Optical nonlinear frequency conversion in parametric processes includes harmonic generations, parameter oscillation and four-wave mixing has been widely applied to generate coherent light sources at new wavelengths, or with broadband spectrum, and to amplify weak signals^1-9. However, due to the centrosymmetry of fused silica fiber, only quite weak surface second-harmonic (SH) can be detected from the pristine optical fibers^{10, 11}. In optical fibers without integrated nonlinear materials, it is usual to facilitate intrinsic harmonics generation under the pump of pulse lasers with watt-level peak power in structures including fiber loops¹², photonic crystal fibers^13-15, and periodically poled fibers^16-18. However, as an inherent resonance nature introduced by whispering-gallery mode, narrow operation bandwidths of fiber loop devices will significantly weaken the extensibility of wavelength modulation, and thus greatly limit broadband applications. It is the same case in periodically poled fibers, where the unchanged poled period leads to the operation of only a narrow bandwidth determined by the quasi-phase matching¹⁹. Therefore, it is still a challenge to efficiently produce SH signal in a broad wavelength range under a continuous wave (CW) pump, which hinders the development of nonlinear parametric processes in various fields such as new wavelength light sources^{20, 21}, high-resolution microscope imaging²², and signal processing²³.

In this work, we report the achievement of narrowband/broadband CW-pumped SH in a microfiber assisted by the layered gallium selenide (GaSe) crystal. For an amorphous microfiber¹¹, by tailoring the waveguide chromatic dispersion in the fabrication process, material dispersion is compensated with mode dispersion^{24, 25}, which makes the phase-matching approximately satisfied for SH. Due to ultrahigh second-order nonlinearity and long-range order structure of the crystalline GaSe, and a large nonlinear interaction length, a bright green SH at 532 nm can be observed with naked eyes. In the popular C-band near 1550 nm, pumped by a picosecond laser, the normalized SH conversion-efficiency per unit length is enhanced by at least 2 orders of magnitude compared with previous schemes implemented with different optical fibers^{3, 14, 24, 26-32}. More importantly, the high conversion-efficiency guarantees the CW laser source pumped SH at 775 nm, and this frequency conversion process can be extended to more than one signal wavelengths by mixing multiple frequencies of CW pumps. Moreover, broadband SH spectrum is also achieved under the pump of a CW superluminescent light-emitting diode (SLED) source with a 79.3 nm bandwidth. Therefore, the proposed scheme, opens up a new avenue to efficient and broadband CW-pumped harmonic generation, and can optimize nonlinear processes in optical fibers for extending applications spanning from new wavelength light sources to signal processing.

Figure 1(a) schematically depicts the layered-GaSe coated microfiber for SH excitation and crystal structure of ε-GaSe used in experiments. The microfiber was fabricated, by the flame drawing technique, with a diameter of approximately 3.3 µm in the tapered region, which is close to the optimal diameter for the phase-matched HE₁₁(ω) and HE₃₁(2ω), EH₁₁(2ω) modes^{24, 27}. The difference between effective refractive indices of HE₃₁(2ω) and EH₁₁(2ω) is on the magnitude of 10⁻⁴, and the two modes degenerate into the same scalar mode. Their modal distributions are shown in insets of Fig. 1(a). The employed ε-GaSe, with D_3h point group with a bilayer stacking order, has a relatively high second-order nonlinear susceptibility^33-36. With the aid of chemical-free transfer method described in supplemental information and many times’ attempts, a relatively complete layered GaSe crystal was transferred on the tapered region of the microfiber. Due to possibly introduced slight mechanical damage to the microfiber, it is necessary to deal with the GaSe-transferred microfiber carefully in following experiments. The optical microscope image of the device is displayed in Fig. 1(b), exhibiting the quite smooth GaSe coating with the length of ~40 μm. As shown in Fig. 1(c), when a source emitting red light at 650 nm was launched into the microfiber, we could see the scattering red light from the GaSe layer under the dark field. The transmission loss of the GaSe-transferred microfiber is measured as approximately 60% at pump wavelength of 1550 nm, and the loss caused independently by the GaSe coating itself can be estimated as 54% due to the >90% transmission of the pristine microfiber.

