Single-frequency narrow-linewidth fiber laser based on whispering gallery resonators and dynamic population gratings

Ziyun Wang; Fangxing Zhang; Ziyu Lei; Jiwen Cui; Jiubin Tan

doi:10.3788/COL202523.040606

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Abstract

Whispering gallery mode resonators (WGMRs) are used as excellent optical feedback components of narrow-linewidth fiber lasers, applied from distributed fiber sensing to optical fiber communication. However, WGMRs lead to output of a few microwatts and serious multi-modes in lasers. In this Letter, we fabricated the specially designed WGMR with an over-coupling structure, and its quality (Q) factor was over 10⁹. It improved laser output power significantly. Based on that, dynamic population gratings were applied successfully in the laser. Finally, a single-frequency WGMR fiber laser was realized. Its linewidth was less than 1.07 kHz, its output power was over 0.107 mW, and its spectral signal-to-noise ratio (SNR) was nearly 50 dB. Our research offers a new scheme of a single-frequency narrow-linewidth WGMR fiber laser.

Keywords

dynamic population grating single-frequency narrow-linewidth fiber laser whispering gallery resonator

1. Introduction

Single-frequency narrow-linewidth fiber lasers have drawn considerable attention due to their outstanding properties of low noises^[1]. They are applied extensively from distributed fiber sensing^[2] to optical fiber communication. There have been different design schemes to guarantee laser single longitudinal mode operation or narrow linewidth such as short-cavities^[3], compound-ring cavities^[4], and ring cavities with all kinds of optical filters^[5]. In addition, some laser linewidth compression methods have been proposed, such as Rayleigh–Brillouin scattering^[6,7] in fiber and self-injection locking^[8].

Whispering gallery mode resonators (WGMRs) offer the advantages of miniature size and high quality (Q) factor, and they are considered excellent optical feedback components used in fiber lasers^[9–13]. The typical linewidth of a WGMR fiber laser is a few kilohertz, even sub-kilohertz^[14]. In general, WGMRs are used as frequency stabilization references^[11], narrow-linewidth optical filters^[14], self-injection locking references^[15,16], or laser main cavities^[17]. Essentially, WGMRs are resonators with high Q factor^[18]. Thus, their resonance bandwidths are narrower compared to other ones. For example, WGMRs with a Q factor of 10⁸ are popular^[19], with a resonance bandwidth of a few MHz (C-band), which are nearly two orders of magnitude narrower than common resonators such as fiber Fabry–Perot etalons. However, WGMR fiber lasers are poor in single-frequency, tunability, and power output. In this Letter, we mainly discuss their single-frequency and power.

The resonance spectrum of a WGMR is regular in theory. In reality, a lot of supported modes are generated with strongly overlapping free spectrum ranges (FSRs) and large mode densities, as shown Fig. 1(a), due to their asphericity or ellipticity^[20]. As a result, multi-modes and mode-hopping lasing are generated frequently. It has been reported that single-frequency WGMR fiber lasers were realized through controlling laser pump power, WGMR coupling distance, and environment temperature strictly. It is difficult and unstable^{[14,17,21–24]}.

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Figure 1.Characteristic of the specially designed WGMR. (a) The transmission spectrum of the WGMR. (b) The backward Rayleigh scattering spectrum of the WGMR. (c) The schematic layout of the WGMR with the over-coupling structure (OCS). a_cw and a_ccw are the amplitudes of the CW and CCW modes of the resonator, respectively. Bⁱⁿ and B^out are the incident and transmitted lights in the resonator. (d) High resolution photograph of the WGMR.

In this Letter, to the best of our knowledge, we first realize dynamic population gratings in a WGMR fiber laser with single-frequency. Its linewidth was less than 1.07 kHz, and its output power was more than 0.107 mW.

2. Principle and Method

Dynamic population gratings (DPGs) induced in an unpumped active fiber by counter-propagating optical fields have an effective effect on suppressing multi-modes or mode-hopping, and they are usually applied in lasers. However, it is difficult to combine DPG and WGMR in the laser loop because enough power is required for effective DPG generation. In reality, WGMR fiber laser power is usually a few microwatts due to weak backward Rayleigh scattering^[14,25], and adding optical amplifiers will induce new phase noises. That is why no research has been reported on it up to now.

The coupling relation of a WGMR is described by ${\begin{cases} \frac{d a_{cw}}{d t} = i Δ ω a_{cw} - \frac{1}{2 τ} a_{cw} + \frac{i}{2 γ} a_{cww} + κ s \\ \frac{d a_{cww}}{d t} = i Δ ω a_{cww} - \frac{1}{2 τ} a_{cww} + \frac{i}{2 γ} a_{cw} \end{cases},$ (1)where $a$ is the amplitude of the counterclockwise (CCW) and clockwise (CW) modes of the resonator, and $s$ denotes the input field ( ${| s |}^{2}$ is the input pump power). The excitation frequency is detuned by $Δ ω$ with respect to the resonance frequency $ω_{0}$ of the initially degenerating modes, and $τ$ is the total lifetime of photons in the resonator, which is related to the Q factor by $Q = ω τ$ . The coupling coefficient $κ$ denotes the coupling of the input wave to the CW mode of the resonator. The relation $κ = \sqrt{1 / τ_{ex}}$ associates the coupling coefficient with a corresponding lifetime, such that $1 / τ = 1 / τ_{ex} + 1 / τ_{0}$ (the intrinsic lifetime, $τ_{0}$ ). The mutual coupling of the CCW and the CW modes is described by a (scattering) lifetime, $γ$ .

