Abstract

Recently, chirped and tilted fiber Bragg gratings (CTFBGs) have received great attention because they can realize suppression of stimulated Raman scattering (SRS) in high-power fiber lasers. In this study, the possible coupling between the core modes and cladding modes in CTFBGs inscribed in large-mode-area double-cladding fibers is investigated for the first time. Theoretical results show that the coupling between the LP11 mode and cladding modes would destroy the transmission spectra envelope only considering the coupling of LP01 for single-mode CTFBGs, which will degenerate the SRS suppression performance. This was confirmed experimentally by measuring the spectral response under different mode excitations. A reliable method is demonstrated to ease the LP11-excitation-induced spectral deterioration by choosing an appropriate chirp rate for the inscription of CTFBGs, which is useful for improving the Raman suppression effect of large-mode-area double-cladding CTFBGs in high-power fiber lasers.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Over the last decade, high-power fiber lasers have seen rapid penetration into various fields, such as industrial manufacturing, scientific research, and medical applications [1], because of their more compact construction, higher energy conversion efficiency and relatively better beam quality compared with their bulk counterparts [1]. To date, 20-kW fiber amplifiers and 8-kW fiber oscillators have been reported [2,3]; however, barriers to achieving higher power still remain, where stimulated Raman scattering (SRS) is one of the key limitations to the power scaling of fiber lasers. To date, many methods have been used to mitigate SRS in fiber lasers [46]. However, conventional mitigations may cause related problem such as transverse mode instability (TMI) [7,8]. Utilization of broad-band rejection filters, such as long-period gratings (LPGs), is another feasible method to mitigate SRS [9]. However, LPGs have inherent cross-sensitivities to multiple external factors, such as, temperature, which would cause an excursion of the central wavelength and a decrease in the suppression ratio [10].

As a kind of wide-band spectral filter, chirped and tilted fiber Bragg gratings (CTFBGs) have received much attention in recent years because of their effective Raman suppression in high-power fiber lasers [1117] along with advantages of an adjustable wavelength range and good thermostability [14]. In 2017, we first reported the application of single-mode CTFBGs for Raman filtering in fiber amplifiers [11]. Then, by inserting CTFBGs between the seed laser and the amplifier stage, we reported impressive suppression of SRS in 5 kW fiber amplifiers including tandem pumping architecture [12] and direct diode pumping architecture [13]. To further expand the applicability of CTFBGs in high-power fiber oscillators and amplifiers, we first studied the fabrication of CTFBGs in large-mode-area double-cladding fibers (LMA-DCFs) with a core/cladding diameter of 20/400 µm [14]. In 2019, Jiao et al. achieved effective Raman suppression in a kW-scale monolithic fiber oscillator using CTFBGs inscribed in 20/400 µm fibers [16]. Recently, Lin et al. reported Raman suppression within the gain fiber of high-power fiber oscillators, also using CTFBGs inscribed in 20/400 µm fibers [17]. Although CTFBGs inscribed in LMA-DCFs have been used for Raman suppression in high-power fiber laser systems, only fundamental mode coupling was considered in these studies. In actual operation of LMA-DCFs, such as 20/400 µm fibers, high-order mode like LP11 would inevitably be excited, which could affect the Raman suppression effect of CTFBGs. Therefore, studying high-order mode coupling in LMA-DCF CTFBGs is necessary, especially for fiber lasers with relatively poor beam quality.

In this paper, we study the possible coupling between the core guided LP11 mode and cladding modes in LMA-DCF CTFBGs for the first time. Simulations show that the transmission envelope is deteriorated considering the coupling of the LP11 mode to the cladding modes. It is theoretically and experimentally verified that the attenuation bandwidth becomes broader with a decrease in the central suppression ratio when high-order mode excited. Furthermore, a feasible method is proposed to promote the coupling efficiency of the CTFBGs by slightly adjusting the chirp rate according to the mode proportion of the input light, which has guiding significance for the property optimization of CTFBGs in Raman suppression of high-power fiber lasers.

2. Simulations

Before the formal spectral simulation, it is vital to compute two categories of databases, including the corresponding coupling constants and resonant wavelengths, both of which are co-decided by the features of the guided modes in the fiber and the structure of the selective grating. We consider the typical modality of optical fibers consisting of a core, a cladding, and surrounding air (Fig. 1(a)). Taking the standard structure of two commercial LMA-DCFs for reference, two core modes are allowed to transmit, including the LP01 (Fig. 1(b)) and LP11 (Fig. 1(c)) core modes. The corresponding structural configurations of the LMA-DCFs are listed in Table 1. In this model, the surrounding is air as LMA CTFBGs are often used without coating. Subsequently, the structure of a CTFBG is discussed in the first subsection.

 figure: Fig. 1.

Fig. 1. The (a) LMA-DCF structure confines the core modes including (b) LP01 and (c) LP11.

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Tables Icon

Table 1. Parameters associated with various kinds of LMA-DCFs (uncoated).

2.1 Structure of CTFBGs

As shown in Fig. 2, CTFBGs are similar in design to a non-uniform period with chirped fiber Bragg gratings (CFBGs), compared with which the grating plane in CTFBGs skews off the fiber axis at an angle of θ. Here the direction of the fiber axis is defined as the z-axis and the direction along which the refractive index (RI) originally alternates is defined as z’. Because of the tilted plane, the period of the grating along the z-axis is lengthened by:

$$\varLambda {\rm{ = }}{{{\varLambda _g}} \mathord{\left/ {\vphantom {{{\Lambda_g}} {\cos \theta }}} \right.} {\cos \theta }},$$
where Λg is the original period along the z’ axis. In addition, considering the chirp introduced in the grating, Λg can be derived as:
$${\varLambda _g}{\rm{(}}z){\rm{ = }}{\varLambda _{g0}}(1 + {{zF} \mathord{\left/ {\vphantom {{zF} L}} \right.} L})\quad{\rm{ (}} - L{\rm{/2}} \le z \le L{\rm{/2),}}$$
where Λg0 is the average period of the grating, F is the chirp coefficient, and L is the length of the grating.

Based on the uncoated structure of an LMA-DCF (Fig. 1(a)), the original RI modulation along the z’ axis can be expressed as:

$${n(r,\varphi ,z^{\prime}) = \left\{ {\begin{array}{lc} {n_1} + {\Delta }n\cos ({\beta _{Bragg}}z^{\prime}) & \textrm{}r \le {a_1}\\ {n_2} & \textrm{}{a_1}{ < }r \le {a_2}\\ {n_3}&{r} > {a_3} \end{array}} \right.},$$
where n1 is the RI of the fiber core, n2 is the RI of the fiber cladding, n3 is the RI of the surrounding atmosphere, Δn is the amplitude of the ac RI modulation and βBragg=2π/Λg representing the Bragg wave vector of a CTFBG with a period Λg along the z’ axis.

 figure: Fig. 2.

Fig. 2. Axial-section schematic of a CTFBG.

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To describe the modulation of the axial RI, a certain coordinate transformation with the original x-z axis rotated by an angle of θ to x′-z′ axis (Fig. 2) can be introduced as follows:

$$z^{\prime} = z\cos \theta - x\sin \theta .$$

Inserting the coordinate transformation into Eq. (3), the modulation of RI in the grating can be rewritten as:

$$\boldsymbol {\Delta} {\boldsymbol {n}_{ac}} = \Delta n\cos [{{\beta_{Bragg}}(z\cos \theta - x\sin \theta )} ],$$
where Δnac represents the alternating part of RI. The expression of index modulation is used in computing the overlap integral in the 4th subsection. In the computing, CTFBGs inscribed in two categories of LMA-DCFs are considered, of which the parameters (Table 2) were set according to the actual fabrication in our laboratory.

Tables Icon

Table 2. Structural parameters of CTFBGs in simulation.

2.2 Cladding mode field distribution

The mode field confined by the fiber structure can be precisely derived by solving the vector wave equation, the solved results of which, however, can be rather complex. As a matter of fact, many reports have shown that the linearly polarized (LP) approximation is also a reliable method for solving the coupling between guided modes and cladding modes with both short- and long- period gratings [1822]. Here, a two-layer model is used to calculate the mode distribution of cladding modes [20], ignoring the fiber core. Although LP simplification was adopted, the complete calculation of the spectral response of CTFBGs still requires a tremendous workload when a large number of cladding modes need to be included, let alone the calculations involving the mutual coupling between core modes because of the LMA condition.

