## Abstract

Measurements of backscattered Raman amplified spontaneous emission in single-mode dual-hole-assisted fiber indicate suppression of Raman gain by more than two orders of magnitude compared to SMF. These results imply that fiber lasers based on the dual-hole-assisted fiber design are effectively immune to SRS, thus enabling significant power scaling beyond current limits from a single-mode core.

©2005 Optical Society of America

## 1. Introduction

Dual-hole-assisted fiber is a type of micro-structured fiber consisting of a glass core and a cladding having two large air-holes running along the fiber length. These holes are adjacent to the core and are symmetrically placed relative to the core center along a common axis comprising the core and holes’ centers.

An important property of dual-hole-assisted fiber is that of having a fundamental-transverse mode cut-off wavelength. Through proper design this cut-off wavelength can be polarization resolved, thus providing the means to achieve single-polarization propagation.

The spectral range between the cut-off wavelengths of each of the two orthogonal polarization modes defines the single-polarization bandwidth of this fiber [1, 2]. Fibers with 30nm single-polarization bandwidth near 1060nm have been made with extinction ratio of 30-50dB and propagation loss of 20-30dB/km.

Recently, the hole-assisted fiber design was incorporated into a double-clad geometry with Yb^{3+} added to the core. By carefully overlapping the single-polarization bandwidth with the gain profile of Yb, single-transverse-mode and single-polarization high power, double-clad all-fiber lasers were demonstrated with output of over 100W [3–5].

The two holes in this fiber provide an anisotropic cladding and a large core-cladding refractive index delta due to the silica-air interface along one of the two orthogonal axes on the fiber cross section. This leads to relatively large “geometric” birefringence, even with a circular core. Indeed, birefringence in the range 10^{-4} to 10^{-3} has been measured and reported [2]. Physically, each of the two orthogonal polarization modes experiences a different degree of proximity to the holes through the boundary conditions; each mode then experiences different effective core-clad deltas. By carefully designing the distance between the core and the holes, and their dimensions, one can arrange for one of the two polarization modes to have an effective refractive index equal to the cladding index (at a first cut-off-wavelength) and so to leak through the sides of the core through coupling to cladding-modes; the other mode has an effective refractive index significantly above the one of the cladding, thus remaining a bound mode at the same wavelength.

## 2. Suppression of Raman gain in dual-hole-assisted fiber

Light propagating at wavelengths longer than the fundamental mode cut-off wavelength in hole-assisted fiber is strongly coupled to cladding-modes, thus experiences a high distributed loss and reduced overlap with the fundamental. This property can be used to make single-transverse-mode fiber devices with virtual suppression of Raman scattering. We discuss below measurements of counter-propagating Raman amplified spontaneous emission (CP-RASE) in single-mode dual-hole-assisted fiber where reduction of Raman gain by several orders of magnitude is demonstrated compared to single-mode fiber SMF-28 ^{R}.

Figure 1 below shows the experimental set-up used to measure CP-RASE using a circulator fusion spliced to the 1486nm pump laser pigtail and the fiber under test. Dual-hole-assisted fiber was tested in this set-up and compared to SMF-28 ^{R}.

The cut-off wavelength near the end of this fiber measured in another set-up with an optical spectrum analyzer is shown in Fig. 2. The fiber has a single-polarization bandwidth of about 40nm between 1465nm and 1505nm; loss at the peak Stokes wavelength λ_{s}=1592 nm is more than 25 dB.

The hole-assisted single-polarization fiber (SPF) with length L=300m was excited with about 1W of power at the pump wavelength λ_{p}=1486 nm. The bottom trace in Fig. 3 shows the measured CP-RASE power for this fiber. For comparison the top two traces in the same figure show the measured CP-RASE power from 50 and 500m of SMF-28 ^{R}. Clearly, the measured power level scales with SMF fiber length as expected; furthermore, 300m of hole-assisted fiber has a power level at least 23dB below that of 500m of SMF.

One can see in Fig. 3 the loss feature characteristic of dual-hole-assisted fiber in the 1500nm to 1520nnm range.

These results can be readily understood using an analytical model for CP-RASE [6]. It predicts that CP-RASE power is given by

where the intrinsic Raman gain is

and the fiber effective area is

In these expressions α_{p},α_{s} are the fiber propagation loss and I_{p}, I_{s} are the intensity transverse profiles at the pump, Stokes wavelengths, respectively. L is the fiber length, g_{R} is the Raman gain coefficient, P is launched pump power, h is Planck’s constant and Δ*v* is optical bandwidth. The expression given above for P_{ASE} is valid when α_{p} L ≪1. Notice that the effective area is a measure of the degree of overlap of the transverse modes involved in the Raman interaction.

