1. Introduction

It is known that the output characteristics of random lasers are defined by the processes of multiple random scattering in an amplifying disordered medium (see [1] for a review), in contrast to conventional lasers where light is trapped in a cavity providing regular mode structure. Different types of disordered media are usually used for random lasing, for example, powders of laser crystals or semiconductors, laser dye suspensions with scattering particles, either as a bulk material or as a fluid filled in a hollow fiber waveguide [2]. It has been shown recently [3] that conventional fibers can also exhibit random lasing properties due to the natural randomness of silica glass leading to Rayleigh backscattering of propagating light. Although the integral Rayleigh reflection in a long single-mode fiber is weak (R~0.1% at ~1.55 μm), the system may overcome lasing threshold if a distributed amplification is provided, e.g. via stimulated Raman scattering. Such random fiber laser can generate stable narrow-band laser radiation in simple and reliable configurations comprising only a passive fiber free of cavity elements (mirrors, frequency selectors, etc.) and a source of pump radiation coupled somehow to the fiber, see [4] for a review. In this sense, the random fiber laser resembles conventional distributed feedback (DFB) fiber lasers [5], but instead of a regular grating inscribed in a short active fiber with population-inversion based gain it employs a weak random grating of natural origin that becomes important in a long passive fiber with pump-induced Raman gain, so it may be called random DFB fiber laser.

One of the intensively studied random DFB fiber laser configurations is the scheme with coinciding directions of pump and output Stokes waves. It has been shown in [6] that the total efficiency of random DFB fiber laser with co-directional pumping decreases exponentially with fiber length that is defined by linear attenuation of pump and laser light in the fiber. So, shortening of the fiber below the characteristic absorption length (~10 km) may sufficiently enhance the laser efficiency, but the threshold pump power will be increased too. So, finding a balance between these factors can result in high efficiency at moderate pumping. Indeed, length reduction to 850 m [7] resulted in record efficiency of the Stokes wave generation amounting to ~70% absolute optical efficiency and ~100% relative quantum conversion efficiency at 11 W pumping provided by conventional Yb-doped fiber laser (YDFL).

Here we study an opportunity to obtain high-efficiency cascaded generation of the next Stokes orders in the forward-pumping scheme of random laser based on the relatively short phosphosilicate fiber with YDFL-induced Raman gain expecting to reach sufficiently higher power and efficiency than in previous realizations of cascaded random fiber lasers with lengths of 2-50 km [8, 9]. In contrast to conventional Raman fiber lasers with cascaded cavity [10–12], where intermediate Stokes components experience sufficient nonlinear losses due to spectral broadening [13], the studied random DFB fiber laser has no cavity and corresponding losses as well.

2. Experimental setup

The phosphosilicate fiber used as Raman medium is featured by a P₂O₅-related component with large Stokes shift value (~1330 cm⁻¹) in addition to a standard Si0₂ component (with several peaks grouped around 450 cm⁻¹), at that both components are used in cascaded Raman lasers [10–12]. To obtain cascaded random lasing at the available pump power (11 W) the fiber length (L = 1.65 km) is doubled in comparison with the one-stage laser in [7]. An experimental scheme of the studied random DFB fiber laser is shown in Fig. 1 together with spectral dependence of the fiber losses.

 

Fig. 1 (a) A scheme of the random DFB fiber laser based on 1.65-km phosphosilicate fiber. (b) Spectral dependence of loss coefficient α in the phosphosilicate fiber.

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Single-mode pump radiation of a 1115-nm Yb-doped fiber laser is coupled to the phosphosilicate fiber via 1115-nm port of 1115/1310 nm wavelength-division multiplexer (WDM). At that, 1310-nm WDM port is terminated by a fiber loop mirror made of 50:50 fused fiber coupler in order to reduce threshold for the lasing based on Rayleigh backscattering distributed along the Raman fiber spliced to the common port of the WDM coupler. An output fiber end is cleaved with an angle of >10⁰ to eliminate Fresnel reflection.

3. Results

Lasing threshold for the first Stokes component (1308 nm, P₂O₅-related) is reached at 3 W pumping, whereas cascaded generation of the second Stokes component (1398 nm, SiO₂-related) is started at 8 W pumping, see Fig. 2(a).Corresponding spectra for the first and second Stokes components are shown in Fig. 3.A sufficient narrowing of the first Stokes component spectrum due to the presence of feedback occurs near the threshold, see Fig. 3(a), with significant broadening at increasing power due to nonlinear processes, similar to conventional Raman fiber lasers [13]. Above the threshold of the cascaded generation, a considerably broader spectrum of the second Stokes component arises, Fig. 3(b). Its width is defined by the SiO₂-related peak that is broader than the P₂O₅ peak of the Raman gain spectrum in phosphosilicate fibers [10]. The second Stokes spectra are also featured by the fine structures that are related to the atmospheric water absorption near 1.4 μm, the broad water-related peak is also seen in the fiber loss spectrum, see Fig. 1(a). Note that the generation of the second P₂O₅-related Stokes component (near 1.58 μm) is suppressed in the studied scheme because of the increasing losses in the fiber loop mirror, WDM and fiber itself, Fig. 1(b). It’s clearly seen that the losses rise steeply at ≥1.5 μm, mainly due to considerable bending of the fiber in the spool.