Because of the small coverage of the RI modulation (only inside the fiber core), the core modes can only couple to some specific groups of cladding modes [18,22] with the modes that have a weak distribution in the core, LP24 and LP34 (Fig. 3(c) and (d)), uncoupled. In the simulation, two groups of cladding modes, LP0n and LP1n, both of which have a strong field intensity distribution in the core, are considered. Typical examples of these two types of mode field distributions are shown in Fig. 3(a) and (b).

 figure: Fig. 3.

Fig. 3. Intensity distribution of several typical cladding modes: (a) LP06, (b) LP1,11, (c) LP24 and (d) LP34.

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The tilt design of the grating plane in the CTFBG is also a kind of anisotropic structure, that affects the mode polarization state. However, considering the small-angle tilt of the grating discussed here, the change in the polarization state of the propagating modes is neglected in the later simulation.

2.3 Resonant wavelengths of CTFBGs

Based on the phase-match condition [23], the corresponding resonant wavelengths of mode coupling can be obtained as

$${{\boldsymbol {\varLambda} _{res}}{\rm{ = }}\frac{{{\varLambda _g}(z)}}{{\cos \theta {n_1}}}\boldsymbol {N} \boldsymbol {\sigma} {\boldsymbol {N}^T}\,{\rm{with}}}$$
$${{\boldsymbol {\varLambda} _{res}}{\rm{ = }}\;\left[ {\begin{array}{{ccc}} {\lambda_{res,01}^{core}}&{\lambda_{res,01 - 11}^{core}}&{\lambda_{res,01 - i}^{clad}}\\ {\lambda_{res,11 - 01}^{core}}&{\lambda_{res,11}^{core}}&{\lambda_{res,11 - i}^{clad}}\\ {\lambda_{res,i - 01}^{core}}&{\lambda_{res,i - 11}^{core}}&{\lambda_{res,i}^{clad}} \end{array}} \right],\boldsymbol {N}{\rm{ = }}\;\left[ {\begin{array}{{cc}} {\begin{array}{{c}} {{n_{core,01}}}\\ {{n_{core,11}}}\\ {{n_{clad,i}}} \end{array}}&{\begin{array}{{c}} {{n_1}}\\ {{n_1}}\\ {{n_1}} \end{array}} \end{array}} \right]\,{\rm{and}}\,\boldsymbol {\sigma} {\rm{ = }}\left[ {\begin{array}{{cc}} 0&1\\ 1&0 \end{array}} \right],}$$
where Λres is a matrix with elements representing each resonant wavelength of the different kinds of mode coupling mentioned above, the superscript ‘core’ and ‘cladding’ of the matrix elements respectively represent the coupling of core modes and mutual coupling between core and cladding modes, the subscript represents the order of the coupling modes, nclad,i is the effective index of the ith cladding mode, and ncore,01 and ncore,11 represent the effective index of the LP01 and LP11 core modes, respectively. Furthermore, based on Eqs. (2) and (6), the bandwidth of each coupling resonance can also be expressed in matrix form as:
$$\Delta {\boldsymbol {\varLambda} _{res}}{\rm{ = }}\frac{{{\varLambda _{g0}}F}}{{\cos \theta {n_1}}}\boldsymbol{N}\boldsymbol{\sigma} {\boldsymbol{N}^T}\,{\rm{with}}$$
$$\Delta {\boldsymbol {\varLambda} _{res}}{\rm{ = }}\;\left[ {\begin{array}{{ccc}} {\Delta \lambda_{res,01}^{core}}&{{\rm{ }}\Delta \lambda_{res,01 - 11}^{core}}&{{\rm{ }}\Delta \lambda_{res,01 - i}^{clad}}\\ {{\rm{ }}\Delta \lambda_{res,11 - 01}^{core}}&{\Delta \lambda_{res,11}^{core}}&{{\rm{ }}\Delta \lambda_{res,11 - i}^{clad}}\\ {{\rm{ }}\Delta \lambda_{res,i - 01}^{core}}&{{\rm{ }}\Delta \lambda_{res,i - 11}^{core}}&{\Delta \lambda_{res,i}^{clad}} \end{array}} \right].$$

Based on the formula deduced above, two important aspects that primarily affect the resonant wavelength and corresponding bandwidth should be manifested. On the one hand, the structural parameters of the CTFBG play a large part in determining the resonant wavelength. Acting as connecting thread filling up the detuning in phase matching, the period Λ along the fiber axis, which is jointly dependent on the original period of the grating Λg and the tilt angle θ, linearly influences the coupling wavelength λres according to Eq. (6).The corresponding bandwidths of each resonance also show a linear growth with an increase in the grating period Λg and chirp rate F according to Eq. (7). On the other hand, it is conspicuous that the effective indices of both pairwise-coupling modes also have a large influence on the determination of individual resonant wavelengths, according to Eq. (6).

Actually, the resonant wavelength of one cladding mode is also proportional to the sum of effective indices (ncore+nclad,i) of the coupling core mode and cladding mode. Therefore, with the LP11 core mode considered, the resonant wavelength of the cladding modes would see a drift for the inter-mode dispersion (difference between ncore,01 and ncore,11) between the LP01 and LP11 core modes. Figure 4(b) visually reveal the resonant wavelength drift of cladding modes for coupling with different core modes.

 figure: Fig. 4.

Fig. 4. (a) Mode dispersion of two typical groups of cladding modes (b) Comparation of resonant wavelengths between coupling with LP01 and LP11 core modes. (ncore and nclad represent effective index of core modes and cladding modes, respectively).

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A shift in the resonance peak wavelength would also occur when the effective indices of cladding modes, which are extraordinarily sensitive to the temperature and RI of the ambient medium, vary with the change in external factors. Moreover, as the increasing inter-mode dispersion between higher-order neighboring modes showed in Fig. 4(a), a larger wavelength spacing between the adjacent resonances could be expected in the shorter wavelength direction, resulting in a series of changes in the envelope of transmission spectra under different tilted angles. Further discussion of the properties of the spectra of CTFBGs will be continued in the next subsection.

2.4 Coupling constants and simulated spectra

Computing of coupling constant is another essential component in simulating the resonance of mode coupling, which can be used to represent the coupling strength of two modes, and coupling constant is mainly defined by the overlap integral of the pair-wise coupling mode field along with the RI modulation. The coupling constant κl,m of the two arbitrary modes coupling with each other can be expressed as [19]:

$${\boldsymbol {\kappa} _{l,m}} = \frac{\omega }{4}\int_0^{2\pi } {d\phi } \int_0^\infty {rdr\Delta \varepsilon (r){\boldsymbol {e}_l} \cdot \boldsymbol {e}_m^\ast } ,$$
where Δε(r) = 2n1Δnac represents the permittivity perturbation in the grating, ω represents the light frequency and el and e*m represent the normalized electric field distributions of the lth and mth guided modes, respectively.

Based on Eqs. (5) and (9), the coupling between two different core modes can be considered non-existent in the ideal fiber Bragg grating (FBG) if RI modulation is considered transversely uniform, because of the inconsistent symmetry of LP01 and LP11 (Fig. 5). Only the modes in the same symmetry can couples with each other. However, the tilted grating plane induces an inhomogeneous profile of cross RI (pink line in Fig. 5), which gives rise to a nonzero overlap integral between the fundamental mode and modes with odd symmetry (gray line in Fig. 5). Basing on Eq. (9), the self-coupling (coupling between the same modes transmitting in opposite directions) and mutual-coupling (coupling between different modes transmitting in opposite directions) constants of the core modes were all calculated as shown in Fig. 6(a), which shows the alternate change in κ01, κ11 and κ01,11, corresponding to self-couplings of LP01 and LP11 and mutual coupling between LP01 and LP11, respectively, with increasing tilt angle (the parameters of the 15/130 μm fiber are used in this part of the simulation). Observing the alternation of coupling constants, an apparent conclusion can be drawn that both the self and mutual coupling of core modes would be dramatically weakened when the tilt angle increases to greater than 4°.

 figure: Fig. 5.

