We demonstrate dispersive wave generation at 4 µm in a dispersion-engineered fluorotellurite fiber pumped by a 1.98 µm femtosecond fiber laser. All-solid fluorotellurite fibers with a core diameter of ∼2.6 µm are fabricated by using a rod-in-tube method. The fluorotellurite fibers have two zero-dispersion wavelengths (ZDWs). The first ZDW is 1.328 µm and the second one is 3.551 µm. As the pump laser is launched into the fluorotellurite fiber, firstly, tunable mid-infrared Raman solitons are generated through higher order soliton compression, soliton fission and soliton self-frequency shift. Then, red-shifted dispersive wave at 4 µm is generated as those Raman solitons meet the second ZDW (∼3.551 µm) and soliton self-frequency shift cancellation occurs. Our results show that dispersion-engineered fluorotellurite fibers are promising nonlinear media for constructing all-fiber 4 µm light sources
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All-fiber mid-infrared (MIR) light sources have attracted much attention due to their potential applications in many fields, such as molecular spectroscopy, biomedicine, hyperspectral microscopy, defense, and security [1–5]. Dispersive wave generation in optical fibers or waveguides, as one of the promising approaches for obtaining optical fiber or waveguide-based MIR light sources, has been widely investigated [6,7]. Generally, dispersive waves are generated at the normal dispersion region of optical fibers, the coherence of the generated dispersive waves can be kept, which are required for many applications, e.g., the generation of MIR frequency combs . In 1995, Nail Akhmediev and Magnus Karlsson investigated the radiation emitted by optical solitons perturbed by higher-order dispersion effects in optical fibers and identified the radiation as Cherenkov radiation (or dispersive wave) . In 2003, Skyabin et al. demonstrated that the soliton self-frequency shift could be cancelled in a silica-core microstructured fiber with a negative dispersion slope and the spectral recoil from the red-shifted dispersive wave acted on the soliton to compensate for the Raman frequency shift. Such a phenomenon was called by soliton self-frequency shift cancellation (SSFSC) . As SSFSC occurs in an optical fiber, the self-frequency shift of a soliton stops suddenly and a dispersive wave appears at its red side when the red-shifted soliton meets the second zero-dispersion wavelength (ZDW) of the fiber. As a result, both the soliton and the red-shifted dispersive wave are frequency locked on the right and left sides of the second ZDW, respectively, and their frequencies are determined by the position of the second ZDW. Therefore, by using SSFSC, red-shifted dispersive waves at any wavelength can be obtained in dispersion-engineered optical fibers or waveguides. In 2011, Dekker et al. reported red-shifted dispersive generation at 2.04 µm in a silica-core microstructured fiber with low OH loss . However, since silica-core optical fibers have very high material loss in the MIR spectral region (> 2.5 µm), they are not suitable for generating MIR dispersive waves .
To generate MIR (> 2.5 µm) dispersive waves, several types of MIR fibers or waveguides with two ZDWs, including fluoride and chalcogenide fibers, gas-filled photonic crystal fibers, Si3N4 and AlN nanophotonic waveguides, have been developed for this purpose. For fluoride fibers, Chen et al. proposed to obtain dispersive wave generation from 2 to 3 µm in a nonuniformly tapered fluoride fiber through numerical simulations . For chalcogenide fibers, Xie et al. demonstrated MIR dispersive wave generation at 4.7 µm in an As2S3-silica double-nanospike waveguide pumped by a femtosecond Cr:ZnS laser at 2.35 µm . For gas-filled hollow-core fibers, Nova et al. demonstrated MIR dispersive wave generation from 3.3 to 4 µm via transient ionization-driven changes in dispersion in gas-filled photonic crystal fiber pumped by a 1030 nm femtosecond laser with a pulse width of 27 fs and a pulse energy of 16 µJ . Moreover, by using gas-filled silica hollow-core fibers as gain media, population inversion or stimulated Raman scattering based mid-infrared lasers beyond the 4 µm wavelength have been demonstrated by several groups [16–18]. For Si3N4 nanophotonic waveguides, Guo et al. reported MIR frequency comb via coherent dispersive wave generation in Si3N4 nanophotonic waveguides and obtained dispersive wave generation in the wavelength range from 2.5 to 4 µm from the waveguides pumped by a 1.55 µm femtosecond fiber laser . Furthermore, they used that source for detection of C2H2 by absorption spectroscopy . Despite recent progress in this field, it is still necessary to explore novel MIR fibers with good chemical and physical properties for constructing all-fiber MIR light sources.
