Fabrication of all-solid AsSe₂–As₂S₅ microstructured optical fiber with two zero-dispersion wavelengths for generation of mid-infrared dispersive waves

In recent years, nonlinear fibers have attracted considerable attention and have been widely used in compact nonlinear optical devices, for applications including optical switching, Raman amplification, wavelength conversion, pulse compression, and broadband supercontinuum (SC) generation.^1–5) There are several approaches for improving the nonlinear coefficients of the fibers, e.g., tapering the fibers, designing microstructured optical fibers (MOFs) with small cores, and fabricating MOFs based on soft glasses or adding metallic nanoparticles in the core.^6–12) In particular, soft-glass MOFs (tellurite, chalcogenide, and fluoride) have been extensively studied because of their wide transparency in the infrared region and high nonlinear refractive index.^13–15) In particular, chalcogenide MOFs exhibit a large transparency window and a high nonlinear material index.^16–21) Depending on the composition, the transmission range of chalcogenide MOFs spans from the visible region to the mid-infrared (MIR) region of ∼12 to 20 µm, and the nonlinear refractive index is tens or hundreds times those of fluoride and tellurite glasses.^22,23) Since Monro et al. proposed the first chalcogenide MOF,²⁴⁾ these MOFs have been applied in MIR SC generation, soliton self-frequency shift, third-harmonic generation, etc.^{20,21,25–29)} We fabricated four-hole AsSe₂–As₂S₅ MOFs for dispersive-wave (DW) generation in the near-infrared region with β₃ > 0.^10,23) However, DW generation in the MIR region with β₃ < 0 has hardly been considered.

On the other hand, all-solid MOFs with an array of isolated rods in the cladding show outstanding advantages compared with holey MOFs^30–32) and have been applied in amplifiers, lasers, tunable bandpass filters, and dispersion-compensation components.^33–35) All-solid MOFs can be divided into two classes according to the guiding mechanism: bandgap antiresonant reflecting optical waveguide MOFs and conventional total internal reflection MOFs.^36,37) Granzow et al. fabricated a hybrid chalcogenide–silica photonic bandgap fiber (PBGF) via the pressure-assisted melt-filling of molten glasses.³⁸⁾ Schmidt et al. fabricated an all-solid PBGF using tellurite and silica glass.³⁹⁾ Toupin et al. fabricated an all-solid chalcogenide MOF based on As₃₈Se₆₂ and As₂S₃ glasses,³²⁾ and Caillaud et al. fabricated an all-solid chalcogenide PBGF based on the same glasses.⁴⁰⁾ Lousteau et al. demonstrated the fabrication and optical assessment of an all-solid tellurite-glass PBGF.⁴¹⁾ Our laboratory has successfully fabricated several all-solid PBGFs.^42,43)

In this work, we first designed and fabricated an all-solid chalcogenide MOF with four rods in the cladding to generate MIR DWs. The high-index background was made of AsSe₂ glass, and the four low-index rods were made of As₂S₅ glass. The MOF was successfully fabricated by the rod-in-tube drawing technique and had two zero-dispersive wavelengths: ∼3,720 and 4,230 nm. By using a pulse of ∼80 MHz and ∼200 fs emitted from an optical parametric oscillator (OPO) as the pump source, the MIR DWs were investigated at different pump wavelengths.

The glass composition is very important for the fabrication of hybrid fibers because during the drawing process, the core and cladding should have compatible properties to avoid cracking at the interface. The compatibility between AsSe₂ and As₂S₅ glasses has been investigated and reported for the fabrication of MOFs.²³⁾ In the present work, we designed an all-solid AsSe₂–As₂S₅ MOF and obtained two zero-dispersive wavelengths in the MIR region.

The all-solid AsSe₂–As₂S₅ MOF was fabricated by the rod-in-tube drawing technique, which comprised four steps. First, a 10-cm-long AsSe₂ rod (∼12 mm diameter) was ultrasonically drilled to form a structured rod with four air holes (∼2.6 mm diameter) surrounding its center. Then, the structured AsSe₂ rod was elongated to a diameter of ∼2.8 mm, as shown in Figs. 1(a) and 1(c). Second, a 10-cm-long As₂S₅ rod (∼12 mm diameter) was elongated to a diameter of ∼0.6 mm, as shown in Figs. 1(b) and 1(d). Third, four elongated As₂S₅ rods were inserted into the four air holes of the elongated AsSe₂ rod to obtain a preform, as shown in Fig. 1(e). Finally, the preform was inserted into an AsSe₂ tube with a center-core diameter of ∼3 mm and drawn into the MOF (∼106 µm diameter) at a temperature of ∼198 °C. During the fiber-drawing process, the nitrogen gas pressure was set as negative to avoid interstitial-hole formation, and no crystallization was observed.

