1. Introduction

Single-frequency lasers operating in the eye-safe wavelength band near 1.6 μm (L-band) are useful for a variety of applications, including high-resolution molecular spectroscopy, coherent laser lidar, pumping source for Tm³⁺-doped laser, and nonlinear frequency conversion [1–7]. To data, the available single-frequency lasers operating at 1.6 μm have already been developed by several methods. Solid-state lasers of the Er³⁺-doped YAG or YLuAG crystals based on free-space configuration with some bulk-optic components can deliver several watts with tens of kHz linewidth [1–3,8–12], but their potential applications are limited by the low conversion efficiency and the high susceptibility to acoustics and vibrations. Although the distributed feedback (DFB) laser diode can offer tens of milliwatts output with a few MHz linewidth [4], the relatively broad spectral linewidth and low signal-to-noise ratio will hamper its further application. In recent years, single-frequency fiber lasers (SFFLs) have attracted much attention due to their promising merits of narrow linewidth, low noise, good beam quality, and robust all-fiber design [13–17]. Unfortunately, most of the previous researches focused on SFFLs are working in C-band (1535–1565 nm) because of the obstacles of a small emission cross-section in the doped fibers and the suppression of amplified spontaneous emission (ASE)/parasitic lasing of Er³⁺ and Yb³⁺ ions [14,18,19]. However, the SFFL above the long-wavelength of 1600 nm is urgently desired and has not been reported so far.

To date, SFFLs based on different cavity technologies have been successfully implemented as short-cavity distributed Bragg reflector (DBR) [13–15], DFB [20,21], and ring cavity with narrow-bandwidth spectral filters [22,23]. Nevertheless, the obtainable output power of DFB fiber laser is relatively low. Moreover, the mode-hopping phenomenon will inevitably arise in ring cavity fiber laser. Overall, the short-cavity DBR fiber laser is particularly attractive due to its compactness, robustness and high-efficiency. For efficient single-longitudinal-mode operation in the DBR configuration, it is necessary to shorten the cavity length for enlarging the longitudinal mode spacing, and this result in the effective cavity length is limited to several centimeters. In addition, longer length of the doped fiber is normally needed during the long-wavelength (>1600 nm) operation owing to a small emission cross-section in fiber, which is only a quarter to a third of that of C-band (see Table 1) [24,25]. So, it is still a challenge for lasing at long-wavelength and suppressing the ASE/parasitic oscillation in a DBR short-cavity configuration.

Table 1. Optical parameters of different doped fibers

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Recently, heavily Er³⁺/Yb³⁺ co-doped phosphate glass fibers (EYPFs) have been already developed and successfully used to implement DBR SFFLs at 1.5 μm [13,14,19]. Phosphate glass is well known for its superior rare-earth ion solubility and low clustering effect. EYPFs with the doping concentrations of several wt% have been reached [14,26–28], resulting in a large absorption and emission cross-section, as well as a high gain per unit length. Therefore, in the case of heavily doped fiber, to effectively balance the cavity length and the longitudinal mode spacing is a potential approach for achieving the long-wavelength SFFL in a DBR short-cavity structure. In this letter, based on a 16-mm-long newly developed heavily EYPF, an efficient linearly-polarized DBR SFFL at 1.6 μm is reported. More than 20 mW of a stable single transverse and longitudinal mode lasing at 1603 nm is achieved.

