## Abstract

Detection of fluorescence from a low quantum yield fluorophore is challenging for a fiber-optic probe, especially when an inexpensive and robust construction is desired. We propose a conceptually straightforward theoretical model to optimize the factors affecting the fluorescence-capture capability of a bifurcated/coaxial fiber-optic probe. Experimentally we verify that such a probe, if optimized, can detect the fluorescence of a polymer fluorophore with a low quantum yield of 0.0065.

© 2012 OSA

## 1. Introduction

A fiber-optic probe wins over other means for chemical species analysis due to its well-known advantages: it is lightweight, flexible, non-toxic, low-loss, cost-effective and has a remote-monitoring capability. These features make it possible to construct an elegant hand-held probe for on-site chemical species assay in various environments [1–8].

A bifurcated fiber probe [3–8] or its improved version, a coaxial fiber probe [3, 4], is often adopted for chemical species assay, whose configuration is shown in Figs. 1(a)
and 1(b), respectively. Either probe architectures could be easily constructed without sophisticated facilities. Its tiny probing end packs, for example, two or seven 430 μm fibers and the protecting sleeve into a cylinder approximately 2 mm in diameter. This small dimension makes bifurcated/coaxial fiber-optic probes widely used for chemical and biological species investigations and for *in vitro/vivo* detection [1–8]. However, the discussions in the relevant research papers seldom evaluate how well the flat-tipped probe detects the weak signal from a low quantum-yield fluorophore. Instead, a popular solution to cope with the weak fluorescent power is to use a fiber-optic probe with a better ability to capture light, such as one with a beveled probing tip. However, in comparison to the flat-tipped probe, the bevel-tipped end is hard to fabricate and offers poor protection of the sensing area. Given these issues, we investigate the use of the flat-tipped coaxial fiber-optic probe to detect the fluorescent signal of the low quantum-yield fluorophore under the simplest procedures and at the lowest possible cost. The fluorophore is a low band-gap polymer, represented here by P1, which contains a D-π-A system and has a low quantum yield ($Q=0.0065$).

## 2. Improving the bifurcated/coaxial fiber-optic probe for low quantum-yield fluorescence detection

Detection of weak fluorescence requires an optimized coaxial fiber-probe with enhanced ability to capture light. To date, this subject has been investigated by a number of papers, with references 4 and 5 being perhaps the most rigorous and comprehensive but very complicated. In this paper, we propose a straightforward and intuitive approach to calculating the fluorescent-power capture ability of a flat-tipped bifurcated/coaxial fiber probe as shown in Fig. 1. Figure 1(c) gives detailed information on the two architectures required for the theoretical investigation. The excitation light and the captured signal light are limited respectively by the excitation cone (e-cone) and the receiving cone (r-cone) represented by$2{\theta}_{0}$. In the most common construction, which has two identical fibers, the angles of these two cones that open to the sample are equal and determined by their numerical aperture $NA=n\mathrm{sin}{\theta}_{0}$, where *n* is the refractive index (RI) of the sample. The e-cone starts to overlap with the r-cone at the distance *H _{0}* from the probe tip. It is obvious that the captured fluorescent light from the sample can only arises from this overlapping or active volume. The shape of this active volume could be understood from the overlapping or active areas of ${S}_{1}$ and $S$, which are formed by two cross sections of the two cones. The excitation power density ${P}_{e\_d}$ varies from

*H*to

_{0}*H*, or obeys:

Thus the fluorescent power${{I}^{\prime}}_{f}$should be expressed by:

Obviously, Eq. (2) has to include the factors representing the characteristics of the fluorophore. For a diluted solution, ${{I}^{\prime}}_{f}$ is related to the excitation power intensity${I}_{e}$, molar absorptivity $\epsilon $, quantum yield $Q$, the concentration $c$ and the path length $l$ by:

where $k$ is a constant coefficient that may be determined by calibration. By applying Eq. (3) to Fig. 1(c), the total fluorescence power captured in the volume $S(h)\cdot dh$ at any depth $h\text{(}{H}_{0}<h\le H\text{)}$ could be written as:Clearly, Eq. (4) is equivalent with Eq. (2) but includes detailed information describing the fluorescence-capable solution.

