1. Introduction

Single-frequency fiber laser sources have attracted sustained attention due to their extremely low noise and ultra-narrow spectral linewidth and have been extensively used for many applications including high-precision metrology, high-resolution spectroscopy, and long-distance coherent detection [1]. Because these applications need single-frequency lasers at different wavelengths, intensive research has been conducted to develop single-frequency fiber lasers with most prevalent rare-earth doped optical fibers [2]. The first single-frequency fiber laser was demonstrated with a 5.1-cm-long Nd³⁺-doped silica fiber in a distributed feedback (DFB) configuration in 1988 [3]. A single-frequency laser with an output power of 0.78 mW and spectral linewidth of 1.3 MHz at 1082 nm was achieved. Compared to DFB fiber lasers, in which a phase-shift fiber Bragg grating (FBG) is inscribed in the gain fiber core, distributed Bragg reflector (DBR) fiber lasers have advantages such as lower noise and much higher stability because the FBGs inscribed in the passive fiber core don’t suffer from thermal issues as with DFB FBGs. A single-frequency DBR fiber laser has been developed as early as 1992 with a 2-cm-long Er³⁺-doped silica fiber laser cavity, where 181 µW output power at 1540 nm was achieved with a measurement resolution-limited linewidth of 6 MHz [4]. However, the gain fiber of a DBR or DFB fiber laser is usually limited to several cm for robust single-frequency operation. The efficiency and output power are thus constrained at low levels due to the low absorbed pump light. Consequently, highly rare-earth doped glass fibers with super high pump absorption stand out as excellent engines for high efficiency single-frequency lasers. Due to their high rare-earth doping capability (up to 10²¹ ions/cm³), rare-earth doped phosphate, germanate, and fluoride glass fibers have been widely used to develop single-frequency fiber lasers with improved efficiency and output power as well as extended operating wavelengths [2]. The normalized fluorescence spectra of these rare-earth ions in corresponding high-solubility host glass materials are plotted in Fig. 1(a). The output power levels and wavelengths of the representative single-frequency fiber lasers are summarized in Fig. 1(b). To date, single-frequency fiber lasers with operating wavelengths ranging from 915 nm to 3.25 µm have been demonstrated with Nd³⁺-, Yb³⁺-, Er³⁺-, Tm³⁺-, Ho³⁺-, and Dy³⁺-doped fibers [5–21].

 

Fig. 1. (a) Normalized fluorescence spectra of the rare-earth doped glasses that have been used to make highly doped fibers for single-frequency lasers operating at different wavelengths. (b) Output power levels and wavelengths of the representative single-frequency fiber lasers based on highly rare-earth doped fibers [5–21].

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Nevertheless, there is high demand for single-frequency fiber lasers below 900 nm, which have found specific applications including water vapor lidar [22], high-resolution and precision spectroscopy [23], and harmonic generation to achieve high-coherence blue lasers and deep UV lasers [24]. In this paper, we report the first single-frequency fiber laser below 900 nm, which was developed with a 2.5-cm 1 wt.% Nd³⁺-doped phosphate fiber in the DBR configuration. An output power of 44.5 mW at 880 nm was obtained at the maximum available pump power of 390 mW, while achieving a slope efficiency of 20.4% with respect to the absorbed pump power.

The partial energy level diagram of Nd³⁺ and the transitions related to the laser emission at 880 nm are plotted in Fig. 2(a). The ions can be excited to level ⁴F_5/2 by absorbing 808 nm pump light and then decay to level ⁴F_3/2 via fast multi-phonon decay. The radiative transitions from the upper laser level ⁴F_3/2 to levels ⁴I_13/2, ⁴I_11/2, and ⁴I_9/2 produce the light at 0.9 µm, 1.05 µm, and 1.3 µm bands with corresponding branching ratios of 0.43, 0.48, and 0.09. Since the transition ⁴F_3/2 → ⁴I_11/2 has the highest branching ratio and the lower laser level is not the ground state, high-efficiency lasers at the 1.05 µm band can be easily achieved with a variety of Nd³⁺-doped materials. However, the 1.05 µm laser transition is a constraint on the 0.9 µm laser, which is associated with a three-level system with the ground state as the lower laser level. Therefore, high pump power density is always required to achieve population inversion for the 0.9 µm laser operation. Nevertheless, this can be easily realized with fiber lasers due to the small core size and long interaction length. Single-frequency fiber lasers in the 0.9 µm wavelength regime have been demonstrated with Nd³⁺-doped silica fibers [25,26]. However, their output power levels and efficiencies were relatively low. Moreover, their emission wavelengths were above 910 nm because the emission peak of Nd³⁺-doped silica is at 934.5 nm. It is very challenging to achieve a single-frequency fiber laser below 900 nm using a Nd³⁺-doped silica fiber due to the significantly diminished emission cross-section at short wavelength [27]. This matter can be settled with Nd³⁺-doped phosphate fibers.

