Fabrication of Step−Index Fluorotellurite Fibers with High Numerical Aperture for Coherent Mid—Infrared Supercontinuum

Abstract

We demonstrate the fabrication process and coherent supercontinuum (SC) generation of fluorotellurite step−index fibers with a high numerical aperture (0.56 and 0.64 at 1552 nm). Two compatible fluorotellurite glass pairs were first explored for fiber fabricating with built−in casting and rod−in−tube techniques in a glovebox. Coherent SC sources from 1200 nm to 2400 nm were generated from the fluorotellurite step−index fibers pumped by a femtosecond fiber laser at 1560 nm. Owing to the excellent dehydration of the fluoride, such fibers are available and promising nonlinear media for achieving coherent mid−infrared (MIR) SC.

1. Introduction

MIR SC sources have attracted significant attention owing to numerous applications in pulse compression [1,2], optical coherence tomography [3,4,5], environmental monitoring [6], and bio−photonic diagnostics [7]. Coherence, which is one of the key properties of the SC, improves the precision or resolution of these applications [8,9,10,11]. There are two main methods to obtain coherent SC, one is to use ultrashort pulse−pumped nonlinear fibers [12], and secondly, a fiber with all normal dispersion (ANDi) is used as the nonlinear medium [13]. The pump pulse width required by the first method is usually less than 100 fs, and these SC sources are massive and limited in many applications [14]. In the second method, the main physical mechanisms of spectrum broadening are self−phase modulation (SPM) and optical wave breaking (OWB), so the SC is highly coherent [15]. Recently, most coherent SC studies have focused on the ANDi nonlinear fibers owing to the relative ease of implementation and all−fiber systems.

Silica photonic crystal fibers (PCFs) with ANDi always act as a nonlinear medium to generate coherent SC, but absorption beyond 1800 nm of silica glass is the major obstacle of MIR SC based on silica fiber [16]. Fluoride, chalcogenide, and tellurite glass fibers with high transmittance and ANDi in the mid−infrared range are promising nonlinear mediums to generate highly coherent MIR SC. Recently, Xiao et al. proposed a microstructured chalcogenide fiber with ANDi for coherent MIR SC generation, and the SC spectrum is from 3823 nm to 13,577 nm based on a 1 cm long fiber [17]. Zhang et al. fabricated step−index chalcogenide fiber with ANDi, and coherent MIR SC from 1.7–12.7 μm was generated from the fiber pumped at 5 μm [18]. Although chalcogenide fiber can generate a wide SC spectrum, high−power applications are limited due to its low damage threshold. Fluoride fibers are another MIR medium for coherent MIR SC generation. Jiang et al. prepared a fluoride PCF with ANDi from 0.2 μm to 2.5 μm; coherent SC was generated from the fiber [19]. However, fluoride PCF fiber is hard to handle due to poor strength and poor chemical stability. Although Li et al. proposed the step−index fluoride fiber with ANDi to generate coherent SC, high peak power pulsed pumping is required to generate broadband coherent MIR SC due to the low nonlinear coefficients of the fluoride glasses [20].

Tellurite glass fiber is an alternative medium for the generation of MIR SC, benefiting from higher nonlinear coefficients and better chemical stability than fluoride glass fiber. Strutynski et al. fabricated step−index tellurite fiber with ANDi; coherent MIR SC from 1500 nm to 3500 nm was generated from the fiber [21]. Saini et al. also prepared a step−index tellurite fiber with ANDi to generate coherent MIR SC from 1340 nm to 2840 nm [22]. Although the step−index tellurite glass fibers are potential mediums to generate coherent MIR SC, the absorption of OH in the glass at 3.3 μm limits its application in the MIR region. Fluorotellurite glass can effectively remove OH in the glass owing to fluoride in its composition [23,24]. Therefore, step−index fluorotellurite glass fibers with ANDi are promising candidates for coherent MIR SC.

In this work, we proposed and fabricated the step−index fluorotellurite fibers with a high numerical aperture (NA). Two different step−index fluorotellurite fibers with varying refractive index differences (0.076 and 0.099 at 1552 nm) are prepared by combining the built−in casting and rod−in−tube techniques. The losses of the fluorotellurite fibers are 2 dB/m and 0.8 dB/m at 1560 nm, respectively. Coherent SC sources from 1200 nm to 2400 nm were generated from the step−index fluorotellurite glass fibers. Our results show that the step−index fluorotellurite glass fibers with high NA are promising nonlinear mediums for MIR nonlinear photonics.

2. Materials and Methods

In our experiments, high−purity (99.99%) oxide and fluoride raw materials were melted in a glovebox filled with nitrogen, and the dew point of the glovebox was controlled below −75 °C. The core and cladding glass compositions of the two different fluorotellurite fibers are summarized in

Table 1. Core and cladding glass compositions of the fluorotellurite fibers.

