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The selection of an appropriate pump concept has a major impact on amplifier cost and power consumption. The energy efficiency of different pump concepts is compared for multi core and multi mode active fibers. In preamplifier stages, pump power density requirements derived from full C-band low noise WDM operation result in superior energy efficiency of direct pumping of individual cores in a multi core fiber with single mode pump lasers compared to cladding pumping with uncooled multi mode lasers. Even better energy efficiency is achieved by direct pumping of the core in multi mode active fibers. Complexity of pump signal combiners for direct pumping of multi core fibers can be reduced by deploying integrated components.
© 2014 Optical Society of America
1. Introduction
An exponential growth of data traffic has been observed in long haul fiber based optical networks over the last two decades and demand will most likely continue to grow due to the emergence of more bandwidth-hungry services [1–4]. Neither residential nor business customers are willing to pay internet access prices proportional to the bandwidth they are using. As a consequence, service providers and carriers have to seek for solutions providing capacity increase together with reduced cost per transported bit.
Operational expenditures (OPEX) and especially electrical energy cost contribute a significant fraction to the total cost of ownership of optical network infrastructure. Power consumption of optical amplifiers has a large impact on the electrical energy supply needed along the link. Inside the amplifier modules, energy used for the generation of the optical pump radiation dominates over requirements of other functions. Therefore, the selection of an appropriate pump concept plays an important role in the design of cost and energy efficient optical amplifiers.
Optimization of pump concepts has commonly been used to reduce module cost and to improve the energy efficiency of single core single mode amplifiers used in transmission systems deploying wavelength division multiplexing (WDM). Space division multiplexing (SDM) does not just offer another degree of freedom for capacity increase but also additional design options for amplifier modules. For example, the pump radiation generated by a single pump laser diode can be supplied to multiple cores in the active fiber to reduce component count and power consumption [5]. Cladding pumping is successfully deployed in high power single mode booster stages to achieve total output powers of several Watt. It can potentially also help to reduce the complexity of supplying pump radiation to several cores in a multi core fiber [6].
The focus of this contribution is to investigate the energy efficiency of different pump concepts for SDM amplifiers. Cladding pumping is compared with direct pumping of cores using analytical calculations and numerical simulations. Active fibers with multiple single mode cores are considered as well as fibers with a single multi mode core.
Most amplifier designs for long haul applications use two different stages: a preamplifier and a booster stage. The main function of the preamplifier stage consist of providing low noise amplification for input signals with low power levels whereas the booster stage supplies output signals with high power levels. As the realization of the main function has a strong impact on the suitability of different pump concepts, preamplifier and booster stages are considered in separate sections.
2. Pump power density requirements of preamplifier stages
When designing preamplifier stages of single core single mode modules for WDM transmission systems, care has to be taken to achieve sufficient gain and low noise figures across the entire C-band ranging from approx. 1528 nm to 1563 nm. If SDM is used to increase capacity, the spectral characteristics of the SDM amplifiers should be compatible with the single core single mode case. This introduces requirements on the spatial pump power density. These requirements can be derived from an analysis of the mechanisms of the amplification process in erbium-doped fibers.
In erbium-doped fiber amplifiers, gain is provided by stimulated emission and transitions between energy levels of the erbium ions which act as an energy storage. A diagram of the most relevant energy levels of the Er3+-ions is depicted in Fig. 1. The stimulated emission required for the gain at wavelengths around 1550 nm corresponds to a transition between the upper laser level 4I13/2 and the lower laser level 4I15/2, which coincides with the ground level.
The linewidth of the transition depends on the environment the erbium ions are exposed to. If the ions are isolated from other atoms, which occurs if they are floating in vacuum, several energy states are degenerate. The energy levels in this case can be depicted by narrow lines as shown on the left side in Fig. 1, resulting in transitions with a linewidth well below 1 nm. Placing the ions in a glass matrix as in a doped silica fiber core exposes them to ligand fields from the surrounding atoms. These fields remove the degeneracy and split the energy states into Stark levels depicted by the blue lines on the right hand side of the energy level diagram.
