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Investigation of tellurium-based chalcogenide double-clad fiber for coherent mid-infrared supercontinuum generation
Optical Fiber Technology 55 (2020) 102144
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Investigation of tellurium-based chalcogenide double-clad fiber for coherent mid-infrared supercontinuum generation ⁎
T
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Jing Xiaoa,c,1, Youmei Tiana,c,1, Zheming Zhaob, , Jinmei Yaod, Xunsi Wanga,c, , Peng Chena,c, Zugang Xuea,c, Xuefeng Penga,c, Peiqing Zhanga,c, Xiang Shena,c, Qiuhua Niea,c, Rongping Wanga,c a
Laboratory of Infrared Material and Devices, The Research Institute of Advanced Technologies, College of Information Science and Engineering, Ningbo University, Ningbo 315211, China b Nanhu College, Jiaxing University, Jiaxing 314001, China c Key Laboratory of Photoelectric Materials and Devices of Zhejiang Province, Ningbo 315211, China d College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Mid-infrared Tellurium-based chalcogenide fiber Double claddings All normal dispersion Coherent supercontinuum generation
Considerable investigations have been carried out for chromatic dispersion tailoring of chalcogenide glass fiber with various structures and different material compositions. Here we proposed a tellurium-based chalcogenide glass fiber with a dual-clad structure in a W-type refractive-index profile. The structure of the fiber based on GeAs-Se-Te glasses was numerically analyzed in detail. The simulation results indicate that an all normal dispersion profile can be realized in this tellurium glass fiber with an optimized dual-cladding structure. Then the optimized tellurium chalcogenide fiber with an all-normal dispersion profile was fabricated by multi-extrusion method. Pumping with a 5 μm ultra-short pulsed laser (150 fs, 1 kHz), abroadband supercontinuum (SC) covering 1.5–11 μm can be generated in the 19 cm-long fiber. The coherence of SC was also investigated by numerical simulation. The result shows that a high coherent SC covering 3.5–10.5 μm can be generated in this all-normal dispersion fiber. In conclusion, all-normal dispersion profile can be realized easily in this tellurium-based glass fiber due to their large materials ZDWs.
1. Introduction In recent years, mid-infrared (MIR) supercontinuum (SC) light sources have attracted considerable attention for potential applications [1–3] including optical IR coherence tomography (OCT) [4], metrology, and spectroscopy [5]. Chalcogenide fiber is promising for MIR SC generation because of its wide transmission window and high nonlinearity [6,7]. The SC sources with high coherence [8], i.e. low spectral intensity noise, can be applied in numerous fields such as multimodal biophotonic imaging and optical frequency combing. Broadband SC is usually generated by pumping the fiber in the anomalous dispersion wavelength region close to the zero-dispersion-wavelength (ZDW) [9]. In this case, the spectral broadening is dominated by soliton fission [10] or modulation instability, which is sensitive to pump-pulse fluctuations and pump laser noise, leading to decoherence of the SC spectrum over the entire SC bandwidth [11]. One approach to solve it is pumping the fiber by an ultra-short pulse in the normal dispersion wavelength
region, where SC generation are mainly dominated by self-phase modulation (SPM) and optical wave breaking (OWB) [12]. In this case, the coherence of the spectra is significantly affected by the stability of the input pulse because the effects of modulation instability are avoided, as that being basically impossible in normal dispersion [13]. Therefore, pumping a fiber at the normal dispersion wavelength region is effective to improve the coherence of the SC spectrum. Recently, more attentions have been paid to the experimental and theoretical analysis of SC generation, especially in the microstructure fibers with all-normal dispersion [13,14]. Numerical simulation has shown that the chromatic dispersion of the microstructure fiber can be tailored in the MIR region. Experimentally, compared with that for the step-index fiber (SIF), which has a step-type refractive index distribution, i.e. core refractive index higher than the cladding refractive index, precise control of the microstructure is essential for the microstructure fiber to achieve low confinement loss and desired dispersion, which in turn becomes challenging for the fiber fabrication [15]. Moreover, there
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Corresponding authors at: Laboratory of Infrared Material and Devices, The Research Institute of Advanced Technologies, College of Information Science and Engineering, Ningbo University, Ningbo 315211, China (X. Wang); Nanhu College, Jiaxing University, Jiaxing 314001, China (Z. Zhao). E-mail addresses: [email protected] (Z. Zhao), [email protected] (X. Wang). 1 Jing Xiao and Youmei Tian contributed equally to this work. https://doi.org/10.1016/j.yofte.2020.102144 Received 9 August 2019; Received in revised form 9 January 2020; Accepted 9 January 2020 1068-5200/ © 2020 Elsevier Inc. All rights reserved.
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are more challenges of microstructure fiber than step-indexed fiber during the fabrication, as there are more defects appearing such as core deformation, bubble-shaping, and axial non-uniformity [16], during the fabrication of microstructure optical fibers. Furthermore, the reproducibility of the microstructure optical fibers and low coupling efficiency may be challenging problems. SIFs, which are more robust than PCFs, are usually pumped in normal dispersion wavelength region to achieve coherent SC generation [17–20]. However, it has certain difficulties to tailor the chromatic dispersion of the SIFs depending on the structural tunability. An approach available is to shift the ZDW in multi-clad fiber, such as a w-type structure [21] where a lower refractive index layer between the core and outer cladding is added. The W-type design and the materials chosen can tailor the fiber chromatic dispersion. The large numerical aperture (NAs) in such a fiber is also making easier coupling between pumping laser and fiber. Most of the works on high coherent SC generation for chalcogenide double-clad fiber have been demonstrated [22–25]. The small absolute value of the chromatic dispersion and high nonlinearity are two key factors for realizing coherent SC generation. In order to broaden the SC generation up to MIR, the double-clad fiber can be pumped by ultra-short pulse with a wavelength in the normal dispersion wavelength region. In this paper, we chose Ge-As-Se-Te (GAST) glasses for fiber fabrication. The GAST has excellent characteristics of long-wave IR transparency and larger material ZDWs [26]. Firstly, we simulated dispersion-shift of GAST fibers with a W-type refractive index profile using the finite-element method (FEM) [27]. The geometry of the proposed fiber as shown in Fig. 1 is described by the following parameters: d0—diameter of core; d1—diameter of inner cladding; d2—diameter of outer cladding; n00—refractive index of core; n01—refractive index of inner cladding; n02—refractive index of outer cladding. These diameters of d0, d1 and d2 were optimized for all-normal dispersion engineering. Subsequently, we fabricated the GAST double-clad performs with a specialized structure by the extrusion method, then a fine W-type MIR fiber with preset diameters was obtained. Finally, we investigated SC generation by simulation as well as experiment in the fiber.
Fig. 2. Refractive indices of core and claddings glasses and the calculated NAs.
