1. Introduction

Transparent dielectric spherical particles scatter light in the far field when their diameter is comparable with or smaller than the wavelength (Mie scattering) [1]. Several papers have reported on detailed computations of the local field distribution in the vicinity or inside of dielectric micrometric particles and structures (see e.g.[2]). It has been shown that in particular cases mi-crometric transparent particles can highly concentrate visible light in the near field [3, 4, 5, 6]. Because of the scale of the structures compared with the wavelength, the focal distance does not obey spherical lens formula of the geometrical optics [4] and low divergence can be obtained despite a large numerical aperture [7]. For a given sphere size and a given wavelength, the distance between the focus and the center of the sphere decreases when the ratio n ₂/n ₁ increases [4]. Typically with visible light and spheres having a 1 μm diameter in air (n ₁ = 1), the condition n ₂ < 1.65 induces focussing outside the sphere. A so-called photonic jet is obtained when the focus is right on the surface or just a few wavelengths behind the sphere. In these particular cases, the FWHM of the intensity distribution outside of the particle goes down to half the wavelength, the diffraction limit is reached [4], and the beam width stays smaller than the wavelength for propagation distances as large as several wavelengths behind the sphere (see in Fig. 1). These features predicted to occur outside of the focussing object, and in its near field, define the specificity of a photonic jet. For example, in free space the intensity of the incoming beam can be concentrated up to 200 times behind a dielectric sphere having a refractive index 1.63 and with a radius of 5 wavelengths [8]. The drastic field enhancement calls for an experiment using non-linear optics that could give evidence for the action of the photonic jets. We therefore report herein on the observation of the enhancement of two-photon excited fluorescence from a dye solution brought about by adding drops of a silica micro-sphere suspension.

Note that these near-field focussing effects occurring outside of the spheres must be distinguished from other known phenomena. High intensity concentrations can also be obtained inside the particle. They have been used to enhance fluorescence and stimulated Raman scattering of molecules located inside the particles [9, 10] but also to explain the explosion of water droplets [11] or the breakdown of gases [12]. The photonic jets are also reminiscent of the local electric field enhancement observed in the vicinity of metal tips, as used in surface-enhance Raman spectroscopy [13]. Finally, photonic jets must also be distinguished from the Whispering Gallery Modes [14] for two reasons: Photonic jets are propagative (not evanescent) components of the electromagnetic field in the forward direction and they are not made of one specific resonant mode of the sphere.

The possibility of concentrating light intensity in the vicinity of micrometer sized objets can have great interest in different domains such as: material processing [15], nanoparticle detections [16], microscopy improvement [17]. In this letter, we consider applications in the field of non-linear optics that could take advantage of the intensity concentration (photonic jet) produced by micrometric dielectric spheres in the near field and we consider the particular case of two-photon fluorescence.

2. Theoretical computation of the intensity concentration

We have water (n ₁ = 1.36) using the rigorous Lorenz-Mie theory [1, 18]. This method makes it possible to analytically find the solutions of the vectorial propagation equation (Helmholtz equation) for a dielectric sphere placed in a plane wave. The computed field is the total field, that is the sum of the scattered field and of the incident one. In this work, we consider dielectric silica spheres with a diameter D = 590 nm ± 100 nm (determined by two ways: chemical parameters of the Stöber reaction and scattering diagram fits) prepared using a specific Stöber reaction [19]. The Ti: sapphire laser excitation is well described by a linearly polarized plane wave at 795 nm. The effective refractive index of the silica spheres is n ₂ = 1.495 around 795 nm [20]. The result of this computation, under neglect of absorption, and using the experimental parameters is presented in Fig. 1. In the limit of high sphere dilution, electromagnetic interactions between spheres are negligible. If the mean distance between spheres is always larger than four times their radius, we are in a single scattering regime [21]. This has been verified by measuring the linear relation between extinction and sphere concentration in water. In this regime, each sphere is considered to interact only with the incident field. The incident field is attenuated by scattering but one particle is considered not to scatter the light scattered by the other ones. In Fig. 1, we can observe an intensity concentration (electric field squared) immediately behind the sphere in the propagation direction (photonic jet), that may be able to enhance the two photon absorption process of molecules dissolved in the surrounding medium. The intensity profile of the electric field on the optical axis is also represented in Fig. 1. The intensity is locally multiplied by 1.8 at a distance of approx. 0.6 microns from the sphere center, i.e. outside of the particle. Our simulations also show that larger spheres may be able to integrate and to concentrate the incident light even more [8].