The spacing between the highest and the lowest Stark levels of a given energy level is wider than the thermal energy Wt at room temperature, which corresponds to the product of the Boltzmann constant kB and the absolute temperature T in Kelvin: Wt = kB T. As a consequence, the population densities, which follow the Boltzmann distribution, differ significantly across the Stark levels.
The probability of transitions between the upper laser level and the lower laser level due to stimulated emission and absorption can be described by cross section spectra. The cross section at a given wavelength is proportional to the sum of all contributing pairs of Stark levels in the upper and the lower laser level with an energy spacing corresponding to the given wavelength and the respective population densities of the Stark levels the transition starts from. As transitions induced by the absorption of photons start from the lower laser level and the population densities of the lower Stark levels, which are further apart from the upper laser level, are higher than the upper Stark levels within the lower laser level, absorption tends to be more likely for larger energy separations, which correspond to shorter wavelengths.
On the other hand, transitions resulting in photon emission start from the upper laser level. In this case, the Stark levels with the higher population density are closer to the lower laser level than the Stark levels with lower population density. Therefore, emission events tend to be more likely at smaller energy spacings, which correspond to longer wavelengths.
The impact of the population density differences between Stark levels on cross section spectra can be calculated by applying the theory proposed by McCumber [7]. It can also be observed in measured absorption and emission cross section spectra as depicted in Fig. 2. Due to the higher population density of the lower Stark levels in the lower laser level, absorption cross sections are larger than emission cross sections at short wavelengths. Emission cross sections are larger than absorption cross sections at longer wavelengths due to the higher population densities of lower Stark levels in the upper laser level.
These relations between emission and absorption cross sections at different wavelengths have an impact on amplifier gain spectra as well as noise figure spectra. Numerical simulations of radiation propagation in erbium doped fibers have been carried out to demonstrate this impact.
The population densities of erbium ions in the 4I15/2, 4I13/2, and 4I11/2 energy states, labeled as 1, 2, and 3 for more simplicity of notation, can be calculated by solving a set of rate equations:
with the stimulated transition ratesand the completeness relationwhere Ni denotes the population density in 1/m3 of erbium ions in the state i = 1, 2, or 3, t the time in s, Aik one divided by the average lifetime in s before a spontaneous transition between the levels i and k, σik the respective absorption or emission cross section in m2, S the spatial power density of radiation in W/m2 at a given wavelength, h Planck’s constant, ν the frequency in Hz, and Nt the total erbium ion concentration in 1/m3.The change of the spatial power density of radiation components along the fiber can be calculated by a set of propagation equations for the spatial power densities of the pump radiation Sp, the signal radiation Ss, and the amplified spontaneous emission (ASE) SASE:
where σE denotes the emission cross section in m2 of the respective transition, z the z-coordinate along the fiber axis, σA the absorption cross section in m2, α the loss coefficient in 1/m at the respective wavelength, B the bandwidth in Hz, and Aeff the effective mode field area in m2.The propagation equations can be used together with the steady state solution of the rate equations to calculate the power of signal and ASE spectral components at the active fiber output as a function of pump and signal power at the fiber input by integrating the propagation equations along the fiber. For the sake of a clearer demonstration and easier interpretation, it is helpful to assume a constant spatial pump power density across the entire core cross section area which is doped with erbium ions. Such a constant pump power density corresponds to the case of a well designed cladding pumped fiber with strong coupling of the cladding modes.
The following parameters have been selected for the simulation: a pump wavelength of 980 nm in a codirectional pump configuration, 36 signal channels with a launch power of −30 dBm per channel in the wavelength range from 1528 nm to 1563 nm with a spacing of 1 nm to sample the gain and noise figure spectra, 201 ASE spectral components in the wavelength range from 1450 nm to 1650 nm with a spacing of 1 nm, an effective mode field area in the signal wavelength range of 26 µm2, an erbium ion concentration of 5.3 x 1024 m−3, which results in an attenuation of the unpumped fiber of 6 dB/m at the wavelength of 1530 nm, and a loss coefficient of 15 dB/m at the pump wavelength. The spatial pump power density was varied in a range from 0.14 GW/m2 to 1.6 GW/m2. For each power density, the fiber length was optimized to achieve a constant gain of 22 dB at the wavelength of 1545 nm. The simulation results with these parameters are depicted in Fig. 3 and Fig. 4.