together with the calculated NAs are presented in Fig. 2. Such high NAs in the DCFs mean that it is easy to couple between pumping laser and fiber. The normalized frequency V of the fiber can be obtained from:
V=
πd 0 πd 0 2 2 ncore NA − nclad = λ λ
(1)
where d0 is the core diameter and λ is the propagating light wavelength. As Eq. (1), the fiber with the d0 of 10 μm is single-moded when the wavelength is longer than 10.6 μm. The Sellmeier coefficient can be calculated by the Sellmeier equation based on measured refractive indices [28]:
n2 (λ ) = 1 +
∑ i
Ai λ2 λ2 − λi2
(2)
where λ is the wavelength, Ai and [29,30] (i = 1, 2, 3) are materialrelated constants, which are listed in Table1. The chromatic dispersion can be calculated by the FEM solver. With the numerical analyzing, effective mode area, effective refractive index of the fundamental mode and other fiber parameters can be derived directly. Based on the effective index, the dispersion distribution of the fiber, including both the waveguide and material dispersion, as conjunctions with wavelength, can be easily figured out. The effective mode area (Aeff) is given by Eq. (3):
λ12
2. Proposed design of dispersion-shifted fiber for all-normal dispersion Fig. 1 shows the transverse cross section and refractive index profiles of GAST double-clad fiber (DCF). In the structure, the refractive index (n01) of the inner cladding is smaller than that of both core (n00) and outer cladding (n02). We chose Ge15As25Se15Te45 with highest refractive index as core material, and Ge20As20Se17Te43 and Ge20As20Se15Te45 are selected as inner cladding and outer cladding, respectively. The refractive indices of the three glasses were measured by an IR ellipsometer (IR-VASE MARKII, J. A. Woollam Co.), and the results
2
Aeff =
+∞ [∫ ∫−∞ |E (x , y )|2 dx dy] +∞ ∫ ∫−∞
|E (x , y )|4 dx dy
(3)
where E is the electric field’s transverse component propagating inside the fiber. The nonlinear coefficient γ [31] can be calculated using the following formula:
γ=
2π n2 λ Aeff
(4)
where Aeff is the effective area of the propagating mode at 5 μm, n2 is the nonlinear refractive indices of Ge20As20Se17Te43 and we estimate the value by the following formula [32]:
n2 = 4.27 × 10−16
(n02 − 1) 4 cm2. W−1 n02
(5)
The refractive index of the fundamental mode, neff is computed as a function of wavelength λ, and then the chromatic dispersion D is calculated from the formula in the following [33]:
λ d 2 Re (neff ) ⎤ D (λ ) = − ⎡ [ps/nm/km] ⎥ c⎢ d λ2 ⎣ ⎦
Fig. 1. Cross-section and refractive index profiles of GAST fiber. 2
(6)
Optical Fiber Technology 55 (2020) 102144
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Table 1 Refractive coefficient of telluride glasses. Materials
A1
A2
A3
λ12
λ 22
λ32
Ge15As25Se15Te45 Ge20As20Se17Te43 Ge20As20Se15Te45
9.3179 8.7503 9.1364
4.7797e−4 3.425e−4 5.7239e−5
7.9541 −25.56 −263.1
0.29015 0.39859 0.31171
270.06 191.88 228.89
8422.7 −17840 −1.5653e5
where c is the light velocity in free space, Re(n eff ) represents the real part of the effective index of fundamental mode. It is well known that chromatic dispersion of a single-mode fiber is a combination of its material dispersion and waveguide dispersion. The small values of fiber chromatic dispersion can be obtained by increasing the waveguide dispersion via tailoring the size of core and claddings. In this paper, we considered only the fundamental mode. The influence of W-type double claddings on the DCFs dispersion is explored in details. Due to the large material ZDW (> 9 μm), we increase waveguide dispersion to shift ZDWs to the long wavelength region. Thus, all-normal dispersion distribution and small absolute dispersion values can be obtained easily in the entire operatingwavelength region of the fiber. Using the method above, we tuned the waveguide dispersion to overlap the material dispersion of fiber core. Then, several DCFs geometries were optimized for consideration. A number of numerical simulations of DCFs were discussed as follows. To reduce the higherorder modes interaction, we chose d0 = 10 μm. In order to identify the influence of geometrical parameters on dispersion values, the d2/d1, d1 and d2 were optimized to introduce a strong waveguide dispersion component. Firstly, the influence of d2/d1 on the dispersion for the DCFs was explored. The chromatic dispersion of the fundamental mode was calculated with increasing d2/d1 while d1 was fixed at 20 μm and 30 μm respectively. The SIFs, d0 of 10 μm and d1 of 20 μm in Fig. 3(a) and 30 μm in Fig. 3(b), are also calculated for comparison. Fig. 3(a) shows the chromatic dispersion change with increasing d2/d1 from 1.5 to 4 when d1 is fixed at 20 μm. One set of the MFD images of the DCFs with the d2/d1 = 4 and d1 = 20 µm at 7 µm, 9.5 µm and 12 µm shown in Fig. 4(a), Fig. 4(b), and Fig. 4(c) respectively might explain why the dispersion curve exhibits these sharp dips near 10 µm. Clearly, there is a crossing between the fundamental core mode and one or more cladding modes (the donut mode at 12um). Dashed curve represents the chromatic dispersion of SIFs consisting of the same materials of core and cladding as that of the core and inner cladding of the GAST DCFs, respectively. However, it is clear that the smaller absolute values of the chromatic dispersion are obtained at d2/d1 = 2 (see the blue line). The result shows that at a wavelength of 12.3 μm, the calculated maximum dispersion with the d2/d1 ratio of 2 is still normal (-0.7979 ps/km/nm). It demonstrates that at d2/d1 = 2, the coherent SC generation has been
Fig. 4. The MFD images of the DCFs with the d2/d1 = 4 and d1 = 20 µm at (a) 7 µm, (b) 9.5 µm and (c) 12 µm. Table 2 Dispersion and ZDW comparison between the DCFs and SIF under different d2/ d1. fiber
d2/d1
ZDW (μm)
|ΔD| (ps/km/nm)
Bandwidth (μm)
DCF (d1 = 20 μm)
1.5 2.0 2.5 3.0 3.5 4.0
10 no no 11.7 11.1 10.6
7.85 5.81 12.61 34.80 62.04 91.90
3 3 3 3 3.2 3
SIF (d1 = 20 μm)
–
9.1
7.11
3
DCF (d1 = 30 μm)
1.5 2.0 2.5 3.0 3.5 4.0
9.5 no 11 10 9.6 9.4
6.78 8.64 35.39 40.35 51.20 76.23
4 4 4 4 4 4
SIF (d1 = 30 μm)
–
9.1
12.01
4
achieved with flattened all-normal dispersion profiles [34]. In addition, the dispersion variation of the fiber within the bandwidth of 3 μm is lower than others, as shown in Table 2, where |ΔD| is the difference value of the maximum and minimum dispersion within a certain wave band, and bandwidth is the length of the wave band. When d1 = 30 μm, the effect of the double claddings on dispersion engineering is similar to that of d1 = 20 μm, and the dispersion values are all normal in such a fiber with d2/d1 = 2. It can be seen in Fig. 3(b) where the dispersion curves are recalculated for DCFs with d1 = 30 μm. In this case, the
Fig. 3. Variations of chromatic dispersion profiles of DCF by changing d2/d1 (a) d1 = 20 μm and (b) d1 = 30 μm. 3
Optical Fiber Technology 55 (2020) 102144
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Fig. 5. (a) Chromatic dispersion profiles of DCFs with d1 = 20, 30, 40, 50 μm with d2/d1 = 2. (b) Chromatic dispersion profiles of DCFs in Fig. 5(a) from 8.5 to 11.5 μm. (c) Dispersion curves of the fabricated DCF and three materials. (d) Dispersion distribution of the fiber with d1 = 30 μm, d2/d1 = 2.
maximum dispersion of −0.2475 ps/km/nm appears at 9.8 μm and the variation of the dispersion is quite small in the same functional bandwidth. Thus, a small and flat chromatic normal dispersion profile can be obtained in a fiber with d2/d1 = 2. The following results further show the influence of the change of d1 from 20 to 50 μm on dispersion when d2/d1 is fixed at 2. The dispersion curves of the DCFs were also recalculated. As shown in the Fig. 5(a), the chromatic dispersion of the fiber with d1 = 20 μm and d1 = 30 μm is flatter than that of the fibers with d1 = 40, 50 μm. And there are no ZDWs for the fibers of d1 = 20 μm and d1 = 30 μm in the whole considered wavelengths range in the fiber with d2/d1 = 2. As the red curve shown in Fig. 5(b), the absolute value of chromatic dispersion is quite small at peak of the dispersion curve near the wavelength of 9.8 μm, which has been mentioned in Fig. 3(b). As shown in Table 3, the flatness of the chromatic dispersion for the fiber is approximately 4.99 ps/km/nm at a range of 8–12 μm in the normal dispersion wavelength region, which is lower than that of SIF and other DCFs. The dispersion curves of designated fiber and three materials are plotted in Fig. 5(c), where bulk Ge15As25Se15Te45 glass exhibits a larger material ZDW of about 9.4 μm (black line). The dispersion curves of the double-clad fibers have similar slopes compared with that of
Ge15As25Se15Te45 bulk glass. The dashed line represents the dispersion profile of the double cladding fiber with d2 = 60 μm, as their d0 and d1 were fixed at 10 μm and 30 μm, respectively. It is reasonable to say that the fiber dispersion values can be strongly affected by the double claddings. As shown in Fig. 5(d), the fiber dispersion profile stands between −1 and 0 ps/km/nm from 9.2 to 10.4 μm, respectively. As indicated above, the proposed DCFs design (d0 = 10 μm, d1 = 30 μm, d2 = 60 μm) exhibits flat normal dispersion and are suitable for the optimal fibers to generate coherent SC. The calculated Aeff and γ of the DCFs are presented in Fig. 6, in which the effective area increases with increasing wavelength. In addition, the value of γ is up to 272 W−1 km−1 at 10.6 μm. The dispersion coefficient up to the 10th-order (β2 to β10) is used to get an accurate fit with the dispersion curve. The simulations made it clear that, ideal flattened dispersion curves of all-normal-dispersion can be achieved in the DCFs with the optimized
Table 3 Dispersion and ZDW comparison under different d1. fiber
d1 (μm)
ZDW (μm)
|ΔD| (ps/km/nm)
Bandwidth (μm)
DCF
20 30 40 50
no no 9.3; 10.5; 11.5 9.3; 9.7; 10.1
7.01 4.99 24.62 23.30
4 4 4 4
SIF
20 30 40 50
9.1 9.1 9.3 9.3
12.01 12.01 9.18 8.79
4 4 4 4
Fig. 6. Effective area and nonlinear coefficient of the fundamental mode calculated in the optimized fiber with d1 = 30 μm, d2/d1 = 2. 4
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structure (d0 = 10 μm, d1 = 30 μm, d2 = 60 μm). Therefore, such an all-normal dispersion DCFs were considered as the best candidate for coherent SC generation.
