Introduction

During the past decade, the increase in data capacity per fiber has slowed relative to the rapid progress in the 1990’s while, at the same time, the demand for capacity continues to grow exponentially1. Current methods for signal multiplexing, i.e. wavelength-, polarization-, time-, and quadrature-division multiplexing, are approaching their fundamental limits so new means of multiplexing are needed. Space-division multiplexing2 in the form of multi-core fibers has already been used to achieve new heights in data capacity from a single laser source3,4; in single-core fibers supporting multiple spatial modes, long-distance propagation of optical signals has been demonstrated5,6; and recently, data transmission in a few-mode multi-core fiber was presented7. One important challenge of mode-division multiplexing (MDM) systems is building multi-mode optical amplifiers, that have mode-equalized amplification of all spatial modes, to compensate for example for distributed fiber loss; it is desirable for a multi-mode amplifier to avoid mode-dependent gain (MDG) in order to maximize capacity8. As for traditional single-mode systems, discrete Erbium-doped fiber amplifiers have been applied to multi-mode systems as well and low MDG has been achieved for some of the modes in fibers with specially designed Erbium-doping profiles9,10,11.

Another approach to counter-balance fiber losses is distributed Raman amplification, which is also widely used already in single-mode networks due to its superior noise properties in the backward-pumped configuration12. Furthermore, it has been shown theoretically that minimal MDG is possible by coupling pump power into a specific combination of spatial modes13, or by optimizing fiber design14, which makes Raman amplifiers a promising candidate for realizing low-loss, multi-mode transmission links over large distances.

Earlier work has demonstrated Raman gain between higher-order modes with the pump in only one mode5,15,16. Besides the obvious challenges related to exciting the pump in a specific combination of modes, it may often also prove difficult to determine the exact mode combination that leads to the lowest possible MDG because the required fiber data are unavailable from the fiber supplier. In this paper, we present an experimental characterization of the intermodal Raman intensity overlap of the guided modes of a two-moded (6 modes counting polarisation and LP11a and LP11b) few-mode fiber (FMF) using mechanically induced long-period gratings (LPGs) to excite the higher-order modes. Using the obtained results, we demonstrate backward pumped Raman amplification of a continuous wave (CW) signal through 10 km of a two-moded fiber with a very low MDG of 0.25 dB per 10 dB gain by pumping in a combination of the LP01 and LP11 modes. The mode-differential gain obtained required no prior knowledge about the Raman intensity overlaps of the fiber.

Results

The purpose of the present work is to characterize the intermodal Raman overlaps and use them to achieve a minimal MDG in a backward-pumped Raman fiber amplifier. This is done by coupling the pump light into the fiber in the correct combination of the LP01- and LP11-modes. As will be discussed in the Methods section below, due to strong mode-coupling, the two-fold quasi-degenerate LP01-modes and four-fold quasi-degenerate LP11-modes are simply considered as two distinct groups of modes. We carry out two measurements: Firstly, the Raman gain of a continuous wave signal in the LP01-mode is measured vs. total pump input power for five different modal compositions of the pump, i.e. different combinations of the LP01- and the LP11-modes. Secondly, both pump and signal are converted to LP11. This data is used to calculate the Raman intensity overlaps relative to the LP01-LP01-overlap, which is all that is needed to find the correct combination of pump modes.

Raman intensity modal overlaps

Assuming both pump, and signal to be CW sources, the signal power , in spatial mode i, and the counter propagating and copropagating pump power , in spatial mode j, is governed by17

where αs and αp are loss coefficients for signal and pump wavelengths λs and λp, and gR is related to the spontaneous Raman scattering cross section. Note that γR and αp,s are assumed mode-independent. The intensity overlap integrals are defined as

with Ii being the intensity of mode i integrated over the entire fiber cross section. Solving (1) and (2) using the undepleted pump approximation, we arrive at an expression for the on/off gain

where Leff = (1 − exp[−αpL])/αp is the effective fiber length and L is the physical fiber length. The setup used is a backwards pumped configuration, where the pump has only two different spatial profiles (corresponding to LP01 and LP11), so Eq. (4) can be reduced to

for the signal in mode i, where ηp is the degree of conversion of the pump from LP01 to LP11 (ηp = 0 when all the pump power is in LP01, and ηp = 1 when all the pump power is in LP11) and Pp is the total input pump power (in all modes). Using the setup which is described in the methods section below, 65 measurements were carried out with 5 different conversion degrees and 13 different pump power levels varying from 0 to 1200 mW for each conversion degree. From the expected form of the gain, Eq. (5), we fitted a function of the form

to the data, where c1 and c2 are fitting parameters. The result is presented in Fig. 1a where data and fitting lines are shown at the five different values of ηp. The obtained values for the fitting parameters are c1 = 8.50 dB/W and c2 = −4.48 dB/W. The theoretical expression is in excellent agreement with the obtained data with these values of the fitting parameters. From these values the ratio of the Raman intensity overlaps between the LP01-LP01-modes and LP01-LP11-modes is obtained

Figure 1
figure 1

(a) Measured Raman gain vs. input pump power for five different pump conversion degrees, ηp; the lines result from the two-parameter fit evaluated at each conversion degree. (b) Measurements of Raman gain for signal and pump in LP11. For comparison is shown the measurement with pump in LP11 and signal in LP01.

