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Supercontinuum generation in a water-filled photonic crystal fiber is reported. By only filling the central hollow core of this fiber with water, the fiber properties are changed such that the air cladding provides broadband guiding. Using a pump wavelength of 1200 nm and few-microjoule pump pulses, the generation of supercontinua with two-octave spectral coverage from 410 to 1640 nm is experimentally demonstrated. Numerical simulations confirm these results, revealing a transition from a soliton-induced mechanism to self-phase modulation dominated spectral broadening with increasing pump power. Compared to supercontinua generated in glass core photonic fibers, the liquid core supercontinua show a higher degree of coherence, and the larger mode field area and the higher damage threshold of the water core enable significantly higher pulse energies of the white light pulses, ranging up to 0.39 μ J.
©2010 Optical Society of America
1. Introduction
The nonlinear optical conversion of short laser pulses into supercontinua has a nearly 40-year tradition, enabling the generation of coherent white-light laser beams encompassing one to several octaves of bandwidth [1,2]. Depending on laser peak power, various geometries have been exploited, including bulk solid or liquid media [3–5], gas-filled hollow-fibers [6], filaments [7], nanowires [8], tapers [9], and photonic crystal fibers (PCFs) [10–12]. Applications range from spectroscopy over pulse compression to linear optical methods. For many of these applications, guided fiber geometries are strongly favored. Confinement in a single-mode fiber prevents a nonlinearly induced spatial break-up of the beam [14], thereby enabling more efficient exploitation of nonlinear optical effects for spectral broadening. In particular, supercontinuum generation in solid-core PCFs found extraordinary attention owing both to the surprising soli-ton dynamics in the anomalous dispersion region [15] and to the large range of applications (for a review, see [12]). Soliton-induced SC generation has proven extremely successful for obtaining bandwidths beyond the optical octave, enabling the generation of spectra that may encompass up to 4 octaves [16, 17]. Despite the large progress, a weakness of this concept is its lack of scalability and its dependence on oscillator pulse energies. Scaling of pulse energies into the microjoule regime is limited by the small fiber diameter and optical damage of the core material. Since soliton-induced SC generation relies on anomalous dispersion above the pump wavelength, it is intrinsically restricted to geometries with strong waveguide dispersion when Ti:sapphire lasers are used as pump sources. Dielectric hollow waveguides filled with a gas can not be used for this purpose, because anomalous dispersion can only be achieved for relatively small diameters in the range of 10 to 80μm, for which the loss in simple hollow capillaries is prohibitively high. Bandgap guiding in hollow-core PCFs, in contrast, allows for much lower losses at the same diameter. Filled with a suitable gas, hollow-core PCFs exhibit anomalous dispersion in the optical range but their intrinsically narrow transmission bandwidth determined by the bandgaps impedes their use for SC generation. In the following, we apply an alternative approach in which a hollow-core PCF is filled with a liquid. In this case the refractive index in the core is higher than in the cladding, and excellent guiding is possible, ensured by a high air filling factor in the air-glass cladding. Guiding in the liquid-filled hollow fiber is therefore similar to step-index fibers. Using such a waveguide, we exploit the advantage of pumping in the anomalous dispersion regime at 1.2 μ m, which is shown to enable a significantly enhanced supercontinuum bandwidth at pulse energies in the microjoule range. A similar set-up with a water-filled PCF for single-octave supercontinuum generation has already been employed by Bozolan et al. [18], using a pump wavelength of 980 nm near the zero-dispersion wavelength.
Numerical simulations confirm that despite of a higher loss in water, spectral broadening arises due to the emission of fundamental solitons formed from the fission of the input pulse for small pump intensities. This mechanism is in close analogy to SC generation in solid-core PCFs. Interestingly, at elevated pump intensities approaching 50 TW/cm2, supercontinua exhibit a high coherence, and the temporal shapes do not show splitting of the pump into fundamental solitons as it was typically found in supercontinuum generation in solid-core PCFs. The large broadening here arises due to self-phase modulation combined with four-wave mixing. This is explained by the fact that the fission length is larger than the length where spectral broadening by self-phase modulation exceeds one octave.
