1. Introduction

Fiber lasers operating in the mid-infrared (mid-IR) spectral range are of great interest due to their potential applications in biological tissue ablation, defense, spectroscopy and remote sensing [1–3]. Compared with conventional solid-state or gas lasers, fiber lasers are more compact in volume and more flexible and thus easier for delivery to the focusing location and target. In the past decades, silica fiber lasers have obtained great success in the near-IR wavelength range, due to its extreme-low transmission loss in one hand and in the other hand to the great gain efficiency of rare-earth ions such as ytterbium (Yb), erbium (Er) and thulium (Tm) in the silica glass host. The available silica fiber laser wavelengths are limited to the emission bands suitable for lasing of the rare-earth ions. An effective route to break this limit is to resort to nonlinear optical effects such as stimulated Raman scattering (SRS), Kerr-nonlinearity induced four-wave mixing (FWM) or supercontinuum generation. However, due to the sharply increasing transmission loss beyond 2 µm and the limited nonlinear optical gain in conventional silica fibers, it is a huge challenge to realize a fiber laser at > 2 µm without additional efforts. One effort has been applied to silica-based germanium (Ge) doped fibers, in which superior Raman, Kerr-nonlinearity gain and mid-IR transmission help to generate Raman lasers beyond 2.4 µm [4], and to broaden supercontinuums towards 3 µm [5]. Other efforts have been applied to silica-based photonic-crystal or hollow-core fibers, where air- or gas-filled, delicate designed microstructures strongly increase the optical nonlinearity [6,7]. Even though these two methods have shown good performances, the first one have to rely on fiber gratings or mirrors at the desired wavelength to match the Raman gain bandwidth which might not be commercially available, the second one have to rely on a short-pulsed pump laser to enhance the optical nonlinearity.

Instead of resorting to delicate optical fibers with increased optical nonlinearity as mentioned above, another efficient route might resort to extremely-low optical nonlinear conversion threshold in microresonators, such as ultrahigh Q-factor WGM microresonators. Benefiting from high Q-factor resonance and low-mode volume (V)-enhanced optical nonlinear interaction (Q²∕V) in WGM microresonators [8,9], a varity of nonlinear optical phenomena have been observed with low thresholds including SRS [10–20] and FWM [21–32]. The low threshold lasing in WGM microresonator also benefits from the fact that a single WGM is pumped using a tunable single frequency laser. This in turn limits the wavelength range of WGM lasing by the pump wavelength itself. Thus, significant progresses are mostly made in the visible and near-IR wavelength range, where tunable single frequency pump lasers are easily available. Nevertheless, the drawback is still there because relying on a tunable single frequency pump laser is conflicting to low-cost and user-friendly applications in the future. This is very the case in the mid-IR wavelength range [26–33], where the available tunable single frequency lasers are rare and relatively expensive. One smart solution to resolve this problem is injection locking, where the narrow linewidth Rayleigh backscattering signal from a microresonator is injected to a gain fiber or semiconductor chip to realize a single frequency lasing [34–37]. In a recent progress, a distributed feedback (DFB) semiconductor laser at 2.05 µm was reported [36] by using crystalline microresonator as the feedback element.

In this work, we demonstrated for the first time, to the best of our knowledge, Raman lasers and Kerr-frequency combs from near-IR to mid-IR spectral range generated from a compact all-silica narrow-linewidth microresonator/fiber laser at ∼2 µm. The high Q-factor microresonator (here, silica microsphere) is employed not only as a mode reflector for the Tm³⁺-doped fiber lasing, but also as a nonlinear initiator for the production of Raman lasing or FWM. The fiber lasing pumped, microresonator initiated, first-order Raman Stokes laser at ∼2.17 µm and anti-Stokes laser at ∼1.82 µm, second-order Raman Stokes laser at ∼2.43 µm and anti-Stokes laser at ∼1.67 µm, as well as third-order Raman Stokes laser at ∼2.75 µm and anti-Stokes laser at ∼1.56 µm were observed, respectively. Furthermore, a 1.98 µm-centered Kerr-frequency combs with bandwidth ∼900 nm was also achieved. Benefiting from the optical nonlinearity enhancement and anomalous dispersion in the microresonator, the nonlinear conversion threshold for generating stimulated anti-Stokes Raman scattering (SARS) or FWM is reduced to milliwatt range.

