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Raman lasers based on mid-infrared fibers operating at 3-5 µm atmospheric transparency window are attractive sources for several applications. Compared to fluoride and chalcogenide fibers, tellurite fibers are more advantageous for high power Raman fiber laser sources at 3-5 µm because of their broader Raman gain bandwidth, much larger Raman shift and better physical and chemical properties. Here we report on our simulations for the development of 10-watt-level 3-5 µm Raman lasers using tellurite fibers as the nonlinear gain medium and readily available continuous-wave (cw) and Q-switched erbium-doped fluoride fiber lasers at 2.8 µm as the pump sources. Our results show that a watt-level or even ten-watt-level fiber laser source in the 3-5 µm atmospheric transparency window can be achieved by utilizing the 1st- and 2nd-order Raman scattering in the tellurite fiber. The presented numerical study provides valuable guidance for future 3-5 um Raman fiber laser development.
© 2015 Optical Society of America
1. Introduction
Mid-infrared (Mid-IR) lasers have attracted significant attention due to their extensive applications in medical surgery [1], spectroscopy [2], gas sensing [3], defense and security [4]. Mid-IR 3-5 µm lasers are interesting because of the atmospheric transparency window [5] and numerous molecular absorption fingerprints [6] at this wavelength range. The 3-5 um lasers can be generated by electrically and optically-pumped semiconductor lasers (antimonide, IV-VI semiconductors, and quantum cascade lasers) [3, 4], optically-pumped rare-earth-doped or transition-metal-doped glass and crystal lasers [7, 8], optical parametric oscillators (OPOs) [9], difference frequency generation (DFG) sources [10], and electrically and optically pumped gas lasers [11–13]. However, semiconductor lasers usually have poor beam quality and low output power. OPOs and DFG sources generally have a more complex configuration requiring careful alignment and maintenance. Gas laser sources have very low efficiency and need numerous free-space accessories. Transition-metal crystal Cr2+:ZnSe or Fe2+:ZnSe lasers capable of producing 10-watt-level output in the 2-5 µm and offering ultra-broad wavelength tunable range are attractive mid-IR laser sources [7, 8]. However, these lasers usually operate at a cryogenic temperature to achieve high efficiency operation and need special thermal management for room-temperature operation. Compared to these bulky and complicated laser systems, mid-IR fiber lasers show great advantages for their compactness, inherent simplicity, outstanding heat-dissipating capability and excellent beam quality. In the last decade, mid-IR fiber lasers have been extensively studied and much progress has been made with ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF) fiber laser technology. Watt-level and even 10-watt-level continuous-wave (cw) erbium (Er3+), holmium (Ho3+), and dysprosium (Dy3+) ion-doped ZBLAN fiber lasers have been demonstrated around 2.8 µm −3 µm range [14–18] and pulsed operation of these lasers has also been demonstrated with various active or passive Q-switching and mode-locking techniques recently [19–24]. However, the emission wavelengths of these fiber lasers are not within the atmospheric transparency window. Some rare-earth (RE) doped ZBLAN fiber lasers in the 3-4 µm range have been demonstrated [25–27]. A 3.22 µm holmium (Ho3+) doped ZBLAN fiber laser was reported with a few milliwatts output at room temperature [25]. Under cryogenic cooling, a Ho3+-doped ZBLAN fiber laser operating at 3.95 μm with a few milliwatts was achieved [26]. Very recently, an Er3+-doped ZBLAN fiber laser at 3.5 µm with an output power of 260 mW at room temperature by use of dual-wavelength pumping technique was reported [27]. However, the emission wavelengths of these RE-doped glass fiber lasers are limited to specific wavelengths by the allowable transitions between energy levels of the RE ions and their power scaling is usually restricted by the significant thermo-optic effects that occur due to the low quantum efficiency. Because non-radiative decay is predominant over direct radiative transitions when the laser wavelength is longer than 4 µm, it is extremely hard to obtain a > 4 µm laser output from a RE-doped ZBLAN fiber laser. Although RE-doped chalcogenide fiber lasers may be able to achieve laser emission beyond 4 µm [28], it is still very difficult to achieve watt-level output due to the low achievable RE doping level (~0.1 mol%) and low damage threshold of chalcogenide. In recent years, fiber lasers based on stimulated Raman scattering have attracted much interest for their capability to generate coherent radiation at any wavelength within the transparency region of the fiber material. Since over 20-watt output at 3 µm has been obtained from RE-doped ZBLAN fiber lasers [15, 16], it should be very promising to develop watt-level or even 10-watt-level laser sources at 3-5 µm using Raman laser technology based on mid-IR optical fibers.
