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Abstract
All-normal dispersion supercontinuum generation (SG) in a large hollow core photonic crystal fiber (PCF) infiltrated with carbon tetrachloride is studied experimentally. The PCF is optimized to have a flat normal dispersion in a broadband range (0.8–1.7 µm) varying from -150 to 0 ps/nm/km. The effective mode area at pump wavelength (λ=1030 nm) is as large as 42.2 µm2 and readily meets the requirements for an all-fiber supercontinuum system. Infiltration of the core with carbon tetrachloride ensures a high nonlinear coefficient of the fiber equal to 22 1/W/km. Using an off-the-shelf 1030 nm fiber laser with 400 fs and 25 nJ input pulses, we generated an all-normal supercontinuum in the 850–1250 nm wavelength range.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The supercontinuum generation (SG) with unique properties, i.e., spatial coherence, broad spectral width and high brightness has become a standard in several applications ranging from metrology to advanced optical coherence tomography [1]. In particular, SG with a high degree of temporal coherence has revolutionized the field of spectroscopy [2], frequency metrology [3], tomography [4,5] and multimodal biophotonic imaging [5,6]. Supercontinuum sources can deliver light pulses with brightness 1-2 orders of magnitude higher than typical synchrotron infrared beamlines in broadband range from the visible up to 10.6 µm, and can be treated as compact table-top synchrotron sources [7]. Supercontinuum generation is typically achieved by launching ultrashort laser pulses into a nonlinear fiber, which are made from silica or highly nonlinear soft glasses, e.g., chalcogenide or tellurite glasses [8–10]. However, silica glass is not transparent in the mid-infrared (MIR) and shows relatively low nonlinearity. Broadband IR range is in particular interesting for biomedical imaging. MIR sources allow improving the penetration depth of optical coherence tomography (OCT) systems. Recently real-time spectral-domain OCT imaging in the MIR with axial resolution as high as 8.6 μm was demonstrated using a SC source [11]. MIR supercontinuum was successfully used for MIR multispectral imaging of tissue. This approach allows to distinguish between epithelial and surrounding connective tissues within colon tissue [12]. The drawback of using soft-glass based fibers for SG is their incompatibility with silica based fiber systems, which is usually required in practical applications. For instance, the chalcogenide glass has zero-dispersion wavelength (ZDW) at mid-infrared [13]. Hence challenging engineering of micro-structures with an additional fiber offering ZDW that coincides with pump wavelength of commercially available high peak-power laser sources is required. Most SG experiments based on chalcogenide fibers were conducted using laboratory expensive and complex systems, i.e., optical parametric amplifiers (OPAs) and oscillators (OPOs), as MIR pump sources [13]. On the other hand, tellurite glass is transparent in the wavelength range below 5.5 µm, which limits its range of applications. Moreover, its linear refractive index is substantially higher and an effective mode area of the fibers is much smaller than that of silica [13] resulting in low coupling efficiency when all-fiber systems with tellurite fibers are considered.
Due to the mentioned drawbacks, alternative solutions for silica based highly nonlinear fibers must be examined for application in SG systems. One of the possible approaches are gas core photonic crystal fibers intensively studied in recent years [14]. The gas core PCFs are typically low loss and offer the possibility to tune both the dispersion and optical nonlinearity by changing the gas pressure and temperature [14]. Cassataro et al. demonstrated the SG from 0.27 µm to 3.1 µm using a gas core anti-resonant PCF with 1.7 µm pump wavelength and 100 fs pulse of 10 µJ input pulse energy [15]. The main disadvantages of this fiber are: challenging low-loss fusion splicing with standard fibers, the limitation of transmission window - a typical feature of band-gap fibers, and, if the fiber is bent, the sensitive excited multimode operation leading to an increase of losses. Moreover, to obtain ultrabroadband spectral broadening, exotic wavelength of ultra-short pulses are required, which is not readily available from standard short-pulse fiber lasers.
