The development of microstructured fibres offers the prospect of improved fibre sensing for low refractive index materials such as liquids and gases. A number of approaches are possible. Here we present a new approach to evanescent field sensing, in which both core and cladding are microstructured. The fibre was fabricated and tested, and simulations and experimental results are shown in the visible region to demonstrate the utility of this approach for sensing.
©2006 Optical Society of America
Microstructured Optical Fibre (MOF) (also known as photonic crystal fibre (PCF) when the fibre holes are periodically arranged) is a special kind of fibre with (in general) air holes running parallel to its axis and for all its length . Two types of guidance are possible in these fibres: hollow core fibres guiding by photonic band gap (PBG) or solid core fibres guiding by total internal reflection (TIR).
Both approaches offer routes to improved chemical and/or biological sensing of low index materials  and there is an increasing body of work exploring these, both for the sensing of bulk materials and surface sensing.
In conventional optical fibres, the only possible approach for sensing low refractive index materials is to use the evanescent field, which is generally very small. To increase the amount of power in the fluid of interest (the light-fluid overlap) several approaches can be applied, including plastic clad fibres (PCS) with the cladding removed  in the sensing region, D-shape fibres and tapers . These approaches, in general, add complexity and make the structure more fragile. A simpler approach is to use the fibre merely to guide the light to a chamber that contains the gas/liquid to be measured where it is then monitored in free space. In this case the measurement is limited to short path lengths, due to practical limitations and the beam divergence.
Microstructured optical fibres have vastly extended the possibilities for fluid sensing, not only because fluids can enter the microstructure directly, but also because the optical properties can be exploited to maximize the measured signal. Filled MOFs can combine the sensitivity of few microns tapered fibre with the mechanical strength of standard fibres, simultaneously offering unprecedented sensitivity and improved handling. A possible drawback could be the added complexity involved in filling and interrogating the fibre from the same point, the fibre tip. Some techniques are, however, being developed to overcome this limitation allowing the material to be inserted through a lateral hole in the fibre [5, 6].
MOFs with fluids can be used in three main configurations regarding the guiding mechanism and the location of the material to be probed:
- Hollow core PBG fibres. These can be completely filled with gas or low refractive index liquid  keeping the same guiding mechanism. Potentially they can present near total light-fluid overlap. The fact its transmittance occurs in specific bands that are sensitive to the holes refractive index and the complex manufacturing process reduces its applications in sensing experiments;
- Liquid core TIR fibres. This approach requires a high air filling fraction cladding and a (selectively filled) liquid core . Again, light-liquid overlap is very strong;
- Solid core MOFs can have their (cladding) holes filled with the material of interest. The transmittance window is broad, being limited, in practical terms, just by material loss. In the other hand, usually just a small fraction of power (the evanescent field) travels in the material to be sensed. The usual way to enhance this figure is by using fibres with a core diameter around the size of the wavelength .
Sensing in microstructured fibres is a new area, and it is not completely clear yet all implications involved with each of the possible configurations. Due to the low spatial overlap of the light and the fluid there has been little exploration of solid core fibres for fluid sensing. There is, however, considerable room to enhance the evanescent field by tuning the microstructure appropriately. In this work we developed a new approach where, both the core and cladding are microstructured (Fig. 1(a), white and grey are polymer, black is air). This design helps to increase the amount of energy that travels in the holes where the material can be inserted. In a different context, a MOF with hole(s) in the core was previously proposed by Koshiba  and Zheltikov  in order to control the waveguide dispersion.
In this work the fibre was fabricated in polymer (PMMA-Polymethyl Methacrylate) using standard techniques  and has a 160 µm outside diameter and a 6.4 µm thick core. Inside the core, the seven holes are 1.75 µm wide with a 2.4 µm pitch (Λcore ) [Fig. 1(a)].
