Open Access
Add to BibSonomy
Abstract
We demonstrate all-normal dispersion supercontinuum generation in chalcogenide photonic crystal fibers pumped at 2070-2080 nm with a femtosecond fiber laser. At 2.9 kW peak power, the generated supercontinuum has a 3 dB bandwidth of 27.6 THz and −20 dB bandwidth of 75.5 THz. We experimentally investigated the supercontinuum evolution inside our sample fiber at various peak powers and fiber lengths and study the impact of fiber water absorption on the generated supercontinuum spectrum. Multiple tests with fiber length— ranging from 0.34 to 10 cm—provide insight on pulse evolution along fiber length. Our simulations, which utilizes the generalized nonlinear Schrodinger equation model, match perfectly the experiments for all tested pump powers and fiber lengths, and confirm that the output pulse has a linear chirp, allowing linear pulse compression.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Supercontinuum generation (SCG) inside photonic crystal fibers (PCFs) have been exhaustively studied, and found applications in various areas [1,2]. Silica PCFs have shown the impressive performance for supercontinuum generation in visible and near infrared bands. To reach longer wavelength towards the mid-infrared (MIR), where many molecular bonds have fundamental vibration frequencies, novel fiber materials and geometries have been investigated over the last few years. Soft glasses are characterized by a low phonon energy, hence showing good transmission in longer wavelength. Fluoride [3], telluride [4] and chalcogenide glasses (ChG) [5–7] are the main candidates for MIR SCG in optical fibers. Among them, ChG has the largest nonlinearity and a suitable viscosity for producing low loss fibers [8], making it the ideal material for MIR fibers. In fact, the first SCG covering the complete molecular fingerprint region was demonstrated inside a ChG fiber as early as 2014 [7]. Later, researchers demonstrated multi-milliwatt SCG inside tapered ChG PCFs [9].
For anomalous dispersion pumping schemes, spectrum broadening is dominated by soliton dynamics and modulation instability. However, soliton dynamics are highly sensitive to the input laser shot noise, leading to complex temporal profile, shot-to-shot fluctuation and degraded coherence [2,10]. In the time domain, soliton fission breaks the SCG into multiple pulses, causing different arriving times. This problem could be greatly suppressed by pumping with sub-100fs pulses at proper wavelength and using short fiber length (less than a few cm), hence compression of the SCG to few-cycle pulses could be possible [11]. For single-pulsed, highly coherent, stable and re-compressible pulses, researches also revisited the use of all-normal dispersion (ANDi) fibers for SCG – the idea of ultrashort pulse generation by self-phase modulation (SPM) dating back to 1984 [12]. Indeed, numerical simulations demonstrated that SPM and optical wave breaking (OWB) dominate such ANDi SCG [13,14]. Also, ANDi SCG typically has an ultra-flat top in frequency domain [14], supporting a shorter pulse duration.
The availability of highly nonlinear silica PCF allows people to study ANDi SCG at moderate pump power and provide more freedom for dispersion engineering. A. M. Heidt, et al. demonstrated the single-pulse property of ANDi SCG theoretically and experimentally [15]. Since SPM and OWB induces linear chirp while preserving single-pulse property, compression of ANDi SCG pulse is feasible [14,16]. In the same year, L. E. Hooper, et al. demonstrated ANDi SCG and experimentally compressed the SCG to 20 fs using a set of prisms [17]. Later, A.M. Heidt., et al. compressed their ANDi SCG down to 5 fs (sub-2 optical cycle) with chirped mirrors [18].
While both silica and silicate PCF ANDi SCG can reach ~2.3μm [19,20], pushing ANDi SCG further towards the MIR requires better transparency. As such, in recent years broad MIR ANDi SCG was demonstrated in ChG tapered step-index fibers [21], and ChG microstructured fibers [22,23]. However, for applications like spectroscopy or pulse re-compression, SCG with improved flatness is advantageous. In particular, efficient pulse re-compression requires not only a large 3-dB bandwidth, but also preferably linear group velocity dispersion (GVD). In addition, pumping with a fiber laser can lead to more compact and robust setups. To such end, a large nonlinear parameter is beneficial, so that efficient broadening can occur at moderate peak power provided directly from a fiber laser. A combination of ChG with a PCF structure, to not only increase nonlinearity but also correctly shape the dispersion, would satisfy such requirements and greatly benefit the SCG bandwidth, flatness and efficiency.