Fig. 3 Gain spectra for different spatial power densities of the pump radiation at the input of the active fiber.
Fig. 4 Noise figure spectra for different spatial power densities of the pump radiation at the input of the active fiber.
The gain spectra for different spatial power densities of the pump radiation shown in Fig. 3 exhibit a clearly visible tilt. This tilt results from the ratios of the absorption and emission cross sections at the different wavelengths. For the largest pump spatial power density of 1.2 GW/m2, the vast majority of erbium ions can be found in the excited state. They possess an energy corresponding to the upper laser level, i. e. the population density N2 is much larger than the population density N1 of the lower laser level. As the probability for a stimulated transition is proportional to the product of the population density for the respective level and the cross section, stimulated emission is by far more likely than absorption. The shape of the gain spectrum for such a large pump spatial power density results mostly from the shape of the emission cross section spectrum.
If the spatial power density of the pump radiation is decreased, the population density of the upper laser level decreases as well, resulting in an increase of the population density of the lower laser level. This increases the probability of transitions induced by absorption and consequently the impact of the absorption cross section spectrum on the gain spectrum is raised. As the ratio of the absorption cross section and the emission cross section increases on the short wavelength side, signal channels on the short wavelength side are affected by absorption much stronger than signal channels on the long wavelength side.
The increasing impact of absorption with decreasing pump spatial power density can also be observed in the noise figure spectra depicted in Fig. 4. The spontaneous emission factor nsp = N2 σE / (N2 σE - N1 σA) is a measure for the local generation of noise. Its wavelength dependence results from the varying impact of absorption and emission cross section spectra. If a large pump spatial power density excites most ions to the upper laser level, the population density of the lower laser level is small and the term N1 σA in the denominator can be neglected, resulting in a spontaneous emission factor close to 1. It represents much higher probability of stimulated emission than probability of absorption and the noise figure approaches the quantum limit of 3 dB.
With decreasing spatial power density of the pump radiation, the population density N1 of the lower laser level increases. This also increases the impact of the term N1 σA in the denominator, resulting in an increase of the spontaneous emission factor and consequently the noise figure. As the ratio of the absorption cross section and the emission cross section is larger on the short wavelength side, the increases of the spontaneous emission factor and the noise figure are also stronger on the short wavelength side than on the long wavelength side. The resulting tilt of the noise figure spectra can be seen clearly in Fig. 4.
The impact of these fundamental relations cannot only be observed in predictions from numerical simulations but also in experimental results. For example, the measured gain and noise figure spectra reported in [8] show low gain and increased noise figure on the short wavelength side around 1530 nm. The launched pump power of Pcl = 4.7 W together with the cladding diameter of Dcl = 100 µm corresponds to a pump spatial power density of Sp = Pcl / ((Dcl/2)2 × π) = 0.60 GW/m2. With this value, less impact of the absorption cross section spectrum should be expected according to the simulation results depicted in Figs. 3 and 4. However, a section with a length of 25 cm at the input of the active fiber was left unpumped in the experiments. Such an unpumped section considerably increases the impact of the absorption cross section spectrum and results in an effective pump spatial power density value well below the one calculated by dividing the launched pump power by the inner cladding cross section area.
The fundamental characteristics of the amplification process provided by the erbium ions introduce requirements on the spatial power density of the pump radiation. According to the numerical simulation results, a value of 0.5 GW/m2 can be selected for decent noise performance and sufficient gain on the short wavelength side of the C-band. The total power needed for pumping a given preamplifier stage is dictated by this requirement on the spatial power density.
Cladding pumping approaches are generally unfavorable for preamplifier stages, as large total pump powers have to be supplied to achieve the required spatial power density in a relatively wide inner cladding cross section area [9]. For example, in a multi core fiber with seven cores and a cladding diameter of Dcl = 90 µm, a total pump power of PC = SP × Acl = 3.2 W is required to achieve the desired power density of SP = 0.5 GW/m2 in the large cladding cross section area Acl = (Dcl/2)2 × π = 6,360 µm2.
