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We experimentally demonstrate multiple dispersive waves (DWs) emitted by multiple mid-infrared solitons in a birefringence tellurite microstuctured optical fiber (BTMOF). To the best of our knowledge, this is the first demonstration of multiple DWs in the non-silica fibers. By using a pulse of ∼80 MHz and ∼200 fs emitted from an optical parametric oscillator (OPO) as the pump source, DWs and solitons are investigated on the fast and slow axes of the BTMOF at the pump wavelength of ∼1800 nm. With the average pump power increasing from ∼200 to 450 mW, the center wavelength of the 1st DW decreases from ∼956 to 890 nm, the 2nd DW from ∼1039 to 997 nm, the 3rd DW from ∼1101 to 1080 nm, and the 4th DW from ∼1160 to 1150 nm. Meanwhile, obvious multiple soliton self-frequency shifts (SSFSs) are observed in the mid-infrared region. Furthermore, DWs and solitons at the pump wavelength of ∼1400 and 2000 nm are investigated at the average pump power of ∼350 mW.
© 2015 Optical Society of America
1. Introduction
Dispersive wave (DW) generation in the optical fibers, also known as the nonsolitonic radiation, is due to the energy transfer from a stable soliton in the anomalous dispersion regime to the narrow-band resonances in the normal dispersion regime [1–5]. DW is an important physical mechanism for supercontinuum (SC) generation, and its frequency is determined by the nonlinear phase-matching (PM) condition with the soliton [6–8]. Since the initial discovery by Beaud et al. [5], many researches on DW have been conducted involving various optical fibers, such as photonic crystal fibers (PCFs) and chalcogenide microstructured optical fibers (MOFs) [9–13]. Now, DW has been widely applied in tunable source, wavelength conversion, time frequency metrology, and optical coherence tomography [14–16]. Recently, great attention has been devoted to the highly efficient DW and multiple DWs in silica optical fibers [7, 12, 17–21]. However, although there is report about multiple DWs emitted form a single soliton in the silica optical fiber [12], multiple DWs emitted by stable multiple solitons are barely touched, especially for the non-silicon fibers.
To generate highly efficient DW and soliton, tellurite MOFs, which have high nonlinear refractive indices and broad transparency ranges, are promising candidates [22–24], and they have already been applied in SC generation, soliton self-frequency shift (SSFS), and third-harmonic generation (THG), etc [25–28].
In the paper, we designed a four-hole birefringence tellurite MOF (BTMOF), and fabricated it by the rod-in-tube drawing technique. A pulse of ∼80 MHz and ∼200 fs from an optical parametric oscillator (OPO) was used as the pump source. DWs and solitons were investigated on the fast and slow axes of the BTMOF at the pump wavelength of ∼1800 nm with the average pump power of ∼200 mW. When the polarization state of the pump pulse was parallel to the fast axis, multiple DWs were emitted by multiple solitons with the average pump power increasing from ∼200 to 450 mW, To the best of our knowledge, this is the first demonstration of multiple DWs in the non-silica fibers. Moreover, DWs and solitons at the pump wavelength of ∼1400 and 2000 nm were investigated at the average pump power of ∼350 mW.
2. Characterization of a BTMOF
The BTMOF (76.5TeO2-6Bi2O3-11.5Li2O-6ZnO, TZLB, mol%) was fabricated by the rod-in-tube drawing technique [29]. First, a cross-shaped TZLB glass rod and two TZLB tubes were prepared by the casting method and the rotational casting method, respectively. The cross-shaped TZLB rod was elongated to prepare the capillary. Then the TZLB capillary was inserted into one TZLB tube and elongated together to produce the preform with four air holes in the cladding. Finally, the preform was inserted into the other TZLB tube and drawn into fiber at the temperature of ∼307 °C. The jacket tube was utilized to decrease the ratio of the core to the cladding size. During the fiber-drawing process, a positive pressure of nitrogen gas which was ∼1∼2 kPa larger than the standard atmospheric pressure filled the four holes to avoid their collapse. The inset of Fig. 1(a) shows the cross-section of the BTMOF. The lengths of the long and short axes of the fiber core were measured to be ∼2.7 and 2.0 μm, respectively. A 6 m-long fiber was used to measure the loss by the cutback technique, and the loss was ∼1.1 dB/m at ∼1800 nm. The fundamental modes and the chromatic dispersions of the fast and slow axes were calculated by a commercial software (Lumerical MODE Solution) using the full-vectorial mode solver technology. The results are shown in Fig. 1(b), which exhibits two zero-dispersive wavelengths: ∼1345 nm for the fast axis and ∼1395 nm for the slow axis. The insets of Fig. 1(b) are the fundamental modes of the fast and slow axes. Figure 1(c) shows the calculated effective mode areas and the nonlinear coefficients of two orthogonally polarized modes from ∼1000 to 2600 nm. We can see that the former increases while the latter decreases with the change in wavelength.
