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Abstract
We demonstrate supercontinuum generation in a liquid-core microstructured optical fiber using carbon disulfide as the core material. The fiber provides a specific dispersion landscape with a zero-dispersion wavelength approaching the telecommunication domain where the corresponding capillary-type counterpart shows unsuitable dispersion properties for soliton fission. The experiments were conducted using two pump lasers with different pulse duration (30 fs and 90 fs) giving rise to different non-instantaneous contributions of carbon disulfide in each case. The presented results demonstrate an extraordinary high conversion efficiency from pump to soliton and to dispersive wave, overall defining a platform that enables studying the impact of non-instantaneous responses on ultrafast soliton dynamics and coherence using straightforward pump lasers and diagnostics.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Supercontinuum generation (SCG) inside optical fibers is a powerful technique for broadband high-power light generation [1–3] and in particular for studying novel nonlinear optical effects such as, soliton fission [4], soliton self-frequency shift [5] and radiation trapping by solitons [6]. In late 1990s, the advent of microstructured optical fibers (MOFs) acquired widespread attention in the scientific community due to its increased ability of modal confinement, high nonlinearity and flexibility of dispersion engineering, which enabled widespread SCG covering the visible to the near-infrared [7–12]. Further advances towards a wider spectral extent into the mid-infrared are possible today by introducing novel materials with extraordinary nonlinear and transmission properties. As such, SCG from soft-glass fibers [1,13–17] and gas-filled hollow-core fibers [18–20] has been reported and proven to be excellent sources for mid-infrared light. Here, SCG in liquid-core optical fibers (LiCOF) has gained increased interest in recent years due to excellent properties of certain inorganic solvents [21,22]. In addition to a high refractive index allowing for strong modal confinement, wide mid-infrared spectral transparency and high nonlinearity, liquids are particular interesting from the nonlinear physics perspective as they exhibit a strong non-instantaneous nonlinearity arising due to slow molecular motion of liquids [23], opening up unique opportunities to explore novel states of light such as hybrid solitonic states as theoretically suggested in [21]. Moreover, LiCOFs offer great flexibility for dispersion engineering such as tuning via mixing liquids [24,25] and through temperature due to high thermo-optical coefficients [26], overall yielding a platform that enables studying ultrafast phenomena that are out-of-reach with current waveguide systems.
Today, soliton fission in LiCOFs based on pure CS2 could practically only be realized in filled silica capillaries that inherently feature zero-dispersion-wavelengths (ZDW) not shorter than 1.8 µm [21,27], requiring expensive Thulium-fiber based femtosecond (fs) laser technology, while diagnostics are commonly less sensitive at such wavelengths. Note that CS2-LiCOFs with homogenous silica cladding theoretically show a ZDW at 1.55 µm for very small liquid strand diameters, while waveguiding at such diameters is highly lossy (i.e., guidance parameter is very small, V < 1) [25]. This issue represents the motivation of this work which aims to push the ZDW of CS2 liquid-core fibers towards telecommunication wavelengths (i.e., 1520 to 1600 nm), where lasers and diagnostics are available off-the-shelf and cost-effective thus enabling to study the ultrafast dynamics of this unusual waveguide system which includes an integrating nonlinearity.
So far, shifting the ZDW to such short wavelengths can be achieved only by exciting higher-order-modes in CS2 which feature ZDWs around 1550 nm [28], or by diluting the core liquid with less nonlinear liquids such as carbon tetrachloride or tetrachloroethylene [24,25].
In this work, we present an experimental study of SCG in a microstructured liquid core optical fiber selectively filled with CS2. Note that SCG from selective filling of MOFs has been experimentally demonstrated using water [29–31], carbontetrachloride [32], toluene [33], and only theoretically presented for CS2 in various numerical works (e.g., [34]). Here, we provide a versatile MOF design together with a robust, easily reproducible method to selectively fill the MOF core with CS2 while keeping the air-hole cladding intact. We demonstrate the performance of our new design by SCG experiments involving two ultrafast light sources with different pulse durations thus probing different levels of non-instantaneous nonlinearity in CS2.