In contrast, direct pumping of the seven cores reduces the area in which the spatial power density has to be achieved to the sum of the core cross section areas. When assuming mode field diameters of DMF = 5.6 µm, corresponding to a mode field area of AM = (DMF/2)2 × π = 25 µm2 per core, only PD = 7 × SP × AM = 87.5 mW of total pump power are required for the spatial power density of 0.5 GW/m2. In this example, the total power needed for cladding pumping is higher than the total power needed for direct pumping by a factor of more than 36. A strong reduction of this factor is difficult due the ratios of involved areas.
Figure 5 depicts a cross section of a multi core fiber with seven cores. The configuration with one central core and six equally spaced outer cores corresponds to hexagonal packing and ensures the maximum spacing between any pair of cores for low coupling efficiency between cores. In order to avoid excessive coupling, the core pitch CP has to be larger than the mode field diameter DMF of a given core at least by a factor of 4. A similar spacing CS is required between the outer cores and the inner cladding boundary in order to avoid excessive losses. For a seven core fiber with one central core and six cores in a ring around the central one, the inner cladding diameter has to be at least Dcl = 2 × N × DMF with a factor N larger than 7.
The area which has to be pumped in case of cladding pumping can be calculated using this relation for the diameters: AC = (Dcl/2)2 × π = (N DMF)2 × π. In case of direct pumping, the area which has to be pumped corresponds to the number of cores times the area per core: AD = 7 × (DMF/2)2 × π. The ratio of the areas which have to be pumped in the two pump configurations follows as AC/AD = 4 N2 / 7. With the assumption that the factor N needs at least a value of 7 for low coupling efficiency between cores, the ratio of the areas is much larger than a factor of 10.
Pump sources for cladding pumping are potentially more energy efficient than pump sources used for direct pumping. Without the need to couple pump radiation into single mode cores, broad area laser diodes can be deployed to generate the pump radiation potentially without cooling. An interesting question is, by which factor the output power of a multi mode pump does exceed the output power of a single mode pump for the same amount of electrical power supply. According to the data sheets of currently used high power single mode laser diodes for 980 nm pumping, the thermoelectric cooler consumes roughly half of the total electrical power supplied to the module for operation at maximum allowed case temperature.
It is rather unlikely that the electrical to optical power conversion efficiency of the multi mode diode exceeds the power conversion efficiency of the single mode diode by far. If a rather optimistic assumption of another factor of 2 is made, the optical output power of the multi mode laser module is larger than the output power of the single mode laser module with cooler for the same amount of electrical power supply by a factor of 4. However, this factor is still much smaller than the ratio of total pump powers needed by the cladding pumping and the direct pumping approaches.
Codoping of erbium with ytterbium can be deployed beneficially to enhance the efficiency of the absorption of pump radiation in the wavelength region below 1000 nm. The enhanced pump absorption helps to increase the output power of amplifiers and lasers [10]. However, the required energy transfer from the ytterbium ions to the erbium ions results in lower population densities of the upper laser level of the erbium ions than in case of direct pumping of erbium with the peak absorption wavelength around 980 nm. As a consequence of this weaker inversion of the erbium ions and the fundamental relations described above, it is difficult to achieve large gain below 1535 nm and noise figures close to the quantum limit, if codoping with ytterbium is applied. In consequence, codoping with ytterbium cannot help to reduce the pump spatial power density which is required to realize preamplifier stages for full C-band operation with decent noise performance.
In the estimation of total pump power required for direct pumping based on the spatial power density approach, two important effects have been neglected. If the pump radiation is guided by the same refractive index step as the signal radiation, interaction of pump radiation with the erbium ions is much stronger. Therefore, attenuation of pump radiation is no longer dominated by background loss as in case of the cladding pumping. Moreover, the pump spatial power density is not constant across the core cross section area and considerably decreases close to the core cladding interface. Both effects can be considered when simulating propagation of radiation components with the rate and propagation equations described above by using an appropriate radial pump power density distribution.
