We report on the simulation of stimulated Raman scattering inhibition by lumped spectral filters both in passive optical transport fibers and in fiber amplifiers. The paper includes a detailed theoretical study that reveals the parameters that have the strongest influence on the suppression of the Raman scattering, such as the filter distribution and the insertion losses at the signal wavelength. This study provides guidelines for the use of spectral filtering elements, such as long period gratings, for Raman scattering inhibition in real-world high power fiber amplifiers.
©2009 Optical Society of America
Non-linear effects such as the stimulated Raman scattering (SRS) limit the maximum power which can be delivered by passive and active fibers. This is a very important problem in high power fiber laser systems. Controlling or suppressing these effects becomes essential as the power exceeds a certain threshold at which the non-linear interactions cannot be neglected anymore.
Stimulated Raman scattering in optical fibers can be inhibited by different techniques. Some of the most popular include the use of special fiber designs that work as distributed spectral filters (hole-assisted and w-type fiber designs are included in this category) [1,2] or the use of lumped filtering elements [3,4]. The most widespread distributed filter concepts, w-type  and hole-assisted fibers , introduce a fundamental mode cut-off at a wavelength shorter than that of the Raman scattering, thereby forbidding its propagation in the fiber. In  an Yb-doped fiber amplifier consisting of 23m of active w-type fiber with 7µm core diameter was demonstrated to suppress Raman. This was achieved by decreasing the fiber cut-off wavelength through bending until the losses at the Raman wavelength amounted to about 5dB/m (20dB/m theoretically) while the insertion losses remained below 1dB/m. The Raman threshold was increased approximately by a factor of 2.4 to ~13kW peak power.
Another SRS suppression technique that has been explored is the ring-type fiber, in which the Raman scattering is resonantly coupled from the fiber core into a core-ring mode. This fiber type was demonstrated to suppress SRS in an amplifier setup with a 10µm core diameter fiber .
Yet another concept to suppress Raman scattering is the use of photonic bandgap fibers, with potentially very high losses per meter as demonstrated for a core diameter of 10µm .
However, these special fiber designs are in general limited in the maximum fiber core size that can be employed and usually provide Raman attenuations of only a few dB/m. These characteristics imply that these special fiber designs are not suitable for high power fiber amplifiers and lasers, where typically large core diameters and short fiber lengths are employed. Hence, for these applications lumped filters could provide a better and more flexible solution. Their main advantages are their inherent Raman inhibition scalability and adaptability to any fiber type. With lumped filters, the Raman inhibition factor can be easily controlled by the number of filters inserted in the fiber and their attenuation at the Raman wavelength.
Lumped spectral filters work as band rejection filters for the Raman scattered light and thereby inhibit the stimulated process. In real laser systems, however, the subsequent integration of lumped filters always leads to insertions losses that decrease the signal power. In this way, both the influence of the total attenuation introduced by the filters at the Raman scattering wavelength and the impact of their insertion losses are theoretically studied in this paper. The results of our simulations are described in section 3 for passive transport fibers and in section 4 for active setups.
Section 5 discusses the feasibility of using long period gratings as spectral filters for SRS inhibition. These structures have ideal characteristics as lumped spectral filtering elements since they combine low insertion losses with high peak attenuation [7–11]. Their main advantages compared to special fiber designs are their adaptability to various fiber types and high attenuations at the Raman wavelength. Finally, section 6 provides a short conclusion and outlook.
2. Simulation of Raman suppression
The study presented in the following is based on simulations carried out using a continuous wave (cw) model. This model solves the rate equations  and incorporates the effects of spontaneous and stimulated Raman scattering as well as amplified spontaneous emission (ASE) (that can act as a seed for the Raman process). Despite it being a cw model, its predictions could be used for the pulsed regime as long as there is no significant pulse walk-off, the Raman response can be considered instantaneous in comparison with the pulse duration (i.e. pulses > 1 ps) and the pulse repetition rate is much shorter than the average lifetime of the excited ions (~1 ms). The simulations enable the determination of the Raman threshold for different fiber lengths in passive fibers, as well as in fiber amplifiers and lasers. On the other hand, the spectral filter is modeled as a strong loss at the Raman wavelength with certain insertion losses at the signal wavelength of 1064 nm.
