Tunable Single-Longitudinal-Mode Thulium–Holmium Co-Doped Fiber Laser with an Ultra-Narrow Linewidth by Utilizing a Triple-Ring Passive Sub-Ring Resonator

Abstract

A low-cost, wavelength-tunable single-longitudinal-mode (SLM) thulium–holmium co-doped fiber laser (THDFL) in a 2 μm band with a simple structure is described in the present paper. To obtain a stable SLM and narrow laser linewidth, a five-coupler-based three-ring (FCTR) filter is utilized in the ring cavity of the fiber laser. Tunable SLM wavelength output from THDFLs with kHz linewidths can be achieved by designing the FCTR filter with an effective free-spectral range and a 3 dB bandwidth at the main resonant peak. The measurement results show that the laser is in the SLM lasing state, with a highly stabilized optical spectrum, a linewidth of approximately 9.45 kHz, an optical signal-to-noise ratio as high as 73.6 dB, and a relative intensity noise of less than −142.66 dB/Hz. Furthermore, the wavelength can be tuned in the range of 2.6 nm. The proposed fiber laser has a wide range of applications, including coherence optical communication, optical fiber sensing, and dense wavelength-division-multiplexing.

1. Introduction

Single-longitudinal-mode (SLM) fiber lasers operating in the 2 μm band have attracted the interest of researchers owing to their unique absorption properties in water molecules and greenhouse gasses, as well as their potential applications in areas such as free-space optical communications, LIDAR atmospheric measurements, high-resolution spectroscopy, and biomedical applications [1,2,3,4,5]. The 2 μm band lasers are in the safe band for the human eye and are the preferred light source for applications related to free-space light transmission. Furthermore, 2 μm band SLM lasers operate at 1.7–2.1 μm, covering the absorption bands of atmospheric gasses, such as H₂O and CO₂, and can also be used as pumping sources for optical parametric oscillators to realize laser output at 3–5 μm [6,7]. In addition, 2 μm band SLM fiber lasers have a higher threshold for nonlinear effects than conventional 1 μm band SLM lasers, providing a major advantage in terms of narrow linewidth, high power, and high-energy laser outputs [8,9]. The fiber laser structure that can realize SLM operation mainly consists of two types: short resonant cavity type and long resonant cavity type. The short cavity type mainly includes distributed feedback and distributed Bragg reflector fiber lasers [10,11,12,13,14,15,16]. These lasers have a simple structure and a stable SLM operation but low laser efficiency due to the short gain in fiber length. Moreover, the above two methods require the gain fiber to have a high gain absorption coefficient, which leads to a higher technical process and greater difficulty in connecting with the fiber Bragg grating (FBG) or etching the FBG onto the gain fiber. High absorption coefficients imply high doping concentrations, and highly rare earth ions can trigger fluorescence bursts [17,18,19]. In addition, due to the short cavity length, the linewidth of the output laser is wide and has poor noise characteristics. Long cavity fiber lasers have the characteristics of a flexible structure, long photon lifetime, high Q-factor, and narrow linewidth, and the laser output power can be increased by simply extending the gain fiber length. However, a longer resonant cavity will lead to dense longitudinal modes inside the cavity. Therefore, filtering and realizing SLM laser output has become a research focus for this type of structured fiber laser. This can be achieved by adding an ultra-narrow band filter based on FBG, a saturated absorber, and a micro-ring resonant cavity inside the cavity. Still, these methods are characterized by high cost, high loss, and poor interference immunity [20,21,22,23,24,25]. Researchers have generally recognized the compound sub-ring cavity as an option that is low cost, stable, and has a flexible structure to realize the single longitudinal mode of fiber laser. In recent years, our group has carried out in-depth research on compound resonant cavity SLM narrow linewidth fiber lasers and pointed out the quantitative combination of theoretical and experimental resonant cavity filter research methods, which are of great significance for the development of single longitudinal mode lasers in the 2 μm wavelength band [26,27]. However, the 2 μm band fiber laser has a unique device performance, loss characteristics, and pumping mode characteristics. As such, the 2 μm band compound resonant cavity SLM fiber laser deserves in-depth investigation.

In this paper, a compound resonant cavity filter is proposed based on the matrix solution method of optical path transmission analysis, which simplifies the process of analyzing the structure of the filter in terms of nodes and transmission optical paths. The filter spectrum of the compound resonant cavity filter is obtained through simulation; the filter characteristics of the filter are described in detail, and the parameter selection process of the filter spectrum is given. The designed filter and the FBG are combined to realize SLM laser output in the ring cavity. The wavelength and power stability characteristics of the output laser are recorded. The optical signal-to-noise ratio (OSNR), relative intensity noise (RIN), frequency noise power spectral density (PSD), and the linewidth of the output laser were measured. Wavelength tuning in the 2.6 nm range was obtained by applying stress to the FBG.