In this manuscript, we demonstrated ANDi SCG using single-mode ChG PCFs. Pumped with a 2080 nm fiber laser, we achieve a −20 dB bandwidth from 1670 to 2880 nm and a 3-dB bandwidth of bandwidth from 1925 to 2340 nm (27.6 THz) at 2.9 kW coupled power. The experimental results match perfectly with the generalized nonlinear Schrodinger equation (GNLSE) simulations at all pump levels. From the simulation, our ANDi SCG completely broadens within the first few millimeters. To find an optimal length, we also investigated the SCG evolution from 3 mm to 10 cm experimentally. We found that the effective length for a complete SCG broadening is around 1 cm. Finally, we simulate the spectrogram of the ANDi SCG pulse. After retrieving the phase of the modelled output pulse, we prove that our pulse has a linear chirp, and that compression is realizable.
2. Experimental setup and fiber parameters
Figure. 1(a) sketches the experimental setup. We used a commercial femtosecond laser utilizing Raman soliton self-frequency shift as the pump. This pump laser is thus tunable from 2050 to 2100 nm, with a repetition rate of 19.03 MHz. The collimated output beam has a diameter of 4 mm at 1/e2 intensity. For our experiment, 2070 and 2080 nm wavelengths are used, where pulse duration is measured to be approximately 79 fs for both wavelengths. Since the laser output is a 1st order soliton, we use sech2 function to simulate the input pulse, as demonstrated in Fig. 1(b). A reflective continuous variable neutral density (ND) filter enables smooth tuning of the pump. The dichroic mirror (DM) reflects a low power 1.55 µm C-band continuous-wave laser to the same beam path as the 2 µm pump laser. The initial alignment is performed with the C-band laser to get a far field diffraction pattern on the infrared camera as the inset of Fig. 1(a), while the pump laser is blocked after ND. Then we switch off the C-band laser and perform final adjustments with the 2 µm pump laser attenuated to 0 dBm. A 100 µm core-sized InF3 multi-mode (MM) fiber then collect the output from fiber-under-test (FUT). An MIR optical spectrum analyzer (OSA), Yokogawa AQ 6736, records the spectrum.
Fig. 1 (a) Experimental setup. M1&M2: un-protected gold coated mirrors; DM: Dichroic mirror, high reflection for 1500~1750 nm and high transmission for 1850~2100nm; ND: neutral density filter; L1: aspherical lens; FUT: fiber under test; inset: far-field image once coupled into FUT core (b) 2080 nm pump spectrum and fitting using sech2 function.
Two single-mode PCFs with identical 4 µm core size but slightly different air-hole sizes were tested for SCG in this experiment, both fabricated by SelenOptics (Rennes, France). In this manuscript, all FUTs, except for FUT2, have a hole-pitch ratio of 0.58 [Fig. 2(a)]. For FUT2, the hole-pitch ratio is 0.49. Since the pumping wavelength is far from the zero dispersion wavelength (ZDW) as seen in Fig. 2(b), dispersion parameters are very close – around 360 ps2/km for all FUTs. Since FUT2 has been stored in normal atmosphere condition for 3 years, we expect strong water absorption. On the contrary, all other FUTs were fabricated within 2 years from the same preform and stored in dry air with silica gels. The nonlinear parameter γ is approximately 1.7 (Wm)−1 for all FUTs at 2080 nm, estimated based on our past experiments [24,25]. The input coupling loss is 7 ± 1 dB, where the uncertainty comes from the mounting angle and cleaving quality of the FUTs. In terms of the linear propagation loss, all FUTs show less than 0.6 dB/m at 2004 nm. We summarize the FUT data in Table 1.
Fig. 2 (a) Manually cleaved fiber facet; (b) Simulated and experimental fiber GVD; the material GeAsSe has ZDW at about 7 µm
Table 1. Data of FUTs in this experiment
The dispersion of all FUTs is simulated using the commercial finite element method COMSOL software package. To confirm the simulation, dispersion of FUT1 was measured by a low-coherence interferometry method [26]. From Fig. 2(b), we can conclude that the simulation matches well with the measured dispersion and FUT1 is ANDi until approximately 2.87 μm, owing to the strong material dispersion [green curve in Fig. 2(b)].