 

Fig. 2. (a) Partial energy level diagram of Nd³⁺ and the transitions related to laser emission at 880 nm. The cooperative decay process between a pair of excited Nd³⁺ ions is also presented. One excited ion on level ⁴F_3/2 goes back to the ground state quickly by transferring its energy to another one on the same level, which is thus excited to a virtual upper level and then returns to the ground state by transferring its energy to acceptors such as color centers and impurities. (b) Normalized fluorescence spectra of Nd³⁺ in silica, phosphosilicate and phosphate glass in the wavelength region of 900 nm [28].

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As shown in Fig. 2(b), our recent spectroscopic study on Nd³⁺-doped phosphate glass reveals that it has a fluorescence peak at 875.6 nm, which is 60-nm shorter than that of Nd³⁺-doped silica glass [28]. Moreover, the detrimental concentration quenching in phosphate glass is much lower than that in silica glass [29,30]. We have demonstrated a 915 nm single-frequency Nd³⁺-doped phosphate fiber laser with a slope efficiency of 7.9% [5], which is much higher than that of 0.6% achieved with Nd³⁺-doped silica fiber [26]. Most recently, an 880-nm fiber laser, albeit not single-frequency, with a world-record efficiency of 42.8% was achieved with 25-cm-long 0.25 wt.% Nd³⁺-doped phosphate fiber [28]. All these achievements inspired us to explore single-frequency fiber lasers at 880 nm using highly Nd³⁺-doped phosphate fibers. It is worth noting that, due to the complex energy level structure of Nd³⁺, highly Nd³⁺-doped phosphate fiber lasers still suffer from concentration quenching even if it is to lesser extent than that of counterpart silica fiber lasers. Highly Nd³⁺-doped phosphate fiber lasers also suffer from cooperative processes, in which two excited ions transfer their energy to acceptors such as color centers and impurities, especially OH^-, as shown in Fig. 2(a). The cooperative process usually becomes significant in high concentration Nd³⁺-doped glass. Therefore, there is an optimum concentration of Nd³⁺ ions doped in phosphate fiber for the 880 nm single-frequency fiber laser. In this work, 2.5-cm-long 1 wt.% Nd³⁺-doped phosphate fiber was used to develop the single-frequency DBR fiber laser at 880 nm. Simulation of 1.5 wt.% and 2 wt.% Nd³⁺-doped phosphate fiber lasers was also conducted for the design of a higher efficiency 880 nm single-frequency fiber laser.

2. Experimental setup and results

The configuration of the DBR single-frequency Nd³⁺-doped phosphate fiber laser at 880 nm is shown in Fig. 3. Two polarized single-mode laser diodes at 808 nm were combined together through a polarization beam combiner (PBC) to provide a maximum available pump power of 390 mW. An 808/880 nm filter-type wavelength division multiplexer (FWDM) was used to couple the pump light into the fiber laser cavity and protect the pump diodes from backward amplified spontaneous emission (ASE). The DBR single-frequency fiber laser cavity was constructed by splicing a piece of 2.5-cm-long 1 wt.% Nd³⁺-doped phosphate fiber to a pair of FBGs with an asymmetric fusion splicing technique developed by NP Photonics [31]. The fiber cavity chain loss measured at 1310 nm was about 1.1 dB, including the splicing loss at two splicing joints, coupling loss, and fiber loss. The absorption coefficient of the 1 wt.% Nd³⁺-doped phosphate fiber at 808 nm was measured to be about 638 dB/m and its geometry is the same as that of commercial passive silica fiber (Coherent, 780-HP), which has a cutoff wavelength of ∼730 nm. The fiber core and cladding diameters are 4.4 and 125 µm, respectively, and the core numerical aperture (NA) is 0.13. The propagation loss of the Nd³⁺-doped phosphate fiber at 1310 nm was measured to be about 2.2 dB/m by a cutback experiment. The FBG pair of the DBR single-frequency fiber laser consists of a high-reflection FBG (HR-FBG) written in a non-polarization-maintaining (non-PM) passive fiber (Coherent, 780-HP), serving as the laser cavity mirror, and a partial-reflection FBG (PR-FBG) written in a PM passive fiber (Coherent, PM780-HP), serving as the output coupler. The HR-FBG has a reflectivity of 99.5% and a 3-dB bandwidth of 0.28 nm. The PR-FBG has a reflectivity of 45% and a 3-dB bandwidth of 0.029 nm. Due to the birefringence of PM780-HP fiber, the PR-FBG has two reflection peaks spacing by 0.24 nm. Although the 3-dB reflection band of the HR-FBG is slightly bigger than the reflection peak spacing of the birefringent PR-FBG, stable single-polarization operation can be achieved as only one reflection peak of the PR-FBG is within the reflection band of the HR-FBG and the mismatching between the reflection peaks of HR-FBG and PR-FBG is very small (< 0.05 nm). Another 808/880 nm PM FWDM was spliced to the other end of the PR-FBG to separate the 808 nm residual pump light and the 880 nm laser light. It should be noted that, the whole laser chain was placed on a piece of aluminum plate and covered with the thermal paste for better heat dissipation. To achieve stable single-frequency operation, the temperature of the fiber laser chain was actively controlled with a high-resolution controller.