Raman fiber lasers using optical fibers as the nonlinear medium can generate laser that cannot be obtained through direct transition between two energy levels of ions. The first Raman fiber laser was demonstrated by K. O. Hill et al. by employing single‐mode glass fibers in a Fabry‐Perot resonator configuration [29]. Later P. N. Kean et al. reported the first compact and stable all-fiber Raman laser based on fiber Bragg gratings in 1988 [30]. Most recently, V. R. Supradeepa et al. demonstrated a more than 300 W cw Raman fiber laser at 1.5 µm with an optical efficiency of 64% [31]. However, these Raman lasers mainly use silica fibers that are opaque in the mid-IR range. ZBLAN, tellurite, and chalcogenide fibers that are highly transparent in mid-IR range have been used in Raman fiber lasers. V. Fortin et al. demonstrated the first Raman laser based on ZBLAN fiber in 2011 [32] and later a watt-level cw Raman fiber laser operating beyond 2.2 µm was achieved by using a pump source at 1.98 µm [33]. However, ZBLAN glass fiber is not an ideal gain medium for Raman lasers due to its inherent low nonlinearity, fragility and hydroscopicity. Chalcogenide fiber having very large nonlinearity [34] and high transparency in the entire mid-IR wavelength range is a good alternative for Raman fiber lasers in the mid-IR region. M. Bernier et al. demonstrated the first Raman fiber laser above 3 μm using a single-mode As2S3 chalcogenide glass fiber and a pulsed pump source at 3.005 µm [35]. Most recently, they developed a cascaded Raman chalcogenide glass fiber laser at 3.77 µm by using two pairs of FBGs directly inscribed in the chalcogenide fiber. A laser output peak power in excess of 100 mW is obtained with a conversion efficiency of about 8.3% with respect to the launched pump power [36]. Some simulation work on chalcogenide fiber Raman lasers has also been done by P. A. Thielen et al. and a 8 W mid-IR fiber Raman laser operating at 6.46 µm pumped by a 10 W 5.59 µm carbon monoxide laser was theoretically proposed [37]. However, chalcogenide fibers have very low damage threshold, which limits their output power and pulsed pumping schemes are often used to reduce thermal effects. Moreover, chalcogenide fibers have relatively narrow Raman gain bandwidth (~50 cm−1) and small Raman shifts (~350 cm−1) [38]. The operating wavelength of a chalcogenide fiber laser based on 2nd-order Raman scattering is still below 4 µm [36]. In order to achieve a laser output at 5 µm, at least 4th order Raman scattering has to be employed. In this case, the construction of the Raman fiber laser will be complex and the efficiency will become very low. Compared to chalcogenide fibers, tellurite fibers have the advantages of better thermal stability [39], stronger corrosion resistance, broader Raman gain bandwidth (~300 cm−1) and larger Raman shift (~750 cm−1) [40]. By taking advantage of this broad gain bandwidth and large Raman shift, A. Mori et al. demonstrated a tellurite fiber Raman amplifier near 1.5 µm with a gain bandwidth of 160 nm [41] and G. Qin et al. reported a widely tunable (1495–1600 nm) ring-cavity tellurite fiber Raman laser with more than 100 nm tunable range [42]. However, all these demonstrations have been at near-infrared wavelengths, where silica fiber lasers are predominant. We have previously developed a 10-watt cw laser and several pulsed lasers around 3 µm [14, 20–22]. Therefore, it is promising to develop high power fiber laser sources operating within the 3-5 µm atmospheric transparency window by using our fiber lasers as pumps for tellurite Raman fiber lasers. In order to obtain insight into tellurite fiber Raman lasers pumped at 3 µm and provide valuable guidance for future 3-5 um Raman fiber laser development, it is essential to investigate the performance of the Raman fiber lasers with different designs. In this paper, we present our numerical simulation studies on 1st- and 2nd-order Raman lasers based on tellurite fibers. Our calculations show that watt-level or even 10-watt-level Raman fiber lasers can be achieved by pumping sub-meter tellurite fibers with 20 W Er3+-doped ZBLAN fiber lasers at 2.8 µm.