During our experiment, we increased average pump power gradually from 0 dBm to a maximum of 15 dBm in 1 dB steps, corresponding to a maximum coupled peak power of 2.9 kW. All data presented in this manuscript were recorded under high sensitivity with chopper mode (“Hi/CHOP1”) of the OSA at 1 nm resolution. We used GNLSE to study the SCG evolution with respect to pump power and propagation length. Due to the short fiber length and small propagation loss, the linear loss term is excluded in the simulation. In addition, as we pump far from strong two-photon-absorption (TPA) region [27], we also ignore the TPA term in the simulation. Due to the short pulse duration, we include the optical shock term in the same manner as [2]. Finally, we use COMSOL to simulate the frequency dependent effective area. This frequency dependent effective area leads to a frequency dependent nonlinear parameter, similar to the method in [14]. Instead of a constant nonlinear parameter, we used this array of nonlinear parameter in our GNLSE simulation. As ANDi SCG is a coherent and deterministic process, one should expect a good matching between the theoretical prediction and experimental result.
3. Result and analysis
3.1 Preliminary tests at 2070nm with cm-long PCFs
For preliminary test of the ANDi SCG, we used FUT1 with 10 cm length to study the PCF performance and accuracy of our simulations. ANDi SCG pumped with femtosecond pulse typically has millimeters effective length for spectrum broadening [15,17,20,21]. We selected the longer length to ease the fiber handling, coupling and to neglect the dispersion contribution from other free-space components. For all measurements in section 3.1, we fixed the pump wavelength at 2070 nm, with a possible maximum coupled peak power of 1.9 kW.
The solid lines in Fig. 3 are experimentally recorded data at different pump powers. From now on, to better illustrate the spectrums, we shift each curve in the plot by 10 dB. At the maximum peak power of 1.9 kW, we measure a −20 dB bandwidth from 1.7 to 2.7 µm. We do not detect any water absorption dip, meaning a dry atmosphere is sufficient to properly store ChG fibers. Water inside the OSA air causes the absorption lines from 2500 nm to 2800 nm. As expected from previous research [13,14], the ANDi SCG shows very flat top, leading to a large 3 dB bandwidth. Indeed, our 3 dB bandwidth covers from 1941 nm to 2301 nm (24 THz), hence can be compressed to few-cycle pulses. The dominant broadening mechanisms, SPM and OWB, are both elastic processes, resulting in a full conversion of pump power into SCG. We measured 2.5 mW output average power, which is smaller than coupled average power owing to 20% loss from Fresnel reflection at the output facet. Further increase of average output power could be achieved by increasing the pump repetition rate, while keeping the peak power at a moderate value (a few kW).
Fig. 3 SCG at different peak powers for FUT 1 (solid line), and the corresponding simulations (dashed line). Lines at different peak power levels are shifted by 10 dB for better representability
For the theoretical study of our ANDi SCG, we have ignored the delay contribution from our dichroic mirror and chalcogenide lens, and the results are depicted by the dotted lines in Fig. 3. As FUT1 length, 10 cm, has much stronger dispersion contribution than the DM and aspherical lens, the simplification is valid for this particular experiment. During the whole simulation process, we only adjust the pump peak power according to the recorded average power to fit the experimental results. Generally, a SCG simulation are based on the mean of multiple runs [2]. ANDi SCG has perfect coherence and maximum phase stability [14,17–19], so in this case only a single run of simulation is sufficient [18]. In section 3.3, we perform the study of pulse evolution during propagation with the dispersion contribution from optical components included.
3.2 Impact of water absorption inside fiber material
From the dispersion in Fig. 1(b), FT2 is expected to produce slightly narrower SCG given the larger GVD of 368 ps2/km at 2070 nm pump. In addition, FUT2 was fabricated more than 3 years ago and stored in lab atmosphere without humidity control. Therefore, this fiber can serve as a good example to study water absorption impact on ANDi SCG under a normal atmospheric/environmental condition, which is critical for field applications. ANDi SCG in our FUTs have millimeter scale effective lengths, so a longer fiber length will not contribute to further broadening of the SCG. However, a longer fiber length can enhance the impact of water absorption and a 80-cm-long fiber was therefore tested in the same setup as depicted before. Compared to the experiments performed with FUT, the coupling loss only slightly varied (<1 dB) while no difference in the linear transmission loss at 2070 nm were observed .
