications in many scenarios, such as its usages for polarization control [10], reshaping of the SBS gain spectrum [11–13], and the generation of THz wave [14]. The SBS polarization pulling is also frequency dependent, performing a spectral polarization spreading behavior [15]. In SMFs, because the fiber birefringence and SBS pulling force are comparable in magnitude, the SBS polarization spreading will be twisted by fiber birefringence, leading to random deviations of Brillouin frequency shift [16]. Moreover, the SBS polarization pulling is capable of reducing the polarization fluctuation of signal light, leading to easy polarization stability in SBS fiber lasers (BFLs) [17,18]. In addition, other SBS polarization effects in specialty fibers are also studied and show interesting performances. J. Fatome et al experimentally observed that under the condition of heavy SBS gain saturation, the state of polarization (SOP) of signal light aggregates onto the large circle perpendicular to the principal axes of PMFs on the Poincaré sphere [19]. The SBS polarization pulling behavior in a spun fiber was also reported, where a polarization-dependent narrow dip at the center of SBS gain spectrum shows up and leads to self-pulsing signal output [20]. In this paper, we report an axial SBS polarization pulling phenomenon in PMFs. By simulation with vectored SBS equations, we find that the SBS polarization pulling in PMFs always heads for one of the two principal axes of PMFs rather than for multiple directions as in low birefringent SMFs [9,15], this theoretical conclusion is confirmed by an SBS fiber laser (BFL) ringing with PMF. The PMF-BFL can lase light fully polarized at either one of the two principal axes of PMFs, depending on the sign of the projection of input pump SOP on polarization vector of PMF, for certain pump power settings. Namely, by adjusting the SOP of pump light between two half spheres divided by the large circle perpendicular to principal axes of PMF on the Poincaré sphere, the PMF-BFL can lase orthogonal polarization switching (OPS) light. The PMF-BFL can also lase depolarized light due to the simultaneous resonances of two principal polarization modes under some circumstances. The conditions for these polarization lasing behaviors are discussed in the paper as well.

2. Principle and simulations

In PMFs where only the linear birefringence exists, under the non-depletion assumption, i.e. the pump power is much larger than the signal power and remains unchanged over the fiber under consideration, the vector propagations of SBS can be expressed as [9,15]:

\frac{d I_{s}}{d z} = r_{0} I_{p} I_{s} (1 + \hat{s} \cdot \hat{p});

\frac{d I_{p}}{d z} = 0;

\frac{d \hat{p}}{d z} = - {\vec{β}}_{l} \times \hat{p};

\frac{d \hat{s}}{d z} = {\vec{β}}_{l} \times \hat{s} + r_{0} I_{p} [\hat{p} - (\hat{s} \cdot \hat{p}) \hat{s}] .

Herein, signal is launched into fiber at z = 0, and pump at z = L.

I_{p, s}

are the powers of pump and signal lights,

\hat{p}

and

\hat{s}

the normalized Stokes vectors of pump and signal lights, and

r_{0}

is the SBS gain coefficient. In PMFs,

{\vec{β}}_{l} = 2 π / L_{b} {\hat{β}}_{l}

, where

L_{b}

is the beat length and

{\hat{β}}_{l}

is the unit vector of

{\vec{β}}_{l}

, lying in the equatorial plane of the Poincaré sphere. Along z-direction,

\hat{s}

and

\hat{p}

rotate oppositely in the two parallel circles perpendicular to

{\hat{β}}_{l}

at the speed of

2 π / L_{b}

under the linear birefringence force. In addition,

\hat{s}

experiences the SBS pulling toward the local

\hat{p}

simultaneously. Because the birefringence force

2 π / L_{b}

of PMF is much larger than the SBS pulling force

r_{0} I_{p}

, Eq. (4) can be simplified as

d \hat{s} / d z = {\vec{β}}_{l} \times \hat{s}

in a fiber segment of beat length, and we can derive the relation that

\frac{d^{2} (\hat{s} \times {\hat{β}}_{l}) \cdot (\hat{p} \times {\hat{β}}_{l})}{d z^{2}} = - 4 {‖ {\overset{⇀}{β}}_{l} ‖}^{2} (\hat{s} \times {\hat{β}}_{l}) \cdot (\hat{p} \times {\hat{β}}_{l}) .