Fig. 1 (a) Calculated modal refractive indices of two axes and the corresponding beat lengths. Inset is the cross-section of the BTMOF. (b) Calculated chromatic dispersion curves of the fast and slow axes. Insets are the fundamental mode fields at ∼1800 nm. (c) Calculated effective mode areas and nonlinear coefficients of the BTMOF.
The strength of modal birefringence is defined by a dimensionless parameter [1]
where nx and ny are the modal refractive indices, and βx and βy are the propagation constants for two orthogonally polarized modes. For a given value of Bm, the two modes exchange their power in a periodic fashion as they propagate inside the fiber with the period, which is defined as polarization beat lengthFigure 1(a) shows the calculated modal refractive indices of two modes and the corresponding beat length. At the wavelength of ∼1800 nm, the beat length of the BTMOF was ∼0.44 mm.3. Experimental results and discussion
The experimental setup for the DW and soliton generation in a 0.8 m-long BTMOF is shown in Fig. 2. The pump source was an OPO (Coherent Inc.) with a pulse width of ∼200 fs and a repetition rate of ∼80 MHz. The idler wavelength of the OPO could be tuned from ∼1800 to 3200 nm and the signal wavelength could be tuned from ∼1060 to 1440 nm. The output beam was linearly polarized. After a neutral density (ND) filter, a half-wave plate (HWP) was inserted to adjust the polarization state of the input laser beam to the axis of the BTMOF. The pulse was coupled into the core of the fiber by lenses: the one for the signal wave had a focal length of ∼3.1 mm and a numerical aperture (NA) of ∼0.68 (THORLABS, C330TME-C, 1050 −1800 nm), while the other for the idle wave had a focal length of ∼4.0 mm and an NA of ∼0.56 (THORLABS, C036TME-D, 1800−3000 nm). The output signal was then butt-coupled into a 0.3 m-long large-mode-area (LMA) fluoride (ZBLAN) fiber with a core diameter of ∼105 μm and the transmission window from ∼0.4 to 5 μm. The nonlinear effect in ZBLAN fiber could be ignored due to the large core size. Finally, the LMA ZBLAN fiber was connected to optical spectrum analyzers (OSAs; Yokogawa AQ6373, 350–1200 nm, and Yokogawa AQ6375, 1200–2400 nm) and an FT-IR spectrometer to record the spectra. For wavelengths from 350 to 2400 nm, the spectra were measured by the OSAs, and for wavelengths over 2400 nm, the spectra were measured by the FT-IR spectrometer.
First, we adjusted the idler wave of the OPO to ∼1800 nm as the pump wavelength, which was in the anomalous dispersion regime and far away from the zero-dispersive wavelength of the BTMOF. At the average pump power of ∼200 mW, the measured spectra with the polarization direction of the pump pulse paralleled to the fast and slow axes are shown in Fig. 3. The coupling efficiency was ∼3%, which was defined as the ratio between the power transmitting in the core and the power before the lens. Because only a little power leaked into the cladding, which can be neglected, the power transmitting in the core can be measured by OSAs from the output end of the BTMOF. There were several possible reasons for the low coupling efficiency: the mode field of the propagation beam from the OPO was not good enough; 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 BTMOF was not smooth. Considering the coupling efficiency, the peak power launched into the core was calculated to be ∼375 W. From Fig. 3, we can see that when the polarization direction of the laser pulse was parallel to the fast axis, the center wavelengths of the 1st DW and the soliton were ∼950 and ∼2320 nm, respectively. When parallel to the slow axis, the center wavelengths of the 1st DW and the soliton were ∼1020 and ∼2130 nm, respectively. It was clear that the fast axis was more advantageous for generating wide SC spectrum. As a result, in the following experiments, the polarization state of the pump pulse was always parallel to the fast axis.