2. Fibre an analysis
The structure was modeled with a vectorial finite element software (COMSOL) . For the numerical analysis just a quarter of the MOF geometric model was considered to avoid extra computational time. Usually, finite element meshes with ~55,000 second order triangular vectorial elements were used, corresponding to matrix systems with ~ 380,000 degrees of freedom. Figure 1(b) shows the calculated fundamental mode at the microstructured core. The plot shows the intensity profile (power flow, time-average, z-direction) along the core cross-section while the arrows indicate the electric optical field direction. The guided optical field, shown in Fig. 1(b), resemble to the linearly polarized HE11 fundamental mode of conventional optical fibers. Two linear orthogonal polarizations, corresponding to the degenerated fundamental modes, were found and present birefringence around 10-5. At λ=633 nm the structure supports about eleven optical modes. The effective index of the fundamental mode was found to be 1.457828 for 633 nm, assuming air filled holes. Higher order modes lead, in general, to an increased overlap with the low index material increasing the sensitivity , while potentially making the results sensitive to launch conditions and mode-mixing. Here, however, all modes have approximately the same fraction of energy traveling in the core holes, keeping the analysis simple.
For some applications, including the cases when interferometric detection is used, or when the sample property to be sensed is phase encoded, a single-mode or few-mode regime is mandatory. In these cases the fibre geometry can be tailored in order to reduce the number of propagating modes by reducing the core size or by having a cladding with small air filling fraction . Careful design and analysis is required to balance the competing requirements: a small number of modes (or a single mode), a high fraction of energy in the air holes and a sufficiently large core to make coupling straightforward.
To quantify the fibre efficiency as a gas or liquid sensor, one important parameter is the sensitivity coefficient r=(nr /ne )f, being nr the refractive index of the sensed material within the fibre holes and ne the modal effective index. The percentage of energy in the holes (f) can be calculated :
where Ex/y is the electric field in the x or y direction and Hx/y is the magnetic field in the x or y direction (beam propagating in the z direction).
The sensitivity coefficient r(%) is shown in Fig. 2 for the transparency region of the material used to manufacture the fibre (PMMA) and for three different filling configurations: (A) all holes are filled with air/gas (n=1), (B) all holes are filled with water (n=1.33) and (C) the cladding holes are filled with air and core holes with water. As expected, the evanescent field overlap with the sample (gas or liquid) is enhanced at longer wavelengths and when the index contrast is reduced. The value of r observed is due the mode spreading within the core holes, while the cladding holes have little influence. At 633 nm the r coefficient assumes values of 4.22% and 4.18% for the fibre completely filled with water (B) and for the fibre with core holes filled with water and cladding holes filled with air (C), respectively. If all holes are filled with air, r=0.883% (A)
To highlight the impact of the core holes we also analyzed a fibre with exactly the same geometry but with a solid core (fibre presented in Fig. 1(a) with missing core holes). In this case, and again for 633 nm, the r coefficient is 0.006 % (air filled fibre) and 0.041% (water filled fibre). This means that the microstructured core increases the fraction of energy in the holes by ~145 times when the fibre is used with gases and ~100 times when used with liquids (n =1.33).
To put these values in perspective, we compared the results of the microstructured-core MOF [Fig. 3(a)] with those of an equivalent fibre with a solid (non-microstructured core) [Fig. 3(b)] with d/Λ=0.9. The fraction of the energy was simulated as a function of the fibre core diameter (D) and the results are presented in Fig. 4 for the cases A and B presented in Fig. 2.
Clearly, the microstructured core is very significant in increasing the sensitivity of the fibre as a sensor. As expected, the sensitivity can also be increased by reducing the size of the structure or by increasing the (d/Λ)core ratio. Scaling down the manufactured fibre by a factor of, e. g., two – D from 6.4 to 3.2 µm – enhances the ‘r’ coefficient from 4.22 % to > 17%. Increasing the (d/Λ)core from 0.72 (fabricated fibre) to 0.80 increases the ‘r’ coefficient to 1.6% and to 7.3% for the air and water filled fibres, respectively.
