1. Introduction

Nonsilica-based infrared optical fibers have attracted much attention as novel transmission media in the infrared wavelength region. They were fabricated in the early 1960's for imaging-bundles, infrared remote sensors, and so on, and these had losses of typically 20,000 dB/km [1]. However, though rapid advances have been made in the development of low attenuation silica-based optical fibers since the announcement in 1970 of a 20 dB/km silica based optical fiber [2], no remarkable progress was made in the development of nonsilica-based infrared fibers. In 1979, a low loss silica fiber with a minimum loss of 0.2 dB/km was successfully fabricated [3]. Then it was widely thought that the ultimate intrinsic loss of optical fiber was achieved. Through the progress in silica-based fiber fabrication technique, it was clarified that the intrinsic optical attenuation in silica-based fibers originates from Rayleigh scattering, infrared absorption edge, and ultraviolet absorption tail. The achieved optical attenuation value almost corresponded to the ultimate intrinsic loss value for a silica-based optical fiber. This means that, if lower optical attenuation fibers are expected, it is required to develop new infrared fiber materials which have the infrared absorption edge at longer wavelengths or smaller Rayleigh scattering loss compared with silica-based glass. In 1977-1978, Pinnow et al. [4], Van Uitert and Wemple [5], and Goodman [6] discussed the possibility of ultralow loss fiber with a loss less than 10⁻²dB/km using infrared transmitting materials. It could be mentioned that their challenging discussions motivated the research on nonsilica-based infrared optical fibers anew. Actually, they suggested halide, chalcogenide and heavy metal oxide glasses as well as halide crystals, as potential candidates of low loss IR fiber materials. The above development story of infrared optical fibers has been reported in detail in Ref. [7].

It could be mentioned that among halide glasses, ZrF₄-based fluoride glasses [8] have been most studied as infrared fiber materials. Though ZrF₄-based fluoride glasses are very unstable against devitrification, much effort has been made to realize low loss infrared fibers in 1980’s. Fortunately, this effort has resulted in the realization of low loss fluoride single mode fiber [9–12] and opened a new prospect on active fiber applications, such as fiber laser and optical amplifiers, and even nonlinear applications. Chalcogenide glasses, such as Ge–S [13], As–S [14], As–Se [15], etc., have been studied again as infrared fiber materials. Several fiber fabrication techniques have been developed [15,16], and have become commercially available. As a result, fiber sensing applications in the infrared region, such as gas, chemical and temperature sensing, and power delivery, etc., have opened [17]. Heavy metal oxide glasses, such as germinate (GeO₂-based glass) [18,19] and tellurite glass (TeO₂-based glass) [20] have been also studied. However, those heavy metal oxide glass fibers did not draw an attractive attention as infrared optical fibers, because they do not always have remarkable properties as infrared transmission media.

In 1990’s, a research on glass materials with large third order nonlinearity is an attractive subject in material science and technology. It was expected that third order nonlinear glasses have possible applications to all optical devices for optical logic, optical switching, optical memory storage and optical computer systems. A large number of glasses have been investigated as candidates of highly nonlinear optical device materials [21–24]. Typical glasses among them are lead oxide-based, bismuth oxide-based, tellurium oxide-based (tellurite) glass, etc. and chalcogenide glass. Their nonlinear properties, for example, glass compositional dependence of nonlinearity, were investigated to develop higher nonlinear glass materials. However, actual photonics devices were not developed using those glasses.

Almost at the same time, the study and development of rare earth-doped optical fiber amplifier and laser extremely prospered. Just after the invention of laser in 1960 [25], the first experiments of optical fiber amplifiers at 1.06 µm were performed using a neodymium (Nd)-doped fiber by Koster and Snitzer [26,27]. After that, many pioneering works were achieved [28–30]. Nonsilica glasses played a large role in the rare-earth-doped optical fiber amplifier and laser technology. Praseodymium (Pr)-doped fluoride fiber was successfully used for the 1.3 µm amplification and laser [31,32]. Mid-infrared (Mid-IR) laser oscillations at 2 µm, 3 µm and 4 µm using thulium (Tm), erbium (Er), holmium (Ho) -doped fluoride fibers [33–35]. Rare earth-doped tellurite and chalcogenide fibers with lower phonon energies than silica fibers make it possible to obtain mid-IR lasing [36–39]. The operational wavelength range of rare earth-doped fibers have been expanded by using fluoride, tellurite and chalcogenide fibers as rare earth hosts. Tellurite glasses have high refractive index of almost or more than 2. The stimulated emission cross sections of rare earth ions proportional to (n² + 2)²/9n for tellurite glasses of almost 2 times higher than those for silica and fluoride glasses lead to the generation of wider amplification gain bands [40]. Actually, the broadband amplification at 1.5 µm of erbium (Er)-doped fiber amplifier was demonstrated using Er-doped tellurite fiber [41,42]. Those performances are difficult to be realized using rare earth-doped silica fibers. Infrared glasses have played an important role to expand the potential of rare earth-doped fiber lasers and optical amplifiers.

Highly nonlinear silica fibers have attracted much attention in recent years because they paved the way for the development of compact nonlinear devices for applications such as supercontinuum (SC) generation, wavelength conversion, pulse compression, parametric amplification, etc. Many experimental and theoretical results are introduced and explained in detail in Ref. [43]. On the other hand, highly nonlinear soft glasses with much higher nonlinearities than silica glass have a serious issue that they have large material dispersion in the near infrared region, especially telecommunication window where many pump laser sources are available and we have many potential applications. The advent of photonic crystal fibers (PCFs), also called microstructured optical fibers (MOFs), in 1995 [44] led to overcoming the chromatic dispersion control issue of highly nonlinear soft glasses, because they have high controllability of chromatic dispersion. They opened one of new frontiers in the field of nonlinear fiber optics.

Highly nonlinear fibers with microstructures have attracted much attention because they paved the way for the development of compact nonlinear devices for applications such as SC generation, wavelength conversion, pulse compression, parametric amplification, etc. [45–47]. Using a highly nonlinear glass material is preferable to obtain a fiber with high nonlinear coefficient. Highly nonlinear soft glasses attracted attention again as MOF materials. MOFs in lead silicate glass [48], bismuth oxide glass [49,50], tellurite glass [51,52] and chalcogenide glass [53,54] have been fabricated to realize high nonlinearity than silica fibers. The advent of PCFs, or MOFs, opened new frontiers in the field of nonlinear fiber optics. One large advantage of highly nonlinear soft glass PCFs or MOFs is that they can have high controllability of chromatic dispersion.

The observation of SC generation in MOFs has had revolutionary impact on nonlinear optics [55]. The subsequent research on SC generation in MOFs has targeted novel MOF development to drastically upgrade the performance of SC. Nowadays more and more groups are employing these new white-light-laser sources, that is, SC light source, for their experiments, which include the studies of self-focusing, shaping, and control of polychromatic light.

As mentioned above, soft glass optical fibers, especially highly nonlinear optical fibers, have expanded their potential and application fields. We have been engaged in soft glass optical fibers, such fluoride, tellurite and chalcogenide glass, for optical signal processing, lightwave generation and waveguide applications. We have studied the applications of stimulated Raman scattering, and stimulated Brillouin scattering for optical signal control [56–63] and SC generation using soft glass optical fibers. Furthermore. we have challenged the research on novel waveguides, for example, transverse Anderson localization [64–66] of mid-infrared light using transversely disordered optical fiber. Here we report our achievements on SC generation and novel waveguides research using the highly nonlinear soft glass optical fibers.

The structure of this paper is as follows. Basic material properties, such as optical transmission, refractive index dispersion, optical nonlinearity, material dispersion and viscosity, for fluoride, tellurite and chalcogenide glasses are presented in Section 2. These properties are quite important for the design and fabrication of optical fibers with special structures for nonlinear optical applications. In Section 3, broadband SC generations using fluoride, tellurite and chalcogenide fibers are presented. Especially, we have developed new MOFs made of tellurite and chalcogenide glasses for highly coherent SC in the mid-IR region. The performance of SC by tellurite and chalcogenide MOFs is reported. In Section 4, a challenge to realize infrared optical image transport through an all-solid tellurite fibers with transversely-disordered refractive index profile is described. We will show new potential of tellurite and chalcogenide fibers to realize infrared image transportation.

2. Material properties of soft glasses for specialty optical fibers

Basic optical properties such as transmission, linear refractive index dispersion, material dispersion and nonlinearity for tellurite and chalcogenide glasses which are used as optical fiber materials in this study are introduced here. Based on those properties, optical fiber structures are designed to control chromatic dispersion and nonlinear phenomena.

2.1 Optical transmission

Figure 1 shows images of tellurite (TeO₂–Bi₂O₃–ZnO–Na₂O), sulfide chalcogenide (As₂S₅) and selenide chalcogenide (AsSe₂, As₂Se₃) glass samples [67]. Their thickness is about 1 mm. Tellurite glass is almost colorless and As₂S₅ glass is transparent in the visible region, though AsSe₂ and As₂Se₃ glasses are not transparent in the visible region. Those glasses have been used as highly nonlinear fiber glasses in this work.

 

Fig. 1. Images of Tellurite, AsSe₂, As₂Se₃ and As₂S₅ glass samples. Adapted with permission from Ref. [67] © Optica.

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Figure 2 shows transmission spectra of silica, fluoride, tellurite, As₂Se₃, AsSe₂ and As₂S₅ glass samples [67]. As can be seen, tellurite and fluoride glasses are transparent up to 7 and 8 µm, respectively, though silica glass is not transparent after 6 µm. However, chalcogenide transmission spectra are much wider. It can be as long as 13 µm for the sulfide chalcogenide As₂S₅ and even beyond 19 µm for the selenide chalcogenide (AsSe₂, As₂Se₃). An absorption band above 9 µm of As₂S₅ glass originates in As–S bonds [68]. Absorption bands from 14 to 16 µm and above 17 µm of AsSe₂ and As₂Se₃ glasses originate in As–Se bonds [68]. An absorption peak at 12.7 µm caused by Se–OH bonds [69] is found only for AsSe₂. More absorption wavelengths due to typical impurities in As–S and As–Se glass systems were mentioned by R. Fairman et al. [70].

 

Fig. 2. Measured transmission spectra of silica, tellurite, fluoride, As₂Se₃, AsSe₂ and As₂S₅ glasses. Adapted with permission from Ref. [67] © Optica.

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2.2 Linear refractive index dispersion

The linear refractive index dispersion is used to calculate chromatic dispersion of optical fiber. To obtain the linear refractive index dispersion, glass prisms made of our tellurite and chalcogenide glasses were measured at 20 different wavelengths from 0.4 to 4.0 µm by using the minimum deviation method [71] with the uncertainness of the measurement is as low as ±10⁻⁴. The measured linear refractive indices were fitted to the Sellmeier equation [72] as given in Eq. (1) and the index value at arbitrary wavelengths between 0.4 and 4.0 µm can be interpolated with high accuracy.

Here, n is the refractive index of the material, λ is the wavelength and A_i, B_i are Sellmeier coefficients. The major drawback of this method is that the linear refractive indices at wavelengths beyond 4.0 µm are unattainable or inaccurately extrapolated, especially at the wavelengths in the mid-IR up to 10 or 20 µm.

However, it is important to determine the wavelength-dependent linear refractive indices in these long wavelength ranges because they are involved in calculations of chromatic dispersion and SC in the mid-infrared which is the major target in this work. For this reason, the interferometric method [73] was employed. Fluoride, tellurite and chalcogenide glass films which are about 0.15 mm-thin were prepared for the FTIR measurements. From the FTIR spectra and their fringe patterns, the linear refractive index can be calculated at more than 330 different wavelengths from 2.0 to 22 µm.

The combination of the two methods mentioned above resulted in more than 350 values of linear refractive index at different wavelengths from 0.4 to 22 µm for each chalcogenide glass, to 5 µm for tellurite glass and to 4.5 µm for fluoride glass. They were fitted to the Sellmeier equation as Eq. (1) where i is equal to 5. In Fig. 3, wavelength-dependent linear refractive indices of fluoride, tellurite, As₂Se₃, AsSe₂ and As₂S₅ glasses are plotted and Table 1 shows their Sellmeier coefficients.

 

Fig. 3. Measured and fitted wavelength-dependent linear refractive index of fluoride, tellurite, As₂Se₃, AsSe₂ and As₂S₅ glass samples. Adapted with permission from Ref. [67] © Optica.

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Table 1. Sellmeier coefficients of fluoride, tellurite, As₂Se₃, AsSe₂ and As₂S₅ chalcogenide glasses. Adapted with permission from Ref. [67] © Optica.

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Figure 4 shows the material dispersions of tellurite, As₂Se₃, AsSe₂ and As₂S₅ glass as well as those of silica and fluoride glass for comparison. The zero dispersion wavelength (ZDW) of fluoride, tellurite, As₂Se₃, AsSe₂ and As₂S₅ glass is 1.72 µm, 2.31 µm, 6.96 µm, and 7.56 µm, respectively. In case of tellurite, As₂Se₃, AsSe₂ and As₂S₅ glass, ZDWs are far from the telecommunication window and has large value in the near infrared region where many lasers are available as pump sources.

 

Fig. 4. Material dispersions of silica, fluoride, tellurite, As₂Se₃, AsSe₂ and As₂S₅ glass.

