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Abstract
A novel single-longitudinal-mode (SLM) fiber laser with a single cylindrical microresonator (CMR) as the filter is proposed. The CMR has a nanoscale variation in radius, in which high-Q localized modes interfere with continuum radiative modes, generating a peak-like transmission spectrum based on the Fano resonance effect. The peak linewidth is sufficiently small to select only one SLM oscillation in a fiber cavity. In an Er-doped fiber laser coupled with the CMR, we achieve a stable SLM laser operation by optimizing the coupling location of the tapered fiber. Stable lasing at 1568 nm with a 3-dB linewidth of ∼15 kHz is obtained. The laser slope efficiency reduction introduced by the CMR for SLM lasing is limited to 1.4%. This scheme can be a competitive approach for the development of compact, highly efficient, and cost-effective SLM fiber lasers.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Single-longitudinal-mode (SLM) fiber lasers are widely used in high-resolution spectroscopy, gas sensors, Doppler light detection and ranging, and medical treatment owing to their outstanding performances including ultrasmall linewidths, large coherence lengths and low noises [1]. In general, owing to their relatively large cavity lengths, the fiber lasers operate at multimode states with closely spaced longitudinal modes on the order of megahertz. Therefore, an ideal approach for the development of SLM fiber lasers is to use a filter whose bandwidth is narrow than the longitudinal mode spacing.
Whispering-gallery-mode (WGM) optical microresonators have attracted large interest as they can confine light inside extremely small cavities with low losses (i. e. small mode volumes and high-Q factors) [2]. Owing to this unique characteristic, the WGM optical microresonators have attracted considerable attention in science and engineering [3–5]. The high-Q modes have very small spectral linewidths and thus can be used as narrow bandwidth filters. In particular, light can be efficiently coupled into a WGM microresonator using an adiabatically tapered fiber by the overlap of their evanescent fields [6]. Using the fiber-to-microresonator coupling scheme it is simple to integrate the microresonators with other fiber-based devices for the development of an all-fiber system. Owing to the ultrasmall linewidths of the optical modes, various types of WGM microresonators, such as microsphere [7,8], microdisk [9,10] and hollow microbubble [11] have been applied to SLM fiber lasers. In such microresonator-based SLM fiber lasers, one of the filter functions can be realized by the backscattering of the light by some imperfections on the microresonator surfaces [7,12]. In this case, the microresonators can be regarded as reflecting mirrors. However, the reflectivity is low and the reflected modes are uncontrollable. Another filter mechanism is the add-drop configuration in which two tapered fibers act as in- and out-ports of the microresonator [8,9,13]. This also leads to complexity and additional insertion loss to the fiber laser cavity.
Fano resonance, originating from the interference between discrete and continuum states, has been observed in various photonic dielectric structures [14]. Commonly, the Fano resonance attributes to the interference between two coupled WGMs whose Q-factors significantly differ [15]. Although a single tapered fiber is coupled to a single microresonator, the Fano resonance can lead to a peak-like transmission spectrum [16,17]. Owing to the high-Q factor of the microresonator, the peaks have ultrasmall linewidths, which provides a promising filter for the realization of SLM fiber lasers. To achieve the Fano resonance in a single microresonator, a dense mode spectrum is always required for an effective overlap of the resonance frequencies between different modes. A spherical microresonator with a certain eccentricity has a rich and dense mode spectrum owing to the splitting of its degenerated axial modes. However, it is inefficiet for application to the SLM fiber laser because the dense mode spectrum leads to too many peaks in the transmission spectrum [18], generating lasing at multiple wavelengths. A cylindrical microresonator (CMR) with a nanoscale variation in radius can generate high-Q resonance modes, with a considerably cleaner mode spectrum than that of the spherical microresonator [19,20]. Moreover, both discrete states of high-Q localized modes and continuum state of radiative modes can be excited in such CMRs if the coupling tapered fiber is thin enough [21]. These two types of modes can interfere with each other and lead to the Fano resonance in a single CMR [22]. Owing to the ultrasmall linewidths of the Fano resonance peaks and cleaner transmission spectrum, the CMR could be an ideal filter for the realization of the SLM lasing. Moreover, the number of modes can be further reduced by controlling the position of the tapered fiber relative to the CMR. In this study, we demonstrate a SLM fiber laser based on the Fano resonance in a CMR. The fabricated CMR exhibits a clean Fano resonance spectrum with ultrasmall linewidths. An SLM laser experiment indicates that the CMR provides an effective and controllable filter function. The experimental results demonstrate that our method is compact and cost-effective for the development of SLM fiber lasers.