For SMF-28 ^{R} near 1500nm, using the numerical values g_{R}=0.7 x 10^{-13} m/W, P=1W, α_{s} =0.25 dB/km and A_{eff} = 65 x 10^{-12} m^{2} one obtains γ_{R} ∼ 4.7dB/km. Given that α_{s}/γ_{R} ≪ 1 and L∼50m, it is clear that P_{ASE} scales as γ_{R} L in this fiber.

In contrast, for hole-assisted fiber, α_{s}/γ_{R} ≫ 1 and P_{ASE} scales as γ_{R}/α_{s}. One can then expect suppression of RASE by several orders of magnitude. The experimental results captured in Fig. 3 show about 23 dB of suppression. This is limited by RASE from the circulator pigtail which had a length of 2-3 meters. The relatively slow rate of change of P_{ASE} with wavelength around 1510nm observed in Fig. 3 compared to the rate of change of α_{s} captured in Fig. 2 is attributed to the fact that the corresponding γ_{R} and α_{s} rates contribute with opposite signs.

Thus dual-hole assisted fiber provides a single-transverse-mode fiber core that is essentially immune to Raman lasing. This is achieved by a combination of a large distributed loss α_{s} and a large A_{eff}. The effective area substantially increases - or the modal overlap decreases- because the Stokes mode leaks out of the core by coupling to the H_{12} cladding mode which has a relatively large mode field diameter.

At the pump wavelength λ_{p} the mode I_{p} is a core bound mode, well approximated by a Gaussian. At the Stokes wavelength λ_{s} most of the power is coupled to the H_{12} cladding mode. Figure 4 shows the calculated normalized intensity distribution of the H_{12} cladding mode of a dual-hole-assisted fiber as a function of fiber radius at a wavelength above but close to cut-off. For the mode shown in this figure, approximately 2% of the total power is confined to the core. Figure 5 shows the effective area A_{eff} for these two modes normalized with respect to the effective area of a standard single-mode fiber, plotted as a function of the power propagating in the core. Clearly γ_{R} can be reduced by one or two orders of magnitude in hole-assisted fiber due to this increase in A_{eff}.

## 3. Suppression of SRS in dual-hole-assisted double-clad fiber lasers

These results have important implications for fiber laser oscillators. In this case, the fiber laser signal is obviously the Raman pump, and one seeks to maximize the laser threshold for Raman oscillation P_{th} in order to avoid simultaneous lasing at the Stokes wavelength. This can be estimated from the expression [7]

where the second term in parenthesis is the laser cavity loss at the Stokes wavelength and the effective length is L_{eff} = (1-Exp[-α_{p} L])/α_{p}. For example, for an Yb-doped fiber laser with g_{R}=10^{-13} m/W , α_{p}=20 dB/km, L_{eff}=40m and a standard 9μm single-mode core with A_{eff}=65 x 10^{-12} m^{2} the proportionality constant in the expression above is about 16W. Angle-polished fiber facets and AR-coatings can lead to low Fresnel reflection of the order of 10^{-3} at λ_{s} which after further assuming negligible propagation loss at the same wavelength leads to P_{th}=110W. Indeed, a 60m fiber laser with a single-mode core was limited by SRS to an output power of 135W [8]. Rayleigh backscattering limits the minimum reflectivity to a cavity loss of about 40dB, thus P_{th} in standard single-mode cores is limited to less than about 150W.

With dual-hole assisted fiber, this limitation is removed and P_{th} is expected to be much larger. For example, assuming a double-clad laser fiber design with a hole-assisted single-mode core diameter of about 10μm and an inner cladding with diameter of 150μm, then the effective area A_{eff} is about 200 times larger than the corresponding area of a standard step-index single-mode fiber with the same core diameter; furthermore, taking α_{s}=20 dB/km for the cladding propagation loss, α_{p}=2 dB/km for the core propagation loss, g_{R}=10^{-13} m/W and L_{eff}=50m one obtains P_{th} of the order of up to several tens of kW’s. While this high level of output power is certainly beyond the damage threshold of fused silica for single-mode cores under CW operation, it clearly opens the door for kW-class CW single-transverse-mode and single-polarization fiber lasers and pulsed single-mode fiber lasers with high peak power free of SRS and SBS.

## 4. Conclusion

Most of the discussion and experiments above have centered on dual-hole assisted fiber with a single-mode core. However, one common way to increase P_{th} is to reduce power density by increasing the fiber laser mode field diameter. To this end, Large Mode Area (LMA) fibers are used with differential bending loss to filter out excited higher order modes (HOM’s). Dual-hole-assisted LMA fiber combined with differential bending is a subject that deserves further work in the near future.

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