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2.3 Optical nonlinearity

Nonlinearity of optical fibers have been manipulated and improved by adding complex microstructure in the cladding of the fibers [74–77]. But, for step-index optical fibers, the nonlinearity basically comes from those of the fiber materials. The nonlinearity of a glass material can be expressed by the nonlinear refractive index n₂. Glasses with high nonlinearity are advantageous to the performance of nonlinear effects in optical fibers. Figure 5 which was reproduced from Refs. [40,74,75] shows the linear and nonlinear refractive indices of several common glass systems such as silica, fluoride, silicate, tellurite and chalcogenide. Among them, chalcogenide glasses show very high nonlinear refractive index more than one hundred times larger than silica glass. In Table 2, the n₂ values of typical chalcogenide glasses are provided in comparison with those of silica, fluoride and tellurite glasses.

 

Fig. 5. Nonlinear refractive index n₂ of silica, fluoride, silicate, tellurite and chalcogenide glass systems. Adapted with permission from Ref. [67] © Optica.

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Table 2. Nonlinear refractive indices of As₂Se₃, AsSe₂ and As₂S₅ chalcogenide glasses. Adapted with permission from Ref. [67] © Optica.

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2.4 Viscosity

Figure 6 shows the viscosity curves of some glasses, such as chalcogenide glass (AsSe₂), the homemade tellurite glasses (TeO–ZnO–La₂O₃–Bi₂O₃), phosphate glass (P₂O₅–ZnO–Na₂O–K₂O), Pyrex 7740 (Borosilicate) and pure silica glass. The viscosity data have been extrapolated to poise, according to the Arrhenius viscosity formula [83], which include the activation energy for viscous flow, the gas constant, and the absolute temperature of the glass flow (Kelvin). The viscosity curve of pure silica glass [84], is also illustrated in Fig. 6. It is seen that tellurite and chalcogenide glasses have steep viscosity curves, and the fiber drawing temperature range is around 50 °C, while pure silica glass has a moderate viscosity change, and the fiber drawing temperature range is almost 600 °C. The fiber drawing temperature range suitable for tellurite and chalcogenide glass fibers is much narrower than silica fiber. Therefore, the precise temperature control is required to perform a stable fiber drawing for tellurite and chalcogenide glasses.

 

Fig. 6. Viscosity of some studied glasses: (1) AsSe₂, (2) TZLB tellurite glass (TeO–ZnO–La₂O₃–Bi₂O₃), (3) P₂O₅–ZnO–Na₂O–K₂O glass, (4) Pyrex 7740 (Borosilicate), and (5) pure silica glass [84].

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3. Supercontinuum generation by soft glass optical fibers

SC light was generated in bulk glass by Alfano and Shapiro in 1970 [85–87], and has since been the subject of numerous investigations in a wide variety of nonlinear media, including solids, organic and inorganic liquids, gases, and various types of waveguide. SC generation has found numerous applications in many fields as spectroscopy, pulse compression, and the design of tunable ultrafast femtosecond laser sources. The advent of the PCF in the late 1990s [88,89] has attracted widespread interest throughout the scientific community and has led to a revolution in the generation of ultra-broadband high brightness spectra through SC generation [90]. SC generation in PCFs has subsequently been widely applied in interdisciplinary fields such as optical coherence tomography, spectroscopy, and optical frequency metrology [90]. A review on commercial products of high power SC light sources expanding from the ultraviolet (UV) to the near-infrared (IR) spectral region, generated from silica PCFs, can be found elsewhere [90]. Especially, mid-IR SC generation has many applications including light ranging, trace gas detection, molecular spectroscopy, and active hyperspectral imaging [91]. Soft glass fibers made of fluoride, tellurite or chalcogenide glass can be used for mid-IR SC generation due to their broad transparency range. SC generation research using soft glass optical fibers has accelerated upgrades of the performance of SC, for example as shown in Refs. [92–105]. Here we describe SC generation from UV to mid-IR range by optical fibers made of fluoride, tellurite and chalcogenide glasses.

3.1. Supercontinuum generation from ultraviolet to mid-infrared using a fluoride fiber

Much attention has been paid to nonsilica fibers (e.g., fluoride [106], SF6 [107], bismuth oxide-based [108], tellurite [109–111], and chalcogenide fibers [112] with high nonlinearity or low transmission loss at the mid-IR region for generating mid-IR SC light. In the case of fluoride fibers, Xia et al. [106] reported ultra-broadband SC generation from 0.8 to 4.5 µm in ZrF₄–BaF₂–LaF₃–AlF₃–NaF (ZBLAN) fluoride fibers by nanosecond diode pumping. In comparison with silica fibers, fluoride fibers not only have high transparency in the UV-visible-near-IR region (the transmission window of silica fiber) but also high transparency in the mid-IR region up to 8 µm. However, the reported long-wavelength edge of SC generation in ZBLAN fluoride fibers is just up to 4.5 µm, which is limited by the confinement loss of ZBLAN fluoride fibers. We have considered from the SC generation through filamentation in fluoride glass [113] that ultra-broadband SC generation from UV to the mid-IR region up to 8 µm could be generated by reducing the length of ZBLAN fluoride fiber and increasing the peak power of the pump laser [114]. Here we demonstrate the SC generation from ultraviolet to mid-IR using a fluoride fiber.

The step-index fluoride fiber (Fiberlabs, in Japan) that we used has a core diameter of 9 µm, a numerical aperture (NA) of 0.2, and a zero dispersion wavelength of 1.65 µm. The inset of Fig. 7(a) shows the calculated dispersion data of the fundamental propagating mode in the above fluoride fiber. The calculated nonlinear coefficient at 1450 nm is 1.44 km⁻¹ W⁻¹, by using a nonlinear refractive index of 2.1 × 10⁻²⁰ m² W⁻¹ [115] for the above fluoride glass. To demonstrate its potential for generating the mid-IR SC light up to 8 µm, we performed simulations by solving the generalized nonlinear Schrödinger equation (GNLSE). In the simulation, we took the calculated dispersion data shown in the inset of Fig. 7(a), the aforementioned nonlinear coefficients, ${\tau _{shock}}$ = 0.81 fs, the pumping wavelength of ∼1.45 µm, the pulse width of ∼180 fs with a hyperbolic secant field profile, the peak power of ∼0.4 MW, the fiber length of ∼2 cm, and the Raman response function derived from the Raman gain spectrum of the above fluoride glass. Figure 7(a) shows the simulated SC spectrum output from a 2 cm-long ZBLAN fluoride fiber without considering the effects of the confinement loss. It is seen that SC light expanding from 0.8 to 7.5 µm would be generated in the 2 cm-long ZBLAN fluoride fiber when pumped at 1450 nm with a peak power of 4 MW. Further increasing of the pump power would make the SC spectrum broadened very much. In general, the real SC spectrum from the step-index waveguide structure would be also limited by the material absorption, and the confinement loss of the fiber. In the case of the above fluoride fiber, the transmission window of fluoride glass is about 200 nm to 8 µm, and the confinement loss of the above fiber becomes very large when the propagating wavelength is larger than 3.5 µm [116]. Therefore, the short wavelength edge of the real SC spectrum would be limited by the material absorption (∼200 nm) and that of the long wavelength edge by the confinement loss of fluoride fiber. That is the reason why the reported long-wavelength edge of SC generation in several meters long ZBLAN fluoride fibers is just up to 4.5 µm [106]. We consider that the effects of the confinement loss on the SC generation would be reduced by decreasing the fiber length to centimeter-long level. As a result, ultra-broadband SC generation from UV to the mid-IR region up to 8 µm could be generated by using a 2 cm-long ZBLAN fluoride fiber and increasing the peak power of the pump laser.

 

Fig. 7. (a) The simulated SC spectrum output from a 2 cm-long ZBLAN fluoride fiber without considering the effects of the confinement loss when pumped at 1450 nm with a peak power of 4 MW. Inset of (a): The calculated dispersion data of the fundamental propagating mode in the fluoride fiber we used. (b) The simulated spectral evolution of SC generation in the 2 cm-long fluoride fiber when pumped at 1450 nm with a peak power of 4 MW. Reproduced from Ref. [114] with the permission of AIP Publishing.

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Figure 7(b) shows the simulated spectral evolution of SC generation in the 2 cm-long fluoride fiber when pumped at 1450 nm with a peak power of 0.4 MW. It is seen that the initial spectral broadening along the fiber length is mainly caused by self-phase modulation (SPM). Further spectral broadening along the fiber length is caused by SPM, Raman scattering, and four-wave mixing. This is because that the pumping wavelength (∼1450 nm) is located in the normal dispersion region and the real fiber length (∼2 cm) is much shorter than the dispersion length (∼2.7 m). In this case, the spectral broadening in fluoride fibers is primarily caused by SPM, Raman scattering and four-wave mixing.

The pump light from a 1450 nm femtosecond laser with a pulse width of ∼180 fs and repetition rate of ∼1 kHz from a tunable optical parametric amplifier system pumped by a 800 nm Ti: sapphire femtosecond laser, was launched into the input end of a short length fluoride fiber. The detail measurement condition is described in Ref. [114].

Figure 8(a) shows the measured SC spectrum from the 2 cm-long fluoride fiber when the average pump power of 1450 nm femtosecond laser was fixed at 20 mW (the corresponding peak power is about 50 MW). It is seen that SC light expanding from UV (∼350 nm; the measurement of the short-wavelength edge of SC spectrum is limited by our OSA) to 6.28 µm could be generated in the 2 cm-long fluoride fiber, which has a 10 dB bandwidth of 4861 nm (the spectral range of 565–5246 nm) and almost covers the transmission window of fluoride fiber. In comparison with the previous report on SC generation in several meters long fluoride fiber [106], the long wavelength edge of SC spectrum was extended from 4.5 to 6.28 µm by reducing the fiber length to the centimeter-long level.

 

Fig. 8. (a) The measured SC spectra from the 2 cm-long fluoride fiber when the average pump power of 1450 nm femtosecond laser was fixed at 20 mW (the corresponding peak power is about 50 MW). (b) A comparison of the long-wavelength edge of SC spectra in 0.9 or 2 cm-long fluoride fiber. Reproduced from Ref. [114] with the permission of AIP Publishing.

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As aforementioned, the simulated results show the long wavelength edge of SC spectrum in the 2 cm-long fluoride fiber would be up to 8 µm when pumped at 1450 nm with a peak power of several MW without considering the effects of the confinement loss. Our measured SC spectrum in the 2 cm-long fluoride fiber just gave a long-wavelength edge of ∼6.28 µm. It means that the long-wavelength edge of SC spectrum was still limited by the confinement loss even for the centimeter-long fluoride fiber. To confirm the effects of the confinement loss on the SC generation, we measured the SC spectrum from a 0.9 cm-long fluoride fiber when the average pump power of 1450 nm femtosecond laser was fixed at 20 mW (the corresponding peak power is about 50 MW). Figure 8(b) shows a comparison of the long-wavelength edge of SC spectrum in a 0.9 or 2 cm-long fluoride fiber. It is seen that the long-wavelength edge of SC spectrum was not further extended by reducing the fiber length from 2 cm to 0.9 cm. It means that the long wavelength edge of SC generation in the above fluoride fibers was limited to ∼6.28 µm by the confinement loss despite the length of the fluoride fiber used. Therefore, to extend the long wavelength edge of SC spectrum in fluoride fiber to 8 µm, the confinement loss of the fiber needs to be reduced by using large NA fluoride fiber, e.g., the air-cladding fluoride MOFs.

In summary, we demonstrated ultra-broadband SC generation from UV to 6.28 µm in a 2 cm-long fluoride fiber pumped by a 1450 nm femtosecond laser. The spectral broadening in the fluoride fiber was caused by SPM, Raman scattering and FWM. The experimental and simulated results showed that fluoride fiber is a promising candidate for generating the mid-IR SC light up to 8 µm.

3.2. Mid-infrared supercontinuum generation in the chalcogenide step-index fiber

The broadest mid-IR SC generation in fluoride fibers is from ultraviolet to 6.28 µm [114], and the broadest in tellurite fibers is from 789 to 4870 nm [109]. Chalcogenide glasses prove to be a more promising candidate, because they present a wider transparency window over 20 µm, and possess a higher nonlinear refractive index up to tens or hundreds of times as those of fluoride and tellurite glasses [117–121]. Numerical simulations have demonstrated the potential of chalcogenide fiber for mid-IR SC generation [122–125]. Petersen et al. in 2014 experimentally observed the broadest mid-IR SC spectrum, spanning 1.4 to 13.3 µm [126]. Further efforts have been made to expand mid-IR SC using chalcogenide fibers [127,128]. Based on the previous works, we strive to extend the SC evolution in mid-IR region from the following aspects: designing chalcogenide fibers with near-zero flattened dispersion, shifting the pump wavelength to the long wavelength region, and decreasing the fiber length to reduce the loss.

Here we demonstrate mid-IR SC generation in a chalcogenide step-index fiber. The step-index fiber with near-zero flattened dispersion was designed based on As₂Se₃ and AsSe₂, and fabricated by the rod-in-tube drawing technique [129]. The pump source was generated by the difference frequency generation (DFG), which had a pulse width of ∼170 fs, a repetition rate of ∼1000 Hz, and a wavelength range tunable from 2.4 to 11 µm. The resulting SC generation was investigated both experimentally and numerically.