In our work, first, the specially designed WGMR with the OCS was fabricated. It was composed of a microrod with the diameter of 5 mm, and a coupling tapered fiber was attached to a microrod. In order to improve the Q factor of the WGMR, high-purity fused silica was chosen as the raw material to decrease absorption loss. Additionally, the smoothness and shape of the WGMR surface were precisely controlled. As a result, the reflectivity of the WGMR was improved due to enhanced backward Rayleigh scattering, compared to a critical-coupling structure (CCS), and the Q factor of the WGMR was still more than $10^{9}$ because it benefited from our machining technology. The Rayleigh scattering spectrum of the WGMR is shown in Fig. 1(b), and the reflectivity is 2.98%–18.11%. The schematic layout and high-resolution photograph of the WGMR are shown in Figs. 1(c) and 1(d), respectively.

The principle of DPG is equivalent to ultranarrow-bandwidth fiber Bragg gratings. Its bandwidth $Δ v$ is described in Eq. (2), $Δ v = \frac{c}{2 π n_{eff} L_{g}} \sqrt{{(κ L_{g})}^{2} + π^{2}},$ (2) $κ = \frac{π δ n_{\max}}{λ},$ (3)where $L_{g}$ and $n_{eff}$ are the length of the induced grating and effective index of the active fibers, respectively; $κ$ is the coupling coefficient; and $δ n_{\max}$ is the maximum refractive index change of the active fibers. In WGMR lasers, most of the incident light is absorbed by active fibers before generating effective DPG, thus leading to none of the mode oscillations in WGMR lasers.

3. Experiments and Results

In order to verify the effects of DPG and OCS-WGMR on the laser, characterization experiments of the following four fiber lasers in the C-band were conducted. Their main cavities were similar and consisted of 976 nm pumps, 980/1550 wavelength division multiplexers, erbium-doped fibers (EDFs), optical isolators, and optical circulators. WGMR and DPG were used as the wavelength-selective elements, connected with the main cavity by optical circulators.

Compared with laser $①$ , laser $②$ was composed of polarization maintaining (PM) fibers. Compared with laser $②$ , the WGR in laser $③$ was over-coupled. Compared with laser $③$ , the DPG filter was added to laser $④$ . The basic fiber laser loop is shown in Fig. 2(a), corresponding to laser $①$ , laser $②$ , and laser $③$ . The length of the fiber laser loop was nearly 10 m. In particular, in order to avoid extra optical loss, instead of using the usual fiber couplers, a WGMR transmission port was used as the output. Figure 2(b) corresponds to laser $④$ , compared to laser $③$ , the unpumped EDF was connected with a WGMR transmission port using a Sagnac-ring (SR). After analysis and testing, the coupling ratio of the SR was set to 10:90, and the 10% port was the output. The absorption coefficient and length of unpumped EDF are 10 dB/km@1550 nm and 1 m, respectively. The range of temperature fluctuation was approximately 0.1°C during testing. The differences between the lasers are shown in Table 1.

Figure 2.Schematic layout of the self-built WGMR fiber lasers. (a) The structure of the laser is filtered only by the WGMR. (b) The DPG is connected with the laser in (a). In all fiber lasers, the length and absorption coefficient of EDF are 0.8 m and 24 dB/km @1550 nm. ISO, optical isolator; CIR, optical circulator; OC, optical coupler; PC, polarization controller.

Number	PM or non-PM	WGMR	DPG
1	non-PM	CCS-WGMR	non
2	PM	CCS-WGMR	non
3	PM	OCS-WGMR	non
4	PM	OCS-WGMR	with DPG

Table 1. Specifications for Four Self-Built WGMR Fiber Lasers

View all Tables

The experiments mainly included laser spectrum, power, and linewidth measurement.