2. Experimental Setup and Principles

2.1. Experimental Configuration

The configuration of the proposed THDFL is shown in Figure 1a. It includes a 1570 nm laser diode (LD, RZPL-1570-5-D-SM-1-1-N, Rayzer, Wuhan, China), two wavelength division multiplexers (WDMs, 1570/2000 nm), a 1.55 m long thulium–holmium co-doped fiber (THDF, TH512, CorActive, Quebec, Canada), a circulator (CIR), an FBG, and a five-coupler-based three-ring (FCTR) filter. The pump source enters the gain fiber through WDM1 to form an amplified spontaneous emission (ASE) spectrum. The absorption coefficient near 1550 nm is 15.4 dB/m, and the numerical aperture is 0.16. The function of the WDM2 is to separate the residual pump light out of the cavity. Port 1 of the CIR is connected to the pigtail of the WDM 2, and port 2 is connected to the FBG. It ensures the unidirectional operation of the laser inside the cavity and prevents spatial hole burning caused by the standing wave effect. The light output through port 3 of the CIR enters the FCTR filter for mode selection. An FCTR filter, made of five 2 × 2 OCs (OC1-5), with coupling ratios of 50:50, is shown in Figure 1b. Here, E1–E20 are the electric-field amplitudes of each light port during operation. The transmission spectrum and the reflection spectrum of the FBG are detected using an ASE, as shown in Figure 1c. The 3 dB bandwidth of the measured FBG was 0.176 nm. The total cavity length of the main resonant cavity was approximately 10.8 m, corresponding to a 19.2 MHz longitudinal mode spacing. The 10% SLM lasing, separated out of the cavity through a 90:10 OC, was measured using an optical spectrum analyzer (OSA, AQ6375E, YOKOGAWA, Tokyo, Japan).

2.2. SLM Operating Principle

Figure 1b shows the running schematic of the proposed FCTR filter, which was assembled using five OCs (OC1, OC2, OC3, OC4, and OC5) with three sub-rings (Ring-1, Ring-2, and Ring-3). The signal-flow graph method, initially proposed by Mason [28], was utilized to analyze the operation of the lasing in the compound ring cavity. Here, $L_1-L_7$ are the fiber lengths; ${\kappa }_i$ is the cross-coupling ratio; ${\gamma }_i$s are the insertion loss of the OCs; $\alpha$ is the fiber loss coefficient; $\delta$ is the fusion splicing loss, and $\beta =2\pi n/\lambda$ is the light propagation constant, where $n$ represents the effective refractive index, and $\lambda$ represents the wavelength. Figure 2 shows the signal-flow graph of the sub-ring cavity, composed of ten nodes and the transmission of the lasing.

As shown in Figure 2, the straight transmittance $C_i$ of the ${\mathrm{OC}}_i$ is defined as

$$C_i=\sqrt{1-{\kappa }_i}\sqrt{1-{\gamma }_i} (i=1,2,3,4,5)$$

(1)

The cross-coupling transmittance $Y_i$ of ${\mathrm{OC}}_i$ is defined as

$$Y_i=i\sqrt{{\kappa }_i}\sqrt{1-{\gamma }_i} (i=1,2,3,4,5)$$

(2)

The propagation gain $D_i$ of the fiber optical path Li is defined as

$$D_i=\sqrt{1-\delta }{e}^{(-\alpha +j\beta )L_i} (i=1,2,3,4,5)$$

(3)

According to Equations (1) to (3), the corresponding process of the optical path transmission is shown as follows:

$$\begin{array}{ll}{E}_1=1& \\ E_3=C_1{E}_1+Y_1{E}_2& E_4=Y_1{E}_1+C_1{E}_2\\ E_5=D_1{E}_4& \\ E_7=C_2{E}_5+Y_2{E}_6& E_8=Y_2{E}_5+C_2{E}_6\\ E_2=D_2{E}_7& E_9=D_6{E}_8\\ E_{11}=C_3{E}_9+Y_3{E}_{10}& E_{12}=Y_3{E}_9+C_3{E}_{10}\\ E_{10}=D_3{E}_{12}& E_{13}=D_7{E}_{11}\\ E_{15}=C_4{E}_{13}+Y_4{E}_{13 }& E_{16}=Y_4{E}_{13}+C_4{E}_{14}\\ E_{17}=D_5{E}_{16}& \\ E_{19}=C_5{E}_{17}+Y_5{E}_{18}& E_{20}=Y_5{E}_{17}+C_4{E}_{18}\\ E_{14}=D_4{E}_{19}& \end{array}$$