2. Linear optical properties of the water-filled photonic crystal fiber
In the following we use a commercially available hollow core photonic crystal fiber (PCF, [19]). This fiber has a 7-cell core with 9.5 μ m inner diameter and has been designed to support transmission in its gas filled core due to the existence of bandgaps in a relatively narrow band from ≈ 790 to 870 nm. Due to the strong third-order dispersion of this guiding concept, the fiber exhibits zero dispersion at midband, i.e., at ≈ 830nm. Filling the central core of the fiber with water (nW = 1.33) the linear transmission properties of the fiber change dramatically, with band gap effects and narrow transmission bands essentially vanishing. The guiding mechanism of light is now similar to that in a step-index fiber because the refractive index in the core is larger than that in the cladding.
For the theoretical description of the linear waveguide properties of this water-filled PCF, we used the effective-cladding model which has been applied to explain the single-mode behavior [20] and to calculate the dispersion of solid-core PCFs [21]. In this method the effective refractive index neff(ω) of the cladding is approximated by that of the fundamental space-filling mode of the photonic crystal using silica-air boundary conditions and periodicity conditions at the boundary of an elementary cell. Using neff(ω) as the effective refractive index of the cladding and the refractive index nW ω of water for the core, one solves the characteristic equation for the propagation constant β ω of the approximate step-index fiber. Dispersion of fused silica and water are calculated using the corresponding Sellmeier equations with parameters given in [22]. The loss parameter of water is included in the model using measured values as reported in [23]. The red curve of Fig. 1 shows the group velocity dispersion deduced from this model for a diameter of the hollow core of 9.5 μ m, a pitch of 2.75μ m, and air hole diameters of 2.68μ m. As can be seen, the zero-dispersion wavelength is at 985 nm, and the group-velocity dispersion is anomalous above this wavelength. In the considered geometry, the waveguide contribution to dispersion is small in comparison with the dispersion of bulk water, and the red curve in Fig. 1 is almost identical to the dispersion curve of bulk water. The loss of the waveguide is also determined by the loss of bulk water shown in the blue curve of Fig. 1. Water has a strong absorption at wavelengths larger than 1400 nm but a small loss deep into the UV for the considered propagation lengths. The water-filled PCF therefore offers a two-octave wide transmission band with dispersion ranging from +50 to -50fs2/mm.
Fig. 1. Group velocity dispersion (red solid curve) and loss (blue dashed curve) of a water-filled HC-PCF with a hollow core diameter of 9.5 μ m.
3. Simulation of nonlinear propagation
Fig. 2. Evolution of spectrum I (z,λ) (a) and of temporal shape I (z,t) (b) with propagation for 40 fs, 2 TW/cm2 pulses with central wavelength at 1200 nm and waveguide parameters as in Fig. 1.
For the numerical simulation of the nonlinear pulse propagation in the waveguide, we have used the so-called forward Maxwell equation [15, 21], which does not use the slowly-varying envelope approximation and is written directly in terms of the electric field E(z,t). This approach allows a correct description of ultrashort temporal features of the electric field or, correspondingly, extremely broad spectra. The group velocity dispersion is included to all orders, and third harmonic generation as well as self-steepening are included intrinsically. The equation is written as
Fig. 3. Spectrum (a) and temporal shape (b) after 1.6 cm propagation. The parameters are the same as in Fig. 2.
Fig. 4. Evolution of spectrum I (z,λ) (a) and temporal shape I (z,t) (b) with propagation for 40 fs, 50 TW/cm2 pulses with central wavelength at 1200 nm and waveguide parameters as in Fig. 1.
