The effects of stimulated Raman scattering (SRS) is demonstrated in chalcogenide microstructured optical fiber (MOF) with all-solid AsSe2 core and As2S5 cladding. The first-order Raman Stokes wave is investigated in the MOFs with different core diameters pumped by the picosecond pulses at 1958 nm. The maximum conversion efficiency of −15.0 dB from the pump to first-order Raman Stokes wave is obtained in the MOF with the core diameter of 2.6 μm. The conversion efficiency decreases when the core diameter deviates from 2.6 μm. When the fiber core is larger, the effective nonlinearity is decreased. When the fiber core is smaller, the mode field is difficult to be confined in the core. The walk-off length between the pump and Stokes wave is crucial to the process of SRS according to the analysis of the experimental data. The Raman effects are simulated numerically. The simulated results can agree well with the experiments. It is the first time to demonstrate the Raman effect in AsSe2-As2S5 MOF, to the best of our knowledge.
© 2016 Optical Society of America
The process of Raman effect was first reported by C. V. Raman in 1928 . It can be described as scattering of a photon by one of the molecules to a lower-frequency photon, while the molecule makes transition to a higher-energy vibrational state. In 1962, the nonlinear phenomenon of stimulated Raman scattering (SRS) was observed in the medium pumped by intense field, where the Stokes wave grew rapidly and most of the pump energy was transferred to it . After that, SRS was reported in different media [3–6].
The SRS in optical fiber was first observed by Stolen et al. . Optical fiber is advantageous for the process of SRS because it has low attenuation, can confine optical energy in the fiber core, and is easy to provide the length of several kilometers for enough Raman gain [7–9]. The Raman effects have been observed in the fibers fabricated by different materials, such as silica , germanosilicate , phosphosilicate , fluoride [12,13], and tellurite [14,15] glass. Chalcogenide glass has wider transmission window and higher nonlinearity than the other glass mentioned above in near-infrared (NIR) and mid-infrared (MIR) region [16–18]. Chalcogenide glass can be transparent from the visible up to the infrared region of 12 or 15 μm depending on the compositions. The nonlinear refractive index of chalcogenide glass can be one- or several-order higher than silica, fluoride or tellurite glass. Therefore, chalcogenide fiber is an excellent candidate to generate different nonlinear effects, especially in the MIR region [17–19].
Many works about the supercontinuum generation in chalcogenide fibers have been demonstrated [19–23]. Chalcogenide fibers has higher Raman gain coefficient than the fibers made by other glass. The process of supercontinuum generation included the Raman effects. In addition, the single process of Raman effects in chalcogenide fibers has also been demonstrated [24–27]. Duhant et al. reported cascaded Raman effect in the MIR region with the wavelength shifting up to the fourth order ranging from 2092 to 2450 nm using a nanosecond pump at 1995 nm in an As38Se62 suspended-core microstructured optical fiber (MOF) . White et al. demonstrated efficient cascaded Raman effects in both NIR and MIR region pumped by nanosecond pulses in large-core As2S3 and As2Se3 optical fibers with the pump wavelength of 1.55 and 1.9 μm, respectively . The fiber laser based on SRS in chalcogenide fibers were demonstrated to obtained the lasing in MIR region [28–31]. Bernier et al. first demonstrated a Raman fiber laser emitting in the MIR region in a single-mode As2S3 chalcogenide fiber, where 3.34 μm lasing was observed by 3 μm pumping . Then, Bernier et al. obtained the lasing with longer wavelength of 3.77 μm by cascaded Raman effects in a 2.8 m long As2S3 fiber .
Except for the material, the lateral structure of the fiber will also affect the process of SRS. Therefore, the MOFs and photonic crystal fibers (PCFs) were used in SRS to optimize the Raman gain because of their good optical mode field, low loss, and tailorable effective nonlinearity. Raman effects have been demonstrated in the MOFs and PCFs with different structures [26,32,33].