As an important physical quantity to show the surface morphology, the thickness of the GaSe coating is carefully investigated by an atomic force microscope (AFM). In-situ characterization at the boundary of GaSe coating on the microfiber is illustrated in Fig. 1(d) and 1(e). Attributed to the stripping of layered GaSe in the transition process companied by external mechanical stress, more than a single thickness (~72 nm and ~50 nm) was identified, revealing that the GaSe coating consists of two parts. As shown in Fig. 1(f), the Raman spectrum acquired from a GaSe sample adhering on a silicon substrate shows three main peaks at 134.2, 214.0 and 308.6 cm⁻¹. These peaks correspond to the$A_{1\text{g}}^1$,$E_{2\text{g}}^1$ and$A_{1\text{g}}^2$ vibrational modes of crystalline GaSe, verifying its bulk nature determined in Fig. 1(d) and 1(e). However, the information already acquired is still insufficient to uniquely determine coverage ratios of two parts on the microfiber surface, and therefore we further investigated the polarization dependent SH experimentally and theoretically. In the experiment, pumped by a 1550 nm linearly polarized laser (pulse width: 7.6 ps, repetition rate: 18.5 MHz) with adjustable polarization direction, the polarization dependent SH was measured. As depicted in Fig. 1(g), at an interval of 180°, two main maximums appear at 155° and 335°. Additionally, two slightly lower sub-maximums were also observed at 75° and 255°, and this implies that the GaSe coating is a combination of two parts with different thicknesses, which agrees well with the characterization results in Fig. 1(d) and 1(e). The polarization dependent SH in Fig. 1(g) fundamentally originated from the quartic relationship between SH intensity and projection of pump electric field on the surface of the GaSe coating (Please see the Supplemental information for details), and formally reflects the relative distribution pattern and coverage ratios of two parts of the GaSe coating. To quantitatively retrieve coverage ratios of two parts, respective polarization dependences were theoretically calculated, as marked by red and blue dashed curves in Fig. 1(g). The red curve represents the theoretical polarization dependence when Part 1 exists alone, and the blue curve indicates the similar meaning. According to the calculation results, Part 1 and Part 2 (Refer to the inset at top right corner of Fig. 1(g)) account for 22% and 34% of the surface of the microfiber, respectively, indicating an equivalent overall coverage ratio of 56%. Considering that only the cross section of the microfiber is examined, the calculated equivalent coverage ratio is approximately 56% based on the assumption of longitudinal uniformity of the GaSe coating. Moreover, the non-circular symmetry of the GaSe coating may slightly distort transversal electric field distribution of pump and SH modes, which would be alleviated if the microfiber is wrapped by a GaSe coating with a higher coverage ratio.

When a pump laser is applied to excite SH, considering accumulated SH from different axial positions of the microfiber, the power of output signal (P_2ω) is determined by^{27, 29, 30, 37, 38}

$P_{2\omega }=P_{\omega }^2{\left|\kappa \right|}^2{L}^2{\text{sinc}}^{\text{2}}\left(\frac{\Delta {\beta }_{\text{SH}}L}{\text{2}}\right)\mathrm{,}$（1）

$\kappa =\frac{{\omega }_0{ϵ}_0}{4N_{\omega }\sqrt{N_{2\omega }}}{\displaystyle \int }{\displaystyle \sum _{jkl}}{\chi }_{jkl}^{(2)}{\text{e}}_{2\omega }^{*j}{\text{e}}_{\omega }^k{\text{e}}_{\omega }^l\text{d}A\mathrm{,}$（2）

$N_i=\frac{1}{2}\left|{\displaystyle \int }{e}_i\times h_i^{*}\cdot \widehat{z}\text{d}A\right|\mathrm{,}i=\mathrm{1,2,}$（3）

where, L is the nonlinear interaction length, and Δβ_SH=2β_ω–β_2ω is the phase-mismatch parameter between the pump and SH signal, where β_ω and β_2ω give their propagation constants, respectively. The nonlinear coupling parameter κ is determined by the coupling of second-order nonlinear polarization to HE₃₁(2ω) or EH₁₁(2ω) mode, in which${\text{e}}_{\omega }^j$ and${\text{e}}_{2\omega }^j$ express the normalized electric field component of pump and signal mode along j axis (j=x′, y′, z′).${\chi }_{jkl}^{(2)}$ is the tensor element of the second-order nonlinearity, possessing the nonzero elements${\chi }_{y^{\text{'}}{y}^{\text{'}}{y}^{\text{'}}}^{(2)}=-{\chi }_{y^{\text{'}}{x}^{\text{'}}{x}^{\text{'}}}^{(2)}=-{\chi }_{x^{\text{'}}{x}^{\text{'}}{y}^{\text{'}}}^{(2)}=-{\chi }_{x^{\text{'}}{y}^{\text{'}}{x}^{\text{'}}}^{(2)}$ when x′ and y′ axes are assigned to zigzag- and armchair direction of GaSe lattice structure³³. Note that the integration in Eq. (2) is performed in the infinite plane perpendicular to the longitudinal direction of the microfiber. N₁ and N₂ in Eq. (3) represent normalization factors for pump and SH modes, respectively.

