Efficient mid-infrared dispersive wave generation through soliton breakup and cascaded Raman amplification in an axially varying fluorotellurite fiber

Linghao Cui; Zhixu Jia; Zhixu Jia; Xiaohui Guo; Yadong Jiao; Yasutake Ohishi; Weiping Qin; Guanshi Qin; Guanshi Qin

doi:10.1364/OME.498793

1. Introduction

In recent years, dispersive wave (DW) generation in optical fibers or waveguides has been widely investigated for constructing coherent mid-infrared (MIR) light sources, which have numerous applications in many fields, such as molecular spectroscopy, biomedicine, hyperspectral microscopy, defense and security [1–7]. DWs are emitted by temporal solitons propagating in the vicinity of a zero-dispersion wavelength in an optical fiber or waveguide via the process of soliton Cherenkov radiation, due to the presence of higher-order dispersion [8,9]. The DW is generated at a lower (or higher) frequency than the soliton if the third-order dispersion (TOD) term is negative (or positive), which results in the spectral recoil of the soliton toward higher (or lower) frequencies as a consequence of the momentum conservation [10–12]. Therefore, red-shifted DWs at a lower frequency (e.g., MIR region) than the soliton can be generated in dispersion-engineered optical fibers or waveguides with negative TOD. Moreover, since DWs are emitted at the normal dispersion region of optical fibers or waveguides, coherent broadband supercontinuum light could be obtained based on the red-shifted DW generation, which is required for many applications, such as the construction of MIR frequency combs [13]. In 2011, Dekker et al. reported red-shifted DWs generation at 2.04 µm in a silica-core microstructured fiber with low OH^- loss [14]. Whereas, limited by the intrinsic absorption loss of the silica glass, silica-core optical fibers are not suitable for generating red-shifted DWs in the MIR spectral region (> 2.5 µm) [15].

Recently, several types of MIR fibers and waveguides (e.g. fluoride and fluorotellurite glass fibers, hollow-core fibers, chalcogenide glass waveguides, Si₃N₄ waveguides) have been developed for generating MIR DWs [13,16–21]. In 2009, Chen et al. proposed to obtain DW generation from 2 to 3 µm in a tapered fluoride fiber through numerical simulations [16]. In 2016, Yao et al. reported tunable MIR DW generation from 2680 to 2725 nm in a homemade birefringent fluorotellurite microstructured fiber pumped by a 1560 nm femtosecond fiber laser [17]. Xie et al. reported MIR DW generation at 4.7 µm in an As₂S₃-silica double-nanospike waveguide pumped by a 2.35 µm femtosecond laser [18]. In 2017, Köttig et al. demonstrated MIR DW generation from 3.3 to 4 µm via transient ionization-induced dispersion changes in an argon-filled kagomé-type anti-resonant reflection hollow-core fiber pumped by a 1.03 µm femtosecond laser [19]. In 2018, Guo et al. reported MIR frequency comb via coherent DW generation in Si₃N₄ nanophotonic waveguides and obtained DW generation from 2.5 to 4 µm in the waveguides pumped by a 1.55 µm femtosecond fiber laser [13]. In 2019, H Ahmad et al. numerically demonstrate MIR DW generation at 6.2 µm in a Si₃N₄ waveguide pumped by a 1.55 µm femtosecond laser [20]. In 2022, M R Karim et al. proposed coherent MIR supercontinuum light via DW generation in CMOS compatible Si-Rich SiN tapered waveguide and obtained DW generation from 3.95 to 7 µm in the waveguide pumped by a 1.55 µm femtosecond laser [21]. However, in previous works, the obtained conversion efficiency of MIR light sources via DW generation is quite low. Therefore, it is necessary to explore novel dispersion-engineered MIR fibers for improving the conversion efficiency of MIR light sources via DW generation.