Figure. 4 shows the recorded SCG spectra (solid lines) together with simulation in the absence of water absorption (dashed lines) at different pump powers (solid lines). Before the blue edge of SCG reaches 1950 nm band, simulation matches perfectly with experimental data. When we further increase the coupled peak power to 200 W, a clear dip appears at about 1935 nm, associated with the O-H bond vibration. Previous research shows more significant absorption peak should be expected centered at 2800 nm [28] (3575 cm−1, fundamental vibration frequency of O-H bond), which strongly hinders the expansion of SCG at higher pump power. Subtracted from the simulation, FUT2 has an absorption peak of 7 dB/m at around 1935 nm. Despite the high water absorption, the ANDi SCG showed great stability for more than 40 min detailed in [29].
Fig. 4 SCG at different peak powers for FUT2 (solid line), and the corresponding simulations (dashed line). Data shows clear trace of O-H bond absorption.
We believe the water absorption mainly comes from moisture inside atmosphere. The wet air travels through PCF air holes and brings water to PCF core. One solution to avoid water absorption is to close the air holes or purge PCF with dry air. On the other hand, results from FUT1 shows no water absorption inside ChG PCG, meaning a dry atmosphere storage condition can well protect the fiber for at least two years. In addition, drying the sample inside a vacuum oven could remove the water from ChG [30].
3.3 SCG evolution and pulse properties
For very short fiber lengths, dispersive optical components’ contribution becomes more significant and therefore cannot be neglected in simulations. The main dispersion contribution comes from the ND filter (fused silica), dichroic mirror (fused silica) and aspherical lens (black diamond, BD-2). We used refractive index equation provided by Thorlabs [31,32] to simulate their delay contributions. The ND filter is 2 mm thick, dichroic mirror is 3 mm thick and the aspherical lens is 2 mm thick. Since the collimated pump laser beam waist (4 mm) is 3 orders of magnitude larger than the beam size in our PCF, their nonlinear parameter is at least 6 orders of magnitude smaller than the FUT and is set to zero in numerical study. GNLSE simulates the complete pulse propagation process from laser output to FUT.
In Fig. 5, we simulated pulse evolution starting with 5 mm propagation inside the free space optics components (indicated before the black line). After the free space optical components, the pulse goes directly into the ChG PCF. The total simulated fiber length is 4 cm with the same properties as FUT1 and the coupled pump peak power is 2 kW. After entering the FUT, pulse evolution occurs mostly within the first 1 cm of propagation [Fig. 5(a)]. In the time domain, the SCG remains a single pulse during the whole propagation length. For a length smaller than 1cm, the pulse maintains a width of less than 1 ps [Fig. 5(b)]. Due to the relatively large dispersion and short input pulse duration, further broadening in spectrum domain is inhibited by the strong pulse broadening in the time domain.
Fig. 5 Simulated pulse evolution in wavelength (a) and time domain (b), at 2kW peak power. The intensity is normalized to 1 (0 dBm) and plotted in dB scale. Dispersion from lens and dichroic mirror is considered (first 5 mm of the simulation).
As a starting point for the experimental investigation, we tested a 2 cm segment (FUT3). Figure 6 shows the SCG evolution with peak power from 30 to 2890 W. The maximum pump power expands the tail of SCG slightly beyond the ANDi region and the SCG spans close to one octave. At this point, the experiment data show a 3 dB bandwidth from 1925 to 2340 nm (27.6 THz), large enough to support a sub-2 optical cycle pulse. The −20 dB bandwidth is 75.5 THz (1670 to 2880 nm).
Fig. 6 Experimental and simulated results of ANDi SCG at different power levels for FUT3. Fiber length is 2 cm. The maximum coupled peak power is 2.9 kW.
From our simulation, even at the highest pump power of 2.9 kW, the pulse remains to be single pulse and highly coherent, i.e. all the advantages of ANDi SCG remain valid. To prove this point, we simulate the first order coherence g12 using the widely-accepted one photon per wavelength noise assumption [10]. Figure 7(a) shows the coherence of the whole SCG band is 1, including the part beyond ANDi region. On the other hand, we plot the evolution of 3 dB bandwidth and −20 dB bandwidth as a function of fiber length in Fig. 7(b). From this simulation, the optimal length for largest 3 dB bandwidth is 7 mm while −20 dB bandwidth only has minor increase after 10 mm of fiber length.
Fig. 7 (a) 1st-order coherence for a peak pump power of 2.89 kW on a 2 cm FUT, corresponding to the maximum power in Fig. 6. (b) Evolution of −20 dB bandwidth and 3 dB bandwidth during propagation. The peak power is 2 kW in this figure.