2. Design and sample preparation
In this section the characteristics and the preparation of the MOF samples are explained. Figure 1(a) represents the desired fiber sample with a silica cladding having air strands while the core is filled with CS2 liquid. Figure 1(b) shows a scanning-electron-microscope (SEM) image of the empty fiber that was produced with the in-house fiber drawing facility. The non-circular shape of the air-holes, which is intrinsic to many high air-filling fraction microstructured fibers [35], arises from the hexagonal stack of capillaries in which the interstitials between the various elements have not been filled. Note that for guiding light inside the core through total internal reflection, the actual shape of the air-holes is not relevant as long as a sufficiently high fraction of air is located within the vicinity of the core region. Figure 1(c) shows the group velocity dispersion of this fiber calculated using Finite Element modelling (Comsol Multiphysics). The dispersion properties of CS2 are taken from [36] while the fiber structure is accounted for through a SEM image of the fiber facet of the fiber sample actually used in the experiment (i.e., not by modelling the cross-section with geometric objects.
Fig. 1. (a) Schematic of the selectively filled MOF including a CS2 core and a air-hole cladding. (b) Scanning-electron-microscope image of the cross-section of the unfilled MOF. (c) Corresponding spectral distribution of the group-velocity-dispersion of the fabricated liquid core MOF featuring a ZDW at 1625nm.
The overall goal is to solely fill the central hole of this fiber with liquid CS2, imposing the light to partially overlap with the air regions and thus leading to a shift of the ZDW to approx. 1.55 µm. The selective filling is achieved via post-processing to isolate the ’core-hole’ of the fiber from the rest of the air-strands allowing for filling of the CS2 only in the desired hole of the fiber. The principle has been previously demonstrated in [32,33,37]. The steps for post-processing are as follows (Fig. 2): First, the fiber was mounted in magnetic fiber clamps, with an arbitrary fiber lengths hanging over, and placed inside a fusion-ring splicer (Fitel Fusion Splicer S184PM-SLDF) for applying a splice arc. The arc-power level was chosen such that a single arc collapses all air holes of the fiber cladding with the central hole remaining open due to its bigger size. Thereafter, the fiber is precisely cleaved at the collapse position (Fig. 2(a)) which was enabled here by using a suitable cleaver (Fitel S326 Optical fiber cleaver) that can mount the magnetic clamps and with a blade being aligned with the splice position of the splicer (Fig. 2(c)). This process is repeated for the other end of the fiber. The final result is a fiber sample with all air holes at each fiber facet being collapsed except the central hole. This post-processed fiber sample was then inserted into opto-fluidic mounts that include fluidic access ports and sealed sapphire windows for light coupling. Bubble-free filling of CS2 into the central hole is achieved via entirely flooding the mounts initiating low-pressure capillary action which takes approximately 1.5 hours for filling a 30 cm long sample (the filling time is calculated using Washburn’s equation [38]). Note that used sample length of 30 cm was chosen solely to make the post-processing of the sample more convenient as the sample needs to be placed into splicer and cleaver and later into the opto-fluidic mounts for liquid filling.
Fig. 2. Schematic of the post-processing of the MOF in order to isolate the core from the air-hole cladding. (a) Cross-section of the microstructured fiber before post-processing. (b) Corresponding cross-section after splice arc and precise cleaving. All the air holes are collapsed except the central hole. (c) Cross-section after filling the central hole with CS2 using capillary action.
3. Experimental setup
In this section the optical setup for SCG from the sample depicted in Fig. 1 is presented (Fig. 3). It includes the fiber sample mounted in the opto-fluidic mounts, femtosecond lasers for excitation and diagnostics (lasers specs described in Table 1). A Yokogawa optical spectrum analyser (OSA) and ABS InGaAs camera (IK1513) were used as diagnostics. Thorlabs aspheric lense C240TME-C (f = 8 mm, NA = 0.5) is used to couple light into the liquid core MOF with a coupling efficiencies of 13-17 % (see Table 1 for coupling efficiency for each pump laser). Note that the coupling efficiency is calculated as $\eta =P_\textrm {out}/P_\textrm {in}$ where $P_\textrm {out}$ is the measured output power after the collimating lens (C230TMD-C Thorlabs, f = 4.5 mm, NA = 0.55) and $P_\textrm {in}$ is the input power measured in front of the in-coupling lens. The output signal is coupled into the OSA via a multimode patch cord (Thorlabs). Power-spectral evolutions were obtained by increasing input power in steps and the spectra were recorded using the OSA at every step. The output spectra show the effect of chromatic aberrations, i.e. higher spectral intensity at optimized wavelength (pump wavelength in this case). This effect was corrected in the data analysis by estimating the chromatic aberration function of the out-coupling lens using an NKT supercontinuum source (see Appendix).