From Eq. (5), the solution of

(\hat{s} \times {\hat{β}}_{l}) \cdot (\hat{p} \times {\hat{β}}_{l})

is a sinusoidal function with the period of

2 ‖ {\overset{⇀}{β}}_{l} ‖ = 4 π / L_{b}

, so that the following approximation is reasonable:

\begin{array}{l} \int_{0}^{L} (\hat{s} \cdot \hat{p}) d z = \int_{0}^{L} [(\hat{s} \times {\hat{β}}_{l}) \cdot (\hat{p} \times {\hat{β}}_{l}) + (\hat{s} \cdot {\hat{β}}_{l}) (\hat{p} \cdot {\hat{β}}_{l})] d z \\ \approx \int_{0}^{L} (\hat{s} \cdot {\hat{β}}_{l}) (\hat{p} \cdot {\hat{β}}_{l}) d z . \end{array}

According to Eq. (2) and

d (\hat{p} \cdot {\vec{β}}_{l}) / d z = - ({\vec{β}}_{l} \times \hat{p}) \cdot {\vec{β}}_{l} \equiv 0

obtained from Eq. (3),

\hat{p} \cdot {\hat{β}}_{l} = {\hat{p}}_{i n} \cdot {\hat{β}}_{l}

and

I_{p} = I_{p 0}

, where

I_{p 0}

and

{\hat{p}}_{i n}

is the input power and SOP of pump light. So that we have

\frac{d I_{s}}{d z} = r_{0} I_{p 0} I_{s} [1 + ({\hat{p}}_{i n} \cdot {\hat{β}}_{l}) (\hat{s} \cdot {\hat{β}}_{l})];

\frac{d (\hat{s} \cdot {\hat{β}}_{l})}{d z} = r_{0} I_{p_{0}} {\hat{p}}_{i n} \cdot {\hat{β}}_{l} [1 - {(\hat{s} \cdot {\hat{β}}_{l})}^{2}] .

Analytically, Eq. (8) indicates that the SOP of signal light will be pulled towards one of two principal axes, depending on the sign of ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ . The axial pulling force is proportional to the pump power and the magnitude of ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ . When ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} = 0$ , the SBS pulling force is zero, no axial SBS pulling works on the signal light, namely $\hat{s}$ simply rotates around ${\hat{β}}_{l}$ along the fiber without migration in the direction of ${\hat{β}}_{l}$ .

From Eq. (7), the SBS gain in PMFs is

G = e^{r_{0} I_{p 0} (L + {\hat{p}}_{i n} \cdot {\hat{β}}_{l} \int_{0}^{L} (\hat{s} \cdot {\hat{β}}_{l}) d z)} .

By taking

{\hat{s}}_{i n}

as the input SOP of signal, at

{\hat{s}}_{i n} \cdot {\hat{β}}_{l} = \pm 1

, signal experiences the maximum or the minimum SBS gain:

G_{\max / \min} ({\hat{p}}_{i n} \cdot {\hat{β}}_{l}) = e^{r_{0} I_{p 0} L (1 \pm | {\hat{p}}_{i n} \cdot {\hat{β}}_{l} |)} .

And at

{\hat{p}}_{i n} \cdot {\hat{β}}_{l}

= 0,

G = G_{\max} = G_{\min} = e^{r_{0} I_{p 0} L}

for arbitrary

{\hat{s}}_{i n}

.

