1. Introduction

Random distributed- feedback Raman laser (RD-RFL) is a new kind of fiber laser assisted by random Rayleigh feedback within optical fiber. It has attracted lots of attention since the first demonstration reported by Turitsyn et al [1], due to its many unique characteristics and huge application potential [2,3 ]. Moreover, RD-RFLs retain many merits from fiber lasers such as high conversion efficiency and simplicity. Recent theoretical and experiment work have demonstrated that RD-RFLs with short cavity fiber could achieve high conversion efficiency [4–6 ]. Besides, RD-RFL has been demonstrated recently the potential to perform as Q-switched fiber laser through Stimulated Brillouin scattering [7]. Furthermore, RD-RFLs with different configurations have various useful features. For example, RD-RFL with complete open cavity shows thermal stability [1,8 ], and RD-RFL with narrow band filter could generate narrow line-width random lasing [9]. Besides, the concept of RD-RFL can be further developed using stimulated Brillouin scattering instead of Raman scattering [10,11 ].

The first-ever reported RD-RFL has a completely open cavity, which is consisted of only a section of single mode fiber (SMF). Many efforts have been made towards reducing the threshold of RD-RFL and generating higher order of lasing, such as using special/active fiber [12,13 ] and designing new cavity structure [14–16 ]. Intuitively, a section of fiber and an FBG is an easy way to form a half-open cavity as in [14]. However, FBGs have some major drawbacks in terms of stability, complexity of fabrication (especially for special wavelength or special fiber), etc. Fiber loop mirror (FLM) serves as another substitute is used to form half-open cavity and generate higher order random lasing [4,17 ] because of its broadband. Moreover, FLM is preferable to be chosen to generate cascaded random lasing with relative lower threshold [18] or higher efficiency [19] while open cavity is still able to generate high-order random lasing with relative high threshold [20]. However, in [18,19 ] the output power is highly nonlinear with regard to the pump power. Recently [15], proposed using low-reflective mirror instead of FBGs and FLM to generate high power lasing, according to the fact that RD-RFL’s properties are sensitive to the small reflection added on the fiber end. In detail, the weak reflection can change the power distribution of random lasing along the cavity, thus influences the threshold and output properties.

In this paper, we propose a novel scheme to form a cascaded RD-RFL assisted by Fresnel reflection, which is promising for high power RD-RFL at new spectral range because of its simplicity and flexibility. We numerically study the power distribution, conversion efficiency and some other key lasing performances of such RD-RFLs. A cascaded RD-RFL assisted by Fresnel reflection is experimentally demonstrated. The simulation and experimental results confirm that weak reflection provided by Fresnel reflection is strong enough to generate cascaded random lasing with proper cavity length. Moreover, for 2^nd order random lasing, it is a backward pump structure thus the output power increase linearly with pump power [21], which is necessary in the applications that need accurate power control [22].

2. Operation principles and simulation results

Figure 1 shows the schematic setup. Without loss of generality, we use an ytterbium-doped fiber laser (YDFL) operating at 1090 nm as pump source. The corresponding first and second Stokes wavelengths are 1140 nm and 1200 nm, respectively. The pump is launched into the fiber cavity via an isolator and a wavelength division multiplexer (WDM). A spool standard single mode fiber (SMF) performs as the Raman gain medium and random distributed feedback mirrors. According to [15], the forward-pumping RD-RFL can be achieved using a low-reflective mirror. Therefore, in this work, a fiber jumper with a FC/PC end is spliced to the 1140 nm port of WDM1, which provides Fresnel reflection for the 1^st order random lasing at the pump side. At the far end of the fiber cavity, another FC/PC jumper is spliced to the 1200 nm port of WDM2, which reflects the 2^nd order random lasing. Apart from the above-mentioned ports, all other ports are angel-cleaved to minimize the end reflection.

 

Fig. 1 Schematic setup (WDM: wavelength division multiplexer, ISO: isolator).