the reports of Ref. [37], the intermodal nonlinear interactions for SC generation is suppressed and negligible, so we assumed single-polarization and single-mode propagation in SC simulation for simplicity. For the designed DCFs, the numerical simulations of the output SC spectra were performed for all-normal dispersion SC generation in a 19cm-long fiber pumped by a wavelength of 5 μm. We performed a simulation with the generalized nonlinear Schrödinger equation (GNLSE) taking the fiber loss, high order dispersion, and stimulated Raman scatting into account. In our simulation, 0.001% RIN of the pump source was introduced. The response function with the same parameters of As40Se60 glass reported in Ref. [38], which is an approximation to the more complex Raman spectrum of the actual glasses is expressed as following [12]:
3. Fabrication of glasses and dispersion-shifted fiber 3.1. Glass synthesis The glass rods for preform were synthesized by the conventional melt-quenching method. Raw materials of Ge, As, Se, Te with prepurification were melted in a rocking furnace to ensure homogeneity, and then the melts were cooled, following by quenching. The obtained glass was annealed to remove the internal stress.
R (t ) = (1 − fR ) δ (t ) + fR (t ) hR (t )
3.2. The fabrication of fiber and preforms based on co-extrusion
(7)
where the response function coefficients are defined as fR = 0.11 and the delayed Raman contribution hR (t ) [39] is given by:
The preform was fabricated using the two-step isolated co-extrusion method [35]. Each glass was prepared in the form of cylindrical rods (Ge20As20Se17Te43, Ge20As20Se15Te45 and Ge15As25Se15Te45). First, the preform with a core-cladding ratio of 1:2 was extruded by a 26 mm core glass rod along with a 46 mm cladding glass rod. Then the composite perform of 9 mm was co-extruded with a ratio of 1:3 by a 26 mm cladding glass. Finally, the structured preform with a ratio of 1:5 was extruded again by a 46 mm Ge15Sb10Se75 glass rod to obtain a small core fiber. The double-clad fiber was fabricated by a conventional preformdrawing process. The co-extruded preform was drawn into DCFs in a home-made drawing tower at 310℃ with N2 protection. Then we obtained the optimized DCFs with a diameter of about 300 μm and d0, d1, d2 of 10 μm, 30 μm and 60 μm, respectively. A low-loss dual-clad tellurium chalcogenide fiber [36] has been reported. However, with a 20 μm core diameter, the fiber was still multi-moded. In this work, a dual-clad tellurium chalcogenide fiber was realized in the optimized structure. The cross-sectional photographs of the DCFs were taken by an optical microscope with a super long depth of view (Keyence, VHX-1000). As shown in Fig. 7, the size of the core and inner-clad and outer-clad diameters were 10 μm, 30 μm and 70 μm respectively. The optical losses of the GAST fiber are nearly the same as that in the reports of Ref. [26].
hR (t ) =
τ12 + τ22 t t exp ⎛− ⎞ sin ⎛ ⎞ τ τ τ1 τ22 2 ⎝ ⎠ ⎝ 1⎠ ⎜
⎟
⎜
⎟
(8)
where τ1 = 15.5 fs and τ1 = 230.5 fs . The parameters used for simulation SC generation in the double cladding fiber are shown in the following Table 4. In addition, the effective mode area dependence of the nonlinear response was also taken into account. Based on the calculated dispersion and nonlinearity, the GNLSE was solved by the Split-step Fourier method including higher order dispersion parameters up to the 10th-order [40]. The spectral broadening was mainly driven by the SPM due to all-normal dispersion profile in the case of d1 = 30 μm and d2/d1 = 2. A femtosecond pulse was used to meet large power for pumping in normal dispersion wavelength region. To clarify the all-normal dispersion on the properties of MIR SC, we compared the measured spectra with numerical simulations. A tunable OPA system (Mirra 900 + Legend Elite + OperA Solo) was used as the pumping source, with a ~150 fs pulse out in a repetition rate of 1 kHz. The beam from the OPA was coupled via a calcium fluoride lens with a focal length of 75 mm into the fiber. The SC output from the fiber was collected by the input slit of a monochromator. A liquid nitrogen-cooled HgCdTe (MCT) detector with a range of 1–16 μm was used to measure the output of the monochromator. Therefore, ~150 fs pulse at 5 μm out from the OPA system was injected into a 19-cm-long DCF. The comparison of the measured SC spectra generation at 5 μm under increasing powers are shown in Fig. 8 (b). We observed that the spectrum became broad when the input power increased. The SC generation under different incident average power were limited to the normal dispersion regime and the dips in the SC spectra were due to the absorption of the Ge15Sb10Se75 out of the fibers. It also has been seen that the flat SC was
4. MIR SC generation in DCFs SC generation was numerically simulated and experimentally measured in these DCFs. There are some researches about the coherence of ANDi SC including the influence of PMI such as Ref. [12]. According to
Fig. 7. Cross-sectional photograph of the DCFs. 5
Optical Fiber Technology 55 (2020) 102144
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Table 4 Parameters for simulation SC generation in the double cladding fiber. Parameter Unit Values
L cm 19
λ
P kW 50/150/200
μm 5
γ −1
−1
m ·W 0.755
TFWHM
fR
τ1
τ2
fs 200
Null 0.11
fs 15.5
fs 230.5
(L: fiber length, P: peak power).
Fig. 9. Degree of first-order coherence in the designed fiber.
resolving the spectrum. The GNLSE for the fundamental mode of the fibers was solved by using commercial software MATLAB to simulate SC generation. Spectral fluctuations from shot to shot in the input pulse was modeled via the one-photon-per-mode noise model [42]. The measured refractive index of the all normal dispersion GAST fiber and the nonlinear coefficient (γ) calculated by using the commercial software COMSOL Multiphysics were used in the simulation. The wavelength dependence of γ can be seen from the Fig. 6. The material loss and confinement of the fiber were not included in the simulation. We observed the high coherence property of the generated supercontinuum was kept because the spectral broadening of the SC is dominated by SPM. Therefore, the coherence property of the generated SC and the normalized intensity were almost unity for the entire spectral range. The normalized intensity and the degree of the first-order coherence 1 1 (λ )| = 1 by launching the |g12 (λ )| is drawn in Fig. 9. Simulations show |g12 150 fs laser pulse at 5 μm, which corresponds to highly coherent for our proposed fiber design from 3.5 to 10.5 μm. 5. Conclusion In this paper, we report a chalcogenide W-type optical fiber structure for highly coherent MIR SC generation. The dispersion profiles of the fibers have been numerically analyzed in order to obtain flat allnormal dispersion profile in MIR region. The results showed that, ZDWs can be shifted to longer wavelengths as the parameters of W-type double-clad fiber change. Therefore, an all normal dispersion profile can be realized in a single-mode fiber with a core size 10 μm, an inner cladding 30 μm and an outer cladding 60 μm. Then, the single-mode fiber with the optimized structure was fabricated via the robust extrusion and preform drawing methods. The study of simulations and experiments for SC generation were also given. A coherent MIR SC extending to 11 μm could be obtained using the 19-cm-long of fiber by 150 fs pulsed laser at 5 μm. For the proposed GAST W-type fiber, the coherence property of the SC was almost unity in the entire spectral range. In conclusion, geometrical flexibility of DCFs and large material ZDWs of GAST glasses provide the all-normal dispersion profile to obtain coherent SC for MIR in the case of femtosecond pulsed laser pumping.
