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We demonstrate the broadband cascaded four-wave mixing (FWM) and supercontinuum (SC) generation in a tellurite MOF which is made from 76.5TeO2-6ZnO-11.5Li2O-6Bi2O3 (TZLB, mol%) glass. By using a 2-μm picosecond laser with the center wavelength of ~1958 nm as the pump source, the broadband FWM with the frequency separation of ~1.1 THz is obtained. The bandwidth of the frequency comb spans a range of ~630 nm from ~1620 to 2250 nm at the average pump power of ~125 mW. With the average pump power increasing to ~800 mW, the broadband mid-infrared SC generation with the spectrum from ~900 to 3900 nm is observed. Changing the pump source to a femtosecond laser (optical parametric oscillator, OPO) with the center wavelength of ~2000 nm, solitons and dispersive waves (DWs) are obtained.
© 2015 Optical Society of America
1. Introduction
Four-wave mixing (FWM), including the degenerate and nondegenerate cases, refers to a nonlinear optical interaction among four waves [1–6]. Photons from one or more waves are annihilated and new photons are created through the third order susceptibility [7–13]. FWM can lead to many applications: wavelength conversion [14], optical demultiplexers [15], optical parametric amplification (OPA) [2], and correlated photons pairs generation in quantum cryptography [16]. Recently, a lot of researches focus on the generation of the cascaded FWM [17, 18], which has great potential for frequency combs [19, 20] and optical instrument testing and fiber sensing [21]. For crystals and waveguides, many reports have demonstrated the mid-infrared optical frequency combs via cascaded FWM [17, 18]. However, for optical fibers frequency combs via cascaded FWM were confined only on the visible region or the telecommunication window [19, 20, 22–25].
On the other hand, the cascaded FWM is one of the important mechanisms for supercontinuum (SC) generation in the optical fibers [26, 27]. In the past decade, SC in the microstructured optical fibers (MOFs) has been widely investigated, especially for the soft-glass MOFs [28–31]. The soft-glass MOFs have higher nonlinearity and wider transmission range, which can support SC generation in the mid-infrared range [32–35]. Xia et al. obtained SC extending to 4.5 μm in ZBLAN fluoride fiber [36] and Qin et al. reported ultrabroadband SC generation from 0.35 to 6.28 μm in the step-index fluoride fiber [37]. Domachuk et al. demonstrated SC with a bandwidth over 4000 nm in a tellurite MOF [38]. Petersen et al. reported SC spanning from 1.4 μm to 13.3 μm in an ultra-high NA chalcogenide step-index fiber [39].
In this work, we demonstrate the broadband cascaded FWM and SC generation in a tellurite MOF which was made from 76.5TeO2-6ZnO-11.5Li2O-6Bi2O3 (TZLB, mol%) glass. The broadband cascaded FWM with the frequency separation of ~1.1 THz and the bandwidth of ~630 nm was observed by pumping the tellurite MOF with a 2-μm picosecond laser. With the average pump power increasing, the broadband mid-infrared SC generation with the spectrum from ~900 to 3900 nm was obtained. Changing pump source to a femtosecond laser, solitons and dispersive waves (DWs) were obtained.
2. Fabrication and characterization of the tellurite MOF
The tellurite MOF with four air holes was fabricated by the rotational casting method and rod-in-tube drawing technique. The TZLB tube (outer diameter of ~12 mm and hole diameter of 6.5 mm) and rod (outer diameter of ~12 mm and center column diameter of ~6 mm) were prepared by the rotational casting method and the casting method in the atmosphere, respectively, as shown in Fig. 1 (a). The fabrication process was similar to Reference [40, 41]. Frist, the rod was elongated to the diameter of ~6.5 mm to match the center hole of the TZLB tube. Second, the elongated rod was inserted into the tube and elongated together to obtain a preform. Third, the preform was inserted into another TZLB tube and drawn into a fiber. The glass transition temperature (Tg) and the softening temperature (Ts) were 288 °C and 307 °C, respectively. During the fiber-drawing process, a positive pressure of nitrogen gas was filled into the outer four holes to avoid their collapse, so the fiber structure was slightly unproportioned to the structure of the preform.