Another approach are liquid core optical fibers (LiCOF). Liquids with highly nonlinear optical properties are used to fill the hollow core of silica fiber or silica capillary [16]. In fact, several organic liquids, e.g., toluene or carbon disulfide, show comparable optical nonlinearity to that of nonlinear glasses commonly used in SG fibers. Carbon tetrachloride (CCl4) and carbon disulfide (CS2) are highly transparent in the near-infrared (NIR) and MIR range [17,18]. Among other advantages of the liquids is their capability to mix with other solutions and consequently one can easily adjust their optical properties, e.g. linear refractive index, to requirements of a given system [19]. Numerical simulations for liquid-core photonic crystal fibers show that it is possible to shift the ZDW and match it with pump wavelength of high-power commercial laser, as well as to obtain all-normal and flat dispersion regime in the spectral range in which SG is expected [20,21]. It is known that SG with high coherence is typically achieved in the normal dispersion regime when subpicosecond pump pulses from low-cost all-fiber lasers are used [22].
The supercontinuum generation studies with LiCOF have become popular in recent years [23–32]. However, most of these works focus on SG in PCF with anomalous dispersion [23, 27–31] where soliton dynamics is a main contributor for SG. The first measurements were reported by Bozolan et al. [23] where a water core PCF was pumped with 100 fs-long pulses at 980 nm wavelength. The pulse broadening in the range of 0.66 - 1.14 µm was achieved with 20 dB dynamics by soliton formation due to the Raman induced self-frequency shift. The water core PCF was further investigated by Bethge et al. [24]. They obtained generation of supercontinuum with two-octave spectral coverage from 410 to 1640 nm in 30 dB dynamics with 7 µJ pulse energy and 45 fs pulse at 1200 nm pump wavelength. Recently Chemnitz et al. [27] reported the hybrid soliton dynamic for SG with CS2 core optical fibers where the SG had a potential for coherent radiation. The two-octave-spanning SG of 1200 - 3000 nm with 1920nm pump wavelength and 350 fs pulse duration was demonstrated for CS2 core fiber [28]. Additionally, soliton fission in a carbon tetrachloroethylene (C2CL4) core fiber resulted in an octave-spanning bandwidth of 1100 - 2400 nm with 1920nm pumping wavelength, 270 fs duration and 0.5 nJ pulse energy [29]. Vieweg et al. used a two-photon direct-laser writing technique to close the individual air-hole in a PCF and applied carbon tetrachloride (CCl4) to infiltrate selected air-holes in the cladding of solid core PCF [30]. A SC in the range 900–1400 nm was obtained using fiber pumped with 210 fs pulses at the wavelength of 780 nm. The stimulated Raman-Kerr scattering for spectral broadening was observed by Fanjoux et al. [31] in an optical fiber with toluene core. The authors achieved moderate spectrum spanning in the range 550 - 870 nm generated with 18 ps pump pulses at 532 nm wavelength.
Among all research related to SG in liquid core fibers only a couple refers to fibers with all-normal dispersion [23–26,32]. In Table 1 we summarize the state-of-the-art experimental results of SG in liquid core PCF with all-normal dispersion.
Table 1. State-of-the-art experimental results on supercontinuum generation in all normal dispersion liquid core optical
It is well known, that dispersion characteristic of optical fibers plays a crucial role in the process of the SG [33]. Most of the SG systems favor silica capillaries infiltrated with high refractive index liquids [25–30]. This approach requires application of the laboratory pump systems due to limited flexibility n a design of dispersion and modal properties of step-index fibers. In contrast, the use of hollow core PCFs allows to determine dispersion and modal characteristics through modification of photonic cladding parameters, such as the size of air holes and the lattice pitch. This way effective parameters of the fiber can be adjusted to parameters offered by commercially available short-pulse fiber laser sources. Use of hollow core silica PCF with core filled with nonlinear liquids, allows to combine the unique design flexibility of PCFs with high nonlinearity of the selected liquids.