 

Fig. 3. Experimental setup of the DBR single-frequency Nd³⁺-doped phosphate fiber laser at 880 nm.

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The output power of the 880-nm single-frequency fiber laser was measured with a power meter (Newport, 918D-IS-1). The output power as a function of the launched pump power is given by the black squares in Fig. 4(a). The pump threshold of the laser is around 65 mW. A maximum output power of 44.5 mW was achieved at a launched pump power of 390 mW, at which level the residual pump power was measured to be 89 mW. Higher output power can be achieved if more powerful single-mode laser diodes at 808 nm are used. The slope efficiency of the laser with respect to the launched pump power is around 14.0%. The output power as a function of the absorbed pump power is given by the red circles in Fig. 4(a). It is clear that, when the residual pump power is excluded, the slope efficiency of this single-frequency fiber laser is 20.4%, which is much higher than that of single-frequency Nd³⁺-doped silica fiber lasers at 9xx nm [25,26], because of the significantly lower concentration quenching effect in Nd³⁺-doped phosphate fiber. However, the efficiency of this single-frequency fiber laser is still much lower than the Stokes efficiency due to quenching effects and cooperative energy transfer processes, which can be mitigated by optimizing the glass composition and fabrication process. Nevertheless, further laser efficiency improvement is anticipated by using a higher concentration Nd³⁺-doped phosphate fiber with acceptable concentration quenching as discussed in the next section.

 

Fig. 4. (a) Output power of the 880-nm single-frequency Nd³⁺-doped phosphate fiber laser with respect to the launched (black) and absorbed (red) pump power. (b) Optical spectrum of the single-frequency fiber laser at the maximum output power of 44.5 mW measured with an OSA resolution of 0.5 nm in a wavelength range of 840-1150 nm. Inset: Optical spectrum measured with an OSA resolution of 0.02 nm in a wavelength range of 879-880.5 nm. (c) Longitudinal mode characteristics at the maximum output power of 44.5 mW measured with a scanning Fabry-Perot interferometer. (d) Measured RIN at the 44.5-mW laser power in a frequency range of 0-5 MHz.

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The optical spectrum of the 880-nm singe-frequency Nd³⁺-doped phosphate fiber laser operating at a maximum output power of 44.5 mW was measured with an optical spectrum analyzer (OSA, YOKOGAWA, AQ6370B). Figure 4(b) shows the optical spectrum measured with a wavelength resolution of 0.5 nm over a wavelength range from 840 nm to 1150 nm. The ASE produced through the competitive transition ⁴F_3/2 → ⁴I_11/2 has a peak at 1060 nm, which is 46 dB lower than the laser peak at 880 nm, indicating that the optical signal-to-noise ratio (OSNR) of this single-frequency fiber laser is better than 46 dB. The optical spectrum measured with a wavelength resolution of 0.02 nm over a wavelength range of 879-880.5 nm is shown in the inset of Fig. 4(b). A measured OSNR of 62 dB tells us that a single-frequency laser with much higher spectral purity can be obtained if we can use a WDM to remove the ASE from the laser output.