In this work, we demonstrate the effects of SRS in the chalcogenide MOFs with all-solid AsSe2 core and As2S5 cladding. The first-order Stokes wave is investigated in the MOFs with different core diameters pumped by the picosecond pulses at 1958 nm. The maximum conversion efficiency of from pump to the first-order Stokes wave is obtained in the MOF with the core diameter of 2.6 μm. The evolution of the first-order Stokes wave with pump power and fiber length is investigated. The affect of the walk-off length on the Raman effects is analyzed. This is the first demonstration of Raman effect in AsSe2-As2S5 MOF, to the best of our knowledge.
2. Experimental conditions
2.1 The AsSe2-As2S5 MOF
The first realization of all-solid chalcogenide MOF was reported by Toupin et al. . It is critical to select the suitable glass composition for the fiber core and cladding during the fabrication of hybrid chalcogenide MOF, for the reason that the core and cladding should have compatible properties to avoid cracking at the interface. The compatibility between AsSe2 and As2S5 glass is very good, according to the report in . The As2S5 glass has high transmission in the spectral range from 0.6 to 9.9 μm [21,36], while the AsSe2 glass is transparent from 0.83 to 18.9 μm . Therefore, the AsSe2 glass can be used as the fiber core when As2S5 glass is used as cladding for fabricating MOFs.
The all-solid AsSe2-As2S5 MOF was fabricated by the rod-in-tube drawing technique . Figure 1(a) shows the cross section of the AsSe2-As2S5 MOF measured by an optical microscope. The MOF has one AsSe2 core and four As2S5 rods [(dark circular area in Fig. 1(a)]. The core diameters used in this work, defined as the diameter of the circle inscribed in the four rods, are ~6.3 (Fiber I), 3.0 (Fiber II), 2.6 (Fiber III) and 2.2 (Fiber IV) μm, respectively. The rod diameters of the four kinds of MOFs corresponding to the fiber cores above are as shown in Table 1. The outer cladding diameters are ~150, 76, 74 and 64 μm, respectively, as shown in Table 1. The transmission spectra of the AsSe2 and As2S5 glasses were measured using the sample with the thickness of 1 mm, which were shown as in Fig. 1(a) of  and Fig. 1(c) of . The attenuation of Fibers I-IV was 1-2 dB/m measured at 2000 nm by the cut-back technique.
The chromatic dispersion of the fundamental mode in Fibers I-IV was simulated by a commercial software (Lumerical MODE Solution) using the full-vectorial mode solver technique, as shown in Fig. 1(b). The Sellmeier expansions of AsSe2 and As2S5 glass used for the simulation were from reference . The data of zero-dispersion wavelength (ZDW) are listed in Table 1. Fiber I has one ZDW at ~4.39 μm. Fiber II has two ZDWs at ~3.52 and ~5.75 μm. Fiber III has also two ZDWs at ~3.49 and ~4.73 μm. Fiber IV has no ZDW. The nonlinear coefficients at 1958 nm of Fibers I-IV were calculated to be ~1133, 4994, 6649 and 9286 W−1km−1, respectively, according to the effective mode areas and the nonlinear-index coefficient of As2Se3 glass as n2 = 1.1 × 10−17 m2W−1 in  and . The Raman-gain coefficient of As-Se fiber is ~2-5 × 10−11 m/W at around 1.5 μm, which is much higher than that of As-S fiber (~4-6 × 10−12 m/W at 1.5 μm) [26,27].
The spontaneous Raman spectra of the As2S5 and AsSe2 bulk glass sample were measured by a Raman spectrometer (JASCO NRS 2100), as shown in Fig. 1(c). The samples with the width of ~1.5 mm were excited by a CW laser with the wavelength of 532 nm and the average power of ~500 mW. The Raman Stokes spectra were recorded in the range from 45 to 1500 cm−1 in the back scattering alignment mode with co-polarization of incident and scattered light mode. According to Fig. 1(c), the Raman shift of the AsSe2 and As2S5 bulk glass could be in the range from ~50 to ~450 cm−1.