In this paper, we reported efficient MIR DW generation at 2.7 µm through soliton breakup and cascaded Raman amplification in an axially varying fluorotellurite fiber pumped by a 1.98 µm femtosecond fiber laser. The input part of the fabricated fluorotellurite fiber had two zero-dispersion wavelengths and the remaining part had an all normal dispersion profile. The operating wavelength of the pump laser was located at the anomalous dispersion region between two zero-dispersion wavelengths (ZDWs) and close to the second ZDW. As the pump light (or a higher-order soliton) was launched into the fluorotellurite fiber, the occurrence of soliton breakup enabled nearly complete conversion of input solitonic radiation into resonant nonsolitonic radiation in the DW regime. Furthermore, the generated DWs were improved by more than two orders of magnitude via cascaded Raman amplification in the fluorotellurite fiber, causing the generation of efficient MIR DWs peaked at 2700 nm with an ultrahigh power division ratio of ∼ 85% and a compressible pulse width of ∼ 61 fs.

2. Experiments and results

Fluorotellurite fiber preforms were fabricated by using rod-in-tube method [22]. The core and cladding materials of fluorotellurite fiber preforms were TeO₂-BaF₂-Y₂O₃ (TBY) and AlF₃-based glasses with good water resistance and high transition temperature [23,24], respectively. Axially varying fluorotellurite fibers were fabricated by using a homemade elongation machine, which was similar to that mentioned in our previous work [22]. The inset of Fig. 1(a) shows the cross section of the above fluorotellurite fiber. By controlling the elongation speed, axially varying fluorotellurite fibers with varied transition regions were prepared. An axially varying fluorotellurite fiber with a transition region length of ∼ 3 m was chosen for generating efficient MIR DWs. Figure 1(a) shows the schematic diagram of the axially varying fluorotellurite fiber. The core diameter of the axially varying fluorotellurite fiber was calculated from the outer diameter of the fiber by using the fixed ratio between them, and the core diameter decreased gradually from 1.64 to 0.9 µm, as shown in Fig. 1(b). Table 1 lists out the first and second ZDWs for the segments with a core diameter of 1.64, 1.6, 1.5, 1.4, 1.3 and 1.2 µm. Figure 1(c) shows the calculated group velocity dispersion (GVD) curves of the fundamental propagation mode in the transition region at the segments with a core diameter of 1.64, 1.6, 1.5, 1.4, 1.3, 1.2, 1.1, 1.0 and 0.9 µm. Figure 1(d) gives out an expanded view of the GVD curves with y-axis ranging from −150 to 500 ps²/km. Figure 1(e) shows the nonlinear coefficients at 1980nm for different core diameters. The nonlinear coefficients for the above segments were 539, 553, 593, 632, 668, 689, 703, 721 and 745 km⁻¹W⁻¹, respectively, which were calculated by using the expression [25]:

(1)$$\gamma = {\raise0.7ex\hbox{${{n_2}\omega }$} \!\mathord{/ {\vphantom {{{n_2}\omega } {c{A_{eff}}}}} }\!\lower0.7ex\hbox{${c{A_{eff}}}$}}$$

where ω is the frequency, c is the speed of light, A_eff is effective mode area. The nonlinear refractive index n₂ is 3.5 × 10⁻¹⁹ m²W⁻¹ for fluorotellurite glasses [26].

Fig. 1. (a) Schematic diagram of the axially varying fluorotellurite fiber. Inset: scanning electron micrograph of the above fluorotellurite fiber. (b) Dependence of the core diameter of the axially varying fluorotellurite fiber on the position of the fiber. (c) Calculated GVD curves, (d) expanded view of the GVD curves with y-axis ranging from −150 to 500 ps²/km, and (e) calculated nonlinear coefficients at 1980nm for fluorotellurite fibers with different core diameters.

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Table 1. ZDWs for fluorotellurite fibers with different core diameters.