2. WGMs in the CMR
Although the CMR has a nanoscale variation in radius, it can provide ultra-high-Q WGMs near the maximum radius, shown in Fig. 1(a). The resonance wavelength of the WGM inside the CMR can be expressed as [23]:
Fig. 1. (a) Excitation of only WGMs in the CMR. The transmission spectrum demonstrates a symmetric Lorentzian lineshape. (b) Excitation of both WGMs and radiation modes in the CMR. The transmission spectrum demonstrates an asymmetric Fano lineshape. (c)-(g) Field distributions of WGMs in the CMR with the quantum numbers [m, q, p] of [354, 1, 1], [343, 2, 5], [335, 3, 25], [354, 1, 15] and [335, 3, 1], respectively. (h) Resonance wavelength as a function of the axial quantum number.
Based on the finite-element method, we calculate the field distributions of the WGMs whose resonance wavelengths are in the range of 1550 to 1555 nm. In this calculation, the maximum radius and profile curvature of the CMR are set to 62.52 µm and 1.33×10−4 µm-1, respectively. We focus only on the quasi-transverse-magnetic polarization modes, whose electric fields are approximately normal to the CMR surface. Figs. 1(c)–1(g) show the field intensity distributions of the WGMs with different quantum numbers. The optical field has a very narrow distribution near the cylinder surface and expands along the z-axis with the increase in axial quantum number. Figure 1(h) shows the resonance wavelengths of three families of WGMs whose azimuthal and radial quantum numbers (m, q) are (354, 1), (343, 2), and (335, 3), respectively, with the increase in axial quantum numbers in the range of 1 to 24. Considering the resonance condition 2πRe=mλm, where Re is the effective radius of the optical path, a smaller Re is obtained for a mode with a larger q. Therefore, to maintain the small variation in resonance wavelength, m for the mode with a larger q should be decreased. On the other hand, owing to the parabolic profile of the CMR, Re is slightly decreased if the field distribution of the WGM is considerably expanded along the z-axis. The resonance wavelength decreases with p as the mode with a larger p has a considerably longer field distribution.
We fabricate the CMR by heating one end of a standard single mode fiber using a CO2 laser. The fiber rotates during the whole heating process to produce an axisymmetric structure. We can modify the profile of the resonator by controlling the laser power and exposure time. This fabrication process not only provides the cylindrical fiber with a parabolic profile but also removes the imperfections on the fiber surface, yielding an ultra-high-Q resonator. In our experiment, the diameter of the fiber used to fabricate the microresonator is 125 µm, which is increased by only tens of nanometers after the exposure by the CO2 laser. As the tapered fiber is moved along the z-axis starting from z = 0, we measure the mode spectra of the cylindrical resonator. Typical mode spectra, recorded successively, are shown in Figs. 2(a)–2(d). The azimuthal and axial mode spaces (Δλm and Δλq) are measured to be approximately 4.3 and 0.03 nm, respectively. Three obvious envelopes of transmission dips are observed within one azimuthal mode space Δλm. The modes in the same envelope have the same azimuthal and radial quantum numbers but different axial quantum numbers. With the change in location of the tapered fiber away from z = 0, the envelope changes into a triangular shape indicating that the modes with longer resonance wavelengths disappear. According to the numerical simulation results in Fig. 1(g), the disappeared modes are lower-axial-number modes whose fields are concentrated around z = 0. This decreases their overlap with the mode field of the tapered fiber gradually moving away, reducing the number of the excited modes in the microresonator, which provides an effective way to clean the mode spectrum. This is more preferable for application as a filter for SLM fiber lasers. However, if the tapered fiber is further moved, only the modes having much larger q values remain. The Q factors of these modes are lower owing to the weak confinement of their long field distributions as well as limited length of the smooth surface of the CMR during the fabrication process. On the other hand, to provide a sufficient coupling strength for these modes, the tapered fiber has to be closer to the resonator, yielding an increased insertion loss, which is reflected in the reduced continuous background of the transmission spectrum in Fig. 2(d).