Equation (5) indicates the overall excitation power incident on the overlapping area $S(h)$at depth $h\text{(}{H}_{0}<h\le H\text{)}$ while Eq. (4) assumes that within the small thickness $dh$ the value ${I}_{e}(h)$ remains unchanged.

To simplify the discussion (a reasonable approach for a diluted solution), we ignore the attenuation of the excitation power when traveling in the solution, and thus:

In contrast to the rigorous but complex treatment of the excitation light beam in [4], Eq. (6) assumes a uniform distribution of excitation power across the entire cross section of the light beam, which not only greatly simplifies the derivation, but also makes the concept easier to understand. Any error associated with this approximation is likely due to overestimating the excitation power in the overlapping volume, and could be greatly reduced by including the power penalty factor in the coefficient $k$in Eq. (4). Critically, since all calculation results given later (Fig. 2 ) are based on ratio to obtain normalized intensities and thus allow the coefficient $k$ to be cancelled out. From this point of view, the results from such an approximation provide a satisfactory degree of accuracy.

With $S(0)=\pi \text{\hspace{0.05em}}{r}^{2}$ and $S(h)=\pi \text{\hspace{0.05em}}{R}^{2}$, where $\text{\hspace{0.05em}}r$ and$R$ are the radius of the fiber core and the radius of the cross section of the e-cone or r-cone at the depth $h\text{(}{H}_{0}<h\le H\text{)}$, we can write:

Any overlapping area $S(h)$ has the same the geometry as $S=S(H)$in Fig. 1(c). The following expression is not difficult to find:

Replacing the associated terms in Eq. (4) with Eqs. (7) and Eq. (8) yields:

By assuming $\gamma =2\times k\cdot Q\cdot \epsilon \cdot c\cdot {P}_{e\_d}(0)$and lossless transmission of $d{{I}^{\prime}}_{f}$ from depth $h=H$ to $h=0$, the captured fluorescent power at the entrance of the r-fiber $(h=0)$, represented by ${I}_{f}(h=0)$, could be straightforwardly written from Eq. (9):

We change Eq. (10) to the form:

Figure 1(c) validates the following relations:

For$h={H}_{0}=t\cdot ctg{\theta}_{0}$, Eq. (12) gives${R}_{0}=r+t$, where $t$is the cladding thickness.

Equation (11) thus becomes:

Equation (13) is further simplified by assuming $u=\frac{R}{r}$ and $w=\frac{r}{R}$:

Assuming ${I}_{f}={I}_{f}(h=0)$ Eq. (14) yields:

Equation (15) expresses the overall fluorescent power captured by the r-fiber from the overlapping volume between ${H}_{0}$and$H$for a lossless liquid solution. For a coaxial fiber-optic probe, there are six identical overlapping volumes that contribute to the overall captured fluorescent power. In this case, we can write:

The calculation of Eqs. (15) and Eq. (16) generates the results presented in Fig. 2, from which we can draw the following conclusions. First, the core radius $r$greatly affects ${I}_{f}$ via ${r}^{3}$, which is reflected by all curves in Figs. 2(a), 2(b), 2(c), 2(e) and 2(f). Second, from Figs. 2(a) and 2(b), when a greater detecting depth *H* is considered, which is meaningful for an extremely low or a lossless sample medium, cladding thickness variation affects ${I}_{f}$on a smaller scale. This becomes obvious when a larger core fiber is involved. A core radius as small as 5 μm, as in a single-mode fiber, yields ${I}_{f}\to 0$ for any cladding thickness. Third, a larger *NA* could lead to a better capturing capability via $ctg{\theta}_{0}$ as described by Fig. 2(c), which also indicates a rapid rise of ${I}_{f}$ for a larger core fiber. Fourth, the benefit of a large *NA* also includes a shorter initial depth *H _{0}*, as shown in Fig. 2(d). The depth

*H*is proportional to the dead space in front of the probe tip. While this might not be a concern for lossless medium such as we assume in this paper for Eqs. (10) and (15), when a lossy medium fills this space – as in fact occurs to most samples – Eqs. (10) and (15) must include the attenuation coefficients for both excitation and fluorescent power, and ${I}_{f}<<{{I}^{\prime}}_{f}$may result. Fifth, instead of altering the

_{0}*NA*, using a smaller cladding thickness

*t*is another efficient way to reduce the dead space, as indicated in Fig. 2(d). This is perhaps a more meaningful option since all spectrometers accepting fiber-optic connection are designed for $NA=0.22$, which is the lowest