(4)

Considering the actual transmittance where the optical path entered port 1 of the OC1 for the first time, the light intensities of ports 2, 6, 10, 14, and 18 were all defined as 0 (E₂ = 0, E₆ = 0, E₁₀ = 0, E₁₄ = 0, and E₁₈ = 0). The above equations can be decomposed into a coefficient matrix $M$, a matrix of unknowns $E$ at each node, and a matrix of constants $B$, as shown in Equation (5).

$$M=\left[\begin{array}{cccccccccccccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& -1& 0& 0& 0& 0& D_2& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ C_1& Y_1& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ Y_1& C_1& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& D_1& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& C_2& Y_2& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& C_2& C_2& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& D_6& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& D_3& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& C_3& Y_3& -1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& Y_3& C_3& 0& -1& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& D_7& 0& -1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& 0& 0& 0& 0& D_4& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& C_4& Y_4& -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& Y_4& C_4& 0& -1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& D_5& -1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& -1& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& C_5& Y_5& -1& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& Y_5& C_5& 0& -1\end{array}\right]E=\left[\begin{array}{c}{E}_1\\ E_2\\ E_3\\ E_4\\ E_5\\ E_6\\ E_7\\ E_8\\ E_9\\ E_{10}\\ E_{11}\\ E_{12}\\ E_{13}\\ E_{14}\\ E_{15}\\ E_{16}\\ E_{17}\\ E_{18}\\ E_{19}\\ E_{20}\end{array}\right],B=\left[\begin{array}{c}1\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\\ 0\end{array}\right],ME=B$$

(5)

The numerical solution $E=M^{-1}B$ can be obtained according to the built-in algorithm of the program. The transmission T of the FCTR filter can be expressed as

$$T=\left({\displaystyle \frac{E_{20}}{E_1}}\right)\cdot {\left({\displaystyle \frac{E_{20}}{E_1}}\right)}^{*}$$

(6)

The transmission spectrum of the FCTR filter can be simulated based on the above theory. The 3 dB bandwidth of FBG was 0.176 nm, corresponding to a frequency range of 12.6 GHz. An FCTR filter was used as the mode-selection mechanism to realize the SLM operation of the laser. To do so, two aspects needed to be satisfied. First, the effective free-spectral range (FSR) of the FCTR should be no less than half of the full width at half the height of the main resonant peak of the FBG. This ensures that only one effective passband of the FCTR is dropped in the reflection channel of the FBG. Second, the mode spacing of the main ring cavity should be 0.5–1 times that of the 3 dB bandwidth of the FCTR filter. According to the Vernier effect [29,30], the FSR of the FCTR filter can be given as $FSR=c/(n\cdot \Delta l)$, where $c$ is the speed of light in a vacuum (3 × 10⁸ m/s), and n = 1.44. Based on the above analysis, the simulated results are shown in Figure 3. Figure 3 shows the transmission spectrum of the FSR filter when L₁ = 0.6, L₂ = 0.6, L₃ = 3, L₄ = 0.42, L₅ = 0.8, L₆ = 1.2, and L₇ = 1.2. The effective FSR was 10.4 GHz. Therefore, inset 1, which is a zoom-in of the FCTR filter, clearly demonstrates that the 3 dB bandwidth of the main resonant peak was 24.9 MHz.

3. Experimental Results

As shown in Figure 4, the optical spectrum of the THDFL with 1.12 W pumping power is measured in a room temperature environment, measured using the optical spectrum analyzer (OSA) (Yokogawa AQ6370D with a resolution of 0.05 nm). The direct output power of the laser is −1.59 dBm. The center wavelength of the EDFL is 2048.39 nm, and the OSNR is approximately 73.6 dB, indicating the excellent mode suppression capability of the proposed THDFL. Additionally, the spectra are measured via repeated OSA scans at 5 min intervals for 60 min, as shown in the inset of Figure 4a. To further quantify f_P and f_λ, Figure 4b shows variations in the wavelength and optical power with observation time. The maximum wavelength and optical power fluctuations were less than 0.02 nm and 0.73 dB, respectively.