1)Laser spectrum. The spectrum was measured with an Anritsu MS9740A optical spectrum analyzer (OSA), with a wavelength accuracy of $\pm 20 pm$ , a dynamic range of 42 dB (0.2 nm from peak wavelength), and a resolution of 0.03 nm (Fig. 3). In laser $①$ , serious multi-mode lasing and amplified spontaneous emission (ASE) were generated, and they were suppressed significantly in laser $②$ . That was because the PM elements controlled the laser polarization, and resonant modes in the WGMR decreased effectively. The lasing power became stronger. However, there were still multi-modes in laser $②$ , shown in Fig. 3(c). The OCS-WGMR was used as the wavelength-selective element in laser $③$ , in contrast with the CCS-WGMR of laser $②$ , and multi-modes still appeared. It was obvious that the spectral signal-to-noise ratio (SNR) improved gradually from laser $①$ to laser $④$ , and it is advantageous for single-frequency operation.In laser $④$ , only one longitudinal mode was observed by the OSA, as the pump power was less than 100 mW (Fig. 4). Because the resolution of the OSA is only 3.75 GHz, larger than the FSR of the laser loop, a fine observation of longitudinal modes was completed using the beating method, and it showed that a single-frequency WGMR fiber laser was realized. In addition, its spectral SNR was nearly 50 dB. To test the single-frequency stability of laser $④$ , its lasing spectrum was measured every 5 min in an hour (Fig. 5). On the whole, laser $④$ was stable in the operation of single-frequency. However, because of environment and temperature, multi-modes still appeared at the end of testing.
2)Laser power. In order to compare the power characteristics among four lasers, the testing curves of the power output versus the pump power were obtained by a power meter, as shown in Fig. 6. The power curve of laser $①$ is shown in Fig. 6(a). It was abnormal and demonstrated that real lasing was not generated completely, and super-fluorescence dominated, as shown in Fig. 3(a). The power curves of laser $②$ , laser $③$ , and laser $④$ are shown in Fig. 6(b). Because the power of laser $②$ and laser $③$ fluctuated sharply during testing, the accurate values could not be recorded. The maximum and minimum power were recorded (dots and circles in Fig. 6), and their averages were considered as the final results (dotted lines in Fig. 6). Compared with laser $①$ , laser $②$ , and laser $③$ , the power of laser $④$ was stable, which demonstrated that the single-mode of laser $④$ was more stable indirectly. Additionally, it showed that laser $③$ power significantly increased compared to laser $②$ , due to the OCS of the WGMR. The slope efficiencies of laser $②$ , laser $③$ , and laser $④$ were 0.86%, 1.35%, and 0.57%, respectively.From the characterization of power and spectrum, it was concluded that, in terms of power, the OCS of the WGMR created conditions for the DPG. Therefore, the scheme of the OCS-WGMR and the DPG is advantageous to single-frequency fiber lasers, and so are PM elements.
3)Laser linewidth. Finally, delayed self-heterodyne interferometry (DSHI) was used to measure the linewidth of laser $④$ , shown in Fig. 7(a). One path of the DSHI had a 50-km optical fiber, corresponding to nearly a 250-µs delay for the signal light. The other path of the interferometer had an acousto-optic modulator (AOM), which was used to generate a frequency shift of 80 MHz. The beat signal was sent to an electrical spectrum analyzer through a photodetector. Lorentz fitting of the beating signal was obtained with a 10-dB linewidth of 6.4 kHz, as shown in Fig. 7(b). The actual linewidth (full-width at half-maximum) was deduced to be $1 / (2 \sqrt{9})$ of the 10-dB linewidth, corresponding to about 1.07 kHz. Actually, the linewidth was less than 1.07 kHz because the 50 km delayed fiber was not long enough for the precise measurement.

Figure 3.Optical spectrum of the self-built lasers. (a), (b), and (d) show the spectra of laser $①$ , laser $②$ , and laser $③$ , respectively, and (c) is an enlarged partial view of (b).

Figure 4.Spectrum of the self-built laser $④$ . (a) The optical spectrum and (b) the radio frequency beating spectra.

Figure 5.Lasing spectrum of single-frequency laser $④$ in 60 min. The power of the pump was 90 mW.

Figure 6.Power output versus power of pump. Solid dots, the measured maximum; circles, the measured minimum; dotted curves, average of the maximum and minimum. (a) The power of the laser $①$ fluctuated abnormally. (b) Pink, blue, and green marks indicated laser $②$ , laser $③$ , and laser $④$ , respectively.

Figure 7.Schematic layout of the DSHI and the spectrum of the beating linewidth. (a) The DSHI used for the measurement of the laser linewidth. OC, optical coupling; AOM, acoustic optical modulator; AWG, arbitrary waveform generator for radio frequency; PD, photodiode; ESA, electronic spectrum analyzer. (b) The spectrum of the beating linewidth. Gray dashed curve, the spectrum measured. Blue solid curve, the spectrum from Lorentz fitting.

4. Conclusion and Prospects

In summary, we proposed a new scheme of a single-frequency narrow-linewidth fiber laser based on the OCS-WGMR and DPG. First, the output of the WGMR fiber laser was improved using the OCS, benefiting from machine technology. DPG technology was successfully applied to the WGMR fiber laser based on a higher laser power. A single-frequency WGMR fiber laser was realized with a 3-dB linewidth of less than 1.07 kHz, and the SNR was nearly 50 dB. Its output power was 0.107 mW under the 100 mW pump power. To the best of our knowledge, this is the first report on a WGMR fiber laser with DPG technology. Additionally, some mode-hopping still appeared because of the environment and temperature. In the future, by optimizing the coupling ratio of the SR and the length of the unpumped EDF, we will further improve the output power and frequency stability of fiber lasers based on the WGMR and DPG. This scheme is helpful for realizing single-frequency narrow-linewidth WGMR fiber lasers.

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