To fully understand the SBS polarization pulling behavior in PMFs and low birefringent SMFs, we simulate the SBS pulling behavior of a 25m uniform linear birefringence fiber with Eqs. (1)-(4). In simulation, $L =$ 25 m, ${\hat{β}}_{l} = (- 1, 0, 0)$ , and $r_{0} =0 .2229[W \cdot m]^{- 1}$ . The input pump and signal powers are $I_{p0} =$ 80 mW and $I_{s0} =$ 0.5 mW. 100 uniformly distributed SOPs (see the blue points on the Poincaré sphere in Fig. 1(a)), plus with two special SOPs of V(−1,0,0) and H(1,0,0), are used as 102- ${\hat{p}}_{i n}$ and 102- ${\hat{s}}_{i n}$ to simulate the SBS polarization pulling behavior statistically. Three PMFs with $L_{b} =$ 0.25, 5, and 40 m are simulated. Although the beat length of PMFs in order of millimeters are not simulated for the sake of computing time, the physical conclusion is the same.

Fig. 1 (a) 100 SOPs uniformly distributed over the Poincaré sphere (blue dots), and the simulated ${\hat{s}}_{o u t}^{\max}$ (red circles at V and H) for different ${\hat{p}}_{i n}$ when $L_{b} =$ 0.25 m; (b) the simulated ${\hat{s}}_{o u t}^{\max}$ for different ${\hat{p}}_{i n}$ when $L_{b} =$ 40 m; (c) simulated relationships between ${\hat{s}}_{o u t}^{\max} \cdot {\hat{β}}_{l}$ and ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ , and (d) simulated curves of $G_{\max}^{}$ and $G_{\min}^{}$ vs. ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ for different beat lengths.

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Figures 1(a) and 1(b) show the behavior of ${\hat{s}}_{o u t}^{\max}$ which refers to the output SOP of signal light experiencing the largest SBS gain among all ${\hat{s}}_{i n}$ for each ${\hat{p}}_{i n}$ , with $L_{b} =$ 0.25 m and 40 m, respectively. In Fig. 1(a), $L_{b} =$ 0.25 m, each ${\hat{s}}_{o u t}^{\max}$ concentrates either at ${\hat{β}}_{l}$ (V) or at $- {\hat{β}}_{l}$ (H) point (see red circles). Whereas when $L_{b} =$ 40 m, ${\hat{s}}_{o u t}^{\max}$ scatters as shown in Fig. 1(b). Namely, the SOP of signal is multi-directionally pulled in low birefringence fiber for different ${\hat{p}}_{i n}$ , but orthogonally (bidirectionally) pulled to principal axes in high birefringence fiber for different ${\hat{p}}_{i n}$ .

Figure 1(c) presents the curves between ${\hat{s}}_{o u t}^{\max} \cdot {\hat{β}}_{l}$ and ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ for $L_{b} =$ 0.25, 5, and 40 m. As $L_{b} =$ 0.25 m or 5 m, where $2 π / L_{b} > > r_{0} I_{p}$ and the approximation in Eq. (6) is fully satisfied. ${\hat{s}}_{o u t}^{\max}$ performs excellent polarization switching effect between ${\hat{β}}_{l}$ and $- {\hat{β}}_{l}$ depending on the sign of ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ . Whereas for $L_{b} =$ 40 m, ${\hat{s}}_{o u t}^{\max}$ performs weaker switching effect due to the failure of the approximation of Eq. (6).

Figure 1(d) gives the simulated $G_{\max}^{}$ and $G_{\min}^{}$ vs. ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ for the three birefringence fibers. The largest $G_{\max}^{}$ and the smallest $G_{\min}^{}$ occur at ${\hat{s}}_{i n} \cdot {\hat{β}}_{l} = \pm 1$ . The SBS gains for other ${\hat{s}}_{i n}$ are between the curves of $G_{\max}^{}$ and $G_{\min}^{}$ . For fibers of $L_{b} =$ 0.25 and 5 m, when $| {\hat{p}}_{i n} \cdot {\hat{β}}_{l} | = 0$ , all signals with arbitrary ${\hat{s}}_{i n}$ experience the equal SBS gain of $G = e^{r_{0} I_{p 0} L}$ . Actually, $G_{\max}^{}$ and $G_{\min}^{}$ curves can also be calculated with Eq. (10). For the low birefringence case of $L_{b} =$ 40 m, there still exists a gap between $G_{\min}^{}$ and $G_{\max}^{}$ at $| {\hat{p}}_{i n} \cdot {\hat{β}}_{l} | = 0$ .