2. Theoretical analysis and calculations

The circulating optical intensity in an ultrahigh-Q WGM microresonator is given by $I = {P_{in}}({\lambda }/2\pi n)(Q/{V_{eff}})$[8], where P_in is the coupled input power, λ is the resonant wavelength, n is the effective infractive index, V_eff is the effective mode volume. Considering a silica microsphere resonator (n = 1.45) with a diameter of 150 µm, Q-factor of 10⁸ at λ = 2.0 µm, the effective mode volume is approximately 1.45×10⁻¹⁴ m³. With P_in = 1 mW coupled into the microresonator, one can have a circulating intensity I of ∼6.1 W/λ². It thus gives a great enhancement to generate nonlinear optical effects such as SRS and FWM in the microresonator.

SRS is a fundamental inelastic scattering process which transfers energy from pump photons to Stokes and anti-Stokes photons through optical phonons [38]. As shown in right upper part of Fig. 1(a), pump photons are coupled into a microresonator, where the enhanced circulating optical intensity helps to generate Stokes and anti-Stokes photons through SRS. Intuitively, a Stokes photon (green) is generated from a lower virtual state to the vibrational state, while the anti-Stokes photon (violet) is generated from a higher virtual state to the ground state, where two pump photons (red) are consumed as illustrated in Fig. 1(b). When Stimulated Stokes Raman scattering appears alone, it is a pure gain process, whose phase matching is automatically realized. However, it is not the case anymore when anti-Stokes Raman scattering appears in the meantime. The coupling between anti-Stokes and Stokes waves might have to rely on the FWM process. It thus turns to a phase matching process [17–20]. The field amplitudes obey the set of time-domain coupled equations [38]

 

Fig. 1. Theoretical analysis and calculations of microresonator-based Raman and Kerr-frequency combs generation. (a) The schematic diagram of the microresonator-based Stokes and anti-Stokes Raman, Kerr-frequency combs generation process. (b) The energy diagram for Stokes and anti-Stokes Raman generation processes. (c) Calculated dispersion of a silica microsphere (diameter of ∼146 µm) from 1.0 to 3.0 µm.

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Similar as the generation of Stokes and anti-Stokes waves simultaneously with phase matching condition, FWM is a pure optical parametric oscillation (OPO) process, where two pump photons are annihilated with the generation of a pair of signal and idler photons in the meantime [38]. If the process is highly efficient and there are excess photons, then additional sidebands can be generated through the secondary FWM processes, thus resulting in a Kerr-frequency comb. More details on generating Kerr-frequency combs by exploring FWM could be referred to [39,40]. The schematic diagram of the microresonator-based Kerr-frequency combs generation process is described in right lower part of Fig. 1(a).

From the above analysis, dispersion plays an important role in both the generation of anti-Stokes waves and Kerr-frequency combs. The dispersion of microresonator mainly contains material dispersion and geometric dispersion, we combine them to simulate the ΔFSR (variation of FSR) variation with different wavelength. Here, we define the dispersion D₂/2π= ΔFSR/2π to denote the difference between the adjacent FSR. This is commonly used for analyzing the dispersion in microresonators,

In this equation R is the radius of the spherical microresonator, N is the relative index of refraction N = n_a/n_s (n_a is index of the medium outside the microresonator), $\textrm{t}_{n}^\textrm{0}$ is the n^th zero solution of the Airy function $\textrm{Ai(t}_{n}^\textrm{0}\textrm{)}$ (and corresponds to the n^th-order Radial mode).

