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Selective filling of photonic crystal fibers with different media enables a plethora of possibilities in linear and nonlinear optics. Using two-photon direct-laser writing we demonstrate full flexibility of individual closing of holes and subsequent filling of photonic crystal fibers with highly nonlinear liquids. We experimentally demonstrate solitonic supercontinuum generation over 600nm bandwidth using a compact femtosecond oscillator as pump source. Encapsulating our fibers at the ends we realize a compact ultrafast nonlinear optofluidic device. Our work is fundamentally important to the field of nonlinear optics as it provides a new platform for investigations of spatio-temporal nonlinear effects and underpins new applications in sensing and communications. Selective filling of different linear and nonlinear liquids, metals, gases, gain media, and liquid crystals into photonic crystal fibers will be the basis of new reconfigurable and versatile optical fiber devices with unprecedented performance. Control over both temporal and spatial dispersion as well as linear and nonlinear coupling will lead to the generation of spatial-temporal solitons, so-called optical bullets.
© 2010 Optical Society of America
1. Introduction
Since their first appearance, photonic crystal fibers (PCF) [1–3] have entered nearly all fields of optics. They allow for tailoring the temporal and spatial dispersion of propagating light, and in combination with nonlinear effects have led to unprecedented broad supercontinua. Their nonlinear optical properties are limited by the Kerr effect in glass and fused silica which they consist of. Non-silica fibers have been developed, such as polymer-based [4] or chalcogenide-based fibers [5], which offer striking possibilities such as an extremely high nonlinearity, but are limited in functionality and flexibility. In a different approach, first attempts have been carried out to fill the photonic structure of silica PCFs with functional media to broaden the range of their applicability even further. Up to now PCFs were filled with metals [6, 7], gases [8], semiconductors [9], liquid crystals [10], and also with different liquids [11, 12], entering the new interdisciplinary field of optofluidics, which marries microfluidics with photonics [13, 14]. Example for a complete fluid-filled fiber is an ARROW-fiber presented by Fuerbach et al. [15] or by Larsen et al. [10], where shifting of the band gap due to a change of temperature was demonstrated.
The formation of spatial solitons due to a slow thermal nonlinearity has been reported in a PCF that was completely filled with fishoil [16]. But as mentioned by the authors of [17] it is not possible in this case to engineer suitable spatial coupling properties in the anomalous dispersion regime which is crucial for the formation of spatio-temporal solitons.
Partially filled PCF have also been fabricated by a number of authors. Kuhlmey et al. reported a single strand filled with a liquid, which was applied to sensing [18]. A common technique to implement this structure is to collapse the surrounding holes by the use of an electric arc [19] and fill the remaining core with the desired liquid. This fabrication method was used by Bethge et al. [20] and Bozolan et al. [21] to generate a supercontinuum in water with very high pump powers.
All these filled devices were limited by the fabrication process resulting in either the entire structure [10, 15, 17] or simple patterns consisting of a single connected area being filled [16, 18, 20]. Thus also the applicability of such devices is limited.
Here in this paper we demonstrate a novel and versatile optofluidic device with a high ultra-fast nonlinearity and a large degree of freedom for tailoring their optical properties. The key idea is summarized schematically in Fig. 1; we fill single strands or arbitrary patterns of a PCF selectively with the desired liquid, which then act as linear or nonlinear optofluidic waveguide embedded in the PCF. With this configuration it is possible to achieve a higher contrast between the refractive index of the core and the effective refractive index of the surrounding photonic structure, compared to a completely filled structure or waveguides written in bulk glass [22–24]. This additional freedom allows tailoring of the dispersion properties of our ultrafast nonlinear optofluidic device (UNOF) over a wide range which is of fundamental importance for the temporal control of optical pulses and crucial to the formation of supercontinuum.
Fig. 1 Schematic drawing of the ultrafast nonlinear optofluidic device. Checkerboard pattern of liquid strands embedded in a PCF acting as nonlinear waveguides. The red light is coupled in and after several centimeters of propagation spectrally broadened light leaves each liquid waveguide.
We utilize the ultrafast Kerr-nonlinearity of liquids such as carbon disulfide (CS2), toluene, carbon tetrachloride (CCl4), or chloroform. Apart from their high nonlinear refractive index n2 which is in CS2 up to 200 times higher [25] than that of fused silica, these liquids are transparent in the visible and the near infrared wavelength regime [26]. Because of the toxicity of CS2 we have chosen toluene and CCl4 for our experiment, which enhances the nonlinearity by a factor of 60 and 6, respectively [27].