3. Experimental verification and discussions

3.1 OPS lasing in PMF SBS fiber laser

Based on this orthogonal SBS polarization switching effect in PMFs, we set up a ring-cavity SBS fiber laser (BFL) as depicted in Fig. 2, and observe the orthogonal polarization switchable lasing light by adjusting the input SOP of pump. In the BFL, the SOP of pump light from a tunable laser (TLS) is adjusted by a polarization adjusting set, consisting of a polarization controller (PC1), a polarizer (P), two 45°-aligned liquid crystal waveplates (LCs), and PC2, for producing desired input pump SOPs. The pump light is amplified by two erbium doped fiber amplifiers (EDFAs) and launched into the fiber ring cavity through an ordinary SMF circulator (Cir).

Fig. 2 Experimental setup of OPS-BFL, in which, TLS: tunable laser; P: polarizer; LC: liquid crystal waveplate; PC: polarization controller; EDFA: Erbium–doped fiber amplifier; Cir: circulator; PBS: polarization beam splitter; PSA: polarization state analyzer; OSA: optical spectrum analyzer; ISO: isolator; Osc: oscilloscope; C1 and C2: couplers; D1 and D2: optical detectors.

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The fiber ring cavity consists of a 20 m PMF, an isolator (ISO), and a polarization controller (PC3). The beat length of the PMF is ~3 mm, fully satisfying the approximation requirement of Eq. (6). The ISO is connected right after the PMF to ensure the SBS pulling effect occurring within the PMF for a clear polarization switching. The lasing light is detected by a 10% coupler (C1), and split by a 1:1 coupler (C2). One beam is split by a polarization beam splitter (PBS) for observing the time domain responses of the light beams orthogonally polarized in principal axes of the PMF by an oscilloscope (Osc). The other beam is used for observing the SOP by a polarization state analyzer (PSA) and the spectrum by an optical spectrum analyzer (OSA).

The entire cavity length of the BFL is around 21 m, with a free-space spectrum of around 10 MHz, which is comparable to the SBS gain bandwidth and enables the single longitude-mode lasing. PC3 is adjusted to ensure the polarization consistence within the cavity.

Figure 3 gives the measured polarization switching performance of the PMF-BFL with a group of 19- ${\hat{p}}_{i n}$ located on one half side of a large circle of the Poincaré sphere, as measured in Fig. 3(a). The generated ${\hat{p}}_{i n}$ pattern is obtained by properly setting the driving voltages of two LCs. We can carefully adjust PC2 to make ${\hat{p}}_{i n, 1}$ and ${\hat{p}}_{i n, 19}$ in accordance with the two principal axes of the PMF, thus the first 9- ${\hat{p}}_{i n}$ residing on the ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} > 0$ side, the last 9- ${\hat{p}}_{i n}$ on the ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} < 0$ side, and the middle one roughly at ${\hat{p}}_{i n, 10} \cdot {\hat{β}}_{l} = 0$ . The BFL begins to lase as the pump power output from EDFA2 exceeds 190 mW for arbitrary ${\hat{p}}_{i n}$ . Considering the measured loss of 2.1 dB between the output of EDFA2 and point 2, the corresponding input pump power is $I_{p 0} =$ 117mW. By switching ${\hat{p}}_{i n}$ in the order of 1-19-2-18-3-17…, the measured SOP of lasing light switches between two fully-polarized orthogonal SOP points $S_{β l}$ and $S_{- β l}$ sharply, as shown in Fig. 3(b). At the last case of ${\hat{p}}_{i n, 10}$ , it stays near the central point of the Poincaré sphere, and the measured DOP decreases to ~4%. Figure 3(c) gives the switch performance of normalized Stokes parameters measured by PSA. Figure 3(d) gives the normalized measurements of D1 and D2 synchronizing to the change of ${\hat{p}}_{i n}$ . Two orthogonally-polarized light beams split by PBS lase alternatively with decreasing light powers as $| {\hat{p}}_{i n} \cdot {\hat{β}}_{l} |$ declines.