2. Theoretical model
Tellurite glass, which has the lowest phonon energy among oxide glasses, has been extensively used in nonlinear photonics devices in the mid-IR due to its good optical transparency in the wavelength range of 0.5-5 µm and high nonlinear refractive index of 5.9 × 10−19 m2/W [43]. Compared to other mid-IR transmitting glasses such as ZBLAN and chalcogenide glasses, tellurite glass not only exhibits better physical and chemical performance, but also has better Raman scattering properties including broad Raman gain bandwidth and large Raman shift [39]. All these advantages make tellurite glass fibers uniquely suitable for high power mid-IR Raman fiber lasers. Generally, the optical properties of a tellurite fiber depend on the glass compositions [40]. In our simulation, the Raman gain coefficient of TeO2-Bi2O3-ZnO-Na2O (TBZN) tellurite fiber that can be fabricated in our lab is used. The Raman gain coefficient as a function of Raman shift is shown in Fig. 1 [40]. Due to the large Raman shift and high Raman gain of tellurite fibers, a Raman fiber laser operating in the 3-5 µm atmospheric transparency window can be achieved by using the 1st- and 2nd-order Raman scattering with a pump wavelength of 2.8 µm. The propagation loss of a tellurite fiber is shown in the inset of Fig. 1. The low propagation loss (< 0.5 dB/m) at 1-4.5 µm indicates that the tellurite fiber is a suitable platform for a mid-IR Raman laser. Although the propagation loss significantly increases as the wavelength approaches 5 µm due to the increased probability of multi-phonon decay, our calculations, as shown below, confirm that a 3-5 µm Raman laser can be achieved by using sub-meter length tellurite fibers.
Fig. 1 Raman gain coefficient of a TBZN tellurite fiber as a function of the Raman shift. Inset shows the propagation loss of the tellurite fiber at 0.5-5 μm wavelength range.
The schematics of Raman fiber lasers based on the 1st- and 2nd-order Raman scattering are shown in Figs. 2(a) and 2(b), respectively. In all cases, a high reflectance (HR) fiber Bragg grating (FBG) works as the cavity mirror, while a partially reflective (PR) FBG acts as the output coupler. In order to increase the efficiency of the Raman fiber laser, an HR FBG at the pump wavelength is employed to reflect the residual pump back into the gain fiber. In the 2nd-order Raman fiber laser, a pair of HR FBGs is utilized to convert the pump light to 1st-order Raman light most efficiently.
Fig. 2 Schematic of the 1st- (upper) and 2nd-order (lower) Raman tellurite fiber laser. HR FBG and PR FBG represent high reflectance fiber Bragg grating and partially reflective fiber Bragg grating, respectively. λp, λ1 and λ2 represent the wavelengths of the pump, the 1st- and 2nd-order Stokes waves, respectively.
For the slowly varying optical fields of the pump and the 1st-order Raman scattered light, the governing equations for the forward and backward powers can be expressed via the following coupled equations [44]:
For the 2nd-order Raman fiber laser, the time dependent partial differential equation for the pump power is the same as (1), while the power of the 1st-order Stokes wave is determined byand that of the 2nd-order stokes wave is determined byIn the Eqs. (1-4), Pp represents the pump power; P1, P2, represent the power of the 1st- and 2nd-order Stokes waves; the superscripts f, b represent the forward and backward propagation directions, respectively; ωp, ω1 and ω2 are the frequencies of the pump, the 1st- and 2nd-order stokes waves, respectively; γ1, γ2 are the Raman gain coefficients of the 1st- and 2nd-order Stokes waves; and vp, v1 and v2 are the group velocities of the pump, the 1st- and 2nd-order Stokes wave, respectively.The boundary conditions for the powers of the pump and the Stokes at the input and output ends of the Raman fiber laser are given by
Where Rp is the reflectance of the HR FBG for the pump, Rkf and Rkf represent the reflectances of the HR and PR FBGs at λk respectively. Pin is the launched pump power and L is the length of the tellurite Raman fiber. The output power of the Raman fiber laser can be obtained byThe simulations of the Raman fiber lasers are accomplished by using the Runge-Kutta method to numerically solve the coupled equations.3. Results and discussion
3.1 Continuous-wave Raman fiber lasers
Both cw and Q-switched RE-doped ZBLAN fiber lasers at 3 µm can be used to pump a Raman tellurite fiber laser in the 3-5 µm wavelength range. In this subsection, the simulation results of cw Raman fiber lasers pumped at the typical wavelength of a free-running cw Er3+-doped ZBLAN fiber laser are presented. Tellurite fiber with a core diameter of 8 µm and a numerical aperture (NA) of 0.15 is used as the Raman gain fiber. All the HR FBGs are assumed to have a reflectance of 99.5% at the desired wavelengths.