Figure 2(a) shows the calculated effective refractive indices of Fibers I-IV according to the fiber structure in Fig. 1(a). We can see that the effective refractive indices at the same wavelength increase with fiber core diameter, which means that Fiver IV has lower effective refractive indices at pump and Stokes wavelength than Fibers I-III. Figures 2(b) and 2(c) show the calculated group velocity of Fibers I-IV, which is used to calculated the walk-off length for the four MOFs.
2.2 Experimental setup
The experimental setup to generate the Raman effects in AsSe2 -As2S5 MOFs is shown as in Fig. 3. The pump source was a picosecond pulse source (AdValue Photonics AP-ML1). The pump pulses with the full width at half maximum (FWHM) of 2.7 ps and repetition rate of 31.94 MHz were generated with the wavelength of 1958 nm. Then the pulses were launched into Fibers I-IV by a focusing lens (Thorlabs C028TME-D) with the focus length of 5.95 mm and numerical aperture (NA) of 0.56 at the design wavelength of 4.1 μm. The transmission of the focusing lens at 1958 nm was measured to be 97.7%. The ends of Fibers I-IV were cleaved well by a diamond stylus to ensure good cross sections. The coupling efficiencies into Fibers I-IV were measured to be ~27%, 15%, 12% and 8%, respectively. The output ends of Fibers I-IV were connected directly with a 0.5 m large-mode-area (LMA) ZBLAN fiber. The LMA ZBLAN fiber had the core diameter of 105 μm and the transmission window from ~0.4 to ~5.0 μm. Then the nonlinear effect in the LMA ZBLAN fiber could be ignored due to the large core diameter. The spectra were measured by an optical spectrum analyzer (OSA) (Yokogawa AQ6375) connected to the LMA ZBLAN fiber.
3. Raman effect in the AsSe2-As2S5 MOFs
3.1 With the core diameter of 6.3 μm
At first, we used an AsSe2-As2S5 MOF with the core diameter of 6.3 μm (Fiber I). The fiber length was 80 cm. Figure 4 shows the measured spectra in Fiber I pumped by picosecond pulses at 1958 nm. The average powers from the pump source were 95 and 120 mW, corresponding to the peak power launched into Fiber I of 291 and 367 W, respectively, considering the transmission of the focusing lens and the coupling efficiency. In Fig. 4, no obvious Raman peak was observed with the pump power increasing from 95 to 120 mW. Only weak self-phase modulation (SPM) effect was observed, because the effective nonlinearity is not high in the 6.3 μm fiber core. The nonlinear coefficient of Fiber I is calculated to be 1133 km−1W−1 at 1958 nm (γp) and 1071 km−1W−1 at 2070 nm (γs), respectively, as shown in Table 1. It can be analyzed according to the pulse-propagation equations of pump and Stokes wave in the fiber as follows :Eqs. (1) and (2), T = t - z/vgp represents retard frame, which is a frame of reference moving with the pump pulse at the group velocity of pump wave (vgp), d = vgp−1- vgs−1 is the walk-off parameter accounting for the group-velocity mismatch between the pump and Stokes pulses, and vgs is the group velocity of Stokes wave. In Eqs. (1) and (2), the fiber loss was neglected because the fiber length used in our experiments was relatively short.
The process of SRS was affected by both the Raman-gain coefficient (gp and gs) and the nonlinear coefficient (γp and γs) of pump and Stokes wave. The nonlinear coefficient could be increased when the core diameter is decreased.
3.2 With the core diameter of 3.0 μm
Then we used an AsSe2-As2S5 MOF with smaller core diameter of 3.0 μm (Fiber II). The pump light was launched into the 45 cm long Fiber II with the average powers from the pump source of 90, 110, 130, 150 and 170 mW. The corresponding peak powers launched into Fiber II were 153, 187, 221, 255 and 289 W, respectively, which were smaller than those in Fiber I. The nonlinear coefficient of Fiber II was calculated to be 4994 km−1W−1 at 1958 nm (γp) and 4723 km−1W−1 at 2070 nm (γs), respectively, as shown in Table 1, which are much higher than those in Fiber I.