The fiber design and optimization were carried out to achieve features of high nonlinearity and near-zero flattened dispersion. As₂Se₃ and AsSe₂ glasses were selected for the core and cladding, respectively, because they have good compatibility, higher nonlinear index, and wider transparency window compared with other chalcogenide glasses (Ge₁₅Ga₃Sb₁₃S₆₉ and As₂S₅) [77,130]. Figure 9(a) shows the measured linear material refractive indices of two glasses, as well as the numerical aperture (NA). For the chalcogenide step-index fiber, the variation of the dispersion with the change of the core diameter was analyzed using the full-vectorial mode solver of a commercial software (Lumerical MODE Solution), as shown in Fig. 9(b). We can see that the number of zero-dispersion wavelength (ZDW) reduces from two to one, with the core diameter increasing from 11 to 17 µm. For fibers with two ZDWs, there is a possibility that red-shifted dispersive waves may be emitted by solitons over the second ZDW region. However, the second ZDW would definitely restrain the soliton evolution. Taking this into consideration, a fiber with the diameter of 15 µm, one ZDW, and near-zero flattened dispersion was selected. The resulting ZDW was calculated to be ∼5.5 µm and the wavelength range between the dispersion of ±7.5 ps/km/nm was from ∼4.5 to 20 µm. Figure 9(c) shows the variation of confinement loss with the change of the core diameter, which confirmed that the chalcogenide step-index fiber with the diameter of 15 µm can support mid-IR transmission.

 

Fig. 9. (a) Measured refractive indices of As₂Se₃ (core) and AsSe₂ (cladding) as well as calculated NA. (b) Calculated dispersions for the fundamental mode of the chalcogenide step-index fiber with the core diameter changing from 11 to 17 µm. (c) Calculated confinement losses of the chalcogenide step-index fiber with the core diameter changing from 11 to 17 µm. Reprinted with permission from Ref. [129] © Optica.

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The chalcogenide step-index fiber was fabricated by the rod-in-tube drawing technique, and the AsSe₂ and As₂Se₃ glass rods were offered by Furukawa Denshi Co., Ltd. The fabrication process is described in detail in Ref. [129]. Figure 10(a) shows photos of the AsSe₂ tube, the initial As₂Se₃ rod, and the elongated As₂Se₃ rod. Figure 10(b) is the measured As₂Se₃ rod loss and the transmission spectrum of a 2 mm-thick As₂Se₃ glass sample. We can see there are several absorption bands from 2.5 to 19 µm, which correspond to the residual O–H, As–O, Se–O, and Se–H pollution in the glass. In particular, the loss resulted from Se–H absorption band centering around 15.2 µm is prominently strong. Consequently, in order to minimize the influence from the loss, the fiber length was reduced to 3 cm in this experiment. Figure 10(c) shows the cross section of the chalcogenide step-index fiber taken by a scanning electron microscope (SEM), in which the As₂Se₃ core diameter was measured to be ∼15 µm. Based on the nonlinear index n₂ = 1.1 × 10⁻¹⁷m² /W [79], the effective mode areas and the nonlinear coefficients of the fundamental mode from 2 to 20 µm were calculated, as shown in Fig. 10(d).

 

Fig. 10. (a) Photos of the AsSe₂ tube, the As₂Se₃ rod, and the elongated As₂Se₃ rod. (b) Measured transmission spectrum of a 2 mm-thick As₂Se₃ sample and the As₂Se₃ rod loss. (c) Cross section of the chalcogenide step-index fiber taken by SEM. (d) Calculated effective mode areas and nonlinear coefficients of the fundamental mode. Reprinted with permission from Ref. [129] © Optica.

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The experimental setup for SC generation in a 3 cm-long chalcogenide step-index fiber is shown in Fig. 11(a). The mid-IR pump source started from a Ti:Sapphire mode-locked seed laser (Coherent Mira 900), which delivered seed pulses with a spectrum bandwidth of ∼12 nm at 800 nm to a Coherent Legend pulse picker regenerative amplifier for boosting the pulse energy to about 1 mJ at a low repetition rate of 1 kHz. The amplified laser pulse passed through a traveling-wave optical parametric amplifier of superfluorescence (TOPAS) to generate a signal beam tunable from 1160 to 1600 nm and an idler beam tunable from 1600 to 2600 nm. The signal and idler beams were collinearly combined together and passed through a DFG unit to generate a mid-IR pulse tunable from 2.5 to 11 µm and with a pulse width of ∼170 fs (full-width at half-maximum, FWHM). During the experimental process, in order to minimize the fiber loss (especially for Se–H absorption band) and maximize the DFG pump power, the wave-length ∼9.8 µm was chosen, which was in the anomalous dispersion region of the fiber. The average pump power measured directly from DFG was ∼3.1 mW. The other experimental conditions are described in Ref. [129] in detail.

 

Fig. 11. Experimental setup for mid-IR SC generation in the 3 cm long chalcogenide step-index fiber. LPF: long-pass filter; PM: parabolic mirror. Reprinted with permission from Ref. [129] © Optica.

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The measured mid-IR SC spectrum and the spectrum of the pump source are shown in Fig. 12. We can see that the SC spectrum covers from ∼2.0 to 15.1 µm. For the 3 cm-long chalcogenide step-index fiber, the nonlinear length is L_NL = $1/\gamma {P_0}$, where $\gamma$ is the nonlinear coefficient and P₀ is the peak power. From Fig. 10(d), we obtained $\gamma$ = 62.3 km⁻¹ W⁻¹ at the pump wavelength of ∼9.8 µm. The dispersion length is L_D = T₀²/|β₂|, where ${T_0} \approx {T_{\textrm{FWHM/1}\textrm{.763}}}$ is the pulse width for hyperbolic-secant shape and β₂ = −369.6 ps²/km at ∼9.8 µm is the dispersion parameter calculated according to Fig. 9(b). For the coupling peak power of ∼2.89 MW, L_NL is 5.55 × 10⁻⁶ m, and L_D is 2.52 × 10⁻² m. Because the fiber length L = 3 cm > L_NL and > LD, the spectrum broadening in the anomalous dispersion region was dominated by the fission of the higher-order solitons. Based on N² = γP₀T₀²/|β₂|, the order of solitons (N) in the fiber was ∼67. In the normal dispersion region, the spectrum broadening was dominated by the radiation of dispersive waves generated under the phase-matching condition. The recessions in the SC spectrum centering around ∼2.9 (1), 5.9 (2) and 10.6 µm (3) would come from the absorption bands of atmospheric water and Se–O. After 11.7 µm, the spectrum declined abruptly (4), which was in accordance with the strong and wide absorption band of Se–H. Moreover, because the wavelength of the SC spectrum was comparable to the fiber core diameter, the output near-field beam profile was measured by a beam profiling camera (WinCamD, FIR2-16-HR) with the measurement range of 2∼16 µm. The image is shown in the inset of Fig. 12, which confirms that the light was confined in the fiber core.

 

Fig. 12. Measured and simulated mid-IR SC spectra in the 3 cm-long chalcogenide step-index fiber at the pump wavelength of ∼9.8 µm with the peak power of ∼2.89 MW. Adapted with permission from Ref. [129] © Optica.

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The SC generation in the chalcogenide step-index fiber was also simulated by the GNLSE, as shown in Fig. 12 [129]. The parameters used for the simulation are as follows, fiber length L = 3 cm, peak power P = 2.89 MW, pump wavelength $\lambda$ = 9,800 nm, and pulse width T_FWHM = 170 fs. Fiber loss , and nonlinear coefficient γ were obtained from Fig. 10(b) and (d). However, there are still some differences, probably due to the following: the disparity between the fiber loss and the rod loss; the disparity between the calculated peak power in the simulation and the actual peak power in the experiment. Moreover, the deviation of the simulated dispersion profile in Fig. 9(b) would affect the shape and range of the simulated SC, and there is also the possibility of coupling to other polarizations or spatial modes in the fiber.

In summary, mid-IR SC spectrum spanning ∼2.0 to 15.1 µm was successfully generated in a 3 cm-long chalcogenide step-index fiber. This study facilitates the development of optical devices operating at wavelengths in the mid-IR region, and improves the fiber-based applications in sensing, medical, and biological imaging areas.

3.3. Supercontinuum generation in the tellurite all-solid hybrid microstructured optical fiber

The soliton dynamics is highly sensitive to noisy processes such as modulation instability and Raman scattering which produce SC with low temporal coherence [90]. To suppress the noise amplification, one approach is to pump the fiber in the normal dispersion regime [90]. In the normal dispersion regime, the spectrum broadening dynamics is mainly based on SPM and optical wave breaking (OWB). In these processes, random noise is not amplified. As a result, the output pulse is highly coherent.

By pumping chalcogenide fibers at long wavelengths such as 7, 8, 10 and 12 µm in the all-normal dispersion regime (AND), highly coherent and broad mid-IR SCs have been generated [131,132]. However, such pumping scheme has some disadvantages in practical applications because only a few laser systems can provide long-wavelength pulses. Besides, these systems are very complex and not maintenance-free. On the contrary, commercial fiber lasers whose central wavelengths are around 1.5 or 2 µm are more attractive for their compactness, high power, robustness and maintenance-free. SC generation with silica PCFs, silicate PCFs, tellurite step-index fibers, tellurite tapered fiber, chalcogenide MOFs, and chalcogenide PCFs have been demonstrated by pumping around 1.5 and 2 µm in the AND regime [133–142]. Stepniewski et al. pumped N-F2 all-solid PCF at 1360 nm and obtained an SC from 950–1850 nm at −20 dB level [134]. Al-Kadry et al. pumped chalcogenide microwires at 1550 nm and obtained an SC from 1400–1900 nm at −20 dB level [136]. Klimczak et al. pumped boron silicate PCF at 2160 nm and obtained an SC from 1500–2600 nm at −20 dB level [137]. Other relevant studies are tabulated in Table 3.

Table 3. SC generation in AND regime pumped near 1.5 or 2 µm. Reproduced from Ref. [144].

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We have shown a tellurite all-solid hybrid microstructured optical fiber (ASHMOF) which has a flattened chromatic dispersion value of −15 ps/km/nm [143]. ASHMOF is a combination of a step-index fiber and a regular MOF, in which it benefits both wave-guiding effects of a step-index and the surrounding microstructured rods. Here, we further exploit the potential of ASHMOF which has high chromatic dispersion controllability. Pumping the ASHMOF with optimized structural parameters at 2 µm, broad and highly coherent SC with high spectral flatness spanning the range from the near to mid-infrared region can be generated [144].

3.3.1. Fiber glass materials and fiber structure design

3.3.1.1 Fiber glass materials

To perform a successful optical fiber fabrication, the glasses must have compatible thermo-mechanical properties. Three tellurite glasses were selected due to their compatible thermo-mechanical properties and suitable refractive index differences: TLWMN (TeO₂–Li₂O–WO₃–MO₃–Nb₂O₅)—highest refractive index, TZNL (TeO₂–ZnO–Na₂O–La₂O₃)—lower refractive index and TZLKAP (TeO₂–ZnO–Li₂O–K₂O–Al₂O₃–P₂O₅)—lowest refractive index. The glass refractive indices are shown in Fig. 13(a). At 2 µm, the refractive index difference between TLWMN and TZNL is 0.1, and the refractive index difference between TLWMN and TZLKAP is 0.46. From refractive index data, the material dispersions were calculated and shown in Fig. 13(b).

 

Fig. 13. (a) Refractive index dispersions and (b) material dispersions of TLWMN, TZNL and TZLKAP. Reproduced from Ref. [144].

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Table 4 shows their softening temperature (T_s) and linear expansion coefficients (α). The softening temperature difference is less than 2 °C and the linear expansion coefficient difference is less than 0.2 × 10⁻⁵/°C. Similarity in thermo-mechanical properties is crucial for successful fiber fabrication using these three glasses [144].

Table 4. Thermo-mechanical properties of tellurite glasses. Reproduced from Ref. [144].

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3.3.1.2 Chromatic dispersion of the step-index optical fiber

As shown in Fig. 14, a step-index fiber with core of TLWMN and cladding of TZNL has an all-normal chromatic dispersion profile when the core diameter is smaller than 3.3 µm. However, the chromatic dispersion in the long-wavelength range is large. As a result, the pulse intensity would decrease rapidly and the SC bandwidth would be narrow [134,138,140]. To benefit the high pulse intensity for efficient SPM as the pulse propagates along the optical fiber, one strategy is to flatten the fiber chromatic dispersion over a wide wavelength range. Some air-holes MOFs have been optimized for flattened chromatic dispersion [145,146]. However, those structures are too complicated to be fabricated in practice.

 

Fig. 14. Chromatic dispersion of a step-index fiber (TLWMN: core and TZNL: cladding) with different core diameters. Reproduced from Ref. [144].

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In our newly proposed fiber, by adding solid rods around the core, the optical field in the core is disturbed and the waveguide dispersion is modified. As a result, the total chromatic dispersion can be flexibly controlled over a wide wavelength range.