For most dielectric optical materials, the wavelength dependence of the refractive index can be approximated by Sellmeier equation

The Sellmeier coefficients A_i and B_i are usually given for wavelength λ in units of µm and the leading terms in silica for the wavelength range 0.21 µm < λ < 3.71 µm are A₁ = 0.6961663, A₂ = 0.4079426, A₃ = 0.8974794, B₁ = 0.0684043, B₂= 0.1162414 and B₃ = 9.896161. Based on the formula (3)∼(6), taking into account of a silica microsphere with diameter of ∼146 µm used in our experiment, the theoretical analysis of the microsphere with its dispersion properties is shown in Fig. 1(c). Figure 1(c) shows D₂/2π varies from 0 to 108 MHz between 1.58 and 3.0 µm, revealing a group velocity dispersion (GVD) that is anomalous over this wavelength range. This offers a possibility that uses the self- (cross-) phase modulation induced by the pump light to compensate the phase mismatch so that both the anti-Stokes Raman or pure FWM process can be efficiently generated.

3. Experimental setup

The experimental setup of the proposed all-silica narrow-linewidth microresonator/fiber laser is schematically shown in Fig. 2(a). The pumping source is a continuous-wave (CW) laser operating at ∼1560 nm wavelength after being amplified by an erbium-doped fiber amplifier (EDFA) to an output power of up to ∼2 W. A high-concentration Tm³⁺-doped fiber (Nufern SM-TSF-5/125, length: 23 cm, core/cladding: 5.5/125 µm, core NA: 0.24) is employed as the 2 µm-wavelength gain medium and its absorption coefficient at 1560 nm is ∼340 dB/m. As depicted by the partial energy-level diagram of Tm³⁺-ions in silica fiber in the inset of Fig. 2(b), it indicates that the generated laser at ∼2 µm is in correspondence to ³F₄→³H₆ transition (solid red arrow). Either ³H₆→³F₄ (∼1.56 µm, solid black arrow) or ³H₆→³H₄ (0.8 µm, solid gray arrow) transitions can be employed as the pumping [41]. Here, we select the former one due to the availability of this laser. To form the Fabry-Pérot fiber cavity, a fiber Bragg grating (FBG) is used as the input mirror, and a fiber-taper-coupled WGM microresonator is used as the output mirror. The fiber Bragg grating (FBG) has a center reflection wavelength of 1980.6 nm and with a 3-dB bandwidth of ∼1.7 nm. The transmission spectrum of it is shown in Fig. 2(c), where the highest reflectivity is ∼99% (−20 dB). The microresonator in our experiment is a silica microsphere with diameter of ∼146 µm. It is fabricated by melting a standard silica fiber (Corning SMF-28) tip using a CO₂ laser, whose microscopic image is depicted in Fig. 2(d). To couple light into and out of the microsphere, a fiber taper with a thinnest diameter of 1–2 µm is used to couple with the microsphere. To control light polarization in the fiber cavity, a fiber polarization controller (FPC-100, OZ optics) is inserted. In the end, the length of the fiber cavity is 3.3 m between the FBG and the microsphere.

 

Fig. 2. (a) The experimental schematic for the all-silica narrow-linewidth microresonator/fiber laser system at ∼2 µm. (b) The partial energy-level diagram of Tm³⁺-ions in silica fiber. The red arrow is the laser emission wavelength, the gray and black solid arrow are the potential pump wavelengths, and the gray dashed arrow illustrates the fast non-radiative relaxation between ³H₄ and ³F₄ level. (c) The transmission spectrum of the FBG. (d) The microscopic image of the silica microsphere in experiment.

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The reflection from the microsphere is due to the modal coupling between clockwise and anticlockwise WGMs induced by intracavity Rayleigh scattering [42–44], which is a unique feature of ultrahigh-Q WGM microresonators. Due to the lack of a tunable single frequency laser at ∼2 µm in our laboratory, the Q-factor of the microsphere around 2 µm can’t be estimated directly. We evaluate the quality of the fabricated microresonator indirectly by resorting to an 1550 nm tunable single frequency laser. It gave a Q-factor of ∼2×10⁸ around 1550 nm for the microsphere used in this experiment. And the reflectivities from certain WGMs could be more than 30%. This is a crucial precondition for application as a mode reflection mirror. The reflection is not only sensitive to the coupling condition between the microresonator and the fiber taper, but also to the polarization states. Since the Tm³⁺-doped silica fiber can provide enough gain to compensate the total laser cavity loss, the narrow-linewidth laser at ∼2 µm is first expected in the laser system.