Fig. 2. Evolution of the transmission spectrum of the CMR. The mode spectrum becomes less dense as the tapered fiber is moved away from the origin along the z-axis. However, the Q-factors of WGMs are reduced if the tapered fiber is far away from the origin (d), owing to that it needs a smaller coupling gap, which yields an increased loss for the WGMs.
3. Fano resonance in the CMR
As shown in Fig. 1(a), the CMR can provide not only high-Q localized WGMs but also radiative modes if the tapered fiber is sufficiently thin and closer to the resonator. As discussed above, these two types of modes interfere with each other yielding rise to the Fano resonance where the localized and the radiative modes stand for the discrete and continuous states in the classical Fano theory, respectively. Figs. 3(a)–3(j) show the evolution of the transmission spectrum of one of the WGMs at ∼1555 nm in Fig. 2(c). It changes from a symmetrical Lorentz lineshape into an asymmetrical Fano-resonance lineshape as the tapered fiber is moved close to the CMR. At the first stage, only a WGM is excited, which exhibits under-coupling to critical coupling with the gradual decrease in e coupling gap. In this case, the continuous background in the transmission spectrum is slightly reduced. This indicates that the radiative modes are excited inefficiently owing to the large gap between the tapered fiber and CMR. The linewidth of the transmission dip is approximately 2.5 MHz corresponding to a Q factor of 7.75×107 at the central wavelength of 1555 nm. If the tapered fiber is further moved closer to the resonator, the continuous background is considerably reduced and the Lorentz lineshape changes into the asymmetric lineshape of the Fano resonance, as shown in Figs. 3(f)–3(j). The reduced continuous background implies that a considerable part of the incident power is coupled to the radiative modes and that some of them couple back to the tapered fiber where they interfere with the localized WGMs. This yields a peak in the transmission spectrum of the CMR. Figure 3(j) shows the very large linewidth of the Fano resonance peak when the tapered fiber is in contact with the resonator. In this case, the Q factor of the localized WGM is reduced owing to the additional scattering loss by the tapered fiber.
Fig. 3. Zoom-in-image of one of WGMs at 1555.5 nm in Fig. 2(c). The mode evolve from the symmetric Lorentz lineshape (a)–(e) to the asymmetrical Fano-resonance lineshape (f)–(j) with the decrease in coupling gap. (k)-(o) Simulation results corresponding to the experimental results in (f)-(j), respectively.
Using the theoretical model of Fano resonance in a single microresonator [16], we numerically simulate the transmission spectrum of the CMR. The results are shown in Figs. 3(k)–3(o), corresponding to the experimental results in Figs. 3(f)–3(j), respectively. The controllable fitting parameters [16] are denoted as κa, γa, κb and γb, which are the coupling strengths (κ) and intrinsic decay rates (γ) of the radiative mode (subscript a) and localized WGM (subscript b), respectively. In this simulation, we assume that the Q-factor of the radiative mode is much larger than that of the WGM owing to its spectral characteristic of continuum state. The fitting parameters [κa, γa, κb, γb] are [13.5, 11, 0.005, 0.0025], [20.5 16, 0.005, 0.0025], [28.5, 26, 0.005, 0.0025] and [130, 120, 0.1, 0.1] for Figs. 3(k)–3(o), respectively. The units of all parameters is in GHz. The coupling strength of the radiation mode increases as well as its intrinsic decay rate when the tapered fiber is moved close to the resonator. However, the parameters for the localized modes do not change except when the tapered fiber is in contact with the resonator owing to the non-negligible scattering loss introduced by the tapered fiber.