Fig. 1 (a) Photos of TZLB tube and rod. (b) Cross section of the tellurite MOF taken by SEM. (c) Calculated chromatic dispersion of the tellurite MOF. Inset is the fundamental mode-field profile at 2000 nm.
Figure 1(b) shows the cross section of the tellurite MOF taken by a scanning electron microscope (SEM). The core and cladding diameters were ~4.9 μm and ~132 μm, respectively. A 10 m-long tellurite MOF was used to measure the loss by the cut-back technique, and the loss was ~0.3 dB/m at ~2000 nm. The nonlinear coefficient (γ) was ~168 km−1 W−1, which was calculated based on the nonlinear refractive index of ~5.9 × 10−19 m2 W−1 for the tellurite glass and the effective mode area of ~11.3 μm2 at the wavelength of ~1958 nm. The profile of the chromatic dispersion of the tellurite MOF was shown in Fig. 1(c), which was calculated by a commercial software (Lumerical MODE Solution) using the full-vectorial mode solver technology. The fundamental mode-field intensity at 2000 nm was shown in the inset of Fig. 1(c), and the zero-dispersive wave (ZDW) of the tellurite MOF was ~1740 nm.
3. Experimental setup
The experimental setup for the cascaded FWM and SC generation in the tellurite MOF was shown in Fig. 2. In experiment, the first pump source was a 2 μm mode-locked fiber laser (Advalue Photonic) with the pulse width of ~2.7 ps. The center wavelength was ~1958 nm with the maximum output power of 1 W at the repetition rate of ~31.9 MHz. The second pump source was an optical parametric oscillator (OPO, Coherent Inc.) with the pulse width of ~200 fs and the repetition rate of ~80 MHz. After a neutral density (ND) filter, the pulse was coupled into the core of the tellurite MOF by a lens with the focus length of ~4.0 mm and the numerical aperture (NA) of ~0.56 (THORLABS, CO36TME-D). The output signal was then butt-coupled into a 0.3 m long large-mode-area (LMA) fluoride (ZBLAN) fiber with the core diameter of ~105 μm and the transmission window from 0.4 to 5 μm. The nonlinear effect in the LMA ZBLAN fiber could be ignored due to the large core size. Finally, the LWA ZBLAN fiber was connected to optical spectrum analyzers (OSAs, 350—1200 nm and 1200—2400 nm) and a Fourier-transform infrared (FT-IR) spectrometer to record the SC spectra.
4. Experimental results and discussion
First, the tellurite MOF was pumped by the 2 μm mode-locked fiber laser with the center wavelength of ~1958 nm locating in the anomalous chromatic dispersion range. The fiber length was 30 cm which was the optimized length obtained through experiments. The spectrum of the pump source was shown in Fig. 3, which had a strong Kelly sideband with the center wavelength of ~1944 nm. The Kelly sideband is a typical spectral characteristic of soliton mode-locked fiber lasers and it could be more significant after strong amplification [42]. In our experiment, the Kelly sideband can be considered as the signal for the cascaded FWM.
The cascaded FWM spectra from the tellurite MOF with different average pump power were shown in Fig. 4. The average powers measured before the lens were ~92, 125 and 164 mW. The coupling efficiency was about ~10%, which was defined as the ratio between the power transmitting in the core and the power before the lens. The power transmitting in the core can be measured by OSA from the output end of the tellurite MOF, and the peak powers launched into the tellurite MOF were calculated to be ~107, 145 and 190 W. There are several reasons for the low coupling efficiency: the mode field of the propagation beam from the OPO (2000 nm) was not good; the spot after the lens was larger than the core; the numerical aperture (NA) of the fiber and the lens did not match well and the surface of the tellurite MOF was not smooth. In Fig. 4(a), the broadband cascaded FWM extended from ~1670 to 2160 nm at the average pump power of ~92 nm, and from ~1620 to 2250 nm at ~125 mW. The frequency separation was ~1.1 THz for the signal and pump wavelengths were fixed at 1944 nm and 1958 nm, respectively. The first order idler wave was observed at ~1972 nm, and the 32 higher order cascaded FWM products can be identified clearly. With the average pump power increasing to 164 mW, no cascaded FWM was observed and only SC spectrum from ~1400 to 2370 nm was obtained. There are two possible reasons. One is the deterioration of the phase-matching condition, and the other is the prominence of other nonlinear effects such as the self-phase modulation (SPM) and the stimulated Raman scattering (SRS). Figure 4(b) shows the enlarged pump, signal and idler waves in the frequency domain. With the average pump power increasing, the idler wave was fixed at ~-1.1 THz (~1972 nm) due to, in which fp, fi and fs were the frequencies of the pump, idler and signal waves, respectively.