Recently we have demonstrated experimentally all-normal SG in range 950 - 1100 nm using large mode area PCF infiltrated with toluene and using a commercial fiber laser emitting 400 fs pulses with 10 nJ pulse energy at 1030 nm wavelength as a pump [32]. Limited spectra broadening was related to high attenuation of toluene in the infrared range [17, 18]. For this reason substitution of toluene with other nonlinear liquid with lower attenuation can be beneficial for further optimization of the SG process. CCl4 is one of the most interesting liquid here, due to its high transmission in visible and near infrared (0.5 - 1.5 µm) range (Fig. 1) [17]. Moreover, it is less toxic, when compared with other highly nonlinear liquids such as CS2 or toluene [34]. Nonlinear refractive index of CCl4 is very high n2 = 1.53*10−19 m2/W at λ=1.064 µm [16]. In particular, it is 5 times higher than fused silica (n2 = 2.74*10−20 m2/W). At the same time the linear refractive index of CCl4 is significantly lower than that of other highly nonlinear liquids and it is very similar to the one of fused silica (Fig. 1(a)). This property allows to obtain a high coupling efficiency of CCl4 core fiber with typical silica fibers used in all-fiber pump laser systems. It must be noted that if a high linear refractive index liquid is introduced into the core, difference of refractive index between core and cladding demand reduction of the core diameter to maintain a single mode performance - otherwise the coupling efficiency is dramatically reduced. We also point out that CCl4 was extensively studied in tunable ultrafast mode coupling [35], and highly efficient guiding of MIR laser light for medical application [36].
Fig. 1. Optical properties of carbon tetrachloride, (a) refractive index and chromatic dispersion of bulk silica and carbon tetrachloride [14], (b) the transmittance of 20 cm thickness sample and imaginary part of the refractive index of carbon tetrachloride (after Kedenburg et al. [17]).
In this paper we present the experimental results of SG in all-normal dispersion photonic crystal fiber with the carbon tetrachloride core. The investigated fiber was fabricated in-house. Next, the hollow core was selectively filled with carbon tetrachloride. Chromatic dispersion was verified using Mach-Zehnder interferometric setup. The dynamics of nonlinear propagation for various input pulses was investigated using nonlinear Schrödinger equation (GNLSE). A pump system was applied during the SG and chromatic dispersion measurements to keep the liquid inside the fiber.
2. Geometrical structure optimization of the carbon-tetrachloride core PCF
In the numerical simulations we considered a regular hexagonal lattice PCF with 5 rings air-holes, defined by the lattice constant Λ and air holes diameter d in the cladding. We assume that large central defect of the lattice is infiltrated with CCl4 and has the diameter Dcore=2.2 Λ, which is in a good agreement with technological requirements of PCF fiber developed by the stack-and-draw method [37].
We study theoretically an influence of geometrical parameters of the PCF on dispersion properties of the fundamental mode using the finite difference numerical method (FDM). Material dispersion of silica and CCl4 considered in the simulations were taken from [17]. Our study is focused on fiber structures with relatively large mode area PCFs, therefore the considered lattice constant must be limited to the range 1 - 5 µm. We assume also that the filling factor defined as the relative inclusion size f = d/Λ vary from 0.3 to 0.8 as it is possible to be fabricated in fiber drawing process [37] and rigid fiber structure when the fiber core is filled with the liquid using high pressure pump [32].
First, we noticed that in the case of small lattice constant (Λ <2 µm), an increase of relative inclusion size shifts noticeably the dispersion toward anomalous range of values, Fig. 2. In particular, the normal dispersion part of the dispersion characteristic is extended to the wavelength of 2 µm with Λ=1 and f = 0.3 as shown in Fig. 2(a).
Fig. 2. Dispersion properties of PCFs with a core infiltrated with carbon tetrachloride for various lattice constants Λ=1 µm (a), Λ=2 µm (b), Λ=3 µm (c), Λ=4 µm (d) and Λ=5 µm (e) and various filling factors f (f = d/Λ). Size of carbon tetrachloride core is equal to 2.2×Λ.