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We consider that, by using the above axially varying fluorotellurite fiber as the nonlinear medium and the 1.98 µm femtosecond fiber laser as the pump source, the pump light (or a higher-order soliton) could experience a temporal breakup and nearly all of its energy could be converted to red-shifted DWs in the MIR spectral region via the process of soliton Cherenkov radiation, since the pumping-wavelength is located at the anomalous dispersion region between two ZDWs and close to the second ZDW of the input part (with a core diameter of ∼ 1.64 µm) of the above fluorotellurite fiber. Meanwhile, the pump light and the generated DWs could experience large pulse broadening in time domain, the generated DWs could be improved very much via cascaded Raman amplification, since the remaining part (with a core diameter of less than 1.2 µm) of the fluorotellurite fiber has an all normal dispersion profile and the nonlinear coefficient (or the Raman gain coefficient) gradually increases with the position of the fluorotellurite fiber (shown in Fig. 1). Therefore, efficient MIR DWs could be generated in the above axially varying fluorotellurite fiber pumped by the 1.98 µm femtosecond fiber laser.

To clarify the potential of the above axially varying fluorotellurite fiber for generating efficient MIR DWs, we performed the following experiments and the experimental setup was shown in Fig. 2. A homemade 1.98 µm femtosecond fiber laser with a pulse width of ∼ 300 fs and a repetition rate of ∼ 50 MHz was used as the pump source. The above axially varying fluorotellurite fiber was used as the nonlinear medium. The pump light was launched into the above axially varying fluorotellurite fiber by using a couple of aspheric lens. The corresponding launched efficiency was measured to be about 20%. The output signals were monitored by using an optical spectrum analyzer (OSA) with a measurement range of 1200–2400 nm or 1900–5500 nm (Yokogawa).

Fig. 2. Experimental setup for efficient MIR DW generation (OSA: optical spectrum analyzer).

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Figure 3(a) shows the dependence of the measured output spectra from the above axially varying fluorotellurite fiber on the launched average power of the 1.98 µm femtosecond fiber laser. With increasing the average pump power to 50 mW, large spectral broadening occurred and the long wavelength edge of the output spectrum was expanded to 2200 nm. Since the pumping wavelength (∼ 1.98 µm) was located at the anomalous dispersion region between two ZDWs and close to the second ZDW of the input part of the above fluorotellurite fiber, the spectral broadening for a pump power of > 50 mW might be mainly caused by self-phase modulation (SPM), the formation of higher-order soliton, soliton fission, soliton self-frequency shift cancellation (SSFSC), and the generation of broadband red-shifted DWs seeded by the solitons (annihilated finally). Interestingly, as the average pump power was increased to over 150 mW, the generated DWs at 2340 nm were improved evidently, accompanying with the spectral broadening in the short wavelength region (< 1.9 µm). For an average pump power of ∼ 250 mW, the long wavelength edge of the output spectrum was expanded to 2552 nm, and the short wavelength edge was expanded to 1589 nm. Since the pump light and the generated red-shifted DWs experience large pulse broadening in time domain in the part with an all normal dispersion profile of the fluorotellurite fiber and the Raman gain coefficient gradually increases with the position of the fluorotellurite fiber (shown in Fig. 1), efficient Raman amplification could occur at the wavelength which is located near the largest peak of the Raman gain coefficient profile of the TBY glass (corresponding to a Raman shift of 785 cm⁻¹) [27]. Therefore, the improvement of the red-shifted DW at 2340 nm might be caused by efficient Raman amplification at 2340 nm for 1.98 µm pumping, and the spectral broadening in the short wavelength region (< 1.9 µm) was caused by anti-Stokes Raman scattering. With further increasing the average pump power to over 250 mW, the red-shifted DW at 2340 nm became stronger and stronger, accompanying with large spectral broadening of the DW at 2340 nm. As expected, as the long wavelength edge of the red-shifted DW was larger than 2500 nm, which was located near the second largest peak of the Raman gain coefficient profile of the TBY glass (corresponding to a Raman shift of 400 cm⁻¹) [27], second-order Raman amplification became efficient, causing the amplification of the DW at 2700 nm. For an average pump power of ∼ 500 mW, efficient MIR DW at 2700 nm was generated via cascaded Raman amplification, the long wavelength edge of the output spectrum was expanded to 3065 nm, and the short wavelength edge was expanded to 1080 nm. The peak at ∼ 1651 and 1423 nm could be ascribed to the first and second-order anti-Stokes Raman scattering, respectively. Figure 4 shows the measured output spectrum (in a linear scale) for an average pump power of ∼ 500 mW. The corresponding power division ratio (> 2500 nm) for the efficient MIR DW in the whole spectrum was calculated to be 85%. Those results showed that the above axially varying fluorotellurite fibers could be used for generating efficient MIR DWs with an ultrahigh power division ratio of 85%.