2. EYPF property and experimental setup

The home-made heavily EYPF with single-cladding structure is designed and fabricated at 660 °C using the rod-in-tube technique. The doping concentration and ratio of Er³⁺/Yb³⁺ is important for energy transfer process and efficient fluorescence emission. Er³⁺ and Yb³⁺ ions are doped uniformly in the core region with the optimal doping concentrations of 1.0 mol% and 2.0 mol%, respectively. According to the measured absorption spectra and Beer-Lambert law [29,30], the absorption cross-section of the core glass can be calculated. Followly, the emission cross-section is finally calculated by using McCumber theory [31,32]. The peak absorption cross-section at 976 nm and emission cross-section at 1603 nm of the core glass is 15.0 × 10⁻²¹ cm² and 2.18 × 10⁻²¹ cm², respectively. Compared with the commercial high-gain silica glass doped fibers, our EYPF has a nearly 2 to 4 times larger emission cross-section at the 1.6 μm band (e.g., @1603 nm and @1610 nm). Table 1 summarizes the optical parameters of different doped fibers for comparison. Furthermore, the emission cross-section at the 1.5 μm band and the absorption cross-section at 976 nm are slso given. Obviously, due to the heavily Er³⁺ and Yb³⁺ ions doping concentration in the phosphate glass, our fiber possesses a larger value of the emission and absorption cross-section than that of the silica glass doped fiber. The designed EYPF has a 7.6 μm/0.142 numerical aperture (NA) core and a 125 μm cladding. Under conditions of the weak guidance approximation, the single-mode cutoff wavelength (λ_c) that is defined as 2π × NA × a/2.405, where a is the core radius of phosphate glass fiber. The calculated λ_c is ~1409 nm, indicating that the EYPF supports only the fundamental transverse mode (LP₀₁) at the lasing wavelength.

The cross section of EYPF is featured via an amplified CCD viewer, as shown in the inset of Fig. 1. The propagation loss of EYPF at 1310 nm is measured to be < 0.04 dB/cm by a cut-back method. The gain characteristic of doped fiber pumped by a 976 nm laser diode (LD) is demonstrated from a 30-mm-long EYPF. Figure 1 shows the net gains versus the pump powers for different input signal powers (P_s of 1.2, 3.6 and 8.4 mW). It is found that the net gain per unit length of this EYPF reaches up to 1.1 dB/cm at 1603 nm, which is very beneficial to our fiber laser operating at long-wavelength with a short-cavity configuration. More details of the fiber properties can be found in our previous papers [14,27,28,33,34].

 

Fig. 1 Net gains versus the pump powers of a 30-mm-long EYPF for different input powers. Inset: cross section of the EYPF.

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The experimental setup of 1.6 μm DBR SFFL is depicted in Fig. 2. The laser cavity is constructed by cleaving a high-reflection fiber Bragg grating (HR-FBG) and a polarization-maintaining partial-reflection FBG (PM-FBG) very close to the grating area, and then directly splicing to a short-length EYPF. The HR-FBG is irradiated with a 3-dB-bandwidth of 0.34 nm and a reflectivity of >99.9% at signal wavelength. The PM-FBG is written in a single-mode PM fiber with a 3-dB-bandwidth of 0.09 nm and a reflectivity of 87.8% at 1602.5 nm. Due to the birefringence of PM fiber, the reflecting spectrum of the PM-FBG splits into two reflection peaks with central wavelengths corresponding to the fast and slow axes. Two FBGs are specially chosen so that only the reflection peak corresponds to the slow axis of the PM-FBG would fall into the center of the HR-FBG. So the polarization state of the lasing wavelength could be locked at the slow axis of PM-FBG. And then the laser output with stable linearly-polarized could be achieved. The laser cavity is directly mounted in a copper tube that is temperature-controlled by a cooling system with an accuracy of ± 0.1 °C. The fiber laser is backward-pumped by a 976 nm fiber-coupled LD through a 980/1610 nm PM wavelength division multiplexer (PM-WDM). The pump port and common port of the PM-WDM are fusion spliced to the LD and the PM-FBG, respectively. The signal port of the PM-WDM is used to collect the laser’s output signal and is fed through a polarization-maintaining isolator (PM-ISO) to reduce back reflections into the laser cavity.

 

Fig. 2 Experiment setup of 1.6 μm linearly-polarized DBR SFFL. (HR-FBG: high-reflection fiber Bragg grating; PM-FBG: polarization-maintaining fiber Bragg grating; EYPF: Er³⁺/Yb³⁺ co-doped phosphate fiber; PM-WDM: polarization-maintaining wavelength division multiplexer; PM-ISO: polarization-maintaining isolator; LD: laser diode).