4. SLM fiber laser
The experimental setup for the analysis of the SLM lasing is based on an Er-doped fiber ring cavity coupled with the CMR, as shown in Fig. 4. To eliminate the perturbations caused by the acoustic waves, the CMR and tapered fiber with the nanopositioning stages are steadily installed on the vibration isolation platform and covered by a small chamber. We use a laser diode (LD, 976 nm) to pump a 1.2-m-long Er-doped fiber. The absorption coefficient of the gain fiber is ∼12 dB/m for the pump light. Therefore, almost all pump light is absorbed before it enters the CMR. A fiber-based isolator and polarization controller (PC) are inserted into the ring cavity to control the laser propagation direction and polarization state, respectively. A 50/50 coupler is used to extract the laser power from the fiber ring cavity. We also use another coupler to couple the light from a tunable laser into the cylindrical resonator for the measurement of its transmission spectrum. As shown in Fig. 4, the blue line indicates the optical path for the measurement of the transmission spectrum of the CMR, which is blocked by a shutter before we start to turn on the fiber laser. The optical path is replaced by the red line when the fiber laser is operated. In this experimental configuration, as the location of the tapered fiber is unchanged upon switching between the two optical paths, a reliable reference is provided for the different transmission spectra of the CMR with the change in tapered fiber location for the analysis of its effect on the fiber laser performance.
Fig. 4. Experimental setup for the analysis of filter function of the CMR for the SLM Er-doped fiber laser. ISO: isolator, EDF: Er-doped fiber, WDM: wavelength division multiplexer. FPI: Fabry-Pérot interferometer, OSA: optical spectrum analyzer, ESA: electrical spectrum analyzer. The red and blue lines indicate the optical path used to tune on the fiber laser and test path for the transmission spectrum of the CMR when tuning off the fiber laser, respectively.
Considering the experimental setup for the analysis of the Fano resonance, we gradually move the tapered fiber close to the resonator. We measure the transmission spectrum of the CMR at different locations of the tapered fiber before we turn on the fiber laser. As the gap between the tapered fiber and resonator is relatively large, only the localized WGMs are excited, in the form of dips in the transmission spectrum. In this case, the CMR does not provide filter function and the fiber laser is operated at multimode states. The laser signals in the Fabry–Pérot (F–P) interferometer are extremely unstable (see Visualization 1). As shown in Fig. 5(c), the electrical spectrum analyzer (ESA) also shows multiple peaks at 13.9 MHz or at its integer multiples, attributed to the beatings between different longitudinal modes of the fiber laser with a total cavity length of ∼14.9 m. Considering that these “dip” WGMs cannot realize the filter function and the relatively high level of the continuum background along with the large gain of the Er-doped fiber, the fiber laser suffers from strong mode competition, which leads to the multimode oscillation.
Fig. 5. (a) Fano resonance transmission spectrum when the tapered fiber is at the initial position and (b) cleaner spectrum after the optimization of the fiber location. (c), (d) are the signals in the ESA when the fiber laser is operated at the MLM and SLM, respectively. (e) Signals of the F–P interferometer for stable SLM lasing, Visualization 1, Visualization 2 and Visualization 3 show the dynamic signals in the F–P interferometer at free running, mode hopping and stable SLM lasing regimes, respectively. (f) Spectrum of the stable SLM lasing in the OSA. (g) Output power as a function of the pump power in three different cases: free running, SLM operation, and tapered fiber in touch with the microresonator.