Table 1. Specification of the pump sources used for the experiment, the light coupling efficiency and sample length in each case
Simulations have been performed on the basis of the model presented in [21] which relies on solving the generalized nonlinear Schrödinger equation describing the spatial and temporal evolution of the pulse envelope when propagating through the nonlinear waveguide. Similar type of numerical models were used in various kinds of numerical studies addressing SCG in liquid core fibers [31,33,39]. In addition, the first degree of coherence $\lvert g_\textrm {mn}^{(1)}\rvert (\lambda )$ is calculated as:
Fig. 3. Schematic of the experimental setup used for the supercontinuum generation experiments using a MOF with CS2-filled core. OSA: optical spectrum analyser. Further details related to the setup can be found in the main text.
4. Results and discussion
The experimental and simulated results of the SCG experiments are summarized in the power-spectral evolution shown in Figs. 4–5. The dotted lines always represent the pump wavelength while the solid lines refer to the ZDW. Note that the left y-axis of Figs. 4–5 represents in-fiber pulse energy, i.e., taking into account the coupling losses and transmission losses of the lens and thus allow a direct comparison to simulations. The right y-axis represents the soliton number calculated as $N^{2}=L_\textrm {D}/L_\textrm {NL}$, $L_\textrm {D}=\tau ^{2}/|\beta _{2}|, (\beta _\textrm {2}=194.53~\mathrm {fs^{2}/cm)}$, $L_\textrm {NL}=1/\gamma P_\textrm {0}$ where $\gamma$ is the nonlinear coefficient and $P_\textrm {0}$ is the peak power [40]. Note that in case of liquids, apart from the electronic contribution, the molecular contribution to the nonlinear refractive index arising due to relatively slow molecular motion of liquids needs to be taken into account [23]. In this case the nonlinear refractive index is defined as $n_\textrm {2,total}=n_\textrm {2,el}+n_\textrm {2,mol}$ where $n_\textrm {2,mol}$ and $n_\textrm {2,el}$ represent the molecular and electronic contributions, respectively, to the nonlinear refractive index. The molecular contribution is dependent on the input pulse duration such as
Here $I(t)$ is the intensity distribution of the excitation pulse and $R(t)$ is the nonlinear response function of the liquid. Here the simulations include both contributions of the nonlinear refractive index of CS2 which were taken from [41] (See Appendix for the detailed calculation of nonlinear response of CS2). Figure 4(a) represents the experimental power-spectral evolution of the SCG from the CS2-filled MOF when pumped by laser-1 (30 fs). The main features of the experimentally determined power-spectral evolution (e.g., symmetric side bands) are qualitatively reproduced by the simulations confirming the overall accuracy of the dispersion model used. The physics of this nonlinear frequency conversion process can be explained as follows: The pump wavelength and ZDW are so close together that the part of the pump spectrum is extending across the ZDW into the AD domain. Therefore pumping very close to ZDW leads to small second-order dispersion pulse deformation and helps the input pulse to maintain its peak power across longer fiber distances thereby producing strong nonlinear effects as well as imposing a stronger impact of higher-order dispersion terms. The initial broadening starts due to the well-known effect of self-phase-modulation and temporal pulse narrowing, quickly followed by soliton fission (at an approximate pulse energy of 0.02 nJ) generating dispersive wave (DW) in normal dispersive (ND) and fundamental soliton in anomalous dispersive (AD) domain. The increased input power leads to soliton fission generating DW at ND, which is accompanied by the soliton-recoil effect simultaneously shifting the soliton deeper into the AD domain [42]. It should be noted that stimulated Raman scattering plays a minor role in the soliton red-shifting as the process is well covered in the simulation which does not include Raman scattering. In addition, it has also been confirmed in simulations that the non-instantaneous response is not the