For these simulations, a fiber with the following parameters has been selected. The cores exhibit a diameter of 4.7 µm with a numerical aperture of 0.23. They are doped homogeneously with an erbium ion concentration of 5.3 × 1024 m−3, which corresponds to an attenuation of the unpumped fiber of 6 dB/m at the wavelength of 1530 nm. All other parameters such as the number of signals, launch powers, etc. have been adopted from the simulations described above. Pump power and fiber length were varied in order to search for the appropriate settings for a gain of 22 dB at the wavelength of 1545 nm with the total signal power growing monotonously along the active fiber.
The obtained gain spectrum for a pump power of 41.3 mW per core and a fiber length of 10.3 m is shown in Fig. 6. The spectral shape resembles the gain spectrum with a spatial power density of the pump radiation of 0.5 GW/m2 in the cladding pumped case. Figure 7 depicts the noise figure spectrum with the red dots. The noise figures are slightly larger than the noise figures for a pump spatial power density of 0.5 GW/m2 in the cladding pumped case. The difference results from the spatial power density distribution of the pump radiation which is constant in the cladding pumping case and decreases with increasing radius in the direct pumping case. The erbium ions close to the core cladding boundary experience less pump spatial power density than the ions close to the fiber axis. Therefore, the population density in the upper laser level decreases with growing radius, which increases the impact of the absorption cross section spectrum. As the noise figure results from the contributions of all erbium ions, a slight increase can be observed due to the weaker inversion close to the core cladding boundary.
This increase of the noise figure can be avoided by omitting erbium ions in the regions with reduced spatial power density of the pump radiation. In order to demonstrate the effect, a partially doped fiber was selected with the same core dimensions, but the doping with erbium ions was confined to a region from the fiber axis up to a radius of 1.31 µm. The doping concentration had to be increased to 8.33 × 1024 m−3 in order to maintain an attenuation of the unpumped fiber of 6 dB/m at the wavelength of 1530 nm. The pump power at the fiber input could be reduced to 35 mW and the length to 10.2 m for obtaining the same gain spectrum as the one shown in Fig. 6. The noise figure spectrum with the partially doped core is depicted in Fig. 7 by the blue circles.
The partial doping of the core helps to reduce noise figures in case of direct pumping. The noise figure spectrum of the directly pumped partially doped core resembles the noise figure spectrum of the fiber which is cladding pumped with a pump spatial power density of 0.5 GW/m2. Partial doping also helps to improve energy efficiency. The pump power per core could be reduced from 41.3 mW to 35 mW for a gain of 22 dB at the wavelength of 1545 nm.
If direct pumping is applied to a multi core fiber with 7 of these partially doped cores, a total pump power of 7 × 35 mW = 245 mW is required. A comparison of this total pump power with the 3.2 W needed for the cladding pumped fiber reveals that the pump power ratio for cladding and direct pumping corresponds to a factor of 13. It is rather unlikely that multi mode pump modules can generate the power required for cladding pumping with the same or less electrical power consumption than the one needed by single mode pump modules for direct pumping, assuming that coupling losses are comparable. Even with the entirely doped core and a total pump power of 7 × 41.3 mW = 289 mW, the multi mode pumps can probably not deliver the power required for cladding pumping, which is higher by a factor of 11 than the power required for direct pumping, with the same electrical power consumption as the single mode pumps.
So far, the investigation has focused on pump concepts for multi core active fibers. Multi mode fibers offer another option for the realization of capacity increase by space division multiplexing. The gain in a multi mode active fiber can also be calculated by using rate equations and propagation equations for the individual modes. For the multi mode simulations, a fiber with the following parameters has been selected. The numerical aperture had the same value of 0.23 as in the single mode case, while the core diameter was increased to 10.5 µm to enable propagation of six modes with two orthogonal polarizations in each mode. In a first step, the entire core was doped with a constant erbium ion concentration of 5.3 × 1024 m−3, which results in an attenuation of 6 dB/m at the wavelength of 1530 nm.