Fig. 5. The fields of the LP01 (even symmetry) and LP11 (odd symmetry) modes are shown in a cross-section of the fiber, where a as the core radius and r as radial coordinate in the transverse profile of the fiber, along with the transverse RI modulation profiles in FBG and CTFBG, respectively. The overlap of two modes with the profile of index modulation in CTFBG show positive value in either side of the fiber core, which means uneven transverse RI modulation can induce mode coupling between modes of different symmetry.

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 figure: Fig. 6.

Fig. 6. Coupling constants of (a) self and mutual interacting between two core modes and (b) self-interacting of LP01 core mode with various core sizes.

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In Fig. 6(b), we show the drop-off of the normalized κ01 for various radii of the fiber core with the increase in tilt angle. The coupling constants with a larger radius show a steeper decrease as the tilt angle increases. In other words, for the CTFBGs fabricated in fibers with larger core sizes, the core mode coupling could be strongly suppressed even with a smaller tilt angle, which has already been repeatedly verified by detecting the reflectivity spectra of CTFBGs [14,16]. Therefore, in the latter spectral simulation, the couplings between the core modes are neglected.

The largest part of the database must be prepared in advance and lies in the calculation of mutual coupling constants that define the interaction strength between core modes and numerous cladding modes. It is further used in the coupled mode equation for spectral computation [24]. The following is an analysis of the evolution of coupling coefficients, along with the corresponding manifestation about the simulated transmission spectra. Figure 7 shows how the mutual coupling coefficients (parameters of 15/130 are still used), which includes four types of coupling (interaction between LP01 and LP0n, LP01 and LP1n, LP11 and LP0n, and LP11 and LP1n), varies with both the radial order n and tilt angle from 0 to 10 degrees. To simplify the simulation, only cases of one pure core mode excitation are considered.

 figure: Fig. 7.

Fig. 7. Mutual coupling constants between allowed (a) LP01 core mode and LP0n cladding modes, (b) LP01 core mode and LP1n cladding modes, (c) LP11 core mode and LP0n cladding modes, and (d) LP11 core mode and LP1n cladding modes evolve with increasing radial order n and growing tilt angle.

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By observing the alternate change in simulated coupling constants shown in Fig. 7, four main regularities can be summarized, matching up with some information which is embodied in the simulated spectra shown in Fig. 8. Firstly, for a larger tilt angle, the radial order of the cladding modes, which strongly couple with the core modes, becomes higher (Fig. 7), leading to a shift in the central wavelength (Fig. 8(a)–(d)), i.e., the larger the tilt angle, the higher the order of the strongly-coupled cladding mode and thus the shorter the central wavelength, because of the smaller effective index of coupled cladding modes. In addition, although the total number of cladding modes with obvious coupling constant remains unchanged while the tilt angle grows (Fig. 7), it still makes sense that, as displayed in Fig. 8(a)–(d), the spectral wavelength range broadens with increasing tilt angle because the wavelength spacing between the higher-order cladding modes would become larger (Fig. 4(b)). Moreover, for a small tilt angle close to zero, stronger coupling is seen in Fig. 7(a) and (d) because of the good field overlap between modes with the same symmetry (LP01 and LP0n are both axis-symmetric while LP11 and LP1n are circuit-symmetric), in contrast with a large tilt angle condition where both core modes exhibit a weaker coupling with axis-symmetric cladding modes (Fig. 7(a) and (c)), which is attributed to the severe axial asymmetry of the RI profile.

 figure: Fig. 8.

Fig. 8. Simulated transmission spectra of CTFBGs (a) inscribed in 15/130 μm fiber with LP01 mode excited, (b) inscribed in 15/130 μm fiber with LP11 mode excited, (c) inscribed in 20/400 μm fiber with LP01 mode excited, and (d) inscribed in 20/400 μm fiber with LP11 mode excited, are displayed including their spectral variation with different tilt angles. More detailed comparison between spectra under different core mode excitation are further exhibited while picking the tilt angle of (e) 4° (15/130 μm fiber) and (f) 6° (20/400 μm fiber) as examples.

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The last point to mention is practically relevant to the application of CTFBGs in SRS filtering. As shown in Fig. 7(a)–(d), all sets of coupling coefficients (either with LP01 or LP11 mode excited) follow an oscillational change with the increasing radial order n of the cladding modes. However, different change rule appears when it comes to the respective radial orders of the cladding modes strongly coupled with the core-guided LP01 mode (Fig. 7(a) and (b)) and LP11 mode (Fig. 7(c) and (d)). The radial orders of cladding modes strongly coupled with LP01 mode are discontinuous compared with the successive radial orders of those strongly coupled with LP11 mode. This different coupling rule is further shown in the spectra of the CTFBG in Fig. 8(e), where the red curve presents two distinct dips. The middle hillock between two dips is just caused by the weaking coupling between LP11 mode and cladding modes with radial orders in the middle-disconnected part. For 1134 nm (the central SRS wavelength of a 1080-nm fiber laser), the suppression ratio has a gap of 9.08 dB between the LP01 coupling (blue spectrum) and LP11 coupling (red spectrum), as the 1134 nm is exactly located in the saddle bewteen two dips in the red curve. In other words, it primarily reveals that some negative influence would be caused to the filtering effect of CTFBGs because of the excited LP11 core mode. This conclusion is further supported by the corresponding experiments, the results of which would be discussed and compared with the simulation in the next section.

3. Experimental results and discussion

3.1 Experimental setup and multimode excitation

The experimental setup shown in Fig. 9 is constructed to realize obvious excitation of multiple core modes in LMA-DCF, where three functional elements are combined, i.e., the mode excitation controller, the signal generator and the receiver. The mode excitation controller consists of a laptop and fusion splicer, the two sides of which fixed the pigtails of the single-mode fiber (HI1060) and LMA-DCF with clamps. By operating the manual controller of the fusion splicer through the laptop, the incident position on the LMA-DCF with respect to the HI1060 can be achieved with high accuracy (Fig. 9). Changing transverse offset between two fiber cores is a common method for excitation of higher-order mode in fibers [25,26].

 figure: Fig. 9.

Fig. 9. Experimental realization of multiple modes excitation. ASE, amplified spontaneous emission; OSA, optical spectrum analyzer.

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The CTFBGs written in LMA-DCF were realized by the UV exposure system with a phase mask rotated by a certain angle around the axis of the inscribed light beam [14]. Two CTFBGs (length of 35 mm) were inscribed on 15/130 and 20/400 μm fibers using a phase mask with periods of 785.8 nm and 788.8 nm, respectively. Rotated by 4° and 6°, the corresponding chirp rates of the phase mask are 0.8 nm/cm and 4 nm/cm, respectively.

To analyze the proportion of the excited core modes quantitatively, the multimode interference effect [27] is introduced theoretically. The power coupling coefficient ημ of the μth core mode can be obtained using an overlap integral:

$${\eta _\nu } = \frac{{{{\left|{\int_0^{2\pi } {d\theta } \int_0^\infty {rdr{\boldsymbol {e}_i}(r,d) \cdot {\boldsymbol {e}_\nu }} } \right|}^2}}}{{{{\left|{\int_0^{2\pi } {d\theta } \int_0^\infty {rdr{\boldsymbol {e}_i}(r,d)} } \right|}^2}{{\left|{\int_0^{2\pi } {d\theta } \int_0^\infty {rdr{\boldsymbol {e}_\nu }} } \right|}^2}}}.$$

Here, ei(r,d) and eν represent the profiles of the incident field and the νth core mode respectively and d is the offset between the centers of the incident field and the receiving fiber core. Based on [Eq. (10)], the variation curves of mode excitation which change with the offset d, are computed and displayed in Fig. 10 (the incident field ei(r,d) was simulated using the parameters of the HI1060 fiber with the a core diameter of 5.3 μm, cladding diameter of 125 μm and numerical aperture of 0.14). When the two core modes see an equivalent excitation, the offset values are 5.0 μm and 5.6 μm, respectively, for 15/130 and 20/400 μm LMA-DCFs.

 figure: Fig. 10.

Fig. 10. Power coupling coefficients of LP01 and LP11 core mode when changing the incident field offset with (a) LMA-GDF-15/130 and (b) LMA-GDF-20/400.