Our selective filling method uses the two-dimensional structure of a PCF as a scaffold for complex patterns. For instance, filling a checkerboard pattern or limited areas of the PCF with the liquid yields an ultrafast nonlinear multi-waveguide device, acting as two-dimensional discrete system embedded into a single PCF which has never been shown before. Furthermore, this concept also allows us to tailor the properties of this discrete nonlinear system to control the pulse propagation in the temporal as well as in the spatial regime, both in the linear as well as in the nonlinear domain. With this advantage the experimental demonstration of spatio-temporal solitons should become feasible [17, 28].
2. Fabrication
Commercially available PCFs are used for our UNOF device as carrier for the liquid strands. In order to selectively fill single strands of the photonic structure with a liquid, the strands which should stay empty have to be blocked individually to prevent the inflow of the liquid. To do so we use a two-photon direct laser writing technique [29] that provides a very precise control of the local polymerization of an appropriate photoresist in three dimensions. To block the single strands we use the photoresist SU-8 from MicroChem [30] because it is widely used and chemically very stable after the light exposure due to its strong cross linking. Single photon polymerization using a UV laser does not provide the desired selectivity due to the lack of suitable depth resolution.
In a first step, the cleaved fiber end of a suitable PCF is completely covered with SU-8. The holes which should be blocked are then illuminated one by one with focused light of a mode-locked Ti:Sapphire femtosecond laser oscillator. Due to two-photon absorption the photoresist starts to polymerize. This procedure is schematically shown in Fig 2(a). The last step in the structuring process is the usual hardbake and developing, where the unexposed photoresist is removed. Figures 2(b)–2(d) shows several examples of selectively closed holes of a PCF.
Fig. 2 (a), Scheme of the direct laser writing technique applied on the photonic structure of a PCF. (b), Name of our institute written in a NL-2.3-790 with a hole diameter of 2.5μm and a hole-to-hole distance of 2.6μm. (c), Checkerboard pattern as the most complex structure also in a NL-2.3-790. (d), Scanning electron microscope picture of the checkerboard pattern, which proves the good sealing of the strands by the cured polymer. (e), Schematic cross section of the filling setup: the structured fiber end is held in the liquid reservoir. The unblocked holes are filled by the capillary force whereas the blocked strands stay unfilled. (f), Three toluene filled rings embedded in a LMA-8 with a hole diameter of 2.7μm and a hole-to-hole distance of 5.6μm.
In order to fill the fiber with liquids we use capillary forces: The structured end of the fiber is kept in a reservoir of the desired liquid [Fig. 2(e)] so that the liquid penetrates the unblocked strands and flows along the complete length of the fiber over several centimeters. By observation of the opposite end of the fiber, one can clearly see the liquid inside the fiber strand as it is shown in Fig. 2(f).
After filling the fiber, optionally both ends can be closed by UV glue in a further step to encapsulate the liquid. Hence an easy-to-handle and compact optofluidic fiber device is achieved [Fig. 3(a)]. A disadvantage of this additional step is the fact that the coupling in and out of fluid waveguides suffers from the rougher surface at the fiber ends. Also the damage threshold is decreased due to the photoresist layers. Therefore, we used the encapsulated devices only for investigating the linear propagation properties. With the direct laser writing technique we are not limited to a single fiber type. By changing the geometry of the fiber the optical properties of our UNOF device can change dramatically, whereas the fabrication process is still the same. In contrast to [31] this is also valid for fibers with a ratio of hole diameter to hole period close to one.
Fig. 3 (a), Simple setup of our optofluidic device, with both ends closed by UV glue after liquid filling. (b), Mode image of the single strand structure in a NL-2.3-790 fiber filled with CCl4 illuminated with a cw HeNe-Laser at 633nm wavelength. It shows clearly that the light propagates in the fundamental mode. (c), Mode image of the three ring structure [Fig. 2(f)] encapsulated in a LMA-8 fiber filled with toluene and illuminated at 1064nm. The light in each waveguide is propagating in the LP11 mode. Strong coupling occurs from strand to strand within each ring and weaker coupling between the rings themselves. Apart from that, all liquid strands indeed act as waveguides. For (b) and (c) the structure of the underlying photonic crystal fiber is schematically superimposed.