Fig. 3 Experimental characterization of PMF-BFL: (a) the 19 generated ${\hat{p}}_{i n}$ ; (b) the measured SOP trajectory of lasing light, (c) the measured time recordings of normalized Stokes parameters, and (d) the normalized measured intensities of two orthogonally polarized light components by D1 and D2 as changing ${\hat{p}}_{i n}$ .

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Figure 4(a) gives the measured relationship between the lasing power normalized by $(I_{P i n} - I_{P i n 10}) / (I_{P i n 1} - I_{P i n 10})$ and ${\hat{p}}_{i n} \cdot {\hat{p}}_{i n, 1}$ , which agrees with the normalized simulation result of Fig. 1(d) by calculating $(G_{\max} - G_{\max, P_{i n} . β_{l} = 0}) / (G_{\max, P_{i n} . β_{l} = 1} - G_{\max, P_{i n} . β_{l} = 0})$ . Figure 4(b) shows the measured lasing spectrums for different ${\hat{p}}_{i n}$ by OSA, all in similar profiles. There is a power difference of 5.67 dB between the maximum case of #1 and the minimum case of #10, as shown in the insert of Fig. 4(b). According to Eq. (10), we can evaluate the SBS gain coefficient:

r_{0} = \ln (G_{\max, {\hat{p}}_{i n} \cdot {\hat{β}}_{l} = 1} / G_{\max, {\hat{p}}_{i n} \cdot {\hat{β}}_{l} = 0}) / I_{p 0} L = 0.2743.

It is comparable to the value of

r_{0} =0 .2229[W \cdot m]^{- 1}

used in simulations.

Fig. 4 (a) Measured and simulated relationships between the normalized $G_{\max}^{}$ and ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ ; (b) measured lasing spectrums for different ${\hat{p}}_{i n}$ .

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3.2 Discussions on fully polarized and depolarized lasing in PMF-BFL

Considering the loss-gain balance in the cavity at lasing threshold point, we obtain the relationship between the lasing threshold pump power $I_{P T H}$ and ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ from Eq. (10) as

I_{P T H} ({\hat{p}}_{i n} \cdot {\hat{β}}_{l}) = \frac{α_{d B} - 10 \lg (1 - K)}{4.34 \cdot r_{0} L (1 \pm | {\hat{p}}_{i n} \cdot {\hat{β}}_{l} |)},

where K is the coupling coefficient of C1,

α_{d B}

the cavity loss in dB. With the measured

α_{d B} = 2.25

dB,

r_{0}

= 0.2743, and K = 0.1, Eq. (12) can be depicted by Fig. 5 with four lasing regions: two orthogonally fully polarized regions of

\pm {\hat{β}}_{l}

, depolarized lasing region, and not lasing region. It is seen that only when

I_{p 0} = I_{P T H 0} = I_{P T H} ({\hat{p}}_{i n} \cdot {\hat{β}}_{l} = 0)

, the BFL performs OPS in all

{\hat{p}}_{i n} \cdot {\hat{β}}_{l} \neq 0

region. When

I_{p 0} > I_{P T H 0}

, the BFL performs OPS in two side regions of

| {\hat{p}}_{i n} \cdot {\hat{β}}_{l} | > | 1 - \frac{α_{d B} - 10 \lg (1 - K)}{4.34 r_{0} L I_{p 0}} |,

where only

G_{\max}^{}

mode resonates. Otherwise in the central region, both

G_{\min}^{}

and

G_{\max}^{}

polarization modes involve resonance, resulting in depolarized light. When

I_{P T H 1} = I_{P T H} ({\hat{p}}_{i n} \cdot {\hat{β}}_{l} = 1) < I_{p 0} < I_{P T H 0}

, the BFL lases fully polarized light at

\pm {\hat{β}}_{l}

in two side regions of the lower curve in Fig. 5, determined by Eq. (13) too.