Glass Compositions (mol%)	Notation
78TeO2−5Bi2O5−10.5ZnO−1.5ZnF2−5Li2O	TBZL
69TeO2−6WO3−15ZnO−5ZnF2−5Na2O	TWZN
60TeO2−30WO3−10PbO−3NaF	TWPN
65TeO2−13ZnO−5ZnF2−5PbF2−8Nb2O5−4GeO2	TZPNG

. In order to find thermally compatible core and cladding fluorotellurite glasses with large refractive index differences, we studied fluorotellurite glasses with different elemental compositions. In our work, two glass pairs were developed for fluorotellurite glass fibers with high NA, namely, TBZL/TWZN and TWPN/TNPZG. In the above compositions, ZnF₂ in the TBZL glass contributes to dehydration, and only 1.5 mol% of ZnF₂ is added to ensure that the TBZL glass does not crystallize during the fiber drawing process. Similarly, 5 mol% ZnF₂ is also added to the TWZN and TZPNG glass. The 3 mol% NaF in TWPN glass not only contributes to eliminating OH from the glass but also decreases the glass transition temperature (T_g) of the TWPN glass, making it compatible with TZPNG.

The main thermal and optical properties of two fluorotellurite glass pairs are summarized in

Table 2. Main thermal and optical properties of the fluorotellurite glasses.

Glass	Tg (°C)	Tx (°C)	∆T (°C)	TEC (×10−6 K−1)	n (1552 nm)
TBZL	301	440	139	17.4	2.078
TWZN	301	445	144	17.3	2.002
TWPN	370	>500	>130	14.0	2.128
TZPNG	350	>500	>150	13.5	2.029

. Glass transition temperature (T_g) and crystallization onset temperature (T_x) were measured by Differential Scanning Calorimetry (DSC) measurements (Netzsch 404). The thermal stability of glass is evaluated by ∆T (∆T = T_g − T_x); fluorotellurite glasses can be drawn fiber without crystallization when ∆T is larger than 100 °C [25]. The thermal expansion coefficient (TEC) of glass was tested using a thermal dilatometer (Netzsch DIL 402EP, Netzsch Analyzing & Testing, Selb, Germany). The refractive indexes (n) of glasses were measured with a prism coupler. The results of ∆T show that each glass exhibits sufficient thermal stability for fiber drawing, and the T_g and TEC of the glass pairs are similar, which means TBZL/TWZN and TWPN/TNPZG glasses have good thermal compatibility for fiber drawing. The numerical apertures (NA) of the glass pairs are calculated to be 0.56 and 0.54 at 1552 nm, respectively.

A Nicolet 6700 series Fourier transform infrared (FTIR) spectrometer was used to measure the infrared transmission spectrums of the fluorotellurite glasses, and the dehydration effects of fluoride are shown in Figure 1. The data on the upper right of the figure is the OH absorption coefficients which were calculated according to [26], and the data on the lower left is the thickness of the fluorotellurite glasses for testing. The results show that TBZL glass has the widest infrared transmission range, but its OH absorption coefficient is 0.03 cm⁻¹. Dehydration of the TBZL glass is poorer than other fluorotellurite glasses because the proportion of fluoride in its composition is only 1.5%mol. The molar percentages of fluoride in the compositions of TWZN, TWPN, and TZPNG glasses are 5%, 3%, and 10%, and the corresponding OH absorption coefficients are 0.01 cm⁻¹, 0.01 cm⁻¹, and 0.004 cm⁻¹, respectively. These results show that the fluoride content in the glass significantly affects the OH content of the glass, and the above−mentioned fluorotellurite glass can be applied in the mid−infrared range. In addition, when the fluorotellurite glass composition is designed, it is necessary to dope as much fluoride as possible to eliminate the OH of the glass, and at the same time, the thermal stability of the glass should meet the requirement for fiber drawing.

The step−index fluorotellurite glass fibers were fabricated by built−in casting and rod−in−tube methods. The core and cladding glass was melted simultaneously, the cladding glass liquid was first poured into the mold and rotated to the cladding tube, and then the core glass liquid was poured into the cladding tube. The cladding tubes were prepared using the built−in casting method for the preparation of small core step−index optical fiber. Figure 2a,b are the preform and tube of fluorotellurite glass fiber. In order to fabricate small core step−index fibers, the fibers were fabricated by the once− or twice−rod−in−tube method. Figure 2c is one of the cross−sections of the TBZL/TWZN fiber, and the cladding and core diameters of the fiber are 120 μm and 3 μm, respectively. Figure 2d is one of the cross−sections of the TWPN/TZPNG fiber, and fibers with core diameters of 2.5 μm and 4 μm were prepared, and their corresponding outer diameters were 130 μm and 200 μm, respectively. The NAs of TBZL/TWZN and TWPN/TZPNG fibers at 1550 nm are 0.56 and 0.64, respectively. The cut−back method was used to measure the losses of the fluorotellurite glass fibers, and losses of the TBZL/TWZN and TWPN/TZPNG fibers are 2 dB/m and 0.8 dB/m at 1550 nm, respectively. These results indicate that no obvious crystallization occurred during fiber preparation, and the losses of these fibers are acceptable owing to the short length used in nonlinear applications.