In the literature  the Raman threshold is defined as the input power at which Raman and signal output power are equal. However, in the context of high power laser systems, this definition is not suitable because signal depletion would have already had taken place. However, signal depletion is contrary to the goals pursued in high power laser systems of reaching the highest possible output powers and clean spectra. Therefore, a new definition of the Raman threshold is required and has been recently proposed in . Following the recommendations given in that paper, in this work the Raman threshold is also defined as the 20dB ratio of signal to Raman power at the fiber output. This value seems acceptable both for passive transport fibers and for active setups used in various applications.
3. Passive Fibers
From the many parameters that can be studied in a system that uses lumped filters for SRS inhibition, possibly the optimum longitudinal position of the filtering element in the fiber is the easiest and first one that comes to mind. The simulation results show that the exact position of the filters is irrelevant as long as it is not placed near the fiber ends. This is illustrated in Fig. 1a through an example, in which a single ideal spectral filter (i.e. without insertion losses) has been used in a 10m long passive fiber with 10µm core diameter. As previously advanced, it can be seen that a filter near either of the fiber ends does not provide an effective Raman suppression. This is because a filter near the beginning cannot attenuate the Raman scattering generated at farther points along the fiber, whereas a filter near the fiber end will only damp the already generated power contained at the Raman wavelength but cannot prevent signal depletion.
As a conclusion, a single spectral filtering element is most effective when placed approximately at the middle point of the fiber. This can be easily explained by assuming that the signal power remains approximately constant during propagation through the whole fiber, in which case the exponent that governs the Raman growth will be constant as well . The latter immediately implies that the output Raman power will only be dependent on the length of the segments in which the filter divides the fiber (assuming that the filter is able to almost completely attenuate the Raman power). Thus, it can be understood that the optimum position for the spectral filter is that that minimizes the lengths of the two fiber segments, i.e. around the middle point.
The same holds true for several filters: they should be placed in such a way as to minimize the length of all the fiber segments. This clearly leads to an equidistant filter distribution as an optimum for Raman inhibition in passive fibers. The simulations show that the small leakage caused by finite Raman attenuation (for example 20dB per filter) does not change this conclusion significantly.
Hence, provided that several filters are evenly distributed along the fiber length, a design parameter in these systems will be the effective Raman attenuation per meter which is defined as the overall attenuation introduced by the filters at the Raman wavelength divided by the fiber length. Thus, for example, two 10 m long fibers one containing five filters of 20 dB and the other containing four filters of 25 dB possess the same effective Raman attenuation of 10 dB/m. This effective attenuation, according to Fig. 1b, leads to a Raman threshold increase by a factor of 2.5 in our example. This quantity, the Raman threshold increase factor, will be used throughout the whole study to characterize SRS suppression. This parameter represents the signal output power at the Raman threshold normalized to the output power at the Raman threshold in a fiber without filtering elements (with 1 being equal to the output power at the Raman threshold in a fiber without filters and 2 meaning a doubling of the Raman threshold).
The value of 20 dB Raman attenuation per lumped filtering element is an average attenuation over the whole Raman gain bandwidth. Unless explicitly said otherwise, we will use this value of Raman attenuation per filter.