The experimental setup for exciting and measuring SH is illustrated in Fig. 2. The pump fundamental waves, provided by linearly polarized near-infrared fiber lasers, were coupled into the single-mode fiber (SMF) through a coarse wavelength division multiplexer (CWDM) and then intensely interacted with the GaSe coating transferred on the microfiber. Additionally, in order to measure the evolution of the SH along the microfiber axis, a positioning stage and a microscopic objective are installed below and above the microfiber. Finally, in order to separate the produced SH from the pump light, a collimating and filtering system consisting of two collimators (central operation wavelength: 780 nm), a dichroic mirror (long pass: 950 nm) and a reflector (coated with aluminum film) was configured to filter out the pump light. The SH intensity was monitored in real-time by a spectrometer.

To check the quality of the fabricated device in an intuitive way, the GaSe-transferred microfiber was first tentatively pumped by a 1064 nm picosecond laser, with a pulsed width of 11 ps and a repetition rate of 19.5 MHz. When an approximately 80 mW pump laser is incident into the microfiber, by using the experimental setup illustrated in Fig. 2, a distinct side emitting green frequency-doubled light could be observed from the microfiber’s surface with naked eyes (Refer to the inset of Fig. 2). Moreover, the rest of green SH at 532 nm coupled into the microfiber and propagated steadily in subsequent fibers. By comparing the two images captured under bright and dark fields, respectively, a small green-spot was identified at the end face of the optical fiber. The zoomed green-spot is shown in the inset of Fig. 2, whose average power was measured as more than 1 μW with a power meter. Therefore, obvious green SH signals emitted from surface and the end face of the fiber prove the high-quality of GaSe-transferred microfiber, which provides great convenience for subsequent experiments implemented with C band pump lasers.

In order to examine the device performance of GaSe-transferred microfiber in the well-required C telecom band, the 1550 nm pulse light was incident into the GaSe-transferred microfiber from the picosecond laser used in the aforementioned polarization dependence experiment. For clear illustration, the SH and third-harmonic (TH) spectra under 0.868 mW were measured and plotted in Fig. 3(a). With the assistance of crystalline GaSe layer, the SH and TH intensities have been greatly enhanced, compared with the intrinsic nonlinear signal from the microfiber. As a result, a detectable SH signal can be observed with very weak pump power. Meanwhile, the diameter (~3.3 μm) of the fabricated microfiber is almost the optimal one for the phase matching. According to Eq. (1), the SH signal will be a quadratic trend (P_2ω∝L²) along the propagation direction in the GaSe coating. To confirm this, we carried out experiments to demonstrate the cumulative result of SH signal along the GaSe-transferred microfiber. The side emitting SH from the GaSe-transferred microfiber was collected using the experimental setup shown in Fig. 2. Starting from the point A shown in the inset of Fig. 3(b) along the positive direction marked with the white arrow, the SH intensity evolves as a quadratic trend when the nonlinear interaction length (or axial coordinate) is less than 17 μm. This quadratic trend supports that approximate phase matching is satisfied between HE₁₁(ω) and HE₃₁(2ω), EH₁₁(2ω), with their transverse mode profiles shown in insets of Fig. 3(b). Due to gradually accumulated phase-mismatching of pump and SH signal, the SH intensity no longer quadratically increased with nonlinear interaction length when axial distance exceeds 17 μm, and the periodic change is calculated under a phase-mismatching parameter of 0.25 rad/μm, as depicted by the red dashed line in Fig. 3(b). Specially, due to the relatively high refractive index (~2.8) of GaSe for the pump and SH, the GaSe layer will introduce the accumulated phase mismatching. And then, the produced SH signal would be weakened especially for a large nonlinear interaction length, and thus there is an optimal coating length.