Fig. 5 Polarization regions of lasing determined by threshold pump power and pump SOP.

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Figure 6 shows the measured lasing performance for different pump powers as ${\hat{p}}_{i n}$ changing orderly. Figure 6(a) shows normalized measurements of D1 and D2 for $I_{p 0} =$ 123, 117, 105, 93, and 80 mW, respectively. When $I_{p 0} =$ 117 mW, the BFL outputs fully polarized light at $+ {\hat{β}}_{l}$ or $- {\hat{β}}_{l}$ for all chosen ${\hat{p}}_{i n}$ with different output powers. When $I_{p 0} =$ 123 mW, there must have been a depolarized lasing region but it is too small to be measured, thus the BFL still performs OPS for the given ${\hat{p}}_{i n}$ . As pump power decreases from 117 mW, the BFL ceases lasing in the central regions where pump power is below lasing threshold. Therefore, by setting $I_{P 0} < I_{P T H 0}$ , the BFL may perform as a polarization filter to select those pump lights with SOPs within two required vicinities of ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} = \pm 1$ , and reshape them to $\pm {\hat{β}}_{l}$ .

Fig. 6 Normalized measurements of D1 and D2 as ${\hat{p}}_{i n}$ changing orderly (a) for different pump powers at point 2 of 123, 117, 105, 93, and 80 mW, and (b) for different pump powers of 130, 148, 179, 210, and 241 mW. (c) Synchronization measurements of DOP by PSA corresponding to the measurements of (b).

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Figure 6(b) shows normalized recordings of D1 and D2 for $I_{p 0} =$ 130, 148, 179, 210, and 241 mW, and Fig. 6(c) shows the corresponding degree of polarization (DOP) measured by PSA. When $I_{p 0} =$ 130 mW, the depolarized lasing light in the central region around ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} = 0$ starts to be observed. The depolarization region increases with the increment of pump power. Two orthogonally polarized lights lase simultaneously with different intensities as changing ${\hat{p}}_{i n}$ , resulting in different DOPs.

Therefore, only if pump power is set to $I_{P T H 0}$ , can the BFL perform OPS over the full region of ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} \neq 0$ .

To investigate the polarization modes of depolarized lasing light, the interference spectrum density of the BFL lasing light is also measured through an SMF Mach-Zehnder interferometer (MZI), where arm length difference is 23 km and the light of one arm is modulated with a 50 MHz RF signal through an electro-optic modulator. Figures 7(a) and 7(b) show measured spectrum densities of fully polarized lasing light at ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} \approx 1$ and of depolarized lasing lights at ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} \approx 0$ , respectively for $I_{p 0} =$ 154 mW. In Fig. 7(a), the single auto-interference peak implies only one polarization mode existing. Whereas, in Fig. 7(b), two side cross-interference peaks prove the coexistence of two polarization modes. Four measurements in 20 minutes are presented. From Eq. (10), all polarization modes have the same resonating priority from the aspect of SBS gain, but actually only those that are of polarization consistence in each loop could maintain resonance. Thus, only the polarization modes at two principal axes will resonate. Practically due to the fact that the resonating longitude modes of the two polarization modes generally do not occur at the top point of their SBS gain spectrums (in more detail, the SBS gain spectrums for two principal axes are about 2~3 MHz apart [21,22]), and are quite sensitive to cavity length due to the index change with temperature or strain, thus the space between the auto-spectral power peak and cross-spectral power peak keeps shifting with the unstable environment in our experiment.