Independently of the particular fiber characteristics, the Raman threshold always increases linearly with the effective Raman attenuation if ideal filters are used. This can be seen in Fig. 1b for a 10m long fiber with 10µm core diameter. Here, each dB/m of effective Raman attenuation increase increments the Raman threshold by approximately 15%. The exact slope depends on the fiber length and geometry as well as on the filter characteristics. The influences of fiber length and geometry on the slope are summarized in Fig. 2 . Thus, in Fig. 2a, the Raman threshold increase factor is plotted as a function of fiber length for 10µm core diameter fibers. As can be seen, for the range of fiber lengths relevant for high power fiber systems (2-50m), the Raman threshold increase per filter (i.e. the slope of Fig. 2a) rises with the fiber length. However, it can be seen that for fiber lengths up to 50m the Raman threshold increase per ideal filter is within 27% ± 3%. This 3% difference in the Raman threshold increase factor is small enough to be neglected. Therefore, in the following, the Raman threshold increase factor per filter will be considered independent of the fiber length.
On the other hand, Fig. 2b summarizes the influence of different core diameters on the Raman threshold increase for a 10m long fiber. From this figure, it can be deduced that the core diameter is even less relevant than the fiber length for the relative Raman threshold increase. In the depicted case the Raman threshold increase per ideal filter can be estimated to be ~27% for core diameters ranging from 6 to 35µm. Larger core diameters are of less interest in this study since self-focusing or fiber damage will arise before the Raman threshold is reached. This relative independence of the Raman threshold increase on the fiber geometry, as deduced from Fig. 2, allows the generalization of the simulation results of this study for a large span of passive fibers in high power laser systems.
Taking into account the unavoidable insertion losses of the filters at the signal wavelength changes the picture significantly. In order to study this point, simulations were carried out for a 10m long fiber with 10µm core diameter and signal insertion losses ranging from 0 to 1dB per filter. In spite of this particularization, the qualitative conclusions extracted from this graph are still valid for different fiber lengths, core diameters and filter attenuations for the Raman scattering. In fact, the minor changes observed in Fig. 2 for different fiber parameters even suggest the quantitative validity (with a certain degree of accuracy) for a wide variety of fibers (lengths shorter than 50 m and 6 to 35 µm core diameters). The simulations results show that the linear growth of the Raman threshold with the number of filters is transformed into a curve that exhibits a maximum, as seen in Fig. 3 . This optimum arises from the fact that from this point on the overall signal losses exceed the signal gains obtained from the SRS inhibition.
After this maximum, the curves discontinue because the Raman threshold cannot be reached any more. This is because beyond this point, the signal is so strongly attenuated by the overall insertion losses introduced by the filters that it cannot reach the Raman threshold power at any point along the fiber.
On the other hand, it is also clearly visible in Fig. 3 that this maximum of Raman threshold increase can be raised by reducing the filter insertion losses. However, a higher maximum implies that the number of filters required to achieve it increases, as illustrated in Fig. 4a . Thus, while the output power of the fiber can be increased by about 30% for insertion losses of 1 dB (T = 0.8) with 4 filters (as shown in Fig. 4b), the input power needs to be more than double (overall insertion losses of 4dB). On the other hand, for T = 0.975 (0.1 dB) the Raman threshold can be increased by a factor of ~4 with ~15 filters and power losses of just 40% (~2dB).
As illustrated in Fig. 4a, the optimum number of filters Nopt that provides the maximum increase of the Raman threshold strongly depends on the insertion losses. Assuming x as the signal transmission per filter (0.8 ≤ x < 0.99), the number of filters providing the maximum Raman threshold increase can be approximated to the nearest lower integer of
Noting that Eq. (1) delivers discrete values and that Fig. 2 shows small variations over a large span of fiber parameters, it can be used as a general statement to estimate the optimum number of filters for certain insertion losses in any fiber.
