A photonic crystal fiber (PCF) with a section of one of the holes next to the solid core filled with an index-matched liquid is studied. Liquid filling alters the core geometry, which locally comprises the original silica core, the liquid channel and the silica around it. It is demonstrated that when light reaches the filled section, it periodically and efficiently couples to the liquid, via the excitation of a number of modes of the composite core, with coupling lengths ranging from tens to hundreds of microns. The resulting modal-interference-modulated spectrum shows temperature sensitivity as high as 5.35 nm/°C. The proposed waveguide geometry presents itself as an interesting way to pump and/or to probe liquid media within the fiber, combining advantages usually found separately in liquid-filled hollow-core PCFs (high light-liquid overlap) and in solid-core PCFs (low insertion losses). Therefore, pumping and luminescence guiding with a PCF filled with a Rhodamine solution is also demonstrated.
©2011 Optical Society of America
Photonic crystal fibers (PCFs) are a class of optical fibers that present a periodic microstructure in their cross section, generally consisting of micron-sized cylindrical holes. Among the numerous novel characteristics provided by this structure is the ability to provide efficient interaction between guided light and liquid materials inserted into the holes, which can also be achieved in liquid-filled non-PCF microstructured fibers [1–17]. Both these fiber types have been exploited to characterize the inserted material and to modify the characteristics of guided light via interaction with liquids presenting specific optical properties. Optofluidic fiber devices have, therefore, been demonstrated for applications in areas such as sensing [1, 4, 7, 8, 12]; nonlinear optics (including the observation of stimulated Raman scattering in ethanol  and the demonstration of supercontinuum generation in water ); and optical amplifier  and laser [16, 17] engineering (including the demonstration of conventional  and random fiber dye lasers ).
In a number of situations, it is important to selectively fill only certain holes of the fiber, while leaving the others unfilled. Several methods have already been demonstrated for this purpose. The most widely used class of methods exploits hole size differences to insert material in all holes of a particular diameter, and is commonly employed to fill the core of hollow-core PCFs [6, 18, 19]. Methods have also been demonstrated to selectively fill some of the holes of a matrix of identical holes, which include fusing the microstructured fiber with a capillary whose bore is aligned with the holes to be filled [5, 9]; blocking the holes that are not to be filled with epoxy or glue [10, 20]; blocking all holes with a solid layer through which holes are micromachined with a laser ; and depositing a photoresist layer onto the fiber tip, which is then selectively laser developed so as to block only chosen holes .
Both solid-core and hollow-core PCFs can exhibit interesting guiding characteristics when some or all of their holes are filled with a liquid. In the case of solid-core PCFs, if the refractive index of the liquid is lower than that of the fiber material, light remains guided in the high optical quality core, but interacts with the inserted material via its evanescent field. The effective efficiency of the interaction depends upon the field overlap with the material, which in turn will depend on the core and hole sizes and on the refractive index difference. In the hollow-core PCFs’ case, selectively filling the core generally yields total-internal reflection guidance and a very efficient interaction, as light-liquid optical overlap is almost complete. However, liquid-core PCFs present coupling loss problems related to the formation of a meniscus at the core-air interface (or, alternatively, require bulky liquid reservoirs coupled to their ends).
In this work we demonstrate a method to obtain high light-liquid overlap in a solid-core PCF, while maintaining light insertion and extraction via the solid core, thus combining advantages normally found separately in liquid- and solid-core PCFs. The method consists of partially filling the extension of a single channel (or hole) adjacent to the solid core with a liquid that is index-matched with silica. The core geometry is, therefore, effectively changed where the liquid exists. When light launched into the solid core reaches the filled section, it couples to more than one mode of the modified structure and, consequently, its transverse intensity distribution oscillates between the solid and liquid regions along the fiber. A very high light-liquid overlap is, then, periodically attained along the fiber, allowing the liquid sample to be pumped or probed, according to the desired application. As a proof of principle experiment, an index-matched solution of Rhodamine 610 was used, which was pumped with light initially coupled to the PCF solid core. A significant part of the detected fluorescence exited the PCF via the solid core, indicating not only the ability to efficiently pump the Rhodamine solution, but also the capability of collecting its fluorescent emission with the solid core.