Figure 3 shows the dispersion of the TBZL/TWZN and TWPN/TZPNG fibers from 1000 nm to 3500 nm. When the core diameter of the TWPN/TZPNG fiber is 4 μm, the zero−dispersion wavelength of the fiber is 1900 nm, but the TWPN/TZPNG fiber with a core diameter of 2.5 μm can achieve ANDi from 1000 nm to 3500 nm. The nonlinear coefficients of the TWPN/TZPNG fibers with a core diameter of 2.5 μm and 4 μm were calculated to be 0.33 m⁻¹ W⁻¹ and 0.1562 m⁻¹ W⁻¹ at 1560 nm, respectively. Additionally, the TBZL/TWZN fiber with a 3 μm core diameter can achieve ANDi, and the nonlinear coefficient of the TBZL/TWZN fiber was calculated to be 0.1275 m⁻¹ W⁻¹ at 1560 nm. The results show that these fibers are promising nonlinear mediums for coherent MIR SC.

3. Results and Discussion

The step−index fluorotellurite fibers were pumped by a 1560 nm fs fiber laser (Carmel Model CLF−10CFF, Carmel, CA, USA) with a pulse width of 88 fs, a repetition rate of 80 MHz, and maximum average power of 2.26 W. A mounted aspheric lens (Thorlabs, Newton, NJ, USA, C430TM−C) was used to couple the pump laser into the fluorotellurite fibers. The SC spectrums were detected by the spectrometers (Yokogawa, Tokyo, Japan) from 1200 nm to 2400 nm. TWPN/TZPNG fibers with core diameters of 2.5 μm and 4 μm and lengths of 1 m were used as nonlinear mediums to generate SC, and the spectrums are shown in Figure 4. Figure 4a shows that the broadening of the SC is symmetrical with the increase in the pump power, which indicates that the broadening mechanism of the SC is mainly dominated by SPM. When the power of the SC is 705 mW, the SC spectrum spans from 1200 nm to 2300 nm, and its flatness in the spectral range of 1200–2250 nm is 20 dB. Figure 4b shows that SC was generated in a TWPN/TZPNG fiber with a core diameter of 4 μm. The results show that the SC broadens asymmetrically with the increase in pump power, the blue−shifted components do not broaden, and the red−shifted components broaden with pump power increasing. The peak of red−shifted components shifts to longer wavelengths as power increases, which is attributed to Raman solitons. These results show that the TWPN/TZPNG fiber with a diameter of 4 μm has an anomalous dispersion region from 1500 nm to 2400 nm. The SC spectrums in the above two fibers clearly indicate the effect of core size on the dispersions of the fibers. Comparing the generation process of the SC in the above two fibers, it can be seen that when the core diameter of the fiber decreases from 4 μm to 2.5 μm, the SC spectrum changes from symmetrical broadening to asymmetrical broadening, which indicates that the TWPN/TZPNG fiber with a diameter of 2.5 μm is ANDi in the region from 1500 nm to 2300 nm. The SC results agree with the above−calculated dispersion results.

TBZL/TWZN fiber with a diameter of 3 μm and length of 0.3 m was used as a nonlinear medium to generate SC, and the spectrum of the SC is shown in Figure 5. When the power of the SC is 508 mW, the SC spectrum spans from 1200 nm to 2400 nm. The broadening of the SC is asymmetric, and the red−shifted components are broader than the blue−shifted components. The reason is that the dispersion of the fluorotellurite fiber at the short wavelength region is steeper and larger than the dispersion at the long wavelength region [20]. Additionally, The SC generated in TBZL/TWZN fiber with a core diameter of 3 μm is highly coherent owing to ANDi from 1000 nm to 3500 nm.