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3.2 Spectral results of CTFBGs

Using the experimental setup shown in Fig. 9, the transmission spectra of both CTFBGs inscribed in 15/130 μm and 20/400 μm fiber with various mode proportions were measured. In Fig. 11(a), the measured spectrum (blue line) of the 15/130 μm CTFBG with only fundamental mode excitation is displayed. With the tilt angle of 4°, the corresponding coupling constants of the LP01 mode are again shown in Fig. 11(b) and (c), where cladding modes whose radial orders are between 14 and 33 show obviously stronger coupling than others. By comparing the phase-matching condition (Fig. 11(d) and (e)) with the measured spectrum, it is shown that the wavelength range matches well with the resonant wavelength range of the strongly coupled cladding modes.

 figure: Fig. 11.

Fig. 11. In (a), the measured and simulated spectra of 15/130 μm CTFBG under fundamental mode excitation are displayed. Used in the spectral simulation, the scatter diagrams of coupling constants of (b) LP0n and (c) LP1n cladding modes at specific 4° tilt angle are plotted, along with the phase matching condition of the strong coupled (d) LP0n and (e) LP1n cladding modes (radial order from 14 to 33).

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Using the same grating parameters of the fabricated 15/130 μm CTFBG, the corresponding simulated spectrum (red dashed line in Fig. 11(a)) was calculated and showed a similar transmission envelope, with a slight red shift compared with the real spectra (blue solid line), which could be due to the fact that the effective indices obtained by the LP method are slightly larger than those of the degenerate vector modes and that the slightly larger tilt angle or smaller RI of core in real can be influential as well. In addition, the 3 dB bandwidth of the simulated spectrum (8.43 nm) is smaller than the measured one (8.96 nm), mostly caused by neglecting the cladding modes with higher angular orders (m > 1).

For a similar full fundamental mode excitation (Fig. 12(c)) in the 20/400 μm fiber, however, it differs slightly. While the red shift is still shown in Fig. 12(c), the spectral range of the simulated spectrum shows a wider bandwidth (10.01 nm) than the measured one (9.82 nm). This difference can be due to setting a higher RI modulation, a longer grating length or a larger chirp rate in the simulation with respect to the real case.

 figure: Fig. 12.

Fig. 12. Simulated (red dashed line) and experimental spectra (blue solid line) of the CTFBG inscribed in 15/130 μm fiber obtained with (a) equivalent core modes excitation and (b) higher-order-core-mode-dominant excitation. The spectra of CTFBG inscribed in 20/400 μm are also displayed as (c) single excitation of LP01 mode excitation and (d) equivalent core mode excitation.

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Theoretically, an equivalent excitation of two core modes can be realized by carefully adjusting the transverse mismatch to the simulated results shown in Fig. 8. The corresponding transmission spectra of 15/130 μm and 20/400 μm CTFBGs are shown in Fig. 12(a) and (d). Both the measured transmission spectra of the two types of CTFBGs show a wider 3 dB bandwidth than the spectra of pure LP01 excitation because of the excitation of multiple core modes. The spectra of the case with a larger transverse offset between the single-mode fiber and 15/130 μm fiber are also displayed in Fig. 12(b). An even broader spectral range is shown by the measured result (blue line) as the proportion of LP11 mode increases. The simulated result (red line) reveals a shallower dip in the shorter wavelength range, as many kinds of cladding modes that can couple with core modes are neglected in the simulation and the impact of these neglected pieces obviously plays a larger part in the shorter wavelength range because of the more severe modal dispersion (Fig. 4(a)). Moreover, with an increase of the higher-order mode proportion, the central suppression ratio (at 1134 nm) of the fabricated 15/130 μm CTFBG shows a faster decrease than the anticipated, decreasing from 9.92 dB to 3.35 dB, which is unfavorable for SRS suppression. In the next subsection, a theoretically feasible method to solve this problem is further discussed.

3.3 Optimized design of CTFBGs

Improving the spectral response is beneficial to the optimization of the CTFBG property for SRS suppression. First, as a natural thought, we attempted to realize the target of eliminating the bad effect (LP11 mode induce) by moving the saddle point of the curve representing LP11 coupling out of the SRS wavelength. This thought can be achieved by using a larger tilt angle. However, as the tilt angle increased, the suppression ratio of the overall wavelength would decrease (Fig. 8(a) and (b)) because of the weaker coupling of all cladding modes. Therefore, optimization of the other CTFBG parameter is discussed in this section.

In Fig. 13(a) and (b), the variation of the simulated transmission spectra that evolve with the changing chirp rate is displayed. As the chirp rate increases, the suppression ratio (at 1134 nm) for the LP01 mode is decreases because of the expansion of the spectral energy distribution. For LP11 mode coupling, the suppression ratio is a competition between the broadening of the spectral range and the superposition of the original two transmission dips. To further judge the effect the chirp rate could have on improving SRS filtering when two core modes were excited, an increase in the suppression ratio (set the suppression ratio of 0.4 nm/cm as the basis point of zero growth) on conditions of different proportions of the LP01 core mode excitation for chirp rate from 0.40 to 0.75 nm/cm is shown in Fig. 13(c).

 figure: Fig. 13.

Fig. 13. Changing transmission spectra of CTFBGs with various chirp rates for (a) LP01 coupling and (b) LP11 coupling. Then with various proportions of LP01 core mode excitation, (c) the improvement of the SRS filtering effect induced by a proper chirp rate is obtained.

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Suggestions can then be drawn from the simulated results of various chirp rates: when the LP01 core mode takes a proportion of greater than 65%, it is better to retain a weak chirp rate at 0.4 nm/cm, as the total filtering effect is on a declining curve, while the chirp rate gradually increases. As the proportion is inferior to 65%, there would be an optimal chirp rate that can balance the reduction of suppression ratio for the LP01 core mode and the increase in that for the LP11 core mode. For the proportion between 45% and 65%, the optimal chirp rate is 0.6 nm/cm. When the LP01 mode shares less than 45% of the total field, the ideal chirp rate should be 0.65 nm/cm.

Determining the best parameters of the CTFBG for SRS filtering would be a time-consuming process of endless searching, which may nevertheless be meaningful for expanding the application of CTFBGs in high-power fiber systems. In the near future, further testing of the simulated results will be carried out experimentally.

4. Conclusions

In conclusion, considering the possible motivation of multiple core modes for LMA fibers, we investigated the coupling characteristics between the LP11 core mode and cladding modes in a CTFBG. By calculating the coupling constants and resonant wavelengths, we simulated the transmission spectra of CTFBGs with different parameters and compared the results of LP01 and LP11 coupling. With respect to the condition of LP01 core mode coupling, simulations show that LP11 coupling can cause spectral widening and a decrease in the suppression ratio for the SRS wavelength, which is further confirmed by the measured spectra with the motivated field of different mode proportions. To find the proper parameters and improve the performance of CTFBGs in the work environment of multiple core mode excitations, transmission spectra under different chirp rates is simulated. Comparing the enhancement of the SRS filtering effect, the optimal chirp rate was chosen under various ratios of mode components. In the future, by finding better parameters and consistently promoting the property of CTFBGs, a superior SRS suppression effect would be expected, which will be a huge advancement for further power scaling of high-power fiber systems.

Funding

State Key Laboratory of Power Systems (SKL-2020-ZR05); National Natural Science Foundation of China (11974427, 12004431); Natural Science Foundation of Hunan Province (2019JJ20023).

Disclosures

The authors declare no conflicts of interest.

References

1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27(11), B63–B92 (2010). [CrossRef]  

2. B. Shiner, “The Impact of Fiber Laser Technology on the World Wide Material Processing Market,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2013), p. AF2J.1.

3. Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020). [CrossRef]  

4. B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018). [CrossRef]  

5. I. Hu, X. Ma, C. Zhu, C. Liu, T. Sosnowski, and A. Galvanauskas, “Experimental demonstration of SRS suppression in chirally-coupled-core fibers,” in Lasers, Sources, and Related Photonic Devices, (Optical Society of America, 2012), p. AT1A.3. [CrossRef]  

6. J. Kim, P. Dupriez, C. Codemard, J. Nilsson, and J. K. Sahu, “Suppression of stimulated Raman scattering in a high power Yb-doped fiber amplifier using a W-type core with fundamental mode cut-off,” Opt. Express 14(12), 5103–5113 (2006). [CrossRef]  

7. C. Jauregui, H. Otto, F. Stutzki, J. Limpert, and A. Tünnermann, “Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening,” Opt. Express 23(16), 20203–20218 (2015). [CrossRef]  

8. J. P. Leidner and J. R. Marciante, “The Impact of Thermal Mode Instability on Core Diameter Scaling in High-Power Fiber Amplifiers,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2016), p. SM4Q.2.