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Based on the schematic setup, we calculate the 1^st- and the 2^nd- order random lasing power distribution along the fiber cavity, in forward and backward directions when the pump power is 8.75 W. The theoretical model and the fiber parameters are following [5]. The reflectivity of the flat-end of the FC/PC connector is experimentally measured ~0.02. In addition, due to the finite isolation of the WDM1 at pump side, 1140 nm port will provide parasitic reflectivity (estimated as 0.00002, assuming a typical 30 dB round-trip isolation of a WDM) to 1200 nm lasing light and vice versa. The calculated power distribution results are shown in Fig. 2(a) . Obviously most of 1140 nm lasing power propagates forward, because Fresnel reflection for this wavelength is placed at the pump side while the 2^nd order random lasing propagates backward. According to the simulation results, we will monitor the 1^st order random lasing power at the right end of the SMF, while the 2^nd order lasing will be monitored at the left end of the SMF.

 

Fig. 2 (a) Power distribution of forward and backward lasing power with 5 km cavity and 8.75 W pumping power; (b) power distributions of forward and backward lasing power with 1km fiber cavity and 23 W pumping power.

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As a comparison, the power distributions of forward and backward lasing with 1km fiber cavity are calculated, as shown in Fig. 2(b). Actually, to achieve equal 2^nd order output power to the case with 5 km fiber cavity, we have to adjust the pump power to 23 W in the case with 1km fiber cavity. Moreover, the power of 1^st order Stokes component is much higher than the cascaded Stokes. It is because of the high threshold of 2^nd order lasing and significant threshold gap between 1^st and 2^nd order lasing; as a result, huge power of 1^st order lasing is stored in fiber cavity hence the slope efficiency of 2^nd order random lasing is high. In addition, if the fiber is shorter, the attenuation is weaker thus it further increases the slope efficiency.

According to the above analysis, one can conclude that short cavity RD-RFL is able to generate high slope efficiency output though the threshold is relatively high. Such similar conclusions about 1^st order random lasing are obtained in recent papers [5]. Nevertheless, the previous work didn’t analyze 2^nd order random fiber lasing with linear output, especially the case with Fresnel reflection which should be simpler and more stable and than other point reflectors within previous half-open cavity RD-RFLs. Similar to [21], we calculate the relationship between slope efficiency (2^nd order) and fiber length based on the schematic setup shown in Fig. 1. The calculated result is shown in Fig. 3(a) . As expected, the slope efficiency is the highest (87.3%) when the fiber length is the shortest (1 km) and the slope efficiency decreases by approximately exponential with fiber length increasing. When the fiber length exceeds 20 km, the slope efficiency is below 40%, which is a significant drop from the peak value.

 

Fig. 3 (a) Slope efficiency vs. fiber length; (b) threshold vs. fiber length.

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Furthermore, the thresholds (2^nd order) with different cavity lengths are calculated, as shown in Fig. 3(b). Obviously, when the fiber is shorter the threshold will be higher, for both 1^st- and 2^nd- order random lasing. It could be understood as that the accumulated Raman gain and the distributed feedback effect are weak when the fiber is short thus it needs more powerful pump to generate random lasing light. According to our calculation, when the fiber length is 1km the threshold of 2^nd order random lasing is 21 W, and it decreases to 5.6 W under the case with 5 km fiber length. However, as the fiber length increases further, the attenuation resulted by the fiber becomes significant thus the effect of gain would be weakened by fiber attenuation.

Finally, in order to achieve the highest conversion efficiency (at 2^nd order Stokes wavelength) for the target output power range, we study the influence of the fiber length. The conversion efficiency is defined as the ratio between 2^nd order output lasing power and pump power. Figure 4 presents the results and the colorbar represents the quantitive efficiency values.

 

Fig. 4 Conversion efficiency (2^nd order output) vs. fiber length and output power.

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Different cavity fiber lengths result in different threshold and slope efficiency. It is clear that if the fiber length is fixed, the conversion efficiency increases with output power and approaches to slope efficiency gradually. However, because of generation of next order random lasing, the conversion efficiency isn’t able to increase infinitely. Therefore, the conversion efficiency is subject to fiber length and targeted output power. Apparently, this result provides us a guideline about how to optimize the cavity length according to the needed output power range.