We note that the luminescence of dye solutions inserted into cladding holes was previously observed [7–9]. Unlike the present work, however, the solutions presented a refractive index that was lower than that of the fiber material, meaning that guided pump light could only interact via its evanescent field, and no mechanism was available to preferentially couple luminescence to the core, rather than to the microstructured cladding. We also point that, although to the best of our knowledge no similar PCF waveguide concept has been reported, coupling between a solid core and liquid-filled holes has been described in the context of refractive index sensing and refractometry [21–23]. In this case, a liquid with an index higher than that of the fiber material fills a hole in the second ring of holes around the core [21, 22] or two holes in the first ring . In the former approach light couples, with a coupling length of over 4 cm , to a liquid channel mode that is beyond cut-off and is, therefore, lost, meaning that applications such as those proposed in the present paper are not possible. In the latter approach , light couples between two higher order modes of the complex core structure, none of which presents a high light field overlap with the liquid material. Other reported refractometry studies used dual-solid-core PCFs with cladding holes filled with the analyte [24–26]. A high field-sample overlap is achieved when light is in the process of coupling between cores, but the field within the liquid is always evanescent. Also, the typical coupling lengths in the mentioned reports are of the order of a millimeter, which may not produce a uniform pumping of the inserted liquid for the applications we propose.
2. Proposed waveguide geometry and principles of operation
Figure 1(a) shows the scheme of the proposed waveguide structure, which includes filling of the final section of one channel adjacent to the PCF solid core with an index-matched liquid. In the region where the liquid is located, a modified (elliptical) core is effectively formed, comprehending the regions of the original core, the filled channel and the silica in its vicinity. When the fundamental mode of the unfilled PCF, coupled to the original silica core at the unfilled PCF input, reaches the modified region, it ceases to be a guided mode, becoming a superposition of modes of the new, filled, structure. As each mode presents a different propagation constant, these modes dephase, giving rise to an evolution of the transverse intensity distribution.
Under certain conditions, it can be shown that all modes periodically rephase along propagation . At these points, the field recovers its original distribution, for which the intensity is concentrated in the region of the central solid core. Thus, the guided radiation periodically couples to the filled region of the modified core and back to the region of the original core. The structure can, then, be used to provide large light-liquid overlap, and therefore to efficiently probe the liquid, at the same time that good fiber coupling conditions are maintained, since there is no liquid at the fiber input. Moreover, this last feature allows the PCF to be spliced to conventional fibers, which is not possible when the liquid fills the channel along all its extension. In the case of luminescent liquid material, as will be shown, the guide can also be used to distributedly pump the material and to collect part of the emission, which becomes coupled and guided in the solid part of the core.
Assuming, for simplicity, that the mode of the unfilled structure couples to only two modes of the filled PCF, the spatial period, L2π, after which the original intensity distribution is recovered is given by
It is seen that L2π depends on the wavelength, meaning that, for a given L, only for certain values of λ the modes become in phase at the output of the filled region, resulting in transmission maxima. More generally, rephasing at the output is achieved whenever L/λ is a multiple of 1/Δneff. The spectral separation between two adjacent maxima is given by [28, 29]
This separation is more conveniently analyzed across large spectral widths if the spectrum is plotted as a function of the reciprocal wavelength, κ = 1/λ. In this case, by simply differentiating κ, the spectral separation is
The fraction (f) of optical energy that overlaps with the liquid depends upon the wavelength and upon the hole diameter (d) and pitch (Λ) of the PCF cladding. For λ = 1300 nm, d = 1.5 µm and Λ = 4.0 µm, such as in the case of the experiments described here, excitation of the two first modes leads to f = 7.5% (when the modes dephase by odd multiples of π). The small hole diameter also results in a high intensity, which is attractive for nonlinear optical applications. For a fixed optical power, the intensity in the filled hole can be calculated to be 2.5 times higher than that in the core of a standard telecommunications fiber (which has an 60 µm2 modal area). Also, higher f values are easily achieved with larger hole diameters (for example, f = 18.5% if d = 2.5 µm with all other parameters kept the same) or at shorter wavelengths.
If the mode of the unfilled PCF couples to more than two filled-PCF modes, the original intensity distribution is only recovered for L/λ = Lκ values for which all modes are back in phase. Nevertheless, at Lκ values for which pairs of modes rephase, the original intensity distribution is partially recovered, giving rise to a locally improved recoupling to the solid core of the unfilled PCF output section. Equations (1) and (2) are, therefore, still valid for describing the spatial and spectral modulations resulting from interference between pairs of modes.
