## Abstract

In this paper, we reported the realization of 2nd-order random lasing in a half-opened fiber cavity, which is formed by a FBG with central wavelength at the 1st–order Raman Stokes wavelength and a single-mode fiber (SMF) performing as a random distributed feedback mirror. Using this proposed method, the threshold of 1st-order (2nd-order) random lasing is reduced to 0.7 (2.0) W, which is nearly 2 times lower than that observed in a completely-opened cavity.

©2012 Optical Society of America

## 1. Introduction

Random lasers are disordered optical structures of stimulated emission in which light waves are both multiply scattered and amplified [1]. Hence, the feedback is provided by light scattering in a gain medium rather than a cavity, as in conventional lasers [2–7].

To overcome the problem of irregular and undirectional output characteristics of random lasers, low-dimensional random structures were proposed [3, 7, 8]. Recently, an important breakthrough in this research area was reported by Turitsyn et. al. [9]. They realized a stable continue-wave (CW) random lasing in a standard single-mode fiber (SMF) based on Raman amplified distributed Rayleigh scattering (RS) feedback. The SMF itself performs as the disorder medium, where RS captured by the fiber waveguide provides positive feedback and the pump-induced Raman gain provides light amplification. Compared with traditional random lasers, the random fiber laser (RFL) shows relative stable output, single-transverse-mode profile, long-distance emission and wide wavelength tunability, which are of great interest in optical communication and optical sensing [10, 11].

Based on similar principle, dual-wavelength random lasing was realized in a 200 km fiber span, wherein the RS performs as random distributed mirrors forming a cavity together with a FBG at each end of the fiber [12]. A tunable RFL with broad wavelength range was proposed [13]. Thanks to the ultra-long laser cavity, a RFL was also used in optical sensing to increase the transmission distance [14, 15]. Churkin et al. studied the output characteristics of RFLs under different operation regimes, wherein a half-opened cavity formed by a fiber Bragg grating (FBG) and a SMF can help reducing the laser threshold to about half, compared with a completely-opened cavity [16]. However, this studied only focused on the 1st-order random lasing.

Recently, Vatnik et al. [17] reported firstly cascaded (2nd-order) random lasing of optical fiber pumped by an ytterbium fiber laser. Due to the completely-opened cavity structure (i.e., the laser cavity is formed only by a span of optical fiber), 2nd-order random lasing needs a pump power of more than 6 W. In this paper, we proposed 2nd-order random lasing at a much lower threshold using a half-opened fiber cavity, wherein a FBG with central wavelength at the 1st-order Raman Stokes wavelength is placed at the pump side and a SMF performs as the gain medium as well as the distributed feedback mirrors [18].

## 2. Experimental results

The schematic diagram of the half-opened cavity random fiber laser (HOCRFL) is given in Fig. 1 . A Raman fiber laser with central wavelength of 1366 nm is used as the pump. The pump is launched into the fiber spool through a 1365/1461 nm wavelength division multiplexer (WDM). A FBG with central wavelength of 1454 nm and reflectivity of 0.979 is spliced between the common port of the WDW and the spool of 50 km SMF. The right tip of the SMF was angle-cleaved to avoid end reflection. The lasing characteristics are monitored at the right end of the SMF.

With the increase of pump power, 1st-order Stokes light generates. The generated light is feedback forwardly and backwardly in the SMF due to distributed RS. At the left end of the SMF, the backscattered light is selectively reflected by the FBG. This forms a multitude of resonant modes with random frequencies. However, since the reflection from the FBG is dominant, only the resonant modes within the refection spectrum of the FBG reach their threshold (when the Raman amplification overcomes the fiber loss) and begin to radiate first. For the 2nd-order Stokes light, resonant modes are formed only by distributed RS feedback, thus, those modes having the largest gain begin to radiate first.