Recently, fluorotellurite fibers based on TeO2-BaF2-Y2O3 (TBY) glasses have been developed by us for constructing high power MIR light sources . Such fibers had a broadband transmission window of 0.4∼6 µm, and stable chemical and thermal properties compared to fluoride and chalcogenide fibers [21–25]. The figure-of-merit parameter for characterizing the thermal mechanical properties of a laser material was also measured for TBY glasses, which indicated that TBY glass fibers might bear stronger thermal shock than fluoride fibers [20,26–28]. Our previous results showed that fluorotellurite fibers based on TBY glasses had a potential for generating MIR (>3 µm) dispersive waves . However, until now, MIR dispersive waves with a wavelength of >3 µm have not yet been demonstrated in fluorotellurite fibers.
In this paper, we reported MIR dispersive wave generation at 4 µm in a dispersion-engineered all-solid fluorotellurite fiber pumped by a 1.98 µm femtosecond fiber laser.
2. Experiments and results
To generate MIR dispersive waves, we designed and fabricated dispersion-engineered fluorotellurite fibers. The core and cladding materials of fluorotellurite fibers are TBY and AlF3-based glasses with good water resistance and high transition temperature (424 °C for the TBY glass, 440 °C for the AlF3-based glass), respectively . Figure 1(a) shows the refractive indices of TBY and AlF3-based glasses measured by a XLS-100 spectroscopic ellipsometer (J. A. Woollam Co., Inc.). Since those two glasses have large refractive index contrast, the numerical aperture of the fabricated fluorotellurite fibers is larger than 1.1 in the MIR spectral region, which is large enough for reducing the confinement loss in the MIR spectral region and controlling the chromatic dispersion of the fiber. Figure 1(b) shows the group velocity dispersion (GVD) curves of fundamental propagation mode in the fiber for different core diameters, which were calculated by using the commercial software (Lumerical MODE Solution) with the full vectorial finite difference method. From the Fig. 1(b), large chromatic dispersion control can be achieved by designing the core diameter. When the fiber core diameter is reduced from 50 µm to 3.4 µm, the fiber has the second ZDW in MIR, which is expected to be used to realize red-shifted MIR dispersion wave. The wavelength of the generated red-shifted MIR dispersive wave can be calculated from the phase matching condition between the soliton and the dispersive wave, which can be expressed as below 
Based on TBY and AlF3-based glasses, we fabricated all-solid fluorotellurite fibers by using a rod-in-tube method. The TBY and AlF3-based glasses were melted at 950 °C. Firstly, a glass rod was made by a modified suction method. The glass rod consisted of a solid core (TBY glass) surrounded by AlF3-based glass. Secondly, the glass rod was drawn and elongated to a thinner rod. Finally, the thinner rod was inserted into an AlF3-based glass tube and drawn into fibers . The inset of Fig. 1(d) shows the cross section of the fabricated fluorotellurite fiber. In our experiments, the fiber had a step-index structure and its core diameter was about 2.6 µm, which was designed for generating red-shifted dispersive wave at 4 µm. The calculated GVD profile of the fundamental propagation mode LP01 in the fiber was shown in Fig. 1(d). The fiber had the first ZDW of ∼1.328 µm and the second ZDW was ∼3.551 µm. The transmission loss at 1.98 µm of the fiber was measured by using a cut-back method and the measured value was about 0.8 dB/m. Figure 2(a) shows the calculated confinement losses of LP01, LP11, LP21 and LP02 modes in the fluorotellurite fiber. Figure 2(b) shows the calculated GVD profiles of those propagation modes. The nonlinear coefficients at 1.98 µm for the LP01, LP11, LP21 and LP02 modes of the fluorotellurite fiber were calculated to be about 97, 75, 98.4 and 122.8 km−1W−1 by using a nonlinear refractive index of 3.5×10−19 m2W−1 for fluorotellurite glasses.