Fig. 5. Spectrum (a) and temporal shape (b) after 0.46 mm for 40 fs, 50 TW/cm2 pulses with central wavelength at 1200 nm.
where E(z,ω) is the Fourier transform of E(z,t), z the propagation coordinate, β ω the wavenumber of the waveguide, and αω the loss coefficient. ng is the effective group refractive index, which determines the velocity of the moving coordinate frame. PNL(z,ω) is the Fourier transform of the time-dependent nonlinear polarization PNL(z,t), which includes an instantaneous contribution due to the electronic hyperpolarizability and a second non-instantaneous contribution
Fig. 6. Spectra (a),(c),(e) and corresponding temporal shapes (b),(d),(f) for propagation distances of 8 cm (a),(b), 2.4 cm (c),(d), and 0.24 cm (e),(f). The input 40 fs pulses at 1200 nm have a peak intensity of 50 TW/cm2. The fiber geometry corresponds to the experimental cross section. In (c) the incoherence 1-g(λ) is illustrated by the green curve.
Here χ3 = (4/3)cε0 nW n2 is the third-order hyperpolarizability, and n2 is the nonlinear refractive index. κslow determines the fraction of the retarded nonlinear response in water, and τslow is the decay time of the retarded response. We have used the parameters n2 = 1.5×10−4 cm2/TW [24], τslow = 120 fs, and κslow = 0.25 [25]. Although the considered fiber supports a large number of modes, we neglect their influence since the input radiation was coupled almost exclusively to the fundamental mode, and nonlinear energy transfer to higher-order modes can be neglected for the considered nonlinearities and propagation lengths.
Fig. 7. Spectrum (red thick curve) and incoherence function (green thin curve) for the model without the retarded nonlinearity contribution (κslow = 0). The input 40-fs pulses at 1200 nm have a peak intensity of 50 TW/cm2, the propagation distance is 2.4 cm.
Using the linear optical properties of the waveguide from Sec. 2 and the non-instantaneous nonlinear response function of water, we solve the propagation equation [Eq. (1)] and simulate pulse propagation and supercontinuum generation for 40 fs pulses at 1200 nm. We first assume a low intensity of 2 TW/cm2 and then repeat the simulation at a higher value of 50 TW/cm2. The spectral and temporal evolution for the former case are presented in Fig. 2. The evolution of the temporal shape in Fig. 2(b) confirms fission of the input pulse into three fundamental solitons after a propagation length of about 0.6 cm resulting in the formation of a supercontinuum. The spectral broadening process is displayed in Fig. 2(a). For clarity, Fig. 3 shows a snapshot after 1.6 cm propagation. Analogous to the case of a solid-core PCF and at comparable intensities, therefore, supercontinuum generation in the water-filled PCFs is related to soliton dynamics and appears due to the emission of non-solitonic radiation at different frequency intervals [15, 21]. The contrasting case of nonlinear pulse propagation at higher intensities of 50 TW/cm2 is shown in Fig. 4. Again, a snapshot of the temporal and spectral shape yet after only 0.46 mm propagation length is shown separately in Fig. 5. In terms of intensities, this situation is now much closer to the experiment as described in Sec. 5. In this case, the spectrum already reaches two-octave coverage after only 0.6 mm propagation, see Fig. 4(a). In the snapshot in Fig. 5(a) the spectrum spans from 390 to 1900 nm wavelength. However, in contrast to low intensities, no indications for fission of the pulse can be seen at this distance. Instead, the temporal shape in Fig. 5(b) shows a smooth pulse shape without the spikes characteristic for soliton fission processes. This is a clear indication for dominance of self-phase modulation. This means that the mechanism of supercontinuum generation fundamentally differs for different intensities, even though the pump is within the anomalous dispersion region in both cases.
