Multi-milliwatt mid-infrared supercontinuum generation in a suspended core chalcogenide fiber

: A low-loss suspended core As 38 Se 62 ﬁber with core diameter of 4.5 μ m and a zero-dispersion wavelength of 3.5 μ m was used for mid-infrared supercontinuum generation. The dispersion of the ﬁber was measured from 2.9 to 4.2 μ m and was in good correspondence with the calculated dispersion. An optical parametric ampliﬁer delivering 320 fs pulses with a peak power of 14.8 kW at a repetition rate of 21 MHz was used to pump 18 cm of suspended core ﬁber at different wavelengths from 3.3 to 4.7 μ m. By pumping at 4.4 μ m with a peak power of 5.2 kW coupled to the ﬁber a supercontinuum spanning from 1.7 to 7.5 μ m with an average output power of 15.6 mW and an average power > 5.0 μ m of 4.7 mW was obtained.


Introduction
The mid-infrared spectral region is of great interest because virtually all organic compounds display distinctive spectral fingerprints therein that reveal information about their chemical structure [1]. The mid-infrared region is, therefore, of key importance to many applications including food quality control [2], gas sensing [3] and medical diagnostics [4]. Supercontinuum laser sources spanning the visible and near-infrared based on optical nonlinear effects in tailored photonic crystal fibers (PCFs) are now commercially available [5]. However, the use of silica fibers as the generating medium has its limitations: the material absorption of silica increases drastically at wavelengths beyond ∼2 μm and this effectively prevents the spectral evolution of the supercontinuum generation (SCG) into the mid-infrared. Research into other nonlinear materials that can open the door to the mid-infrared spectral region has intensified in recent years. Several non-silica materials have been proposed as candidates for mid-infrared fibers, including tellurite [6], fluoride [7,8], heavy metal oxide [9] and chalcogenide based materials [10]. However, the change of nonlinear material will inevitably change the fiber properties. Generally, efficient and broadband SCG is obtained by pumping close to the zero dispersion wavelength (ZDW) of the fiber. Silica fibers, especially PCFs, can be designed to have their ZDW at the wavelength of commercially available fiber lasers, such as ytterbium (1.06 μm) or erbium lasers (1.55 μm) [11]. The current state-of-the art in supercontinuum sources covering the near to mid-infrared region of the spectrum is based on fluoride or tellurite fibers which cover the 1-4.75 μm spectral range [8,12,13]. Again, the material absorption at the long wavelength edge dictates the upper limit. Chalcogenide glasses, on the other hand, have been shown to be promising candidates for highly-nonlinear photonic devices [10,14] including mid-infrared SCG as they can transmit light out to 25 μm [15] and they possess high nonlinear refractive indices, up to a factor of 1,000 more than silica [16]. For As 2 Se 3 the ZDW of the material is around 7 μm, but it can be tailored using waveguide dispersion to ∼ 5μm in a 10 μm core step-index As 2 Se 3 fiber [17,18]. Recently, Hudson et al. generated a 1.6-5.9 μm SC in a step-index As 2 S 3 fiber with a core diameter of 9 μm by pumping at 3.1 μm [19], Théberge et al. used a step-index As 2 S 3 fiber with a 100 μm core to generate an SC spanning from 1.5 to 7.0 μm by pumping at 4.56 μm based on self-focusing and beam filamentation [20], and Petersen et al. used 100 fs pulses at 6.3 μm to generate SC spanning from 1.4 to 13.3 μm in 85 mm of ultra high NA As 2 Se 3 step-index fiber with a 16 μm core [21]. Al-kadry et al. shifted the ZDW all the way down to 1.73 μm by tapering an As 2 Se 3 fiber down to a diameter of 1.28 μm [22]. However, tapering to small dimensions comes with the cost of power handling and the second ZDW may eventually limit the SCG at longer wavelengths. An alternative approach to shift the ZDW to shorter wavelengths is to fabricate microstructured optical fibers (MOFs). Mouawad et al. succeeded in generating supercontinuum from 0.6 to 4.1 μm in an As 2 S 3 suspended core fiber with a core diameter of 3.4 μm pumped at 2.5 μm [23], and Cheng et al. demonstrated a supercontinuum spanning from 1.3 to 5.4 μm in an AsSe 2 -As 2 S 5 hybrid MOF [24]. Kubat et al. numerically demonstrated that by cascading a ZBLAN-based SC into a As 2 S 3 grapefruit MOF with a core diameter of 5 μm it is possible to generate SC out to 9 μm [25]. Other types of waveguides and bulk materials have also been used for SCG, and Yu et al. recently reported on a supercontinuum spanning from 1.8 to 7.5 μm in a chalcogenide rib waveguide with a 2.5 μm thick core layer [26]. Liao et al. obtained an SC from 0. 39-7.4 μm at -20 dB in a 32 mm ZBLAN sample [27] and Pigeon et al. generated a 2-20 μm supercontinuum in a 67 mm GaAs sample by pumping with a CO 2 laser at 9.3 μm [28]. The drawback of using bulk samples for SCG is, however, the lack of confinement which will require higher power.