Fig. 8. (a) Simulated SC results in the DCFs with the pump wavelength of 5 μm under various powers. (b) Measured SC results from designed fiber obtained with 150 fs input pulses injected at the different input powers.
observed under the input power of 20 mW. However, the SC bandwidth somewhat was reduced because of pumping in all-normal regime because the broadening of SC was mainly dominated by SPM and OWB above the noise and visibly grows in strength in long wavelengths. The strong SPM leads to OWB via self-steepening and third-order dispersion, and thus significant broadening of the spectrum [37], but the OWB in the end halts the broadening process. So it is the SPM generated up until the OWB point that will decide the obtainable SC bandwidth. Thus, the SC spectrum was not generated at wavelengths above 11 μm. This could be due to the fact that that the loss of fiber increases rapidly and the pulse power was attenuated quickly when the wavelength is longer than 11 µm, thus SPM effects were weakened further to limit the broadening of the pulse. The maximum pump power was up to 200 kW. As that the coherence is a key parameter for measuring the quality of the generated SC. We quantified it by means of the modulus of the complex degree of first-order coherence at each wavelength in the SC, which can be defined as following [41]: 1 |g12 (λ, t1 − t2)| =
CRediT authorship contribution statement Jing Xiao: Methodology, Data curation, Writing - original draft. Youmei Tian: Software, Data curation, Writing - original draft. Zheming Zhao: Validation, Investigation. Jinmei Yao: Software, Formal analysis. Xunsi Wang: Conceptualization, Resources, Writing review & editing, Validation. Peng Chen: Validation. Zugang Xue: Validation. Xuefeng Peng: Software. Peiqing Zhang: Software. Xiang Shen: Supervision. Qiuhua Nie: Supervision. Rongping Wang: Writing - review & editing, Supervision.
〈E1 ∗ (λ, t1) E2 (λ, t2) 〉 1
[ 〈 |E1 (λ, t1)|2 〉〈 |E2 (λ, t2)|2 〉 ] 2
(9)
where E1 (λ ) and E2 (λ ) are the output spectrum from the fiber and t is the time measured at the resolution time scale of the spectrometer for 6
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[26] Z. Zhao, X. Wang, S. Dai, Z. Pan, S. Liu, L. Sun, P. Zhang, Z. Liu, Q. Nie, X. Shen, R. Wang, 1.5-14 μm midinfrared supercontinuum generation in a low-loss Te-based chalcogenide step-index fiber, Opt. Lett. 41 (2016) 5222–5225. [27] E. Coscelli, F. Poli, J. Li, A. Cucinotta, S. Selleri, Dispersion engineering of highly nonlinear chalcogenide suspended-core fibers, IEEE Photonics J. 7 (2015) 8. [28] E. Magi, L. Fu, H. Nguyen, M. Lamont, D. Yeom, B. Eggleton, Enhanced Kerr nonlinearity in sub-wavelength diameter As2Se3 chalcogenide fiber tapers, Opt. Express 15 (2007) 10324–10329. [29] E. Mcbrearty, K. Lewis, P. Mason, A. Seddon, Chalcogenide glass films for the bonding of GaAs optical parametric oscillator elements, Proc SPIE 5273 (2004) 430–439. [30] H. Saghaei, M. Ebnaliheidari, M. Moravvejfarshi, Midinfrared supercontinuum generation via As2Se3 chalcogenide photonic crystal fibers, Appl. Optics 54 (2015) 2015–2079. [31] M. Foster, K. Moll, A. Gaeta, Optimal waveguide dimensions for nonlinear interactions, Opt. Express 12 (2004) 2880–2887. [32] T. Wang, X. Gai, W. Wei, R. Wang, Z. Yang, X. Shen, S. Madden, B. Lutherdavies, Systematic z-scan measurements of the third order nonlinearity of chalcogenide glasses, Op. Mater. Express 4 (2014) 1011–1022. [33] G. Agrawal, Fiber Optic Communication Systems, 4rd ed., (2010). [34] A. Heidt, A. Hartung, G. Bosman, P. Krok, E. Rohwer, H. Schwoerer, H. Bartelt, Coherent octave spanning near-infrared and visible supercontinuum generation in all-normal dispersion photonic crystal fibers, Opt. Express 19 (2011) 3775–3787. [35] C. Jiang, X. Wang, M. Zhu, H. Xu, Q. Nie, S. Dai, G. Tao, X. Shen, C. Chen, Q. Zhu, F. Liao, P. Zhang, P. Zhang, Z. Liu, X. Zhang, Preparation of chalcogenide glass fiber using an improved extrusion method, Opt. Eng. 55 (2016) 8. [36] K. Jiao, J. Yao, Z. Zhao, X. Wang, N. Si, X. Wang, P. Chen, Z. Xue, Y. Tian, B. Zhang, P. Zhang, S. Dai, Q. Nie, P. Wang, Mid-infrared flattened supercontinuum generation in all-normal dispersion tellurium chalcogenide fiber, Opt. Express 27 (2019) 2036–2043. [37] I. Shavrin, S. Novotny, H. Ludvigsen, Mode excitation and supercontinuum generation in a few-mode suspended-core fiber, Opt. Express 21 (2013) 32141–32150. [38] B. Ung, M. Skorobogatiy, Chalcogenide microporous fibers for linear and nonlinear applications in the mid-infrared, Opt. Express 18 (2010) 8647–8659. [39] H. Ahmad, M. Karim, B. Rahman, Modeling of dispersion engineered chalcogenide rib waveguide for ultraflat mid-infrared supercontinuum generation in all-normal dispersion regime, A Appl. Phys. B-Lasers Opt. 124 (2018) 10. [40] H. Seferyan, Supercontinuum Generation in Optical Fibers, edited by J.M. Dudley and J.R. Taylor, Contemp. Phys. 53 (2012) 1–2. [41] J. Dudley, S. Coen, Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers, Opt. Lett. 27 (2002) 1180–1182. [42] U. Møller, Y. 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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment The National Natural Science Foundation of China (Grant Nos. 61705091, 61875097, 61627815 and 61775109); Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LY20F050010 and LR18F050002); Program for Science and Technology of Jiaxing, China (Grant No. 2017AY13010); and the K. C. Wong Magna Fund in Ningbo University, China. Jing Xiao and Youmei Tian contribute equally to this work. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.yofte.2020.102144. References [1] M. Kumar, M.N. Islam, F. Terry, M.J. Freeman, A. Chan, M. Neelakandan, T. Manzur, Stand-off detection of solid targets with diffuse reflection spectroscopy using a high-power mid-infrared supercontinuum source, Appl. Opt. 51 (2012) 2794–2807. [2] T. Mikkonen, C. Amiot, A. Aalto, K. Patokoski, G. Genty, J. Toivonen, Broadband cantilever-enhanced photoacoustic spectroscopy in the mid-IR using a supercontinuum, Opt. Lett. 43 (2018) 5094–5097. [3] C.R. Petersen, N. Prtljaga, M. Farries, J. Ward, B. Napier, G.R. Lloyd, J. Nallala, N. Stone, O. Bang, Mid-infrared multispectral tissue imaging using a chalcogenide fiber supercontinuum source, Optics Lett. 43 (2018) 999–1002. [4] I. Zorin, R. Su, A. Prylepa, J. Kilgus, M. Brandstetter, B. Heise, Mid-infrared Fourierdomain optical coherence tomography with a pyroelectric linear array, Opt. Express 26 (2018) 33428–33439. [5] C. Amiot, A. Aalto, P. Ryczkowski, J. Toivonen, G. Genty, Cavity enhanced absorption spectroscopy in the mid-infrared using a supercontinuum source, Appl. Phys. Lett. 111 (2017) 4. [6] J. Sanghera, C. Florea, L. Shaw, P. Pureza, V. Nguyen, M. Bashkansky, Z. Dutton, I.D. Aggarwal, Non-linear properties of chalcogenide glasses and fibers, J. NonCryst. Solids 354 (2008) 462–467. [7] Y. Sun, S. Dai, P. Zhang, X. Wang, Y. Xu, Z. Liu, F. Chen, Y. Wu, Y. Zhang, R. Wang, G. Tao, Fabrication and characterization of multimaterial chalcogenide glass fiber tapers with high numerical apertures, Opt. Express 23 (2015) 23472–23483. [8] H. Tu, S.A. Boppart, Coherent fiber supercontinuum for biophotonics, Laser Photonics Rev. 7 (2013) 628–645. [9] J. Dudley, G. Genty, S. Coen, Supercontinuum generation in photonic crystal fiber, Rev. Mod. Phys. 78 (2006) 1135–1184. [10] J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. Knight, W.J. Wadsworth, P. St, J. Russell, G. Korrn, Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers, Phys. Rev. Lett. 88 (2002) 173901. [11] I.B. Gonzalo, R.D. Engelsholm, M.P. Sørensen, O. Bang, Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation, Scientific Rep. 8 (2018) 6579. [12] A.M. Heidt, J.S. Feehan, J.H.V. Price, T. Feurer, Limits of coherent supercontinuum generation in normal dispersion fibers, J. Opt. Soc. Am. B 34 (2017) 764–1755. [13] A. Muir, J. Knight, L. Hooper, P. Mosley, W. Wadsworth, Coherent supercontinuum generation in photonic crystal fiber with all-normal group velocity dispersion, Opt. Express 19 (2011) 4902–4907. [14] G. Tao, H. Heidepriem, A. Stolyarov, S. Danto, J. Badding, Y. Fink, J. Ballato, A.F. Abouraddy, Infrared fibers, Adv. Opt. Photonics 7 (2015) 379–458. [15] F. Poletti, X. Feng, G. Ponzo, M. Petrovich, W. Loh, D. Richardson, All-solid highly nonlinear singlemode fibers with a tailored dispersion profile, Opt. Express 19 (2011) 66–80.