The prevalence of self-phase modulation at higher intensities can be explained qualitatively by the fact that the length Loct ≈ LNL ω0 / Δω0 at which self-phase modulation leads to a spectral width exceeding one octave is smaller than the fission length Lfission ≈ NLNL. Here the nonlinear length LNL is defined as LNL = (γP0)−1 with the nonlinear coefficient γ, the central frequency and the spectral width of the input pulse ω0 and ω0, respectively, and the soliton number N = √LD/LNL, LD = (τ0)2/ ∣β2(ω0) ∣ [26]. In the case of the low-intensity pulse one can estimate N = 5 and LNL = 0.63 mm, ω0/Δω0 ≈ 10. Therefore, the fission length Lfission ≈ 5LNL is smaller than Loct ≈ 10LNL. In this case the mechanism of soliton-induced supercontinuum generation dominates over self-phase modulation. In the high-intensity case we have N = 29 and LNL = 0.025 mm, and the fission length is larger than the length Loct ≈ 10LNL. Therefore spectral broadening is dominated by self-phase modulation. After the pulse has evolved to such broad spectrum, a higher-order soliton can not be formed anymore, and the known effect of soliton fission does not appear due to the influence of loss and higher-order effects. Although soliton dynamics obviously do not play a role here, weak or anomalous dispersion is nevertheless an important requirement for the spectral broadening efficiency of the self-phase dominated mechanism. Strong normal dispersion effectively limits the spectral broadening effect due to temporal stretching, and it also limits the decrease of the maximum intensity by dispersive effects.
In Figs. 6(a)–6(f), the spectra and corresponding temporal shapes of the high-intensity pulses are presented for larger propagation lengths. Upon further propagation, the pulse envelope continues to smoothen and extends under the action of the group velocity dispersion to several picoseconds. At a propagation distance of 0.24 cm, the theoretical spectra show reasonable agreement with the experimental ones in Sec. 5. In the simulations, water absorption leads to extinction of the spectral components in the range above 1200 nm upon further propagation. It is important to note that in the experiment these components can be guided in the cladding modes of the fiber. Although the field extension into the cladding is insignificant and the cladding does not itself contribute to the spectral broadening, cladding modes can preserve the radiation above 1300 nm which is coupled to them by fiber imperfections. This effect cannot easily be considered in the simulations. Note, however, that the numerically computed spectra are significantly broader than those for bulk water, even if an identical anomalous dispersion is considered (see, e.g., [3]). Focusing a laser tightly to a spot size comparable to the fiber diameter limits the effective interaction zone to a few hundred microns due to diffraction and the maximum obtainable nonlinearity due to the on-set of filamentation.
In Fig. 6(c) the incoherence 1-g(λ) is shown as the green curve. The first-order coherence function g(λ) is defined as
where the average in the numerator is taken over all non-identical pairs of noise realizations a, b, while in the denominator the average is taken over all noise realizations [12]. The quantity g(λ) directly corresponds to the visibility V = g = (Imax - Imin) / (Imax + Imin) measured in interference experiments. Although the input pulse parameters correspond to a high soliton number N = 29 we can observe a high average output coherence of 0.97. Note that in soliton-induced supercontinuum generation the spectrum becomes incoherent if the soliton number is larger than N ≈ 10 [12]. Despite the larger pulse energies and the relatively high soliton number, the coherence properties have therefore improved compared to solid-core PCFs in the nanojoule regime. This improved coherence properties appear because spectral broadening is now caused by self-phase modulation, which, in general, preserves a high coherence. This novel high-intensity regime appears interesting for the generation of highly coherent supercontinua with longer input pulses. In contrast, such conditions are difficult to meet in solid-core PCFs due the requirement of a soliton number N ≤ 10 for maintenance of coherence.
Finally, in order to elucidate the role of the slow component in the nonlinear polarization Eq. (2), Fig. 7 shows simulation results computed with the same input parameters and at identical propagation distance as in Fig. 6, but without the influence of the retarded nonlinearity, i.e., κslow = 0. It can be seen that the spectrum at 2.4 cm is slightly narrower than for the previous case and that the average coherence is roughly the same, i.e., 0.96. Therefore, we do not expect a marked influence of the slow component.