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by comparing (5) and (6). This result agrees well with the value of 0.48 obtained from simulated mode-profiles provided by the fiber supplier.

Subsequently, the signal was coupled to the LP11-mode with the highest attainable efficiency, (ηp > 0.99), and the pump was converted to the LP11-mode with an efficiency of ηp = 0.925, see the Methods section for details, and the Raman gain of the LP11-signal was measured vs. the input pump power. A linear function of the type

was fitted to the data. From this the ratio is calculated, taking into account the pump conversion degree. The slope obtained from the fit to the LP11-LP11 -data was c3 = 4.74 dB/W. We assume wavelength independence of the overlap integrals (i.e. that the LP01-LP11 and LP11-LP01 overlaps are nearly identical). By comparison of Eqs (8) and (6) to (5) we note that c1 = kF01,01 and c3 = k(F01,11 + ηp(F11,11 − F01,11)) with . Using Eq. (7) for the ratio F01,11/F01,01, these two expressions can be rearranged to give

This is compared to the simulated values for LP11a-LP11a and LP11a-LP11b of 0.72 and 0.24, respectively. The measured overlap is, as expected, an intermediate value that depends on the mode-coupling within the LP11 mode-group. In Table 1 the measured overlaps are summarized, and in Table 2 the simulated overlaps are shown. Notice that the overlaps are normalized so that the LP01-LP01-overlap equals one.

Table 1 Measured values for overlap integrals relative to the LP01-LP01 overlap.
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Table 2 Simulated overlap integrals for all modes.
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Mode-equalized Gain Based on Measured Overlaps

Since the LP11-LP11 and LP11-LP01 intensity overlaps often turn out to be very similar in FMFs, relatively low differential gain can be obtained by simply launching the pump completely into LP11. This was experimentally verified by R. Ryf et al.6 where a differential gain of 0.5 dB per 10 dB of gain was observed. For the fiber used in this work, such a scheme results in a differential gain of 1 dB per 10 dB of gain as obtained from the data shown in Fig. 2b (the differential gain in the figure is slightly lower since the pump is only converted 95% into LP11). Using our knowledge of the intensity overlap integrals, the condition for equal signal gain across the two signal-modes, G11 = G01, can be written as

Figure 2
figure 2

(a) Raman gain for both a LP01 and LP11-signal with a pump in the mixture of 83% LP11 and 17% LP01 demonstrating near-equal gain for the two signals. (b) MDG between the two signal modes for pump almost completely converted to LP11 and pump in the mixture of 83% LP11 and 17% LP01. A line for 0.5 dB gain difference per 10 dB gain is included for reference.

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This equation can be solved, using the experimentally obtained values for the ratios F11,11/F01,01 and F01,11/F01,01, to obtain an equal-gain pump conversion of

In Fig. 2a the results of measuring a signal launched first completely in LP01 and then completely in LP11 with a pump conversion of ηp = 0.83, i.e. slightly below the optimal value, are shown. From the figure it is clear that very little mode-dependent gain remains (compare with Fig. 1b). The mode-differential gain as a function of the mean gain is seen in Fig. 2b, showing a residual MDG of only 0.25 dB per 10 dB of Raman gain as obtained from the fitted lines. This differential mode gain is, to the best of our knowledge, the lowest that has so far been experimentally demonstrated. The reason for the fluctuation in MDG is most likely due to mode coupling between LP11a and LP11b. The LPG preferentially couples to the LP01 mode that we detect in the optical spectrum analyzer (OSA), as explained in the Methods section. This means that any mode coupling between LP11a and LP11b shows up as a small variation in the measured amplified signal. In the ηp = 0.83 (blue dot) measurement the back coupling is slightly more unstable compared to the ηp = 0.95 (red circle). This is due to the different configuration of the back coupling LPG.

Methods

The intermodal Raman gain is measured using the experimental setup shown in Fig. 3. The setup is a distributed backwards pumped multi-mode Raman amplifier with a CW laser operated at 1550 nm as the signal source, and an unpolarized 1455 nm Raman fiber laser used for optical pumping. The characterized fiber is a 10 km, 2-moded graded-index fiber.

Figure 3
figure 3

The experimental setup used for all measurements.