Fig. 7 Measured spectrum densities of (a) fully polarized lasing light as ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} = 1$ and (b) depolarized lasing light as ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} \approx 0$ , for $I_{p 0} =$ 154 mW.

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3.3 Influence of pump depletion

The above OPS performance works under the assumption of free pump depletion. Actually pump depletion occurs all the time, especially in long fibers. To examine this we simulate the pump-depletion induced impairment on OPS. Figure 8 gives the simulation results for different input signal powers of 40, 20, 5, and 2 mW with $I_{p 0} =$ 80 mW and $L_{b} =$ 5 m. Other parameters are the same as those used in previous simulations. Figure 8(a) shows the distributions of $G_{\max}^{}$ and $G_{\min}^{}$ vs. ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ for different input signal powers. Figure 8(b) shows that the switching performance of ${\hat{s}}_{o u t}^{\max} \cdot {\hat{β}}_{l}$ will be impaired by larger signal powers. But if the ratio of $I_{p 0} / I_{s 0}$ is larger than 40, non-depletion assumption will still be reasonable.

Fig. 8 Simulated influence of pump-depletion on OPS performance: (a) distributions of $G_{\max}^{}$ and $G_{\min}^{}$ over ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ and (b) switching performance of ${\hat{s}}_{o u t}^{\max} \cdot {\hat{β}}_{l}$ , for different input signal powers with $I_{p 0} = 80$ mW.

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4. Conclusions

In this paper, we proposed and simulated the SBS axial polarization pulling effect in PMFs, where due to the regular linear birefringence, the overall SBS polarization pulling will head either for ${\hat{β}}_{l}$ or for $- {\hat{β}}_{l}$ , depending on the sign of ${\hat{p}}_{i n} \cdot {\hat{β}}_{l}$ . Based on this physics, we set up a normal PMF-BFL and demonstrated an OPS effect by changing ${\hat{p}}_{i n}$ between two half spheres divided by the large circle of ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} = 0$ on the Poincaré sphere. We measured the relationship between lasing powers and ${\hat{p}}_{i n}$ -location, with results consistent to the simulation prediction. Moreover, we discussed the influence of pump power on the behavior of polarization switching. It is found that the OPS for full ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} \neq 0$ range occurs only under the condition of $I_{p 0} = I_{P T H 0}$ , otherwise, OPS occurs partially for ${\hat{p}}_{i n}$ in two pump power dependent vicinities of $\pm {\hat{β}}_{l}$ . The depolarization lasing was also explored, which verified the understanding of the coexistence of two orthogonal polarization modes. At last, we also simulated the impairment of pump-depletion on OPS.

The discovered SBS axial polarization pulling in PMFs and the OPS behavior in PMF-BFL provide potential in polarization-related applications. For example, the two excellent switched orthogonal polarizations can actually be thought as the result of logic operation between ${\hat{p}}_{i n}$ and ${\hat{β}}_{l}$ . It may also perform as a polarization filter to select those SOPs in two orthogonal polarization regions and reshape them to $\pm {\hat{β}}_{l}$ . In addition, the equilibrium of SBS gain in PMF when ${\hat{p}}_{i n} \cdot {\hat{β}}_{l} = 0$ may also be utilized to replace the polarization scrambling in SBS sensing systems.

Funding

National Natural Science Foundation of China (NSFC) (61575118, 91750108).

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Orthogonal polarization switchable lasing based on axial polarization pulling of SBS in polarization-maintaining fiber

Abstract

1. Introduction

2. Principle and simulations

3. Experimental verification and discussions

3.1 OPS lasing in PMF SBS fiber laser

3.2 Discussions on fully polarized and depolarized lasing in PMF-BFL

3.3 Influence of pump depletion

4. Conclusions

Funding

References

Cited By

Figures (8)

Equations (13)

Optics Express