Figure 2(a) and 2(b) give the output spectra of the HOCRFL for pump power at 0.701 and 0.911 W, respectively. In Fig. 2(a), the pump power is slightly beyond the threshold of the 1st-order random lasing. Numerous narrowband wavelength components are found in the output spectrum. These narrowband components change stochastically due to cascade Brillouin scattering effect. This is similar to the near-threshold operation regime of a RFL with a completely-opened cavity [9, 12]. However, because of the wavelength-selective reflection from the FBG, the bandwidth of random lasing is less than 0.3 nm in our case. When pump power increases, complex nonlinear interactions (i.e., four-wave mixing and phase modulation) take effect. As a result, the stochastic narrowband components are broadened and superposed, generating a uniform spectrum. This also suppresses Brillouin scattering dynamics, leading to stable CW random lasing as shown in Fig. 2(b).

With further increase of pump power, the spectrum of the 1st-order random lasing broadens. Its output power increases. For pump power beyond a critical value, the 2nd-order Stokes light also begins to emit. Figure 3 shows the output spectrum of the HOCRFL pumped at 2.265 W. In this case, that the 2nd-order random lasing is in the near-threshold regime, i.e., irregular dynamics and narrowband wavelength components appear in the spectrum, seeing Fig. 3(b). Figure 3(a) indicates that the 1st-order random lasing also exhibits similar output characteristics correspondingly. The 2nd-order random lasing has a relative broad spectrum that is determined by the gain profile, because the feedback is only provided by RS. This is the same to random lasing in a completely-opened fiber cavity.

Figure 4 shows the spectra of the HOCRFL pumped at 2.944 W. In this case, both the 1st and 2nd -order random lasing are stable. In Fig. 4(a), the 1st-order random lasing has a spectrum bandwidth of ~0.898 nm which is three times larger than the bandwidth of FBG. It is supposed that both the nonlinear effect and the 2nd-order random lasing contribute to the spectrum broadening. In Fig. 4(b), there are two peaks localized nearby the Raman gain maxima. The one at the shorter wavelength (1.55nm) with a bandwidth of ~1.183 nm is much more pronounced, which is similar to the results reported in reference [9].

Figure 5(a) shows the output power of the HOCRFL as a function of pump power. The dot and the triangle correspond to the 1st and the 2nd -order random lasing, respectively. The threshold pump power for 1st (2nd) -order random lasing is found to be ~0.7 W (~2 W). Obviously, the threshold of 1st and 2nd –order random lasing is much smaller for the HOCRFL than for a RFL with a completely-opened cavity [17]. It is also observed that the power of 2nd-order random lasing exceeds that of the 1st-order when pump power is larger than ~2.4 W.

For comparison, we also studied the output power of a RFL with a completely-opened cavity. The RFL has a same structure as described in Fig. 1, except that the FBG is removed. Figure 5(b) indicates that the threshold of 1st-order random lasing is ~1.4 W, and no obvious 2nd-order random lasing is observed for pump increased to 3.5 W. Hence, the use of a FBG at one side of the laser cavity can help to reduce the lasing threshold greatly, while keeping random lasing characteristics of the laser.

## 3. Theoretical analysis

The lasing characteristics of the HOCRFL can be analyzed theoretically using the steady-state light propagation equations [9, 12, 19].

*P*

_{0,1,2}denotes the optical power,

*z*denotes the coordinate of the wave propagation direction,

*a*

_{0,1,2}( = 0.306, 0.24, 0.193 dB⋅km

^{−1}) is the fiber loss,

*g*

_{1,2}( = 0.54, 0.44 W

^{−1}km

^{−1}, respectively) is the Raman gain index,

*ε*

_{0,1,2}( = 1 × 10

^{−4}, 6 × 10

^{−5}, 4.5 × 10

^{−5}km

^{−1}, respectively) is the Rayleigh backscattering coefficient,

*f*

_{0,1,2}( =

*c*/

*λ*

_{0,1,2},

*c*is the vacuum light speed and

*λ*

_{0,1,2}is the wavelength) is the wave frequency. The symbol Γ

_{1,2}denotes the population of phonon, where Δ

*f*

_{1,2}( = 0.05, 0.17 THz, respectively) is the lasing bandwidth,

*h*is the Plank’s constant,

*K*is the Boltzmann’s constant and

_{B}*T*( = 298 K) is the absolute temperature of the laser.

