1. Introduction

Random distributed feedback (RDFB) Raman fiber lasers turned out to be a promising light source [1–3] with simple design owing to the nature of the Rayleigh backscattering caused feedback, presenting in every optical fiber, and Raman amplification which is simply achieved as powerful pump sources are commercially available nowadays. RDFB lasers versatility can be attributed to the all-fiber architecture and a number of unique properties including multi-wavelength generation [4–6] using spectral filters, high power operation with high efficiency [7–9]. Thus, RDFB lasers exhibit generation efficiencies approaching the quantum limit for both random and linearly polarized radiation [9,10], and demonstrate possibilities for special regimes of generation such as efficient Q-switching [11,12].

Up to date, some good attempts have been done for studying mechanisms of generation spectrum formation of random distributed feedback fiber laser. It’s known [1] that above the threshold the generation spectrum becomes much narrower than the spectral profile of the Raman gain (∼10 nm). Well above the threshold, the generated spectrum exhibits power broadening: the higher is the pump power, the broader is the generation spectrum. The observed spectral broadening is somehow similar to spectral broadening in conventional Raman fiber lasers. Recently, a kinetic model was proposed [13] that satisfactorily describes nonlinear broadening of the first Stokes component spectrum above the threshold using integral equations. This model was further developed in [14] where analytical solution providing good predictions for higher Stokes orders has been given.

It should be noted that the kinetic theory [13] was performed and its experimental verification has been made for a phosphosilicate fiber which has a single peak in Raman gain spectral profile. However, many of RDFB lasers demonstrated so far were based on conventional germano-silicate fibers and operated without adding spectral filters, thus they have a more sophisticated spectrum with double-humped shape because of Raman gain profile consisting of two peaks of virtually equal strength. Each of these subcomponents within a single Stokes component may have its own dependence on pump level [3, 14–16]. While it’s possible to avoid multipeak fine structure in a generated Stokes component by spectral filters such as fiber Bragg gratings, an acousto-optic tunable filter or Fabry-Perot interferometers [17–20], for possible applications it’s essential to construct a model which could predict spectral shape and number of subcomponents arising in generation of RDFB lasers.

A powerful tool for describing properties of the RDFB laser is a power balance model. It is a simplest model of the random fiber laser which does not include spectral properties or nonlinear effects. Despite that, it proved to provide precise description of the generation power, the generation threshold, and the generation efficiency of a random fiber laser [3], and was used to optimize the laser performance [21]. Different modifications of the power balance model such as considering different polarizations separately or different spectral components within amplification range may be fruitful for describing power properties of partially polarized lasers [22] or describing spectral narrowing near generation threshold [2,13].

Here we perform investigations of multipeak structure of different Stokes components in cascaded generation of RDFB laser. We use power balance model implying different spectral subcomponents within each Stokes component to predict their powers and prove that considering power transfer between adjacent subcomponent together with Rayleigh backscattering is sufficient to explain this spectral feature.

2. Experiment

The experimental data has been measured for the setup previously described in [9,14], which is schematically shown on Fig. 1. We used a powerful linearly polarized pump source at 1054 nm to achieve multicomponent Stokes generation. The pump laser was based on ytterbium-doped active fiber and had a master-oscillator power-amplifier (MOPA) scheme. Polarized pump radiation was launched into a fiber span using a high-power 1050/1100 nm filtered wavelength division multiplexer (WDM). Two different pieces of 500 m or 1 km of single-mode PM fiber of the Panda type (Fujikura SM98-PS-U25D) were used as a lasing medium. The 1100-nm port of the FWDM was spliced to a PM fiber coupler with coupling ratio of 50/50 at 1050 nm, forming a PM fiber loop mirror (FLM). The FLM reflection coefficient R was equal to 91% at 1.11 μm (1st Stokes), 66% at 1.17 μm (2nd Stokes), 36% at 1.23 μm (3rd Stokes), and as low as 12% at 1.3 μm (4th Stokes) in accordance with coupling ratio of the PM fiber coupler at these wavelengths. Whole scheme was performed with polarization maintaining components, thus generation was polarized too. Fresnel reflection at the output fiber end was avoided with angle-cleaved output facet with angles being larger than 10°.