To verify the experimentally observed results, the generalized nonlinear Schrodinger equation was used to simulate the SC generated from the TBZL/TWZN fiber, and the coherence of the SC was simulated by calculating the spectrum with random noise seeds 108 times [27]. Fiberdesk software was used to solve the nonlinear Schrodinger equation. Loss of fiber α, high order dispersion β, SPM, self−steepening, and Raman response are considered in the equation:

$$\frac{\partial \mathrm{A}}{\partial \mathrm{z}}+\frac{\mathsf{\alpha }}{2}\mathrm{A}-{\displaystyle \sum }_{\mathrm{k}\ge 2}\frac{{\mathrm{i}}^{\mathrm{k}+1}}{\mathrm{k}!}{\mathsf{\beta }}_{\mathrm{k}}\frac{{\partial }^{\mathrm{k}}\mathrm{A}}{\partial {\mathrm{T}}^{\mathrm{k}}}=\mathrm{i}\mathsf{\gamma }(1+\frac{\mathrm{i}}{{\mathsf{\omega }}_0}\frac{\partial }{\partial \mathrm{T}})\times (\mathrm{A}(\mathrm{z},\mathrm{T}){{\displaystyle \int }}_{-\infty }^{\infty }\mathrm{R}\left({\mathrm{T}}^{\prime }\right){\left|\mathrm{A}(\mathrm{z},\mathrm{T}-{\mathrm{T}}^{\prime })\right|}^2{\mathrm{dT}}^{\prime })$$

(1)

where A is the electric field envelope, z is fiber length, ω₀ is the carrier frequency,γ is the nonlinear coefficient. In this simulation, z and γ are 0.3 m and 0.1275 m⁻¹ W⁻¹, respectively.

R(t) is the Raman response function modeled as:

$$\mathrm{R}\left(\mathrm{t}\right)=\left(1-{\mathrm{f}}_{\mathrm{R}}\right)\mathsf{\delta }\left(\mathrm{t}\right){+\mathrm{f}}_{\mathrm{R}}{\mathrm{h}}_{\mathrm{R}}\left(\mathrm{t}\right)=\left(1-{\mathrm{f}}_{\mathrm{R}}\right)\mathsf{\delta }\left(\mathrm{t}\right){+\mathrm{f}}_{\mathrm{R}}\frac{{\mathsf{\tau }}_1^2{+\mathsf{\tau }}_2^2}{{\mathsf{\tau }}_1{\mathsf{\tau }}_2^2}\exp (-{\mathrm{t}/\mathsf{\tau }}_2{\left)\sin \right(\mathrm{t}/\mathsf{\tau }}_1)$$

(2)

In this simulation, τ₁, τ₂, and f_R (parameters of Raman response) of the fluorotellurite glass were 0.00745, 0.0242, and 0.5, respectively [28].

According to calculated dispersion of the TBZL/TWZN fiber, Taylor expansion was carried out at 1560 nm, β₂ to β₁₁ are 0.11835, 0.00015576, 4.33487 × 10⁻⁷, −2.34572 × 10⁻⁹, 1.86267 × 10⁻¹¹, −1.75839 × 10⁻¹³, 1.44712 × 10⁻¹⁵, −7.45031 × 10⁻¹⁸, 1.78245 × 10⁻²⁰, and −3.4487 × 10⁻²⁴, respectively.

The coherence of SC is defined as:

$$\left|{\mathrm{g}}_{12}{(\mathsf{\lambda },\mathrm{t}}_1-{\mathrm{t}}_2)\right|=\left|\frac{\langle {\mathrm{E}}_1^{*}{(\mathsf{\lambda },\mathrm{t}}_1{)\mathrm{E}}_2{(\mathsf{\lambda },\mathrm{t}}_2)\rangle }{\sqrt{{\langle \left|{\mathrm{E}}_1{(\mathsf{\lambda },\mathrm{t}}_1)\right|}^2\rangle }{\langle \left|{\mathrm{E}}_2{(\mathsf{\lambda },\mathrm{t}}_2)\right|}^2\rangle }\right|$$

(3)

where E₁ and E₂ are SC generated with input with different random noise seeds in the simulation. An ensemble average of 128 independent simulations are used to calculate the coherence of the SC.

Figure 6 shows that the simulated SC result agrees with the experiment, and the coherence of the SC is 1 from 1200 nm to 2400 nm. These results indicate that a coherent SC spectrum expanding from 1200 nm to 2400 nm can be generated using an ANDi step−index fluorotellurite fiber. Moreover, these fibers are alternative candidates for highly coherent SC in the MIR region.

4. Conclusions

In conclusion, step−index fluorotellurite fibers with high NA (0.56 and 0.64) were proposed and fabricated by built−in casting and rod−in−tube techniques. The fibers have thermally compatible core and cladding glasses with large refractive index differences. Losses of the TBZL/TWZN and TWPN/TZPNG fluorotellurite fibers are 2 dB/m and 0.8 dB/m at 1560 nm, respectively. Coherent near− and mid−infrared SC from 1200 nm to 2400 nm was generated from the step−index fluorotellurite glass fibers. A sufficiently large refractive index difference with a small core diameter can tailor the step−index fluorotellurite fibers to ANDi; fluoride in the fluorotellurite glass significantly removes the OH content of the glass, so the step−index fluorotellurite fibers with high NA are a promising candidate for coherent MIR SC.