3. Experimental setups
For the experiments, either mineral oil (with index matched to that of silica to within 10−2 in the 1000-1550 nm wavelength range) or a 65:35 vol% mixture of ethylene glycol:glycerin (index matched to within 10−2 across the visible wavelength range) were used as filling liquids. These were inserted into the selected channel next to the core (see Fig. 1(a)) with the use of a micropipette (with an outer diameter of ~1 μm), which was glued to a syringe containing the liquid. Pressure was applied to the syringe, inducing the liquid to fill the selected fiber hole. Filling stopped when the pressure was interrupted and the micropipette removed from the hole. The used solid-core PCF was NKT’s model NL-5-1065, which is shown in Fig. 1(b) and presents a 5.0-µm diameter solid core and a cladding microstructure with 1.5-µm diameter holes and a 4.0-µm pitch.
In order to determine the filled-section lengths in the various samples produced, a commercial frequency-domain optical backscatter reflectometer with a 30-μm spatial resolution was used. The reflectometer detected the spectral modulation appearing as a consequence of the interference from light reflected at the beginning and at the end of the filled section. The modulation period of this Fabry-Perot cavity was used to determine the liquid channel extension. This measurement could be undertaken during or after the filling process. The former case made possible to cease filling, through removal of the pipette, when the desired filled length was reached, with an estimated length accuracy of ~0.5 mm. Although better accuracies are believed to be achievable, so far no attempt was made to improve this parameter, as the exact filling length is not critical for a range of envisaged applications (see, for example, section 5.2).
After filling a length of the channel adjacent to the solid core, the fiber was characterized using the setup depicted in Fig. 2 . Light from a commercial supercontinuum source (Toptica FFS-cont) emitting in the infrared (800-2000 nm) was coupled to the PCF entrance with the help of a microscope objective, initially propagating along the unfilled PCF until it reached the filled region. At the fiber exit, a second microscope objective collected light leaving the PCF and directed it toward a CMOS camera or a highly multimode fiber connected to an optical spectrum analyzer (OSA). In some cases, an iris placed after the second objective was employed to select light from the solid core or from the liquid channel.
4. Results, analysis and discussion
The inset of Fig. 2 shows the output image of a filled fiber obtained with the CMOS camera. As in this case the liquid filled the PCF all the way to its output, one clearly observes that part of the light couples to the liquid channel, as desired. Figure 3(a) shows the output spectrum from a PCF with a 3.3-mm-long channel filled with mineral oil, as measured by the OSA. A clear modulation with a ~27 nm maxima separation is visible around a wavelength of 1250 nm. As noted in section 2, this corresponds to the beating of a pair of modes of the filled structure, with maxima being obtained for specific Lκ values. It is, thus, more convenient to analyze the spectrum in terms of the reciprocal wavelength, for which the spectral periodicity is measured to be Δκ ~0.017 μm−1. In addition, taking the Fast Fourier Transform (FFT) of the spectrum (as a function of κ) reveals the presence of other periodicities, as can be seen in the top part of Fig. 3(c). At least 4 peaks are visible, with two of them, corresponding to 1/Δκ = 44 μm and 1/Δκ = 55 μm, dominating. The latter peak corresponds to Δκ ~0.018 μm−1, being identified as the ~27 nm maxima separation in the main part of Fig. 3(a).
In order to help in the analysis of the experimental data, the modes of the filled fiber were investigated via a full-vector finite element simulation using COMSOL Multiphysics. The cross section of the fiber was discretized by high-density meshes of ~260.000 second order triangular edge-elements and a circular anisotropic perfectly matched layer was included as a truncation technique. The refractive index of silica was evaluated by the Sellmeier equation and we assume that the silica-liquid index matching is perfect. Only two guided modes were identified and are visible in Fig. 4 , together with their modal indices over the spectral region of interest. The modes shown were quasi-degenerated with modes at the orthogonal polarization, with modal phase birefringences in the 10−6-10−5 range found. In addition, the method described in  was used to determine the cladding effective index, with the results also shown in Fig. 4. Material dispersion was accounted for through the use of silica’s Sellmeier equation.