The values obtained by the preceding equation can be inserted into the following linear relation to estimate the corresponding Raman threshold increase factor Rinc (Nopt ≥ 4):
As before, in virtue of Fig. 2, Eq. (2), although originally obtained for a 10m long fiber with 10µm core diameter, can be regarded as a general rule of thumb to estimate the Raman threshold increase factor in any passive fiber relevant for high-power laser systems. Hence, considering good but still realistic filters (signal transmission of 0.975, i.e. insertion losses of 0.1 dB) with an average Raman attenuation of 20 dB in the complete Raman gain bandwidth, the optimum number of filters Nopt, as obtained from Eq. (1), is 16. This, in turn, using Eq. (2) provides a maximum Raman threshold increase factor Rinc of 4.2. These results from the approximate equations can be compared with those obtained from the numerical simulations (Raman threshold increase factor of 4 with 15 filters) to conclude that Eq. (1) and Eq. (2) are reasonably accurate and can, therefore, be used to estimate the amount of Raman inhibition that can be obtained in passive fibers when using lumped filters. According to these results, Raman threshold increase factors much higher than 4 do not seem realistic when using real-world lumped filters in passive fibers.
4. Fiber amplifiers
The simulations for active setups have been carried out for a 2 m long Yb-doped double clad fiber with a core diameter of 10 µm and a cladding diameter of 125 µm. The ion concentration amounts to 8.5·1025, the pump wavelength is 976 nm and the signal wavelength is 1064 nm. We have chosen this particular wavelength as representative of the longer wavelength region of the Ytterbium gain spectrum. In systems where SRS is a problem (as the ones under analysis in this paper), longer emission wavelengths should be preferred since for significantly shorter wavelengths, i.e. for example 1030 nm, the gain and ASE are much higher at the Raman wavelength, leading to an even smaller Raman threshold .
When applying the model to an amplifier setup, the effect of the filter position (similar to Fig. 1a for the passive case) has to be studied separately for the co- and counter-propagating configurations near the Raman threshold. The difference between these setups arises from the different signal growth evolution in them . Figure 5 shows the influence of the filter position on the Raman threshold for both setups. Using the relative filter position (0.5 meaning that the filter is placed in the middle of the fiber), these two diagrams are valid for any fiber length and realistic core sizes (6 to 35µm core diameters).
In a co-propagating amplifier setup the signal power saturates at some point of the fiber length. Therefore, from this point on, the signal power can be considered as nearly constant over a large fiber length. This leads to the intuitive idea that the effect of the filter position in co-propagating setups should be comparable to that in passive fibers (Fig. 1a). The behavior depicted in Fig. 5a verifies this. While in a passive fiber placing a single filter in the region between 20 and 80% of the fiber length led to approximately the same Raman inhibition levels, the same happens in a co-propagating amplifier when placing the filter anywhere between 30 and 80% of the fiber length. The filter cannot reach its full Raman inhibition capacity when placed within the first third of the fiber because here the signal growth is still very fast.
In counter-propagating amplifiers, on the other hand, the signal grows exponentially throughout the whole fiber. This explains why placing a filter in the first half of the fiber cannot provide the best Raman inhibition when using one single filter (Fig. 5b). In this configuration significant Raman power will only be generated in the second half of the fiber and especially near the fiber end. As a conclusion, the filter can be placed anywhere between 50 and 90% of the fiber length to obtain the most effective Raman inhibition.
In both cases, placing the single filter in the middle of the fiber combines the highest Raman inhibition with easiness of setting up. When employing more than one filter, the strategy of dividing the fiber in similar segments as mentioned in section 3 is still valid. This is true in spite of the fact that, given the non-uniform growth of the signal power along the fiber, it is reasonable to think that the optimum filter distribution must be non-equidistant. However, our simulations show that no significant performance improvement is obtained when placing the filters in a non-equidistant manner. Therefore, in the following we will still consider the equidistant distribution of filters as the method of choice since it is easy and does not lead to a significant loss in Raman inhibition performance.
The normalization in Fig. 5 comes at the cost of losing information about the absolute values for the Raman thresholds. When employing the same fiber length in both setups, the absolute Raman threshold is much lower in a co-propagating amplifier because in this case the signal saturates and the high power propagates over a much longer length than in counter-propagating setups.