 

Fig. 2 (а) Output power for the pump wave at 1115 nm (blue), the first Stokes wave at 1308 nm (orange) and the second Stokes wave at 1398 nm (red) at the angled-cleaved fiber end; (b) corresponding absolute optical efficiency (squares) and relative quantum efficiency (crosses) for conversion of pump power to the first (orange) and the second (red) Stokes waves.

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Fig. 3 Spectra of the Stokes components at different pump powers: (a) first, and (b) second.

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Figure 2(a) shows that below the lasing threshold only transmitted pump power at 1115 nm is measured at the output end that is related to the input pump power via linear attenuation factor, $P_p^{out}/P_p^{in}=\exp (-{\alpha }_{p}L)\approx 0.54$. A linear fit for the dependence $P_p^{out}(P_p^{in})$ is shown by the dashed line. Above the first lasing threshold ($P_p^{in}$> 3 W), transmitted pump power $P_p^{out}$ deviates deeply from the linear fit demonstrating almost full depletion already at $P_p^{in}$~5 W. Herewith, the generated first Stokes power $P_{1s}^{}$approaches this linear fit demonstrating almost full conversion of the pump radiation to the wavelength of 1308 nm with maximum power $P_{1s}^{}$≈4 W at $P_p^{in}\approx$7.5 W. Above the second threshold ($P_p^{in}$>8 W), the transmitted power for both the pump and the first Stokes waves tends to zero, while the second Stokes output power $P_{2s}^{}$grows towards the same linear fit for the transmitted pump power (dashed line) reaching 5.2 W at $P_p^{in}\approx$11.1 W.

An absolute optical efficiency calculated as a ratio of the corresponding output power $P_{is}^{}(i=1,2)$ to the input pump power $P_p^{in}$amounts to about 53% and 47% for the first and the second Stokes waves, accordingly (squares in Fig. 2(b)). The efficiency for the first Stokes generation is even higher than the maximum possible efficiency calculated according to formula ${\eta }_{\max }=\exp (-{\alpha }_{p}L)h{\nu }_s/h{\nu }_p=0.48$, obtained in [6] for pump to Stokes wave (with corresponding frequencies ν_p,s) conversion in random fiber laser under the assumption of equal attenuation factors, α_p≈α_s. The above values mean also nearly 100% efficiency for the process of first-to-second Stokes wave conversion inside the fiber. Note that we haven’t adjusted the setup parameters to obtain such a high efficiency, but the results appear to be comparable and even higher than those obtained in well-optimized configurations of a two-stage Raman laser with cascaded cavity made of fiber Bragg gratings (FBGs) [12, 14].

To analyze the obtained data in more detail, we calculated the number of photons emitted from the laser output, $N_{is}^{out}=P_{is}^{out}/h{\nu }_{is}$, for both Stokes waves (i = 1,2). If one relates these numbers to the number of pump photons reaching far end of the fiber span in a passive regime (if no generation of the Stokes wave is supposed) given by $N_p^{out}=P_p^{in}{e}^{-{\alpha }_{p}L}/h{\nu }_p$, we can obtain relative quantum efficiency for conversion of the pump photons to the generated photons at the fiber output (z = L). Doing this, we have found that the transfer of energy to the new spectral band in the cascaded random fiber laser is accompanied by the increase of output photon number for the first Stokes wave (before second threshold), $N_{1s}^{out}/N_p^{out}=1.09$, and even for the second Stokes wave, $N_{2s}^{out}/N_p^{out}=1.03$, in the high-power limit, see Fig. 2(b). Since pump photons are fully converted into the Stokes photons these limiting values characterize the ratio of generated photon to absorbed pump photon numbers, i.e. the relative quantum efficiency. Increase of this ratio above 1 for the first Stokes wave may be explained in analogy with [7]: pump-to-Stokes conversion occurs in the short fiber part near WDM, while Stokes wave has lower attenuation at its propagation along the fiber. Appearance of the second Stokes component changes longitudinal distributions of all waves, therefore it is necessary to study this case too.

To do that we calculate longitudinal power distributions using the power balance model, similar to [15], reducing it to photon numbers by normalization on corresponding quantum energy, similar to the experimental data processing above. Then the obtained photon numbers$N_{is}^{}(z)$ have been normalized to the number of input pump photon $N_p^{in}(z=0)$, corresponding distributions are shown in Fig. 4(a).Using the model we can also calculate the values of output power for all three waves and compare them with the experimental data. These calculations have been performed with the following parameters that correspond to the experiment: Raman gain is$g_{1s}=1.35$, $g_{2s}=1.05$1/W/km for the first and second Stokes waves correspondingly, total losses (including contributions of the distributed losses arising from Rayleigh scattering and microbending and of the lumped losses at splice points) are ${\alpha }_p=0.35$, ${\alpha }_{1s}=0.2$, ${\alpha }_{2s}=0.3$1/km, Rayleigh backscattering factor is Q = 0.0017. A comparison of the calculated and measured powers, Fig. 4(b), show their good agreement except small deviations at high pump powers. This allows us to use the model for a quantitative analysis of longitudinal distributions.