4. Fiber preparation
The major difficulty in using water in a partially air-clad geometry arises from selective filling of the central hollow core of a photonic crystal fiber. Several methods have been discussed for sealing the microchannels in the cladding region lest intruding water corrupt the index contrast required for guiding in these fibers. Martelli et al. [27] suggested splicing of a fiber with single hollow core to selectively seal off the air holes in the cladding. Huang et al. [28] demonstrated the use of an UV curable adhesive for the same purpose. Several publications suggest the use of a fusion splicer for collapsing the cladding part of the microstructure [29,30]. We modified this technique by shifting the electrodes of the fusion splicer approximately 100 μ m in direction of the fiber, i.e., away from its end face, as to avoid a reduction of the core diameter in the collapsed region. This bottleneck effect has previously been found disadvantageous for applications.
In our experiments, we used a standard single-mode-fiber fusion splicer (Fitel type S148S). The device employs a distance between the electrodes of 1.6 mm and allows for current adjustment in the range from 8 to 14 mA. Compared to the parameters given in [30], we used a relatively low current of 9.41 mA at an increased arc exposure time of 550 ms. The fiber was not pulled or otherwise mechanically stressed during the arc exposure. We found that these parameters enable collapsing of the microstructured cladding without significantly reducing the diameter of the central hollow core. We convinced ourselves from the absence of a bottleneck by filling a hollow fiber with water both from the collapsed end and from the far end, and observed identical filling velocities. Figure 8(a) shows a micrograph of the partially collapsed fiber structure as seen from the side. This micrograph indicates a total length of the modified microstructure of about 380 μ m, with the length of the collapsed region being less than 60 μ m. As only the latter prevents index guiding, the resulting loss is minor compared to absorption losses in the water.
Fig. 8. (a) Micrograph of the collapsed fiber as seen from the side. (b) Sketch of the windowed cuvette and the water-filled fiber. Input coupling is from the right. Blue colors indicate water-filled areas, black the aluminum cuvette body, and light gray colors brass fittings that are sealed with the aid of an o-ring. Light is launched into the fiber through a window from the right. The distance between window and collapsed cladding is smaller than the focal length of the lens. No particular measures were taken on the output side on the left.
For a wetting liquid such as water, the horizontally arranged core can be filled making use of capillary forces only, without any need for external pressure. A further problem is the formation of a meniscus at the fiber ends [29], which may act as a focusing lens of variable focal length, changing slowly due to evaporation. To avoid this effect, we used a windowed cuvette, see Fig. 8(b). This cell features drainage holes to prevent the formation of air bubbles. Figure 9 shows a micrograph of the fiber end face, clearly indicating selective filling of only the central hollow core. The fiber tip is located as close as possible to the thin glass window to avoid excessive dispersion on the input coupling side. We use an f = 18 mm lens for launching into the fiber. This set-up enables a launching efficiency of < 30% in the absence of absorption and nonlinear optical effects.
Fig. 9. (a) Photograph of the supercontinuum generated in the liquid core of the water-filled fiber mounted inside the windowed cuvette. Orientation is as in Fig. 8(b). The grating-dispersed supercontinuum has been projected onto a screen behind the set-up. (b) Micrograph of the rear end of the fiber demonstrating that the core is selectively filled with water.
In our experiments we have chosen a length of the water filled fiber of 7.2cm with a gap of 500 mm between front end and window. The meniscus of the rear fiber tip can be easily compensated by a simple lens.
5. Experiments
Fig. 10. Measured spectra of a supercontinuum generated in 7.2 cm of water filled hollow core fiber. (a) Full range on a logarithmic scale. Red colors indicate a background from scattered light, recorded while no light was coupled into the water core. (b) Visible wavelength range on a linear scale.