An important point, however, is that, although a solid core MOF could allow a sensitivity coefficient ‘r’ as high as a microstructured core MOF one, the core diameter would be much smaller (Fig. 4). Having such tiny core can increase alignment precision requirements apart decreasing the field overlap between the mode of the MOF and the mode of a standard fibre.
To evaluate this question we modeled the coupling efficiency from a Gaussian optical beam coupling to the fundamental mode of the fibre. The maximum coupling efficiency was studied as a function of the Gaussian modal radius (a) using the overlap factor ψ . This radius (a) represents the half-width at 1/e of the maximum intensity, being the electric field profile defined as: E⃗≈E⃗x exp(-r 2/(2a 2)). The results are shown in Fig. 5. For λ=633nm, the overlap factor of the manufactured fibre and a Gaussian optical beam occurs for a=1.5µm, and is 52% and 63% when holes are filled with air or water, respectively. For a regular MOF structure [Fig. 3(b)], as the guided mode resembles a Gaussian profile, the overlap can be >90% . It is important to recognize, however, that designing a structure such that the guided mode has a more Gaussian shape can minimize this difference.
However, more important than the absolute value of the coupling efficiency is the Gaussian radius where it occurs. For a water filled fibre, and for 633nm, to reach r~5% the core should be around 1 µm thick when using a solid core MOF or ~6µm when dealing with microstructured core MOFs (Fig. 4). In these cases, to obtain the maximum coupling, ‘a’ should be 0.5 µm and 1.5 µm respectively (some results at Fig. 5). For the solid core fibre (Λ=1 µm), by using a Gaussian with 1.5 µm the coupling efficiency drops to less than 20%. This means that the microstructured core design offers an alternative means of obtaining a high light-fluid overlap while keeping a large core area.
The fibre structure was based in the triangular-lattice design where the core presents a circular-like shape. Optimization of the structure may further increase the size of the evanescent field, including the possibility of using suspended core fibres . These fibres offer high sensitivity while using large holes which allows for both faster filling and the incorporation of particles (such as cells). The trade-off however is that the cores required are very small.
3. Experimental results
The fibres were firstly tested using a He-Ne laser, which was launched into the fibre using a 20x objective lens (NA=0.40). Figure 6(a) shows an image of the fibre end-face made using a 40x objective in a CCD camera. This image passed then through a polarizing beam splitter and the decomposed imaged for both vertical and horizontal polarizations are shown in Figs. 6(b) and 6(c). By comparing all three images at Fig. 6 it can be seen that it is possible to launch the light around the central hole of the core. The fibre is in the multimode regime but it is possible to couple the light mainly in a linearly polarized mode [Fig. 6(b)].
For inserting liquids in the microstructured fibre we use a selective-filling [19–21] technique that allows filling all holes or just the external (big) ones or just the tiny core ones. Here the process involves pressurizing an UV-curable polymer inside the fibre through one of its tips . The distance filled by liquid polymer will be longer for larger holes than for smaller ones and, after drying it, the fiber can be cleaved in a position where the smaller holes are open but the larger ones are blocked. The process can be repeated if one wants the opposite situation, smaller holes blocked and larger ones free to be accessed. Figure 7 shows the fibre end face in the situation where all holes are blocked [Fig. 7(a)] and where the big (external) holes are blocked and the core ones are open [Fig. 7(b)]. Figure 7(c) shows a lateral picture of the fibre so that it is possible to see the polymer inside the fibre.
After doing the process described above, the fibre can then be liquid filled. In this work we filled just the core holes of the fibre with Methylene Blue (MeB) dye diluted in water. The aim was to show possible applications in liquid sensing through absorbance measurement. For real applications in sensing setups (including a light source, fibre and detector) the filling of the holes is an important issue to be addressed, a common problem that arises in any microstructured optical fibre. Some of the solutions that have been proposed include: a) using a cell in one (or both) fibre tip(s) to access the holes while keeping the core free to be illuminated and b) access the longitudinal holes thought a lateral hole in the fibre cladding [5, 6].