The longitudinal mode characteristics of this single-frequency Nd³⁺-doped phosphate fiber laser was investigated using a scanning Fabry–Perot (FP) interferometer (Thorlabs, SA210-8B) with a free spectral range (FSR) of 10 GHz and finesse of 180. Robust single-longitudinal-mode operation without any mode-hopping or multi-longitudinal mode oscillation was achieved when the temperature of the whole fiber laser cavity became stable. As shown by the FP scanning curve in Fig. 4(c), there are no other transmission peaks within the FSR of the scanning interferometer, confirming the single-longitudinal-mode operation of this DBR fiber laser.

The relative intensity noise (RIN) of this single-frequency Nd³⁺-doped phosphate fiber laser was measured with a photodetector (Thorlabs, DET01CFC) and a spectrum analyzer (Advantest, R3131A). Figure 4(d) shows the measured RIN of the single-frequency laser at a maximum output power of 44.5 mW. A RIN peak of -117 dB/Hz attributed to the relaxation oscillation was observed at a frequency of 1.13 MHz. Beyond the relaxation oscillation frequency, the RIN decreases rapidly and approaches the sensitivity-limited level of -155 dB/Hz of our measurement setup.

3. Simulation and results

To understand the less-than-ideal efficiency of this DBR single-frequency fiber laser and identify approaches to improving the laser performance, we conducted simulations on a Nd³⁺-doped phosphate fiber laser with a numerical model including pair-induced quenching and cooperative energy transfer, which have been identified as major detrimental factors on the efficiencies of highly doped fiber lasers [32,33]. Because the excited ions in level ⁴F_5/2 decay to level ⁴F_3/2 very quickly via multi-phonon decay, the 880-nm Nd³⁺-doped laser system can be simplified with the ion populations N₁ in the ground state and N₂ in the excited state. Considering pair-induced quenching, the total number of ions N_tot can be divided into singular and paired populations ($N_{tot}^S$ and $N_{tot}^P$):

The partial energy-level diagrams and the transitions for singular and paired ions related to the 880 nm Nd³⁺-doped phosphate fiber laser are shown in Fig. 5(a) and 5(b), respectively. For singular Nd³⁺ ions, the cooperative decay process between two excited ions is included in our model and thus corresponding rate equation can be written as

 

Fig. 5. Partial energy-level diagrams and the transitions for (a) singular and (b) paired ions related to the 880 nm Nd³⁺-doped phosphate fiber laser. R₁₃ is the absorption rate at the pump wavelength, W₁₂ and W₂₁ are the absorption and emission rates at the laser wavelength, A₂₁ and W_nr are spontaneous emission rate and non-radiative rate of excited Nd³⁺ ions, and D is cooperative decay rate of two excited singular Nd³⁺-ions.

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For the pair-induced clusters, similar to [32], only two steady states are considered in our model: pair state 1 (P₁), in which two ions are in the ground state, and pair state 2 (P₂), in which one ion is in the ground state and the other one is in the excited state. Because the excited paired ions decay to the ground state very quickly due to the quenching effect, pair state 3 (P₃) is not considered in the steady state model. Therefore, the rate equation for paired ions can be written as

Lastly, the evolution equations of pump and signal power along the gain fiber are expressed as

The signal power levels at the cavity ends are subjected to the boundary conditions as follows:

In order to determine the clustered ion fraction 2k and cooperative decay rate D of the 1 wt.% Nd³⁺-doped phosphate fiber, experiments and simulations of the 2.5-cm fiber laser with various PR-FBG reflectivities were carried out first. Three 2.5-cm 1 wt.% Nd³⁺-doped phosphate fiber lasers with PR-FBG reflectivities of 45%, 68% and 88%, were built and their output powers were measured to be 44.5, 40.6 and 22.1 mW, respectively, at a pump power of 390 mW as shown in Fig. 6(a). The output power as a function of pump power for a 2.5-cm 1 wt.% Nd³⁺-doped phosphate fiber laser with PR-FBG reflectivity of 45% was measured and is shown in Fig. 6(b). 2k and D were estimated to be 21.5% and 4×10⁻²³ m³/s, respectively, based on excellent agreement between simulation and experiment, as shown in Fig. 6(a) and 6(b). The simulation result of Fig. 6(a) also tells us that a maximum output power of 47.6 mW can be obtained for a 2.5-cm 1 wt.% Nd³⁺-doped phosphate fiber laser with a PR-FBG reflectivity of 50%. The results for 2k = 11% with D = 4×10⁻²³ m³/s and 2k = 21.5% with D = 8×10⁻²³ m³/s are also shown in Fig. 6(b). When the clustered ion fraction 2k decreases from 21.5% to 11%, the laser threshold decreases slightly from 82.6 mW to 73 mW, while the slope efficiency increases from 14.5% to 17.8%. When the cooperative decay rate D is doubled, the laser threshold increases significantly from 82.6 mW to 117.4 mW while the slope efficiency doesn’t have a noticeable change. Therefore, both concentration quenching and cooperative decay impair the laser performance of Nd³⁺-doped phosphate fiber lasers. Clustered ions predominantly reduce the laser slope efficiency while cooperative decay only increases the laser threshold.