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Optical Fiber Technology journal homepage: www.elsevier.com/locate/yofte
Investigation of tellurium-based chalcogenide double-clad fiber for coherent mid-infrared supercontinuum generation ⁎
T
⁎
Jing Xiaoa,c,1, Youmei Tiana,c,1, Zheming Zhaob, , Jinmei Yaod, Xunsi Wanga,c, , Peng Chena,c, Zugang Xuea,c, Xuefeng Penga,c, Peiqing Zhanga,c, Xiang Shena,c, Qiuhua Niea,c, Rongping Wanga,c a
Laboratory of Infrared Material and Devices, The Research Institute of Advanced Technologies, College of Information Science and Engineering, Ningbo University, Ningbo 315211, China b Nanhu College, Jiaxing University, Jiaxing 314001, China c Key Laboratory of Photoelectric Materials and Devices of Zhejiang Province, Ningbo 315211, China d College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Mid-infrared Tellurium-based chalcogenide fiber Double claddings All normal dispersion Coherent supercontinuum generation
Considerable investigations have been carried out for chromatic dispersion tailoring of chalcogenide glass fiber with various structures and different material compositions. Here we proposed a tellurium-based chalcogenide glass fiber with a dual-clad structure in a W-type refractive-index profile. The structure of the fiber based on GeAs-Se-Te glasses was numerically analyzed in detail. The simulation results indicate that an all normal dispersion profile can be realized in this tellurium glass fiber with an optimized dual-cladding structure. Then the optimized tellurium chalcogenide fiber with an all-normal dispersion profile was fabricated by multi-extrusion method. Pumping with a 5 μm ultra-short pulsed laser (150 fs, 1 kHz), abroadband supercontinuum (SC) covering 1.5–11 μm can be generated in the 19 cm-long fiber. The coherence of SC was also investigated by numerical simulation. The result shows that a high coherent SC covering 3.5–10.5 μm can be generated in this all-normal dispersion fiber. In conclusion, all-normal dispersion profile can be realized easily in this tellurium-based glass fiber due to their large materials ZDWs.
1. Introduction In recent years, mid-infrared (MIR) supercontinuum (SC) light sources have attracted considerable attention for potential applications [1–3] including optical IR coherence tomography (OCT) [4], metrology, and spectroscopy [5]. Chalcogenide fiber is promising for MIR SC generation because of its wide transmission window and high nonlinearity [6,7]. The SC sources with high coherence [8], i.e. low spectral intensity noise, can be applied in numerous fields such as multimodal biophotonic imaging and optical frequency combing. Broadband SC is usually generated by pumping the fiber in the anomalous dispersion wavelength region close to the zero-dispersion-wavelength (ZDW) [9]. In this case, the spectral broadening is dominated by soliton fission [10] or modulation instability, which is sensitive to pump-pulse fluctuations and pump laser noise, leading to decoherence of the SC spectrum over the entire SC bandwidth [11]. One approach to solve it is pumping the fiber by an ultra-short pulse in the normal dispersion wavelength
region, where SC generation are mainly dominated by self-phase modulation (SPM) and optical wave breaking (OWB) [12]. In this case, the coherence of the spectra is significantly affected by the stability of the input pulse because the effects of modulation instability are avoided, as that being basically impossible in normal dispersion [13]. Therefore, pumping a fiber at the normal dispersion wavelength region is effective to improve the coherence of the SC spectrum. Recently, more attentions have been paid to the experimental and theoretical analysis of SC generation, especially in the microstructure fibers with all-normal dispersion [13,14]. Numerical simulation has shown that the chromatic dispersion of the microstructure fiber can be tailored in the MIR region. Experimentally, compared with that for the step-index fiber (SIF), which has a step-type refractive index distribution, i.e. core refractive index higher than the cladding refractive index, precise control of the microstructure is essential for the microstructure fiber to achieve low confinement loss and desired dispersion, which in turn becomes challenging for the fiber fabrication [15]. Moreover, there
⁎
Corresponding authors at: Laboratory of Infrared Material and Devices, The Research Institute of Advanced Technologies, College of Information Science and Engineering, Ningbo University, Ningbo 315211, China (X. Wang); Nanhu College, Jiaxing University, Jiaxing 314001, China (Z. Zhao). E-mail addresses: [email protected] (Z. Zhao), [email protected] (X. Wang). 1 Jing Xiao and Youmei Tian contributed equally to this work. https://doi.org/10.1016/j.yofte.2020.102144 Received 9 August 2019; Received in revised form 9 January 2020; Accepted 9 January 2020 1068-5200/ © 2020 Elsevier Inc. All rights reserved.
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are more challenges of microstructure fiber than step-indexed fiber during the fabrication, as there are more defects appearing such as core deformation, bubble-shaping, and axial non-uniformity [16], during the fabrication of microstructure optical fibers. Furthermore, the reproducibility of the microstructure optical fibers and low coupling efficiency may be challenging problems. SIFs, which are more robust than PCFs, are usually pumped in normal dispersion wavelength region to achieve coherent SC generation [17–20]. However, it has certain difficulties to tailor the chromatic dispersion of the SIFs depending on the structural tunability. An approach available is to shift the ZDW in multi-clad fiber, such as a w-type structure [21] where a lower refractive index layer between the core and outer cladding is added. The W-type design and the materials chosen can tailor the fiber chromatic dispersion. The large numerical aperture (NAs) in such a fiber is also making easier coupling between pumping laser and fiber. Most of the works on high coherent SC generation for chalcogenide double-clad fiber have been demonstrated [22–25]. The small absolute value of the chromatic dispersion and high nonlinearity are two key factors for realizing coherent SC generation. In order to broaden the SC generation up to MIR, the double-clad fiber can be pumped by ultra-short pulse with a wavelength in the normal dispersion wavelength region. In this paper, we chose Ge-As-Se-Te (GAST) glasses for fiber fabrication. The GAST has excellent characteristics of long-wave IR transparency and larger material ZDWs [26]. Firstly, we simulated dispersion-shift of GAST fibers with a W-type refractive index profile using the finite-element method (FEM) [27]. The geometry of the proposed fiber as shown in Fig. 1 is described by the following parameters: d0—diameter of core; d1—diameter of inner cladding; d2—diameter of outer cladding; n00—refractive index of core; n01—refractive index of inner cladding; n02—refractive index of outer cladding. These diameters of d0, d1 and d2 were optimized for all-normal dispersion engineering. Subsequently, we fabricated the GAST double-clad performs with a specialized structure by the extrusion method, then a fine W-type MIR fiber with preset diameters was obtained. Finally, we investigated SC generation by simulation as well as experiment in the fiber.