3.3.1.3 Chromatic dispersion of the tellurite all-solid hybrid microstructured optical fiber

Figure 15 shows the cross-section of the tellurite ASHMOF with its refractive index profile. The core material is TLWMN which has the highest refractive index. The cladding material is TZNL. And the rod material is TZLKAP which has the lowest refractive index among the three materials.

 

Fig. 15. Cross-section of the tellurite ASHMOF and its refractive index profile. Λ is the distance between two adjacent rods. Reproduced from Ref. [144].

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Chromatic dispersion was calculated with the full vectorial finite element method (Lumerical Mode Solutions) which gives precise results for microstructured fibers. Here we optimize the fiber structural parameters to obtain flattened chromatic dispersion profiles. With a fixed core diameter (d_core), the rod distance (Λ) and the ratio of rod distance to rod diameter (d_rod) are changed to control the chromatic dispersion [147].

Figure 16(a) shows the chromatic dispersion change of the tellurite ASHMOF when Λ/d_rod is changed and d_core and Λ are fixed at 3.2 µm and 4.2 µm, respectively. When Λ/d is decreased, the chromatic dispersion slope in the wavelength range from 2.3 to 4 µm becomes less negative. When Λ/d_rod = 2.7, the chromatic dispersion in this range is flattened. With smaller values of Λ/d_rod, the chromatic dispersion slope becomes positive and the dispersion is anomalous in this wavelength range.

 

Fig. 16. Chromatic dispersions of tellurite ASHMOFs (a) Λ = 4.2 µm, Λ/d_rod is changed; (b) Λ/d_rod= 2.7, d_rod is changed; (c) a near-zero flattened chromatic dispersion profile; and (d) different flattened chromatic dispersion profiles, the structural parameters are shown in Table 5. Reproduced from Ref. [144].

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Table 5. Structural parameters of tellurite ASHMOFs. Reproduced from Ref. [144].

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As shown in Fig. 16(b), with a constant value of Λ/d_rod, the change of d_rod significantly effects the dispersion curve. When d_rod increases gradually from 1 to 2 µm, the chromatic dispersion curve changes from a parabolic curve to a quartic curve. The dispersion curve becomes more flattened and at d_rod = 1.55 µm, it is flattened from 2.3 to 4 µm. We were able to obtain ultra-flattened chromatic dispersion by performing small adjustment of the fiber structural parameters. The tellurite ASHMOF with a core diameter of 3.188 µm, Λ of 4.2 µm and Λ/d_rod of 2.738 realizes an ultra-flattened chromatic dispersion with variation of ± 0.2 ps/km/nm in the wavelength range from 2.5 to 3.7 µm as shown in Fig. 16(c). This is the most flattened chromatic dispersion ever suggested in this wavelength range.

In addition, we were able to optimize the tellurite ASHMOF structural parameters to obtain different flattened chromatic dispersion profiles as shown in Fig. 4(d). Variation of the flattened values was within ± 0.5 ps/km/nm in the wavelength range of more than 1000 nm. The respective structural parameters are shown in Table 5.

The tellurite ASHMOFs can effectively operate as single-mode fiber, because the effective refractive index difference between the fundamental mode and the nearest high-order mode is as large as 0.056 and such a large difference ensures an extremely low coupling between the two modes [144,148]. Proper launching of the pump light would excite only the fundamental mode and the single-mode propagation can be kept. This will be confirmed by experiment in Section 3.3.4.

3.3.2. Simulation of supercontimuum generation in the dispersion flattened tellurite all-solid hybrid microstructured optical fiber

The tellurite ASHMOFs with chromatic dispersion profiles in Fig. 16(d) are suitable for SC generation using thulium-doped fiber lasers with the operation wavelength around 2 µm. We modeled the pulse evolution by solving the GNLSE given by Eq. (2) in the frequency domain with noise-included input pulse [149]:

In Eq. (2), $\tilde{A}$(z, ω) represents the complex spectral envelope of the electric field and z is the travel distance.

The linear operator including dispersion and loss is given by:

The nonlinear coefficient in this equation is defined by:

The employed noise model was one-photon-per-mode with random phase noise [150]. Coherence was assessed by calculating the modulus of the complex degree of the first-order coherence g₁₂ given by Eq. (7) whose values are from 0 to 1. When ∣g₁₂∣ is unity, it means perfectly coherent.

For each assessment of coherence, we performed 20 independent simulations. It means we used 190 pairs of SC to calculate g₁₂. Details of simulation parameters are described in Ref. [151]. The simulation pump pulse has a center wavelength of 2 µm, a pulse width of 200 fs and a peak power of 15 kW. Such parameters are accessible with commercial fiber lasers. The fiber length in simulation was 5 cm.

Figures 17(a)–(c) show SC spectra and coherence corresponding to the tellurite ASHMOFs with d_core = 3.3, 3 and 2.6 µm shown in Table 5. The corresponding dispersion profiles have flattened values of 5, −10 and −36 ps/km/nm. In the anomalous dispersion regime (D = 5 ps/km/nm), the soliton dynamics is dominant and the spectrum is expanded to more than 4 µm, but there is many dips in the spectrum and the coherence is low as shown in Fig. 17(a). In the normal dispersion regime, SPM and OWB are the main driving processes for the spectral broadening. With a favorable value of flattened dispersion (D = −10 ps/km/nm), the spectrum can be expanded to 3.4 µm. SPM-induced spectral broadening components is phase-related to the pump pulse. Thus the noisy process is suppressed, and the output SC is highly coherent as shown in Fig. 17(b). The SC has narrower spectral bandwidth and the long-wavelength edge is shorter than 3 µm when the fiber has larger normal dispersion as shown in Fig. 17(c). As a conclusion for this section, to obtain a broad and coherent SC with high spectral flatness, the normal chromatic dispersion absolute values should not be too large so that the bandwidth can be broadened considerably before OWB happens. Moreover, the normal chromatic dispersion absolute values should not be too small or else OWB would not happen and the spectrum would be narrow and would have low spectral flatness.

 

Fig. 17. (a)−(c) SC spectra and coherence of the tellurite ASHOMFs in Table 5 with d_core = 3.3, 3 and 2.6 µm, respectively. The pump wavelength is 2 µm and the peak power is 15 kW. Reproduced from Ref. [144].

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3.3.3. Tellurite all-solid hybrid microstructured optical fiber fabrication

The tellurite ASHMOF was fabricated by the rod-in-tube technique. The glass rods were prepared by casting melted oxide powders into the brass mold. Fabrication process has three steps as shown in Fig. 18(a). In step 1, the TLWMN core rod, TZLKAP rods were prepared and elongated to diameters of 3 mm (1A) and 1.45 mm (1B), respectively. The TZNL rod was drilled using ultra-sonic drills to form a structure (1C) with a central hole of 3 mm diameter and six surrounding holes of 1.5 mm diameter. Images of the real rods and tube are shown in the bottom of Fig. 18(a). In step 2, the TLWMN and TZLKAP rods were inserted into the drilled TZNL rod for elongation to form a preform (2A). In step 3, this preform was inserted into a TZNL tube (2B) for fiber drawing to obtain the ASHMOF (3A).

 

Fig. 18. (a) Illustration of the fabrication process for an all-solid hybrid microstructured fiber, and (b) cross-section of the fabricated tellurite ASHMOF. Reproduced from Ref. [144].

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The fabricated tellurite ASHMOF cross-section is shown in Fig. 18(a). Its core diameter is 3 µm, the rods diameter and the rod distance are ∼1.45 µm and ∼4 µm, respectively. During fiber fabrication, we observed a fluctuation of ± 0.5% in the fiber outer diameter. Figure 19(a) shows the calculated chromatic dispersions of the fundamental and high-order modes. The chromatic dispersions of the fundamental mode considering the structure fluctuation are shown in solid and dashed blue lines. We see that the change of chromatic dispersion due to the structure fluctuation is small, less than 1 ps/km/nm. Compared to an air hole hybrid MOF with a buffer layer having the dispersion fluctuation of ±4 ps/km/nm [152], the chromatic dispersion fluctuation of the tellurite ASHMOF is much smaller. This characteristic is due to the special design of the tellurite ASHMOF. When the fiber diameter increases, the rod distance increases and the contribution of the waveguide dispersion becomes weaker. At the same time, when the rod diameter increases, the contribution of waveguide dispersion becomes stronger. These two counter-effects create a small change of chromatic dispersion when the fiber diameter fluctuates. The nearest high-order mode also has normal chromatic dispersion. However, the dispersion profile has a steep slope. At 2 µm, the chromatic dispersion value of the nearest high-order mode is −160 ps/km/nm as compared to that of −10 ps/km/nm of the fundamental mode.

 

Fig. 19. (a) Chromatic dispersions and (b) the material loss and confinement loss of the fundamental mode and the nearest high-order mode of the fabricated tellurite ASHMOF. In (a) dashed lines are chromatic dispersion profiles with ±0.5% structure fluctuation. Reproduced from Ref. [144].

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Figure 19(b) shows the material loss and the confinement losses of the fundamental mode and the nearest high-order mode. The material loss was measured with an FTIR spectrometer (Perkin Elmer Spectrum 100) using TLWMN glasses with thickness of 0.8–1.5 mm. The glass has low loss up to ∼5 µm. The peak at 3.3 µm is due to –OH absorption. The confinement loss was calculated with Lumerical Mode Solutions. In the fundamental mode, the confinement loss is almost zero up to ∼4 µm. In the nearest high-order mode, the confinement loss becomes high at wavelengths longer than 2.3 µm.

3.3.4. Supercontinuum generation experiment

SC spectrum measurements were carried out using the similar experimental setup in Section 3.2. Figure 20 shows the SC spectra with different coupled powers from 21 to 66 µW. The powers were calculated by integrating the measured SC power spectral density. When the coupled power was 21 µW, the SC extended from 1.7 to 2.6 µm as shown in Fig. 20(a). New spectral components were generated to both sides of the SC spectrum through SPM and OWB. However, the broadened bandwidth was limited. With the increase of pump power, the SC was more broadened. The effect of dispersion profiles started to manifest itself at the coupled power of 32 µW as shown in Fig. 20(b). Because the dispersion profiles is flattened in the long-wavelength region, and has steep slope in the short-wavelength region, the SC spectrum was asymmetric with more expansion to the long-wavelength region. The spectrum was smooth and had a flat-top profile. With a maximum coupled power of 66 µW, the SC spectrum was broadest. It extended from 1.4 to 3.0 µm at the −20 dB level with high spectral flatness as shown in Fig. 20(c).

 

Fig. 20. SC power spectral density (PSD) with different coupled powers, the pump wavelength is 2 µm. The SC spectra were measured with two OSAs: AQ 6375 (blue line) and AQ 6377 (orange line). Reproduced from Ref. [144].

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Many spectral components had power exchange through cross-phase modulation (XPM) during propagation making the spectrum flattened. The main spectral components from 1.9 to 2.85 µm is within the −3 dB level. This is the most flattened SC spectrum obtained by pumping at 2 µm in the normal dispersion regime. Moreover, the mid-IR spectral components (components with wavelength longer than 2 µm) of the SC is 52 µW, which is 78 % of the SC power. This fact shows that the ASHMOF is very suitable for expanding the SC into the mid-IR using a short-wavelength pumping laser at 2 µm.

Figure 20(d) shows the SC spectrum when a 10 cm long tellurite ASHMOF was used. The spectrum shows no significant difference as compared to that of the 5 cm long fiber. This implies the SC spectrum is stable with fiber length and a short segment of the tellurite ASHMOF can be employed for broad mid-IR SC generation. The above SC spectra were recorded when the fundamental mode was excited.

The tellurite ASHMOF was proposed for chromatic dispersion control. We have exploited the potential of our newly proposed tellurite ASHMOF for chromatic dispersion controllability. Ultra-flattened chromatic dispersion profile with variation of as small as ±0.2 ps/km/nm over the wide wavelength range from 2.5 to 3.7 µm can be obtained. The fibers with flattened chromatic dispersion profiles have high potential for broadband mid-IR SC generation.

SC generation experiments with different pump powers at 2 µm were performed. By pumping the fabricated fiber at 2 µm, a broad and highly coherent SC with high spectral flatness was obtained. The SC with such good qualities is useful for applications such as spectroscopy, optical coherent tomography.

3.4. Supercontimuum generation in the chalcogenide all-solid hybrid microstructured optical fiber

Mid-IR SC generation has attracted a lot of research interest in recent years because of their potential applications in spectroscopy, biomedical imaging, optical coherence tomography and remote sensing [153–157]. Among various media for mid-IR SC generation, chalcogenide optical fibers are usually the media of choice due to their wide transmission in the mid-IR as well as high nonlinearity and the generated SC is the broadest SC that have been reported so far [126,127,129]. The ZDWs of chalcogenide glasses are longer than 5 µm, thus chalcogenide fibers were usually pumped at long wavelengths (6 ∼10 µm) to be benefited from the soliton dynamics for efficient expansion of the SC spectrum. By pumping a step-index As₂Se₃/Ge₁₀As_23.4Se_66.6 fiber at 6.3 µm, Petersen et al. reported an SC from 1.4 to 13.3 µm [126]. Cheng et al. reported an SC from 2 to 15.1 µm by pumping a step-index As₂Se₃/AsSe₂ fiber at 9.8 µm [129]. Zhao et al. reported an SC from 2 to 16 µm by pumping a double-clad Te-based chalcogenide fiber at 7 µm [127]. For such a long-wavelength pumping scheme, the pump sources are usually difference frequency generation (DFG) laser systems which consist of many amplification stages and have very large footprints. This limits the applications of the generated SC within only the laboratory environment. Besides, there is little possibility for scaling the SC power because the DFG laser power is normally just a few to a few tens milliwatts. To scale up the power, the pump source can be high-power fiber lasers whose central wavelengths are around 1.5 or 2 µm. To utilize these short-wavelength pumping for SC generation, chalcogenide fibers could be concatenated with another fiber such as silica or fluoride fiber and SC generation would be cascaded from near to mid-IR [123,158]. Another approach is to control the chromatic dispersion of the fibers, i.e. shifting the ZDW to shorter wavelengths so that they can be directly pumped using short-wavelength pulses [159,160].