Pump power and fiber length were adjusted to achieve monotonous growth of the total power in each mode. Furthermore, pump powers in different modes were varied to search for operating conditions with a gain in each mode as close as possible to 22 dB at a wavelength of 1545 nm. Figure 8 shows calculated gain spectra for a fiber with a length of 12 m. A pump power of 20 mW was launched into the LP01 mode and 70 mW in each of the LP21 modes. Decent gain spectra could be achieved for the LP01 signal mode, the two LP11 modes and the two LP21 modes, whereas the gain for the LP02 mode was significantly smaller.
The noise figure spectra shown in Fig. 9 reveal that the noise figures for the LP02 mode are only slightly higher than the ones for the other modes. Decent noise performance comparable to the single mode case can be achieved for the LP01 signal mode, the two LP11 modes and the two LP21 modes.
Due to the reduced gain of the LP02 mode, the proposed amplifier would be suitable for signal transmission in 5 modes only. A total pump power of 160 mW is required to achieve sufficient gain in these 5 modes. A multi core fiber with 5 directly pumped entirely doped cores would need a total pump power of 5 × 41.3 mW = 206.5 mW. The multi mode fiber is obviously more power efficient, as the modes are sharing the same core area and are packed more densely [5].
Variation of the erbium ion doping concentration in the radial direction has helped to improve the amplification characteristics of the directly pumped single mode core. It can also be applied in the multi mode case to reduce the gain variation between modes. Figure 10 shows a doping profile which was chosen for this purpose. It is characterized by a higher erbium ion concentration close to the fiber axis, less doping in an inner ring around the axis, and higher ion concentration again in an outer ring. The motivation of this choice of doping profile is to favor the LP02 mode, which has a spatial power density distribution similar to the doping profile.
Gain and noise figure spectra obtained with this doping profile are depicted in Fig. 11 and Fig. 12, respectively. These results were achieved for a fiber with a length of 15 m, a pump power of 100 mW in the LP02 mode, 20 mW in each of the two LP21 modes, and 25 mW in each of the two LP31 modes, corresponding to a total pump power of 190 mW. With this pump power distribution, decent gain and noise figure spectra can be achieved for all 6 signal modes which can propagate along the fiber.
A directly pumped fiber with 6 partially doped cores needs a total pump power of 6 × 35 mW = 210 mW. Again the multi mode fiber is more energy efficient for this case with individual optimization of doping profiles for the respective fiber type. For a direct pumped multi core fiber with 6 entirely doped cores, a total pump power of 6 × 41.3 mW = 247.8 mW would be required, corresponding to an even better energy efficiency of the multi mode fiber which was also doped up to the core cladding boundary.
3. Pump concepts for booster stages
The power consumption of the booster stage is dictated by conservation of energy. The total power of the signals leaving the amplifier cannot be higher than the sum of signal and pump powers coupled into the amplifier. Consequently, high power pumps are required for high total signal output powers. Several concepts can be applied to improve the optical pump to signal power conversion efficiency, such as counterdirectional pumping or pumping at 1480 nm. Due to the weak interaction of pump radiation with erbium ions in cladding pumping configurations, where the majority of the pump power propagates in the inner cladding which is not doped with erbium ions, this pump concept tends to achieve inferior power conversion efficiency compared to direct pumping.
However, cladding pumping may still be helpful to meet total output power requirements. In SDM amplifiers with many cores and many WDM channels, the required total output power can exceed 1 W. For example, in a fiber with 19 single mode cores, 100 WDM channels per core and a channel output power of 3 dBm, the total output power sums up to 3.8 W. As currently available single mode pump laser modules provide output powers of less than 1 W, several of these modules would be necessary to generate sufficient pump power for direct pumping of single mode cores. Such high total output powers of erbium doped fibers with single mode cores are more easily achieved with cladding pumping approaches.
Multi mode active fibers can provide advantages with respect to high total signal output powers. Direct pumping of multi mode cores using multi mode laser modules is possible without the need for cladding pumping [11]. So the higher output power from multi mode pump modules, which usually exceeds the one available from single mode pump modules, can be deployed beneficially in case of active fibers with multi mode cores.