3. Linear propagation
We first investigate the linear propagation properties of our UNOF device. The setup is shown in Fig. 3(a). The simplest pattern is the single strand structure. The mode image of this structure embedded in a PCF filled with CCl4 is given in Fig. 3(b) which shows the fundamental mode [32]. The fiber chosen for this example, the NL-2.3-790, has a hole-to-hole distance of Λ = 2.6 μm and a hole diameter of d = 2.5 μm [33].
In a UNOF fiber filled with CCl4 or toluene the guiding mechanism is total internal reflection because the refractive index of CCl44 (n = 1.4503@1.03 μm [34]) and toluene (n = 1.4816@1.03 μm [35]) is slightly higher than that of fused silica (n = 1.4497@1.03μm). The filled liquid strand acts as the core and the surrounding photonic structure as the cladding.
The same mechanism is valid for each fluid waveguide in a more complex structure. The mode image in Fig. 3(c) shows the end of an LMA-8 fiber with a toluene filled three-ring structure. In each fluid waveguide, the light is propagating in a higher order mode - this is consistent with the calculated normalized frequency V = 2.47 [36], which lies above the single mode criteria. The LMA-8 fiber used for this example has a hole-to-hole distance of Λ = 5.6μm and a hole diameter of d = 2.7 μm [37].
If the UNOF contains more than one liquid-filled strand, it can act as a multi-waveguide array and coupling between fluid waveguides occurs. The coupling depends on the distance between two adjacent waveguides and the refractive index difference between the strands and the surrounding. For the LMA-8 UNOF filled with toluene, the coupling length between two adjacent waveguides can be estimated for the fundamental mode by the supermode method to be Lc = 9.8mm [38, 39]. Thus in the three ring structure filled with toluene the waveguides are mutually coupled [Fig. 3(c)]. By changing the hole-to-hole distance Λ, by variation of the hole diameter d of the used PCF, or by changing the liquid refractive index, the coupling of the waveguides in the UNOF device can be adjusted to match the requirements for a certain propagation characteristic.
By changing the filled strand medium or the geometry of the fiber, the dispersion properties of the UNOF device can be tailored. If an additional temperature change or mixtures of different liquids are allowed, another degree of freedom is added to engineer the dispersion properties almost continuously. Just by replacing the liquid in a single filled strand of the NL-2.3-790 fiber one can shift the zero-dispersion wavelength (ZDW) from 790nm for chloroform to 1270nm for CS2 over almost 500nm (see also Fig. 4c for the dispersion of a CCl4 filled UNOF). Apart from the linear propagation regime, this high degree of freedom in dispersion engineering is crucial when entering the nonlinear propagation domain, as it is well known [40].
Fig. 4 (a), Spectral evolution for different input powers of a 26cm long fiber with a single strand filled with CCl4 and with a core diameter of 2.5μm. The pump power was increased from 10mW to 100mW, while spectral broadening could be observed. For the highest incoupled power of 100mW a 600nm wide spectrum could be obtained. Because the fiber is pumped in the anomalous dispersion regime, solitons can form. The red shifting soliton in the near infrared wavelength regime as well as the corresponding non-solitonic radiation in the blue wavelength regime [44] could be measured. (b), Comparison between measurement and simulation of a 19cm long fiber with a single strand filled with CCl4 with a core diameter of 2.5μm and pumped with an input power of 330mW. (c), Comparison of different core media. As core medium fused silica and CCl4 in a 19cm long fiber were used. The core size for both fibers was 2.5μm and the incoupled power was 330mW. Additionally the dispersion curve for both fibers is also shown. Here one can see that the pump wavelength of 1030nm lies in the anomalous dispersion regime.
4. Nonlinear propagation
Filling our devices with highly nonlinear liquids and managing the dispersion, we demonstrate nonlinear effects including self-phase modulation (SPM), soliton formation and fission [40,41] resulting in a octave-wide spectral broadening.
We pump our UNOF device (the single strand structure embedded in a NL-2.3-790 filled with CCl4) with a Yb:KGW femtosecond oscillator [42] at 44MHz which provides 210fs long pulses at a center wavelength of 1030nm. The propagation takes place in the fundamental mode [Fig. 3(b)]. Numerical simulations [Fig. 4(c)] indicate that the ZDW of our device is at 900nm with a group velocity dispersion parameter at 1030nm of D = 51ps/km/nm; hence the pump wavelength of 1030nm lies in the anomalous dispersion regime, which allows soliton formation.