For the lattice constant Λ > 2 µm the PCF dispersion is mainly determined by diameter of the core and an influence of diameter of the air holes in the photonic cladding is negligible. The same dispersion characteristics can be obtained when PCF is replace by a capillary. However, it is important to note that that photonic cladding plays an important role, since it has a significant influence on guiding and modal properties of the fiber due to the fact that refractive indices of CCl4 and silica are very similar (see Fig. 1(a)).
The use of the large core PCFs (Λ> 4 µm) ensures a flat normal dispersion up to 1.7 µm or even above, as shown in Fig. 2(d). Additionally, for large mode area fibers it is possible to obtain the high coupling efficiency with the all-fiber short-pulse laser system, since the latter also use large mode area fibers for delivery of high-power ultra-short pulses [38]. According to our numerical analysis the coupling efficiency at pump wavelength of 1030 nm of PCF with the lattice constant Λ = 4 µm and the filling factor f = 0.8 coupled to LMA-8 fiber [39] and SMF-28 fiber [40] are as high as 91 and 76%, respectively.
As we noticed above the large core CCl4 PCF with the lattice constant of Λ = 4 µm offers dispersion characteristics comparable to large core step-index capillary fiber with a core filled with CCl4. However, the effective mode area of both types of fibers are very different. The effective mode areas of the large core step-index fiber with CCl4 core is equal to 292 µm2, therefore its nonlinearity is also low. A PCF considered in this manuscript with similar dispersion characteristics has the effective mode area as small as 42.2 µm2. Therefore, the fundamental mode is better confined within the core area, and consequently has lower bending losses and higher nonlinear coefficient γ.
It must be noted that the large core CCl4 PCF studied here with the lattice constant of Λ = 4 µm, is not single mode at 1030 nm (Fig. 3). It can effectively guide two modes since the confinement losses of the fundamental mode LP01 and higher order mode LP11 are comparable (see Fig. 4). The remaining modes undergo significantly higher attenuation. In practice one of the modes can be selectively excited since LP01 and LP11 modes have spatially different overlap with pump beam in the case of free space or fiber interconnect excitations. Moreover, higher order modes do not influence significantly SG efficiency when pump pulse is short enough (< 10 ps). In this case the walk-off between the fundamental mode and the higher order modes is long enough to prevent from efficient power transfer between the modes [41].
Fig. 3. Effective refractive index (a) and conferment losses for the fundamental LP01 and higher order LP11 modes.
Fig. 4. Scanning electron microscopy (SEM) image of the hollow-core silica PCF (a), image of the end faced of the PCF fiber with the hollow core infiltrated selectively with carbon tetrachloride (b).
3. Measurement of the linear properties of the investigated fiber
We fabricated the large-hollow core PCF using fused silica capillaries with standard stack-and-draw method [37]. The diameter of the fiber outer was 123.2 µm, average of the lattice constant Λ = 4.45 µm, Dcore = 9.8 µm, and diameter of air-hole d = 3.7 µm (Fig. 4(a)). The developed fiber has the lattice constant 10% larger than the one selected in the simulations presented in the previous section. However, changes of dispersion characteristics are very small for the fibers with relatively large change of the lattice constant in the range Λ = 4 - 5 µm and/or the relative inclusion size varying in the range 0.3–0.8, as shown in Fig. 2(d). Therefore we expect the dispersion characteristics of developed fiber to be similar to the designed one.
In the next step we have used a fusion splicer to close air holes in the photonic cladding. This method was described in detail in our previous work [32]. The fiber was mounted in a custom-made microfluidic reservoir filled with carbon tetrachloride. The reservoir has optical window to couple light from an external source into the liquid core fiber, and liquid input connected with a microfluidic pump system as shown in Fig. 5. The reservoir was fully filled with carbon tetrachloride and constantly pumped using a pressure of 200 kPa. Since the input end of the fiber was immersed in the reservoir filled with the liquid, the fiber core was constantly filled without any presence of air bubbles. The system required 8 minutes for initial filling of 20 cm long fiber samples. Selective infiltration of the fiber was monitored with a CCD camera which allow to observe the end face of the fiber and verify the core infiltration progress. Figure 4(b) presents the cross-section of the PCF with carbon tetrachloride in the core.
