## Abstract

The conversion efficiency of double-clad Raman fiber laser is limited by the cladding-to-core area ratio. To get high conversion efficiency, the inner-cladding-to-core area ratio has to be less than about 8, which limits the brightness enhancement. To overcome the problem, a cascaded-cladding-pumped cascaded Raman fiber laser with multiple-clad fiber as the Raman gain medium is proposed. A theoretical model of Raman fiber amplifier with multiple-clad fiber is developed, and numerical simulation proves that the proposed scheme can improve the conversion efficiency and brightness enhancement of cladding pumped Raman fiber laser.

© 2015 Optical Society of America

## 1. Introduction

In recent years, high power fiber lasers and amplifiers have already played important roles in many fields of application. Current ways to obtain high power fiber lasers mainly rely on the cladding pumped rare earth ion doped fiber lasers, primarily Yb-doped fiber lasers [1]. However, rare earth doped fiber lasers can only operate at limited wavelengths. Raman fiber lasers are attractive due to their wavelength flexibility and high conversion efficiency. Until now, most researches on Raman fiber laser concentrate on the core-pumped scheme [2,3]. In 2013, OFS Optics Corporation demonstrated a high-conversion-efficiency 1480 nm cascaded Raman fiber laser with an output power of 301 W [4]. In 2014, an integrated ytterbium-Raman fiber amplifier scheme was proposed for further power scaling and demonstrated with a single-mode linearly-polarized output power of 300 W [5] and a near-single-mode laser of 1.3 kW at 1120 nm [6].

Cladding pumped Raman fiber laser was proposed by Nilsson *et al.* in 2002 [7]. Different from core pumped Raman fiber laser, the cladding pumped Raman fiber laser emits light with higher brightness than the pump laser, which is an important property of usual lasers. However, if the cladding-to-core area ratio is too large, the intensity generated in the core can greatly exceed that in the cladding long before the pump laser is depleted. It leads to the generation of parasitic second-order Stokes light in the core, limiting the conversion from pump light to first Stokes light [8]. To increase the conversion efficiency, the area ratio between the inner cladding and core has to be less than ~8 [9], which then limit the actual enhancement of brightness. A specially designed W-type fiber can be used to improve the cladding to core area ratio. However, the improvement is limited, as the area ratio can only be increased to about ~40 [8,10].

In this paper, we propose a cascaded-cladding-pumped cascaded Raman fiber laser architecture with multiple-clad fiber as gain medium to overcome the inner-cladding-to-core area ratio restriction. To verify the idea, a theoretical model of cascaded-cladding-pumped cascaded Raman fiber amplifier (RFA) is developed. Numerical simulation proves that the newly proposed scheme can improve the conversion efficiency and brightness enhancement.

## 2. The proposal and theoretical model

In a cascaded-cladding-pumped cascaded Raman fiber laser or amplifier, a specially designed multi-cladding fiber is used as gain medium. The low brightness pump light is coupled into the second cladding (first inner cladding) of the fiber, first Raman Stokes light is generated in the third cladding. Similarly, the generated Stokes light will act as pump light and generate the higher-order Stokes light in the fourth cladding. Such processes happen cascadedly until the single-mode laser is generated in the fiber core. If one designs the neighboring claddings with small area ratio (for example, less than 8), parasitic second Stokes laser could be suppressed. As a result, by introducing the intermediate claddings, the restriction on the cladding to core area ratio could be released. In the following, we investigate a cascaded-cladding-pumped cascaded Raman fiber amplifier as a typical realization.

Figure 1 shows an exploded view of an *m*-cladding (*m*>2) fiber. The cladding constraining the pump light is marked as cladding 1, and the cladding where the pump light propagates is marked as cladding 2. To match commercial fibers, the diameter of the cladding 2 and core are set to be 105 μm and 10 μm, respectively. The NA of cladding 2 is set as 0.22 and NA of all the inner cladding and core is set as 0.07. The core diameter of 10 μm is chosen to guarantee single-mode operation. We assume the cladding 2 is pure silica, whose refractive index *n* is known. Then *n* of all the inner claddings and core can be calculated. The refractive index *n* is controlled by GeO_{2} doping concentration. Because for a given wavelength, the refractive index increases linearly with the GeO_{2} concentration, the GeO_{2} doping concentration in the inner claddings and core can be deduced [11]. Finally, the peak Raman gain coefficient also increases linearly with the GeO_{2} doping concentration, which can be calculated as well [11].