 

Fig. 1 (a) Experimental scheme of a cascaded random distributed feedback Raman fiber laser. (b) Measured Raman amplification profile of the PM fiber.

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For proper calculations of the output powers we performed measurements of linear losses and Raman gain of the PM fiber in the whole range of frequency shifts including small detuning. Linear losses amount to 0.2 1/km for λ = 1054 nm. In order to measure Raman gain, we have utilized two methods, one of those is deriving the Raman gain profile around its maximum from a measurement of amplified spontaneous emission spectrum following the method proposed in [23], and another one consists in direct on-off gain measurement for a small signal. The pump laser for these measurements was the same as for pumping random distributed feedback laser. The latter method is preferable for measurements of Raman gain for small detuning, while the former one has a lack of additional spontaneous noise from a pump laser, thus impeding the derivations of the Raman gain. The results of measurements are shown in Fig. 1(b). Thus, the measured values of Raman gain (for pump wave at 1054 nm) amount to 2.1 1/W/km at maximum (at 13.3 THz shift, first peak), 2.05 1/W/km (at 14.6 THz shift, second peak), and 0.15 1/W/km for detuning of 1.3 THz, that corresponds to the frequency shift between two subcomponents.

We have studied multipeak structures for cascaded generation for two different setups – one of them based on 500 m of the PM fiber and another one based on 1 km of the same type of the PM fiber. Power of each spectral line within each Stokes component was calculated from the spectra measured at the output of the laser using the optical spectrum analyzer (OSA) Yokogawa AQ6370 together with the total output laser power measured by a power meter. The experimental results of spectral and power measurements with increasing the input pump power up to 11 W are shown in Fig. 2(a) and Fig. 2(b) (squares), correspondingly. One can see that the 1st Stokes line has two-peak structure while the 2nd Stokes line consists of a single peak. Besides, initially the first line of the 1st Stokes spectrum corresponding to the Raman shift of 13.3 THz is generated (the threshold power is 5 W), then the second one corresponding to the Raman shift of 14.6 THz becomes dominating (the threshold power is 7 W).

 

Fig. 2 Experimental and numerical data for the laser based on 0.5 km of the PM fiber. (a) Upper: spectra of the pump, first and second Stokes components measured at the output with increasing input pump power from 2 W to 11 W. Lower: corresponding numerical scheme. (b) Output powers for each subcomponent of the 1st Stokes line.

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3. Results and discussion

We use a particular implementation of the general balance model briefly described in [3]. Our model comprises (i + 1) subcomponents for a Stokes component with number i to take into account power transfer from each subcomponent of (i-1)-th Stokes component into two subcomponents of i-th one because of double-humped shape of Raman gain. The model also considers power transfer between adjacent subcomponents in the i-th component due to the presence of Raman amplification at small detuning frequencies. Rayleigh backscattering is comprised as the feedback which is uniformly distributed along z axis.

The power transfer channels are schematically shown on Fig. 2(a), where lines state for different subcomponents in Stokes components, while arrows depict power transfer channels. Mathematically, modelling has been done for the following equation set:

Here P is the pump wave power, S_ij is the power for j-th subcomponent in i-th Stokes component co-propagating (“+”) or counter-propagating (“-”) with the pump wave. For generality of the equation set form, we considered P as S₀₁ component. α_i is the linear losses for i-th Stokes component, g_ij→lm is the Raman amplification for m-th subcomponent in l-th Stokes component pumped by j-th subcomponent of i-th Stokes component, λ_i is a wavelength of i-th component. ε_i = Qα_i is the Rayleigh backscattering coefficient, which is calculated using approximation of Q~0.002 [24]. Whole values including Raman gains and losses were calculated using fiber parameters from those measured for the pump wave and given in previous section. Gain coefficient scaling was done considering inverse dependence on an effective area of the waveguided mode and on the pump wavelength [25]. Boundary conditions used for the calculations correspond to the half-open scheme with forward pumping used in experiment [3].