 

Fig. 4 (a) Variation of relative number of photons along the fiber for the pump wave (blue curve), first Stokes wave (orange curve) and second Stokes wave (red curve). The photons distribution for linear pump attenuation is shown by blue dashed line. Calculations are made for 10 W input pump power. Orange dashed line – first Stokes wave at 7.5 W pump power (below second threshold). (b) Comparison of the calculated and experimental values for output power of the pump, first and second Stokes components (the same color map, lines are numerics while squares are experiment).

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Without lasing only the pump wave with linear attenuation is present (blue dashed line). Well above the first threshold, the pump wave is almost fully converted into the first Stokes wave at first hundreds meters, corresponding distribution of the first Stokes wave at its maximum output power (near the second threshold) is shown by orange dotted line. Since attenuation of the Stokes wave is lower than that for the pump wave, corresponding number of photons at the output end increases. Note that backward Stokes wave is much weaker, though it is taken into account in the round-trip gain-to-loss balance, making this scheme principally different from the amplified spontaneous emission without feedback (see [7] for more details).

Well above the threshold of the second Stokes wave generation (solid lines in Fig. 4(a)), the first Stokes distribution takes a specific shape with maximum in the center of the fiber and negligibly small values at both fiber ends. So, it is almost fully converted into the second Stokes wave inside the fiber, whereas the second Stokes wave reaches its maximum at the fiber output end. Herewith, number of photons for the second Stokes wave at the exit becomes exceeding that for the undepleted pump wave in the absence of generation. Taking into account the rest 1st Stokes photons the excess for all generated photons is more than 15%.

3. Discussion

So, the main feature of the cascaded random fiber laser is the specific longitudinal power distribution with separation of components along the fiber: pump wave is fully depleted in the first third of the fiber length while the second Stokes wave is generated in the last third of the fiber and the intermediate first Stokes wave is naturally trapped in between. Note that similar separation of components is observed recently in the pulsed cascaded Raman fiber laser with low-reflection point-action output mirror [16]. Lower attenuation for the Stokes waves results in increasing number of photons at the output end as compared with linearly attenuated pump photons. Herewith, at the maximum laser power, practically full conversion of the pump wave as well as intermediate first Stokes wave into the second Stokes wave occurs. This is quite different from the case of cascaded Raman fiber laser (RFL) with linear cavity, where distributions of components overlap. In conventional RFLs the first Stokes wave is trapped in the intermediate cavity made of highly-reflecting FBGs providing nearly constant intensity along the fiber [17]. High intensity inside the cavity leads to nonlinear spectral broadening resulting in high losses at reflection from relatively narrowband FBGs and to efficiency reduction as a consequence [18,19]. Besides, the condition of gain to loss balance for the intermediate component in the laser cavity also leads to an increase of the residual pump power at the output end with the increase of the second Stokes power, in order to compensate extra losses by means of increasing integral (over length) pump-induced gain. Because of the random (broadband and distributed) nature of the feedback in our case, the effects reducing the efficiency of cascaded generation are fully eliminated due to the self-consistent spatial redistribution of the pump and Stokes waves along the cavity-free fiber span.

Specific distributions of the components in the cascaded random fiber laser also explain the fact that the spectral width of the first Stokes component doesn’t decrease with decreasing its output power while the second Stokes component is generated (see Fig. 3(a)). The next Stokes orders can be also generated in this scheme at higher pump power and/or longer fiber, more efficiently than in very long systems at 1.55 μm [20]. The length of the cascaded random fiber laser may be optimized in terms of the maximum power at the desired Stokes component for the available pump power. At high pump powers (100-200 W) much shorter fibers (≤100 m) may be employed that will result in further increase of the absolute optical efficiency of random Raman lasers. It is expected that the higher efficiency and output power than that for the 150 W Raman fiber laser with FBG cavity [21] is possible for the cavity-free random fiber laser, and not only for the first Stokes wave. It is also promising to combine this approach with the direct high-power LD-pumping of gradient-index fibers [22]. One should also compare pump-to-Stokes intensity noise transfer in the random fiber laser with that in conventional cascaded RFLs [23].

4. Conclusions

We have obtained high-efficiency cascaded generation in random distributed feedback Raman fiber laser with ~100% relative conversion efficiency of the absorbed pump photons into the second Stokes wave photons. The obtained values for absolute and quantum conversion efficiencies are considerably higher than maximum efficiencies demonstrated before in random fiber lasers [8,9], as well as in the 1.4-μm phosphosilicate Raman fiber laser with linear cavity formed by fiber Bragg gratings [11], and the 1.48-μm phosphosilicate fiber laser with the linear cavity of length shortened down to ~50 m [12].