By increasing the incident average power from 5.6 to 27.3 mW, the SH power increased quadratically with a fitting slope of 2.10±0.01, as shown in Fig. 3(c), which was in real-time monitored by a high-precision power meter (Thorlabs, PM320E) instead of the spectrometer. It is notable that the measured maximum average power of SH was up to approximately 16 nW, corresponding to a normalized frequency conversion-efficiency of 0.08 %W⁻¹mm⁻¹ on the unit nonlinear interaction length (The average power of SH and pump light is used in the calculation of conversion-efficiency). The efficiency is at least 2 orders of magnitude higher than most previously reported experiments conducted with other optical fibers^{3, 14, 24, 26-32}, as listed in Table 1. Provided that the pulse width and repetition rate of SH signal are the same as that of pump laser (7.6 ps, 18.5 MHz), abovementioned 16 nW average power of SH corresponds to approximately 0.1 mW peak power. Subsequently, the pump average power was reduced to 10 μW, but SH signal in the inset of Fig. 3(c) still remained detectable by the spectrometer, demonstrating the microwatt-level excitation threshold. Considering the high conversion-efficiency, we replaced the pulse laser with a 1550 nm CW laser to excite the SH. According to the intensity evolution of SH signal shown in Fig. 3(d), CW-pumped SH scales quadratically with excitation power from 0.7 to 14.5 mW with a fitting slope of 1.94±0.01. Compared with the excitation power of 1 mW under CW pump in the previous report²⁴, the threshold of producing detectable SH in GaSe-transferred microfiber has been reduced to approximately 0.7 mW. It is important to note that, whatever the high conversion-efficiency pumped by a picosecond laser or the low threshold power pumped by a CW laser, these can be attributed to the ultrahigh second-order nonlinearity, large nonlinear interaction length and especially the long-range order structure of the crystalline GaSe. Compared with randomly distributed GaSe nanosheets, the long-range order structure of the GaSe crystal ensures the homogeneous constructive interference of SH excited at different axial positions, promoting the approximately two orders of magnitude’s enhancement of SH.

Further, CW pumped frequency conversion process supplied by a single laser source can be extended to more than one signal wavelengths by mixing multiple frequencies of pump light. As an example, three CW tunable lasers (TL) within O/C/L bands (1270/1550/1590 nm for TL₁/TL₂/TL₃) were coupled together through a coarse wavelength division multiplexer (CWDM) shown in Fig. 2 to implement the multi-frequencies conversion process. The corresponding typical spectrum is shown in Fig. 4(a), when the pump power of TL₁/TL₂/TL₃ is fixed at 10/15/10 mW separately. It should be noted that the total number of SH and SF equals to n+${\text{C}}_n^{\text{2}}$=n(n+1)/2, where n is the number of pump wavelengths and also SH signals.${\text{C}}_n^{\text{2}}$ represents the number of combinations when two of the n pump wavelengths are selected, namely the number of sum-frequency (SF) signals. In the experiment, n=3 leads to overall six observable frequency conversion signals, in which three SH signals for 2ω₁/2ω₂/2ω₃ at 635/775/795 nm and three SF signals for ω₁+ω₂, ω₁+ω₃ and ω₂+ω₃ at 698.05, 706.05 and 784.87 nm (Please see the Supplemental information for inherent distribution pattern of SH and SF peaks in the frequency region). Moreover, we investigated the power dependence of six frequency conversion signals on the power of TL₁, by changing its power from 0 to 10 mW. From the evolution shown in Fig. 4(b), we can observe three gradually grown SH (2ω₁) and SF signals (ω₁+ω₂, ω₁+ω₃) with the pump power, while intensities of the rest three frequency conversion signals remain almost unchanged. Corresponding slopes of power dependences for 2ω₁, ω₁+ω₂, ω₁+ω₃ are 1.95±0.03, 0.97±0.01 and 0.99±0.01, respectively. Subsequently, similar power dependence characteristics were investigated by changing pump power of TL₂ and TL₃, respectively, with their evolutions illustrated in Fig. 4(d, f). The three increased signal intensities of 2ω₂, ω₁+ω₂, ω₂+ω₃ (Or 2ω₃, ω₁+ω₃, ω₂+ω₃) under pump of TL₂ (TL₃) present log-log plotted slopes of 1.92±0.01 / 0.98±0.01 / 1.05±0.01 (1.99±0.01 / 1.00±0.01 / 0.99±0.01), as shown in Fig. 4(e) and Fig. 4(g). These good agreements with theoretical predictions prove that the proposed device operates as an excellent platform for multi-frequencies conversion.