From Fig. 4 it is seen that the modal index difference, Δneff, for the two modes found range from 1.2 × 10−3 to 2.2 × 10−3 in the 1050-1450 nm wavelength range (over which most of the experimental spectrum lay). Using these values, the 3.3-mm filled length and Eq. (3), a 1/Δκ between 4 and 7 μm is calculated for the associated spectral modulation, which would be overshadowed by the 1/Δκ = 0 peak in Fig. 3(c) and very close to the FFT resolution (3.6 µm). This resolution is limited by the width of the experimental spectrum, which, in turn, is ultimately limited by chromatic aberration in the objective lenses that prevented the supercontinnum spectrum from being efficiently launched into and extracted from the PCF over a span wider than ~500 nm. The peaks seen in the FFT trace are, therefore, believed to correspond to beating involving core modes beyond their cutoff. As previously noted , higher-order modes can survive in PCFs for tens of centimeters, which is much longer then the filled length in this case.
From Eq. (3), one can see that Δκ decreases with increasing L values. The peaks in the FFT trace are, therefore, expected to shift toward higher values and become more spaced out. Figure 3(b) shows the transmission spectrum obtained with a PCF with a 4.2-mm-long filled section. Indeed, the FFT trace (bottom trace in Fig. 3(c)) exhibits 15 peaks with amplitudes within 50% the amplitude of the highest peak (1/Δκ = 13 μm), each corresponding to the beating of pairs of modes. From Eq. (3), the peak at 1/Δκ = 13 μm corresponds to a Δneff = 3 × 10−3, matching, to within the FFT resolution, the expected index difference for the two first modes of the filled structure. The coupling to a range of modes is actually beneficial for the intended application of pumping and probing the liquid material, because each mode pair presents a different L2π, meaning that along the filled length mode pairs are continuously becoming out of phase and, thus, overlapping with the liquid channel. After using Eq. (3) for evaluating the Δneff values corresponding to the peaks shown in the bottom FFT trace of Fig. 3(c), L2π values ranging from 37 to 400 μm can be calculated with Eq. (1) and a mean wavelength of 1250 nm. This indicates that even for sub-millimeter filled lengths, liquid-light interaction can be considerable. The lengths over which light couples to the liquid channel are, therefore, one to two orders of magnitude shorter than those achieve using other experimental setups proposed in the literature [22–26].
From the cladding effective index and the fundamental mode index, Fig. 4, it is possible to calculate the Δneff that a beating involving the fundamental mode and a mode exactly at cutoff would present, corresponding to Δneff = 5.4 × 10−3 at 1050 nm and Δneff = 9.1 × 10−3 at 1450 nm. Using Eq. (3) and L = 4.2 mm, this would correspond to peaks at 1/Δκ ~22 μm and 1/Δκ ~38 μm, respectively, in the bottom trace of Fig. 3(c) (marked as vertical lines). It is seen that most of the peaks in the Fourier trace appear beyond these lines, confirming that core modes beyond cutoff are involved. Peaks to the left of these lines can be due to the beating between two modes beyond cutoff.
Note that peaks corresponding to the higher values of 1/Δκ are wider, which may be a consequence of material and waveguide group velocity dispersion. Also, direct inspection of the experimental spectra indicates that different periodicities dominate over different spectral ranges, which is possibly a consequence of the varying modal loss values at different wavelengths.
At some wavelength ranges spanning 100-150 nm, individual periodicities can be identified and studied, corresponding to the beating of a single mode pair. The beating around a wavelength of 1.25 μm was then studied. The spectra shown in Fig. 5(a) correspond to measurements using the PCF with the 4.2-mm filling and an iris to allow independently collecting light coming from the solid core or the liquid channel and its surrounding. It is possible to see that spectral maxima from the solid core approximately correspond to spectral minima from the channel region (and vice-versa), as expected if only two modes interfere. Deviations from this pattern are mostly due to the more complex interference process, which, as seen, involves a number of other modes. The high temperature sensitivity of the spectrum (see section 5.1) also somewhat contributed to the mentioned deviations.
We also studied the periodicity dominantly visible around 1.25 μm for a range of oil filling lengths. Figure 5(b) shows the obtained reciprocal wavelength spectral periodicity (Δκ) as a function of the filled section length in a log-log scale. The linear fit to the experimental data gives a power dependence of –(1.2 ± 0.2), which agrees well with the expected 1/L dependence given by Eq. (3). This indicates that indeed the periodicities observed in the different PCF samples correspond to beating between the same pair of modes.