4. Experimental results and discussion

4.1. Narrow-linewidth ∼2 µm laser

The results of the all-silica narrow-linewidth microresonator/fiber laser at ∼2 µm are shown in Fig. 3. As shown in Fig. 3(a), the output optical spectrum with a center wavelength of ∼1979.93 nm is measured with an optical spectrum analyzer (OSA, Model: Bristol 721, Resolution bandwidth: 12 GHz) and the pump power at 1560 nm is ∼0.95 W. The signal to noise ratio of the spectrum is slightly higher than 10 dB, which is mainly limited by the OSA noise floor and the optical power collected by the OSA. The linewidth of this laser is measured by employing the self-heterodyne method at zero frequency with 1.2 km-delayed fiber (Corning SMF-28) [45–47]. The experimental measurement (blue solid line), fitting curve (red solid line), and the equipment background noise (black dashed line) are shown in Fig. 3(b), respectively. A simplified Lorentzian model was used to fit the line-shape of the experimental data, which gives a 3-dB linewidth of ∼9 MHz. This linewidth can be reduced in the future by utilizing a microresonator with higher quality factor, a FBG with narrower bandwidth, and by improving the stability of the microresonator/fiber-taper coupling system. Moreover, the output power of the lasing versus pump power is shown in Fig. 3(c). It can be deduced that the threshold of the narrow-linewidth laser is ∼0.87 W by linearly fitting the experimental data, the total output power is more than 15 mW and the slope efficiency is ∼4.2%. This low slope efficiency might result from the low optical reflectivity of the microresonator mirror.

 

Fig. 3. The experimental results of the all-silica narrow-linewidth microresonator/fiber laser at ∼2 µm. (a) A typical optical output spectrum of the narrow-linewidth laser with a center wavelength of ∼1979.93 nm. (b) The linewidth measurement of the narrow-linewidth laser with a RBW of 100 kHz by employing a self-heterodyne method. The blue solid line is the experimental data, the red solid line is the fitting line and the black dashed line is the background noise floor of the instrument. (c) Output power of the narrow-linewidth laser versus pump power.

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4.2. Raman Stokes and anti-Stokes lasers

By optimizing the fiber polarization as well as the microresonator/fiber taper coupling condition, the Raman Stokes and anti-Stokes lasers are both achieved in the mean time once the newly generated ∼1980nm laser is beyond the Raman lasing threshold. The coupling between the microresonator and the fiber taper is optimized by finely tuning the gap between the microresonator and fiber taper using a nano-translation stage. An optimum coupling condition helps a lot in reaching a broadband nonlinear optical spectrum. Moreover, in order to reduce the optical loss of silica-fiber at > 2 µm waveband, we tried to shorten the length of fiber taper at the laser output port after the microsphere. As shown in Fig. 4(a)-Fig. 4(c), the spectra of first- to third-order Raman Stokes and anti-Stokes lasers are measured with the pump power of 1.41, 1.78, 1.98 W, respectively. The Raman frequency shifts (RFSs) between adjacent order Stokes lines can be calculated by the formula Δν=c/λ_n-c/λ_n+1. As depicted in Fig. 4(a)-Fig. 4(c), the cascaded RFSs are about 13, 14, 14 THz, respectively. The RFSs are different because silica has a large Raman gain bandwidth ranging from 0∼40 THz [38], and the Raman gain peak in silica is mainly located from 12 to 15 THz. The measured RFSs here are in good agreement with this expected Raman gain values for silica, confirming that the observed behavior is due to Raman scattering. The threshold pump power is evaluated when each order Raman laser is firstly observed on the OSA. Using this method, the thresholds for the three-order Raman laser are estimated to be 1.31, 1.76, 1.92 W, respectively.

 

Fig. 4. The optical spectra of the Raman Stokes and anti-Stokes lasers under different pump powers. (a) The optical spectra of one-order Raman Stokes and anti-Stokes lasers under pump power of 1.41 W. (b) The optical spectra of two-order Raman Stokes and anti-Stokes lasers under pump power of 1.78 W. (c) The optical spectra of three-order Raman Stokes and anti-Stokes lasers under pump power of 1.98 W.