We then tested FUT4 (3.4 mm), FUT5 (7.1 mm) and FUT6 (9.7 mm) and summarize their data in Fig. 8. All these short FUTs were prepared by manual cleaving. For better illustration, we show three power levels (0.5, 1 and 2 kW) for each FUT. The inset of Fig. 8 is the picture of FUT4. At the maximum pump power, FUT4 has −20 dB bandwidth of 49 THz and 3 dB bandwidth of 16 THz. Experiment results from FUT4 confirm that we have correctly included the effect of free space optical components in our simulation. Clearly, FUT4 is not long enough for complete broadening of the SCG process, as expected from simulations.
Fig. 8 SCG at different pump powers for FUT4, FUT5 and FUT6. The simulations (dashed) is superimposed onto the experiment data (solid). Inset: picture of FUT4.
From Fig. 5, FUT6 is close to the optimal length for a complete broadening at 2 kW peak power. At 2 kW peak power, the ANDi SCG from FUT6 shows the same coverage as FUT3. The small difference comes from variations in coupling efficiency. The maximum 3-dB bandwidth of FUT6 is 23.3 THz, within 4% difference compared with FUT3. In the time domain, simulations indicate 600 fs pulse duration. Notably from Fig. 7(b), the slope of 3 dB bandwidth expansion converges to zero with longer fiber, which is in accordance with the result in [18].This is also seen by comparing the results for FUT5 and FUT6. Though the −20 dB bandwidth is slightly smaller than for FUT3, both FUT5 and FUT6 show approximately an identical 3-dB bandwidth of 23 THz at 2 kW peak power. However, the shorter length of FUT5 outputs a less dispersed pulse.
A linearly chirp pulse greatly simplifies the pulse recompression setup. Due to the linear dispersion from our FUT, we expect linear chirp from the ANDi SCG pulse. Since FUT5 has the optimal length, we retrieve the pulse properties from simulation. Figure 9(a) shows the simulated spectrogram of FUT5 (7.1 mm length) output at peak power of 2 kW. The bandwidth, 23 THz, leads to a transform-limited pulse duration of 13.7 fs, assuming a sech2 pulse. For a 2080 nm center wavelength, it can support a 2-cycle pulse. The spectrogram shows FUT5 outputs a single pulse with simple phase distribution. Indeed, the output chirp is linear for the complete span of SCG, shown in Fig. 9(b). With a linear chirp, the FUT5 output pulse can be easily compressed with chirped mirrors in 2 µm band. However, due to the difficulty to get chirped mirror at this band, current compression can use grating pair or prism pair constitutions.
Fig. 9 (a) Simulated spectrogram of FUT5 output pulse, amplitude is normalized to 0 dBm; (b) this pulse has a linear chirp. In both plot, the frequency is normalized to the pump
4. Conclusion
In conclusion, we studied ANDi SCG inside ChG PCF experimentally and theoretically. Pumping with a fiber laser at moderate peak power level, we experimentally show a −20 dB bandwidth from 1670 to 2880 nm and a 3 dB bandwidth of bandwidth from 1925 to 2340 nm (27.6 THz) using a 2 cm PCF segment. As expected for ANDi SCG, we manage to match our experiment data and theoretical data at all pump powers. Water absorption could pose a big obstacle to ANDi SCG inside ChG, but one can overcome this problem by properly storing the fibers. In addition, we demonstrated pulse evolution along our PCF and found the optimal fiber length for both maximum −20 dB and 3 dB bandwidth. At last, we simulate the output pulse spectrogram. With a linearly chirped output pulse, one can compress the pulse with a relatively simple setup. Currently, the output average power is 2.5 mW at 2 kW coupled peak power. In future, we plan to increase laser repetition rate to100 MHz and pulse duration to 200 fs, leading to an average output power from fiber at 50 mW. Furthermore, recent experiment demonstrated broadband amplification of sub-2 cycle 2000 nm pulse using Kerr instability [33]. Such method could also amplify compressed pulse from ANDi SCG. We believe our study shows ChG PCF could be a good platform to generate few-cycle pulse at MIR.
Funding
H2020 European Research Council (ERC) ERC-2012-StG 306630-MATISSE.
Acknowledgment
The authors would like to thank Prof. Minglie Hu, from Tianjin University, for his valuable suggestions on paper structure and fruitful discussions.