As the tapered fiber approaches the resonator, many peaks instead of dips appear in the transmission spectrum of the CMR, as shown in Fig. 5(a). At this moment, the signals in the F–P interferometer become more stable, indicating the filter function of the cylindrical resonator and thus the laser turns to the SLM operation. However, the signals in the F–P interferometer switch between two peaks within one scan period (the mode hopping, see Visualization 2). The corresponding transmission spectrum of the CMR is shown in Fig. 5(a). Many peaks coexist in the transmission spectrum. We can easily identify two peaks with similar amplitudes, and thus the two laser modes have similar gains and compete with each other. As described above, to reduce the number of transmission peaks, we move the tapered fiber away from the z = 0 to eliminate the WGMs with small axial quantum numbers. Simultaneously, we control the gap between the tapered fiber and microresonator to obtain Fano resonance peaks. Figure 5(b) shows the considerably cleaner transmission spectrum after the optimization of the location of the tapered fiber. Using this transmission spectrum of the CMR, a stable SLM operating is achieved, as no signal appears in the ESA as shown in Fig. 5(d). Simultaneously, in the F–P interferometer, two stable peaks appear within one scan period, as shown in Fig. 5(e) and Visualization 3. As expected, the fewer peaks in the transmission spectrum of the CMR will facilitate the SLM operation in the fiber laser. In addition to the filter function of the cylindrical resonator, the limited gain band of the Er-doped fiber provides a second step of wavelength selecting. The maximum gain in our Er-doped fiber laser is approximately 1557 nm. Owing to the combined effects of the Er-doped fiber and the CMR, the central wavelength of the SLM laser is 1556.98 nm by an optical spectrum analyzer (OSA). The side-mode suppression ratio is over 55 dB, as shown in Fig. 5(f). Another advantage of our SLM laser is its long-term stability. The field distribution of the optical modes inside the CMR can considerably expand along the z-axis. The larger mode volume than that of the spherical microresonator reduces the laser fluctuation caused by the heat summation. We do not observe change in laser wavelength in the OSA during the increase in the pump power. Finally, when we place the tapered fiber in contact with the microresonator, the mode hopping reappears, as the scattering of the taper fiber increaes the linewidth of the localized WGM, as shown in Fig. 3(j). It is sufficient for allow two adjacent laser longitudinal modes to pass the filter.
Figure 5(g) shows the measured output power as a function of the pump power at three lasing cases, free running without the coupling of the microresonator, SLM operation and tapered fiber in contact with the microresonator, with slope efficiencies of 14.55%, 13.14% and 9.35%, respectively. The decreased slop efficiency is attributed to the insertion loss originating from the coupling with the microresonator. However, a loss in slope efficiency induced to the fiber laser of only 10% is acceptable loss for SLM operation. The measurement of the laser linewidth is resolution limited by 0.02 nm and 7.5 MHz owing to our OSA (Yokogawa, AQ6370D) and F-P interferometer (Thorlabs, SA200-12B), respectively. We use the heterodyne method by measuring the beating signals between our SLM laser and commercial LD having an ultra-narrow linewidth (Toptica, CTL1550, ∼5 kHz). The linewidth is approximately 15 kHz according to the heterodyne signal after a Lorentzian fitting indicated by the red line in Fig. 6.
Fig. 6. Heterodyne signal of the SLM fiber laser. The red line is the Lorentzian fitting of the measured data.
5. Conclusion
We investigated the filter function of the Fano resonance in the single CMR. The peaks with ultrasmall linewidths and controllable number of modes in the transmission spectrum of the microresonator were demonstrated by changing the coupling location of the tapered fiber. In the Er-doped fiber cavity, we achieved a stable SLM lasing at 1568 nm with the 3 dB laser linewidth of ∼15 kHz after the optimization of the location of the tapered fiber. Moreover, owing to the much large mode fiber of the CMR, our SLM laser exhibited a long-term stability for the laser wavelength. The reduction in laser slope efficiency caused by the microresonator for SLM lasing was only 1.4%. Owing to the side-coupled fiber-microresonator coupling system, the Fano-resonance-based filter enables a compact configuration and high efficiency for SLM fiber lasers.
Funding
National Natural Science Foundation of China (NSFC) (61805112, U1730119); Natural Science Foundation of Jiangsu Province (BK20181003); Postgraduates Innovation Program of Jiangsu Province (KYCX17_1654).
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