Fig. 2. Refractive indices of core and claddings glasses and the calculated NAs.
together with the calculated NAs are presented in Fig. 2. Such high NAs in the DCFs mean that it is easy to couple between pumping laser and fiber. The normalized frequency V of the fiber can be obtained from:
V=
πd 0 πd 0 2 2 ncore NA − nclad = λ λ
(1)
where d0 is the core diameter and λ is the propagating light wavelength. As Eq. (1), the fiber with the d0 of 10 μm is single-moded when the wavelength is longer than 10.6 μm. The Sellmeier coefficient can be calculated by the Sellmeier equation based on measured refractive indices [28]:
n2 (λ ) = 1 +
∑ i
Ai λ2 λ2 − λi2
(2)
where λ is the wavelength, Ai and [29,30] (i = 1, 2, 3) are materialrelated constants, which are listed in Table1. The chromatic dispersion can be calculated by the FEM solver. With the numerical analyzing, effective mode area, effective refractive index of the fundamental mode and other fiber parameters can be derived directly. Based on the effective index, the dispersion distribution of the fiber, including both the waveguide and material dispersion, as conjunctions with wavelength, can be easily figured out. The effective mode area (Aeff) is given by Eq. (3):
λ12
2. Proposed design of dispersion-shifted fiber for all-normal dispersion Fig. 1 shows the transverse cross section and refractive index profiles of GAST double-clad fiber (DCF). In the structure, the refractive index (n01) of the inner cladding is smaller than that of both core (n00) and outer cladding (n02). We chose Ge15As25Se15Te45 with highest refractive index as core material, and Ge20As20Se17Te43 and Ge20As20Se15Te45 are selected as inner cladding and outer cladding, respectively. The refractive indices of the three glasses were measured by an IR ellipsometer (IR-VASE MARKII, J. A. Woollam Co.), and the results
2
Aeff =
+∞ [∫ ∫−∞ |E (x , y )|2 dx dy] +∞ ∫ ∫−∞
|E (x , y )|4 dx dy
(3)
where E is the electric field’s transverse component propagating inside the fiber. The nonlinear coefficient γ [31] can be calculated using the following formula:
γ=
2π n2 λ Aeff
(4)
where Aeff is the effective area of the propagating mode at 5 μm, n2 is the nonlinear refractive indices of Ge20As20Se17Te43 and we estimate the value by the following formula [32]:
n2 = 4.27 × 10−16
(n02 − 1) 4 cm2. W−1 n02
(5)
The refractive index of the fundamental mode, neff is computed as a function of wavelength λ, and then the chromatic dispersion D is calculated from the formula in the following [33]:
λ d 2 Re (neff ) ⎤ D (λ ) = − ⎡ [ps/nm/km] ⎥ c⎢ d λ2 ⎣ ⎦
Fig. 1. Cross-section and refractive index profiles of GAST fiber. 2
(6)
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Table 1 Refractive coefficient of telluride glasses. Materials
A1
A2
A3
λ12
λ 22
λ32
Ge15As25Se15Te45 Ge20As20Se17Te43 Ge20As20Se15Te45
9.3179 8.7503 9.1364
4.7797e−4 3.425e−4 5.7239e−5
7.9541 −25.56 −263.1
0.29015 0.39859 0.31171
270.06 191.88 228.89
8422.7 −17840 −1.5653e5
where c is the light velocity in free space, Re(n eff ) represents the real part of the effective index of fundamental mode. It is well known that chromatic dispersion of a single-mode fiber is a combination of its material dispersion and waveguide dispersion. The small values of fiber chromatic dispersion can be obtained by increasing the waveguide dispersion via tailoring the size of core and claddings. In this paper, we considered only the fundamental mode. The influence of W-type double claddings on the DCFs dispersion is explored in details. Due to the large material ZDW (> 9 μm), we increase waveguide dispersion to shift ZDWs to the long wavelength region. Thus, all-normal dispersion distribution and small absolute dispersion values can be obtained easily in the entire operatingwavelength region of the fiber. Using the method above, we tuned the waveguide dispersion to overlap the material dispersion of fiber core. Then, several DCFs geometries were optimized for consideration. A number of numerical simulations of DCFs were discussed as follows. To reduce the higherorder modes interaction, we chose d0 = 10 μm. In order to identify the influence of geometrical parameters on dispersion values, the d2/d1, d1 and d2 were optimized to introduce a strong waveguide dispersion component. Firstly, the influence of d2/d1 on the dispersion for the DCFs was explored. The chromatic dispersion of the fundamental mode was calculated with increasing d2/d1 while d1 was fixed at 20 μm and 30 μm respectively. The SIFs, d0 of 10 μm and d1 of 20 μm in Fig. 3(a) and 30 μm in Fig. 3(b), are also calculated for comparison. Fig. 3(a) shows the chromatic dispersion change with increasing d2/d1 from 1.5 to 4 when d1 is fixed at 20 μm. One set of the MFD images of the DCFs with the d2/d1 = 4 and d1 = 20 µm at 7 µm, 9.5 µm and 12 µm shown in Fig. 4(a), Fig. 4(b), and Fig. 4(c) respectively might explain why the dispersion curve exhibits these sharp dips near 10 µm. Clearly, there is a crossing between the fundamental core mode and one or more cladding modes (the donut mode at 12um). Dashed curve represents the chromatic dispersion of SIFs consisting of the same materials of core and cladding as that of the core and inner cladding of the GAST DCFs, respectively. However, it is clear that the smaller absolute values of the chromatic dispersion are obtained at d2/d1 = 2 (see the blue line). The result shows that at a wavelength of 12.3 μm, the calculated maximum dispersion with the d2/d1 ratio of 2 is still normal (-0.7979 ps/km/nm). It demonstrates that at d2/d1 = 2, the coherent SC generation has been
Fig. 4. The MFD images of the DCFs with the d2/d1 = 4 and d1 = 20 µm at (a) 7 µm, (b) 9.5 µm and (c) 12 µm. Table 2 Dispersion and ZDW comparison between the DCFs and SIF under different d2/ d1. fiber
d2/d1
ZDW (μm)
|ΔD| (ps/km/nm)
Bandwidth (μm)
DCF (d1 = 20 μm)
1.5 2.0 2.5 3.0 3.5 4.0
10 no no 11.7 11.1 10.6
7.85 5.81 12.61 34.80 62.04 91.90
3 3 3 3 3.2 3
SIF (d1 = 20 μm)
–
9.1
7.11
3
DCF (d1 = 30 μm)
1.5 2.0 2.5 3.0 3.5 4.0
9.5 no 11 10 9.6 9.4
6.78 8.64 35.39 40.35 51.20 76.23
4 4 4 4 4 4
SIF (d1 = 30 μm)
–
9.1
12.01
4
achieved with flattened all-normal dispersion profiles [34]. In addition, the dispersion variation of the fiber within the bandwidth of 3 μm is lower than others, as shown in Table 2, where |ΔD| is the difference value of the maximum and minimum dispersion within a certain wave band, and bandwidth is the length of the wave band. When d1 = 30 μm, the effect of the double claddings on dispersion engineering is similar to that of d1 = 20 μm, and the dispersion values are all normal in such a fiber with d2/d1 = 2. It can be seen in Fig. 3(b) where the dispersion curves are recalculated for DCFs with d1 = 30 μm. In this case, the
Fig. 3. Variations of chromatic dispersion profiles of DCF by changing d2/d1 (a) d1 = 20 μm and (b) d1 = 30 μm. 3
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Fig. 5. (a) Chromatic dispersion profiles of DCFs with d1 = 20, 30, 40, 50 μm with d2/d1 = 2. (b) Chromatic dispersion profiles of DCFs in Fig. 5(a) from 8.5 to 11.5 μm. (c) Dispersion curves of the fabricated DCF and three materials. (d) Dispersion distribution of the fiber with d1 = 30 μm, d2/d1 = 2.