ISO: Isolator, OSA: optical spectrum analyser, PC: polarization controller, LPG: long period grating, FMF: few-mode fiber. Red lines signify FMF and black lines single mode fiber with crosses indicating splices. The number on the gratings indicate pitch.

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Higher-Order Mode excitation

The excitation of higher-order modes is achieved by use of mechanically induced LPGs, which are created by pressing the fiber between a periodically grooved aluminum block and a rubber pad. This creates a periodic perturbation in the fiber index, which induces mode coupling if the pitch of the induced gratings matches the difference in propagation constants of the modes18.

Using a broadband supercontinuum source at the signal input the mode-converted wavelengths are observed in the OSA2 as a drop in the power spectrum due to the FMF to single mode fiber splice working as a mode filter. The effective pitch of the LPG is changed by adjusting the angle of the grooves with respect to the fiber, until maximum mode-conversion is achieved at the signal wavelength. The use of a supercontinuum source for calibration is not strictly necessary if the difference in propagation constant for the modes of interest is known, but it facilitates the excitation process. Based on the knowledge of the propagation constants the pitch for the pump wavelength was calculated to be 527 μm, which is in excellent agreement with the 523 μm pitch experimentally observed at maximum conversion. The LPGs are polarization dependent18, so a polarization controller (PC) is used to optimize conversion of the polarized signal source. After propagation through the fiber the signal is converted back to the fundamental mode using a second LPG.

From standard mode-coupling theory the coupling strength between the modes in a step-index fiber is given by19

where ψ1,2 are the scalar mode profiles of the fiber. Since the grooves of the mechanical block are only applied to the fiber from one direction, the perturbation Δε(r, ϕ, z) is asymmetric with respect to this direction. Since the LP01 mode is a circularly symmetric mode, we expect that mainly the LP11 mode which is spatially asymmetric with respect to the pertubation direction is excited in the induced grating. However, since we use an unpolarized pump, both polarizations of this spatial mode are excited resulting in an almost equal excitation of the four full-vectorial modes (TE01, TM01, HE21a and HE21b) that constitute the pseudo-LP11 modes. The strong coupling between these modes is expected to quickly smooth out any difference in the excitation17. Thus, following a similar approach as Antonelli et al.20, we only consider the excitation of the quasi-degenerate groups of modes, LP01 and LP11, consisting of two and four nearly degenerate modes, respectively. In this regard, the measured overlaps are essentially an average over these groups.

Characterization of fiber under test

For all measurements the signal power launched is 0.4 mW, and the launched pump power is varied from 0 to 1200 mW. For each pump power the on/off gain is measured by OSA2. The ratio of the LP01-LP01 and LP01-LP11 overlaps is found with the signal in LP01 and the pump in varying mixtures of both LP11 and LP01 by adjusting LPG2 to the desired pump mode conversion.

For the LP11-LP11 gain measurement LPG1 and PC1 were adjusted to obtain more than 99% signal conversion, and LPG2 was adjusted to obtain a maximum of ηp = 0.92 pump conversion; The lower pump conversion is due to the pump being unpolarized. The LPG2 conversion bandwidth is large enough such that, by optimizing PC2, 12 dB of the signal is converted back to LP01. The back conversion is necessary due to the mode-filtering effect of the single-mode to multi-mode fiber splice. The gain of the back converted signal is the LP11-LP11 gain.

Equal modal gain measurement

To equalize the modal gain, we first adjust LPG2 so that we are pumping in a combination of the LP11 and LP01 modes very close to the optimal value 85% conversion as obtained from the previous measurements, see Eq. (11). We then first adjust LPG1 and PC1 to maximize signal conversion (ηp > 0.99) and measure the gain of this mode. Then LPG1 is lifted so that the signal is a pure LP01-mode and the gain for this mode is measured. The difference in the gain for these two signal-modes then gives the mode-differential gain.

Conclusion

We have experimentally characterized the intermodal Raman overlaps in a few-mode fiber by varying the launched pump power and the conversion efficiencies of the pump and signal using mechanically induced long-period gratings for mode excitation. The overlap integrals (relative to the LP01-LP01 overlap) for all modal combinations were obtained in this way for a specific few-mode fiber. By use of the obtained overlaps, it was further demonstrated how a mode-differential gain of only 0.25 dB per 10 dB overall gain is obtained by pumping in a specific combination of the LP11 and LP01 modes. In the specific few-mode fiber under test, the differential gain was shown to be significantly lower when pumping in the determined combination of modes compared to when pumping only in LP11.

Additional Information

How to cite this article: Christensen, E. N. et al. Experimental characterization of Raman overlaps between mode-groups. Sci. Rep. 6, 34693; doi: 10.1038/srep34693 (2016).