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Abstract
We report a design, analysis, and numerical modeling of a tapered chalcogenide step-index fiber for broadband high-power mid-infrared supercontinuum extending from the 1.5–14.5 µm molecular ‘fingerprint region’. The reported tapered chalcogenide fiber structure is able to generate a broadband supercontinuum spectrum with output average power of 82 mW (27.7 mW for the wavelengths >5 µm) when it is pumped with 200 fs laser pulses with a repetition rate of 76 MHz and average power of 200 mW at 3.5 µm. Such a bright and broadband mid-infrared supercontinuum light source covering both the 3–5 µm and 8–13 µm atmospheric windows and most of the molecular fingerprint spectral region has practical applications in various fields, including mid-infrared spectroscopy, imaging, and biomedical diagnostics.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Light generation in the mid-infrared spectral region is particularly important for the number of potential applications including optical communications [1], optical coherence tomography (OCT) [2,3], fluorescence lifetime imaging microscopy [4], mid-infrared multispectral tissue imaging [5], frequency metrology [6], food quality control [7], spectroscopy [8,9], gas sensing [10], and early cancer diagnostics [11]. Various sorts of light sources based on solid state laser technology including quantum cascade lasers (QCLs) and optical parametric oscillator (OPOs) have been reported earlier for the creation of light in the mid-infrared region [12–14]. For most of the practical applications an intense, compact and broadband mid-infrared supercontinuum (SC) light sources are required [15–18]. Although, the QCLs offer high spatial coherence properties of SC light, but their typical tuning range is only about 100 cm−1. The mid-IR sources based on parametric oscillators require multiple lasers, which are somewhat complex, expensive to maintain.
During the last two decades SC generation in the mid-infrared region using optical fibers has emerged as a dramatic and stimulating research field. Kulkarni et al. demonstrated the SC spectrum extending from ∼1.9–4.5 µm with ∼2.6 W average output power by employing 8.5 m long ZrF4-BaF2-LaF3-AlF3-NaF (ZBLAN) glass fiber [19]. Liu et al. numerically reported a mid-infrared SC spectra extending from 2.5 to 5 µm with high output average power using a single mode fluoride fiber pumped by picosecond fiber laser at 1.56 µm [20]. Swiderski et al. reported a high power SC spectrum extending from 0.85 to 4.2 µm with average output power of 2.24 W using ZBLAN fiber pumped with 2.75 W laser power at 1.55 µm [21]. Agger et al. provided a detailed comparison between the modeling and experiments on the SC generation in ZBLAN step-index fiber [22]. Kubat et al. presented a numerical study on mid-infrared SC generation extending from 1 to 4.5 µm in a uniform and tapered ZBLAN fiber [23]. Theberge et al. showed that the spectral bandwidth of SC spectrum can be enhanced above 5 µm by using fluoroindate glass fiber [24]. The advantage of the ZBLAN and fluoroindate fibers is their low material zero dispersion wavelength which is important for anomalous dispersion pumping using commonly available laser sources [25,26]. However, it is not possible to extend the bandwidth of the SC spectrum further using ZBLAN optical fibers because of its high material loss at longer wavelengths.
The small-core suspended type fibers in tellurite glasses can be used to tailor the zero dispersion at shorter wavelengths and to enhance the nonlinearity [27–30]. However, such small core fibers are not suitable for practical applications in the high average output power due to their low coupling efficiency. Recently, Kedenburg et al. demonstrated a broadband mid-infrared SC spectrum extending from 1.3 to 5.3 µm with high output power of 150 mW using a robust step-index tellurite fibers pumped by high repetition rate femtosecond laser [31]. Even though it is possible to obtain watt level output average power using the fluoride and tellurite based optical fibers, but, the performance of these fibers is limited up to the wavelength of ∼5 µm.