The SLM lasing stability of the proposed THDFL with the FCTR filter was investigated on a 12.5 GHz photodetector (PD, ET-5000F) and a 26.5 GHz signal analyzer (Keysight, N9020A, Santa Rosa, CA, USA), as shown in Figure 5a. The scanning range of the radio frequency (RF) spectrum was set to 0–100 MHz with a resolution bandwidth (RBW) of 1 MHz, and the inset shows continuous monitoring for 60 min. The RF spectrum over the scanning range of 0–500 MHz is shown in Figure 5b. There was no beat frequency signal with a non-zero frequency, proving that the laser worked at SLM output. In addition, the RF spectral range of 0–1000 MHz is given in Figure 5c, and the non-zero component was not observed. Unless a severe disturbance was imposed, the THDFL functioned in stable SLM states without mode-hopping. To further investigate the mode-selection ability of the FCTR filter, the effect of the longitudinal mode in the main cavity without FCTR was obtained, as shown in Figure 5d. The spacing of the main cavity’s longitudinal mode was 19.2 MHz.

The RIN spectrum of the laser in 2049.66 nm is measured using a 12.5 GHz PD and a signal analyzer. An oscilloscope (Tektronix, DPO7104, Billmstar, Oregon, USA) was also used to measure the direct voltage of the PD output. The laser output power was attenuated to 0.8 mW to prevent saturation of the PD. The laser outputs with an FCTR filter in the laser cavity were measured, as shown in Figure 6, over a frequency range of 0–5 MHz. It should be noted that a relaxation oscillation frequency peak of −99.7 dB/Hz can be observed in the inset at around 28.4 kHz, and several noise peaks resulting from external disturbances, the measurement system, or the pump were also captured.

Linewidth is an important parameter for measuring the performance of lasers, and it is especially important to measure the linewidth of lasers with high accuracy. In the measurement of linewidth in the 2 μm band, since the transmission loss of a single-mode fiber in this band is about 20 dB/km, the delay fiber required for the traditional, delayed self-heterodyne linewidth measurement method introduces great loss and noise problems, which affects the measurement accuracy. The demodulation method based on a 3 × 3 coupler is a passive demodulation method with a stable output signal. There is no need to introduce carrier modulation into the optical path, and the optical path is simple [31]. Thus, the frequency noise of the output laser is measured using a laboratory-made unbalanced Michelson interferometer based on a 3 × 3 coupler [32]. Based on the β-separation method [33], the laser linewidths at different measurement times were calculated. The results are shown in Figure 7.

The laser linewidth at different integration times (0.001 s, 0.005 s, 0.01 s, 0.05 s, 0.1 s, 0.5 s, and 1 s) were 9.45, 21.75, 59.01, 164.06, 206.54, 407.23, and 706.89 kHz, respectively. As the measurement time increases, the laser linewidth value, caused by the technical noise generated by environmental vibration or low-frequency signal interference, gradually increases. In addition, the accumulation of thermal effects of pumping for a long-term operation leads to a high fiber temperature, increasing the low-frequency thermal noise of the laser [34,35].

The output center wavelength of an FBG can be tuned by applying different techniques to the FBG. Common techniques include applying axial stress to the FBG, applying a slight bend to the FBG, adjusting the temperature of the FBG, and using the Vernier effect. Compared to other methods, applying axial stresses to the grating is simple and allows for the precise control of the tuning range. The left knob of the micro-displacement stage is fixed, and the right knob is adjusted to move the stage to the right to apply stress to the grating in the horizontal direction.

Figure 8 shows the laser output spectrum in the 2048.39–2051.03 nm band, with a continuous tuning range of 2.6 nm. The OSNR of the laser in the wavelength tuning range is >60.26 dB. However, due to the fragility of the grating’s bare fibers and their reusability, the grating was not further stressed.

4. Conclusions

A compound resonant cavity SLM THDFL based on the FCTR mode-selection filters is proposed and experimentally demonstrated. The FCTR filter enlarges the longitudinal mode spacing, which can realize the SLM output of the laser. The main resonant peak of the FCTR filter has an ultra-narrow band-filtering characteristic, which further ensures the long-term stability of the laser SLM operation. The center wavelength of the laser is 2048.39 nm with an OSNR of 73.6 dB when the pump power is 1.12 W. The wavelength and power fluctuations of the laser are less than 0.02 nm and 0.73 dB, respectively, during a 60 min measurement period. The RIN is less than −142.66 dB/Hz at frequencies higher than 0.5 MHz, and the linewidth is 9.45 kHz at an integration time of 0.001 s. The proposed 2 μm band SLM fiber laser does not use expensive ultra-narrow band filter pieces, is simple and inexpensive to fabricate, and has a good prospect for practical application, with potential applications in the fields of free-space optical communication, LIDAR, and optical sensing.