Fig. 3. (a) Dependence of the measured output spectra from the axially varying fluorotellurite fiber on the launched average power of the 1.98 µm femtosecond fiber laser (the pump power from bottom to top is 10, 50, 100, 150, 200, 250, 300, 350, 400, 450 and 500 mW, respectively). (b) Simulated (the dashed black and blue curve) and the measured (the solid red curve) spectra output from the axially varying fluorotellurite fiber for a same average pump power of ∼ 500 mW.

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Fig. 4. Measured output spectrum in a linear scale for an average pump power of ∼ 500 mW.

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To verify the mechanism for the generation of the efficient MIR DW at 2700 nm, we performed numerical simulations by solving the generalized nonlinear Schrödinger equations [25]:

(2)$$\frac{{\partial A}}{{\partial z}} + \frac{1}{2}\alpha A - i\sum\limits_{n = 1}^\infty {\frac{{{i^n}{\beta _n}}}{{n!}}\frac{{{\partial ^n}A}}{{\partial {t^n}}}} = i\left( {\gamma ({\omega_0}) + i{\gamma_1}\frac{\partial }{{\partial t}}} \right)\left( {A(z,t)\int_0^\infty {R(t^{\prime}){{|{A(z,t - t^{\prime})} |}^2}d} t^{\prime}} \right)$$

where A is amplitude, α is the fiber loss (0.6 dB/m used in the simulation), β is propagation constant, ω₀ is the center frequency of the input pulse.

The nonlinear response function R(t) can be expressed by [25]:

(3)$$R(t) = (1 - {f_R})\delta (t) + {f_R}{h_R}(t)$$

(4)$${h_R}(t) = (\tau _1^{ - 2} + \textrm{ }\tau _2^{ - 2}){\tau _1}exp( - t/{\tau _2})sin(t/{\tau _1})$$

where f_R is the fractional contribution of the delayed Raman response to nonlinear polarization (0.064), τ₁ and τ₂ are the damping time of vibrations.

A split-step Fourier method was used to solve the nonlinear Schrödinger equation [25]. In the Fourier domain, the sum in Eq. (2) can be replaced by

(5)$$\sum\limits_{n = 2}^\infty {\frac{{{\beta _n}}}{{n!}}} {({\omega - {\omega_0}} )^n}\mathop A\limits^\sim{=} [{\beta (\omega )- \beta ({{\omega_0}} )- {\beta_1}(\omega )({\omega - {\omega_0}} )} ]\mathop A\limits^\sim $$