In addition to the SC bandwidth, coherence is also an important factor for practical applications. In the above-mentioned research, SC generation has taken advantage of the soliton dynamics. However, SC generation based on soliton dynamics suffered from large pulse fluctuation in both phase and amplitude or in other words, the generated SC has a low temporal coherence [90]. On the other hand, a pumping scheme in the all-normal dispersion regime of the fiber has been proven to produce highly coherent SC by suppression of noisy processes such as modulation instability (MI) or spontaneous Raman scattering [133]. Considering the advantage of robust commercial fiber lasers at 1.5 and 2 µm, coherent SC generation with short-wavelength pumping around 1.5 and 2 µm has been demonstrated using silica, tellurite and chalcogenide fibers [135–143]. By pumping in the all-normal dispersion regime, coherent SC has been obtained. However, the long-wavelength edge could not reach 4 µm. Recent advancement in fiber lasers has extended the central wavelength beyond 3 µm with average powers of a few tens Watts [161–163]. Besides, Pr-doped and Dy-doped chalcogenide fibers have shown emission spectra up to 5, and 6 µm making them attractive as potential media for mid-IR fiber lasers [164–166]. Thus, it is worth investigating SC generation in the all-normal dispersion regime in this range of pump wavelengths, i.e., 3 to 5 µm.

In Ref. [144], we have proposed a novel ASHMOF consisting of three tellurite glasses. Such a fiber possesses excellent chromatic dispersion controllability. It is attractive to apply that structure to chalcogenide optical fibers and find out whether the excellent dispersion controllability is still applicable. Then, it will be very useful for extending the SC long-wavelength edge further into the mid-IR, especially for covering the entire transparent atmospheric windows, i.e., 3–5 µm and 8–13 µm. Here, a chalcogenide ASHMOF is fabricated and SC generation with such a fiber is performed [167]. The obtained SC are among the broadest SC using a short-wavelength pump in the all-normal dispersion regime.

3.4.1. Fiber design and chromatic dispersion

The fiber structure of the chalcogenide ASHMOF is shown in Fig. 21. It has a central core surrounded by six additional rods. The core, cladding and rod glasses are As₂Se₃, AsSe₂ and As₂S₅, respectively. These three glasses were chosen because of their good transmission in the mid-IR and their compatible thermo-mechanical properties for fiber drawing as well as suitable refractive index difference. Their optical properties are described in Section 2. At 3 µm, the refractive index difference of As₂Se₃ and AsSe₂ is 0.072, and the refractive index difference of As₂Se₃ and As₂S₅ is 0.543. Such a large refractive index difference between the core and the rod glass ensures efficient modification of chromatic dispersion. The ZDWs of these glasses are around 6∼7 µm. With a suitable fiber design, it is possible to shift the ZDW to shorter wavelengths or to obtain an all-normal chromatic dispersion profile which is of our interest here.

 

Fig. 21. Cross-section of the chalcogenide ASHMOF, Λ is the rod distance. Reprinted with permission from Ref. [167] © Optica.

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Calculation of chromatic dispersion was performed by the full-vectorial finite element method with a commercial software (Lumerical Mode Solutions). By adding solid rods around the core, the optical field in the core is disturbed and the waveguide dispersion is modified. The total chromatic dispersion D can be flexibly controlled over a wide wavelength range.

The ASHMOF with a large core and a large refractive index difference between the core and the cladding is a multi-mode fiber. The effective indices of the first two modes of the ASHMOF was calculated. The effective index difference between the two modes increases with wavelengths. At 3 µm, the effective index difference is 0.016, and at 5 µm, the effective index difference is 0.032. The effective index difference between the two modes increases with wavelengths. Such large effective index differences together with the high loss of the nearest high-order mode allow the chalcogenide ASHMOF to operate as a quasi-single-mode fiber by suppressing the mode coupling [168]. Moreover, the nearest high-order mode has a cut-off wavelength of ∼8 µm which means the optical field cannot propagate in this mode at wavelengths longer than 8 µm.

We optimized the structural parameters, i.e., the core diameter, the rod distance and the ratio of rod distance to rod diameter of this chalcogenide ASHMOF to obtain different flattened chromatic dispersion profiles with flatness of ±1 ps/km/nm as shown in Fig. 22 [167]. These results imply the excellent chromatic dispersion controllability of the chalcogenide ASHMOF. For example, a flattened all-normal chromatic dispersion with value of 1 ± 1 ps/km/nm is obtained when d_core = 9.2 µm, Λ = 12.32 µm and Λ/d_rod = 3.225. Especially, when d_core = 9.74 µm, Λ = 13.2 µm and Λ/d_rod = 3.3, an ultra-flattened chromatic dispersion profile with flatness as small as ± 0.4 ps/km/nm from 6 to 13.2 µm can be obtained. To the best of our knowledge, this is the most-flattened chromatic dispersion ever suggested with chalcogenide fiber over such a wide wavelength range [167].

 

Fig. 22. An ultra-flattened and near-zero chromatic dispersion profile of the chalcogenide ASHMOF. Adapted with permission from Ref. [167] © Optica.

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Such a fiber with an ultra-flattened and near-zero chromatic dispersion profile is highly suitable for applications such as mid-IR optical fiber parametric amplification or frequency comb expansion. Here we study SC generation in a fiber with a flattened dispersion profile shown in Fig. 23(a) to demonstrate SC generation in the all-normal dispersion regime.

 

Fig. 23. (a) Chromatic dispersion of a chalcogenide ASHMOF and (b), and (c) simulated output SC spectra with different pump wavelengths (b) 3 µm to 5 µm, and (c) 6 to 10 µm of the chalcogenide ASHMOF. Reprinted with permission from Ref. [167] © Optica.

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3.4.2. Simulation of supercontinuum generation in the chalcogenide all-solid hybrid microstructured optical fiber

We modeled the pulse evolution by solving the GNLSE given by Eq. (2) in the frequency domain with noise-included input pulse [149]. The value of n₂ for As₂Se₃ was estimated based on Refs. [79,120,169], which gives a value of 5.46 × 10⁻¹⁸ m²/W at 3 µm.

The Raman response function is modeled as:

In Eq. (8), f_R is the fractional contribution of delayed Raman response, τ₁ is the Raman period which is related with the phonon oscillation frequency, and τ₂ defines the characteristic damping time of the network of vibrating atoms; Θ(t) is the Heaviside step function and δ(t) is the Dirac delta function. The values of f_R, τ₁, and τ₂ are 0.115, 23.1 fs, and 195 fs, respectively Ref. [170].

The employed noise model is one-photon-per-mode with random phase noise [150]. Coherence was assessed by calculating the modulus of the complex degree of first-order coherence g₁₂ given by Eq. (7). For each assessment of coherence, we performed 20 independent simulations. It means we used 190 pairs of SC to calculate g₁₂.

3.4.3. Suoercontinuum generation with different pump wavelengths

To show the potential of the chalcogenide ASHMOF in SC generation, the pump wavelength was changed from 3 to 10 µm. In the simulation, the simulated peak power was 20 kW, the pulse width was 200 fs and the fiber length was 10 cm. As shown in Fig. 23(a), the chromatic dispersion profile of ASHMOF is flattened with a value of ∼ –5 ps/km/nm in the wavelength range from 5.2 to 11.2 µm. The fiber structural parameters are d_core = 8 µm, Λ = 11 µm, and Λ/d_rod = 3.412. Figures 23(b) and (c) show the simulated output SC spectra of ASHMOF with two pumping schemes: short-wavelength pumping [Fig. 23(b)], and long-wavelength pumping [Fig. 23(c)]. When the pump wavelength is 3 µm, the SC spectrum is from 2 to 5.9 µm at the –40 dB level which is more than one octave. When the pump wavelength is changed to 4 and 5 µm, the SC long-wavelength edge continues to be shifted to longer wavelengths and the SC bandwidth became broader.

When the pump wavelength is 5 µm, the SC spectrum of the chalcogenide ASHMOF spans a wavelength range from 2.5 to 9.2 µm at the –40 dB level which was nearly two octaves. These results show the potential of the chalcogenide ASHMOF in SC generation using short-wavelength pumping. With longer pump wavelengths, e.g. 6 to 10 µm, the long-wavelength edge reaches further to the mid-IR region, e.g. 10.2 to 15.9 µm. Thus, the chalcogenide ASHMOF can also be applied for SC generation using long-wavelength pumping. It should be noted that the simulation is valid for single-mode operation as discussed in Section 3.2. If the mode-coupling occurs, the SC bandwidth will be narrower as compared to the case of fundamental mode propagation. The reason is that the modal dispersion will reduce the pulse intensity quickly. As a result, spectral broadening based on SPM will become less efficient.

We calculated the spectral evolution along the fiber when the pump wavelength is 5 µm. The SC spectrum reaches its maximum bandwidth when the travel distance is around 3.5 cm [167]. Further propagation of the pulse along the fiber does not significantly change the bandwidth. In the next simulation, we studied SC generation with different pump powers but limited the fiber length to 5 cm. This does not affect the discussion about the dependence of SC bandwidth on pump power.

3.4.4. Supercontinuum generation with different pump powers

Figure 24 shows the output SC spectra when the pump peak power at 5 µm is 20, 30, 50, 80 and 100 kW. When the pump peak power is increased from 20 to 30 and 50 kW, both short- and long-wavelength edges are expanded to both sides. At 50 kW of peak power, the SC spectrum is from 1.9 to 10.8 µm at the –40 dB level which is more than 2 octaves.

 

Fig. 24. Output SC spectra of the chalcogenide ASHMOF with different pump peak powers when the pump wavelength is 5 µm. Reprinted with permission from Ref. [167] © Optica.

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Further increase of the pump peak power to 80, and 100 kW does not shift the short-wavelength edge significantly. This can be explained by the low material transmission of chalcogenide and the large absolute value of chromatic dispersion at wavelengths shorter than 2 µm. However, the long-wavelength edge continues to be shifted to longer wavelengths with higher pump powers. At 100 kW of pump peak power, the long-wavelength edge can reach 12.4 µm. The SC also has a good spectral flatness with the spectrum expanding from 2 to 11.5 µm at the –10 dB level.

To have an insight in the spectral broadening dynamics, the spectrograms at different travel distances z along the fiber when the pump peak power is 30 kW are shown in Figs. 25(a)–(d). At z = 0.185 cm, under SPM, the spectrum was broadened to both sides as shown in Fig. 25(a). At z = 0.555 cm, OWB happened first in the short wavelength region as shown in Fig. 25(b). The spectral side lobe on the left side of the spectrum and oscillation on the trailing edge of the pulse in the time domain are characteristics of OWB [43]. At z = 2.22 cm, OWB happened at the right side of the spectrum. Here, we can see the effect of flattened chromatic dispersion in the long-wavelength region. With a flattened and small chromatic dispersion on the long-wavelength side, OWB happened at a later time as compared to the short-wavelength side. Thus, the spectrum was expanded more to the long-wavelength region. After OWB happened, the energy transfers among different wavelength components helped smooth the spectrum as shown in Fig. 25(d). During the spectral broadening, SPM and OWB were the main processes, thus the coherence of the pulse was kept to unity as shown in Fig. 25(e). To clarify the potential of this newly proposed fiber, fiber fabrication and SC generation experiments are shown in the next Sections.

 

Fig. 25. Spectrograms at different travel distances z when the pump wavelength is 5 µm, and peak power is 30 kW: (a) z = 0.185 cm, (b) z = 0.555 cm, (c) z = 2.22 cm, and (d) z = 3.33 cm and (e) output SC spectrum with its coherence. Reprinted with permission from Ref. [167] © Optica.

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3.4.5. Chalcogenide all-solid hybrid microstructured optical fiber fabrication

The fabrication process of the chalcogenide ASHMOF is similar to that of the tellurite ASHMOF [167]. The fiber cross-section image taken with an SEM is shown in Fig. 26(a).

 

Fig. 26. (a) SEM image of the fabricated fiber: the circle in the center is As₂Se₃, the black circles are As₂S₅, the background is AsSe₂, (b) the chromatic dispersion calculated based on the SEM image and the effective mode area (EMA) of the fiber, (c) the fiber loss calculated from the material loss and the confinement loss, and (d) the fiber far-field light spot. In (b), chromatic dispersion of the designed chalcogenide ASHMOF is displayed for comparison. Reprinted with permission from Ref. [167] © Optica.