It is worth mentioning that the value of *a*_{0,1,2} are experimentally tested, while *g*_{1,2} and *ε*_{0,1,2} are fitting parameters based on typical experimental values [16, 17, 19, 20]. To better fit our experimental results, values of *g*_{1,2} are chosen slightly larger (the increase is less than 5%) than that given in the references, and a 0.8 dB insertion loss (experimentally tested value) at the output end is considered. The boundary conditions are${P}_{0}^{+}(0)={P}_{in}$ and ${P}_{1}^{+}(0)={R}_{1}{P}_{1}^{-}(0)$, where *P _{in}* denotes the pump power, and

*R*

_{1}is the reflectivity of the FBG. Taking these conditions into consideration, the model can be solved numerically through the shooting method. In the simulation, Eqs. (1)–(3) are integrated along the

*z*direction to get the power distribution of the forward (backward) propagating waves, ${P}_{1,2,3}^{+}(z)$[${P}_{1,2,3}^{-}(z)$], using guessed value of ${P}_{1,2,3}^{-}(z)$[${P}_{1,2,3}^{+}(z)$] as the know condition. Then the guessed power distributions are replaced by the integration results, and a next integration of Eqs. (1)–(3) is done to renew the values of ${P}_{1,2,3}^{\pm}(z)$. This procedure is repeated untilled the difference of results between the last two integrations are less than 10

^{−5}.

The solid and doted curves in Fig. 5 correspond to the numerically calculated output power of the 1st-order and 2nd-order random lasing, respectively. It is seen that the numerical results are in accordance with the experimental results. The small mismatch might arise from the ignoring of spectrum characteristic and nonlinear effect in the theoretical model.

Using the same numerical method, the power distribution of the RFL along the fiber length is simulated in Fig. 6 . The pump power is chosen at 1.8 W. The solid and dotted curves correspond to the forward and backward propagating light, respectively. For the completely-opened cavity (see Fig. 6(b)), the backward propagating light is relative strong at the pump side. For the half-opened cavity (see Fig. 6(a)), the FBG feedback most of the backward propagating light which re-enters the SMF and is re-amplified by the pump, changing the power distribution and reducing the laser threshold considerably.

## 4. Conclusions

In summary, we have studied the 2nd-order random lasing in a half-opened fiber cavity. Due to the wavelength-selective feedback of FBG, the threshold of 1st-order and 2nd-order random lasing are reduced to 0.7 and 2.0 W, respectively, which is much smaller than that of a completely-opened cavity. For the 1st-order random lasing, the laser cavity is half-opened (i.e., the central wavelength of the FBG is at the 1st Raman stokes wavelength), so the lasing does not correspond to a certain cavity resonance. It has random lasing characteristics with spectrum tailored by the FBG. For the 2nd-order random lasing, the cavity can be thought of as completely-opened, so the spectrum of random lasing is determined by the Raman gain.

In fact, the central wavelength of the FBG can be changed intentionally to control the wavelength of the 1st and 2nd -order random lasing. Besides, there also exists a relative wide range of pump power, where the 1st and 2nd -order random lasing coexist. These characteristics provide a flexible method to generate high-order or mixed-order random emission, which may found its applications in optical communication as well as optical sensing.

## Acknowledgment

The authors would like to thank Dr. X. F. Chen and Prof. L. Zhang in Aston University for providing the 1454nm FBG. This work is supported by the National Natural Science Foundation of China under Grant 61106045 and the Fundamental Research Funds for the Central Universities under Grant 2011J001.

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