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3. Results and discussion

In principle, the cavity length is limited by the length of doped fiber and the grating effective length of two FBGs in a linear-cavity fiber laser [35]. For efficient single-longitudinal-mode operation in a DBR fiber laser, a short cavity length is necessary for enlarging the longitudinal mode spacing. On the other hand, the doped fiber should be chosen as long as possible to enhance the pump absorption and thus assure the long-wavelength lasing and optical efficiency. Firstly, the physical grating length of a pair of silica FBGs is shortened to approximately 5 mm in the writing process, while compared with that of the FBGs (a few centimeters) used in the research work of others [13–15,19,36]. So, it means that the length of EYPF could be further increased for a restricted cavity length.

During the development, an investigation to optimize the length of EYPF is then carried out in our experiment. Based on the described simulation model, numerical modeling of the fiber laser is conducted [24,37,38]. In the modeling, the pump power of 300 mW, the reflectivity of the PM-FBG of 90% and the fiber length of 20 mm are assumed. The output powers as a function of the fiber length and the reflectivity of output FBG are calculated, as shown in Fig. 3(a). It is noted that, the output power varies with the reflectivity of PM-FBG according to a parabolic distribution. While the reflectivity is higher than approximately 75%, the effective lasing would occur based on the simulation. As is known to us all, a high reflectivity of the output FBG is sufficient to suppress the ASE in a fiber laser, which results in the corresponding reduction of optical efficiency. Thus, the actual reflectivity of 87.8% is chosen for the PM-FBG in the experiment. It is found that the output power rises linearly versus the length of EYPF in the simulation. The calculated maximal conversion efficiency is about 13.2% with the fiber length of 25 mm and the reflectivity of 90%. There is no power saturation phenomenon being observed, which indicates that the output power will rise further with the fiber length increasing.

 

Fig. 3 (a) Simulation results of output powers as a function of the fiber lengths (blue line) at the reflectivity of 90% and the reflectivity of PM-FBG (red point) at the fiber length of 20 mm. (b) Single longitudinal mode operation of the fiber laser with a 16-mm-long EYPF.

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In order to achieve single-frequency operation, the condition of Δν_q >1/2 × Δν_FWHM should be satisfied in a laser cavity, where Δν_q is the spacing of two adjacent longitudinal modes and Δν_FWHM is the full width at half maximum (FWHM) of the gain curve. As for Δν_FWHM, it is calculated to be 10.5 GHz, which is determined by the reflection bandwidth of output FBG (3-dB-bandwidth: 0.09 nm). In this case, the calculated effective cavity length should be less than 19 mm, including the length of EYPF and the grating effective length of two FBGs. Since both of the physical grating lengths are 5 mm, the calculated effective lengths of the PM-FBG and the HR-FBG are 1.4 mm and 0.6 mm, respectively. Therefore, the calculated optimal length of EYPF is about 17 mm from the datas. Consequently, the fiber length of 20 mm that is longer than the optimal length, which is chosen in the experiment. By using the cut-back method from 20 mm so as to find the longest fiber length can be employed, which allows stable single-longitudinal-mode operating. For each of the cavity samples, the longitudinal mode characteristics are measured by a scanning Fabry–Perot interferometer (FPI). The FPI has a finesse of 200, a resolution of 7.5 MHz and a free spectral range (FSR) of 1.5 GHz. Within a scanning circle, the laser operates in multi-longitudinal-modes with the fiber length of 20 mm. When the EYPF is cut to about 16 mm, stable single-longitudinal-mode output is produced, as shown in Fig. 3(b). It can be seen that there is no any peaks between the main resonances of the interferometer, which clearly indicates that the laser operates on only one longitudinal mode. In this case, the effective cavity length is around 18 mm, giving a longitudinal mode spacing of >5.5 GHz. Therefore, a 16-mm-long heavily EYPF is selected for the DBR fiber laser in the experimental measurement below.

The output power of the fiber laser as a function of the pump power is shown in Fig. 4(a). The lasing threshold is around 50 mW. When the pump power is above the threshold, the output power is approximately linearly increased with the pump power. The maximum output power of 21 mW is obtained at the pump power of about 230 mW. The corresponding optical-to-optical conversion efficiency and slope efficiency is about 9.1% and 11.6%, respectively. The low conversion efficiency results from the low net gain coefficient of the EYPF at 1.6 μm, as well as the high reflectivity of output FBG in this demonstration.