In comparison to the fluoride and tellurite optical fibers, the chalcogenide (such as As2S3, As2S5, As2Se3, and AsSe2) optical fibers offer higher nonlinearity and broad transmission window [32,33]. Earlier, a lot of sincere efforts have been made by the researchers to extend the mid-infrared bandwidth of the SC spectrum using chalcogenide fibers and waveguides [34–39]. Kubat et al. reported a numerical modeling of the mid-infrared SC generation in the high numerical aperture (NA) chalcogenide step-index fiber pumped with 50 ps long laser pulses of the peak power of 4.7 kW at 4.5 µm [40]. A numerical modeling on multi-modal SC generation in chalcogenide glass fiber has been carried out by taking into account both the polarization and the necessary higher order modes [41]. Petersen et al. demonstrated mid-infrared SC spectrum covering 1.4–13.3 µm molecular fingerprint region using a chalcogenide step-index fiber [42]. Cheng et al. reported the broadest SC spectrum extending from 2–15.1 µm using a 3 cm long As2Se3 chalcogenide step-index fiber pumped with 170 fs laser pumping at 9.8 µm [43]. However, the output average power from the above mentioned fibers was very low. Therefore, there is a trade-off between spectral broadening and the high average output power of an SC spectrum. Recently, Zhang et al. demonstrated the broadest SC spectrum expending from 2.2–12 µm with an output average power of 17 mW using a small core chalcogenide glass step-index fiber [44]. The small-core diameter of this fiber reduces the coupling efficiency and the pump power damage threshold of the fiber end-facet. More recently, Petersen et al. addressed the challenge of the trade-off between broadband SC spectrum and its average output power by proving a tapered large-mode-area chalcogenide photonic crystal fiber [45]. The highest average output power of 57.3 mW (35.4 mW) covering a spectral bandwidth from 1–8 µm (1–11.5 µm) has been reported using a tapered photonic crystal fibers pumped by high repetition rate optical parametric generation source with an average power of 231 mW at 4 µm [45]. However, tapering of a photonic crystal fiber requires complex system and expertise to confirm the design integrity and the degree of air hole collapse in the cladding region. Further, large diffusion surface of the glass in a photonic crystal fiber structure results in the accumulation of undesirable O-H defects and absorption of the evanescent field.
Moller et al. reported a review on the state-of-the-art in fiber tapers and concluded that the tapering of the photonic crystal fibers is an effective way to blue shift the visible part of the spectrum [46]. Sorensenet et al. showed that the gradient of the taper has a high impact on the available power at the blue edge and explained this effect by the concept of the group-acceleration mismatch [47,48]. It has been verified that the noise at the spectral edge of generated SC is independent on the pump power in uniform as well as tapered fiber [49]. Very recently, it has been demonstrated that the current SC sources can match the brightness of a synchrotron from visible to 10.6 µm and it is expected that the SC sources would be able to cover all the spectral region (2–12.5 µm) that is key importance in the mid-IR applications including IR spectroscopy and microscopy [50]. From the measurement point of view, it is worthwhile to mentioned here that the Fresnel loss can be reduced significantly by nanoimprinting of the fiber end facet [51].
In this work, we report the design, analysis and numerical modeling of a tapered chalcogenide step-index optical fiber for the broadband mid-infrared SC spectrum with high average output power. The average power of the SC spectrum is distributing well towards the longer wavelengths region. Using appropriate input pulse and fiber geometrical parameters a mid-infrared SC spectrum spanning 1.5–14.5 µm with an average output power of 82 mW (27.7 mW for the wavelength > 5 µm) is obtained. Such broadband high power mid-infrared SC sources are extremely applicable for the practical applications in diverse fields such as high resolution mid-infrared spectroscopy, gas sensing, food quality control and bio-photonic diagnostics. This paper is organized in five sections. Section-I provides a brief introduction and overview of the previous works on the high power SC generation in optical fibers. Section-II explains the design of the proposed tapered chalcogenide step-index optical fiber. In section-III, detailed description of the method of analysis is provided. Section-IV is committed to the results and discussion. Finally, the conclusion of this work is summarized in the Section-V.
2. Design of the tapered chalcogenide fiber
We present a design of the tapered chalcogenide step-index optical fiber with AsSe2 as a core and As2S5 as a cladding materials. As shown in Fig. 1, the core diameters at the input and output ends are represented by d1 and d2, respectively. The fiber has three parts longitudinally. The first part is uniform having large-core diameter of d1 µm. The second part is a tapered region with successive decreasing core size from d1 µm to d2 µm. The third region is uniform with fixed core diameter of d2 µm. The length of the first uniform region is denoted by L1. The length of the tapered region is given by L2, and L represents the total length of the fiber. To improve the broadening of SC spectrum towards longer wavelengths, it is better to keep the first uniform region short [45]. Keeping this in mind, the geometrical parameters of the tapered step-index fiber has been optimized for broadband SC spectra with high average output power. The numerical values of the optimized geometrical parameters of the reported tapered fiber structure are given in Table 1. The input pump properties also significantly affect the characteristic of the output SC spectrum. It is verified that the pump source with high repetition rate is desirable to obtain high output average power of broadband SC spectrum [4,9]. The numerical values of the pulse parameters of the input laser used in this work are provided in Table 2.
Fig. 1. The schematic of the longitudinal cross-section of the designed tapered chalcogenide optical fiber with AsSe2 glass as a core and As2S5 glass as a cladding materials.