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As shown in Fig. 4(a), the first-order Raman Stokes laser at ∼2.17 µm and anti-Stokes laser at ∼1.82 µm are observed when the pump power is 1.41 W. And the total output power is measured to be ∼10.3 mW. When the pump power is increased to be ∼1.78 W, Fig. 4(b) depicted that the second-order Raman Stokes laser at ∼2.43 µm and anti-Stokes laser at ∼1.67 µm can be excited, with a total output power of ∼17.2 mW. Interestingly, when the pump power is increased to be 1.98 W, the third-order Raman Stokes laser at ∼2.75 µm and anti-Stokes laser at ∼1.56 µm can be achieved, and the spectrum is illustrated in Fig. 4(c). The generation of ∼2.75 µm Raman Stokes laser seems counterintuitive due to high optical loss in silica material at mid-IR waveband. However, we clearly observed the third-order Raman Stokes laser at ∼2.75 µm reproducibly. In order to explain this, we analyze it from a simple Raman laser threshold model [10–13]. Here, we only consider the simplest case that the third order Raman Stokes laser is pumped from the second-order Raman Stokes laser, and do not consider the coupling between other Stokes lines or coupling between Stokes and anti-Stokes lines. The threshold pump power for the next-order Raman Stokes laser can be derived as [10–13]

In our experiment, the first-order Raman Stokes and anti-Stokes lasers are observed with a pump power ranging from ∼1.31 to ∼1.74 W. Within this pump power range, the first-order Raman anti-Stokes laser power versus pump power is shown in Fig. 5(a), and it follows a second order dependence as expected [18]. Moreover, the linear power correlation between the first-order Raman anti-Stokes laser and the Stokes laser is also shown in Fig. 5(b).

 

Fig. 5. (a) Dependence of the first-order Raman anti-Stokes emission power on the input power. (b) Dependence of the first-order Raman anti-Stokes emission power on the first-order Raman Stokes emission power.

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4.3. Kerr-frequency combs

In this part, we demonstrate generation of Kerr-frequency combs in the microresonator/fiber laser system. As we have shown in the theoritical background, the microresonator used in our experiment has anomalous dispersion at wavelengths in the mid-IR range. The first pair of Kerr sidebands would be generated where the Kerr parametric gain is balanced with the optical loss and the phase mismatch is compensated by self- and cross-phase modulation induced nonlinear frequency pulling. The cascaded sidebands would be subsequently generated with similar processes which not only receive energy from the “pump” (here is the 1.98 µm laser), but also from former generated sidebands. The final comb is realized until the necessary pump power and phase matching are not enough any more.

Figure 6 shows the evolution of a comb from only one pair of sidebands (Fig. 6(a)) to a comb with bandwidth of ∼900 nm (Fig. 6(f)), where the corresponding pump powers are 1.52, 1.57, 1.63, 1.75, 1.82 W and 1.87 W at 1560 nm, respectively. At the beginning of the comb generation, as shown in Fig. 6(a), there are only two Kerr sidebands which are located on the both sides of the center wavelength at ∼1980.88 nm. As the pump power is increased to 1.57 W, the Kerr-nonlinearity is enhanced, and two pair of sidebands are generated in total as depicted in Fig. 6(b). Similarly, we see at least three pairs of Kerr sidebands in Fig. 6(c), and at least seven pairs of Kerr sidebands in Fig. 6(d). By further increasing the pump power, typical Kerr-comb spectra are broadened from near-IR (1600 nm) to mid-IR (> 2400 nm), as shown in Fig. 6(e) and 6(f), respectively.

 

Fig. 6. The evolution of Kerr-frequency combs under different pump power. (a)–(f) Optical spectra of the microresonator-based Kerr-frequency combs under pump power of 1.52 W, 1.57 W, 1.63 W, 1.75 W, 1.82 W and 1.87 W, respectively. And the mode spacing between adjacent main comb teeth is 2 FSRs.