*NA*found in Figs. 2(c) and 2(d). For this reason, Fig. 2 emphasizes the results for $NA=0.22$. Sixth, the standard multimode fiber for fiber-optic communication, with its core/cladding diameter of 50 / 125 μm and $NA=0.22$, is an inexpensive and convenient fiber to use in construction of the bifurcated/coaxial fiber-optic probe. However, the limited capability of this fiber to capture fluorescent power, as evidenced in Fig. 2(e), contrasts with the fluorescence-capture ability of the fiber with core/cladding diameter of 400/430 μm and $NA=0.22$ used here. Seventh, the high performance of the fiber-optic probe presented in this work is evident in all parts of Fig. 2. For the reasons outlined above, this must be considered the optimal design taking into account all the factors discussed so far.

## 3. Experiments and discussions

A P1 solution is prepared by dissolving 2.9 mg P1 in 1 ml of CHCL_{3} and stirring for one hour and further diluted in 10 ml DMF solvent. After filtering, the P1 solution (3 × 10^{−4} M) is ready. For the purpose of performance comparison, we also prepared a rhodamine 6G (R6G) water solution (29 μg / ml) as the high quantum-yield ($Q=0.95$) fluorophore.

The coaxial fiber-optic probe shown in Fig. 1(b), with optimized performance as illustrated in Fig. 2, is used for fluorescence measurement. All fibers are identical, having a core/cladding diameter of 400/430 μm and *NA* of 0.22. The excitation light (633 nm for P1 and 532 nm for R6G) is launched to the e-lead that comprises six e-fibers surrounding one r-fiber in the probing end. The r-fiber constitutes the r-lead and is connected to an Ocean Optics QE65000 spectrometer, which is interrogated by a laptop via USB connection. The Ocean Optics SpectraSuite software package is used to record the fluorescence spectra.

In the first experiment, the fluorescent spectrum is recorded by immersing the fiber probing tip into the R6G solution. Similarly, the second experiment is carried out by immersing the probing end into the P1 solution. The experimental result in Fig. 3(a)
shows that the R6G affords a high quality fluorescent spectrum owing to its high quantum yield (*Q =* 0.95*)* that requires only 3 ms integration time, with complete elimination of the excitation laser trace even without an emission filter. Yet, despite the very low quantum yield (*Q =* 0.0065) of the P1 solution, which produces a fluorescent power 150 times weaker than R6G, Fig. 3(b) indicates that the optimized coaxial probe is still able to capture the fluorescent spectrum from P1, albeit with an integration time of 5,000 ms. However, this 5,000 ms integration time leads to a strong excitation-power trace in the captured spectrum in Fig. 3(b), an effect stemming from the limitation of the fiber probe itself. Since a fiber-optic-based system affords many well known advantages but at the cost of an enormous power penalty during both excitation and fluorescent light coupling, a high integration time is needed in order for the QE65000 spectrometer to respond to the weak P1 fluorescence.

## 4. Conclusions

In conclusion, this paper proposes a straightforward model for calculating and optimizing the ability of a coaxial fiber-optic probe to capture fluorescent light from a lossless liquid. The analytical expression obtained shows how the captured fluorescent power is affected by such important parameters as the molar absorptivity, the sample concentration, the quantum yield, the excitation power intensity, the dimensions of the fiber core and cladding, and the value of *NA*. The fiber parameters for maximum possible fluorescent power capture, presented here in a series of graphs, could be used to optimize the fiber-optic probe by matching the demands of various measurement environments and a particular spectrometer design. Evaluation of the performance of the coaxial fiber-optic probe optimized on the basis of this model shows a satisfactory quality of the fluorescence spectrum captured from a polymer fluorophore with an extremely low quantum yield of 0.0065. The lowest concentration this probe can cope with is 3 × 10^{−4} M.

The work presented here paves the way towards using the coaxial fiber probe to detect trace heavy metal by turning on and off fluorescence of this P1 polymer via titration measurement, which will be discussed in our next paper.

## Acknowledgments

The authors gratefully acknowledge support for this work from the Natural Sciences and Engineering Research Council of Canada, from the Canada Research Chairs Program and from the Ministère de Développement économique, Innovation et Exportation du Québec.

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