Propagation losses at a filled fiber section are associated both to scattering, especially at the beginning and end of the liquid plug, and to the inability to perfectly recover the original intensity distribution at the end of the section. We performed cutback measurements in order to determine the insertion loss of 1.8-mm and 3.2-mm long filled PCF sections. Light of a tunable laser (1510 nm < λ < 1640 nm) was tuned to a PCF transmission peak and coupled into the waveguide. A loss of 3 dB was measured for both fiber samples around 1550 nm, which is reasonably low, taking into account the diversity of modes that are excited. Losses are expected to be lower at shorter wavelengths, as modes beyond cutoff approach their cutoff point.
5. Prospective applications
The proposed waveguide geometry is a powerful and flexible method to induce high light-liquid sample overlap, while maintaining high quality light coupling conditions. A wide range of potential applications can, thus, be envisaged, including those in the fields of spectroscopy, non-linear optics, optical sources and sensing. In this paper, we preliminarily investigate the waveguide characteristics that would allow for the development of devices in the two latter mentioned fields.
5.1 Temperature sensitivity
It was observed that the transmission spectra of oil-filled PCFs presented very high temperature sensitivities, thus opening up prospective applications as temperature sensors. This characteristic is not surprising, as the effective indices of the excited modes are not expected to present exactly the same dependence on temperature. Indeed, a number of temperature sensors have been demonstrated based on modal interferometers . The temperature sensitivity was, then, studied and quantified for a sample with a 1.8-mm filled length, which was exposed to a temperature variation of 2.0°C, from 22.7°C to 24.7°C, obtained by changing the room temperature. Temperature measurements were taken with a digital thermometer (0.1°C resolution), while the transmission spectrum was monitored with the OSA. Figure 6(a) shows the spectral red shift resulting from temperature increase. Figure 6(b) shows the position of a transmission peak as a function of the temperature, as well as a linear fit corresponding to a temperature sensitivity of (5.35 ± 0.02) nm/°C. Independent measurements were performed 3 times, all agreeing with one another to within 0.04 nm/°C. The obtained temperature sensitivity is approximately 400 times larger than that of fiber Bragg gratings and 100 times larger than that of the modal interferometer reported in , allowing for the development of ultrasensitive temperature sensors. The improved temperature sensitivity is attributed to the thermo-optic coefficient of mineral oil, which we measured to be an order of magnitude larger than that of silica  (by spectral analysis of a Fabry-Perot etalon filled with the liquid).
It should be noted, however, that the spectral modulation period observed in this case (Fig. 6(a)) is 45 nm, which indicates that the sensor would only provide complete temperature determination over ~8.0°C operating range. For larger temperature variations a transmission peak reaches the spectral position occupied by the adjacent peak, which can lead to errors in determining the temperature. A larger operating range can be obtained with a reduced filling length, L, which increases Δλ. Naturally, this also leads to broader transmission peaks and, thus, to a larger uncertainty in determining their spectral position (which can still be much smaller then the peak width, if data processing methods are used). The narrow temperature range in the characterized PCF, as well as the limitations of the system chosen for varying temperature, lead to the low number of measured points in Fig. 6(b). Nevertheless, as already noted, the good observed reproducibility validates the obtained results.
5.2 Distributed pumping of a dye solution
Another possible application for the proposed waveguide is the distributed pumping of luminescent materials, such as quantum-dot colloids and dye solutions. As light coupled into the PCF periodically overlaps with the infiltrated liquid, the structure allows that the colloid/solution be gradually pumped along all the filled length. Moreover, the emission can be collected by the solid core, avoiding reabsorption by the fluorophores. This waveguide structure is an alternative to index-guiding fibers with cores filled with luminescent liquids, the lengths of which are usually limited to few centimeters by the strong pump absorption . In the proposed structure, pump absorption is much more gradual, which guarantees that the luminescent material is more evenly pumped along all the filled channel extent.