9. C. J. F. J. D. Nodop, “Suppression of stimulated Raman scattering employing long period gratings in double-clad fiber amplifiers,” Opt. Lett. 35(17), 2982–2984 (2010). [CrossRef]  

10. P. Simões, L. Ferreira, and P. E. E. K. Lopes, “Sensitivity and reliability of LPG temperature sensors using total transmitted power,” in Advanced Photonics 2013, (Optical Society of America, 2013), p. JT3A.30.

11. M. Wang, Y. Zhang, Z. Wang, J. Sun, J. Cao, J. Leng, X. Gu, and X. Xu, “Fabrication of chirped and tilted fiber Bragg gratings and suppression of stimulated Raman scattering in fiber amplifiers,” Opt. Express 25(2), 1529–1534 (2017). [CrossRef]  

12. M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019). [CrossRef]  

13. X. Tian, X. Zhao, M. Wang, and Z. Wang, “Effective suppression of stimulated Raman scattering in direct laser diode pumped 5 kilowatt fiber amplifier using chirped and tilted fiber Bragg gratings,” Laser Phys. Lett. 17(8), 085104 (2020). [CrossRef]  

14. M. Wang, Z. Li, L. Liu, Z. Wang, X. Gu, and X. Xiaojun, “Fabrication of chirped and tilted fiber Bragg gratings on large-mode-area doubled-cladding fibers by phase-mask technique,” Appl. Opt. 57(16), 4376–4380 (2018). [CrossRef]  

15. X. Tian, X. Zhao, M. Wang, Q. Hu, L. Hongye, B. Rao, H. Xiao, and Z. Wang, “Influence of Bragg reflection of chirped titled fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers,” Opt. Express 28(13), 19508–19517 (2020). [CrossRef]  

16. K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019). [CrossRef]  

17. W. Lin, M. Desjardins-Carrière, B. Sévigny, J. Magné, and M. Rochette, “Raman suppression within the gain fiber of high-power fiber lasers,” Appl. Opt. 59(31), 9660–9666 (2020). [CrossRef]  

18. H. Li, X. Zhao, B. Rao, M. Wang, and Z. Wang, “Building-up and suppression of cladding mode coupling in fiber Bragg gratings,” J. Opt. (Bristol, U. K.) 22(7), 075704 (2020). [CrossRef]  

19. T. Erdogan, “Cladding-mode resonances in short- and long-period fiber grating filters,” J. Opt. Soc. Am. A 17(11), 2113 (2000). [CrossRef]  

20. M. Heck, G. Schwartz, R. Krämer, D. Richter, T. Goebel, C. Matzdorf, A. Tünnermann, and S. Nolte, “Control of higher-order cladding mode excitation with tailored femtosecond-written long period fiber gratings,” Opt. Express 27(4), 4292–4302 (2019). [CrossRef]  

21. A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” Quantum Electron. 45(3), 235–239 (2015). [CrossRef]  

22. D. Feng, X. Qiao, and J. Albert, “Off-axis ultraviolet-written fiber Bragg gratings for directional bending measurements,” Opt. Lett. 41(6), 1201–1204 (2016). [CrossRef]  

23. R. Kashyap, Fiber Bragg Gratings (Elsevier, 2010), Chap. 4.

24. A. Bialiayeu, The Sensitivity Enhancement of Tilted Fibre Bragg Grating Sensors with Polarization Dependent Resonant Nano-Scale Coatings (GRIN Publishing, 2015), Chap. 2.

25. W. Mohammed and X. Gu, “Fiber Bragg grating in large-mode-area fiber for high power fiber laser applications,” Appl. Opt. 49(28), 5297–5301 (2010). [CrossRef]  

26. W. Wendy, Q. Tan, X. Li, J. Ge, W. Jiang, D. Liang, and C. Haiwen, “Analysis of mode characteristics of fiber Bragg gratings in large-mode-area double-clad fibers,” J. Opt. Soc. Am. B 36(3), 768 (2019). [CrossRef]  

27. W. S. Mohammed, A. Mehta, and E. G. Johnson, “Wavelength tunable fiber lens based on multimode interference,” J. Lightwave Technol. 22(2), 469–477 (2004). [CrossRef]  

References

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  • |

  1. D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: current status and future perspectives,” J. Opt. Soc. Am. B 27(11), B63–B92 (2010).
    [Crossref]
  2. B. Shiner, “The Impact of Fiber Laser Technology on the World Wide Material Processing Market,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2013), p. AF2J.1.
  3. Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
    [Crossref]
  4. B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
    [Crossref]
  5. I. Hu, X. Ma, C. Zhu, C. Liu, T. Sosnowski, and A. Galvanauskas, “Experimental demonstration of SRS suppression in chirally-coupled-core fibers,” in Lasers, Sources, and Related Photonic Devices, (Optical Society of America, 2012), p. AT1A.3.
    [Crossref]
  6. J. Kim, P. Dupriez, C. Codemard, J. Nilsson, and J. K. Sahu, “Suppression of stimulated Raman scattering in a high power Yb-doped fiber amplifier using a W-type core with fundamental mode cut-off,” Opt. Express 14(12), 5103–5113 (2006).
    [Crossref]
  7. C. Jauregui, H. Otto, F. Stutzki, J. Limpert, and A. Tünnermann, “Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening,” Opt. Express 23(16), 20203–20218 (2015).
    [Crossref]
  8. J. P. Leidner and J. R. Marciante, “The Impact of Thermal Mode Instability on Core Diameter Scaling in High-Power Fiber Amplifiers,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2016), p. SM4Q.2.
  9. C. J. F. J. D. Nodop, “Suppression of stimulated Raman scattering employing long period gratings in double-clad fiber amplifiers,” Opt. Lett. 35(17), 2982–2984 (2010).
    [Crossref]
  10. P. Simões, L. Ferreira, and P. E. E. K. Lopes, “Sensitivity and reliability of LPG temperature sensors using total transmitted power,” in Advanced Photonics 2013, (Optical Society of America, 2013), p. JT3A.30.
  11. M. Wang, Y. Zhang, Z. Wang, J. Sun, J. Cao, J. Leng, X. Gu, and X. Xu, “Fabrication of chirped and tilted fiber Bragg gratings and suppression of stimulated Raman scattering in fiber amplifiers,” Opt. Express 25(2), 1529–1534 (2017).
    [Crossref]
  12. M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019).
    [Crossref]
  13. X. Tian, X. Zhao, M. Wang, and Z. Wang, “Effective suppression of stimulated Raman scattering in direct laser diode pumped 5 kilowatt fiber amplifier using chirped and tilted fiber Bragg gratings,” Laser Phys. Lett. 17(8), 085104 (2020).
    [Crossref]
  14. M. Wang, Z. Li, L. Liu, Z. Wang, X. Gu, and X. Xiaojun, “Fabrication of chirped and tilted fiber Bragg gratings on large-mode-area doubled-cladding fibers by phase-mask technique,” Appl. Opt. 57(16), 4376–4380 (2018).
    [Crossref]
  15. X. Tian, X. Zhao, M. Wang, Q. Hu, L. Hongye, B. Rao, H. Xiao, and Z. Wang, “Influence of Bragg reflection of chirped titled fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers,” Opt. Express 28(13), 19508–19517 (2020).
    [Crossref]
  16. K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019).
    [Crossref]
  17. W. Lin, M. Desjardins-Carrière, B. Sévigny, J. Magné, and M. Rochette, “Raman suppression within the gain fiber of high-power fiber lasers,” Appl. Opt. 59(31), 9660–9666 (2020).
    [Crossref]
  18. H. Li, X. Zhao, B. Rao, M. Wang, and Z. Wang, “Building-up and suppression of cladding mode coupling in fiber Bragg gratings,” J. Opt. (Bristol, U. K.) 22(7), 075704 (2020).
    [Crossref]
  19. T. Erdogan, “Cladding-mode resonances in short- and long-period fiber grating filters,” J. Opt. Soc. Am. A 17(11), 2113 (2000).
    [Crossref]
  20. M. Heck, G. Schwartz, R. Krämer, D. Richter, T. Goebel, C. Matzdorf, A. Tünnermann, and S. Nolte, “Control of higher-order cladding mode excitation with tailored femtosecond-written long period fiber gratings,” Opt. Express 27(4), 4292–4302 (2019).
    [Crossref]
  21. A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” Quantum Electron. 45(3), 235–239 (2015).
    [Crossref]
  22. D. Feng, X. Qiao, and J. Albert, “Off-axis ultraviolet-written fiber Bragg gratings for directional bending measurements,” Opt. Lett. 41(6), 1201–1204 (2016).
    [Crossref]
  23. R. Kashyap, Fiber Bragg Gratings (Elsevier, 2010), Chap. 4.
  24. A. Bialiayeu, The Sensitivity Enhancement of Tilted Fibre Bragg Grating Sensors with Polarization Dependent Resonant Nano-Scale Coatings (GRIN Publishing, 2015), Chap. 2.
  25. W. Mohammed and X. Gu, “Fiber Bragg grating in large-mode-area fiber for high power fiber laser applications,” Appl. Opt. 49(28), 5297–5301 (2010).
    [Crossref]
  26. W. Wendy, Q. Tan, X. Li, J. Ge, W. Jiang, D. Liang, and C. Haiwen, “Analysis of mode characteristics of fiber Bragg gratings in large-mode-area double-clad fibers,” J. Opt. Soc. Am. B 36(3), 768 (2019).
    [Crossref]
  27. W. S. Mohammed, A. Mehta, and E. G. Johnson, “Wavelength tunable fiber lens based on multimode interference,” J. Lightwave Technol. 22(2), 469–477 (2004).
    [Crossref]