maximum dispersion of −0.2475 ps/km/nm appears at 9.8 μm and the variation of the dispersion is quite small in the same functional bandwidth. Thus, a small and flat chromatic normal dispersion profile can be obtained in a fiber with d2/d1 = 2. The following results further show the influence of the change of d1 from 20 to 50 μm on dispersion when d2/d1 is fixed at 2. The dispersion curves of the DCFs were also recalculated. As shown in the Fig. 5(a), the chromatic dispersion of the fiber with d1 = 20 μm and d1 = 30 μm is flatter than that of the fibers with d1 = 40, 50 μm. And there are no ZDWs for the fibers of d1 = 20 μm and d1 = 30 μm in the whole considered wavelengths range in the fiber with d2/d1 = 2. As the red curve shown in Fig. 5(b), the absolute value of chromatic dispersion is quite small at peak of the dispersion curve near the wavelength of 9.8 μm, which has been mentioned in Fig. 3(b). As shown in Table 3, the flatness of the chromatic dispersion for the fiber is approximately 4.99 ps/km/nm at a range of 8–12 μm in the normal dispersion wavelength region, which is lower than that of SIF and other DCFs. The dispersion curves of designated fiber and three materials are plotted in Fig. 5(c), where bulk Ge15As25Se15Te45 glass exhibits a larger material ZDW of about 9.4 μm (black line). The dispersion curves of the double-clad fibers have similar slopes compared with that of
Ge15As25Se15Te45 bulk glass. The dashed line represents the dispersion profile of the double cladding fiber with d2 = 60 μm, as their d0 and d1 were fixed at 10 μm and 30 μm, respectively. It is reasonable to say that the fiber dispersion values can be strongly affected by the double claddings. As shown in Fig. 5(d), the fiber dispersion profile stands between −1 and 0 ps/km/nm from 9.2 to 10.4 μm, respectively. As indicated above, the proposed DCFs design (d0 = 10 μm, d1 = 30 μm, d2 = 60 μm) exhibits flat normal dispersion and are suitable for the optimal fibers to generate coherent SC. The calculated Aeff and γ of the DCFs are presented in Fig. 6, in which the effective area increases with increasing wavelength. In addition, the value of γ is up to 272 W−1 km−1 at 10.6 μm. The dispersion coefficient up to the 10th-order (β2 to β10) is used to get an accurate fit with the dispersion curve. The simulations made it clear that, ideal flattened dispersion curves of all-normal-dispersion can be achieved in the DCFs with the optimized
Table 3 Dispersion and ZDW comparison under different d1. fiber
d1 (μm)
ZDW (μm)
|ΔD| (ps/km/nm)
Bandwidth (μm)
DCF
20 30 40 50
no no 9.3; 10.5; 11.5 9.3; 9.7; 10.1
7.01 4.99 24.62 23.30
4 4 4 4
SIF
20 30 40 50
9.1 9.1 9.3 9.3
12.01 12.01 9.18 8.79
4 4 4 4
Fig. 6. Effective area and nonlinear coefficient of the fundamental mode calculated in the optimized fiber with d1 = 30 μm, d2/d1 = 2. 4
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structure (d0 = 10 μm, d1 = 30 μm, d2 = 60 μm). Therefore, such an all-normal dispersion DCFs were considered as the best candidate for coherent SC generation.
the reports of Ref. [37], the intermodal nonlinear interactions for SC generation is suppressed and negligible, so we assumed single-polarization and single-mode propagation in SC simulation for simplicity. For the designed DCFs, the numerical simulations of the output SC spectra were performed for all-normal dispersion SC generation in a 19cm-long fiber pumped by a wavelength of 5 μm. We performed a simulation with the generalized nonlinear Schrödinger equation (GNLSE) taking the fiber loss, high order dispersion, and stimulated Raman scatting into account. In our simulation, 0.001% RIN of the pump source was introduced. The response function with the same parameters of As40Se60 glass reported in Ref. [38], which is an approximation to the more complex Raman spectrum of the actual glasses is expressed as following [12]:
3. Fabrication of glasses and dispersion-shifted fiber 3.1. Glass synthesis The glass rods for preform were synthesized by the conventional melt-quenching method. Raw materials of Ge, As, Se, Te with prepurification were melted in a rocking furnace to ensure homogeneity, and then the melts were cooled, following by quenching. The obtained glass was annealed to remove the internal stress.
R (t ) = (1 − fR ) δ (t ) + fR (t ) hR (t )
3.2. The fabrication of fiber and preforms based on co-extrusion
(7)
where the response function coefficients are defined as fR = 0.11 and the delayed Raman contribution hR (t ) [39] is given by:
The preform was fabricated using the two-step isolated co-extrusion method [35]. Each glass was prepared in the form of cylindrical rods (Ge20As20Se17Te43, Ge20As20Se15Te45 and Ge15As25Se15Te45). First, the preform with a core-cladding ratio of 1:2 was extruded by a 26 mm core glass rod along with a 46 mm cladding glass rod. Then the composite perform of 9 mm was co-extruded with a ratio of 1:3 by a 26 mm cladding glass. Finally, the structured preform with a ratio of 1:5 was extruded again by a 46 mm Ge15Sb10Se75 glass rod to obtain a small core fiber. The double-clad fiber was fabricated by a conventional preformdrawing process. The co-extruded preform was drawn into DCFs in a home-made drawing tower at 310℃ with N2 protection. Then we obtained the optimized DCFs with a diameter of about 300 μm and d0, d1, d2 of 10 μm, 30 μm and 60 μm, respectively. A low-loss dual-clad tellurium chalcogenide fiber [36] has been reported. However, with a 20 μm core diameter, the fiber was still multi-moded. In this work, a dual-clad tellurium chalcogenide fiber was realized in the optimized structure. The cross-sectional photographs of the DCFs were taken by an optical microscope with a super long depth of view (Keyence, VHX-1000). As shown in Fig. 7, the size of the core and inner-clad and outer-clad diameters were 10 μm, 30 μm and 70 μm respectively. The optical losses of the GAST fiber are nearly the same as that in the reports of Ref. [26].
hR (t ) =
τ12 + τ22 t t exp ⎛− ⎞ sin ⎛ ⎞ τ τ τ1 τ22 2 ⎝ ⎠ ⎝ 1⎠ ⎜
⎟
⎜
⎟
(8)
where τ1 = 15.5 fs and τ1 = 230.5 fs . The parameters used for simulation SC generation in the double cladding fiber are shown in the following Table 4. In addition, the effective mode area dependence of the nonlinear response was also taken into account. Based on the calculated dispersion and nonlinearity, the GNLSE was solved by the Split-step Fourier method including higher order dispersion parameters up to the 10th-order [40]. The spectral broadening was mainly driven by the SPM due to all-normal dispersion profile in the case of d1 = 30 μm and d2/d1 = 2. A femtosecond pulse was used to meet large power for pumping in normal dispersion wavelength region. To clarify the all-normal dispersion on the properties of MIR SC, we compared the measured spectra with numerical simulations. A tunable OPA system (Mirra 900 + Legend Elite + OperA Solo) was used as the pumping source, with a ~150 fs pulse out in a repetition rate of 1 kHz. The beam from the OPA was coupled via a calcium fluoride lens with a focal length of 75 mm into the fiber. The SC output from the fiber was collected by the input slit of a monochromator. A liquid nitrogen-cooled HgCdTe (MCT) detector with a range of 1–16 μm was used to measure the output of the monochromator. Therefore, ~150 fs pulse at 5 μm out from the OPA system was injected into a 19-cm-long DCF. The comparison of the measured SC spectra generation at 5 μm under increasing powers are shown in Fig. 8 (b). We observed that the spectrum became broad when the input power increased. The SC generation under different incident average power were limited to the normal dispersion regime and the dips in the SC spectra were due to the absorption of the Ge15Sb10Se75 out of the fibers. It also has been seen that the flat SC was
4. MIR SC generation in DCFs SC generation was numerically simulated and experimentally measured in these DCFs. There are some researches about the coherence of ANDi SC including the influence of PMI such as Ref. [12]. According to
Fig. 7. Cross-sectional photograph of the DCFs. 5
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J. Xiao, et al.
Table 4 Parameters for simulation SC generation in the double cladding fiber. Parameter Unit Values
L cm 19
λ
P kW 50/150/200
μm 5
γ −1
−1
m ·W 0.755
TFWHM
fR
τ1
τ2
fs 200
Null 0.11
fs 15.5
fs 230.5
(L: fiber length, P: peak power).