Firstly, we have performed calculations for a numerical model considering two Stokes components only, and have compared it to the experimental data for the 500-m laser. Results of modelling of the power are shown on Fig. 2(b) by solid lines. In numerical simulations, energy transfer occurs from the first to the second subcomponent in the first Stokes component resulting in generation at the 2nd subcomponent above 8 W of the input pump power. This is in full agreement with experimental observations. Cascaded generation isn’t achieved in the experiment for given pump levels. Note that in the experiment there are residual signs of second and third subcomponents in the spectrum of the second Stokes component. These subcomponents have amplitudes of two orders of magnitudes lower than the main subcomponent. In the numerics the similar ratio between powers of main and side subcomponents of second Stokes was reproduced.

Then, we have performed similar comparison between the numerical model and experimental observations in case when the longer spool of 1 km of the PM fiber was used as a lasing medium. This case differs from the previous one by number of Stokes components generated at the given maximum pump power. As the threshold in random distributed feedback Raman laser decreases with increasing the fiber spool length [3], generation of more cascades of Stokes components can be achieved. In the experiment, successive generation of three Stokes components was obtained. Numerical simulation for the scheme was performed using the previously described equation set complemented with four equations for subcomponents of the third Stokes component. Mutual power transfer between subcomponents was also considered (see the scheme in the Fig. 3(a), lower panel). To accelerate computations, in the numerical simulations we don’t consider subcomponents which don’t possesses considerable amount of power as pumps for subsequent subcomponents. As well as in the case of shorter fiber, numerical simulations of RDFB laser thresholds powers demonstrate good agreement with experimental data, see Fig. 3(b). Here only first Stokes component has two subcomponent peaks while second and third Stokes components comprise single subcomponent. Second and third Stokes components have low-power side-band subcomponents, which don’t generate in both experiment and numerics.

 

Fig. 3 Experimental and numerical data for the random distributed feedback laser based on 1 km of the PM fiber. (a) Upper: spectra of pump and three Stokes components with increasing of input pump power from 2.4 W to 8.3 W. Lower: corresponding numerical scheme (b) Output powers for each component. Symbols are for experimental data, solid lines are for numerical results.

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The number of subcomponents is a result of competition between the process of generation of subsequent subcomponent from the previous one and the process of cascaded generation of subsequent Stokes component that in its term is determined by interplay of Rayleigh backscattering process and Raman amplification at the small detuning. To illustrate it, we have performed simulations for a hypothetical case of absence of Rayleigh feedback, that is Q = 0. In this case, the threshold of cascaded generation is sufficiently higher [1], thus power freely transfers between subcomponents, and two-peak structure appears in both the first and second Stokes waves, see Fig. 4(a). And inversely, if Raman amplification at small detuning is taken away of the numerical model, a distinct single peaks appear in each Stokes component, see Fig. 4(b).

 

Fig. 4 Numerical results for cascaded Raman generation in the 1 km of the PM fiber where (a) Rayleigh backscattering is absent (b) Raman gain for small detuning of 1.3 THz is set to zero.

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4. Conclusion

To conclude, we have studied multipeak structure of different Stokes components in a cascaded generation of random distributed feedback fiber laser, caused by double-humped shape of Raman gain in germanosilicate optical fibers. We performed experimental measurements and proved numerically that the number of peaks in spectral structure of each Stokes component is well described in terms of power balance model, comprising the specific shape of Raman amplification curve and allowing power transfer between different subcomponents within each individual Stokes component. A number of peaks appearing at each Stokes component depends on relations between the thresholds of generation of subsequent Stokes cascade and subsequent subcomponent in the same Stokes cascade.