2020 (5)

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

X. Tian, X. Zhao, M. Wang, and Z. Wang, “Effective suppression of stimulated Raman scattering in direct laser diode pumped 5 kilowatt fiber amplifier using chirped and tilted fiber Bragg gratings,” Laser Phys. Lett. 17(8), 085104 (2020).
[Crossref]

X. Tian, X. Zhao, M. Wang, Q. Hu, L. Hongye, B. Rao, H. Xiao, and Z. Wang, “Influence of Bragg reflection of chirped titled fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers,” Opt. Express 28(13), 19508–19517 (2020).
[Crossref]

W. Lin, M. Desjardins-Carrière, B. Sévigny, J. Magné, and M. Rochette, “Raman suppression within the gain fiber of high-power fiber lasers,” Appl. Opt. 59(31), 9660–9666 (2020).
[Crossref]

H. Li, X. Zhao, B. Rao, M. Wang, and Z. Wang, “Building-up and suppression of cladding mode coupling in fiber Bragg gratings,” J. Opt. (Bristol, U. K.) 22(7), 075704 (2020).
[Crossref]

2019 (4)

K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019).
[Crossref]

M. Heck, G. Schwartz, R. Krämer, D. Richter, T. Goebel, C. Matzdorf, A. Tünnermann, and S. Nolte, “Control of higher-order cladding mode excitation with tailored femtosecond-written long period fiber gratings,” Opt. Express 27(4), 4292–4302 (2019).
[Crossref]

W. Wendy, Q. Tan, X. Li, J. Ge, W. Jiang, D. Liang, and C. Haiwen, “Analysis of mode characteristics of fiber Bragg gratings in large-mode-area double-clad fibers,” J. Opt. Soc. Am. B 36(3), 768 (2019).
[Crossref]

M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019).
[Crossref]

2018 (2)

M. Wang, Z. Li, L. Liu, Z. Wang, X. Gu, and X. Xiaojun, “Fabrication of chirped and tilted fiber Bragg gratings on large-mode-area doubled-cladding fibers by phase-mask technique,” Appl. Opt. 57(16), 4376–4380 (2018).
[Crossref]

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

2017 (1)

2016 (1)

2015 (2)

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

C. Jauregui, H. Otto, F. Stutzki, J. Limpert, and A. Tünnermann, “Simplified modelling the mode instability threshold of high power fiber amplifiers in the presence of photodarkening,” Opt. Express 23(16), 20203–20218 (2015).
[Crossref]

2010 (3)

2006 (1)

2004 (1)

2000 (1)

Albert, J.

Babin, S.

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

Bialiayeu, A.

A. Bialiayeu, The Sensitivity Enhancement of Tilted Fibre Bragg Grating Sensors with Polarization Dependent Resonant Nano-Scale Coatings (GRIN Publishing, 2015), Chap. 2.

Cao, J.

Clarkson, W. A.

Codemard, C.

Desjardins-Carrière, M.

Dostovalov, A. V.

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

Dupriez, P.

Erdogan, T.

Feng, D.

Ferreira, L.

P. Simões, L. Ferreira, and P. E. E. K. Lopes, “Sensitivity and reliability of LPG temperature sensors using total transmitted power,” in Advanced Photonics 2013, (Optical Society of America, 2013), p. JT3A.30.

Galvanauskas, A.

I. Hu, X. Ma, C. Zhu, C. Liu, T. Sosnowski, and A. Galvanauskas, “Experimental demonstration of SRS suppression in chirally-coupled-core fibers,” in Lasers, Sources, and Related Photonic Devices, (Optical Society of America, 2012), p. AT1A.3.
[Crossref]

Ge, J.

Goebel, T.

Gu, X.

Guan, Z.

K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019).
[Crossref]

Haiwen, C.

Heck, M.

Hongye, L.

Hu, I.

I. Hu, X. Ma, C. Zhu, C. Liu, T. Sosnowski, and A. Galvanauskas, “Experimental demonstration of SRS suppression in chirally-coupled-core fibers,” in Lasers, Sources, and Related Photonic Devices, (Optical Society of America, 2012), p. AT1A.3.
[Crossref]

Hu, Q.

X. Tian, X. Zhao, M. Wang, Q. Hu, L. Hongye, B. Rao, H. Xiao, and Z. Wang, “Influence of Bragg reflection of chirped titled fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers,” Opt. Express 28(13), 19508–19517 (2020).
[Crossref]

M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019).
[Crossref]

Ikoma, S.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Jauregui, C.

Jiang, W.

Jiao, K.

K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019).
[Crossref]

Johnson, E. G.

Kashyap, R.

R. Kashyap, Fiber Bragg Gratings (Elsevier, 2010), Chap. 4.

Kim, J.

Kitahara, R.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Kiyoyama, W.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Krämer, R.

Kurihara, T.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Leidner, J. P.

J. P. Leidner and J. R. Marciante, “The Impact of Thermal Mode Instability on Core Diameter Scaling in High-Power Fiber Amplifiers,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2016), p. SM4Q.2.

Leng, J.

Li, H.

H. Li, X. Zhao, B. Rao, M. Wang, and Z. Wang, “Building-up and suppression of cladding mode coupling in fiber Bragg gratings,” J. Opt. (Bristol, U. K.) 22(7), 075704 (2020).
[Crossref]

Li, X.

Li, Z.

Liang, D.

Limpert, J.

Lin, W.

Liu, C.

I. Hu, X. Ma, C. Zhu, C. Liu, T. Sosnowski, and A. Galvanauskas, “Experimental demonstration of SRS suppression in chirally-coupled-core fibers,” in Lasers, Sources, and Related Photonic Devices, (Optical Society of America, 2012), p. AT1A.3.
[Crossref]

Liu, L.

M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019).
[Crossref]

M. Wang, Z. Li, L. Liu, Z. Wang, X. Gu, and X. Xiaojun, “Fabrication of chirped and tilted fiber Bragg gratings on large-mode-area doubled-cladding fibers by phase-mask technique,” Appl. Opt. 57(16), 4376–4380 (2018).
[Crossref]

Lopes, P. E. E. K.

P. Simões, L. Ferreira, and P. E. E. K. Lopes, “Sensitivity and reliability of LPG temperature sensors using total transmitted power,” in Advanced Photonics 2013, (Optical Society of America, 2013), p. JT3A.30.

Lu, Q.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

Ma, P.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

Ma, X.

I. Hu, X. Ma, C. Zhu, C. Liu, T. Sosnowski, and A. Galvanauskas, “Experimental demonstration of SRS suppression in chirally-coupled-core fibers,” in Lasers, Sources, and Related Photonic Devices, (Optical Society of America, 2012), p. AT1A.3.
[Crossref]

Magné, J.

Marciante, J. R.

J. P. Leidner and J. R. Marciante, “The Impact of Thermal Mode Instability on Core Diameter Scaling in High-Power Fiber Amplifiers,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2016), p. SM4Q.2.