Fig. 5. Custom-made microfluidic reservoir for infiltration of hollow core fibers and direct light coupling: (a) a schematic of the microfluidic reservoir and (b) the experimental setup. The microfluidic reservoir is fully filled with carbon tetrachloride and connected to microfluidic pump to maintain increased pressure in the system. Glass window allows to couple light from external source with external microscope objective into the liquid core fiber.
Dispersion characteristics of the developed fiber with liquid core were calculated using air hole diameters received from SEM image and then verified experimentally by Mach-Zehnder interferometer setup. The experimental results match well the simulated ones (see Fig. 6). The dispersion has ZWD at 1.7 µm and the value of dispersion varies between -150 and 10 ps/nm/km in wavelength range 0.85 - 2 µm.
Fig. 6. Measured dispersion characteristic of the developed PCF with core infiltrated with carbon tetrachloride. The PCF has the lattice constant Λ = 4.45 µm, and the diameter of the air-holes in the photonic cladding is 3.7 µm. The core dimeter is 9.8 µm.
We have calculated confinement losses and the effective mode area for the developed PCF. The losses are similar to the ones calculated for an ideal structure, since material losses of carbon tetrachloride have dominant contribution and the waveguide losses are negligible. We note that loss peak of 2.5 dB/m present at 1.4 µm may have an influence on degradation of SG dynamic. To minimize this effect only a short segment of the fiber should be used for SG.
4. Simulation of supercontinuum generation
We modelled SG in the developed PCF using the split-step Fourier method, based on GNLSE [21,33]. In the simulations we took into account measured dispersion characteristics, wavelength dependent losses and effective mode area. Fractional Raman contribution to nonlinear processes in CCl4 was 0.18 [42]. We neglect an influence of second guided mode LP11 on nonlinear performance of the fiber. The nonlinear coefficient (Fig. 7) was calculated using Eq. (1), where Aeff denotes effective mode area of the fundamental mode and n2 – nonlinear refractive index of carbon tetrachloride.
Large core fibers show usually low nonlinear coefficient. For investigated fiber, the nonlinear coefficient is relatively high (20.5 - 23 W-1km-1 in the range 0.8 - 2 µm) even though the effective mode area of the fundamental mode is large 41 - 45.1 µm2 (Fig. 7).Fig. 7. Effective mode area and the nonlinear refractive index for the investigated fiber. The blue lines depicts nonlinear coefficient, while the red trace represents the mode area.
In the simulations we assumed pulse parameters of the fiber laser used further in the experiments for generation of supercontinuum. The initial pulse parameters are as follows: pulse duration 400 fs, central pumped wavelength 1030 nm, Gaussian shape of the pulse and input energy pulse varying in the range of 4 - 25 nJ, which corresponds to the peak power of 10 - 62.5 kW.
In our nonlinear propagation simulations, we have taken an approach where noise is represented by a single photon with random phase added to each simulation time bin (single-photon-per-mode noise related to spontaneous emission). This noise model is usually chosen for simulations assuming pumping from mode-locked lasers [22]. A phase diffusion model has been proposed to account for effects of pump spectral linewidth on spectral broadening [43], although it is not suitable for simulation of pumping with broad gain band sources like mode-locked lasers [44]. Recently, noise models including not only one-photon-per-mode, but other contributions, such as intensity stability, have been implemented in modelling of supercontinuum generation, including mode-locked laser pumping [45,46]. This approach revealed the contribution of supercontinuum noise to be weaker, than that of laser shot noise. Compared to a simple one-photon-per-mode noise implementations, stronger decoherence has been observed at spectral edges of spectrally broad supercontinuum pulses [45]. Our experimental results showed moderate spectral broadening contained within 850-1200 nm wavelength range, hence the simple noise model used in our work can reasonably be considered robust. We note, that use of the complex noise model, including the technical terms related to laser shot-to-shot performance, would be beneficial for modelling accuracy in a tetrachloride-filled fiber system optimized for increased nonlinearity, ie. with smaller effective mode area, than the one studied in our work.