3.1.1 First-order Raman fiber lasers
1st-order Raman fiber lasers pumped by a 20 W cw Er3+-doped ZBLAN fiber laser at 2.8 µm were investigated first. Since the Raman gain peak of tellurite glass is at a frequency shift of 740 cm−1 as shown in Fig. 1, the output power of the 1st-order Raman laser operating at 3.53 µm was calculated as a function of the fiber length and the reflectance of the output FBG coupler and is presented by a contour plot shown in Fig. 3. It is found that a maximum output power of 6.75 W can be obtained at 3.53 µm, when the Raman fiber length is 1 m and the output FBG coupler has a reflectance of 90%. The most attractive feature of a Raman fiber laser is that it can operate at any wavelength within the Raman gain band. Therefore, it is essential to investigate the operating wavelength range of the Raman fiber laser. When the Raman fiber length and the reflectance of the output FBG coupler are fixed at 1 m and 90%, respectively, the output power of the Raman fiber laser as a function of operating wavelength was calculated and is shown in Fig. 4. The maximum output power of 7.42 W can be obtained at 3.16 µm, which is larger than that of 3.53 µm at the Raman gain peak due to the larger quantum efficiency. Because the Raman gain coefficient around 3.3 µm is less than 1 × 10−12m/W, the 20 W pump power is still below the laser threshold and lasing cannot be established at 3.26 µm – 3.36 µm when the fiber length is 1 m and the output coupler reflectance is 90%. The laser threshold of the Raman fiber laser at 3.3 µm can be reduced by increasing the reflectance of the output coupler and the fiber length as will be demonstrated below.
Fig. 3 Output power of a 3.53 µm 1st-order Raman fiber laser as a function of the Raman fiber length and the reflectance of the output FBG coupler at a pump power of 20 W. The numbers besides the contour curves are the output powers.
Fig. 4 Output power of the 1st-order Raman fiber laser as a function of wavelength at a pump power of 20 W when the Raman gain fiber length and the reflectance of the output FBG coupler are fixed at 1 m and 90%, respectively.
In order to achieve clear insight into the dependence of the output power of the 3.53 µm 1st-order Raman fiber laser on the length of the Raman gain fiber and the reflectance of the output FBG coupler, the output power as a function of the length of the Raman fiber for different reflectance of the output FBG coupler and as a function of the reflectance of the output FBG coupler for different lengths of the Raman fiber were calculated and are shown in Figs. 5(a) and 5(b), respectively. As seen in Fig. 5(a), the Raman fiber laser starts to lase with a shorter fiber length as the reflectance of the output FBG coupler becomes higher. Figure 5(a) also indicates that the optimum fiber length giving the maximum output reduces with the increased reflectance of the output FBG coupler and the dependence of the output power on the Raman gain fiber length becomes critical as the reflectance of the output FBG coupler becomes large. Figure 5(b) shows the optimum reflectance of the output FBG coupler increases with reduced Raman fiber length and the dependence of the output power on the reflectance of the output FBG coupler becomes critical as the Raman fiber becomes short. Both figures provide sufficient information and guidance for the design and development of the 1st-order Raman fiber laser.
Fig. 5 Output power of the 3.53 µm 1st-order Raman fiber laser (a) as a function of the fiber length for different reflectance of the output FBG coupler and (b) as a function of the reflectance of the output FBG coupler for different fiber lengths when the pump power is 20 W.
The output power as a function of the pump power for different fiber lengths when the reflectance of the output FBG coupler is 90% and for different reflectances of the output FBG coupler when the Raman gain fiber length is 1m is shown in Figs. 6(a) and 6(b), respectively. Clearly, the pump threshold power of the 3.53 µm 1st-order Raman fiber laser increases with increased Raman fiber length, while it reduces with increased reflectance of the output FBG coupler. Its slope efficiency reduces with increased Raman fiber length, while it increases with increased reflectance of the output FBG coupler. Therefore, there is a tradeoff between high slope efficiency and low pump threshold. Elaborate design of the Raman fiber laser is necessary to achieve the required specifications.