In the Raman fiber amplifier model with an *m*-cladding fiber, the *i*th-order Stokes seed light is injected into cladding (*i* + 2). The *(m-1)*th-order Stokes signal light is injected into the core. The *m*th-order spontaneous Stokes light builds up from noise. There is concern on accidentally polluting an outer cladding when coupling seed lasers into their desired claddings. Therefore, the model considers the spillovers. Meanwhile, the possible power overflow to the adjacent outer cladding due to the Rayleigh scattering effect is also considered. Then a set of power coupled equations including pump and Stokes light are given as followed [9]:

*P*represents the pump power.

_{0}*P*(

_{i}*i*= 1…

*m-1*) represent

*i*th-order Stokes power propagating in the cladding

*(i + 2)*. (Here, it is noted that cladding

*(m + 1)*represent the core).

*P*' is the part of

_{i}*i*th-order Stokes light in the outer cladding (

*i*+ 1) due to the spillover. The

*P*and

_{m}*P*are the undesirable parasitic

_{m}'*m*th-order Stokes power in the core and cladding

*m*.

*α*represent the fiber background losses of the pump.

_{0}*α*and

_{i}'*α*represent the fiber background losses of

_{i}*i*th-order Stokes light propagating in the cladding

*(i + 1)*and cladding

*(i + 2)*, respectively.

*g*is the Raman gain coefficient of

_{i}*i*th-order Stokes light stimulated by

*(i-1)*th-order Stokes light.

*A*is the effective area of the fiber at

_{i}*i*th-order Stokes wave, and

*λ*∕

_{i + 1}*λ*represents the quantum defect of Raman scattering process. $x$represents the overflow ratio from cladding

_{i}*(i + 1)*to cladding

*i*caused by the Rayleigh scattering effect.

The intermediate Stokes light propagates in multiple fiber regions of different refractive index. For example, in a RFA with four cladding fiber, the 1st-order Stokes light will be amplified in cladding 3, cladding 4 and core. But each of them has different GeO_{2} concentration and therefore different Raman gain coefficient. For simplicity, the distribution of the pump and intermediate Stokes light across the respective fiber region is assumed to be uniform. Thus, the effective Raman gain coefficient for the intermediate Stokes light is calculated by weighted average according to the area of these regions.

*S*is the

_{j}*j*th-cladding area.

*S*is the core area.

_{core}*g*is the peak gain coefficient of

_{Rj}*j*th cladding at the

*i*th-order Stokes wavelength.

## 3. Simulation results and analysis

In the simulation, the background loss of pump light and Stokes signal light are set as 3 dB/km and 2 dB/km, respectively [9]. The *m*th-order spontaneous Stokes light is simulated with a seed light power of *hνΔν*, where *h* and *ν* represent Planck constant and frequency of Stokes light, respectively. *Δν* is the bandwidth of the beam that is being scattered [12], which is set as 10 nm. The pump laser is assumed to be a CW 5 kW Yb fiber laser at 1070 nm or a long-pulsed (ns or longer) laser with a peak power of 5 kW. The latter is more available. For the simulation of Raman fiber laser they are equivalent, because Raman scattering is an instantaneous process. The power of Stokes seed lasers are set as 50, 0.1, 0.01 watts arbitrarily. Later we will show that selection of these input parameters is not critical. The spillover ratio when seeding the amplifier is assumed to be 1% in the following calculation. And we will investigate the influence of the spillover ratio at the end of this section. The effect of overflowing to the adjacent outer cladding due to the Rayleigh scattering is found to be negligible even with a$x$of 10^{−6} m^{−1}.

Firstly, a double-clad RFA is simulated. Figure 2(a) shows the power evolution along the fiber, when the inner cladding and core diameter of the gain fiber are 105 μm and 10 μm, respectively. The 1st-Stokes laser propagates in the core (*P _{1}*) grows up to ~736 W at ~104 m. After that, the parasitic second Stokes light increases quickly and depletes the first Stokes Raman laser. The conversion efficiency versus cladding-to-core area ratio is calculated by varying the core diameter, as shown in Fig. 2(b). When the cladding-to-core area ratio is small, the conversion efficiency is almost constant. When the cladding-to-core area ratio is larger than ~8, the conversion efficiency drops quickly.