As a proof of principle experiment, a hole next to the solid core of a PCF sample had its final 5.0 cm filled with a solution of Rhodamine 610 (10−3 Mol/l) in the index-matched ethylene glycol:glycerin mixture. For this experiment, a solid-state laser operating at 473 nm replaced the supercontinuum source in the setup shown in Fig. 2, and served as the pump. In Fig. 7(a) , the blue, solid, curve shows the fluorescence spectrum obtained. The power measured right before the first objective lens (see Fig. 2) was 6.2 mW; at the exit (after the second objective lens) a total power of 0.89 mW was measured, from which 0.26 μW corresponded to the emission peaking at 595 nm (this was measured using a 550 nm long-pass filter right at the fiber exit). If the pump coupling loss can be estimated to be ~50%, an optical efficiency as low as ~8 × 10−5 can be calculated. On the other hand, only ~70% of the pump power was used, meaning that the emission power and efficiency can potentially be increased for longer filled lengths. Figure 7(b) shows an image of the filled PCF exit, in which it is possible to note that the fluorescence is coupled to and guided through the original solid core. Note that, because the filled region of the hole next to the core does not reach the fiber tip, no fluorescence is visible at its output. As splicing the PCF input and output to conventional fibers is possible, an all-fiber dye emission source is feasible.
For comparison, a control experiment was performed, in which a 5.5-cm-long hollow-core PCF had its core (~10 μm in diameter) totally filled with the same Rhodamine 610 solution. Using the same pump laser, this sample presented a total output power of 8.70 μW, from which 1.20 μW (measured with the 550 nm long-pass filter at the PCF exit) corresponded to the emission centered at 627 nm, seen as the red, dashed, curve in Fig. 7(a). Assuming a ~10% pump coupling efficiency (expected to be lower than with the solid-core PCF because of the meniscus and evaporation issues discussed earlier) an optical efficiency and pump usage of ~2 × 10−3 and 99%, respectively, are estimated. It is, therefore, clear that increasing the filled length will only decrease the optical conversion efficiency and emission power. Also, fusion splicing to conventional fibers cannot be accomplished with this PCF.
A comparison between the solid-core and hollow-core PCF spectra reveals that the emission peak is substantially red-shifted in the latter case, which indicates reabsorption of part of the fluorescence generated in the first centimeters of the waveguide and a subsequent reemission at longer wavelengths. This observation indicates that in this fiber the pump field does not efficiently excite the dye molecules close to the end of the structure, and corroborates the expectation that that for fibers with longer filling lengths, or for higher dye concentrations, the waveguide structure proposed in the present work will become more efficient, being able to generate and transmit larger fluorescence powers. We also note that for fibers that are several centimeters long only the two guided modes of the filled structure are expected to survive, which contributes to pump loss and a decrease in efficiency. In this sense, increasing the diameter of the effective core of the filled region (e.g. by filling all holes of the first cladding ring) can possibly increase the number of guided modes and, therefore, favor the proposed pumping scheme.
This paper presented the proposal and demonstration of a post-processed PCF structure consisting of a solid-core fiber, the microstructure of which presented one hole next to the core filled with an index-matched liquid. We showed that light propagating along the original solid core efficiently couples to the liquid-filled channel via excitation of a number of modes of the composite waveguide structure. The resulting fiber presents a modulated output spectrum, whose periodicities correspond to beating between pairs of modes. The modulated spectrum presents high temperature sensitivity, shifting at a rate of 5.35 nm/°C, and meaning that temperature sensors can be envisaged.
The demonstrated geometry allows efficiently probing and/or pumping a liquid sample while offering high optical quality and spliceable fiber ends. As a demonstration of this application, a new way to gradually pump luminescent liquids was proposed, in which a 5.0-cm-long channel adjacent to the solid core of a PCF was filled with an index-matched Rhodamine 610 solution. Comparison with a hollow-core PCF with the core selectively filled with the same solution revealed that the proposed waveguide allows for longer filled lengths and/or higher dye concentrations. The waveguide geometry, therefore, presents itself as an interesting method for pumping luminescent materials in a distributed way along a large fiber extension, thus avoiding that all the pump power is absorbed in the first fiber centimeters.
This work is supported by CNPq (including funding from INCTs FOTONICOM e INFo), CAPES/PROCAD, FAPESP (INCT FOTONICOM), and Fundo Mackenzie de Pesquisa. The authors thank A. M. Brito-Silva for helping with the Rhodamine sample preparation.
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