Table 1. The geometrical parameters of the proposed tapered chalcogenide optical fiber
Table 2. Input pulse parameters
3. Method of analysis
3.1 Linear properties of the fiber
To calculate the effective indices of the fundamental mode propagating through the fiber, a full vectorial finite-element-method (FEM) based software ‘COMSOL Multiphysics’ was employed. The wavelength dependent refractive indices of the AsSe2 and As2S5 chalcogenide materials were fitted using the following Sellmeier equation [52]
The Sellmeier coefficients are given in the Table 3.Table 3. The Sellmeier coefficients
In the broadening of SC spectrum, the group velocity dispersion plays a vital role because it determines the degree to which different spectral components of the ultra-short pulse propagate at different phase velocities through the fiber. The group velocity dispersion is related to the wavelength dependent effective-indices of the propagating mode according to the following equation [53]
The effective-mode-area of the propagating mode in the fiber geometry is calculated by the relation [53]
3.2 Nonlinear properties of the fiber
The following hyperbolic secant pulse is considered as an input pulse in the simulation
The spectrum of the SC generated in the tapered chalcogenide step-index optical fiber was calculated using the generalized nonlinear Schrodinger equation [54]
The change of the variables is shown as
The Raman response function is given by the relation
4. Results and discussion
The step-index fiber has a core made up of AsSe2 and a cladding made up of the As2S5 chalcogenide glasses. Figure 2 represents the spectral variation of the material refractive indices of both the glasses. The calculated NA and the difference in the refractive indices of the core and cladding of the step-index fiber is shown in Fig. 3. The difference between the refractive indices of the core and cladding glasses is about 0.46 with NA of 1.51 at 3.5 µm.
Fig. 3. The wavelength dependence of the numerical aperture (NA) of the fiber and the refractive index difference (Δn) of AsSe2 and As2S5 chalcogenide glasses.
The material loss of the AsSe2 glass is shown in Fig. 4. The small absorption peak around 2.9 µm is corresponding to the OH impurity in AsSe2 glass, while the absorption peak around 12.7 µm originating from Se-OH bonds [56]. The simulated confinement loss of the propagating fundamental mode of the fiber with the core diameters of 3 µm and 15 µm is shown in Fig. 5. The confinement loss for the fundamental mode is very small for the fibers with core diameters of 3 µm and 15 µm.
Fig. 5. The confinement loss of fundamental mode of the fiber with core diameter of (a) 3 µm; and (b) 15 µm.
As illustrated in Fig. 6, the chromatic dispersion of the fundamental mode was calculated for various core diameters of the step-index fiber. When the core size is < 7 µm, the fiber possesses two zero dispersion wavelengths. When the diameter of the core is 7 µm or larger, the fiber exhibit only one zero dispersion wavelength. With increasing the core diameter, the first zero dispersion wavelength increases. Figure 7 depicts the zero dispersion wavelengths for various core diameters of the step-index fiber. From Fig. 7 it is clear that the first zero dispersion wavelength of fiber can be varied from 3.02 µm to 5.19 µm by changing the core diameter of the fiber within the range of 3 µm – 15 µm. The wavelength dependent effective-mode-area of the fundamental mode and corresponding nonlinear coefficients of the fiber are shown in Fig. 8 and Fig. 9, respectively. Simulated results indicate that the effective-mode-area of the fundamental mode varies from 5.32 µm2 to 91.30 µm2 at the pump wavelength of 3.5 µm when core size increases from 3 µm to 15 µm. The corresponding nonlinear coefficient at 3.5 µm decreases from 1755.0 W−1×km−1 to 102.2 W−1×km−1.
Fig. 6. The chromatic dispersion profile of the chalcogenide fiber for the core diameters from 3 µm to 15 µm.
Fig. 8. The variations of the effective-mode-area of the fundamental modes with various core diameters of the fiber varying from 3 µm to 15 µm.
Fig. 9. The variations in the nonlinear coefficient of the fibers with core diameters varying from 3 µm to 15 µm.
Figure 10 demonstrates the evolution of the SC spectrum along the 4 cm long tapered step-index fiber with d1 = 15 µm, d2 = 3 µm, L1 = 1 cm, and L2 = 2 cm. For pumping, we considered a hyperbolic secant pulse of the width of 200 fs with high repetition rate of 76 MHz and an average power of 200 mW at 3.5 µm. In the initial stage of pulse propagation, the spectrum exhibits approximately symmetric spectral broadening due to the self-phase modulation (SPM). After the propagation of about 2.5 cm fiber segment, spectrum experiences a significant spectral broadening with the expansion of distinctive spectral peaks on the short and long wavelength sides of the pump due to the dispersive wave generation. Within the 3 cm length of the tapered fiber the maximum broadening in the SC spectrum is achieved and no further broadening is observed after 3 cm length. Further propagation along the fiber results in increased flatness of the SC spectrum.