The bulk absorption coefficient ‘α’ of MeB for several concentrations (C) is shown in Fig. 8. These values were obtained by measuring, with a spectrophotometer, the different solutions in a 1 mm cuvette. The spectra show two peaks, one at 664 nm corresponding to the monomer form of the molecule and one at 612 nm due to dimer (P-type) formation. The inset shows the evolution of the peaks values (664 and 612 nm) in function of the dye concentration. As expected the bulk absorption coefficients of both the monomer and dimer forms are linearly dependent to the concentration ‘C’. The absorption of the solution is characterized by an absorbance α=αmolar . C, where ‘αmolar ’, the molar absorption coefficient, can be written as :
being fM the fraction of molecules in the monomer form and αM and αD the molar absorption coefficients of the monomer and dimer respectively. In a water solution αM /αD ~2.3 for the dimer in its most common configuration (sandwich P-type, peak seen at Fig. 8 around 612 nm) or ~23 for the more unusual end-to-end configuration (N-type) .
As can be seen from Fig. 8, in such concentration range, the main contribution for the overall absorption comes from the monomer. In more concentrated solutions aggregation of the dye molecules can occur and the relative contribution of monomer and dimer will differ.
A 18 cm long fibre like the one of Fig. 1 was filled with MeB with concentration of 3.77.10-5 mol/l (~10 times more concentrated than the last point in Fig. 8). α is estimated, extrapolating the data (bulk) from Fig. 8, to be around 53 cm-1 and 35 cm-1 for the monomer and P-type dimer respectively. A supercontinuum source  was coupled in the fibre core by means of a 20x objective lens. The end face of the fibre was coupled to a large core standard fibre that directed the signal to an optical spectrum analyzer (OSA). An image of the output face was taken to ensure the light was traveling in the fibre core.
Figure 9 shows the spectra transmitted through a water-filled fibre and through a MeB filled fibre. The inset shows the difference (in dB) between these two signals. To aid the comparison the bulk measurement shown in Fig. 8 (at the highest concentration) was also added. These results highlight several interesting features. Most striking is that the P-dimer peak is relatively far stronger in the fibre measurement. While increased dimerisation is expected at higher concentrations, in bulk material this peak becomes stronger than the monomer peak only for concentrations an order of magnitude higher than we used in the fibre case . Less obviously, the monomer peak in the fibre case is slight shifted when comparing with the bulk measurement. The likely reason for these spectral differences is the role of surface interactions.
There is a few dB of noise in the fibre measurement. This is due to different coupling conditions between the two fibres and can, potentially, be improved by using a source with flatter and more stable spectrum.
Evanescent field sensors preferentially probe surface effects, as the intensity of the field diminishes rapidly away from the hole interface (Fig. 10). This fast decrease is a general trend of evanescent field waves. Inside a liquid-filled core-hole the optical intensity drops to 1/e of its maximum value in just ~100 nm from the surface of the hole.
This is likely to be particularly significant in this case because of surface interactions between fibre and dye. It is known that the concentration around a waveguide/fibre can be very different from the bulk concentration [24, 25]. Our results are consistent with surface-induced aggregation of the dye what makes a quantitative comparison with the bulk measurements difficult. Not only are the physical systems different, but the absorption coefficients are themselves influenced by surface interactions.
