Power scaling on tellurite glass Raman fibre lasers for mid-infrared applications
1 Introduction
Laser emissions at the mid-infrared (IR) wavelength ranging from 2 to have been widely applied in the fields of medical surgery, spectroscopy, gas detection and security, thanks to the tremendous molecular absorption fingerprints and atmospheric transparency window located within this spectral band[1–6]. Most of these applications require high power and high brightness. Over the decades, researchers have developed semiconductor lasers, optical parametric oscillators and solid-state lasers to generate mid-IR lasers. In particular, the solid-state lasers based on various rare-earth (RE) dopants, including , , and so on, have been widely studied[7, 8]. Although semiconductor lasers, gas lasers and solid-state lasers can generate mid-IR lasers over the watt level, they usually have disadvantages including poor beam brightness, low conversion efficiency and complicated configurations[9, 10]. Recently, fibre lasers have been attracting significant interest because of their unique features such as excellent beam quality, high conversion efficiency, high surface area/volume ratio for easy heat dissipation, inherent simplicity and compactness[11–13]. In addition, compared with RE-doped fibre lasers, Raman fibre lasers (RFLs) are a wavelength-agile alternative for producing gain and power within optical fibres[14]. In these, the emission wavelength is determined by the pump wavelength and Raman shift, which can be one or several cascaded Stokes orders, and is restricted by the transparency range of the fibre rather than by the spectral bands of stimulated emission. The combination of their unique optical features makes the cascaded RFLs capable for power scaling at wavelengths beyond .
Over the last decade, significant efforts have been made to scale the power of cascaded RFLs using typical silicate glass fibre at wavelengths between 1 and . To date, the maximum output power of the cascaded RFL has reached up to 300 W at 1480 nm with 65% conversion efficiency[15]. Unfortunately, for the mid-IR wavelength exceeding , new glass materials have to be considered due to the poor transparency of silica. Further, in order to reach mid-IR wavelength, fluoride, chalcogenide or tellurite glass-based fibres act as potential candidates[1]. Recently, the RFL at in the chalcogenide fibre has been demonstrated first with quasi-continuous average power of 47 mW[16]. Besides, the cascaded RFL at based on chalcogenide fibre was reported as the longest wavelength [17]. However, both the small Raman shift of 250– and low thermal damage threshold below hinder the employment of chalcogenide fibre to achieve power scaling in mid-IR[18]. In another aspect, the RFL based on the fluoride fibre was reported with a record output power of 3.7 W at , indicating the feasibility of high power operation[19]. But it is challenging to produce long wavelengths in the mid-IR region through the cascaded Raman shift, due to the relatively low Raman gain coefficient of pumped at [20].
Compared with fluoride and chalcogenide fibres, tellurite fibres offer the potential for watts-level emission at longer wavelengths than via cascaded Raman shift. The remarkable properties of tellurite fibre include the strong Raman gain coefficient and the large Raman shift, which can be up to 100 times higher than in fluorides and twice larger than in chalcogenides, respectively[21–23]. Additionally, the large transparency of tellurite fibre extends far in the IR. Recently, the RFL and cascaded RFL in ––ZnO– (TBZN) tellurite fibre pumped by a 20 W Er-doped fluoride fibre laser (EDFFL) at have been investigated theoretically[24]. However, the peak Raman gain coefficient scales inversely with pump wavelength[25–27]. Thus, the Raman gain coefficient in the case of EDFFL pumping at should be , according to the measured value of with 632.8 nm pump wavelength[28–30]. Moreover, the maximum power of EDFFL at the current state has been scaled up to 30 W[31]. Based on the calculation in Section
Compared with EDFFL, the Tm-doped fibre laser (TDFL) emitting at can be an attractive pump source for first-order and cascaded RFL in mid-IR. The output power of TDFL has been improved to the kilowatt level allowing much higher Raman gain than EDFFL[32]. For long-wavelength generation in mid-IR, the strong Raman gain coefficient and the large Raman shift of tellurite fibre help to overcome the relatively short pump wavelength. Towards power scaling over tens of watts in mid-IR fibre laser, it is necessary to theoretically analyse the TDFL-pumped RFL and cascaded RFL based on tellurite fibres. The output performance of the third-order cascaded tellurite RFL at has been discussed numerically in Ref. [33]. The maximum output power could reach 45.2 W under 100 W pump power at .