In the case of 25 nJ input pulse energy, the SG from 850 to 1250 nm within 20 dB dynamic is as predicted with numerical simulations, as shown in Fig. 8. We observe the dynamics of pulse broadening typical for all normal dispersion SG. Over the first centimeters of propagation, the spectrum is broadened due to self-phase modulation. Later, the group delay trace (shown for three points along the pulse propagation in fiber) transforms gradually into S-shape due to the instantaneous linear frequency variation in time. The optical wavelength breaking (OWB) occurs at the wings of spectrum induced by four-wave mixing (FWM). OWB occurred earlier on the blue-side and the new generated wavelengths around 850 nm appear at the distance of 6 cm of propagation. Next, OWB occurs at the red-side at the 8 cm and new wavelengths are generated around 1250 nm. During further propagation along the fiber, the group delay trace of the pulse is stretched out and the pulse spectrum flattens on the wings, albeit no new wavelengths appear beyond 20 cm of propagation.
Fig. 8. Broadness of the spectrum along length of the fiber and temporal shape at various length of the propagation with input pulse energy 25 nJ, pulse duration 400 fs, and pump wavelength 1030 nm. The color bar indicates normalized intensity in logarithmic scale.
The performance of spectrum broadening at the 20 cm for various input energy pulses is presented in Fig. 9. In the case of low input pulse energy (below 4 nJ), the SC is narrow and it benefits mainly from SPM. The OWB contributes significantly when the input pulse reaches energy above 7 nJ. For input pulse energy of 25 nJ we expect broadening in the range 840-1340 nm of wavelengths.
Fig. 9. Numerical simulation of evolution of the pulse spectrum for increasing input pulse energy: (a) supercontinuum spectra obtained for various input pulse energies at the 20 cm of propagation along the fiber, (b) intensity distribution in supercontinuum obtained for selected input pulse energies. The color bar indicates normalized intensity in logarithmic scale.
Further increase of SC bandwidth can be expected if we increase pulse peak power or increase nonlinear coefficient of the fiber by means of reduction of core diameter. However, in the last case we lose coupling efficiency and therefore decrease input pulse energy when coupling with standard single mode fiber in an all-fiber system is used. Hence, we conclude that 25 nJ of input pulse energy is the limit that can be obtained with currently commercially available low-cost femtosecond fiber lasers with the standard fiber coupling system [47, 48].
Temporal coherence of SG in the analyzed PCF has been investigated by calculating according to Eq. (2) the modulus of the complex degree of first-order coherence to estimate its characteristic [49]:
5. Measurement of supercontinuum generation
SG in the PCF with the carbon tetrachloride core was verified experimentally in the setup shown in Fig. 10. As a pump source we used a femtosecond fiber laser (Menlo, BlueCut) emitting 400 fs pulses with the central wavelength of 1.03 µm and 10 MHz repetition rate. The pump beam was coupled with microscope objective MO1 into the cleaved end faced of fiber. The second end facet of the fiber with collapsed air holes in the cladding was embedded into the reservoir covering carbon tetrachloride. Carbon tetrachloride evaporates at the ambient temperature. In order to avoid lack of the liquid at the input end of the fiber, the reservoir was connected to microfluidic pump system to maintain liquid in the core during the measurement. During the experiment, a microfluidic pump system was set at ΔP = 200 kPa. The output beam was collected with a microscope objective MO2 and directed into a large core multimode fiber coupled to a spectrometer. In this setup, two spectrometers for ranges 0.4 -1.1 µm and 0.9 - 1.7 µm were used. The length of tested fiber was 20 cm. This length ensures optimum broadening of the spectra as it was confirmed in the previous section by our numerical simulations.
Fig. 10. Schematic of experimental setup used for supercontinuum generation in tetrachloride infiltrated hollow core fiber.