Fig. 6 Output power of the 3.53 µm Raman fiber laser as a function of the pump power (a) for different fiber lengths when the reflectance of the output FBG coupler is 90% and (b) for different reflectances of the output FBG coupler when the Raman gain fiber length is 1 m.
The Raman gain coefficient of tellurite glass has a minimum (0.8 × 10−12 m/W) at a Raman shift of 542 cm−1, corresponding to a Raman laser wavelength of 3.3 µm for a pump wavelength of 2.8 µm. As shown in Fig. 4, the 3.3 µm 1st-order Raman fiber laser with a fiber length of 1 m and the output FBG coupler of 90% cannot lase even at a power of 20 W. Therefore, it is critical to study the performance of the 3.3 µm 1st-order Raman fiber laser and optimize the Raman laser to achieve the maximum output power at 3.3 µm. The output power of the 1st-order Raman fiber laser at 3.3 µm as a function of the fiber length and the reflection of the output FBG coupler is presented in a contour plot shown in Fig. 7. A maximum output power of 0.78 W can be obtained when the Raman fiber length is 1.25 m and the reflectance of the output FBG coupler is 98%. However, the maximum conversion efficiency of the 3.3 µm Raman fiber laser is only about 3.9% due to the small Raman gain coefficient. When the Raman fiber length and the reflection of the output FBG coupler are fixed at 1.25 m and 98%, respectively, the output power of the Raman fiber laser as a function of the wavelength is calculated and is shown in Fig. 8. In this case, a Raman fiber laser operating in a wavelength range from 2.9 µm to 3.62 µm can be obtained. The output power at 3.3 µm is a minimum due to a minimum Raman gain coefficient at a Raman shift of 542 cm−1. Nevertheless, the efficiency of a Raman fiber laser at 3.3 µm can be significantly increased by changing the pump wavelength. As shown in Fig. 8(b), the output power at 3.3 µm will be 6.3 W and the efficiency will be as high as 31.5% when the pump wavelength is 2.9 µm.
Fig. 7 Output power of a 3.3 µm 1st-order Raman fiber laser as a function of the Raman fiber length and the reflectance of the output FBG coupler at a pump power of 20 W. The values beside the contour curves are the output powers.
Fig. 8 Output power of the 1st-order Raman fiber laser as a function of wavelength at a pump power of 20 W. (a) The Raman gain fiber length and the reflectance of the output FBG coupler are fixed at 1.25 m and 98%, respectively and the pump laser is at 2.8 µm; (b) the Raman gain fiber length and the reflection of the output FBG coupler are fixed at 1 m and 90%, respectively and the pump laser is at 2.9 µm.
3.1.2 Second-order Raman fiber lasers
Because the wavelength of a 1st-order Raman fiber laser pumped at 2.8 µm cannot exceed 3.62 µm, a Raman fiber laser operating a wavelength beyond 3.62 µm can be achieved by either increasing the pump wavelength or by using 2nd-order Raman scattering. Because the emission wavelength of a high efficiency RE-doped ZBLAN fiber laser is usually limited to be below 3.1 µm [45], using 2nd-order Raman scattering is the most effective approach to extend the operating wavelength of a Raman laser. The configuration of a 2nd-order Raman fiber laser is depicted in Fig. 2. A pair of HR FBGs at a wavelength within the Raman shift relative to the pump wavelength is used to form a high Q-value fiber cavity for the 1st-order Raman Stokes, which is converted to the 2nd-order Raman Stokes by the nested cavity consisting of the HR and PR FBGs as well as the tellurite fiber. In this subsection, the simulation results for the 2nd-order Raman fiber laser are presented.