References and links
1. J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009). [CrossRef]
2. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
3. X. Jiang, N. Y. Joly, M. A. Finger, F. Babic, G. K. L. Wong, J. C. Travers, and P. S. J. Russell, “Deep-ultraviolet to mid-infrared supercontinuum generated in solid-core ZBLAN photonic crystal fibre,” Nat. Photonics 9(2), 133–139 (2015). [CrossRef]
4. Z. Zhao, B. Wu, X. Wang, Z. Pan, Z. Liu, P. Zhang, X. Shen, Q. Nie, S. Dai, and R. Wang, “Mid-infrared supercontinuum covering 2.0–16 μm in a low-loss telluride single-mode fiber,” Laser Photonics Rev. 11(2), 1700005 (2017). [CrossRef]
5. T. Cheng, K. Nagasaka, T. H. Tuan, X. Xue, M. Matsumoto, H. Tezuka, T. Suzuki, and Y. Ohishi, “Mid-infrared supercontinuum generation spanning 2.0 to 15.1 μm in a chalcogenide step-index fiber,” Opt. Lett. 41(9), 2117–2120 (2016). [CrossRef] [PubMed]
6. Z. Zhao, X. Wang, S. Dai, Z. Pan, S. Liu, L. Sun, P. Zhang, Z. Liu, Q. Nie, X. Shen, and R. Wang, “1.5-14 μm midinfrared supercontinuum generation in a low-loss Te-based chalcogenide step-index fiber,” Opt. Lett. 41(22), 5222–5225 (2016). [CrossRef] [PubMed]
7. C. R. Petersen, U. Møller, I. Kubat, B. Zhou, S. Dupont, J. Ramsay, T. Benson, S. Sujecki, N. Abdel-Moneim, Z. Tang, D. Furniss, A. Seddon, and O. Bang, “Mid-infrared supercontinuum covering the 1.4–13.3 μm molecular fingerprint region using ultra-high NA chalcogenide step-index fibre,” Nat. Photonics 8(11), 830–834 (2014). [CrossRef]
8. G. Tao, H. Ebendorff-Heidepriem, A. M. Stolyarov, S. Danto, J. V. Badding, Y. Fink, J. Ballato, and A. F. Abouraddy, “Infrared fibers,” Adv. Opt. Photonics 7(2), 379–458 (2015). [CrossRef]
9. C. R. Petersen, R. D. Engelsholm, C. Markos, L. Brilland, C. Caillaud, J. Trolès, and O. Bang, “Increased mid-infrared supercontinuum bandwidth and average power by tapering large-mode-area chalcogenide photonic crystal fibers,” Opt. Express 25(13), 15336–15348 (2017). [CrossRef] [PubMed]
10. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27(13), 1180–1182 (2002). [CrossRef] [PubMed]
11. J. Dudley and S. Coen, “Fundamental limits to few-cycle pulse generation from compression of supercontinuum spectra generated in photonic crystal fiber,” Opt. Express 12(11), 2423–2428 (2004). [CrossRef] [PubMed]
12. W. J. Tomlinson, R. H. Stolen, and C. V. Shank, “Compression of optical pulses chirped by self-phase modulation in fibers,” J. Opt. Soc. Am. B 1(2), 139–149 (1984). [CrossRef]
13. C. Finot, B. Kibler, L. Provost, and S. Wabnitz, “Beneficial impact of wave-breaking for coherent continuum formation in normally dispersive nonlinear fibers,” J. Opt. Soc. Am. B 25(11), 1938–1948 (2008). [CrossRef]
14. A. M. Heidt, “Pulse preserving flat-top supercontinuum generation in all-normal dispersion photonic crystal fibers,” J. Opt. Soc. Am. B 27(3), 550–559 (2010). [CrossRef]
15. A. M. Heidt, A. Hartung, G. W. Bosman, P. Krok, E. G. Rohwer, H. Schwoerer, and H. Bartelt, “Coherent octave spanning near-infrared and visible supercontinuum generation in all-normal dispersion photonic crystal fibers,” Opt. Express 19(4), 3775–3787 (2011). [CrossRef] [PubMed]
16. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, “Optical wave breaking of pulses in nonlinear optical fibers,” Opt. Lett. 10(9), 457–459 (1985). [CrossRef] [PubMed]
17. L. E. Hooper, P. J. Mosley, A. C. Muir, W. J. Wadsworth, and J. C. Knight, “Coherent supercontinuum generation in photonic crystal fiber with all-normal group velocity dispersion,” Opt. Express 19(6), 4902–4907 (2011). [CrossRef] [PubMed]