Then the influence of intermediate cladding on the conversion efficiency is studied. Three-cladding RFA is simulated with fixed cladding 2 and core diameter of 105 μm and 10 μm. Figure 3(a) shows the conversion efficiency as function of the radius of cladding 3. It is found that too small or too large radius result in low conversion efficiency of pump light to 1st-order Stokes light(*P _{1}*) or 1st-order Stokes light to 2nd-order Stokes light(

*P*), respectively, which leads to low overall conversion efficiency. There is an optimum radius for cladding 3, which gives the highest efficiency. The optimum radius is found to be 18μm in the simulation. Maximum 2.1 kW 2nd-order Stokes light at 1181 nm can be achieved with an optical conversion efficiency of 41%. The power evolution along the fiber is calculated and shown in Fig. 3(b). It is seen that the rapid growth of 2nd-order Stokes light clamps the conversion of pump light to 1st-order Stokes light, leading to the low overall conversion efficiency. Similarly, if the fiber is too long, the parasitic third Stokes light, both

_{2}*P*and

_{3}'*P*build up, which overlap together in the Fig. 3(b). Note that both the 1st-Stokes light propagating in the cladding 2 (

_{3},*P*) and the 2nd-Stokes light in the cladding 3 (

_{1}'*P*) don’t grow up.

_{2}'Then the number of cladding is increased to four. By adjusting the radius of cladding 3 and cladding 4, a maximum output power of 3.0 kW at 1246 nm 3rd-order Raman Stokes is achieved with conversion efficiency of 59.6%, as shown in Fig. 4(a). With the optimal core and cladding radius (5/12.5/26/52.5μm), the evolution of pump light and all the Stokes components as functions of fiber length is shown in the Fig. 4(b). Similarly, the parasitic 4th-Stokes light, both *P _{4}'* and

*P*grow up, which overlap together in the Fig. 4(b).

_{4},For RFA with five-cladding fiber as gain medium, the optimal core and cladding radius is found to be 5/5.5/14/27/52.5 μm. The maximum output power is 2.7 kW at 1318 nm. The dependence of conversion efficiency on the number of cladding is summarized in Fig. 5(a), which shows that the maximum conversion is achieved with four-cladding fiber (three Raman cascades). Further increase of the intermediate claddings cannot promote the overall conversion efficiency, because the efficiency of the intermediate Raman conversion doesn't increase much when the area ratio of neighboring claddings is less than 8 as seen in Fig. 2(b). Instead, it will decrease because of the extra loss of power in the extra step of Raman shifting.

The brightness enhancement of RFA with multiple cladding fiber is calculated [9]. The results are also shown in Fig. 5(a). So with a four-cladding fiber, one can increase the conversion efficiency from 13% to 59%, and increase the brightness enhancement from 650 to 2800. For the optimized four cladding fiber, the GeO_{2} concentration of each cladding is 0 mol%, 1.2 mol%, 2.4 mol% and 3.6 mol% from cladding 2 to core, respectively.

The Stokes light powers as functions of pump power is simulated, since the power curves with fixed gain fiber lengths are what one could easily measure in experiments. Figure 5(b) shows the calculated power curves with a 300m-long four-cladding fiber. With the increase of pump power, the Stokes lights are generated cascadedly. The cascading process becomes sharper at higher order Stokes, since laser intensity is higher with smaller beam cross-section. When the pump power is larger than 5 kW, the calculated parasitic 4th-order Stokes light power increases linearly with the pump power, which is an artifact caused by the absence of parasitic higher order stokes light in the power coupled equations. In reality, spontaneous higher order cascaded-Raman Stokes light will be generated at longer wavelengths [13].

The sensitivity of output power on seeding powers and spillover ratio is investigated as well. For example, Fig. 6(a) shows the dependence of amplifier output on the 2nd and 3rd Stokes seed power in a four cladding design. With a variation of seed powers over two order of magnitude from 0.01 to 1 W, the amplifier output changes from 3.1 kW to 2.5 kW only. Saw-tooth contour line is observed in the numerical calculation, which is interesting to verify experimentally. For a fixed 3rd Stokes seed power, with the increase of 2nd Stokes seed power, the signal light output decreases and then increases in the small range, and then decrease again, which occurs in some parameters. The phenomenon is believed to be a result of gain competition between different order of Stokes. Figure 6(b) shows the dependence of amplifier output on the seeding spillover ratio. Increasing the spillover ratio from 1% to 5%, the amplifier output decreases slightly. These results show that the amplifier performance is not sensitive to the seeding power and spillover ratio. Therefore, we believe seeding the fiber amplifier with combination of dichroic mirrors is feasible.

## 4. Conclusion

In summary, we propose a cascaded-cladding-pumped cascaded Raman fiber laser with multiple-clad fiber as Raman gain medium, to overcome the brightness enhancement limitation in double-clad cladding-pumped Raman fiber laser. A theoretical model of Raman fiber amplifier with multiple-clad fiber is developed and the numerical simulation results prove that the proposed scheme can indeed improve the conversion efficiency and brightness enhancement. In the next step, we will work on an experimental demonstration of multiple cladding cascaded Raman fiber laser.

## Acknowledgment

The work is supported by the National Natural Science Foundation of China (No. 61378026).

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