The experiments are performed with 45 fs laser pulses from an optical parametric amplifier (OPA), pumped by an 800 nm regenerative Ti:sapphire amplifier at a repetition rate of 1 kHz. The OPA was tuned to a center wavelength of 1.2 μ m. The output power of the OPA was attenuated, and the energy per pulse launched into the core mode was 7 μ J, corresponding to an input peak power of ≈ 150MW. In our experiments, we observed a total coupling and transmission efficiency of about 6%, resulting in an output energy of the continuum of 390 nJ. This may appear a rather low value at first sight. However, it surpasses the computed transmission of 1200 nm light in a 7.2 cm long water column by a factor 100, cf. Fig. 1.
Figure 10(a) shows the spectral power density of the generated supercontinuum in a logarithmic plot. The spectrum, measured at -20 dB below peak, covers a bandwidth of 1.0 μ m, ranging from 500 nm to 1.5 μ m. The -30 dBm bandwidth spans a spectral range of ≈ 1.2 μ m, starting at 430 nm and ranging to ≈ 1.6 μ m. We attribute the significantly higher cut-off in the infrared to light that is guided in cladding modes because water absorption should otherwise inhibit supercontinuum generation above approximately 1.2 μ m. For comparison, Fig. 10(a) also shows the background radiation, which is mainly caused by scattered laser light. One can identify the Ti:sapphire laser at 800 nm and the 1.2 μ m signal wave of the OPA.
The supercontinua show the highest spectral power densities in the vicinity of the 1.2 μ m OPA pump. The spectrum exhibits two symmetric maxima at ≈ 1100 and 1350 nm. In addition to the symmetric broadening, a second optical octave at roughly 10 times lower power densities can be seen below 800 nm, see the linear plot in Fig. 10(b). The photograph of the spectrally dispersed supercontinuum in Fig. 9(a) further confirms coverage deep into the blue spectral range. Appearance of this band in the visible is only explainable by solitonic effects, as was discussed in Sec. 3.
6. Discussion and Conclusion
We studied theoretically and experimentally supercontinuum generation in a water-filled PCF with a 9.5 μ m core pumped with μJ femtosecond pulses in the region of anomalous dispersion. Our experiments demonstrate that two-octave broad high power supercontinua can be realized by using 40fs pulses from an OPA at a pump wavelength of 1.2 μ m with a pulse energy of 7 μ J, which is twice as broad as previously reported with a similar set-up [18]. We conducted numerical simulations that show good agreement with the experiments. Our numerical simulations also show that in such a system two-octave spectral broadening comes along with an unexpectedly high degree of coherence. Increasing the pump intensity, a transition from soliton-induced spectral broadening to self-phase modulation induced supercontinuum generation is observed. The latter regime enables the generation of highly coherent spectra, even for elevated pump intensities or for long pulses. Given the much higher resulting output energies of the super-continuum in the range of 400 nJ, the optimized source is highly interesting for applications that require wide spectral coverage with simultaneously high pulse energy or high peak power. One interesting application may lie in the efficient nonlinear optical processes accessible at the megawatt peak powers that are still present after supercontinuum generation. Another interesting application may be digital holography [31], where multi-wavelength contouring can be exploited to increase the depth of field, in particular when more than octave-spanning spectra are available. At the same time, this method demands at least microjoule energies, dictated by the well depth of modern megapixel ccd sensors. Extending the highly efficient supercontinuum generation into the microjoule pulse energy regime, it appears that our optimized source is much better suited for these applications than previous sources.
Acknowledgments
We gratefully acknowledge Ilaria Cacciari from Istituto di Fisica Applicata ‘Nello Carrara’ del Consiglio Nazionale delle Ricerche, Firenze, Italy, for providing detailed calibration information about the Fitel fusion splicer employed in the experiments. We thank Gunnar Schulz for his contribution to designing the windowed cuvette and exploring selective filling procedures. We specifically thank reviewer 2 for helpful suggestions that lead to a clarification of the discussion. We acknowledge financial support from the German Research Foundation (DFG).
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