In this paper we present experimental results on SCG in a low-loss 18 cm As 38 Se 62 suspended core fiber with a core diameter of 4.5 μm pumped at different wavelengths from 3.3 to 4.7 μm with 320 fs pulses from an optical parametric amplifier (OPA). Pumping at 4.4 μm with a peak power of 5.2 kW coupled to the fiber we obtained a supercontinuum spanning from 1.7-7.5 μm with an average output power of 15.6 mW and an average power >5.0 μm of 4.7 mW. When pumping at 4.7 μm we obtained an average output power of 16.0 mW and an average power >5.0 μm of 7.5 mW. However the supercontinuum did in this case contain dips below -20 dB and this limited the total bandwidth. This is to our knowledge the furthest into the mid-infrared reported in a chalcogenide MOF. The presented experiment is entirely reproducible using components that can be purchased and represents a practical solution for e.g. mid-infrared spectroscopy.

Experimental setup and optical parameters of fiber
The experimental setup is shown schematically in Fig. 1(a). The mid-infrared OPA consists of a high power pulsed Yb fs laser which is used to pump a 10 mm long PPLN crystal. A tunable semiconductor laser was used as a seed to generate light from 3.3-4.7 μm. The average output power of the mid-infrared OPA was up to 250 mW at 4 μm with a pulse duration of 320 fs at a repetition rate of 21 MHz [26]. However, for SCG the maximum power was set to 100 mW, which corresponds to a peak power of 14.8 kW. The light from the mid-infrared OPA was sent through a chopper and a polarizer pair in order to control the polarization and power. The light was coupled with an NA = 0.85 molded chalcogenide lens to the 18 cm long suspended core fiber with a core diameter of 4.5 μm . The output from the fiber was collected by either a similar molded lens for insertion loss measurements, or a reflective objective lens for spectroscopic measurements that were performed using a Newport Cornerstone 1/4 m monochromator. Either a PbSe or a MCT detector connected to a lock-in amplifier was used to record the spectra in the range 1.5-4.0 μm and 4.0-8.5 μm, respectively. Filters were used to prevent higher order grating reflections from reaching the detectors. At wavelengths > 4.0 μm the data was corrected for the detector responsivity, which was provided by the manufacturer and shown in Fig. 1 The total insertion loss of the fiber plus the coupling lenses was measured to be 7.5 dB and thus the power delivered to the fiber was estimated to be 3.75 dB lower than the measured average power after the chopper. This corresponds to 118 W of peak power delivered to the fiber for every mW of average power measured after the chopper.