Due to the higher nonlinear coefficient, the first-order Raman Stokes peak was observed even by the lower pump peak power, as shown in Fig. 5(a). In Fig. 5(a), a Raman Stokes peak at ~2065 nm began to emerge at the pump power of 110 mW, which was the threshold of SRS in Fiber II. With the pump power increasing to 150 mW, the intensity of Stokes peak became higher. The Stokes peak did not increase further when the pump power was higher than 150 mW, only that it was broadened by the SPM effect. The conversion efficiency was as low as −36.6 dB. The wavelength of the Stokes peak varied in the range of 2065-2075 nm with the pump power increasing, which corresponded to the spontaneous Raman spectra in Fig. 1(c).
Figures 5(b) and (c) show the Raman spectra generated in 90 and 190 cm long Fiber II. The Stokes peaks in Fig. 5(c) are wider than those in Fig. 5(b), because the Stokes peaks in Fig. 5(c) experienced stronger SPM effects in the longer fiber. Compared to Fig. 5(a), the Raman peaks in Figs. 5(b) and 5(c) were not increased even the longer fibers were used.
Figures 6(a)-6(c) show the variation of Raman spectra versus the fiber length at the same pump power. By 90 mW pumping, no Stokes peak was observed with the fiber length increasing from 45 to 190 cm, as shown in Fig. 6(a). By 110 mW pumping, the Stokes peak could be observed in 45 cm long fiber; it became a little wider in 90 and 190 cm long fiber due to the SPM effect, as shown in Fig. 6(b). In Fig. 6(c) by 130 mW pumping, the evolution was similar to that in Fig. 6(b).
3.3 With the core diameter of 2.6 μm
We decreased the core diameter of the AsSe2-As2S5 MOF further to 2.6 μm (Fiber III). The fiber length was 45 cm. The nonlinear coefficient of Fiber III is calculated to be 6649 km−1W−1 at 1958 nm (γp) and 6289 km−1W−1 at 2070 nm (γs), respectively, as shown in Table 1, which are higher than those in Fiber I and Fiber II. The pump light was launched into Fiber III with the average powers from the pump source of 30, 40, 56, 70, 90, 110 and 130 mW. The corresponding peak powers launched into the MOF were 41, 54, 76, 95, 122, 150 and 177 W, respectively, which were much smaller than those in Fibers I and II.
The Raman spectra generated in Fiber III are shown as in Fig. 7. The first-order Raman peak at ~2060 nm began to emerge at 40 mw pumping. The Raman threshold of 40 mW was much smaller than that in Fiber II. The intensity of the Stokes peak increased with the pump power increasing from 40 to 110 mW. The Stokes peak did not increase further when the pump power was higher than 110 mW, but it was broadened by the SPM effect, which is the same as the case in Fig. 5(a). The wavelength of the Stokes peak varied in the range of 2060-2070 nm with the pump power increasing, corresponding to the spontaneous Raman spectra in Fig. 1(c). The conversion efficiency was −15.0 dB, which was improved by 21.6 dB comparing to that in Fiber II.
3.4 With the core diameter of 2.2 μm
To decrease the fiber core further, we used Fiber IV with the core diameter of 2.2 μm. The nonlinear coefficient of Fiber IV was calculated to be 9286 km−1W−1 at 1958 nm (γp) and 8783 km−1W−1 at 2070 nm (γs), respectively, as shown in Table 1, which are much higher than those in Fibers I-III. The measured Raman spectra are shown as in Fig. 8.
In Fig. 8(a), the pump light was launched into the 90 cm long fiber with the average powers from the pump source of 56 and 90 mW. The corresponding peak powers launched into Fiber IV were 51 and 82 W, respectively. The Stokes peak at 2070 nm began to appear at 56 mW pumping. The Raman threshold was ~56 mW. Figure 8(b) shows the Raman spectra generated with different fiber lengths by 90 mW pumping. The Stokes peak had no obvious increase with the fiber length increasing from 50 to 60 cm; it became wider with the fiber length increasing to 90 cm, which is the same as the cases in Figs. 6(b) and 6(c).