First, a 2nd-order Raman fiber laser in which both the 1st- and 2nd-order Raman shifts are at the Raman gain peak (740 cm−1) is investigated. The operating wavelength of this Raman fiber pumped at 2.8 µm is 4.77 µm. Referring to the configuration illustrated in Fig. 2(b), two highly reflective FBGs at 3.53 µm and the tellurite fiber form the 1st-order Raman fiber laser cavity. A highly reflective FBG and a partially reflective FBG at 4.77 µm nested with the 1st-order Raman fiber laser form a cascaded Raman fiber laser, i.e., the pump power is transferred to the 1st-order Raman laser at 3.53 µm first, and then transferred to the 2nd-order Raman laser at 4.77 µm. The output power of the 2nd-order Raman fiber laser as a function of the fiber length and the reflectance of the output FBG coupler at a pump power of 20 W are presented by a contour plot shown in Fig. 9. A maximum output power of 2.82 W can be obtained when the Raman fiber length is 0.34 m and the reflectance of the output FBG coupler is 40.5%. When the Raman fiber length and the reflectance of the output FBG coupler are fixed at 0.34 m and 40.5%, respectively, the output power of a Raman fiber laser operating from 3.7 µm to 5 µm was calculated and is shown in Fig. 10. Due to the small Raman gains close to the pump wavelength and at a Raman shift of 542 cm−1, a 2nd-order Raman laser cannot be established in the two wavelength ranges 4.25 - 4.5 µm and 3.6 - 4.05 µm when the pump power is 20 W. This problem can be solved by properly selecting the Raman shifts of the 1st and 2nd order Raman scattering.
Fig. 9 Output power of a 4.77 µm 2nd-order Raman fiber laser as a function of the Raman fiber length and the reflectance of the output FBG coupler when the pump power is 20 W and the 1st-order Stokes oscillates at 3.53 µm. The values beside the contour curves are the output powers.
Fig. 10 Output power of the 2nd-order Raman fiber laser as a function of wavelength at a pump power of 20 W when the Raman gain fiber length and the reflectance of the output FBG coupler are fixed at 0.34 m and 40.5%, respectively, and the 1st-order Stokes oscillates at 3.53 µm.
For instance, a Raman fiber laser can operate at 4.36 µm when the 1st-order Raman shift is at 740 cm−1 and the 2nd-order Raman shift is at 542 cm−1, i.e., the maximum reflectance wavelength of the HR FBGs for the 1st-order Raman laser is at 3.53 µm and that of the 2nd-order Raman laser is at 4.36 µm. It was found that a maximum output power of 1.51 W at a pump power of 20 W can be obtained when the Raman fiber length is 0.19 m and the reflectance of the output FBG coupler is 88%. Under the same conditions, the output power of the Raman fiber laser as a function of the wavelength was calculated and is shown in Fig. 11(a). Clearly, the Raman fiber laser can operate at any wavelength between 3.6 µm and 5.0 µm. The efficiency of the Raman fiber laser based on this configuration, however, is much lower than that shown in Fig. 10. Nevertheless, our simulation results summarized in Fig. 11(b) confirm that a Raman tellurite fiber laser pumped at 2.8 µm can operate at any wavelength within the 3-5 µm atmospheric transparency window by elaborately designing the Raman laser cavity.
Fig. 11 (a) Output power of the 2nd-order Raman fiber laser as a function of wavelength at a pump power of 20 W when the Raman gain fiber length and the reflectance of the output FBG coupler are fixed at 0.19 m and 88%, respectively, and the 1st-order Stokes oscillates at 3.53 µm. (b) Summary of the calculation results plotted in Fig. 4, Fig. 8, Fig. 10 and Fig. 11(a) shows the feasibility of obtaining a fiber laser at any wavelength between 3 and 5 µm by utilizing 1st-order and 2nd-order Raman scattering in tellurite fiber.
3.2 Q-switched laser pumped Raman tellurite fiber lasers
Q-switched lasers usually have higher peak power than cw lasers and thus enable high-efficiency low threshold Raman lasers. Q-switched fiber lasers at 3 µm have been extensively studied [19–22]. We have successfully demonstrated Q-switched Er3+-doped and Ho3+-doped ZBLAN fiber lasers using Fe2+:ZnSe and graphene saturable absorbers [20–22]. Q-switched pulses with pulse energies of 1.67 µJ and peak powers of 0.58 W have been obtained [22]. Using an Er3+-doped ZBLAN fiber amplifier, we have increased the pulse energy to 24 µJ with a peak power of 11.4 W. It is quite feasible to obtain a pulse energy of 300 µJ with a peak power of 143 W by using more powerful pump sources [24]. Therefore, Q-switched fiber lasers at 3 µm are very promising pump sources for high-efficiency tellurite fiber Raman lasers. In this subsection, tellurite fiber Raman lasers pumped by 2 µs Q-switched fiber lasers at a repetition rate of 40 kHz are investigated.