origin of the soliton red-shift. The short wavelength side-lobe of the spectra i.e. DW, blue-shifts at the same rate as the soliton red-shifts with increased pulse energy due to the four-wave-mixing (FWM) between soliton and DW [43]. A remarkable conversion efficiency between pump and the spectral side-lobes (i.e. soliton and DW) can be observed due to continuous FWM between DW and soliton leading to a red-shift of the soliton and a blue-shift of the DW wavelength with increased pulse energy known as optical trapping of DW [6,8,44,45]. Figure 4(d) and (e) show the energy conversion efficiencies (CE) from pump to soliton and to DW, respectively, as a function of the input pulse energy. The curves are calculated in the following way: The DW and soliton wavelengths were selected by searching for the intensity maxima across the spectral interval of relevance and the energy was integrated within a 100 nm spectral window referred to as soliton or DW energy. The ratio between the soliton or DW energy and the total energy across the spectrum yields the corresponding CE. The plots reveal approximately 50 % CE for soliton and 40 % for DW while showing a reasonable agreement between simulations and experiment (Note that the peak around 0.15 nJ in the experimental data corresponds to an erroneous data point in the measurements and can be seen in Figure 4 as well). Additionally the first degree of coherence $\lvert g_\textrm {mn}^{(1)}\rvert (\lambda )$ is presented in Figure 4(c), revealing that coherence reaches unity across almost the entire spectral supercontinuum bandwidth suggesting an excellent shot-to-shot stability of the generated supercontinuum [46]. Figure 5 represents the spectral-power evolution of the SCG using CS2-filled MOF when pumped by laser-2 (90 fs). Similar to the 30 fs case symmetric spectral side lobes i.e. DW and soliton can be observed, blue- and red-shifting respectively with increased pulse energy. In this case the longer pump pulse duration leads to an increased molecular contribution of the nonlinear response i.e. $f_\textrm {m} = 0.43$ compared to that of the 30 fs case where $f_\textrm {m} = 0.14$ where $f_\textrm {m}$ is the molecular fraction calculated as $f_\textrm {m}=n_{2,mol}/n_{2,total}$. However, the power-spectral evolution of the 30 fs and the 90 fs case have similar spectral dynamics at the same pulse energies (note that the maximum pulse energy for the 90 fs case (Fig. 5) is 0.63 nJ while for the 30 fs case (Fig. 4) it is 0.32 nJ) indicating that the effect of non-instantaneous response on spectral dynamics of SCG is not dominant at molecular fraction of 0.43. Overall the experimental (Fig. 5(a)) and simulated (Fig. 5(b)) results are in good qualitative agreement. The primarily observed differences is associated with OH absorption lines around 1.45 µm which were observed in the experimental data but are not included in the simulations. It is to be noted that the impact of this OH absorption is observed for this MOF but has not been seen for the liquid-filled capillaries confirming the presence of OH bonds on the silica surfaces predominantly within the air holes in the cladding. Due to this reason CE plots of soliton and DW are not presented as the CE for simulations is underestimated due to the lack of OH absorption data. Note that these absorption lines were also observed for the 30 fs case (Figure 4) but were less apparent due to the originally less light generated around this spectral region.
Fig. 4. (a) Experimental and (b) simulated energy-spectral evolution of the supercontinuum produced using a MOF with a CS2 core (as shown in Fig. 2(a)) and pumped using an ultrafast laser ($\lambda$ = 1590 nm, $\tau$ = 30 fs, $f_{\textrm {rep}}$ = 80 MHz). The dotted lines refer to the pump wavelength while solid line is the ZDW of the fiber. (c) first degree of coherence of the SCG calculated at the maximum pulse energy used in experiment and simulations (0.32 nJ corresponding to the soliton number $N_\textrm {sol}=7.4$). (d) Simulated (green) and experimental (pink) conversion efficiencies (CEs) from (d) pump to soliton and (e) pump to DW both as functions of pulse energy.