Comparing to Fiber III, the Raman threshold in Fiber IV was higher, the Raman peak was much weaker at the same pump level, and the conversion efficiency was much lower (−35.2 dB at 90 mW pumping). The Raman spectra generated in Fiber IV are inferior to those in Fiber III, although Fiber IV has higher nonlinear coefficient. The possible reason is that both the pump and Stokes wave were difficult to be confined in the fiber core as small as 2.2 μm, while the energy came into fiber cladding and was converted to evanescent wave.
Table 2 shows the group velocity (vgp and vgs) and calculated walk-off length LW of Fibers I-IV according to the data in Figs. 2(b) and 2(c). We can see that the walk-off lengths of Fibers I-IV are 7.30, 8.49, 8.94 and 9.46 cm, respectively.
According to the experimental results described above, the first-order Raman Stokes peak could be generated in Fibers II-IV, but could not be generated in Fiber I. For Fiber I, the nonlinear coefficient was much smaller that those of Fibers II-IV. So the threshold of the Raman effect was much higher in Fiber I. Even a long length of 85 cm was used, the threshold could not be decreased because of the walk-off length LW between the pump and Stokes wave was very short.
The nonlinear coefficient increased from Fiber II to Fiber IV. So the Stokes peak began to appear in Fiber II. The maximum conversion efficiency of the Raman effect was obtained in Fiber III. But the conversion efficiency decreased in Fiber IV whose core diameter was decreased further to 2.2 μm. Because the optical mode fields of the pump and Stokes wave were difficult to be confined in such small core entirely and the energy was converted to evanescent wave.
With the pump power increasing, the intensity of Stokes peak increased, as shown in Figs. 5, 7 and 8(a). But the intensity of Stokes peak did not increase further after the pump power arrived some level, such as 150 mW in Fig. 5(a) and 110 mW in Fig. 7. The reasons are: (1) the increased pump power had little interaction with Stokes wave and could not be converted to Stokes wave effectively due to the short walk-off length; (2) some of the energy was used to broaden the Raman spectrum by the SPM effect.
The intensity of Stokes wave did not increase with the fiber length increasing even a 190 cm long fiber was used, as shown in Fig. 6 and Fig. 8(b). The reasons are: (1) the fiber attenuation depleted some of the pump power; (2) the pump and Stokes wave had no interaction with each other in the increased fiber part due to the short walk-off length.
In Fiber III, the conversion efficiency was maximal, but there was no higher-order Stokes wave emerged with the pump power increasing to 130 mW. It was because of the short walk-off length between pump, first- and higher-order Stokes wave. Besides, the fiber attenuation and the SPM effect also depleted the energy of first-order Stokes wave.
According to the analysis above, except for the pump power, the Raman-gain coefficient and the nonlinear coefficient, the walk-off length is crucial for the Raman effects in Fibers I-IV. We consider two ways to increase the walk-off length. First, the MOF would be designed to provide the similar group velocity for the pump and different-order Stokes waves, which will increase the walk-off length between them. Second, the pump pulses with longer duration would be used to increase the walk-off length, such as the nanosecond pulses. We believe that the conversion efficiency, the intensity of Stokes wave and the order of Raman effects will be improved obviously with the walk-off length increased.
3.6 Numerical simulations
The Raman effects in Fibers I-IV were simulated numerically according to Eqs. (1) and (2). The fractional Raman contribution fR of the AsSe2 glass is 0.148 according to references  and . The Raman-gain coefficient gp and gs were calculated to be ~1.53 × 10−11 m/W at 1958 nm and ~1.45 × 10−11 m/W at 2070 nm, respectively, using the datum of 2 × 10−11 m/W in reference . The GVD coefficient β2p and β2s are from Fig. 1(b). The nonlinear coefficient γp and γs are shown as in Table 1. The transmission attenuations used in the simulations are 1, 1.5, 1.7 and 2 dB/m for Fibers I-IV, respectively.