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Figure 2(a) shows the effective refractive index of the fundamental mode, which was calculated by using the full-vectorial mode solver of commercial software (Lumerical MODE Solution). The insets show cross sections of the all-solid AsSe₂–As₂S₅ MOF taken by an optical microscope and the fundamental mode-field profile at 2,000 nm. The AsSe₂ core was ∼3.1 µm, which was defined as the diameter of the circle inscribed in the square core. The sizes of the four As₂S₅ rods were ∼5.9–6.2 µm. An 8-m-long MOF was used to measure the loss by the cutback technique, and the loss was ∼1.9 dB/m at 2,000 nm. The nonlinear coefficient at 3,000 nm was calculated to be ∼4 × 10³ km⁻¹ W⁻¹ according to the effective mode area, A_eff = 5.76 µm², and the nonlinear index of the As₂Se₃ glass, n₂ = 1.1 × 10⁻¹⁷ m² W⁻¹.⁴⁴⁾ As shown in Fig. 2(b), the calculated chromatic dispersion of the fundamental mode exhibits two zero-dispersive wavelengths: ∼3,720 and 4,230 nm. At ∼3,970 nm, β₃ = 0. In comparison, for the AsSe₂ MOF of the same structure but with four air holes, as shown in Fig. 2(c), the chromatic dispersion curve exhibits only one zero-dispersive wavelength: ∼2,770 nm. Figure 2(d) shows the group-velocity curve of the all-solid AsSe₂–As₂S₅ MOF.

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The experimental setup for MIR DW generation in a 2-cm-long all-solid AsSe₂–As₂S₅ MOF is shown in Fig. 3. The pump source was an OPO (Coherent Inc.), with a pulse width of ∼200 fs and a repetition rate of ∼80 MHz. The pumping was performed by a Ti:sapphire laser with a wavelength of 800 nm. The idler wavelength of the OPO could be tuned from ∼1,800 to 4,000 nm, and the signal wavelength could be tuned from ∼1,000 to 1,440 nm. The output beam was linearly polarized. The pulse was coupled to the core of the MOF by a lens with a focal length of ∼5.95 mm and a numerical aperture (NA) of ∼0.56 (THORLABS C028TME-E, 3,000–5,000 nm). The transmission efficiency of the lens was higher than 90%. The output signal was butt-coupled into a 0.3-m-long large-mode-area (LMA) fluoride (ZBLAN) fiber with a core diameter of ∼105 µm and a transmission window of ∼0.4 to 6 µm. The nonlinear effect in the ZBLAN fiber was ignored owing to the large core size. Finally, the LMA ZBLAN fiber was connected to a Fourier transform infrared spectrometer to record the spectra.

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First, we used a pump wavelength of ∼3,200 nm, which was far from the first zero-dispersive wavelength of the all-solid AsSe₂–As₂S₅ MOF. The average pump power measured before the lens was ∼180 mW. For such a 2-cm-long fiber, the fiber loss can be neglected; thus, the input power was treated approximately the same as the output power measured by OSA from the output end of the MOF. The coupling efficiency was calculated to be only ∼6%. There are several possible reasons for this: 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 NA of the fiber and the lens did not match well, or the surface of the MOF was not smooth. The peak power launched into the fiber was calculated to be ∼675 W, and Fig. 4 shows the SC spectrum with the range of ∼2,200 to 4,210 nm. The spectrum broadening was dominated by the self-phase modulation (SPM) and stimulated Raman scattering (SRS) because the pump wavelength was in the normal chromatic-dispersion region. When the spectrum exceeded the first zero-dispersive wavelength (∼3,720 nm), the residual power became too low to form a soliton; thus, no soliton was observed in the anomalous dispersion regime from ∼3,720 to 4,230 nm. Then, the pump wavelength shifted gradually toward the first zero-dispersive wavelength. At a pump wavelength of ∼3,240 nm, the average pump power and peak power were ∼160 mW and ∼600 W, respectively. The main mechanism of the spectrum broadening was still dominated by the SPM and SRS. However, the residual power after the first zero-dispersive wavelength was enough to form the soliton, and the center wavelength of the soliton was ∼4,036 nm, which was in the region of β₃ < 0. Consequently, the frequency shift of the DW emitted by the soliton was negative, and the center wavelength of the DW was ∼5,033 nm, which was longer than that of the soliton. The pump wavelength was further increased to ∼3,420 and 3,460 nm, and the average pump power and peak power were kept the same as those at ∼3,240 nm. The residual powers after the first zero-dispersive wavelength increased further, and the center wavelengths of the solitons were shifted to ∼4,170 and 4,200 nm. Simultaneously, the center wavelengths of the DWs were shifted toward the short wavelength, to ∼4,930 and 4,900 nm. This experiment shows that while the center wavelength of the solitons shifted to the longer wavelength, the center wavelength of the DWs shifted to the shorter wavelength. The experimental results agree well with the group velocity curve shown in Fig. 2(d). Furthermore, the spectra decreased rapidly beyond ∼4,230 nm. There are two possible reasons for this: 1) the soliton cannot exceed the second zero-dispersive wavelength (∼4,230 nm) or 2) the absorption band induced by SeH and CO₂ around 4,300–4,600 nm.¹⁷⁾