Figure 4(a) shows the spectral evolution in a 26cm long filled single strand for increasing input powers. For low input powers, spectral broadening occurs due to SPM. For higher input powers soliton formation and the Raman-shifting of solitons become clearly observable [40, 41]. For an input power of 100mW a spectral broadening of 600nm is obtained, covering the spectral region from 700nm to 1300nm. With an overall throughput of 10–15% including coupling-, confinement- and material losses, the corresponding peak power inside the fiber with less than 2kW is extremely low compared to previous results in optofluidic supercontinuum generation experiments, where peak powers of MW were required [20, 21, 43]. In Fig. 4(b) a spectrum of a 19cm long UNOF is shown revealing the red-shifting soliton as well as the non-solitonic radiation in the blue [40, 44]. The input power is 331mW with a throughput of about 6%.
CCl4 is transparent in the visible as well as in the infrared and has a high nonlinear refractive index of n2 = 15 · 10−20 m2/W [25], six times that of fused silica. The underlying process for this high Kerr-nonlinearity is the molecular reorientation [45, 46], which takes place within several hundreds of femtoseconds, in contrast to the almost instantaneous nonlinearity of fused silica [47, 48]. Single strands filled with slowly responding liquids can also give rise to new propagation effects, such as the existence of so-called linearons [49].
By using toluene with a higher nonlinear refractive index of n2 = 170 · 10−20 m2/W [25] the nonlinearity of our device could be increased even further. In Fig. 4(c) we show the spectrum of an ordinary PCF with a glass core. The potential of our UNOF fiber is demonstrated in comparison by replacing the core medium with CCl4, which enhances the spectral broadening substantially.
5. Simulation
The dispersion properties of the UNOF device can be simulated by solving its eigenvalue equation [47], and the effective refractive index of the photonic structure is calculated numerically by using [50]. The propagation constant β combined with the nonlinearity γ and response function R(T) as a function of time allows us to simulate the system by numerically solving the generalized nonlinear Schrödinger equation (GNLSE) [40, 46]:
This is carried out using a split-step Fourier-method, where A is the envelope of the electric field of the pulse, βk is the kth derivative of the propagation constant β(ω) with respect to the frequency ω. Self-steepening and optical shocks are governed by τshock. γ is the nonlinearity of the device [47] which is proportional to the nonlinear refractive index n2. For our case shown in Fig. 4(b) γ is about 370W−1km−1.R(T) describes the delayed response function of the medium [51] which for the liquid is mainly given by the molecular reorientation. The vibrational molecular Raman response and the electronic contribution are also included. Figure 4(b) demonstrates the excellent agreement of measurement and simulation, which reproduces correctly the main features of the spectrum. The mismatch of the wavelength of the non-solitonic radiation arises from the uncertainty of the given refractive index of CCl4 [34] and of the effective index calculated by [50].
6. Conclusion
In conclusion, we have presented the novel fabrication method and the application of a new versatile optofluidic device with a high ultrafast nonlinearity. We have shown that the selective closing with direct laser writing and selective filling of a PCF opens a new field with complete control of the linear and nonlinear optical properties. Our approach can be extended to selectively closed PCF filled with different media such as metals, semiconductors, gasses, gain media, liquid crystals, etc. Our concept is as well applicable to photonic crystals and other photonic structures.
As examples for the versatility of our ultrafast nonlinear optofluidic devices we have demonstrated propagation in a complex shaped liquid waveguide array in a toluene filled LMA-8 fiber with a high inter-waveguide coupling, as well as nonlinear propagation in a single strand structure. We were able to manage the dispersion to demonstrate ultrafast soliton formation and fission, resulting in a 600nm wide spectral broadening with low peak powers enabled by the remarkable high nonlinearity of the liquids.
Our UNOF device allows to tailor the dispersion, spatial coupling, and spatial arrangement of a waveguide array, as well as the optical nonlinearity in a two dimensional discrete system. Such ultrafast nonlinear optofluidic devices might be at heart of future terabit photonic networks for example for novel switching, multiplexing, or mixing devices. In future our device should provide us the possibility to observe ultrafast nonlinear spatio-temporal solitons (optical bullets) in a discrete two dimensional waveguide system due to the complete control of the optical properties.
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