Figure 9 shows the simulated spectra in the 80 cm long Fiber I with different pump powers. The peak powers used for the simulations are 291 and 367 W, the same as those in Fig. 4. In Fig. 9, the SPM effect is obvious, because it is easy to be accumulated with the relatively lower attenuation of Fiber I. Therefore, the Raman Stokes peak is covered by the SPM spectrum, which is corresponding to Fig. 4. In Fig. 9, the SPM spectra are a little wider than those in Fig. 4 because the parameters such as peak powers used in the simulations may have slight difference with the practical situation.
Figures 10(a)-10(c) show the simulated Raman spectra with different pump powers in 45, 90 and 190 cm long Fiber II. The peak powers used in Figs. 10(a)-10(c) are the same as those in Figs. 5(a)-5(c). In Fig. 10(a), the first-order Raman Stokes peak at around 2060 nm increases with the peak powers, which is corresponding to Fig. 5(a). The threshold of Raman effect in Fig. 10(a) is smaller than that in Fig. 5(a) according to the Raman spectra evolving with the peak powers. In Figs. 10(b) and 10(c), the Raman peaks increase a little with the peak powers. According to Figs. 10(a)-10(c), the Raman Stokes peaks are not increased obviously with increasing the fiber length, which is corresponding to Figs. 5 and 6.
Figure 11 shows the simulated Raman spectra in the 45 cm long Fiber III with different pump powers, in which the peak powers are the same as those in Fig. 7. In Fig. 11, the intensity of the first-order Raman peak at around 2060 nm increases with the peak power. The conversion efficiency is high at the maximum pump power. The Raman spectra are broadened with increasing the peak power due to the SPM effect, which are disadvantageous to the generation of higher-order Raman Stokes peaks. All these evolving rules in Fig. 11 can agree with those in Fig. 7 very well. The slight difference is that a weak second-order Raman peak at around 2170 nm begins to appear when the peak power arrives 177 W in Fig. 11. This second-order Raman peak did not appear in Fig. 7. The possible reason is that the intensity was too weak to be resolved by the OSA.
Figures 12(a) and 12(b) show the simulated Raman spectra in Fiber IV. The peak powers are the same as those in Fig. 8. In Fig. 12 (a), the first-order Raman peak at around 2060 nm increases with the peak power increasing. The Stokes peak has no obvious increase with the fiber length increasing in Fig. 12(b). The evolving of Raman effect in Fig. 12 is corresponding to that in Fig. 8.
According to Figs. 9-12, numerically simulated results can agree well with the experimental results. There is still slight difference between the simulated and experimental results. The possible reason are: 1) the defects existed in the MOFs, such as the nonuniformity along the fiber; 2) the parameters for the simulations deviated from the experiments slightly; 3) the higher-order nonlinear effects were not included in the simulation.
We demonstrated the SRS in four kinds of chalcogenide MOFs with all-solid AsSe2 core and As2S5 cladding. The first-order Raman Stokes wave was generated in the MOFs with different core diameters pumped by the picosecond pulses at 1958 nm. The maximum conversion efficiency of −15.0 dB from pump light to the first-order Raman Stokes wave was obtained in the MOF with the core of 2.6 μm. It decreased when the core diameter deviated from 2.6 μm due to the smaller nonlinearity or the poor ability to confine the optical mode in the fiber core. The evolution of the first-order Stokes wave with pump power and fiber length was investigated. The intensity of Stokes peak did not increase with the fiber length due to the short walk-off lengths of the MOFs. Numerically simulated results were provided by the pulse-propagation equations of pump and Stokes wave, which could agree well with the experimental results. We believe that the conversion efficiency, the intensity of Stokes wave and the order of Raman effects will be improved obviously by increasing the walk-off length.
This work was supported by MEXT, Support Program for Forming Strategic Research Infrastructure (2011-2015). It was also supported by the National Natural Science Foundation of China (NSFC) (grants 11374084 and 61307056) and the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (grants TP2014061).
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