Multi-peak-spectra Generation with Multiple Dispersive Waves and Solitons in a Birefringence Tellurite Microstructured Optical Fiber

Tonglei Cheng *, Tong Hoang Tuan, Xiaojie Xue, Dinghuan Deng, Takenobu Suzuki, Yasutake Ohishi,

Research Center for Advanced Photon Technology, Toyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468-8511, Japan

Corresponding author: chengtonglei@gmail.com

Abstract We demonstrate multiple dispersive waves emitted by multiple solitons in a birefringence tellurite microstuctured optical fiber. Obvious multiple soliton self-frequency shifts are observed in the mid-infrared region. Introduction Dispersive wave (DW) generation in the optical fibers, also known as the nonsolitonic radiation or the Cherenkov radiation(CR), 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]. 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. Since the initial discovery by Akhmediev et al. [2], many researches on DW have been conducted involving various optical fibers, such as photonic crystal fibers (PCFs) and chalcogenide microstructured optical fibers (MOFs) [3]. Recently, great attention has been devoted to the highly efficient DW and multiple DWs in silica optical fibers [4]. However, multiple DWs emitted by stable multiple solitons are barely touched, especially for the non-silica fibers.

To generate highly efficient DWs and solitons, tellurite MOFs, which have high nonlinear refractive indices and broad transparency ranges, are promising candidates [5], and they have already been applied into SC generation, soliton self-frequency shift (SSFS), and third-harmonic generation (THG), etc.

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 an average pump power of 200 mW. When the average pump power increased to 350 and 450 mW, multiple DWs were emitted by multiple solitons. Moreover, DWs and solitons at the pump wavelengths of 1400 and 2000 nm were investigated at an average pump power of 350 mW. Characterization of a BTMOF

The BTMOF (76.5TeO2-6Bi2O3-11.5Li2O-6ZnO, TZLB, mol%) fabricated by the rod-in-tube drawing technique has a square core surrounded by four air holes, as shown in the inset of Fig. 1(a). The lengths of the long and short axes of the fiber core were measured to be approximately 2.7 and 2.0 m, respectively. At the wavelength of

1800 nm, the loss was 1.1 dB/m, measured by the cutback technique. 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 waves (ZDWs): 1345 nm for the fast axis and 1395 nm for the slow axis. Fig. 1(c) shows the 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 a change in wavelength.

The strength of modal birefringence is defined by a dimensionless parameter [1]

yxyx

m nnkB 0

(1) where nx and ny are the modal refractive indices, and x and y 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 in the fiber with the period, which is defined as polarization beat length

yxyxB nnL

2 (2)

Figure 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.

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Fig. 1: (a) Beat length and two orthogonally polarized modal refractive indices of the BTMOF. Inset is the cross-section of the BTMOF. (b) Calculated chromatic dispersion curves for the fast and slow axes. Insets are the fundamental mode-field profiles at 1800 nm. (c) Effective mode areas and nonlinear coefficients of the BTMOF.

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, 18003000 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 m and the transmission window from 0.4 to 5 m. 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, 3501200 nm, and Yokogawa AQ6375, 12002400 nm) and an FT-IR spectroscopy to record the spectra. At wavelengths from 350 to 2400 nm, the spectra were measured by the OSAs, and at wavelengths over 2400 nm, the spectra were measured by FT-IR spectroscopy.

Fig. 2: Experimental configuration for DW and soliton generation in the BTMOF.

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 two ZDWs of the BTMOF. At the average pump power of 200 mW, the measured spectra with the polarization direction of the pump pulse parallel 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. 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 a wider SC spectrum. As a result, in the following experiments, the polarization state of the pump pulse was always parallel to the fast axis.

Fig. 3: DW and soliton spectra of the fast axis and slow axis at 1800 nm, 200 mW.

Figure 4 shows multiple DWs emitted by multiple solitons at the average pump power of 200, 350, and 450 mW. 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. 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. Multiple soliton behavior observed in this experiment

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was due to the breakup of high-order solitons in the presence of Raman scattering and self-steepening. Meanwhile, multiple DWs were trapped by multiple solitons under the nonlinear phase-matching 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 a low average pump power of 200 mW, only the 1st DW was obtained. This is because it was difficult for the 2nd, 3rd, and 4th DW to satisfy the nonlinear phase-matching 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.

To show the generated multiple DWs and solitons as a function of the pump wavelength, DWs and solitons at the pump wavelengths of 1400 and 2000 nm were further investigated at an average pump power of 350 mW, as shown in Fig. 5. 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. When compared with the pump wavelength of 1800 nm, the number of solitons and DWs becomes less. This is because the pump wavelength moves far away from the ZDW, making it more difficult for multiple solitons to form. Furthermore, due to the phase mismatch 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 ZDW, 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 ZDW, the prominence of other nonlinear effects covered the DWs and solitons, and rendered them unobserved. Furthermore, because the OH impurities in the tellurite glass are difficult to be removed thoroughly during the fabrication process, the output pump power becomes low at 2.8 m.

Fig. 5: Measured spectra with the average pump power of 350 mW at the pump wavelength of 1400, 1800 and 2000 nm. 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. 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 ZDW, SC spectrum from 870 to 2680 nm was obtained. Acknowledgements

Tonglei Cheng acknowledges the support of the JSPS Postdoctoral Fellowship. This work is supported by MEXT, Support Program for Forming Strategic Research Infrastructure (2011-2015) and Daiko Foundation.

References

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[5] T. L. Cheng, W. Q. Gao, M. S. Liao, Z. C. Duan, D. H. Deng, M. Matsumoto, T. Misumi, T. Suzuki, and Y. Ohishi, Tunable third-harmonic generation in a chalcogenide-tellurite hybrid optical fiber with high refractive index difference, Opt. Lett. 39, 10051007 (2014).

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