In this paper, we use the finite difference method (FDM) to solve the power coupling equations with boundary conditions in the TDFL-pumped tellurite RFLs with first and cascaded Stokes orders. The model has been verified by comparing results with those in Ref. [20]. The influences of the fibre length and output reflectance on laser output performance are investigated, while the optimized parameters are determined for the first-order, second-order and third-order RFL, respectively.
2 Theoretical model
The material of the fibre composition determines the Raman shift and the Raman gain coefficient[21]. Here, we apply the tellurite fibre based on TBZN glass as the Raman gain medium, which has been investigated widely to generate tuneable RFL covering the band[28–30, 34]. Thanks to the current fabrication technology by the developed rod-in-tube method, the TBZN fibre shows advantages on relatively higher Raman gain coefficient and lower propagation loss than other tellurite compositions[30]. The measured Raman gain spectrum with linearly polarized pump source at 632.8 nm is shown in Figure
Fig. 2. The schematic of the all-fibrized (a) first-order and (b) cascaded RFLs. TDFL: Tm-doped fibre laser; HR: high reflectance; PR: partial reflectance.
The schematic of the all-fibrized first-order and cascaded RFLs are shown in Figures
Assuming that the pump power is high enough to generate Stokes waves, we neglect the effect of spontaneous Raman scattering. We also neglect polarization effects. For simplicity, the spectral widths of pump and Stokes waves in our model are considered to be narrow enough (i.e., single frequency). Under the steady-state condition, the standard differential equations describing the evolutions of the pump and the Stokes along the -order RFL in both copropagating and counterpropagating directions can be written as
The differential equations at fibre front () and rear () ends satisfy the boundary condition considering insertion losses of FBGs and splicing losses of the fibres as follows:
Fig. 3. Calculated output power versus launched pump power for fluoride RFL in Ref. [20]. FDM: finite difference method.
The solution of the standard differential equations with boundary conditions can be performed directly by different numerical modelling, such as shooting algorithm, Runge–Kutta algorithm, and relaxation oscillation method[18, 20, 24]. However, the shooting algorithm is sensitive on the setting of initial values. Especially for cascaded RFLs, the computation becomes very cumbersome as the number of Stokes orders increases. Nevertheless, Runge–Kutta algorithm is easy to trap in local optimum leading to possible nonconvergence. Otherwise, some numerical methods such as relaxation oscillation method have to make assumptions to simplify the computation process, which may not be in accordance with the real physical process. Here we demonstrate the FDM introduced in Ref. [35]. The novelty of this model is considering the interaction between forward- and backward-propagating waves, which is independent on the guessed initial values and provides convergence and simplicity without the need for any approximations.
The accuracy of the numerical model has been verified by comparing the simulation results with those in Ref. [20], considering a single-pass fluoride RFL pumped by 1940 nm. The peak Raman gain coefficient is , while the first-order Stokes emits at 2185 nm. The fluoride Raman fibre has a core NA of 0.23 and core diameter of , whose propagation losses at pump and laser wavelengths are 0.02 and separately. The input and output FBGs at laser wavelength with insertion losses of 0.19 dB and 0.09 dB are defined to have the reflectance of 99.95% and 95%, respectively. As shown in Figure
3 Results and discussion
Longer pump wavelength produces higher conversion efficiency and output power, thanks to less Raman shift and shorter fibre lengths. Thus for mid-IR RFL, EDFFL emission around is preferred ideally. However, the maximum pump power provided by EDFFL in the current state is only about 30 W at [31]. The corresponding peak Raman gain coefficient of the TBZN fibre at that wavelength is around . Therefore, the laser threshold of the first-order RFL pumped by can be estimated according to Equations (
Fig. 4. (a) Measured propagation loss spectrum of the TBZN fibre in Ref. [24]; (b) threshold power as a function of fibre length for output reflectance of 90%, 95% and 99%.
3.1 First-order Raman fibre laser
Corresponding to the damage intensity threshold of TBZN fibre, the incident peak power could be 50 kW for core area of [21]. However, the exact power limit in the TBZN fibre should be quantified according to the simulated heat dissipation. We here only discuss the RFL laser performance with pump power below 300 W, which has been demonstrated in our group[37]. The peak Raman gain coefficient and first-order Stokes emission wavelength are calculated to be and , respectively. As shown in Figure
Figure
Furthermore, the dependence of the output power on the fibre length for different output reflectance is shown in Figure
Fig. 5. Output power of the first-order RFL as a function of (a) output reflectance for fibre length of 0.3 m, 0.5 m, 1 m, 2 m, and (b) fibre length for output reflectance of 5%, 10%, 15% and 20%.