Fig. 4 (a) Cascaded FWM spectra from the tellurite MOF with the average pump power of ~92, 125 and 164 mW. (b) Enlarged pump, signal and idler waves in the frequency domain with the frequency separation of ~1.1 THz.
The phase-matching condition of the cascaded FWM in the tellurite MOF was calculated as following. For the degenerate FWM, the pump wave is annihilated ω1 = ω2 = ωp, and simultaneously the idler and signal waves are created. And the conservation of energy and nonlinear phase-matching should satisfy the following equations
where ωp, ωi and ωs are the angular frequencies of the pump, idler and signal waves, respectively, and P is the pump power. Δβ is the linear phase mismatch and can be expressed bywhere n(ωi), n(ωs) and n(ωp) are the refraction indexes at ωi, ωs and ωp, respectively. The linear phase mismatch calculated by Eq. (3) can include all the high-order dispersions [43]. Figure 5 shows the phase-matching condition of cascaded FWM with the peak pump power of ~107, 145, 190, 581, 755 and 929 W. We can see that the phase-matching condition at ~1944 nm (signal) becomes deteriorate with the peak pump power increasing. When the peak pump power is ~107 W, κ is 8.2 m−1. And when the peak pump power is ~929 W, κ is 300 m−1. Therefore the cascaded FWM can be easily obtained at low power, but the generation efficiency of the cascaded FWM would decline with the pump power increasing.Fig. 5 Calculated phase-matching condition with the peak pump power of ~107, 145, 190, 581, 755 and 929 W from 1820 to 2100 nm.
With the average pump power increasing to ~500, 650 and 800 mW, the broadband mid-infrared SC was generated in the tellurite MOF, as shown in Fig. 6. The peak powers launched into the fiber were calculated to be ~581, 755 and 929 W. At the average pump power of ~500 mW, the SC spectral range covered ~2450 nm from ~1030 to 3480 nm. Increasing the average pump power to ~800 mW, the SC spectral range became ~3000 nm from ~900 to 3900 nm which was wider than the previous reports [31, 44].
Fig. 6 Measured SC in the tellurite MOF at the pump wavelengths of ~1958 nm with the average pump power of ~500, 650 and 800 mW.
The nonlinear length is LNL = 1/γP0, where γ is the nonlinear coefficient and P0 is the peak power. The dispersion length is LD = T02/|β2|, where T0 ≈TFWHM/1.763 is the pulse width for hyperbolic-secant shape and β2 = −147 ps2/km at ~1958 nm is the dispersion parameter calculated according to Fig. 1(c). LNL decreased from ~1.02 to 0.64 cm when the peak pump power increased from ~581 to 929 W. LD was calculated to be ~15.9 m. In the experiment, the fiber length L = 30 cm >> LNL and L <<LD, thus the group-velocity dispersion (GVD) effect was negligible and only the nonlinear effects were dominant for SC generation [45]. Optical soliton was difficult to form during the pulse evolution, although the pump wavelength was in the anomalous chromatic dispersion region the tellurite MOF. Therefore, the mechanism of spectrum broadening was mainly dominated by SPM, SRS and the cascaded FWM. On the other hand, a strong absorption peak appeared in SC spectrum, which may be induced by the fundamental vibration mode of OH bond (the OH impurities in the glass).