To clarify the potential of the dispersion-engineered all-solid fluorotellurite fiber for the generation of MIR dispersive waves, we performed the following experiments and the experimental setup was shown in Fig. 3(a). A 1.98 µm femtosecond fiber laser with a pulse width of ∼200 fs, a repetition rate of ∼50 MHz was used as the pump source. An isolator was used to protect from any feedback. Figure 3(b) shows the output spectrum of the 1.98 µm femtosecond fiber laser. Figure 3(c) shows a single pulse profile of the 1.98 µm femtosecond fiber laser measured by using an autocorrelator. The above dispersion-engineered all-solid fluorotellurite fiber was used as the nonlinear medium. The pump light was launched into the above fluorotellurite fiber by using a couple of aspheric lens and the measured coupling efficiency was about 48%. The output signals were monitored by using an optical spectrum analyzer with a measurement range of 1200–2400 nm or 1900–5500 nm (Yokogawa).
Figure 4(a) shows the measured spectral evolution of output signals from a 1 m long fluorotellurite fiber with the average power of the 1.98 µm femtosecond laser. With increasing the average pump power to 0.2 W, large spectral broadening occurred. Since the pumping wavelength was located at the anomalous dispersion region of the fluorotellurite fiber, the spectral broadening for a pump power of ≥ 0.2 W was caused by self-phase modulation (SPM), the formation of higher-order soliton, soliton fission, SSFS, and the generation of blue-shifted dispersive waves. Interestingly, as the average pump power was increased to 0.5 W, the Raman soliton met the second ZDW and the SSFSC occurred. Meanwhile, the red-shifted dispersive wave at 4 µm was observed. With further increasing the average pump power to over 0.5 W, the red-shifted dispersive wave at 4 µm became stronger and stronger, and the operation wavelength of the red-shifted dispersive wave was kept around 4 µm, which was a feature of SSFSC. The solid red curve in Fig. 4(b) shows the measured spectrum output from the fluorotellurite fiber for an average pump power of ∼ 1 W. The relative total output power was measured to be ∼ 0.573 W. The integral intensity ratio for the 4 µm dispersive wave was calculated to be about 2.1%, corresponding to a conversion efficiency of ∼ 1.2%, an output power of ∼12 mW and a pulse energy of about 0.24 nJ. In addition, we investigated the long time stability of by monitoring the spectrum and power of the 4 µm dispersive wave output from the fluorotellurite fiber with an average pump power of ∼ 1 W for 3 hours, and no obvious fluctuation was observed. Not that, the output spectra from the fluorotellurite fiber were independent on the polarization of the pump laser.