The microscope objective MO1 generates a 16 µm diameter spot at its focus, which is larger than the diameter of core. This limits the coupling efficiency into the fiber to 56%. On the other hand low numerical aperture of the input microscope objective allow to excite selectively the fundamental mode. The single mode operation of the tested fiber was verified for low input energy pulses. We measured a far-field image of the output beam with linear CCD camera. Beam intensity distribution was fitted with the Gaussian profile as shown in Fig. 11. We have obtained a very good match between both profiles. It confirms a single mode excitation of the fiber.
Fig. 11. Far-field image of output beam from the tested fiber (a), a cross-section of the output beam fitted with Gaussian profile (b).
The experimental results of SG are presented in Fig. 12. The spectral broadening for 4nJ and 25nJ input pulses was recorded. These energies correspond to the average powers of 4 and 25 mW, respectively. The broadening covers a wavelength range 850 - 1250 nm for the 25 nJ incident pulse energy that corresponds to 62.5 kW of peak power. The overall agreement between simulation and the experiment is remarkably good. It confirms the dominant role of single mode regime and all-normal dispersion features of observed SC dynamics.
Fig. 12. Experimental results of supercontinuum generation in PCF with carbon tetrachloride core pumped with 400 fs pulses for low energy of 4 nJ (a) and high energy of 25 nJ (b) pulses with central wavelength of 1030 nm. Simulation results are provided for reference.
During supercontinuum generation we observed some fluctuation and reduction of supercontinuum spectral width over time. We suppose that this phenomenon is related to pulse coupling stability into the fiber in the microfluidic reservoir resulting from the flow of tetrachloride constantly pumped into the system by a microfluidic pump (Fig. 10). It is not to related to damage threshold of the fiber infiltrated with carbon tetrachloride. The input end of the fiber is immersed in liquid in the microfluidic reservoir (Fig. 5). It allows to distribute heat generated at the beam focused at the fiber facet. Previously SG in volume samples of carbon tetrachloride was reported when pumped with 33 fs pulses with energy of 1µJ at 810 nm, which corresponds to 27 MW of peak power [50]. Pump pulse energy, used in our experiment was 3 orders of magnitude lower, which confirms stability of carbon tetrachloride in our system. Recorded supercontinuum spectrum is relatively broad for a moderately pumped all-normal dispersion fiber. However, we do not take advantage from broad transmission window of carbon tetrachloride, which covers range from the visible 0.5 µm to around 11 µm in the mid-infrared [18]. To increase spectral coverage of generated supercontinuum, a fiber with higher nonlinear coefficient should be considered and a pump source with higher peak power and wavelength optimized to fiber dispersion characteristics should be used. In case of considered fiber structure, we can still increase the bandwidth of supercontinuum when a pump laser with central wavelength of 1550 nm is used. Dispersion of developed fiber is relatively large – 85 ps/km/nm at a wavelength of 1030 nm. It limits efficiency of SC in the currently investigated setup. Normal dispersion at the wavelength of 1550 nm in the developed fiber is much smaller -10 ps/km/nm, moreover it is flatter. This type of dispersion characteristics favors broadening of spectra when pumped with short pulses.
Supercontinuum spectra, shown in Fig. 12, have a roughly -30 dB noise floor, which can be considered reasonable for a measurement performed with a compact, Czerny-Turner CCD-based spectrometer. The measured spectrum has a notable structure with almost 10 dB dynamics. This structure does not depend significantly on spectrometer integration time. We assign this to very limited contribution of modulation instability to the spectral formation, which would otherwise flatten out the spectrum as expected for a noise-driven supercontinuum. The developed tetrachloride-filled fiber did not have any intentional birefringence and possible polarization effects can be reasonably related to the observed spectral structure, which is consistent with previous studies reported by other groups either in all-normal dispersion fibers [51] or in fibers with a zero-dispersion wavelength [52]. In particular polarization mode instability can be responsible significantly for increase of noise in the generated spectra. To reduce noise, shorter pump pulses or birefringent fibers should be used [53].