4.1 Co-propagating amplifier
The fiber length of the co-propagating amplifier without filters was optimized to extract the highest possible power with the given pump power. As seen in Fig. 6a , the simulations of Raman inhibition by lumped spectral filters in a co-propagating amplifier show that the Raman threshold increase factor is still highly sensitive to the insertion losses of the filters (although less than in passive fibers). This is due to the fact that in the co-propagating setup the signal power grows very fast at the beginning of the fiber and then propagates over a longer fiber distance with a relative small growth (i.e. we have the situation of an almost constant power propagating along the fiber as in the passive case). This fact has a twofold effect. On the one hand it means that in the co-propagating case more Raman scattering should be generated than in the counter-propagating setup that will be discussed next. On the other hand it also implies that each filter should have a stronger effect in Raman inhibition. Hence, compared to the counter-propagating amplifier, in principle higher Raman threshold increase factors should be expected in this configuration.
Additionally, in contrast to passive fibers, no maxima can be observed in Fig. 6a. Here instead, the slope efficiency decreases slowly with the number of filters towards a value defined by the insertion losses. Increasing the number of filters implies higher losses that are compensated by the amplifier gain. This is why no maxima appear, but the amplifier efficiency is reduced instead (Fig. 6b). Furthermore, the higher the insertion losses, the smaller the Raman threshold increase factor. Thus, between 10 and 20 filters, the Raman inhibition per filter is reduced from 21% (T = 1) to 16% (T = 0.95). This behavior is due to the fact that the signal is not so strongly amplified in the last part of the fiber. This implies that increasing the pump power cannot compensate for the filter insertion losses as efficiently as in counter-propagating setups and, therefore, the amplifier efficiency is more severely reduced in this case (see Fig. 6b). This drop in amplifier efficiency is the factor that ultimately limits the maximum Raman inhibition factor that can be obtained. This way, if the amplifier efficiency should not drop by more than 15% in high power laser systems (a value that seems reasonable in real-world amplifiers), one could reach a Raman threshold increase factor of 2 to 3 with about 5 to 10 filters that exhibit signal transmissions equal to or better than 0.975.
4.2 Counter-propagating amplifier
For the counter-propagating amplifier case, the simulations were carried out using the same fiber parameters as before. The results show that, contrary to the co-propagating case, the insertion losses at the signal wavelength have almost no influence on the Raman threshold increase factor (Fig. 7a ). This is due to the fact that the signal losses can be exactly compensated simply by increasing the pump power. From Fig. 7a it can be deduced that the Raman threshold increase per filter amounts to about an average value of 16%, although the behavior is not completely linear any longer. For more than 10 filters, the Raman inhibition per filter is reduced to about 14%.
This apparent immunity to the insertion losses of the filters comes at the cost of worsened amplifier efficiency. The amplifier efficiency increasingly drops with a larger number of filtering elements (Fig. 7b). In any case, thanks to the fact that the main signal growth takes place near the fiber end, the total efficiency decrease is smaller in this setup than in the co-propagating case. In spite of it, this drop in amplifier efficiency is, as before, the factor that ultimately limits the maximum achievable Raman threshold increase factor. Hence, if the amplifier efficiency should not drop by more than 15% in high power laser systems, one can reach at most a Raman threshold increase factor of 3 with about 10 filters if their signal transmission is better than 0.95.
As mentioned before, in counter-propagating configurations the signal grows extremely fast towards the fiber output. This implies that high signal power only propagates over a short fiber distance. Therefore, as predicted in the previous subsection, this leads to much higher Raman thresholds in this configuration than in co-propagating amplifiers.
4.3 Summary and Discussion
It is worth noting that all the amplifier simulations were carried out using the same seed power (about one order of magnitude smaller than the Raman threshold). However, additional simulations showed that the seed power has little influence on the Raman inhibition performance (around 1% of slope change in the worst case) as long as it does not generate significant Raman power itself. This small influence is due to the fact that the simulated amplifiers operated in the saturated regime. In this regime, the output power is mainly governed by the launched pump power .