Nonetheless, it is instructive to quantify the absorption behavior of the solution in the fibre. From the Lambert-Beer law:
where ‘P0 ’ is the incident power and ‘d’ is the interaction length. When the absorbing medium is probed by an evanescent field it is also necessary to take in account the effective fraction of power ‘r’ that is located in the absorbing medium. In this case:
As the fraction of energy within the holes are around the same for all core modes we can simply use the average value (r(%) ~4.28±0.15, Fig. 2). In the other hand α is actually unknown, as not all the terms in Eq. (2) can be determined. The experimental results can however be compared to theory using the bulk absorption coefficients. These calculations suggest an absorption which is ~5 times stronger than measured value (Fig. 9), based on the common P-type dimer peak (α=35 cm-1). The longer wavelength peak was not used because of uncertainty as to how it should be interpreted given the spectral shift in the fibre measurement.
The origin of the discrepancy between the expected and measured values is unclear. Other studies [25, 26] using Methylene Blue in optical fibre evanescent field sensors have highlighted absorptions above that expected by the Lambert-Beer law. These studies however (using the monomer peak) were based on measurements for solutions that were at least an order of magnitude less concentrated that ours, and used silica fibres, that may have different surface interactions. More detailed studies are being undertaken, including the concentration and pH dependences of absorption to determine the nature of the aggregates and the role of the surface.
Another source of error when comparing the experimental result and the one from Eq. (4) is that the modeling of the fibre used an idealized structure. Imperfections in the structure are likely to reduce the evanescent field and so the measured absorption. An indication of the sensitivity to variations in the microstructure can be gained by some representative calculations. Reducing the value of (d/Λ)core by 15% or 30% for example reduces the effective fraction of power in the holes by a factor of 2.1 or 4.6 respectively. Similarly, reducing just the central hole size by 15% reduces the ‘r’ factor by 30%.
While the exact cause of the discrepancy is unclear, the role of the surface is certainly critical in determining the nature of the absorbing species in evanescent field sensors, and thus that the expectation of agreement with bulk solutions is generally misplaced.
We have shown a new approach to enhance the evanescent field when using microstructured optical fibres for gas/liquid sensing. This is achieved using microstructured core (guiding by total internal reflection) where the optical mode spreads, via evanescent field, within the low refractive index regions (holes). This enhancement is a particularly difficult task when dealing with short wavelengths as it is (usually) the case with polymeric fibres or, in general, when the interest lies in the UV / visible region. By using such approach, the increase in sensitivity does not rely on using very small core, allowing coupling the light in with a large Gaussian beam when comparing with the solid core PCF with the same fraction of energy in the holes.
As the fluid to be measured/characterized is probed by an evanescent field, which drops dramatically from the fibre surface, the material is sensed just in a thin layer near hole’s interface. Any surface effect is then maximized by using this approach.
Experimental measurements were carried out with MeB filling the core holes of the fibre and the measured values were below those that would have been expected in a bulk solution. This is due the differences between our model (idealized fibre and “bulk” absorption coefficient) and the real experiment, which includes fibre imperfections and surface interactions between fibre and dye.
Further work is underway to explore the nature of the interaction between the surface and the dye, its effect on aggregation behavior, and how it may be suppressed or enhanced. It is clear that measurements in optical waveguides experience more complex interactions than those found in bulk solutions, and therefore the expectation should be that the Lambert-Beer law may not apply. While in our case the experimental results gave weaker absorption values, for other test solutions, the surface interactions could enhance the sensitivity of the measurement compared to a bulk sample.
The evanescent field concentration around the holes can then be potentially either a drawback or an advantage, depending on the specific application. To minimize surface-related effects hollow core PBG fibre or a liquid core index guiding fibre (see Introduction) can be used. This is an issue that should also be considered when choosing the specific approach to be used with filled MOFs and fluids.
This work was supported by FAPESP (Fundação para o Amparo da Pesquisa no Estado de São Paulo) under project numbers 05/51689-2, 03/13053-3 and 03/03824-2, and by the Australian Research Council, and University of Sydney International Development Fund. C.M.B. Cordeiro acknowledges Gustavo Wiederhecker for helpful discussions and Eliane M. dos Santos for her help with Fig. 7. M. C. J. Large and C.M.B. Cordeiro wish to thank Felicity Cox for discussions.
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