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The core and rod diameters and rod distance are 7.95, 4.46 and 12.15 µm, respectively. Based on the SEM image, chromatic dispersion was calculated and shown in Fig. 26(b). Compared to the chromatic dispersion of the designed fiber, that of the fabricated fiber has some discrepancy in the range of wavelengths longer than 10 µm. However, the difference is small, and basically, we obtained the targeted chromatic dispersion profile. Compared to a double-cladding fiber which has been fabricated in our previous work [132], the chalcogenide ASHMOF has better chromatic dispersion controllability with a more flattened dispersion profile. It is expected to generate broader SC generation using short-wavelength pumping. The fiber loss is shown in Fig. 26(c). It was calculated by including both the material loss and the confinement loss of the fiber. There was very high loss of ∼ 50 dB/m for wavelengths longer than 13 µm. Thus a short fiber of 3.7 cm in length was employed for SC generation experiments. The fiber far-field light spot is shown in Fig. 26(d). It was captured with a mid-IR beam imager (WinCamD FIR2-16-HR) when a beam with wavelength of 3 µm was injected into the fiber. The light spot shows that most of the light intensity was distributed in the fundamental mode of the fiber.

3.4.6. Supercontinuum generation experiment

SC spectrum measurements were carried out using the similar experimental setup in Section 3.2. Kept in mind that the future fiber lasers can operate in the wavelength range of 3 ∼ 5 µm which is the emission wavelength range of Pr or Dy doped chalcogenide fibers, we studied SC generation using pump wavelength in this range.

Figure 27 shows the SC spectra with various pump powers when the pump wavelength was 3 µm. With a pump power of 0.5 mW, the bandwidth was about 0.7 µm from 2.6 to 3.3 µm, and the left side of the spectrum was more flattened (2.7–3.0 µm at the –5 dB level). Initially, SPM would broaden the spectrum to both sides. Then OBW would happen on the left side first because of the steeper slope of the chromatic dispersion profile on this side. When the pump power was increased to 1 and 1.5 mW, the left side showed insignificant expansion while the long-wavelength edge continuously moved to the right and reached 3.7 µm. At 1.5 mW of pump power, the bandwidth was 1.3 µm. With a maximum pump power of 3.7 mW, the output SC power was 0.3 mW, and the bandwidth was 3.2 µm expanding from 2.2 µm to 5.4 µm, and the flat-top profile was from 2.5 to 4.5 µm at the –10 dB level. To the best of our knowledge, this is the broadest SC pumped at 3 µm in the all-normal chromatic dispersion chalcogenide fiber. Although there were significant flows of N₂ in the laser cavity (4 L/min), in the monochromator (20 mL/min) and in the measuring chamber (10 L/min), we could not remove the absorption of water and CO₂ completely. Absorption at ∼2.9 µm (water) and ∼4.2 µm (CO₂) can be seen in the figures. To further reduce the absorption, higher flows of N₂ in a small measuring chamber can be employed and the gas lines as well as the equipment set-up must be redesigned. For that reason, the other measurements were carried out in normal laboratory air ambience without affecting the result discussion.

 

Fig. 27. Measured output SC spectra with different input powers, the pump wavelength was 3 µm. Reprinted with permission from Ref. [167] © Optica.

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At the pump wavelength of 4 µm and the pump power of 4.5 mW, the SC power was 0.37 mW and the SC spectrum was from 2.2 to 8.0 µm as shown in Fig. 28(a). The spectrum was smooth and had a flat-top profile which are characteristics of SC generation dynamics by SPM and OWB. At the pump wavelength of 5 µm, although the pump power was 3.9 mW, smaller than the pump power at 4 µm, the SC power in this case was 0.32 mW and the SC bandwidth was broader as shown in Fig. 28(b). The SC long-wavelength edge reached 10.2 µm with a flattened and smooth spectrum profile and a bandwidth of 5.7 µm (from 2.8 to 8.5 µm) at the –10 dB level. The pump wavelength in this case was in the flattened region of the chromatic dispersion profile and the chromatic dispersion value at this wavelength was small (–6.5 ps/km/nm) resulting in efficient spectral broadening by SPM.

 

Fig. 28. Measured output SC spectra when the pump wavelength was (a) 4 µm, and the pump power was 4.5 mW and (b) 5 µm, and the pump power was 3.9 mW. Reprinted with permission from Ref. [167] © Optica.

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From the above results, it could be expected that pumping at longer wavelengths would produce broader SC spectra. Thus, we performed pumping the fiber at 8, 9, and 10 µm. For these experiments, a different lens (Thorlabs C028TME-F) with anti-reflection coating from 8 to 10 µm was used. The respective spectra are shown in Fig. 29. It is interesting to find out that while the long-wavelength edge could be expanded to ∼13 µm (pumped at 8 µm), and 14 µm (pumped at 10 µm), the short-wavelength edge also moved to the right making the SC spectrum not much broader as compared to that with the pump wavelength of 5 µm. Such a similar trend was also observed in Ref. [131]. But it has not been explained. In our case, there were two reasons for this trend. First, while the chromatic dispersion is almost constant from 5 to 10 µm, the effective mode area is larger at longer wavelengths as shown in Fig. 28(b). This would reduce the nonlinear coefficient. Second, the pump power was smaller at longer wavelengths. These two factors resulted in a decrease in the SC bandwidth.

 

Fig. 29. Measured output SC spectra with pump wavelengths of 8, 9 and 10 µm. The pump powers were 2.0 mW, 1.8 mW and 1.0 mW, respectively. Reprinted with permission from Ref. [167] © Optica.

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It is worth comparing SC bandwidth in this research to other related research. As can be seen from Table 6, even with smaller input power, e.g., about 4 to 5 times smaller to those reported in Refs. [79,169], the generated SC in this research are among the broadest SC reported when the fiber was pumped in the normal dispersion regime. These results show the great potential of the chalcogenide ASHMOF in coherent and broad SCG. Moreover, the generated SC have good spectral flatness making them highly applicable for spectroscopy and optical coherence tomography.

Table 6. SCG using short wavelength pump (3–5 µm). Reprinted with permission from Ref. [167] © Optica.

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Here we fabricated a chalcogenide ASHMOF using three glasses As₂Se₃, AsSe₂ and As₂S₅ for broad mid-IR SC generation with high coherence and good spectral flatness. The fiber possesses a flattened all-normal chromatic dispersion profile with value of –5 ps/km/nm and variation of ±1 ps/km/nm over the wavelength range from 5.2 to 11.2 µm. Broad mid-IR SC generations were demonstrated. The generated SC were among the broadest SC with good spectral flatness when the fiber was pumped at 3, 4, and 5 µm in the normal dispersion regime. Although the output SC powers were relatively low because of the low input powers, it is possible to scale up the power by using fiber lasers with higher repetition rate as the input pump.

4. Infrared image transport through optical fibers with transversely-disordered refractive index profile

Anderson localization was found as the absence of electron-waves in disordered media [64] and then observed in various other wave phenomena [175–178]. Transverse Anderson localization (TAL) of light was proposed by H. de Raedt et al. [179,180]. After the theoretical proposal, TAL of light was experimentally demonstrated in several two-dimensional optical media. TAL of light requires the refractive index distribution that is random in the transverse direction but invariant in the longitudinal direction. TAL of visible light was first observed in a disordered two-dimensional photonic lattice [181]. Recently, optical image transport using the transverse localization of light has been demonstrated in a polymer disordered optical fiber made of poly methyl methacrylate (PMMA) and poly styrene (PS) whose refractive index difference is 0.1 [182,183]. The transported visual image quality was even better or comparable with those obtained by using commercial multicore image fiber. The numerical and experimental results showed that highly disordered optical fibers with large refractive index difference can transport high quality optical images. Moreover, as compared with other advanced fiber-based imaging methods, no additional pre- and post-processing is required to obtain the image and it can be easily operated in a fully flexible endoscopic system [183]. Those properties are very advantageous to optical imaging applications in biological and medical fields. On the other hand, the image resolution in polymer disordered optical fibers is currently limited by the optical attenuation as well as the quality of cleaving and polishing surfaces of the polymer fibers [183]. A disordered silica glass optical fiber with random air hole, high refractive index difference and high filling fraction has been proposed as an alternative medium but the image transport properties have not been demonstrated yet [184].

Based on the shortcomings of previous works and the knowledge of highly nonlinear glasses, we have considered tellurite and chalcogenide glasses as promising media to realize the transverse localization of light. We have studied tellurite and chalcogenide glass based all-solid tellurite optical glass rod, and fiber with transversely disordered refractive index profiles for near-IR to mid-IR image transport. Compared to the glass-air random structure, the all-solid structure is advantageous because it is easier to be fabricated, easier to control the filling fraction and it has higher mechanical stability due to the absence of air-hole structures.

We demonstrated the transverse localization of light and the near-IR image transport at 1.55 µm for the first time to the best of our knowledge by using a tellurite all-solid transversely disordered optical rod (ASTDOR) [185].

Furthermore, in order to improve its compactness, flexibility and to enable more potential biological and medical applications which can only be achieved in the field of optical fiber optics, a tellurite ASTDOF whose outer diameter is about 125 µm was successfully fabricated. Numerical study was carried out to clarify appropriate designs of the fiber structures and to investigate their properties of near-IR optical image transport. By using a 10 cm-long segment of the fabricated tellurite ASTDOF, we experimentally transported the optical image of three vertical slits whose width was as small as 14 µm by using the CW probe beam whose wavelength was tuned from 1.44 to 1.60 µm [186].

Mid-IR imaging has great potential for biomedical applications. Many fundamental molecular vibration absorptions are included in the mid-IR region [187,188]. Moreover, the peak wavelength of thermal emission at human body temperature is about 9.3 µm in the mid-IR region. Thus, mid-IR images provide the temperature with non-contact and non-invasive [189]. Chalcogenide glasses have been used as materials of mid-IR optical fibers, some of which can transport mid-IR optical image [190–192]. However, no results have ever been reported on TAL and optical image transport of the mid-IR light in TDOFs.

We successfully fabricated a chalcogenide ASTDOF. We observed the TAL of mid-IR light in the chalcogenide ASTDOF for the first time to our best knowledge, and clarified the localization by using a cross-sectional image of the fabricated chalcogenide ASTDOF in order to optimize fiber parameters for high-resolution mid-IR image transport [193]. Here, we show the potential of TDOF made of tellurite and chalcogenide glasses as near-IR to mid-IR image transportation media.

4.1. Near-infrared optical image transport though the tellurite all-solid transversely disordered optical rod and fiber

4.1.1. Tellurite all-solid tellurite transversely disordered optical rod fabrication

Two tellurite glass compositions of 70TeO₂–8Li₂O–17WO₃–3MoO₃–2Nb₂O₅ (TLWMN) and 75TeO₂–15ZnO–5Na₂O–5La₂O₃ (TZNL) which have a small difference in softening temperature (about 0.5 °C), compatible thermal expansions from room to 400 °C and broad transmission range from about 0.4 up to 6.0 µm were developed for TDOR fabrication process. The thermal expansion properties of these TLWMN and TZNL glasses are similar when the temperature is raised from 200 to 400 °C and the difference between their T_s is as small as 0.5 °C [185]. The compatible thermal properties of the TLWMN and TZNL tellurite glasses are very advantageous to the stability of the following fabrication process. At 1.55 µm, the refractive index difference between the TLWMN and TZNL glasses is Δn = 0.095 [185].

TLWMN and TZNL glass rods were prepared by using dry melting method. These two rods were drawn down to fibers whose diameters were 150 µm by using our home-designed fiber drawing tower at a temperature of 440°C. In total, 4500 fiber segments which were 15 cm-long were randomly stacked together. By this way, a bundle of fibers composed of both TLWMN and TZNL tellurite glasses was obtained with a disordered refractive index profile in the transverse dimension and the outer diameter was about 12 mm. The ratio between the number of TLWMN and TZNL fibers was 1:1 so that the filling fraction (f) was 0.5 as given by Eq. (9)

 

Fig. 30. Schematic image of the fabrication process to fabricate the tellurite ASTDOR. Reprinted with permission from Ref. [185] © Optica.

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Fig. 31. Images of the tellurite ASTDOR and a random square region in its cross-section. Reprinted with permission from Ref. [185] © Optica.

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4.1.2. Near-field intensity profile for the tellurite all-solid transversely disordered optical rod

In order to investigate the light beam guidance and localization properties in the fabricated tellurite ASTDOR, an experimental setup was constructed as shown in Fig. 32 [185]. A CW light source at 1.55 µm (Agilent-8164B laser source) guided by a single mode optical fiber (Thorlabs 980 HP) was launched into a 10-cm long tellurite ASTDOR by using butt-coupling method. The near-field intensity at the output facet of the tellurite ASTDOR was recorded by a CCD camera of a beam profiler (Hamamatsu C5840) when the 980HP fiber was scanned across the input facet. The measurement was repeated more than 10 times for each of 3 different fabricated tellurite ASTDORs.

 

Fig. 32. Experimental setup for the near-field intensity measurements. Reprinted with permission from Ref. [185] © Optica.