For comparison, a 1st-order Raman laser operating at the Raman gain peak with a Raman shift of 740 cm−1, corresponding to a Raman laser wavelength of 3.53 µm when pumped at 2.8 µm, is investigated first. When the average power of the Q-switched laser source is 20 W, the output power of the 3.53 µm Raman fiber laser as a function of the fiber length and the reflectance of the output FBG coupler is presented as a contour plot shown in Fig. 12(a). A maximum output power of 13.6 W can be obtained when the fiber length is 0.5 m and the reflectance of the PR FBG coupler is 48%. Clearly, compared to a cw laser pumping scheme, the conversion efficiency of the Raman laser pumped by a Q-switched laser is increased by a factor of two. When the fiber length is 0.5 m and the reflectance of the output FBG coupler is 48%, the output power of the Q-switched 3.53 µm Raman fiber laser as a function of the average pump power was calculated and is shown by the red curve in Fig. 12(b). For comparison, the output power of the cw 3.53 µm Raman fiber laser as a function of the pump power when the fiber length is 1 m and the reflectance of the output FBG coupler is 90% is also plotted as a blue curve in Fig. 12(b). Obviously, even though the gain fiber of the Q-switched Raman laser is 0.5 m, which is half of the 1 m gain fiber of the cw Raman laser, the threshold of the Q-switched Raman laser is still lower than that of the cw Raman laser. The conversion efficiency of the Q-switched Raman laser can be as high as 70%, which is significantly larger than that of the cw Raman laser. The pulse shapes of the pump pulse and the output Raman signal pulse are plotted in Fig. 13. Because the Raman gain is nonlinearly dependent on the pump power, the Raman signal pulse doesn’t have long tails like the pump pulse and its pulse width is also slightly narrower than that of the pump pulse.
Fig. 12 Output power of Q-switched 1st-order Raman fiber laser at 3.53 µm as a function of the Raman fiber length and the reflectance of the output FBG coupler when the Q-switched 2.8 µm pump laser has an average power of 20 W. (a) The contour plot and (b) the output power of the Q-switched (red) and cw (blue) Raman fiber laser at 3.53 µm as a function of the pump power.
Fig. 13 The pulse shapes of the pump pulse and the output Raman signal pulse when the Raman gain fiber length is 0.5 m and the reflectance of the output FBG coupler is 48%. The inset shows the normalized pulse shapes of the pump and the Raman signal (the input pulse is assumed to be Gaussian).
2nd-order Raman fiber lasers pumped by a Q-switched laser at 2.8 µm have also been investigated. The output power of a Q-switched 2nd-order Raman fiber laser operating at 4.77 µm as a function of the fiber length and the reflectance of the output FBG coupler was calculated and a maximum output power of 7.0 W can be obtained when the Raman fiber length is 0.5 m and the reflectance of the output FBG coupler is 40%. The conversion efficiency of the Q-switched 2nd-order Raman laser is 35%, which is nearly 2.5 times of that of the cw laser counterpart. The output power of the Q-switched 2nd-order Raman laser as a function of the pump power is plotted as a red curve in Fig. 14. Obviously, the conversion efficiency of the Q-switched laser is significantly larger than that of the cw 2nd-order Raman laser, which is presented as a blue curve in Fig. 14. The threshold of the Q-switched 2nd-order Raman laser is only 3 W, which is much smaller than the 13 W threshold of the cw 2nd-order Raman laser. Therefore, the tellurite fiber Raman laser pumped by a Q-switched Er-doped fiber laser at 2.8 µm will exhibit better performance than when pumped by a cw laser in terms of higher conversion efficiency and much lower pump threshold.
Fig. 14 The output power of the Q-switched (red) and cw (blue) 2nd-order Raman fiber laser at 4.77 µm as a function of the pump power.
4. Conclusion
In this paper numerical simulations of tellurite fiber Raman lasers pumped by readily available Er3+-doped ZBLAN fiber lasers have been presented. Our simulation results have shown that fiber laser sources operating at any wavelength within the 3-5 µm atmospheric transparency window can be achieved by employing 1st-and 2nd-order Raman scattering of tellurite fibers. Q-switched Raman fiber lasers have much higher conversion efficiency and much lower threshold than corresponding cw Raman fiber lasers. The calculation results can provide useful guidance for the design and development of high power tellurite fiber Raman lasers at 3-5 µm.
Acknowledgments
This work was supported by National Science Foundation Engineering Research Center for Integrated Access Networks (Grant #EEC-0812072) and the Photonics Initiative of the University of Arizona (TRIF). Lixiang Geng and Li Li would like to thank Chinese Scholarship Council for financial support.
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