The As 38 Se 62 suspended core fiber had a core diameter of 4.5 μm and was manufactured by Perfos. The fiber has been fabricated by the molding technique described in [29]. A SEM image of the fiber is shown in Fig. 2(a). Core transmission up to 8 μm was verified in an this measurement. However, to estimate the loss of the 4.5 μm suspended core fiber, the fiber loss of a 6-hole suspended core fiber with a core diameter of 20 μm was measured by the cut-back method in an FTIR from 1.4-8.5 μm and shown as the solid black curve in Fig. 2(a). It has been shown that by decreasing the core size the fiber loss will increase due to microdeformations [30][31][32]. Troles et al. characterized the fiber loss in As 38 Se 62 microstructured optical fibers that are similar to the one used here. They found that a 3 μm suspended core fiber had a 0.4 dB higher loss than a 20 μm suspended core fiber at a wavelength of 1.55 μm [33]. Adam et al. measured the material loss of bulk As 2 Se 3 similar to the material used for the 4.5 μm suspended core fiber, and the material transmission window was from 1 to 8.5 μm [34].
To estimate the loss of the 4.5 μm suspended core fiber we added 0.4 dB to the fiber loss measurement of the 20 μm suspended core fiber and extrapolated the loss in both ends of the transmission window at 1 and 10 μm to be 100 dB/m. The total estimated fiber loss of the 4.5 μm suspended core fiber is shown as the dashed red line in Fig. 2(a). The absorption band at 4.3 μm and the bands at 2.9 and 6.2 μm are due to Se-H and water pollution, respectively [33].
The fiber dispersion, and in particular the location of the ZDW, is of great importance for the SCG process [35][36][37]. Based on the fiber geometry provided by Perfos and the As 2 Se 3 material refractive index measurements from Amorphous Materials Inc. [38], which were in good agreement with the refractive index of As 38 Se 62 [39], the fiber dispersions of the slow and fast axis were calculated in COMSOL Multiphysics and are shown in Fig. 2(b). Because of its geometry, the fiber is slightly birefringent with a birefringence of 4.2·10 −4 at 3.5 μm. The effect of SCG in a birefringent fiber has been showed by Deng et al. [40], we did however not see any difference due to the fiber orientation neither when measuring the dispersion nor when generating supercontinuum. Thus, no special care was taken to orient the fiber to account for the birefringence. The fiber dispersion of the suspended core fiber was measured by means of spectral-domain white light interferometry using a ZBLAN-fiber-based supercontinuum source generating light from 1.5-4.5 μm. The dispersion measurement setup consisted of a balanced Mach-Zehnder interferometer wherein a 165 mm test fiber was placed in one arm and the reference arm could be varied in length by a translation stage. Matching the optical path delay of the two arms gives rise to an interference pattern. By fitting the position of fringe peaks and valleys to a modified Cauchy dispersion equation the dispersion of the fundamental mode can be extracted [41]. The measured dispersion from 2.9-4.2 μm, which represents the average over several measurements, is shown as the solid red curve in Fig. 2(b). There is a good agreement between the measured and calculated fiber dispersion. The measured ZDW was 3.50 μm while the calculated ZDW was 3.52 μm and 3.55 μm for the slow and fast axis, respectively.

Experimental results and simulations
Supercontinuum spectra at different input powers pumped at 3.3 μm and 3.5 μm are shown in Figs. 3(a) and 3(b), respectively. As expected the supercontinuum spectra are broadened for increasing powers both when pumping in the normal dispersion regime at 3.3 μm as well as at the ZDW at 3.5 μm.