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The nonlinear propagation process in the all-solid AsSe₂–As₂S₅ MOF at a pump wavelength of ∼3,460 nm was simulated by the generalized nonlinear Schrödinger equation (GNLSE).^2,45) The total response function R(t), including the instantaneous electronic [δ(t)] and the delayed Raman response [h_R(t)], is given as

$$\begin{equation} R(t) = (1 - f_{\text{r}})\delta(t) + f_{\text{r}}h_{\text{R}}(t). \end{equation} \tag{ 1 }$$

f_r represents the fractional contribution of the delayed Raman response, which can be calculated using the Kramers–Kroning relation:⁴⁶⁾

$$\begin{equation} f_{\text{r}} = \frac{\lambda}{2\pi^{2}n_{2}}\int_{0}^{\infty}\frac{g_{\text{R}}(f)}{f}\,df, \end{equation} \tag{ 2 }$$

where g_R(f) is the Raman gain spectrum. By taking the inverse Fourier transformation of the Raman gain and fitting it with a Lorentzian profile, we deduce the delayed Raman response h_R(t), which is expressed by Green's function for a damped harmonic oscillator:⁴⁷⁾

$$\begin{equation} h_{\text{R}}(t) = \frac{\tau_{1}^{2} + \pi_{2}^{2}}{\tau_{1}\tau_{2}^{2}}\exp \left(-\frac{t}{\tau_{2}}\right)\sin\left(\frac{t}{\tau_{1}}\right). \end{equation} \tag{ 3 }$$

Table I lists the parameters used for the simulation: the fiber length L, peak power P, pump wavelength λ, fiber loss α, nonlinear coefficient γ, pulse width T_FWHM, etc.

Figure 5 compares the experiment and simulation for the nonlinear propagation process in a 2-cm-long all-solid AsSe₂–As₂S₅ MOF at a pump wavelength of 3,460 nm and peak power of 600 W. The simulation agrees well with the experiment, especially regarding the peaks of the solitons and DWs. However, there are differences, probably arising from the following: the neglect of the absorption loss of the OH, SeH, and CO₂ contamination in the simulation process; the effect of the deviation of the simulated dispersion profile shown in Fig. 1(c) on the shape and range of the simulated SC; and the disparity between the calculated peak power in the simulation and the actual peak power in the experiment.

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In summary, we designed and fabricated an all-solid AsSe₂–As₂S₅ MOF wherein the background was made of AsSe₂ glass and four rods in the cladding were made of As₂S₅ glass. The MOF had two zero-dispersive wavelengths in the MIR region: ∼3,720 and 4,230 nm. When the all-solid AsSe₂–As₂S₅ MOF was pumped by an OPO at pump wavelengths of ∼3,240, 3,420, and 3,460 nm, solitons were observed in the β₃ < 0 region, and MIR DWs were emitted around 5,000 nm. While the center wavelength of the solitons shifted to the longer wavelength, the center wavelength of the DWs shifted to the shorter wavelength. Furthermore, the nonlinear propagation process at the pump wavelength of ∼3,460 nm was simulated by the GNLSE, and the simulation results agree well with the experiment.

Acknowledgments