 

Fig. 6. (a) Measured and calculated output power of the 880-nm 2.5-cm Nd³⁺-doped phosphate fiber laser with different PR-FBGs pumped at 390 mW. (b) Measured and calculated laser output power as a function of the pump power for the 880-nm 2.5-cm Nd³⁺-doped phosphate fiber laser with PR-FBG reflectivity of 45% and different clustered ion fractions and cooperative energy transfer parameters. A clustered ion fraction of 21.5% and cooperative energy transfer parameter of 4×10⁻²³ m³/s were obtained by fitting the experimental results.

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To predict the potential performance improvement of the 880-nm single-frequency fiber laser that could be achieved by optimizing the Nd³⁺ doping level and mitigating the concentration quenching, simulation of the single-frequency DBR lasers using 2.5-cm 1.5 wt.% and 2 wt.% Nd³⁺-doped phosphate fibers was conducted. The output power as a function of the PR-FBG reflectivity was calculated for both the 2.5-cm 1.5 wt.% and 2 wt.% Nd³⁺-doped phosphate fiber lasers pumped at 390 mW and results are shown in Fig. 7(a) and 7(b), respectively. Maximum output power of 82 mW and 102.9 mW can be achieved with the 1.5 wt.% and 2 wt.% Nd³⁺-doped phosphate fiber, respectively, when the clustered ion fraction is maintained to be 21.5%. Compared to the 1-wt.% Nd³⁺-doped phosphate fiber laser, the optimum PR-FBG reflectivity of the fiber lasers producing the maximum output power changes from 50% to 40% and 30%, respectively. Moreover, significant increase of the output power can be achieved with low reflectivity PR-FBGs. However, when the PR-FBG reflectivity exceeds 60%, the power improvement becomes small. Because the clustered ion fraction generally increases with the increasing Nd³⁺ concentration, the simulations of 1.5 wt.% and 2 wt.% Nd³⁺-doped phosphate fiber lasers were also conducted with increased clustered ion fractions and the results are shown by the blue and purple symbols in Fig. 7(a) and 7(b), respectively. It is clear that the output power decreases as the clustered ion fraction 2k increases. It should be noted that, the output power levels of single-frequency DBR fiber lasers at 880 nm based on 1.5 wt.% Nd³⁺-doped phosphate fiber with clustered ion fraction 2k of 47% and 2 wt.% Nd³⁺-doped phosphate fiber with 2k of 60% are comparable to that of the 1 wt.% Nd³⁺-doped phosphate fiber used in our experiment. The corresponding curves are nearly indistinguishable in Fig. 7(a) and 7(b). It tells us that an 880-nm single-frequency laser with higher output power can be achieved with 1.5 wt.% and 2 wt.% Nd³⁺-doped phosphate fibers when their clustered ion fractions 2k are kept below 47% and 60%, respectively.

 

Fig. 7. Calculated output power versus the PR-FBG reflectivity for the 880-nm 2.5-cm Nd³⁺-doped phosphate fiber lasers with dopant concentrations of (a) 1.5 wt.% and (b) 2 wt.%. The calculated result for a 1 wt.% Nd³⁺-doped phosphate fiber laser is also included in both figures for comparison.

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4. Conclusion

In conclusion, we have demonstrated an 880 nm single-frequency DBR fiber laser based on a 2.5-cm 1 wt.% Nd³⁺-doped phosphate fiber. An output power of 44.5 mW and a slope efficiency of 20.4% with respect to the absorbed pump power were obtained. Higher efficiency single-frequency DBR fiber lasers at 880 nm can be achieved with 1.5 wt.% or 2 wt.% Nd³⁺-doped phosphate fiber with reduced ion clustering.