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It is worth noting that the mode spacing between adjacent main comb teeth is 2 FSRs in all spectra in Fig. 6. In general, the mode spacing could be changed by changing the pump detuning, polarization and pump power when using a tunable single frequency pump source [39,40]. In our case, the “pump” power at 1.98 µm is changed with the 1560 nm pump power sent to the fiber cavity. The detuning between the “pump” and the resonance is resulted from a thermal stability in the microresonator. In this situation, the thermal-effect and Kerr-nonlinearity induced resonance frequency shift is going towards a steady state when the “pump” induced heating is well dissipated to the microresonator and further to the environment [52]. The mode spacing is not changed in our cases means that these steady states might result in similar detunings in our microresonator. A fast scanning of the pump power (1560 nm) or the polarization in the fiber cavity might break one steady state to reach another so that the mode spacing can be changed in the future. It is interesting to mention that the comb in Fig. 6(e) most likely resides in the initial state of chaotic comb [53,54]. Because soliton combs are shown to have more and more applications in the past years, starting from a comb state like the one shown in Fig. 6(e), it is possible to realize a soliton comb by further optimize our system in the future, as the one shown in a similar work in [55]. By further increasing the pump power, the comb bandwidth does not increase significantly after 1.87 W as shown in Fig. 6(f). This means it has reached a limit where the Kerr-nonlinear gain can not further compensate the optical losses beyond this bandwidth in the microresonator. Besides, some relatively weak peaks appear around the main comb teeth in Fig. 6(e) and 6(f), which are probably generated from higher-order WGMs or different polarization modes of the microresonator. It is also worth noting that Raman Stokes and anti-Stokes lines are not observed during the generation of Kerr-frequency combs. This is probably because the pump induced gain is not enough to drive these two nonlinear processes simultaneously.

5. Conclusion

In conclusion, we have proposed and experimentally demonstrated an all-silica narrow-linewidth microresonator/fiber laser at 2 µm directly pumped by a laser at ∼1.56 µm. The maximum output power of narrow-linewidth laser is more than 15 mW with a slope efficiency of 4.2% and a linewidth of ∼9 MHz. The ultrahigh Q-factor silica-microsphere is not only employed as a reflection mirror for the thulium-doped fiber lasing but also as an initiator of nonlinear optical effects that introduces SRS, SARS and FWM subsequently. By controlling the coupling condition between the fiber taper and microresonator, optimizing the fiber polarization states, as well as the pump power, first-order Raman Stokes laser at ∼2.17 µm and anti-Stokes laser at ∼1.82 µm, second-order Raman Stokes laser at ∼2.43 µm and anti-Stokes laser at ∼1.67 µm, as well as third-order Raman Stokes at ∼2.75 µm and anti-Stokes laser at ∼1.56 µm could be achieved. Moreover, Kerr-frequency combs with bandwidth of ∼900 nm and center wavelength of 1.98 µm are also realized in the experiment. This self-injection locking method gets rid of expensive tunable pump sources in the mid-IR wavelength. By further exploring this laser system as done in a most recent work [55], even a turnkey soliton comb is possible in the future. To this end, several measures could be taken in the future, i.e. using a low-noise pump source at 1560 nm (including feedback loops for current/power locking), preparing isolated environment for microresonator/fiber-taper coupling, and using high dynamic signal-to-noise-ratio optical spectrum analyzer for spectrum analysis, etc.

This ultra-high Q factor microresonator initiated nonlinear frequency conversion from near-IR to mid-IR greatly extends the lasing wavelength in this all-silica hybrid laser system. Specially, it demonstrates a method to solve a problem long reside in conventional all-silica fiber lasers that is super hard to generate laser wavelengths beyond 2 µm except to resort to other highly nonlinear materials or novel fiber structures [4–7]. The generation of Raman laser at 2.75 µm seems counter-intuitive in this all-silica structure, but it in turn shows the powerfulness of the ultrahigh Q-factor silica microresonator, in which the threshold power for nonlinear conversion is greatly reduced even in the mid-IR wavelength range. More interestingly, this wavelength is in the emission range of an Er³⁺-doped ZBLAN fiber [2], and thus can be power amplified for future applications.