Achieving broadband SH with high efficiency is a significant challenge regardless of whether the experimental scheme is free-space with bulky material or a compact device of optical fiber. However, in the proposed fully integrated micro-nano optics platform, a superluminescent light-emitting diode (SLED) source with a broadband optical spectrum and low power spectral intensity, was used to achieve a broadband SH in the GaSe-transferred microfiber (Similar experimental results implemented by an amplified spontaneous emission (ASE) source is given in the Supplemental information). From spectral evolution in Fig. 5(a), we can observe a gradually grown broadband SH that is centered around 773 nm, when the pump power is changed from 1.8 to 13.9 mW. By extracting maximum intensity of each spectrum, the slope of power dependence is calculated as 2.01±0.02, which agrees well with theoretical value 2, as shown in Fig. 5(b). Then, we compared the Gaussian-shaped spectrum of broadband SH with that of SLED source, as shown in Fig. 5(c). According to the top subplot in Fig. 5(c), the smooth spectrum of the SLED source covers the whole C-band, possessing a 79.3 nm full width at −10 dB maximum (1514.5~1593.8 nm). In contrast, the produced SH continuum spans from 761.9 to 790.2 nm, revealing a 28.3 nm bandwidth. This bandwidth is a relatively large one compared with previous reports^{3, 14, 24, 26-32}, demonstrating the excellent operation performance of the GaSe-transferred microfiber. The more than half reduced bandwidth with respect to the SLED spectrum is attributed to the frequency double process, and the ratio between SH and pump bandwidths is 0.357, which is very close to the theoretical value of 0.354 (Please see the Supplemental information for the details of derivation). Note that the theoretical ratio between SH and pump bandwidths is determined by the specific profile of pump spectrum. Compared with broadened SH ensured by self-phase modulation and cross-phase modulation³⁹, a broadband frequency-double signal can be produced in a simpler way in our scheme without utilizing third-order nonlinearity of the device itself. The additional merit of the scheme is that the modulation of spectrum intensity can be fulfilled simply by varying the injected pump power rather than modulating the reverse-biased voltage in a silicon waveguide, which is considered as a reliable method intuitively.

To evaluate the nonlinear conversion performance, the detailed comparisons are given based on schemes listed in Table 1. In the scheme with photonic crystal fibers^{14, 26}, the SH signal is detected to follow a sinc² dependence on the Xe gas pressure, with a conversion-efficiency of 5×10⁻¹¹ %W⁻¹mm⁻¹. By functionalizing the hollow-core fiber with molybdenum-disulfide (MoS₂) or GaSe nanosheets^{3, 30}, the SH signal is enhanced to three orders of magnitude that of monolayered MoS₂, with a conversion-efficiency of 4×10⁻⁴ %W⁻¹mm⁻¹. The SH signal can also be enhanced in special optical fibers such as the doped fiber³¹, suspended-core fiber²⁸, and birefringent fiber³². Widely tunable SH is produced in the range of 850 to 1502 nm with a conversion-efficiency of 1.1×10⁻⁷ %W⁻¹mm⁻¹. However, the photonic bandgap effect or large propagation losses of guided modes in above schemes hinder the efficient and broadband SH excitation. Recently, the conversion-efficiency could be further enhanced by coating the monolayer tungsten-disulfide (WS₂), layered GaSe or indium-selenide (InSe) nanosheets on microfibers^{24, 27, 29}. In our proposed scheme, the layered GaSe crystal with a long-range ordered structure was wrapped around the microfiber. Such a device with a short nonlinear interaction length (only several tens of micrometers), can not only obtain the CW-pumped narrowband SH, but also the broadband (28.3 nm) SH continuum pumped by a SLED source with low power spectral density and multi-frequencies mixing processes supported by three CW light sources. The proposed scheme therefore provides a new strategy to construct compact in-fiber or on-chip photonic devices for optical nonlinear processes.

In summary, we report an accessible strategy to efficiently realize the narrowband/broadband CW-pumped SH in a GaSe-transferred microfiber. Benefitting from the ultrahigh second-order nonlinearity and the long-range order structure of transferred GaSe coating, 532 nm green SH signal at the microwatt level can be observed with naked eyes. As expected, under the C-band picosecond pulse pump of 1550 nm, quite high frequency conversion-efficiency up to 0.08 %W⁻¹mm⁻¹ has been realized. The conversion-efficiency is enhanced by at least 2 orders of magnitude in comparison with previous reports implemented with other fibers^{3, 14, 24, 26-32}. Then, by replacing the pump as a 1550 nm CW laser, we demonstrate CW pumped quasi-monochromatic SH signal at 775 nm. Furthermore, six SH and SF signals at different wavelengths are achieved under the simultaneous pump of three CW lasers. Consequently, the well-established CW operation brings about SLED pumped broadband SH with a bandwidth up to 28.3 nm. By applying chemical vapor deposition method to grow a few atomic layers of nonlinear crystals onto the microfiber^{3, 15, 40}, it is promising to the scalable fabrication of the proposed frequency-conversion device. Therefore, we believe that this work is important not only for the enhancement of nonlinear parametric processes in fiber optics, but also for advancing various CW and broadband light sources at new wavelength regions.