 

Fig. 4 (a) Measured laser output power as a function of the pump power. (b) Output spectrum of the fiber laser.

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With the maximal output power of the fiber laser, the output spectrum is recorded by an optical spectrum analyzer (OSA) with a spectrum resolution of 0.1 nm, as plotted in Fig. 4(b). It clearly shows that the signal-to-noise ratio (SNR) of this single-frequency fiber laser is higher than 62 dB and the laser spectrum centered at around 1603 nm. Moreover, thanks to using the EYPF with a larger emission cross-section (see Table 1), the output spectrum does not suffer from any obvious ASE or parasitic lasing. The negligible ASE at around C-band is occurred, which results in a slight SNR reduction of fiber laser. It is believed that the improvement in SNR can be possible by providing that available ASE filtering components.

To investigate laser linewidth of the fiber laser, the delayed self-heterodyne method is performed with a 10-km-long single-mode fiber delay. The sweep time of the electrical spectrum analyzer is about 0.12 s with a resolution bandwidth of 100 Hz. Figure 5(a) shows the linewidth result of the measurement. The typical heterodyne signal is fitted to a Lorentzian profile to estimate the spectral linewidth. It is found that about 38 kHz with −20 dB from the peak, indicating the fiber laser possesses a linewidth of <1.9 kHz FWHM (full width at half maximum). Furthermore, the polarization state of the DBR SFFL is analyzed using an optical polarization analyzer. The measured polarization-extinction ratio (PER) of >25 dB is obtained from the fiber laser, which confirms that the laser output is linearly-polarized and the polarization state is stable.

 

Fig. 5 (a) Measured self-heterodyne spectrum of the fiber laser. (b) Measured RIN of the fiber laser and the SNL are also shown for comparison in the frequency band of 0–50 MHz. Inset: power stability of the fiber laser over 2.5 hours.

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The relative intensity noise (RIN) of the fiber laser is measured using an electrical spectrum analyzer with a resolution bandwidth of 1 kHz. In the measurement, the laser power is attenuated to ~0.5 mW before injected into photoelectric detector. Figure 5(b) shows the RIN in the frequency range of 0–50 MHz and the calculated shot noise limit (SNL) of –153 dB/Hz @0.5 mW is also shown for comparison. Here, the SNL is calculated by 2hν/P, where h is the Planck constant, ν is the lasing frequency and P is the laser power [16,39]. One can see that the RIN spectra are dominated by peaks at the relaxation oscillation frequency (ROF) in about 0.35 MHz with the RIN level of around –90 dB/Hz and then decreases monotonically toward high frequencies. The ROF is depended on the laser cavity layout and the pump current. While the frequencies from 1 to 50 MHz, the RIN of the fiber laser drops from –120 to –150 dB/Hz, which approaches the calculated SNL. And for frequencies above 5 MHz, the obtained RIN of the SFFL is less than –140 dB/Hz. The stability of the fiber laser is also an important characteristic. For the evaluation, the output power of the SFFL is fixed at ~15 mW. The power stability is measured for every ~0.02 minute over more than 2.5 hours by utilizing an optical power meter, and the testing data is depicted in the inset of Fig. 5(b). It is observed that the SFFL is stable with output power fluctuation relative to the average power of less than 1% during the entire period. This shows that the proposed SFFL is suitable to be utilized over a long period of time.

4. Conclusion

In conclusion, an efficient linearly-polarized single-frequency DBR Er³⁺/Yb³⁺ co-doped phosphate glass fiber laser operating at 1603 nm is developed. By optimizing the cavity parameters and employing the 16-mm-long EYPF with a larger emission cross-section, more than 20 mW of a stable single-frequency laser is obtained. It provides a SNR of greater than 62 dB, a laser linewidth of less than 1.9 kHz and a PER of higher than 25 dB. The measured RIN of fiber laser is less than –140 dB/Hz at frequencies of over 5 MHz. The results show that the L-band low noise narrow linewidth SFFL would be a promising candidate for high-resolution molecular spectroscopy and coherent lidar applications.