To verify the mechanism for the generation of the 4 µm dispersive wave, we performed numerical simulations by solving the generalized nonlinear Schrödinger equations. In the simulations, we took the parameters of the above fluorotellurite fiber; the calculated nonlinear coefficients; the calculated group velocity dispersion curves shown in Fig. 1(d); the pump laser with an operating wavelength of ∼ 1.98 µm, a pulse width of ∼ 200 fs, and a repetition rate of 50 MHz, and the one-photon-per-mode model for representing input noise; and the Raman response function derived from the Raman gain spectrum of fluorotellurite glass . Figure 4(b) shows a comparison of the simulated (the dashed black curve) and measured (the solid red curve) spectra output from the fluorotellurite fiber for a same average pump power of ∼ 1 W. The simulated result agreed with the measured one for fluorotellurite fiber, indicating that the parameters used in the simulations were appropriate. The difference between the experimental and simulated spectra in the range from 2.2 µm to 3.3 µm might be due to that only the dispersion curve for the fundamental mode of the fluorotellurite fiber was considered in the simulation. The relatively flat, measured spectrum in the spectral range of 2.2-3.3 µm, as shown in Fig. 4(b) (the solid red curve), may be a combined result for the pump light being coupled into the different order modes of the fluorotellurite fiber. Figure 5(a)–5(d) show the simulated output spectra for LP01, LP11, LP21 and LP02 modes in the fluorotellurite fiber when the launched average pump power was fixed at 1 W, respectively. The red solid curve shows the measured spectrum output from the fluorotellurite fiber with the launched average pump power of 1 W. The simulated results show that the 4 µm dispersive wave can be only obtained when the pump light is coupled into the fundamental mode of the fluorotellurite fiber. In the future, we will try to measure coherence and mode characteristics of the generated 4 µm dispersive wave, and improve its performance by further optimizing the parameters of the fluorotellurite fiber and the pump laser.
Figure 4(c) showed the simulated spectral evolution of output signals from the fluorotellurite fiber with the average pump power of the 1.98 µm femtosecond laser. For the 1 m long dispersion-engineered fluorotellurite fibers, dispersive waves are emitted by optical solitons perturbed by higher-order dispersion effects in optical fibers, which can be described as follows. Optical solitons can be generated when soliton fission occurs as the operating wavelength of the pump light (e.g., an ultrashort pulsed laser) is located in the anomalous dispersion region of an optical fiber. Subsequently, optical soliton can exhibit a strong SSFS in the fiber, because the low frequency portion of the soliton spectrum experiences Raman gain at the expense of the high-frequency portion. Interestingly, as the red-shifted soliton moves into the spectral region in which the dispersion slope of the dispersion engineered fiber with two ZDWs is negative (β3<0), the soliton would emit a radiation band with a wavelength of longer than the second ZDW through the Cherenkov mechanism . The emitted radiation through the Cherenkov mechanism is called by the red-shifted dispersive wave. Because of the momentum conservation, as the dispersive wave is emitted in the normal dispersion regime, the soliton recoils further into the anomalous dispersion regime, the spectral recoil mechanism is responsible for the suppression of SSFS . As far as the spectral recoil is large enough, the SSFS cancellation occurs and the dispersive wave is amplified with an increase of the pump power. The above results showed that MIR dispersive waves at 4 µm could be obtained in the dispersion-engineered all-solid fluorotellurite fiber pumped by a 1.98 µm femtosecond fiber laser.
In addition, we simulated the spectral and temporal evolution of MIR dispersive waves generation in the above fluorotellurite fiber for an average pump power of ∼1 W, as shown in Fig. 6(a) and (b). It is obvious that, the mechanisms of spectral broadening were a combination of SPM, the formation of higher-order soliton, soliton fission, the generation of breathing soliton, SSFS, the generation of blue-shifted dispersive wave, SSFSC, and the generation of red-shifted dispersive wave. The corresponding temporal evolution of MIR dispersive wave generation was shown in Fig. 6(b), which confirmed the above interpretation. Figure 6(c) showed the simulated spectrograms of output pulse. The spectrograms display the temporal and spectral characteristics of the soliton and dispersive wave. From the spectrograms, the pulse width of the dispersive waves was estimated to be ∼ 1.5 ps.
In summary, we demonstrate dispersive wave generation at 4 µm in a dispersion-engineered fluorotellurite fiber pumped by a 1.98 µm femtosecond fiber laser. Our results show that dispersion-engineered fluorotellurite fibers are promising nonlinear media for constructing all-fiber 4 µm light sources.
National Key Research and Development Program of China (2020YFB1805800); National Natural Science Foundation of China (62090063, 62075082, U20A20210, 61827821); Opened Fund of the State Key Laboratory of Integrated Optoelectronics.
The authors declare no conflicts of interest.
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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