We replaced the 2-μm picosecond laser in Fig. 2 with an OPO and retained other components. The wavelength of the OPO could be tuned from 1.8 to 3.0 μm and the output was linearly polarized. The OPO was operated at ~2000 nm in our experiment. The SC spectra were shown in Fig. 7 with the average pump power of ~80, 150, 220, 300 and 350 mW. The peak powers launched into the fiber were shown in Table 1, which were calculated corroding to the coupling efficiency of ~10%. At the maximal average pump power of ~350 mW, the SC spectral range covered ~1750 nm from ~1020 to 2770 nm. Compared with the SC spectra generated by the 2 μm mode-locked fiber laser, obvious solitons were formed in the tellurite MOF. This is because the fiber length L = 30 cm ≥ LNL and ≥ LD. LNL was calculated based on γ = ~156 km−1 W−1 at 2000 nm and it decreased from ~1.28 to 0.29 cm with the pump peak power increasing from ~500 to 2188 W. LD was ~7.8 cm, calculated based on β2 = −165 ps2/km at 2000 nm. At the low peak power (~80 mW), the SC generation was dominated by the SPM effect and the fundamental soliton. With the pump peak power increasing, it exceeded what was needed to form the fundamental soliton and the high-order soliton fission with several peaks appeared. We can see that the 3rd soliton and DW were formed and the 2nd soliton broke up into two peaks at ~220 mW. In the experiment, the SC spectral evolution for the redshift was mainly due to the soliton dynamics, and the blueshift was mainly due to SPM and the DW emitted by the solitons.
Fig. 7 Measured SC in the tellurite MOF at the pump wavelengths of ~2000 nm with the average pump power of ~80, 150, 220 300 and 350 mW.
Table 1. Launched peak powers in the tellurite MOF corresponding to the average pump powers.
With the power increasing and exceeding the Raman threshold, the soliton pulses changed those central frequencies and the obvious SSFSs were observed in the mid-infrared range. The fundamental soliton with carrier frequency shift Δν from 30.8 to 40.4 THz (~484 to 738 nm in wavelength) was obtained with the average pump power increasing from ~80 to 350 mW. In Fig. 8, the fundamental soliton wavelength shift was shown as a function of the average pump power (~80, 150, 220, 300 and 350 mW). At the power of ~350 mW, SSFS of the fundamental soliton was so large that the loss of pulse energy to excited phonons (owing to the Raman nature of the process) weakened SSFS [46]. The output signal did not extend above ~2800 nm, and the main reason may be that the tellurite MOF had a strong absorption due to OH, which also induced the decrease of the soliton power. Compared with the pump source, the fundamental soliton pulse was compressed and the fundamental soliton could be applied as a mid-infrared source.
Fig. 8 Fundamental soliton wavelength shift corresponding to the average pump power of ~80, 150, 220 300 and 350 mW.
The DWs emitted by the solitons are governed by nonlinear phase-matching condition [45]
where βn(ωsoliton) is the nth derivative of the propagation parameter β with respect to the pump wavelength, and n = 6 is considered in the paper. ωsoliton and Psoliton are the central frequency and peak power of the soliton, respectively, and ωDW is the central frequency of DW. The experimental and calculated center wavelengths of the 1st DW (λDW) with different average pump power were shown in Fig. 9. At the average pump power of ~80, 150, 220 300 and 350 mW, the experimental 1st λDW were ~1290, 1210, 1190, 1160 and 1135 nm while the calculated λDW were ~1302, 1235, 1198, 1166 and 1125 nm. Due to the nonlinear phase shift and the calculated dispersion terms [47], there was a discrepancy between the experimental and the calculated values and in this experiment it was limited within the range of ~25 nm.Fig. 9 Experimental and calculated 1st λDW at the average pump power of ~80, 150, 220, 300 and 350 mW.
5. Conclusions
In summary, a tellurite MOF was fabricated for the cascaded FWM and SC generation in the paper. With the 2-μm picosecond laser as the pump source, the broadband cascaded FWM with the frequency separation of ~1.1 THz and the spectral range of ~630 nm (from ~1620 to 2250 nm) was obtained at the average pump power of ~125 mW. Increasing the average pump power to ~800 mW, the broadband mid-infrared SC with the spectral range of ~3000 nm (from ~900 to 3900 nm) was observed. Moreover, with the femtosecond laser (~2000 nm) as the pump source, the fundamental soliton and DWs were obtained respectively.
Acknowledgment
Tonglei Cheng acknowledges the support of the JSPS Postdoctoral Fellowship. This work is supported by MEXT, the Support Program for Forming Strategic Research Infrastructure (2011-2015).
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