Fig. 9. Degree of first-order coherence in the designed fiber.
resolving the spectrum. The GNLSE for the fundamental mode of the fibers was solved by using commercial software MATLAB to simulate SC generation. Spectral fluctuations from shot to shot in the input pulse was modeled via the one-photon-per-mode noise model [42]. The measured refractive index of the all normal dispersion GAST fiber and the nonlinear coefficient (γ) calculated by using the commercial software COMSOL Multiphysics were used in the simulation. The wavelength dependence of γ can be seen from the Fig. 6. The material loss and confinement of the fiber were not included in the simulation. We observed the high coherence property of the generated supercontinuum was kept because the spectral broadening of the SC is dominated by SPM. Therefore, the coherence property of the generated SC and the normalized intensity were almost unity for the entire spectral range. The normalized intensity and the degree of the first-order coherence 1 1 (λ )| = 1 by launching the |g12 (λ )| is drawn in Fig. 9. Simulations show |g12 150 fs laser pulse at 5 μm, which corresponds to highly coherent for our proposed fiber design from 3.5 to 10.5 μm. 5. Conclusion In this paper, we report a chalcogenide W-type optical fiber structure for highly coherent MIR SC generation. The dispersion profiles of the fibers have been numerically analyzed in order to obtain flat allnormal dispersion profile in MIR region. The results showed that, ZDWs can be shifted to longer wavelengths as the parameters of W-type double-clad fiber change. Therefore, an all normal dispersion profile can be realized in a single-mode fiber with a core size 10 μm, an inner cladding 30 μm and an outer cladding 60 μm. Then, the single-mode fiber with the optimized structure was fabricated via the robust extrusion and preform drawing methods. The study of simulations and experiments for SC generation were also given. A coherent MIR SC extending to 11 μm could be obtained using the 19-cm-long of fiber by 150 fs pulsed laser at 5 μm. For the proposed GAST W-type fiber, the coherence property of the SC was almost unity in the entire spectral range. In conclusion, geometrical flexibility of DCFs and large material ZDWs of GAST glasses provide the all-normal dispersion profile to obtain coherent SC for MIR in the case of femtosecond pulsed laser pumping.
Fig. 8. (a) Simulated SC results in the DCFs with the pump wavelength of 5 μm under various powers. (b) Measured SC results from designed fiber obtained with 150 fs input pulses injected at the different input powers.
observed under the input power of 20 mW. However, the SC bandwidth somewhat was reduced because of pumping in all-normal regime because the broadening of SC was mainly dominated by SPM and OWB above the noise and visibly grows in strength in long wavelengths. The strong SPM leads to OWB via self-steepening and third-order dispersion, and thus significant broadening of the spectrum [37], but the OWB in the end halts the broadening process. So it is the SPM generated up until the OWB point that will decide the obtainable SC bandwidth. Thus, the SC spectrum was not generated at wavelengths above 11 μm. This could be due to the fact that that the loss of fiber increases rapidly and the pulse power was attenuated quickly when the wavelength is longer than 11 µm, thus SPM effects were weakened further to limit the broadening of the pulse. The maximum pump power was up to 200 kW. As that the coherence is a key parameter for measuring the quality of the generated SC. We quantified it by means of the modulus of the complex degree of first-order coherence at each wavelength in the SC, which can be defined as following [41]: 1 |g12 (λ, t1 − t2)| =
CRediT authorship contribution statement Jing Xiao: Methodology, Data curation, Writing - original draft. Youmei Tian: Software, Data curation, Writing - original draft. Zheming Zhao: Validation, Investigation. Jinmei Yao: Software, Formal analysis. Xunsi Wang: Conceptualization, Resources, Writing review & editing, Validation. Peng Chen: Validation. Zugang Xue: Validation. Xuefeng Peng: Software. Peiqing Zhang: Software. Xiang Shen: Supervision. Qiuhua Nie: Supervision. Rongping Wang: Writing - review & editing, Supervision.
〈E1 ∗ (λ, t1) E2 (λ, t2) 〉 1
[ 〈 |E1 (λ, t1)|2 〉〈 |E2 (λ, t2)|2 〉 ] 2
(9)
where E1 (λ ) and E2 (λ ) are the output spectrum from the fiber and t is the time measured at the resolution time scale of the spectrometer for 6
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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment The National Natural Science Foundation of China (Grant Nos. 61705091, 61875097, 61627815 and 61775109); Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LY20F050010 and LR18F050002); Program for Science and Technology of Jiaxing, China (Grant No. 2017AY13010); and the K. C. Wong Magna Fund in Ningbo University, China. Jing Xiao and Youmei Tian contribute equally to this work. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.yofte.2020.102144. References [1] M. Kumar, M.N. Islam, F. Terry, M.J. Freeman, A. Chan, M. Neelakandan, T. Manzur, Stand-off detection of solid targets with diffuse reflection spectroscopy using a high-power mid-infrared supercontinuum source, Appl. Opt. 51 (2012) 2794–2807. [2] T. Mikkonen, C. Amiot, A. Aalto, K. Patokoski, G. Genty, J. Toivonen, Broadband cantilever-enhanced photoacoustic spectroscopy in the mid-IR using a supercontinuum, Opt. Lett. 43 (2018) 5094–5097. [3] C.R. Petersen, N. Prtljaga, M. Farries, J. Ward, B. Napier, G.R. Lloyd, J. Nallala, N. Stone, O. Bang, Mid-infrared multispectral tissue imaging using a chalcogenide fiber supercontinuum source, Optics Lett. 43 (2018) 999–1002. [4] I. Zorin, R. Su, A. Prylepa, J. Kilgus, M. Brandstetter, B. Heise, Mid-infrared Fourierdomain optical coherence tomography with a pyroelectric linear array, Opt. Express 26 (2018) 33428–33439. [5] C. Amiot, A. Aalto, P. Ryczkowski, J. Toivonen, G. Genty, Cavity enhanced absorption spectroscopy in the mid-infrared using a supercontinuum source, Appl. Phys. Lett. 111 (2017) 4. [6] J. Sanghera, C. Florea, L. Shaw, P. Pureza, V. Nguyen, M. Bashkansky, Z. Dutton, I.D. Aggarwal, Non-linear properties of chalcogenide glasses and fibers, J. NonCryst. Solids 354 (2008) 462–467. [7] Y. Sun, S. Dai, P. Zhang, X. Wang, Y. Xu, Z. Liu, F. Chen, Y. Wu, Y. Zhang, R. Wang, G. Tao, Fabrication and characterization of multimaterial chalcogenide glass fiber tapers with high numerical apertures, Opt. Express 23 (2015) 23472–23483. [8] H. Tu, S.A. Boppart, Coherent fiber supercontinuum for biophotonics, Laser Photonics Rev. 7 (2013) 628–645. [9] J. Dudley, G. Genty, S. Coen, Supercontinuum generation in photonic crystal fiber, Rev. Mod. Phys. 78 (2006) 1135–1184. [10] J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. Knight, W.J. Wadsworth, P. St, J. Russell, G. Korrn, Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers, Phys. Rev. Lett. 88 (2002) 173901. [11] I.B. Gonzalo, R.D. Engelsholm, M.P. Sørensen, O. Bang, Polarization noise places severe constraints on coherence of all-normal dispersion femtosecond supercontinuum generation, Scientific Rep. 8 (2018) 6579. [12] A.M. Heidt, J.S. Feehan, J.H.V. Price, T. Feurer, Limits of coherent supercontinuum generation in normal dispersion fibers, J. Opt. Soc. Am. B 34 (2017) 764–1755. [13] A. Muir, J. Knight, L. Hooper, P. Mosley, W. Wadsworth, Coherent supercontinuum generation in photonic crystal fiber with all-normal group velocity dispersion, Opt. Express 19 (2011) 4902–4907. [14] G. Tao, H. Heidepriem, A. Stolyarov, S. Danto, J. Badding, Y. Fink, J. Ballato, A.F. Abouraddy, Infrared fibers, Adv. Opt. Photonics 7 (2015) 379–458. [15] F. Poletti, X. Feng, G. Ponzo, M. Petrovich, W. Loh, D. Richardson, All-solid highly nonlinear singlemode fibers with a tailored dispersion profile, Opt. Express 19 (2011) 66–80.
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