Fig. 10. The evolution of the SC spectrum along the 4 cm long tapered fiber with d1=15 µm, d2=3 µm, L1=1 cm, and L2=2 cm.
The broadening of the SC spectrum at the output of the 4 cm long tapered step-index fiber is shown in Fig. 11. The spectral broadening from 1.5 to 14.5 µm has been obtained at −30 dB level with an average output power of 82 mW. Such high power SC broadening is achieved when the tapered step-index fiber is pumped with 200 fs laser pulses of an average power of 200 mW and repetition rate of 76 MHz at 3.5 µm. Clearly, the generated SC spectrum contains both the important atmospheric windows i.e. 3–5 µm and 8–13 µm and most molecular ‘fingerprint regions’. To better visualize the process of SC generation along the fiber length, the spectrograms at various length of the tapered fiber has been illustrated in Fig. 12. Initially, the spectral broadening is dominated by the phenomena of SPM and optical wave breaking (OWB). At 2 cm length of the tapered fiber the SC spectrum crosses the first zero dispersion wavelength and the spectral energy start to transfer to the anomalous dispersion regime. At propagation length of 3 cm, there is a completed spectral broadening achieved at both the short and long wavelength sides. No additional spectral broadening has been observed on further propagation.
Fig. 11. The spectral broadening of the SC spectrum at the output of 4 cm long tapered fiber with d1=15 µm, d2=3 µm, L1=1 cm, and L2=2 cm.
Fig. 12. The spectrograms at the various lengths of the chalcogenide tapered fiber with d1=15 µm, d2=3 µm, L1=1 cm, and L2=2 cm. white dotted lines indicates the zero dispersion wavelengths.
While performing experiment there are coupling losses, so ultimately the launched power would be reduced. We have simulated the fiber structure for various input average powers to see the effect of spectral broadening and the output average power. The effect of the input average power on the spectral broadening of SC spectrum and corresponding output average power from 4 cm long tapered chalcogenide fiber have been illustrated in Fig. 13. The average output power of generated SC spectrum for the input average power of 200 mW, 150 mW, and 100 mW is 82 mW, 48.4 mW, and 36 mW, respectively. Finally, the comparison of the average output power of SC spectrum generating from the 4 cm long tapered fiber with various core diameters is shown in Fig. 14. The variation of the total average output power of entire generated SC spectrum with fiber length is shown in Fig. 14(a), while the average output power of generated SC spectrum for the wavelengths greater than 5 µm is depicted in Fig. 14(b). It is to be noted that after the propagation of 2 cm, the average output power of the spectrum for wavelengths greater than 5 µm increases rapidly. However, there is a small decay in the average output power after 3 cm length of the fiber because of the propagation loss. Indeed, the response of the fiber with the core diameter of 15 µm is better in terms of the higher average output power at longer wavelengths. For the pump average power of 200 mW, a total average output power of 82 mW, with 27.7 mW power distribution for the wavelengths greater than 5 µm, is obtained for the first time using a 4 cm long tapered chalcogenide step-index fiber.
Fig. 13. The effect of input average power on the spectral broadening of the generated SC spectrum from the tapered fiber.
Fig. 14. The comparison of the average output power of the tapered fiber with d1=9, 12, & 15 µm; (a) the total average output power along the fiber length; (b) Average output power at the wavelengths >5 µm along the fiber length.
5. Conclusions
In summary, we report the design of a tapered chalcogenide step-index optical fiber for the broadband SC spectrum extending from 1.5 to 14.5 µm at −30 dB level with an output average power of 82 mW. Such bright and broadband mid-infrared spectrum is obtained by launching the 200 fs laser pulses with an average power of 200 mW into a short length (i.e. 4 cm) of step-index tapered chalcogenide optical fiber. The results of the numerical modeling confirm that the SC power is efficiently distributed in such a way that it provides better power of 27.7 mW at the wavelengths larger than 5 µm. Apparently, this type of tapered chalcogenide step-index optical fiber offering broadband SC spectrum covering both the atmospheric windows, i.e. 3–5 µm and 8–13 µm with high average power can be a good candidate for various important applications including high resolution mid-infrared spectroscopy, gas sensing, food quality control and bio-photonic diagnostics.
Funding
Japan Society for the Promotion of Science (JSPS) (15H02250, 17K18891, 18H01504).
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