The different behavior in co- and counter-propagating amplifiers in Fig. 6a and Fig. 7a is caused by the very different inversion distributions along the fiber in both configurations. Where the inversion is high enough, the active fiber can compensate the losses introduced by the filter. On the other hand, if the inversion is not so high, these losses will have an appreciable effect on the output signal. In this context, in counter-propagating amplifiers the highest inversion (i.e. the strongest amplification) is found near the fiber end, i.e. the pump side. This section comes after the signal has gone through the majority of the filters. Thus, the fiber gain is able to compensate for these extra losses. On the other hand, in co-propagating amplifiers the highest inversion (i.e. the main amplification) is found near the front end of the fiber. After this section the inversion/amplification levels are not so high and, therefore the fiber gain cannot fully compensate for the insertion losses of the filters that come afterwards (i.e. the majority of the filters).
The smaller Raman inhibition per filter in the counter-propagating case is caused by the signal power development in the fiber. As shown in Fig. 5, filters placed near the fiber input are less efficient due to a small signal (and Raman) power. Increasing the number of filters also means, in turn, that more and more filters are placed where they are less efficient, i.e. near the fiber ends. This, additionally, leads to a stronger excursion from linearity in counter-propagating amplifiers, because there the filters reach the highest efficiency at a point farther along the fiber (Fig. 5).
In a direct comparison of co- and counter-propagating amplifiers, without taking into account the amplifier efficiency drop, Fig. 6a and Fig. 7a show different Raman threshold increase factors, as explained above. Thus, in the co-propagating case with 10 filters the Raman threshold increase factor varies between 2.4 and 3.2 for signal transmissions in the range of 0.8 to 0.975. For the counter-propagating case, on the other hand, (again with 10 filters) this value amounts to 2.9 for all simulated signal transmissions.
As a consequence of the previous sections, it can be concluded that Raman inhibition can potentially be more efficient in co-propagating amplifiers provided that the filter insertion losses are not too high. However co-propagating amplifiers have a much reduced Raman threshold to start with. This makes counter-propagating amplifiers the configuration of choice if the systems are limited by Raman scattering. An additional advantage of the counter-propagating setups is their higher tolerance with respect to the filter insertion losses.
We have additionally studied the wavelength dependence of the Raman inhibition factor. We have found that for 1064 nm the Raman threshold increase per filter reaches an average value of 16% in a counter-propagating amplifier, as shown before. However, working with a signal wavelength of 1030 nm, this value was found to be even higher (~20%). Still, this higher percentage of increase cannot compensate for the smaller absolute Raman threshold at 1030 nm, so as said before it is more advantageous to work at the longer wavelength range of the gain bandwidth.
To confirm both, the qualitative and the quantitative universality of the conclusions obtained on Raman inhibition in amplifiers, another fiber amplifier was simulated. This time we used a 8 m long Yb-doped fiber with a core diameter of 20 µm, a cladding diameter of 400 µm and an ion concentration of 6·1025 at a pump wavelength of 976 nm and a signal wavelength of 1080 nm. Once again Figs. 6 and 7 were reproduced without significant changes.
5. Long period gratings
In actual setups the filtering elements could be long period gratings (LPGs). These structures are characterized by low insertion losses combined with high peak attenuations [7–11]. These characteristics, in principle, make LPGs ideal candidates for Raman inhibition.
As it is known, in an optical fiber orthogonal modes do not exchange energy. However, periodic perturbations of the index of refraction, that can be induced using for example a CO2-laser or UV exposure (see for example  for a review), can couple these modes. For the purpose of Raman suppression the power in the Raman amplification bandwidth that propagates in the fiber core should be coupled into discrete cladding modes. These cladding modes can eventually become lossy if the index of refraction of the fiber coating is higher as that from silica (single-clad fibers). Thus with a LPG, that makes this coupling possible, the Raman scattering can be strongly damped, i.e. the Raman threshold is increased. As said before, this is only valid for single-clad fibers. In double-clad fibers the cladding modes can propagate in the cladding albeit with a much lower intensity due to the higher mode area (which in turns means that this light cannot stimulate Raman scattering any longer). A negative aspect is that a subsequent long period grating may not only couple the newly generated Raman scattered light out of the core and into the cladding but also, potentially, light from the cladding (that was out-coupled by the previous LPG) into the core. This effect has to be avoided especially in active double clad fibers. However, it is worth noting that we expect this effect to be attenuated by the mode mixing that takes place in the pump core of the double-clad fibers. A way to further prevent this back-coupling from happening is to slightly detune the resonance wavelength of each LPG. This way, adjacent gratings can no longer efficiently couple light propagating in the cladding back into the core.