Fig. 6. (a) Power distribution along the fibre length in first-order RFL pumped by TDFL; (b) output power of first-order Stokes versus pump power.
Figure
Fig. 7. Power evolution of (a) pump, (b) first-order Stokes, (c) second-order Stokes waves in second-order RFL pumped by TDFL.
Fig. 8. Output power of second-order RFL as a function of (a) output reflectance for fibre length of 0.5 m, 1 m, 2 m and 3.1 m, (b) fibre length for output reflectance of 5%, 10%, 15% and 20%.
3.2 Second-order Raman fibre laser
To achieve longer signal wavelength, one could apply the cascaded RFL with multi-order Stokes generation. In the case of TDFL pumping, the second-order Stokes emits at considering Raman shift from first-order Stokes. Note that the second-order Raman gain coefficient becomes due to longer pump wavelength. On the basis of first-order RFL, the second-order RFL cavity adds the HR and PR FBGs at input and output ends, respectively, while the PR FBG at is replaced by HR FBG. Here, we define the fibre parameters and HR FBG reflectance as before. As shown in Figure
Figure
In order to find how the output reflectance and fibre length affect the laser characteristics, we illustrate the relationship between the output power of second-order RFL and the output reflectance in Figure
Not only the output power, but also the slope efficiency and threshold should be considered for cavity optimization. Figure
3.3 Third-order Raman fibre laser
For mid-IR laser beyond , it is attractive to apply the third-order RFL lasing at , thanks to the uniform heat dissipation along the relatively long fibre. Here we simulate the third-order RFL with the same TBZN fibre as the subsections above, while the propagation loss at is set to [24]. The Raman gain coefficient pumped by second-order Stokes is estimated to be . Except for the output FBG for last-order Stokes, all the FBGs in the cavity are HR with 99.5% reflectance. The fibre length and reflectance of output FBG are the variables to be optimized. The intracavity power distribution of each wave along the 5.5 m fibre with 45% output reflectance is shown in Figure
Fig. 10. Longitudinal power evolution of (a) pump, (b) first-order Stokes, (c) second-order Stokes, (d) third-order Stokes in third-order RFL pumped by TDFL.
Fig. 11. Output power of third-order RFL as a function of (a) output reflectance for fibre length of 4.5 m, 5.5 m, 9 m and 11 m, (b) fibre length for output reflectance of 40%, 45%, 50% and 55%.
The variations in output power of the generated third-order Stokes with output reflectance for fibre length of 4.5 m, 5.5 m, 9 m and 11 m are shown in Figure
As shown in Figure
4 Conclusion
In this paper, we have demonstrated the numerical simulations on the TDFL-pumped tellurite RFLs emitting in the mid-IR region for the first time. Although the EDFFL contributes to less fibre component and shorter fibre length, thanks to the long pump wavelength, the maximum pump power is still below the threshold of the tellurite RFLs. As a candidate to pump the mid-IR RFLs, the TDFL has presented significant potential on power scaling over hundreds of watts within the spectral range of 2– and tens of watts beyond , respectively. In the case of TDFL pumping, the first-order and cascaded RFLs with second and third-order Stokes generations based on TBZN fibre have been analysed and optimized, indicating strong dependence of the output power on both the fibre length and output reflectance. The optimum fibre length and output reflectance are found to be 1.3 m and 5% for first-order RFL separately, leading to the highest output power of 162 W. For cascaded RFL emitting at , the fibre length and output reflectance are optimized to be 3.1 m and 5%, respectively, ensuring the maximum output power of 92 W. The highest output power of the third-order cascaded RFL at is obtained to be 16 W with fibre length of 5.5 m and output reflectance of 45%. Except for the fibre length and output reflectance, both the fibre propagation loss and FBG insertion loss would determine the laser performance. In order to achieve further power scaling, more efforts should be made for developing techniques of fibre fabrication and FBG writing to minimize the insertion loss, which are also necessary for wavelength extension beyond .
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Article Outline
Tianfu Yao, Liangjin Huang, Pu Zhou, Bing Lei, Jinyong Leng, Jinbao Chen. Power scaling on tellurite glass Raman fibre lasers for mid-infrared applications[J]. High Power Laser Science and Engineering, 2018, 6(2): 02000e24.