Matzdorf, C.

Mehta, A.

Mohammed, W.

Mohammed, W. S.

Nakanishi, Y.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Nakayama, M.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Nilsson, J.

Nodop, C. J. F. J. D.

Nolte, S.

Otto, H.

Qiao, X.

Rao, B.

Richardson, D. J.

Richter, D.

Rochette, M.

Sahu, J. K.

Schwartz, G.

Sévigny, B.

Shen, H.

K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019).
[Crossref]

Shi, C.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

Shima, K.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Shiner, B.

B. Shiner, “The Impact of Fiber Laser Technology on the World Wide Material Processing Market,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2013), p. AF2J.1.

Shirakura, Y.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Shu, J.

K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019).
[Crossref]

Simões, P.

P. Simões, L. Ferreira, and P. E. E. K. Lopes, “Sensitivity and reliability of LPG temperature sensors using total transmitted power,” in Advanced Photonics 2013, (Optical Society of America, 2013), p. JT3A.30.

Sosnowski, T.

I. Hu, X. Ma, C. Zhu, C. Liu, T. Sosnowski, and A. Galvanauskas, “Experimental demonstration of SRS suppression in chirally-coupled-core fibers,” in Lasers, Sources, and Related Photonic Devices, (Optical Society of America, 2012), p. AT1A.3.
[Crossref]

Stutzki, F.

Su, R.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

Sun, J.

Tan, Q.

Tao, R.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

Tian, X.

X. Tian, X. Zhao, M. Wang, and Z. Wang, “Effective suppression of stimulated Raman scattering in direct laser diode pumped 5 kilowatt fiber amplifier using chirped and tilted fiber Bragg gratings,” Laser Phys. Lett. 17(8), 085104 (2020).
[Crossref]

X. Tian, X. Zhao, M. Wang, Q. Hu, L. Hongye, B. Rao, H. Xiao, and Z. Wang, “Influence of Bragg reflection of chirped titled fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers,” Opt. Express 28(13), 19508–19517 (2020).
[Crossref]

Tünnermann, A.

Wang, M.

X. Tian, X. Zhao, M. Wang, Q. Hu, L. Hongye, B. Rao, H. Xiao, and Z. Wang, “Influence of Bragg reflection of chirped titled fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers,” Opt. Express 28(13), 19508–19517 (2020).
[Crossref]

X. Tian, X. Zhao, M. Wang, and Z. Wang, “Effective suppression of stimulated Raman scattering in direct laser diode pumped 5 kilowatt fiber amplifier using chirped and tilted fiber Bragg gratings,” Laser Phys. Lett. 17(8), 085104 (2020).
[Crossref]

H. Li, X. Zhao, B. Rao, M. Wang, and Z. Wang, “Building-up and suppression of cladding mode coupling in fiber Bragg gratings,” J. Opt. (Bristol, U. K.) 22(7), 075704 (2020).
[Crossref]

M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019).
[Crossref]

M. Wang, Z. Li, L. Liu, Z. Wang, X. Gu, and X. Xiaojun, “Fabrication of chirped and tilted fiber Bragg gratings on large-mode-area doubled-cladding fibers by phase-mask technique,” Appl. Opt. 57(16), 4376–4380 (2018).
[Crossref]

M. Wang, Y. Zhang, Z. Wang, J. Sun, J. Cao, J. Leng, X. Gu, and X. Xu, “Fabrication of chirped and tilted fiber Bragg gratings and suppression of stimulated Raman scattering in fiber amplifiers,” Opt. Express 25(2), 1529–1534 (2017).
[Crossref]

Wang, X.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

Wang, Y.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Wang, Z.

X. Tian, X. Zhao, M. Wang, and Z. Wang, “Effective suppression of stimulated Raman scattering in direct laser diode pumped 5 kilowatt fiber amplifier using chirped and tilted fiber Bragg gratings,” Laser Phys. Lett. 17(8), 085104 (2020).
[Crossref]

H. Li, X. Zhao, B. Rao, M. Wang, and Z. Wang, “Building-up and suppression of cladding mode coupling in fiber Bragg gratings,” J. Opt. (Bristol, U. K.) 22(7), 075704 (2020).
[Crossref]

X. Tian, X. Zhao, M. Wang, Q. Hu, L. Hongye, B. Rao, H. Xiao, and Z. Wang, “Influence of Bragg reflection of chirped titled fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers,” Opt. Express 28(13), 19508–19517 (2020).
[Crossref]

M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019).
[Crossref]

M. Wang, Z. Li, L. Liu, Z. Wang, X. Gu, and X. Xiaojun, “Fabrication of chirped and tilted fiber Bragg gratings on large-mode-area doubled-cladding fibers by phase-mask technique,” Appl. Opt. 57(16), 4376–4380 (2018).
[Crossref]

M. Wang, Y. Zhang, Z. Wang, J. Sun, J. Cao, J. Leng, X. Gu, and X. Xu, “Fabrication of chirped and tilted fiber Bragg gratings and suppression of stimulated Raman scattering in fiber amplifiers,” Opt. Express 25(2), 1529–1534 (2017).
[Crossref]

Wendy, W.

Wolf, A.

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

Xiao, H.

X. Tian, X. Zhao, M. Wang, Q. Hu, L. Hongye, B. Rao, H. Xiao, and Z. Wang, “Influence of Bragg reflection of chirped titled fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers,” Opt. Express 28(13), 19508–19517 (2020).
[Crossref]

M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019).
[Crossref]

Xiaojun, X.

Xu, X.

M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019).
[Crossref]

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

M. Wang, Y. Zhang, Z. Wang, J. Sun, J. Cao, J. Leng, X. Gu, and X. Xu, “Fabrication of chirped and tilted fiber Bragg gratings and suppression of stimulated Raman scattering in fiber amplifiers,” Opt. Express 25(2), 1529–1534 (2017).
[Crossref]

Yamamoto, T.

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Yang, B.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

Yang, F.

K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019).
[Crossref]

Zhang, H.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

Zhang, Y.

Zhao, X.

X. Tian, X. Zhao, M. Wang, and Z. Wang, “Effective suppression of stimulated Raman scattering in direct laser diode pumped 5 kilowatt fiber amplifier using chirped and tilted fiber Bragg gratings,” Laser Phys. Lett. 17(8), 085104 (2020).
[Crossref]

X. Tian, X. Zhao, M. Wang, Q. Hu, L. Hongye, B. Rao, H. Xiao, and Z. Wang, “Influence of Bragg reflection of chirped titled fiber Bragg grating on Raman suppression in high-power tandem pumping fiber amplifiers,” Opt. Express 28(13), 19508–19517 (2020).
[Crossref]

H. Li, X. Zhao, B. Rao, M. Wang, and Z. Wang, “Building-up and suppression of cladding mode coupling in fiber Bragg gratings,” J. Opt. (Bristol, U. K.) 22(7), 075704 (2020).
[Crossref]

Zhou, P.

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

Zhu, C.

I. Hu, X. Ma, C. Zhu, C. Liu, T. Sosnowski, and A. Galvanauskas, “Experimental demonstration of SRS suppression in chirally-coupled-core fibers,” in Lasers, Sources, and Related Photonic Devices, (Optical Society of America, 2012), p. AT1A.3.
[Crossref]

Zhu, R.