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As a result, the output beam remained localized after its propagation and its near-field profile was observed with a visually localized spot. Figure 33 shows a typical near-field intensity profile of a localized beam which was experimentally obtained from our measurement [185]. In Fig. 34, the corresponding cross section of the intensity profile was analyzed and plotted with exponentially decaying tails [185]. It has been reported by Karbasi et al. that when the disorder of transverse refractive index profile and localized beam are absent, the beam profile would fill the entire cross section of the fiber after a few millimeters [181]. Contrarily, the exponentially decaying tails of the near-field intensity profile which were shown in Figs. 33 and 34 provide clear evidence of the beam localization.

 

Fig. 33. Typical near-field intensity profile of a localized beam at the output facet of a 10-cm long tellurite ASTDOR fabricated in this work. Reprinted with permission from Ref. [185] © Optica.

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Fig. 34. Cross section of the corresponding near-field intensity profile shown in Fig. 34. Reprinted with permission from Ref. [185] © Optica.

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4.1.3. Near-infrared optical image transport through the tellurite all-solid transversely disordered optical rod

To investigate the near-IR optical image transport capability of the fabricated tellurite ASTDOR, a test target (Thorlabs, 1951 U.S. Air Force) was installed in front of a 10 cm-long tellurite ASTDOR in the experimental setup as shown in Fig. 35 [185]. Optical images of the number from group 6 on the test target were launched into of the tellurite ASTDOR by using the same laser source at 1.55 µm in section 3A. The images of the numbers 3, 4 and 5 of group 6 on the test target was transported [185]. The size of each number from group 6 on the test target is the same and their heights are about 300 µm. The Hamamatsu-C2741-03 beam profiler was used in this measurement due to its higher sensitivity as compared to that of the Hamamatsu-C5840 in Fig. 32.

 

Fig. 35. Experimental setup for the measurement of near-IR optical image transport in a 10-cm long tellurite ASTDOR. Reprinted with permission from Ref. [185] © Optica. The 1951 U.S. Air Force test target was used and images of numbers 3, 4 and 5 of group 6 were transported. (https://www.thorlabs.com/images/GuideImages/4339_R3L3S1N_SGL.jpg)

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Figure 36 shows near-IR optical images of the numbers 3, 4 and 5 which were captured at the output facet of the tellurite ASTDOR [185]. The captured images are visually clear with high contrast and high brightness. It is remarkable that the quality of our transported optical images can be comparable or higher than the results which were obtained by using a polymer Anderson localized fiber and by a commercially available multicore imaging optical fiber [183]. Based on the scale bar in Fig. 36, the estimated height of each number is approximately 1.3 times larger than the real size on the test target [185]. The increasing in the height of the number can be caused by the diffusive broadening occurred when the light propagated in the tellurite ASTDOR. But due to the localization of the light beam, the broadening effect is less such that localized beam and clear transported optical images can be observed. This result is also consistent with the concept of the transverse localization of light.

 

Fig. 36. Transported images of numbers (3, 4 and 5) on the 1951 U.S. Air Force test target after a 10-cm long tellurite ASTDOR by using a CW probe beam at 1550 nm. Reprinted with permission from Ref. [185] © Optica.

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In addition, it has been reported that shorter wavelengths result in a stronger localization effect and a smaller localization beam radius [184,194]. Consequently, laser light sources at 0.405 µm and 0.633 µm were used to study the properties of localization of light in case of polymer Anderson localized fibers [182,183,194] and commercially available multicore imaging optical fibers [183]. However, it is very interesting that optical images at the wavelength of 1.55 µm which is far from the aforementioned visible lights can be transported by the transverse localization effect using our tellurite ASTDOF.

Another factor that can strengthen the transverse localization effect is the refractive index difference in the transverse profile. It has been demonstrated that larger refractive index difference between the host medium and the disorder sites results in strong localization and smaller value of the beam radius [194,195]. In this work, transverse localization effect and near-IR optical image transport were obtained experimentally by using our tellurite ASTDOR although the refractive index difference is about 0.095 at 1.55 µm. But, tellurite glasses with refractive index difference up to 0.49 have been demonstrated in practice by our group [196,197]. Therefor it is reasonable to expect that by using tellurite transversely disordered optical fibers with larger refractive index difference, higher performances of transverse localization of light and near-IR optical image transport can be obtained in the near future.

To the best of our knowledge, this is the first time that an all-solid tellurite glass rod with a transversely disordered refractive index profile was fabricated as a medium to study the transverse localization of light and near-IR image transport. The quality of our transported optical images can be comparable or higher than the results which were obtained by a polymer Anderson localized fiber and by a commercially available multicore imaging optical fiber. With the advantages of using tellurite glasses and all-solid structure, the tellurite ASTDOR is a promising candidate for the transverse localization of light and near-IR optical image transport applications.

4.1.4. Tellurite all-solid transversely disordered optical fiber fabrication

4.1.4.1. Design of fiber structure parameters

Based on the refractive index data of the TLWMN and TZNL tellurite glasses, numerical calculations were carried out to understand the light beam propagation through waveguide media which have periodic and disordered refractive index profiles in the transverse planes as shown in Figs. 37(a) and (b), respectively [186]. The waveguide media have TLWMN and TZNL glasses as high and low refractive index components. In the transverse plane, the ratio between them was 1 : 1 and the size of each unit was 1 × 1 µm² . An incident Gaussian beam at 1.55 µm was assumed to propagate through a 100 µm distance in the longitudinal dimension of the waveguide media. At each value of the propagation distance z, the beam radius is calculated by Eq. (10) where E(x, y) is the electric field of the light obtained by numerically solving Maxwell’s equations using the finite-difference beam propagation method [195,198] and semi-vector scheme [195]. The transverse electric field along the propagation length z is governed by Eqs. (11) and (12). In these equations, E_x and E_y are the electric field components in the x and y direction, k₀ is the wave number, n₀ is the reference index which makes the slowly varying envelope approximations valid [198] and n = n(x, y) is the refractive index.

 

Fig. 37. (a) and (b) are schematic images of transverse planes with periodic and disordered refractive index profiles, respectively. (c) and (d) show evolution of the light beam calculated after 100 µm propagation distance in waveguide media with corresponding transverse planes in Figs. 37 (a) and (b). Reprinted with permission from Ref. [186] © Optica.

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The evolutions of the light beam in periodic and disordered media after a 100 µm propagation distance are shown in Figs. 37(c) and (d), respectively, and the change of the beam radius with the propagation length is plotted in Fig. 38 [186]. As can be seen, the beam radius rapidly increases from 1.55 to about 15 µm when the Gaussian beam propagates in the periodic media. In contrast, the beam radius is restrained from expanding in the disordered refractive index profile which is related to the effect of transverse localization of light [195].

 

Fig. 38. The change of the beam radius with the propagation length by using waveguide media with periodic and disordered refractive index profiles. Reprinted with permission from Ref. [186] © Optica.

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A schematic image of the tellurite ASTDOF is plotted in Fig. 39 [186]. High and low refractive index units are shown in gray and black hexagonal units, respectively. The size of each unit is equal to the distance between the central of two adjacent units and is defined as the pitch p. The ratio between TLWMN and TZNL units is related to the filling fraction (f) which is defined as Eq. (9) where S_TLWMN and S_TZNL are the number of TLWMN and TZNL units, respectively. The fiber length was set as 10 cm.

 

Fig. 39. Fiber profile and parameters which are designed for the calculation in this work. Reprinted with permission from Ref. [186] © Optica.

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In addition, the evolution of the light beam after a propagation distance was discussed not only by the beam radius R_beam but also the displacement parameter D_beam which is illustrated in Fig. 40 [186] and is given by Eq. (13) where P = (x, y) is the transverse position vector. The beam radius shows how the beam expands and the displacement parameter D_beam shows the deviation of the central of the beam from its original position. Small values of R_beam and D_beam suggest that the difference between the input image and the the transported image at the output is small, in other words, their similarity is high.

 

Fig. 40. Evolution of the light beam after propagating a 10 cm-long tellurite ASTDOF. Reprinted with permission from Ref. [186] © Optica.

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In Fig. 41, schematic images of the transverse refractive index profile of ASTDOFs are plotted when f is 0.2, 0.5 and 0.8 [186]. When the filling fraction f is high (f = 0.8), the quantity of high-index units is dominant. They are easy to connect and form large clusters in the trans-verse plane. The presence of large high-index clusters can reduce the disorder of the refractive index profile and results in large values of R_beam and D_beam at the output which is harmful to the quality of the transported image. On the other hand, when the filling fraction is too low (f = 0.2), large low-index clusters are easy to form and the quantity of high-index units is too less. As a result, the transported image is obtained with a very low resolution. Therefore, in the scope of this work, calculations and experiments were performed with a moderate value of filling fraction (f = 0.5).

 

Fig. 41. Schematic images of the transverse refractive index profile of tellurite ASTDOFs with different values of filling fraction f = 0.2, 0.5 and 0.8. High and low refractive index units were shown in gray and black hexagonal units, respectively. Reprinted with permission from Ref. [186] © Optica.

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In Figs. 42(a) and (b), the dependence of R_beam and D_beam on the pitch p was investigated numerically [186]. A Gaussian CW beam at 1.55 µm was assumed to couple to the 10 cm-long tellurite ASTDOF. The input R_beam was 1.55 µm. The calculation area was as large as 100 × 100 µm². The filling fraction f is constant at 0.5 and p varies from 0.517 to 2.067 µm. For each value of p, the calculation was repeated 30 times. As a result, small values of R_beam and D_beam can be obtained when p is from 0.775 to 1.550 µm. The mean value of R_beam can be as small as 4.4 µm and the mean value of D_beam can be as small as 2.8 µm when p is 1.033 µm. Based on this calculation, the tellurite ASTDOF in which p is about 1.033 µm is expected to be realized in the fiber fabrication process.

 

Fig. 42. Dependence of R_beam and D_beam on the pitch p when filling fraction f is constant at 0.5. Reprinted with permission from Ref. [186] © Optica.

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4.1.4.2. Tellurite all-solid transversely disordered optical fiber fabrication

The tellurite ASTDOF was successfully fabricated using the similar process for the tellurite ASTDOR made of our developed tellurite glasses described in Section 4.1.1. The fabrication process started with the preparation of TLWMN and TZNL glass rods using the dry melting method. These two glass rods were drawn down to fibers whose diameters were 100 µm by using our home-designed fiber drawing tower at a temperature of 440 °C. In total, 5000 fiber segments of each TLWMN and TZNL glasses were obtained. They were 15 cm long and were randomly stacked together. The ratio between the number of TLWMN and TZNL fibers was 1 : 1 so that the filling fraction (f) was 0.5. By this way, a bundle of fibers composed of both TLWMN and TZNL tellurite glasses with a disordered refractive index profile in the transverse plane was formed. This bundle of fibers was stacked in a TZNL cladding tube whose inner and outer diameters were 10 and 12 mm, respectively. Finally, they were drawn down to form the tellurite ASTDOF whose outer diameter was about 125 µm. During the fiber drawing process, a negative pressure of −4.0 kPa was applied to ensure that the interior air gaps between each TLWMN and TZNL units were removed. By this fabrication technique, a transversely-disordered refractive index profile was obtained and was maintained invariant in the longitudinal dimension of the tellurite ASTDOF. The whole fabrication process is schematically illustrated in Fig. 43 [186].

 

Fig. 43. Schematic image of the fabrication process of the tellurite ASTDOF. Reprinted with permission from Ref. [186] © Optica.

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In Figs. 44(a) and (b), images of TLWMN and TZNL fiber units before and after they were randomly stacked in the TZNL cladding tube are shown. In addition, cross-sectional images of the final all-solid TDOF and of a random square region are shown in Figs. 44(c) and (d). A disordered tellurite glass profile can be seen in the center of the fiber. The dark random dots represent the high-index units (TLWMN glass) and the bright background consists of low-index units (TZNL glass) [186].

 

Fig. 44. (a) Separate TLWMN and TZNL glass fibers, (b) TLWMN and TZNL fibers after randomly stacked inside a TZNL cladding tube whose inner diameter is 10 mm, (c) cross-sectional image of the final tellurite ASTDOF and (d) image of a random square region in the center of the tellurite ASTDOF. Reprinted with permission from Ref. [186] © Optica.

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4.1.5. Near-infrared optical image transport by the tellurite all-solid transversely disordered optical fiber

An experimental setup was constructed, as shown in Fig. 45, to investigate the transport of near-IR optical images in the fabricated tellurite ASTDOF [186]. A CW tunable light source around 1.55 µm (Agilent-8164B laser source) guided by a single mode optical fiber (Thorlabs 980 HP) was used as an incident probe beam. A test target (1951 U.S. Air Force) was installed in front of the 10 cm-long segment of the tellurite ASTDOF. Optical image of three vertical slits on the test target was launched into of the tellurite ASTDOF when the probe beam passed through them. At the output of the tellurite ASTDOF, the image was captured by the CCD camera of a beam profiler (Hamamatsu C2741). In this experimental setup, the wavelength of the light source can be tuned to 1.44, 1.50, 1.55 and 1.60 µm. The width of the vertical slit was chosen as 11 or 14 µm and TDOFs with different values of p of 1.0, 1.5 and 2.0 µm were measured.

 

Fig. 45. Experimental setup to investigate the transport of near-IR optical images in the fabricated tellurite ASTDOF. Reprinted with permission from Ref. [186] © Optica.