Fig. 5. (a) Experimental and (b) simulated energy-spectral evolution of the supercontinuum generated in the CS2-MOF (as shown in Fig. 2(a)) when being pumped with laser-2 ($\lambda$ = 1590 nm, $\tau$ = 90 fs, $f_\textrm {rep}$ = 40 MHz). Dotted line: pump wavelength. Solid line: ZDW. (c) First degree of coherence of SCG process calculated at the maximum pulse energy used in experiment and simulations (0.63 nJ corresponding to a soliton number $N_{\textrm {sol}}=18.9$).
Similar to the 30 fs case the calculated first order degree of coherence (Figure 5(c)) suggests a significant shot-to-shot stability of the SCG process also in this case. To allow for the direct comparison of the two cases Table 2 represents all the calculated linear and nonlinear parameters of the fiber sample used at two different pulse durations where $L_\textrm {sample}$ is the sample length and $L_\textrm {fiss}$ refers to fission length calculated as $L_{fiss}=L_{D}/N_{sol}$ [43], (the subscripts ’el’, ’mol’ are related to electronic and molecular contributions while ’total’ is used when both molecular and electronic contributions are considered).
Table 2. Linear and nonlinear optical parameters of microstructured fiber sample having a CS2 core.
5. Conclusion
Due to the liquid environment, fibers with liquid cores offer the unique property of providing a non-instantaneous, integrating nonlinearity, which suggest the observation of novel ultrafast phenomena, especially related to soliton dynamics and supercontinuum generation. So far, soliton-mediated SCG in CS2 fibers has been realised exclusively in filled silica capillaries, which for practically relevant core diameters have ZDWs larger than 1.8 µm, limiting the choice of suitable pump lasers and diagnostics. This work presents for the first time, to the best of our knowledge, soliton-mediated SCG in a CS2-core fiber that shows a ZDW and AD in close proximity to telecommunication wavelengths. Via a robust and reproducible post-processing procedure the core hole of an air-hole based microstructured fiber was isolated from the remaining cladding, allowing for solely filling the core with CS2 across 30 cm. Two ultrafast pump lasers operating at telecommunication wavelengths were used to demonstrate soliton fission and spectral broadening from 1 µm to 2.2 µm while different pulse duration give rise to different non-instantaneous contributions of CS2 in each case. The observed frequency broadening process can be explained on the basis of soliton fission and DW formation, while an extraordinary high conversion efficiency from pump to soliton and to dispersive wave is observed. Our results represent a step towards exploiting this unusual type of nonlinearity for the observation of novel light states in the context of soliton dynamics and ultrafast supercontinuum generation based on easily available and powerful pump lasers and diagnostics. As example the presented device represents a platform to experimentally investigate hybrid solitons that were theoretically predicted by Chemnitz et al. [21] at pulse durations of hundreds of femtoseconds while application in dispersion-sensitive applications such a degenerated four-wave mixing can be envisioned.
6. Appendix
6.1. Chromatic aberration correction
Fig. 6. (a) Schematic setup for the estimation of chromatic aberrations involved in the supercontinuum spectra acquisition. L2 is the lens used as out-coupling lens for all the measurements presented in Figs. 4(a), 5(a). In step-1 the reference spectrum is acquired. In step-2, L2 is moved to optimise the spectrum at 1590 nm which gives the estimation for the chromatic aberrations of this particular lens when optimised at certain wavelength, (b) spectrum acquired when optimised at 1590 nm normalised with respect to the reference spectrum.
Fig. 7. Experimental data 90 fs pulse duration (a) before and (b) after chromatic aberration correction using the transfer function obtained in Fig. 6.