K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019).
[Crossref]

Appl. Opt. (3)

High Power Laser Sci. (1)

K. Jiao, J. Shu, H. Shen, Z. Guan, F. Yang, and R. Zhu, “Fabrication of kW-level chirped and tilted fiber Bragg gratings and filtering of stimulated Raman scattering in high-power CW oscillators,” High Power Laser Sci. 7, e31 (2019).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. (Bristol, U. K.) (2)

H. Li, X. Zhao, B. Rao, M. Wang, and Z. Wang, “Building-up and suppression of cladding mode coupling in fiber Bragg gratings,” J. Opt. (Bristol, U. K.) 22(7), 075704 (2020).
[Crossref]

B. Yang, H. Zhang, C. Shi, R. Tao, R. Su, P. Ma, X. Wang, P. Zhou, X. Xu, and Q. Lu, “3.05 kW monolithic fiber laser oscillator with simultaneous optimizations of stimulated Raman scattering and transverse mode instability,” J. Opt. (Bristol, U. K.) 20(2), 025802 (2018).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Laser Phys. Lett. (1)

X. Tian, X. Zhao, M. Wang, and Z. Wang, “Effective suppression of stimulated Raman scattering in direct laser diode pumped 5 kilowatt fiber amplifier using chirped and tilted fiber Bragg gratings,” Laser Phys. Lett. 17(8), 085104 (2020).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Photonics Res. (1)

M. Wang, Z. Wang, L. Liu, Q. Hu, H. Xiao, and X. Xu, “Effective suppression of stimulated Raman scattering in half 10 kW tandem pumping fiber lasers using chirped and tilted fiber Bragg gratings,” Photonics Res. 7(2), 167–171 (2019).
[Crossref]

Proc. SPIE (1)

Y. Wang, R. Kitahara, W. Kiyoyama, Y. Shirakura, T. Kurihara, Y. Nakanishi, T. Yamamoto, M. Nakayama, S. Ikoma, and K. Shima, “8-kW single-stage all-fiber Yb-doped fiber laser with a BPP of 0.50 mm-mrad,” Proc. SPIE 11260, 1126022 (2020).
[Crossref]

Quantum Electron. (1)

A. V. Dostovalov, A. Wolf, and S. Babin, “Long-period fibre grating writing with a slit-apertured femtosecond laser beam (λ = 1026 nm),” Quantum Electron. 45(3), 235–239 (2015).
[Crossref]

Other (6)

P. Simões, L. Ferreira, and P. E. E. K. Lopes, “Sensitivity and reliability of LPG temperature sensors using total transmitted power,” in Advanced Photonics 2013, (Optical Society of America, 2013), p. JT3A.30.

J. P. Leidner and J. R. Marciante, “The Impact of Thermal Mode Instability on Core Diameter Scaling in High-Power Fiber Amplifiers,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2016), p. SM4Q.2.

B. Shiner, “The Impact of Fiber Laser Technology on the World Wide Material Processing Market,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2013), p. AF2J.1.

I. Hu, X. Ma, C. Zhu, C. Liu, T. Sosnowski, and A. Galvanauskas, “Experimental demonstration of SRS suppression in chirally-coupled-core fibers,” in Lasers, Sources, and Related Photonic Devices, (Optical Society of America, 2012), p. AT1A.3.
[Crossref]

R. Kashyap, Fiber Bragg Gratings (Elsevier, 2010), Chap. 4.

A. Bialiayeu, The Sensitivity Enhancement of Tilted Fibre Bragg Grating Sensors with Polarization Dependent Resonant Nano-Scale Coatings (GRIN Publishing, 2015), Chap. 2.

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Figures (13)

Fig. 1.
Fig. 1. The (a) LMA-DCF structure confines the core modes including (b) LP01 and (c) LP11.
Fig. 2.
Fig. 2. Axial-section schematic of a CTFBG.
Fig. 3.
Fig. 3. Intensity distribution of several typical cladding modes: (a) LP06, (b) LP1,11, (c) LP24 and (d) LP34.
Fig. 4.
Fig. 4. (a) Mode dispersion of two typical groups of cladding modes (b) Comparation of resonant wavelengths between coupling with LP01 and LP11 core modes. (ncore and nclad represent effective index of core modes and cladding modes, respectively).
Fig. 5.
Fig. 5. The fields of the LP01 (even symmetry) and LP11 (odd symmetry) modes are shown in a cross-section of the fiber, where a as the core radius and r as radial coordinate in the transverse profile of the fiber, along with the transverse RI modulation profiles in FBG and CTFBG, respectively. The overlap of two modes with the profile of index modulation in CTFBG show positive value in either side of the fiber core, which means uneven transverse RI modulation can induce mode coupling between modes of different symmetry.
Fig. 6.
Fig. 6. Coupling constants of (a) self and mutual interacting between two core modes and (b) self-interacting of LP01 core mode with various core sizes.
Fig. 7.
Fig. 7. Mutual coupling constants between allowed (a) LP01 core mode and LP0n cladding modes, (b) LP01 core mode and LP1n cladding modes, (c) LP11 core mode and LP0n cladding modes, and (d) LP11 core mode and LP1n cladding modes evolve with increasing radial order n and growing tilt angle.
Fig. 8.
Fig. 8. Simulated transmission spectra of CTFBGs (a) inscribed in 15/130 μm fiber with LP01 mode excited, (b) inscribed in 15/130 μm fiber with LP11 mode excited, (c) inscribed in 20/400 μm fiber with LP01 mode excited, and (d) inscribed in 20/400 μm fiber with LP11 mode excited, are displayed including their spectral variation with different tilt angles. More detailed comparison between spectra under different core mode excitation are further exhibited while picking the tilt angle of (e) 4° (15/130 μm fiber) and (f) 6° (20/400 μm fiber) as examples.
Fig. 9.
Fig. 9. Experimental realization of multiple modes excitation. ASE, amplified spontaneous emission; OSA, optical spectrum analyzer.
Fig. 10.
Fig. 10. Power coupling coefficients of LP01 and LP11 core mode when changing the incident field offset with (a) LMA-GDF-15/130 and (b) LMA-GDF-20/400.
Fig. 11.
Fig. 11. In (a), the measured and simulated spectra of 15/130 μm CTFBG under fundamental mode excitation are displayed. Used in the spectral simulation, the scatter diagrams of coupling constants of (b) LP0n and (c) LP1n cladding modes at specific 4° tilt angle are plotted, along with the phase matching condition of the strong coupled (d) LP0n and (e) LP1n cladding modes (radial order from 14 to 33).
Fig. 12.
Fig. 12. Simulated (red dashed line) and experimental spectra (blue solid line) of the CTFBG inscribed in 15/130 μm fiber obtained with (a) equivalent core modes excitation and (b) higher-order-core-mode-dominant excitation. The spectra of CTFBG inscribed in 20/400 μm are also displayed as (c) single excitation of LP01 mode excitation and (d) equivalent core mode excitation.
Fig. 13.
Fig. 13. Changing transmission spectra of CTFBGs with various chirp rates for (a) LP01 coupling and (b) LP11 coupling. Then with various proportions of LP01 core mode excitation, (c) the improvement of the SRS filtering effect induced by a proper chirp rate is obtained.

Tables (2)

Tables Icon

Table 1. Parameters associated with various kinds of LMA-DCFs (uncoated).

Tables Icon

Table 2. Structural parameters of CTFBGs in simulation.

Equations (11)

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Λ = Λ g / Λ g cos θ cos θ ,
Λ g ( z ) = Λ g 0 ( 1 + z F / z F L L ) ( L / 2 z L / 2 ) ,
n ( r , φ , z ) = { n 1 + Δ n cos ( β B r a g g z ) r a 1 n 2 a 1 < r a 2 n 3 r > a 3 ,
z = z cos θ x sin θ .
Δ n a c = Δ n cos [ β B r a g g ( z cos θ x sin θ ) ] ,
Λ r e s = Λ g ( z ) cos θ n 1 N σ N T w i t h
Λ r e s = [ λ r e s , 01 c o r e λ r e s , 01 11 c o r e λ r e s , 01 i c l a d λ r e s , 11 01 c o r e λ r e s , 11 c o r e λ r e s , 11 i c l a d λ r e s , i 01 c o r e λ r e s , i 11 c o r e λ r e s , i c l a d ] , N = [ n c o r e , 01 n c o r e , 11 n c l a d , i n 1 n 1 n 1 ] a n d σ = [ 0 1 1 0 ] ,
Δ Λ r e s = Λ g 0 F cos θ n 1 N σ N T w i t h
Δ Λ r e s = [ Δ λ r e s , 01 c o r e Δ λ r e s , 01 11 c o r e Δ λ r e s , 01 i c l a d Δ λ r e s , 11 01 c o r e Δ λ r e s , 11 c o r e Δ λ r e s , 11 i c l a d Δ λ r e s , i 01 c o r e Δ λ r e s , i 11 c o r e Δ λ r e s , i c l a d ] .
κ l , m = ω 4 0 2 π d ϕ 0 r d r Δ ε ( r ) e l e m ,
η ν = | 0 2 π d θ 0 r d r e i ( r , d ) e ν | 2 | 0 2 π d θ 0 r d r e i ( r , d ) | 2 | 0 2 π d θ 0 r d r e ν | 2 .

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