18. A. M. Heidt, J. Rothhardt, A. Hartung, H. Bartelt, E. G. Rohwer, J. Limpert, and A. Tünnermann, “High quality sub-two cycle pulses from compression of supercontinuum generated in all-normal dispersion photonic crystal fiber,” Opt. Express 19(15), 13873–13879 (2011). [CrossRef] [PubMed]
19. M. Klimczak, B. Siwicki, P. Skibiński, D. Pysz, R. Stępień, A. Heidt, C. Radzewicz, and R. Buczyński, “Coherent supercontinuum generation up to 2.3 µm in all-solid soft-glass photonic crystal fibers with flat all-normal dispersion,” Opt. Express 22(15), 18824–18832 (2014). [CrossRef] [PubMed]
20. K. Tarnowski, T. Martynkien, P. Mergo, K. Poturaj, G. Soboń, and W. Urbańczyk, “Coherent supercontinuum generation up to 2.2 µm in an all-normal dispersion microstructured silica fiber,” Opt. Express 24(26), 30523–30536 (2016). [CrossRef] [PubMed]
21. L. Liu, T. Cheng, K. Nagasaka, H. Tong, G. Qin, T. Suzuki, and Y. Ohishi, “Coherent mid-infrared supercontinuum generation in all-solid chalcogenide microstructured fibers with all-normal dispersion,” Opt. Lett. 41(2), 392–395 (2016). [CrossRef] [PubMed]
22. A. Al-Kadry, L. Li, M. El Amraoui, T. North, Y. Messaddeq, and M. Rochette, “Broadband supercontinuum generation in all-normal dispersion chalcogenide microwires,” Opt. Lett. 40(20), 4687–4690 (2015). [CrossRef] [PubMed]
23. D. D. Hudson, S. Antipov, L. Li, I. Alamgir, T. Hu, M. E. Amraoui, Y. Messaddeq, M. Rochette, S. D. Jackson, and A. Fuerbach, “Toward all-fiber supercontinuum spanning the mid-infrared,” Optica 4(10), 1163–1166 (2017). [CrossRef]
24. S. Xing, D. Grassani, S. Kharitonov, L. Brilland, C. Caillaud, J. Trolès, and C.-S. Brès, “Mid-infrared continuous-wave parametric amplification in chalcogenide microstructured fibers,” Optica 4(6), 643–648 (2017). [CrossRef]
25. S. Xing, D. Grassani, S. Kharitonov, A. Billat, and C.-S. Brès, “Characterization and modeling of microstructured chalcogenide fibers for efficient mid-infrared wavelength conversion,” Opt. Express 24(9), 9741–9750 (2016). [CrossRef] [PubMed]
26. S. Kharitonov, A. Billat, and C.-S. Brès, “Kerr nonlinearity and dispersion characterization of core-pumped thulium-doped fiber at 2 μm,” Opt. Lett. 41(14), 3173–3176 (2016). [CrossRef] [PubMed]
27. J. T. Gopinath, M. Soljačić, E. P. Ippen, V. N. Fuflyigin, W. A. King, and M. Shurgalin, “Third order nonlinearities in Ge-As-Se-based glasses for telecommunications applications,” J. Appl. Phys. 96(11), 6931–6933 (2004). [CrossRef]
28. P. Toupin, L. Brilland, D. Méchin, J.-L. Adam, and J. Troles, “Optical Aging of Chalcogenide Microstructured Optical Fibers,” J. Lightwave Technol. 32(13), 2428–2432 (2014). [CrossRef]
29. S. Xing, S. Kharitonov, J. Hu, D. Grassani, and C.-S. Brès, “MIR supercontinuum in all-normal dispersion Chalcogenide photonic crystal fibers pumped with 2μm femtosecond laser,” in Advanced Solid State Lasers (Optical Society of America2017), p. ATu5A. 3.
30. L. Li, “Chalcogenide Microwires Cladded with Hydrogen-and Fluorine-based Polymers and Their Applications,” PhD thesis, McGill University Libraries, 2017.
31. Refractive index of black diamond: https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=4791
32. Refractive index of fused silica: https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6973
33. G. Vampa, T. J. Hammond, M. Nesrallah, A. Y. Naumov, P. B. Corkum, and T. Brabec, “Light amplification by seeded Kerr instability,” Science 359(6376), 673–675 (2018). [CrossRef] [PubMed]