The spectra presented in Fig. 4(a) and 5(a) are acquired by coupling the output light from the MOF into the multi-mode patch-chord connected to the OSA. Thorlabs aspheric lens C230TMD-C is used to focus the generated supercontinuum light into the patch-chord. The spectra acquired are broadband and involve chromatic aberrations due to the focusing lens. All the spectra were optimised for pump wavelength i.e. 1590 nm and have higher intensity at the pump wavelength than the rest of the spectrum. These chromatic aberrations were corrected by applying a transfer function on all the acquired spectra which was obtained using a 4f setup depicted in Fig. 6(a). A lens C240TME-C is used as L1 which has almost numerical aperture close to the CS2 filled microstructured fiber, i.e. 0.5. L2 is lens C230TMD-C whose chromatic aberrations are to be corrected. First of all, the collimated light from the supercontinuum source is coupled into the OSA via multi-mode patch-chord without using any lens. This coupling of collimated light in the patch-chord is low but is still enough for our purpose. In the next step the light from NKT source is coupled into the patch-chord using the setup depicted in Fig. 6(a), step-1. The spectrum acquired is same as the original spectrum of the light source, meaning that no aberrations were produced since the light is still collimated. In the next step, (Fig. 6(a) step-2), the lens L2 is moved so that the light is focused in to the patch-chord. This time the chromatic aberration can be observed and a certain wavelength can be optimised by moving the lens L2 slightly. We optimised the spectra for 1590 nm (which is the pump wavelength of our SCG experiment (presented in Figures 4(a) and 5(a)) and all the spectra acquired were optimised at the pump wavelength). The acquired spectrum is normalised with respect to the reference spectrum obtained in step-1 and contains the modal attenuation of the MMF used (provided by Thorlabs webpage). The final spectrum is presented in Fig. 6(b) and is used to correct all the experimental spectra presented in Fig. 4(a) and 5(a). Figure 7 demonstrates the spectral-power evolution of SCG when pump source with 90 fs pulse duration was used. The difference before (Fig. 7(a)) and after (Fig. 7(b)) chromatic aberration correction can be noted.
6.2. Nonlinear response of CS2
The total nonlinear response of CS2 (n2,total) consists of electronic (n2,el) and molecular (n2,mol) contributions where n2,el is calculated as;
where $n_{0}$ is the linear refractive index, $\epsilon _0$ the vaccum permittivity, $\chi ^{(3)}$ the electronic third-order susceptibility which is $1.35\times 10^{-21}$ esu for CS2, $c$ is the speed of light in vacuum. The molecular contribution is represented as Eq. (2) where $R(t)$ is the nonlinear response function of CS2 which is represented as a sum of three responses i.e.The summation over $m$ denotes the molecular processes i.e. diffusion, collision, libration and are described in [41] in great detail. Table 3 represents the corresponding parameters used for the calculation of molecular response function of CS2 where $\tau _{r,m}$ and $\tau _{f,m}$ are the rise and fall time respectively for the corresponding molecular processes, $\omega _0$ is the central frequency and $\sigma$ is the spectral bandwidth
Table 3. Fit parameters of third-order response of CS2
6.3. Properties of the collapsed sections of the MSF
Fig. 8. Side view of the fiber after applying the splicer-arc. The total length of the collapse section is around 320 µm (indicated by the black line). The fiber was cleaved in the middle of the collapse making the collapse length at each end of the fiber roughly 160 µm
Within the collapsed area, the diameter of the core decreases from about 3.1 µm to about 2.6 µm at the tip of the fiber, which serves as the entry point for the liquid into the fiber. The total length of the collapse region is about 320 µm (Fig. 8) yielding a length of the collapsed section in the final fiber of about 160 µm as the fiber was cleaved in the center of the collapse.
6.4. Fiber geometry
The detailed geometrical parameters of the MSF can be seen in Fig. 9. It can be seen that the diameter of the small holes surrounding the central hole is varying between approximately 588 µm and 701 µm while the silica strands between the air holes have width in the range of 503 µm–513 µm.
Funding
Natural Sciences and Engineering Research Council of Canada (Banting postdoctoral fellowship program); Deutsche Forschungsgemeinschaft (SCHM2655/11-1, SCHM2655/12-1, SCHM2655/3-2).
Acknowledgments
We acknowledge support by the German Research Foundation and the Open Access Publication Fund of the Thueringer Universitaets- und Landesbibliothek Jena Projekt-Nr. 433052568.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are available from the corresponding author upon request.
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