In the simulations, the axially varying fluorotellurite fiber was divided to serval segments, and the calculation was performed segment by segment with decreased core diameter along the fiber length. We took the parameters of the above axially varying fluorotellurite fiber. The calculated GVD curves shown in Fig. 1(c); the calculated nonlinear coefficients; and an unchirped pump laser with an operating wavelength of ∼ 1.98 µm, a pulse width of ∼ 300 fs, and a repetition rate of 50 MHz; the one-photon-per-mode model for representing input noise; and the Raman response function derived from the Raman gain spectrum of fluorotellurite glass [26]. Figure 3(b) shows a comparison of the simulated (the dashed black curve) and the measured (the solid red curve) spectra output from the above axially varying fluorotellurite fiber for a same average pump power of ∼ 500 mW. The simulated result agreed with the measured one, which indicated that the parameters used in the simulations were appropriate. Figures 5(a) and 5(b) show the measured (re-plotted from the data shown in Fig. 3(a)) and simulated spectral evolution of output signals from the above axially varying fluorotellurite fiber with the launched average power of the 1.98 µm femtosecond fiber laser, respectively. Figure 5(c) shows the simulated temporal evolution of output signals from the fluorotellurite fiber with the launched average power of the 1.98 µm femtosecond fiber laser. It was shown that, with gradually increasing the average pump power to 50 mW, high-order soliton was generated from the fluorotellurite fiber since the pumping wavelength (∼ 1.98 µm) was located at the anomalous dispersion region between two ZDWs of the fiber. With increasing the average pump power to over 50 mW, the long wavelength edge of the generated high-order soliton exceeded the second ZDW and red-shifted DWs were generated via the process of soliton Cherenkov radiation. Interestingly, in temporal domain (shown in Fig. 5(c)), the generated DWs traveled faster than all other spectral components since the TOD term at the pumping wavelength of the fiber was negative. With further increasing the average pump power to over 450 mW, the generated DWs were improved by cascaded Raman amplification, causing the generation of efficient MIR DW at 2700 nm. In temporal domain, the pump light and the generated red-shifted DWs experienced large pulse broadening (shown in Fig. 5(c)), which made cascaded Raman amplification become possible. The simulated spectral evolution with the average pump power agreed with the measured results (shown in Fig. 5(a)). We also performed numerical simulations without considering the effect of cascaded Raman gain for an average pump power of ∼ 500 mW, and the calculated result was shown in Fig. 3(b) (the dashed blue curve). The corresponding power division ratio (>2500 nm) for the MIR DW in the whole spectrum was calculated to be 62.7% (much lower than that obtained in our above experiments). The results further confirmed that the generated DWs were effectively amplified by cascaded Raman scattering in the fluorotellurite fibers, and resulted in the generation of efficient mid-infrared DWs peaked at 2700 nm.

Fig. 5. (a), (b) Measured and simulated spectral evolution (c) Simulated temporal evolution of output signals from the fluorotellurite fiber with the launched average power of the 1.98 µm femtosecond fiber laser, respectively.

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To further demonstrate the mechanism for the generation of the efficient MIR DW at 2700 nm, as discussed in [9], we investigated the spectral evolution over propagation distance in the axially varying fluorotellurite fiber for a fixed pump power of ∼ 500 mW at 1.98 µm, as shown in Fig. 6(a). As expected, broadband MIR DW generation was achieved within the initial 0.3 m long fiber. With further propagation of the generated signals inside the fluorotellurite fiber from 0.3 to 2 m, attributing to the normal dispersion profile of the fiber, the pulse widths would be broadened and the Raman amplification would become the dominant effect, which resulted in the intensity improvement of the red-shifted DW at 2340 nm (corresponding to a Raman shift of ∼785 cm⁻¹ for 1.98 µm pumping). With further propagation inside the above fluorotellurite fiber from 2 to 3 m, the red-shifted DW at 2340 nm became stronger and stronger, accompanying with large spectral broadening. As the long wavelength edge of the red-shifted DW was larger than 2500 nm, second-order Raman amplification would become efficient, resulting in the generation of efficient MIR DW at 2700 nm (corresponding to a Raman shift of ∼400 cm⁻¹ for 2340 nm pumping). The emission peaked at 1651 nm could be ascribed to first-order anti-stokes Raman scattering. The corresponding simulated spectral and temporal evolutions (as shown in Figs. 6(b) and 6(c)) confirmed the above interpretations.

Fig. 6. (a), (b) Measured and simulated spectral evolution over propagation distance in the axially varying fluorotellurite fiber for a fixed pump power of ∼ 500 mW. (c) Corresponding numerical temporal evolution of the generated signals.

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Figure 7(a) shows the measured output spectra from fluorotellurite fibers with different core diameters pumped by the same ∼ 1.98 µm femtosecond fiber laser. With the decrease of core diameter from 1.64 to 1.61 µm, the central wavelength of the generated red-shifted DW changed gradually from 2.64 to 2.34 µm. In addition, we calculated the theoretical central wavelength of the red-shifted DW by using the phase matching (PM) equation [11,12]:

(6)$$\sum\limits_{n \ge 2}^\infty {\frac{{{{({\omega _D} - {\omega _S})}^n}}}{{n!}}} {\beta _n}({\omega _S}) = \frac{1}{2}\gamma {P_S}$$

where ω_D and ω_S are frequencies of the dispersive wave and the soliton, respectively. β_n(ω_S) is the n-th order derivative of the propagation parameter β at the soliton wavelength, P_S is the peak power of the soliton, and γ is the nonlinear coefficient. Figure 7(b) shows the dependence of the wavelength of the DW on core diameter. The second ZDWs shifts over fiber length, which makes the spectral location of the DW change over length. The wavelength of the red-shift DWs for the segments of 1.64, 1.63, 1.62 and 1.61 µm were 2.64, 2.56, 2.46 and 2.34 µm, respectively. The experiment results agreed with the calculated results.

Fig. 7. (a) Measured output spectra from fluorotellurite fibers with different core diameters pumped by the same 1.98 µm femtosecond fiber lase (the core diameter from bottom to top is 1.64, 1.63, 1.62 and 1.61µm, respectively). (b) Calculated DW central wavelength for fluorotellurite fibers with different core diameters.

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In addition, the modulus of the complex degree of first-order coherence of the efficient mid-infrared DWs was calculated. Figure 8 showed the corresponding simulated coherence of the spectrum for a pump power of ∼ 500 mW. The results showed that the modulus of the complex degree of coherence in the spectral region was nearly 1 and coherent MIR DW was generated. By considering second-order dispersion compensation via a simple grating or a prism pair, we performed numerical simulations on pulse compression of the efficient MIR DW at 2700 nm. Figure 9(a) shows the output pulse profile of the efficient MIR DW at 2700 nm generated from the axially varying fluorotellurite fiber. It exhibits a pulse duration of ∼ 51 ps, the slope of the chirp is 20/300 THz/ps. For a linear chirped pulse, the pulse width can be compressed by using a second-order dispersion compensation method [25]:

(7)$$\frac{{{T_1}}}{{{T_0}}} = {\left[ {{{\left( {1 + \frac{{C{\beta_2}}}{{T_0^2}}} \right)}^2} + {{\left( {\frac{{{\beta_2}}}{{T_0^2}}} \right)}^2}} \right]^{1/2}}$$

where T₀ and T₁ are the pulse widths before and after compression, C is the chirp parameter, β₂ is the total second-order dispersion of the compressor. In this case, the pulse duration of the generated MIR DW at 2700 nm can be compressed to ∼ 61 fs (as shown in Fig. 8(b)) for a β₂ value of −195 ps², which can be provided via a simple grating or a prism pair [28,29]. In the future, we will try to measure the pulse profiles of the generated MIR DW in experiment.

Fig. 8. Simulated modulus of the complex degree of coherence of the spectrum for a pump power of ∼ 500 mW.

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Fig. 9. Pulse and chirp profiles of the efficient MIR DW at 2700 nm (a) before and (b) after compression.

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3. Conclusions

In summary, we demonstrated the generation of efficient MIR DWs peaked at 2700 nm with an ultrahigh power division ratio of ∼ 85% and a compressible pulse width of ∼ 61 fs in the axially varying fluorotellurite fiber pumped by a 1.98 µm femtosecond fiber laser. Efficient MIR DWs were generated via soliton breakup and cascaded Raman amplification. Our work presented a way to realize ultrahigh-efficiency MIR coherent light generation.

Funding

National Natural Science Foundation of China ( 62090063, 62075082, U20A20210, 61827821,U22A2085, 62235014, 62205121); the Opened Fund of the State Key Laboratory on Integrated Optoelectronics.

Disclosures

The authors declare no conflicts of interest.

Data availability

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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Core diameter (µm)	1.64	1.6	1.5	1.4	1.3	1.2
The first ZDW (µm)	1.192	1.19	1.185	1.18	1.173	1.158
The second ZDW(µm)	2.096	2.033	1.876	1.655	1.547	1.348

Efficient mid-infrared dispersive wave generation through soliton breakup and cascaded Raman amplification in an axially varying fluorotellurite fiber

Abstract

1. Introduction

2. Experiments and results

3. Conclusions

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (1)

Equations (7)

Optical Materials Express