The SCG was modelled using the generalized nonlinear Schrödinger equation (GNLSE) for single mode and single-polarization with a chirp-free Gaussian-shaped pump pulse as the initial condition. A one-photon-per-mode noise model was used to model the spectral fluctuations from shot to shot in the input pulse [35,42]. The GNLSE was solved in the frequency domain in the interaction picture and included the frequency dependence of the effective area as detailed in [43]. A wavelength dependent Kerr coefficient estimated by Romanova et al. [44] was used together with the Raman response measured by Ung and Skorobogatiy [45]. To account for any possible coupling to higher-order modes [46,47] and coupling between the polarization states [48,49] only 2/3 of the peak power was used in the simulations compared to the experiments.   When the pump wavelength was shifted from 3.5 to 4.7 μm the solitonic long wavelength edge moved to longer wavelengths in the simulated spectra, and accordingly the short wavelength edge, consisting of group-velocity matched dispersive waves was shifted to shorter wavelengths. As a result the broadest numerical spectrum spanning 1.65-7.70 μm was obtained when pumping at 4.7 μm. There was still a good agreement between the numerical and experimental results. However the same clear trend of the long wavelength edge moving to longer wavelengths when pumping at longer wavelengths was not observed in the experiments. In the experiments the supercontinuum spectrum was clearly broadened when the pump was shifted from 3.5 to 3.9 μm, while it was more or less constant with a pump wavelength between 3.9 and 4.7 μm. The absence of a long wavelength extension when pumping at longer wavelengths in the experiments can be explained by coupling instability, e.g. if coupling to the core is slightly off-centered a larger fraction of the power will be coupled to higher-order modes [47] thereby limiting the broadening process. The broadest experimental supercontinuum spectrum spanning from 1.7 to 7.5 μm was obtained when pumping at 4.4 μm, and the average output power was in this case 15.6 mW with a chalcogenide lens at the fiber output and the chopper off. Based on the spectrum and the average output power we calculated the average power >5.0 μm to be 4.7 mW. When pumping at 4.7 μm parts of the supercontinuum spectrum from 2.0 to 3.5 μm was below -20 dB. Here the average output power was 16.0 mW and with an average power >5.0 μm of 7.5 mW.

Numerical investigation of the supercontinuum generation process
The dynamics of SCG is well-known. Nonetheless, we will here make a numerical investigation of the initial SCG broadening process and the influence of the Raman contribution. Figure 5 compares numerically calculated density plots of the supercontinuum spectral and temporal evolution along the fiber length for different input powers pumped at 3.5 μm. The supercontinuum spectrum broadens as the input power is increased and there is a good correspondence between the measured and simulated results. The initial SCG is dominated by self-phase modulation (SPM) indicated by the symmetric (in frequency) spectral broadening and the z-independent temporal profile. The SPM is then followed by soliton dynamics in the long wavelength part, and the solitonic traces can be observed in the temporal density plots in Figs. 5(g)-5(i).
To verify that the spectral edges in fact are determined by a soliton and corresponding groupvelocity matched dispersive waves the group-velocity matched short wavelength edge was determined from the measured long wavelength edge and compared to the measured short wavelength edge at different input powers in Table 1. In all cases there is a good agreement between the measured and the estimated short wavelength edge.  Fig. 5 it can be difficult to determine whether soliton-self-frequency shift (SSFS) is present and influences the broadening process. In Fig. 6 we compare simulations for pumping at 3.5 μm including and excluding the Raman contribution, which is the driving force behind SSFS. Both the temporal and spectral density plots and the spectra in Fig. 6 indicate that SSFS plays a minor role when pumping at 3.5 μm. However, as we move the pump away from the ZDW the dispersion and nonlinearity of the fiber will change. This is illustrated in Fig.  7 where we compare simulations for pumping at 4.4 μm including and excluding the Raman contribution. Again, the supercontinuum broadening process is initiated by SPM. Compared to pumping at 3.5 μm the supercontinuum broadens faster and more. Furthermore, SSFS plays a more dominant role, which is clearly seen in the long-wavelength edges of the spectra in Fig.  7(a).

Conclusion
We have presented experimental results on SCG in a low-loss As 38 Se 62 suspended core fiber with a core diameter of 4.5 μm pumped at different wavelengths from 3.3 to 4.7 μm with 320 fs pulses from an OPA. When pumping at 4.4 μm with a peak power of 5.2 kW coupled to the fiber we obtained a supercontinuum spanning from 1.7-7.5 μm with an average output power of 15.6 mW and an average power >5.0 μm of 4.7 mW. The dispersion was measured from 2.9 to 4.2 μm and it was in good correspondence with the calculated dispersion. Simulations based on the generalized nonlinear Schrödinger equation were in good agreement with the measured spectra. Furthermore, simulations confirmed that the SCG was initiated by self-phase modulation, which were the main driving forces, followed by soliton dynamics and soliton selffrequency shift, which increased with increasing pump wavelength in the anomalous dispersion regime.