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The first measurement was carried out by using a 10-cm long segment of the tellurite ASTDOF in which p was 1.0 µm. The wavelength of the probe beam was set at 1.55 µm and the slit width was 14 µm. The photo of three vertical slits taken by an optical microscope (Nikon, Eclipse-ME600) is shown in Fig. 46(a) [186]. Their optical image at 1.55 µm which transported through the fiber was captured as shown in Fig. 46(b). The image was obtained with high brightness and contrast and the pattern of three vertical slits can be found. To confirm the measured result, numerical calculation was performed with the same experimental conditions. As shown in Fig. 46(c), the transported image which was simulated can reproduce the experimental result in Fig. 46(b).

 

Fig. 46. (a) Photo of three vertical slits on the test target (slit width = 14 µm), (b) transported optical image at 1.55 µm of three slits in Fig. 47 (a) captured at the output of the 10 cm-long segment of the tellurite ASTDOF and (c) corresponding transported image obtained by numerical calculation. Reprinted with permission from Ref. [186] © Optica.

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In order to consider the result in a qualitative view point, the zero mean normalized cross-correlation method (ZNCC) [199–201] which is widely used in template matching application was introduced. Compared to other approaches for the image matching measurement, ZNCC provides better robustness since it tolerates uniform brightness variations thanks to the subtraction of the local mean value [200]. The parameter R_ZNCC which expresses the zero mean normalized cross-correlation between the input image and the corresponding transported image at the output of the 10 cm-long tellurite ASTDOF was calculated as Eq. (14) where I (x, y), O (x, y) are the input and output intensity of the light at the position (x, y), $\bar{I}$ and $\bar{O}$ are the average light intensity at the input and output, respectively. The value of R_ZNCC can vary from −1 to 1. The higher the R_ZNCC is, the more similar the input and output images are

The experiment was further extended by investigating the image transport properties of the tellurite ASTDOF when the value of p was 1.5 and 2.0 µm and the slit width was 11 and 14 µm. In Fig. 47, the plot of three vertical slits on the test target was used as the input image [186]. Transported images at the output of the tellurite ASTDOF and the calculated R_ZNCC are shown correspondingly to each value of p. The wavelength of the probe beam is constant at 1.55 µm. For the 14 µm slit width, the calculated R_ZNCC slightly decreases from 0.354 to 0.345 when the ratio p/λ increases about two times from 0.65 to 1.29. In Figs. 47(a)–(c), the pattern of three vertical slits still can be recognized although it becomes dimmer in Fig. 48(c). But, for the 11 µm slit width, the calculated R_ZNCC decreases markedly from 0.342 to 0.198 and the pattern of three vertical slits becomes faded as shown in Figs. 47(d)–(f). In this experiment, the tellurite ASTDOF in which p is 1.0 µm provides a transported image with high contrast, high brightness and higher matching ratio than the others. In addition, it can be inferred from the result that the transversely-disordered profile with small value of p can provide transported images with higher resolution and higher matching ratio. When the tellurite ASTDOF was used to transport the input image at different wavelengths from 1.44 to 1.50, 1.55 and 1.60 µm, the results were collected and shown in Figs. 48(a)–(d), respectively [186]. As can be seen, the transported images are not only clear, with high brightness but also the pattern of the three vertical slits can be observed obviously. The value of R_ZNCC slightly changes from 0.328 to 0.364.

 

Fig. 47. Transported images of three vertical slits measured at the output of the 10 cm-long tellurite ASTDOF and calculated values of R_ZNCC when the input wavelength is 1.55 µm. Reprinted with permission from Ref. [186] © Optica.

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Fig. 48. Transported images of three vertical slits measured at the output of the 10 cm-long tellurite ASTDOF and calculated values of R_ZNCC when the input wavelength is tuned from 1.44 to 1.60 µm. Reprinted with permission from Ref. [186] © Optica.

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We experimentally demonstrated the transport of near-IR optical images in the 10 cm-long all-solid tellurite glass optical fiber with transversely-disordered refractive index profile. The image of three vertical slits whose width is as small as 14 µm on a test target was transported successfully at 1.44, 1.50, 1.55 and 1.60 µm.

The transported images were obtained with high contrast, high brightness and high matching ratio. These results of this paper present a new potential approach for optical image transport in biological and medical imaging applications. As a new contribution to this field, the current work firstly aims at extending the working spectral range of optical image transport from the visible range at 405 and 633 nm in previous works [182,183] to the near-IR range, especially from 700 nm to 2500 nm, because this region has been known as the most efficient region for lights to be transmitted through biological tissues [202,203].

4.2. Transverse Anderson localization of mid-infrared light through the all-solid chalcogenide transversely disordered optical fiber

4.2.1. All-solid chalcogenide transversely disordered optical fiber fabrication

The fabrication of the chalcogenide ASTDOF required AsSe₂ rods, As₂S₅ rods, and an As₂S₅ tube. The fabrication process of the chalcogenide TDOF is similar to that of the tellurite ASTDOF in Section 4.1.4 [193]. A cross-sectional image of the fabricated chalcogenide ASTDOF was captured by using an SEM (JEOL, JSM-6490A) and shown in Fig. 49 [193]. In Fig 49, the bright regions are occupied by AsSe₂ and dark regions are occupied by As₂S₅. No large gaps are observed in the cross section of the chalcogenide ASTDOF due to applying the negative pressure during the drawing process.

 

Fig. 49. SEM cross-sectional images of the fabricated chalcogenide ASTDOF. The diameter of the area of random refractive index distribution is 169 µm. Reprinted with permission from Ref. [193] © Optica.

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We demonstrated TAL of mid-IR by using a 6 cm-long chalcogenide ASTDOF, which was cleaved using a cleaver (Vytran, LDC401) to ensure both flat surfaces with no cracks. A light beam from a tunable femtosecond laser (Coherent, Chameleon) was coupled into the chalcogenide ASTDOF by using a lens (Thorlabs, C036TME-E). The wavelength of the beam was tuned to 3.0 µm. The output light collimated by a lens (Thorlabs, C028TME-E) was observed by using a mid-IR beam profiler (DataRay, WinCamD-IR-BB).

Figure 50 shows the near-field intensity profiles for 4 different launch positions [193]. When an input position was moved, the localized light was shifted to the direction corresponding to the input movement. Figure 51 shows the intensity plots obtained from Fig. 50(d) along with the vertical and horizontal direction [193]. The smallest full width at half maximum (FWHM) of the localized light corresponding to the vertical and horizontal direction is 14 and 11 µm as shown in Fig. 51. Figures 50 and 51 indicate that the incident light propagated as non-localized modes as well as localized modes. We must suppress the non-localized modes because these modes behave as background noise and reduce the contrast of optical images.

 

Fig. 50. Near-field intensity profiles of the output light for different launch positions. These profiles are displayed under the same color bar scale. These profiles are collected under the same exposure time and displayed under the same color bar scale. Reprinted with permission from Ref. [193] © Optica.

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Fig. 51. Intensity plots of the localized beam profile of Fig. 50 (d). The plots of (a) and (b) show the intensity on the horizontal and vertical lines through the maximum intensity point. Blue dashed lines are the fitted curves to the two-term Gaussian beam profiles. Reprinted with permission from Ref. [193] © Optica.

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4.2.2. Simulation of localized modes of the chalcogenide all-solid transversely disordered optical fiber

We can optimize the unit size of AsSe₂ and As₂S₅ elements of the chalcogenide ASTDOF in order to obtain smaller beam sizes. The smaller the beam size is, the higher the resolution of the mid-IR image transport is. To estimate the expansion of the localized modes of the chalcogenide ASTDOF, we defined

 

Fig. 52. Geometry of the chalcogenide ASTDOF for calculating localized modes. The refractive index is randomly distributed in the area enclosed by the red dashed line. Reprinted with permission from Ref. [193] © Optica.

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Figure 53 shows element diameter dependence of the average effective mode diameter of the 1^st to 100th-order propagation modes for the wavelength of 3 µm (λ = 3 µm) [186]. When D_ele/λ is 0.4, the average of effective mode diameter is the smallest. In our earlier paper regarding the tellurite ASTDOF [186], the refractive index difference is about 0.1. When D_ele/λ of the tellurite ASTDOF is about 0.7, the area is the smallest. Moreover, B. Abaie et al. [204,205] discussed the element size dependence of the mode diameter.

 

Fig. 53. Element diameter dependence of the average effective mode diameter of the 1st to 100th-order propagation modes for the wavelength of 3 µm. The error bars are the statistical standard deviations of D_mode. Red points were obtained from Fig. 51 (a) and (b). Reprinted with permission from Ref. [193] © Optica.

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Although we can evaluate the diameter of each localized mode by numerical simulation, the intensity profiles of Fig. 51 include localized and non-localized modes. To separate the intensity profile of Fig. 51 from localized and non-localized modes and compare the numerical simulation and experimental results, we fitted the intensity profiles to the two-term Gaussian beam profiles of the form

Figure 54 shows element diameter dependence of the average effective mode diameter of the 1st to 100th-order propagation modes for the wavelengths of 3–11µm. At each wavelength, the average of effective mode diameter is the smallest with D_ele/λ = 0.4 because the refractive index difference is almost constant in this wavelength range.

 

Fig. 54. Element diameter dependence of the average effective mode diameter of the 1^st to 100th-order propagation modes for the wavelengths of 3–11 µm. The error bars are the statistical standard deviations of D_mode. Reprinted with permission from Ref. [193] © Optica.

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All-solid tellurite glass rod and fiber with a transversely disordered refractive index profile were fabricated with tellurite and chalcogenide glasses for the transverse localization of light and the near-IR to mid-IR image transport. It was shown that after a CW probe beam at 1.55 µm propagated in a 10 cm-long tellurite ASTDOR, and the beam became localized. In addition, near-IR optical images at 1.55 µm of numbers on the test target were transported. The transported images were obtained with high contrast, high brightness and high matching ratio. The quality of our transported optical images through the tellurite ASTDOF can be comparable or higher than the results which were obtained by a polymer Anderson localized fiber and by a commercially available multicore imaging optical fiber. With the advantages of using tellurite glasses and all-solid structure, the tellurite ASTDOF is a promising candidate for the near-IR optical image transport applications.

In addition, we successfully fabricated a transversely disordered optical fiber made of AsSe₂ and As₂S₅ glasses. We demonstrated the localization of the mid-IR light after the light propagated in the chalcogenide ASTDOF. It was shown from numerical simulation of localized modes of the fabricated chalcogenide ASTDOF in order to optimize the unit size of AsSe₂ and As₂S₅ that the small beam diameter can be obtained when the unit size is 0.4 times larger than the wavelength. It was clarified that the high-resolution mid-IR image transport can be achieved by using the chalcogenide ASTDOF. The results achieved here present a new potential approach for near-IR to mid-IR image transport in biological and medical imaging applications.

5. Conclusion

Soft glass optical fibers made of fluoride, tellurite or chalcogenide glass were used for mid-IR SC generation due to their broad transparency property. We demonstrated SC generation from ultra-violet to mid-IR range by optical fibers made of fluoride, tellurite and chalcogenide glasses. We demonstrated ultra-broadband SC generation from UV to 6.28 µm in a one cm-long fluoride fiber. Mid-IR SC spectrum spanning ∼2.0 to 15.1 µm was successfully generated in a 3 cm long chalcogenide step-index fiber.

The ASHMOFs made of tellurite and chalcogenide glasses were developed for chromatic dispersion control. We exploited the potential of our newly proposed ASHMOF for chromatic dispersion controllability. It was shown that in case of the tellurite ASHMOF, ultra-flattened chromatic dispersion profile with variation of as small as ± 0.2 ps/km/nm over the wide wavelength range from 2.5 to 3.7 µm can be obtained.

It was shown that the chalcogenide ASHMOF possessed a flattened all-normal chromatic dispersion profile with value of – 5 ps/km/nm and variation of ± 1 ps/km/nm over the wavelength range from 5.2 to 11.2 µm. These fibers with flattened chromatic dispersion profiles can have high potential for the broadband mid-IR SC generation.

All-solid tellurite rod and fiber with a transversely disordered refractive index profile were fabricated with tellurite and chalcogenide glasses for the transverse localization of light and near-IR to mid-IR image transport. It was shown that the transported images were obtained with high contrast, high brightness and high matching ratio after a CW probe beam at 1.55 µm propagated in a 10-cm-long tellurite ASTDOR. The quality of our transported optical images through the tellurite ASTDOF can be comparable or higher than the results which were obtained by a polymer Anderson localized fiber and by a commercially available multicore imaging optical fiber. We also successfully fabricated an optical fiber with a transversely disordered refractive index profile made of AsSe₂ and As₂S₅ glasses. We demonstrated the localization of the mid-IR light after the light propagated in the chalcogenide ASTDOF. It was shown that the small beam diameter can be obtained when the unit size is 0.4 times larger than the wavelength. It was clarified that the high-resolution mid-IR image transport can be achieved by using the chalcogenide ASTDOF. The results achieved here present a new potential approach for near-IR to mid-IR image transport in biological and medical imaging applications.

As mentioned above, we have successfully demonstrated the broadband SC generation and IR image transportation using soft glass optical fibers, such as fluoride, tellurite and chalcogenide optical fibers. It can be concluded through the results obtained here that the application field for soft glass optical fibers can be largely expanded.