3. The experimental demonstration

According to the above analysis and considering the ability of our pump source, we select the SMF length as 5 km in our experiment. The cascaded RD-RFL assisted by Fresnel reflection is built, following the schematic setup shown in Fig. 1. In the experiment, we monitor the 1^st order random lasing power at the right end of the SMF cavity, while the 2^nd order lasing is monitored at the left end of the SMF cavity. Figure 5 shows the input-output curve of the proposed RD-RFL. The star and triangle markers in Fig. 5 represent output power versus pump power for 1^st- and 2^nd order random lasing, respectively. As expected, the output power of 2^nd order random lasing increases linearly with pump power above the threshold. The 2^nd order lasing experimental data are linearly fit (blue solid curve in Fig. 5), and the slope efficiency is calculated as 48.8% and the R² coefficient is 99.87%. Also, the thresholds of 1^st- and 2^nd order random lasing are measured as 2.4 W and 4.6 W, respectively. The maximum achievable output power of 1140 nm is 1.6 W, and the maximum generated output power of 1200 nm is 1.98 W (after calibration), limited by the 8.75 W pump power. Also, we calculate the input-output curve using the calibrated fiber parameters. In detail, the isolation of 1140 nm port to 1200 nm Stokes light is 10 dB, and the isolation of 1200 nm port to 1140 nm Stokes light is 17 dB. So the parasitic reflectivity is set to be 0.002 and 0.0004 respectively for 1200 nm and 1140 nm lasing; the 2^nd order Raman gain coefficient is set to be 0.78 W⁻¹km⁻¹. The simulation results are shown as red line in Fig. 5. It can be seen that the simulation curve matches the experimental data well.

 

Fig. 5 Experimental and simulation results of lasing power vs. pump power.

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The optical spectra of generation random lasing are also recorded, as shown in Fig. 6 . We record the spectrum of 1^st order random lasing when the pump power is 2.74 W, which exceeds the threshold of 1^st order lasing and below the threshold of cascaded generation. The 2^nd order random lasing’s spectrum are measured when the pump power is 8.42 W. As one can see, there is ~9 nm wavelength spacing between the two peaks at each order output which is determined by the Raman gain profile. In detail, the 1^st order random lasing has a typical RD-RFL spectrum profile [1]. However, the left peak of 2^nd order random lasing spectrum tends to be divergent. It is due to a small fraction of Stokes light penetrated into the YDFL through the 1090 nm isolator under high pump power, which results in the disturbance of YDFL pump light [20].

 

Fig. 6 Spectra of 2^nd order random lasing (inset: spectra of 1^st order random lasing).

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Finally, to ensure the random lasing behavior of 2^nd order random lasing, the radio frequency (RF) spectrum is recorded with 8.75 W pump power. A 125 MHz photo-detector and an electrical oscilloscope (500 MHz) are used, and the frequency resolution is set as 50 Hz. The results are shown in Fig. 7 . It is clear that there is no longitudinal mode beating corresponding to c/2nl ≈ 20 kHz spacing, although the parasitic reflectivity is not trivial. Moreover, to further investigate the RF characteristics, we analyze the full 125 MHz spectrum of 2^nd order random lasing and pump source as inset in Fig. 7, with 100 kHz frequency resolution. It can be seen that the 1200 nm lasing inherits the resonance frequency (~11.4 MHz) from the pump source.

 

Fig. 7 0-125kHz RF spectrum of the cascaded random lasing output (frequency resolution: 50 Hz), inset: 0-125MHz spectrum of cascaded random lasing and pump source (frequency resolution: 100 kHz).

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4. Conclusions

We design a cascaded RD-RFL assisted by Fresnel reflection, which is with great simplicity and high-efficiency. Although Fresnel reflection only provides very small reflection, it is sufficient to assist the random lasing inside the fiber cavity. We simulate the power distribution, conversion efficiency and some other performances of the proposed system; the results could provide the necessary information to build such cascaded RD-RFLs with highest conversion efficiency for the targeted output power. The experimentally demonstrated 2^nd order random lasing output is linear with 48.8% slope efficiency, and the maximum output lasing power of 1200 nm is ~2 W (limited by 8.75 W pump power). Moreover, the modeless feature of the cascaded lasing is demonstrated. The proposed scheme facilitates the RD-RFL operating at new wavelength ranges, and the linear output feature is favorable in various applications.