Recently SG modeling results for silica-based PCF with similar all-normal dispersion characteristics (up to 1.8 µm) and comparable nonlinear coefficient and effective mode area (γ=3.5 W-1km-1 and Aeff=29.9 µm2, respectively) was reported by Rao at al. [54]. The authors shown that using 125 fs pump pulses with central wavelength of 1550 nm and the peak power of 9 kW a low-noise ANDi SC within all-normal dispersion range in 1.35–1.8 can be obtained. These results indicate a potential for further increase of SC generation efficiency of our proposed liquid core fiber, if pump wavelength is shifted form 1030 nm to 1550 nm to reduce absolute value of dispersion at the pump wavelength.
The observed dynamic of supercontinuum spectra growth indicates self-phase modulation mechanism for low energy pulses and further contribution of OWB and four wave mixing phenomena for high energy pulses, as predicted in simulations presented in the previous section. The further broadening of spectra is limited in this case by nonlinear coefficient of the fiber and its dispersion characteristics. According to simulation we do not expect significant increase of SC range when peak power delivered by femtosecond source is increased. Increase of SC bandwidth requires reduction of effective mode area and modification of photonic cladding. However, in this case a trade-off between coupling efficiency and the fiber nonlinear coefficient in case of the all-fiber systems can be expected.
The main motivation of this research was to investigate feasibility of development of an all-fiber system integrating a liquid core fiber and standard single mode fiber, but we used only free space coupling system in the experiment. Development of an all-fiber system composed of a hollow core fiber infiltrated with carbon tetrachloride and standard single mode fibers is challenging. Carbon tetrachloride is very volatile and fusion splicing, as well as direct mechanical interconnection of liquid core fiber with standard single mode fiber are still open issues. In the system with the microfluidic reservoir also a fiber with reduced core diameter can be used. This way high coupling efficiency would be maintained and the nonlinear coefficient in the fiber can be further increased. However, the system for SG would not all-fiber or compact anymore in this case.
Modelling and experimental results shows that the investigated liquid-filled fiber structure has the potential for coherent, pulse preserving, supercontinuum generation in all-fiber system when femtosecond laser pumping is applied. However, further analysis of coherence properties, e.g., using Michelson interferometry, for the considered liquid-core fiber should be performed to verify relations between coherence and the dispersion, as well as birefringence induced effects. It is known that coherence degradation and an increase of noise in all-normal PCFs can occur due to Raman scattering and polarization induced beating [55,56].
6. Conclusion
An all-normal dispersion supercontinuum generation in a large effective mode area photonic crystal fiber with a core infiltrated with carbon tetrachloride was investigated. We have designed and developed a silica glass fiber with low all-normal dispersion that varies from -150 to 0 ps/nm/km in the wavelength range 0.8 - 1.7 µm. The fiber has a hollow core with the diameter of 9.8 µm and photonic cladding composed of 5 rings of air holes with the diameter of 3.7 µm, ordered in hexagonal lattice with the lattice constant 4.45 µm. After selectively filling of the core with carbon tetrachloride, the fiber has a large effective mode area of 42.2 µm2 and large nonlinear coefficient of 22.1 1/W/km at a pump wavelength of 1030 nm. Due to its large mode area, the fiber can be efficiently coupled with all-fiber femtosecond lasers. The developed fiber can guide two modes, the LP01 and the LP11. We showed that the fundamental mode of the fiber can be selectively excited. We verified experimentally a generation of the flat all-normal dispersion supercontinuum in the range of 850 - 1250 nm using off-the-shelf 1030 nm ytterbium-doped fiber laser with 400 fs and 25 nJ input pulses. The nonlinear dynamic of SG and the measured dispersion characteristics indicate clearly that our system has a potential for coherent SG in a large-mode-area nonlinear fiber structure.
Funding
Fundacja na rzecz Nauki Polskiej (FNP) (TEAM TECH/2016-1/1); National Foundation for Science and Technology Development (NAFOSTED) (103.03-2014.62); Narodowe Centrum Nauki (NCN) (UMO-2016/21/B/ST7/02249, UMO-2016/21/M/ST2/00261).
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