In all-solid fibers typical LPGs exhibit several resonances that correspond to the coupling of the core mode to different cladding modes (the shortest wavelength resonance corresponding to coupling to the lowest order cladding mode). To minimize insertion losses at the signal range, it is advantageous to select the lowest order resonance for Raman inhibition. This would avoid unwanted losses caused by lower order resonances.
In addition to all-solid fibers, LPGs can be written into photonic crystal fibers with core diameters up to 25 µm . This demonstrates the unique versatility of this approach for Raman suppression.
In order to optimize the performance, it is of key importance that the grating resonance bandwidth is matched to the Raman gain profile. This can be done by using several slightly detuned gratings  or by increasing the resonance bandwidth. The former increases complexity, the latter may imply higher signal losses.
In [10,11] LPGs were shown to exhibit peak attenuations of 30 dB combined with insertion losses in the range 0.1 to 0.25dB (T = 0.975 - 0.94). Due to the broad Raman gain bandwidth (20 to 40 THz) in fused silica, considering an average Raman attenuation of 20 dB for the whole wavelength range seems reasonable. With these parameters, according to Fig. 3 and Fig. 4 as well as Eq. (1) and Eq. (2), it would be possible to use between 10 and 16 LPGs (depending on the insertion losses) in a passive fiber to reach a maximum Raman threshold increase factor of 3 to 4. In an amplifier, on the other hand, one could reach a Raman threshold increase factor of 3 with 10 LPGs and an amplifier efficiency decrease of about 15%.
Compared to the distributed Raman suppression techniques [1,2 and 5,] introduced in section 1, lumped spectral filters in general and LPGs in particular offer potentially higher Raman attenuations per meter. Furthermore, LPGs are adaptable to many fiber types [7–11] and can even be implemented into existing setups.
It was shown that incorporating lumped spectral filters in passive fibers increases the Raman threshold provided that the insertion losses of the filters are kept low. The study provides a generalized estimation of Raman inhibition for different fiber lengths and core diameters. Expressions were derived that allow the calculation of the expected Raman threshold increase as well as the required number of filters for a wide span of passive fiber parameters relevant for high power laser applications. This study identified the insertion losses of lumped spectral filters as the main limitation for Raman inhibition. Hence, using this technique it is estimated that the maximum Raman threshold will be approximately a factor 4 higher in passive fibers.
In amplifier setups the signal losses can be compensated by raising the pump power, but this leads to a reduced amplifying efficiency. The differences between co- and counter-propagating setups were pointed out, and it was shown that counter-propagating amplifiers are more immune against filter insertion losses. Even though there are no inherent limiting factors, some practical issues introduce a cap on the maximum Raman threshold increase that can be obtained. As limiting effects come the amplifier efficiency reduction and the technical feasibility of the filters. This leads to a realistic maximum Raman threshold increase factor of about 3.
Long period gratings were proposed as promising lumped spectral filters for Raman inhibition. Employing, for example, passive transport fibers shorter than 50m length with 10 to 16 LPGs, each exhibiting an average 20 dB Raman attenuation and 0.25 to 0.1dB insertion losses, it is possible obtain an increase of the Raman threshold by a factor 3 to 4. In amplifier setups it seems feasible to obtain a Raman threshold increase by a factor of 3 with 10 LPGs.
We acknowledge support by the Federal Ministry of Education and Research (BMBF) within the FaBri-project (13N9100).
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