The fundamental characteristics of the amplification process based on erbium ions also apply to the booster stage. In this case, noise performance is less important, as the input signal power levels of the booster stage are usually chosen much higher than the input signal power levels of the preamplifier stage. Hence, the total noise figure is dominated by the contribution of the preamplifier stage. Requirements on the pump spatial power density still apply in the case of booster stages in order to achieve sufficient gain at wavelengths around 1530 nm for C-band WDM operation.
If spectral hole burning is neglected and the laser line is assumed to be purely homogeneously broadened, the shape of the gain spectrum results from the average inversion, i. e. the population densities of erbium ions averaged along the active fiber length. According to the simulation results depicted in Fig. 3, an average inversion around 0.2 GW/m2 is necessary to achieve sufficient gain on the short wavelength side of the C-band. This means that the spatial power density of the pump radiation has to be higher than the average value close to the point where the pump radiation is launched into the active fiber in order to be able to tolerate lower values after some propagation of the pump radiation with attenuation.
In order to meet these requirements, it may be advantageous to combine codirectional direct pumping with counterdirectional cladding pumping in case of single mode cores. The direct pumping helps to achieve sufficient pump spatial power density for decent gain across the entire C-band and to avoid problems with excess noise generation. The cladding pumping helps to provide sufficient power in order to meet the total output power requirements. So the combination benefits from the individual strengths of both pumping concepts.
4. Coupling the pump radiation into the active fiber
It has been mentioned in the literature that cladding pumping can be deployed beneficially to reduce the complexity of coupling the pump radiation into the active fiber [8]. In the initial proof of concept of amplification in multi core fiber, pump and signal radiation was combined using multiple separate couplers based on single mode technology [12]. Proposals have also been made to integrate the pump and signal combiner in a single device for a reduction of the component count [9].
A block diagram of the concept is shown in Fig. 13. Fiber tapers are deployed to increase the spacing of cores. With sufficient spacing, the signals can be converted to parallel collimated beams by a gradient index lens (GRIN) array. The beams of the signal radiation are combined with the beams of the pump radiation by a dichroic mirror. For coupling of the combined pump and signal radiation into the erbium-doped cores of the active multi core fiber, an inverse structure of GRIN lens array and fiber taper can be deployed.
The initially proposed concept deploys three GRIN lens arrays, two fiber tapers, one dichroic mirror and one fiber bundle supplying the pump radiation. Further integration and reduction of component count is possible by combining the variable waveguide spacing function and the beam collimation function in a single device as shown in Fig. 14. Three dimensional (3D) waveguide structures and the GRIN lens array can both be fabricated by direct laser inscription. The resulting device provides capabilities to convert the output signals from the multi core fiber to parallel collimated beams and vice versa.
Depending on the output power which can be generated by a single commercially available single mode pump laser module and the total power required for direct pumping of the cores, the output signals from a number of laser modules smaller than the number of cores in the multi core fiber can be split up passively. The passive splitter function can also be provided by a waveguide device. With such approaches, the number of components required for combining the pump and the signal radiation can be reduced significantly compared to realization of this function with separate single mode devices.
5. Summary and conclusions
Fundamental characteristics of the amplification process in erbium-doped fibers have been analyzed to derive requirements for the spatial power density of pump radiation. These requirements have been deployed to compare the energy efficiency of different pump concepts for multi core and multi mode fiber. Analytical studies and numerical simulations have revealed that cladding pumping should be considered less energy efficient than direct pumping of erbium-doped cores in multi core fibers of preamplifier stages when decent noise performance and full C-band operation is required. Multi mode fibers are even more energy efficient in this application due to the denser packing of modes.
In case of booster stages with multi core active fibers, codirectional direct pumping can be combined beneficially with counterdirectional cladding pumping to achieve flat gain for full C-band operation together with sufficient output power for many modes and WDM channels. The complexity of direct pumping of multi core fiber cores can be reduced by integration of pump signal combiners. Fabrication of 3D laser inscribed waveguides which combine a taper function with a beam collimation function helps to reduce the component count even further.
Acknowledgments
The authors would like to thank the German research funding association Deutsche Forschungsgemeinschaft (DFG) for supporting this work and the project under the grant number Kr 3596/5-1.
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