Figure 4 shows multiple DWs emitted by multiple solitons at the average pump power of ∼200, 350, and 450 mW. To the best of our knowledge, this is the first demonstration of multiple DWs in the non-silica fibers. The coupling efficiency was the same (∼3%), and the peak powers launched into the core of the BTMOF were calculated to be ∼375, 656, and 844 W. 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 is the dispersion parameter calculated according to Fig. 1(b). At the peak power of ∼375 W, LNL = 4.56 × 10−3 m and LD = 3.73 × 10−2 m. The fiber length L>> LD and L>> LNL, so optical solitons can be formed in the BTMOF. With an increase in the average pump power, multiple soliton pulses changed their central frequencies and obvious multiple SSFSs were observed in the mid-infrared region. The center wavelength of the 1st soliton increased from ∼2320 to 2550 nm, the 2nd soliton from ∼1970 to 2350 nm, the 3rd soliton from ∼2005 to 2015 nm, and the 4th soliton from ∼1840 to 1900 nm. Compared with the silica-based fibers, tellurite-based fibers have a special Raman gain spectrum [29, 30]. For TZLB-based fibers, they have at least double peaks, higher gain coefficient and wider Raman shift. These Raman gain properties lead to the formation of multiple solitons in the BTMOF. Meanwhile, multiple DWs were trapped by multiple solitons under the nonlinear PM condition, which was the main reason for the blueshift of the spectral evolution. With an increase in the average pump power, the center wavelength of the 1st DW decreased from ∼956 to 890 nm, the 2nd DW from ∼1039 to 997 nm, the 3rd DW from ∼1101 to 1080 nm, and the 4th DW from ∼1160 to 1150 nm. Apart from this, we also noticed that at the low average pump power of ∼200 mW, only the 1st DW was obtained. This was because it was difficult for the 2nd, 3rd, and 4th DW to satisfy the nonlinear PM condition at the low power.
Fig. 4 Multiple DWs emitted by multiple solitons with the average pump power of ∼200, 350, and 450 mW at ∼1800 nm.
The wavelength location of DWs are predicted by the nonlinear PM condition with solitons [1]
where βn(ωS) is the nth derivative of the dispersion coefficient with respect to the soliton wavelength and n = 6 is considered in the paper. ωS and PS are the center frequency and peak power of the soliton, respectively. ωDW is the center frequency of DW. Theoretically, when the third−order dispersion β3 > 0, ωDW would be larger than ωS and DW would shift to the blueshift region. Based on the PM condition, the calculated center wavelengths of the 1st DW with the average pump powers of ∼200, 350, and 450 mW are shown in Fig. 5(a). And the calculated center wavelengths of the 1st, 2nd, 3rd and 4th DW at the average pump power of ∼450 mW are shown in Fig. 5(b). The discrepancy between the calculated and experimental results was limited within the range of ∼23 nm, which was induced by the nonlinear phase shift [31].Fig. 5 (a) Calculated phase mismatching for the 1st DW at the average pump power of ∼200, 350, and 450 mW. (b) Calculated phase mismatching for the 1st, 2nd, 3rd and 4th DW at the average pump power of ∼450 mW.
To show the generated multiple DWs and solitons as a function of the pump wavelength, DWs and solitons at the pump wavelength of ∼1400 and 2000 nm were further investigated at the average pump power of ∼350 mW, as shown in Fig. 6. When the pump wavelength increased to ∼2000 nm, only the 1st soliton, the 2nd soliton, and the 1st DW were observed, whose center wavelengths were ∼2630, ∼2220, and ∼844 nm, respectively. Compared with the pump wavelength of ∼1800 nm, the number of solitons and DWs became less. This was because the pump wavelength moved farther away from the zero-dispersive wavelength, making it more difficult for multiple solitons to form. Furthermore, due to the phase mismatching of the 2nd soliton, the 2nd DW was not observed. When the pump wavelength decreased to ∼1400 nm (the signal wavelength from OPO) which was close to the zero-dispersive wavelength, the lens was changed to C330TME-C. Under this condition, SC spectrum from ∼870 to 2680 nm was obtained. The spectral evolution for the redshift was mainly due to the Raman soliton dynamics, and the blueshift was mainly due to the self-phase modulation (SPM) and the DWs emitted by the solitons. Near the zero-dispersive wavelength, the prominence of other nonlinear effects covered the DWs and solitons, and rendered them unobserved. Furthermore, because the OH impurities in the tellurite glass were difficult to be removed thoroughly during the fabrication process, the output pump power became low at ∼2.8 μm.
Fig. 6 Measured spectra with the average pump power of ∼350 mW at the pump wavelength of ∼1400, 1800 and 2000 nm.
4. Conclusions
We designed and fabricated a four-hole BTMOF in which multiple DWs were emitted by stable multiple solitons. At the pump wavelength of ∼1800 nm, obvious multiple SSFSs were obtained in the mid-infrared region with the average pump power increasing from ∼200 to 450 mW. Meanwhile, the center wavelength of the 1st DW decreased from ∼956 to 890 nm, the 2nd DW from ∼1039 to 997 nm, the 3rd DW from ∼1101 to 1080 nm, and the 4th DW from ∼1160 to 1150 nm. The calculated and experimental center wavelengths of the 1st DW corresponded well with each other. By increasing the pump wavelength to ∼2000 nm, only the 1st soliton, the 2nd soliton, and the 1st DW were observed. Decreasing the pump wavelength to ∼1400 nm which was close to the zero-dispersive wavelength, SC spectrum from ∼870 to 2680 nm was obtained.
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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