3. Experimental setup

The enhancement of non-linear effects by these photonic jets has been verified experimentally in the case of two-photon fluorescence on biological markers like Rhodamine, Fluorescein and Coumarin. The excitation light pulses source is a 27 MHz Ti:sapphire laser producing 35 – 40 fs pulses at 795 nm ± 10 nm. Rhodamine B (LC 6100) is known to have a relatively strong two-photon absorption cross section around 800 nm (600–700.10^-50 cm⁴s), larger than the one of Rhodamine 6G, but with a fluorescence quantum yield of 0.5 only [22]. We have prepared an aqueous stock solution buffered at pH 7 with 0.21 mMolL^-1 of Rhodamine. A buffered solution is used to minimize a possible pH change after adding the spherical particles. The refractive index of the obtained medium is n ₁ = 1.36. The optical density of these solution is OD=1.86 for one millimeter path length at 560 nm (Fig. 4). The stock solution was divided into 8 equivalent volumes (12 mL). Samples were prepared, one without sphere and the others with respectively 2, 4, 6, 8, 10, 12 and 20 μL of a sphere suspension. This procedure ensures a high dilution of the sphere suspensions. In our case, about 1.4 × 10⁹ spheres are contained in 1 μL of the sphere suspension. After addition of the spheres, the effect on the extinction spectrum was measured: OD=1.91 for one millimeter path length at 560 nm for the solution containing 7 × 10¹¹ spheres/L (figure 4). Note that at this concentration, the mean distance between spheres is 13 μm. The sphere size and concentration are determined by two means: chemical parameters in the Stöber reaction and by dynamic light scattering using a commercial instrument (Autosizer 4700).

 

Fig. 1. Electric field intensity map, around the silica sphere (map) and on the optical axis (curve), for an unitary plane wave. D = 590 nm, λ _o = 795 nm, n ₁ = 1.36, n ₂ = 1.495. The incident wave is linearly polarized along the x-axis and propagates in the z direction. The sphere is centered on the 0 position.

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A schematic description of the experimental setup is given in Fig. 2. The samples were circulated in a 0.5 mm path length flow cell by use of a peristaltic pump. This circulation allows to have a good homogeneity of the solution and to minimize possible triplet accumulation in the photo-excited sample volume. The flow cell was placed between two reflective microscope objectives (numerical aperture NA=0.28) with 13.4 mm effective focal length. The first objective focuses the laser pulses into the flowing sample. The maximum laser power on the sample is 170 ± 20 mW. The focal spot diameter is 15 μm determined by measuring the transmission through a 20 μm pinhole. The second objective collects the fluorescence in a transmission geometry and focuses onto a 300 μm diameter pinhole, which serves as an intermediate focus for confocal detection of the two-photon excited sample volume. The pinhole is imaged through two plane-convex lenses on the input slit of a 25 cm focal length monochromator equipped with a Peltier-cooled CCD (Spec 10, Roper Scientific) and having a spectral resolution of 3 nm. A color filter (Schott BG 39) rejects the transmitted pump beam. Spectra are acquired as an average of up to 40 background free exposures. Working in a confocal detection mode (300 μm pinhole) allows the detection of the fluorescence from a constant volume in the sample. This volume is defined by the laser focus from which the fluorescence originates in a sphere-free sample. When spheres are added to the sample, light scattering deteriorates the focus conditions, thus enlarging the focus volume. The photonic nanojets might then lead to two-photon fluorescence outside the initial focal volume. In order to avoid these complications and to compare the fluorescence intensity for a given focus volume, a confocal detection mode is advantageous.

 

Fig. 2. Schematic description of the experimental setup. The Ti:sapphire laser produces 35–40 fs pulses at 795 nm with a repetition rate of 27Mhz.

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4. Observation of non-linear fluorescence enhancement

Figure 3 shows the two-photon excited fluorescence of rhodamin B centered at 576 nm. The signal increases by approx. 35% when a small amount of spheres is added (5×10¹¹ spheres/L). The inset shows in a loglog representation the excitation power dependence of the spectrally integrated fluorescence emitted by samples with silica spheres. With and without spheres, a dependence close to quadratic is observed, demonstrating that the fluorescence is two-photon excited as expected. We want to stress that for all the concentrations used, we are in a single scattering regime.

Note that fluorescence enhancement or even stimulated emission have been observed in the past in scattering media [23, 24], leading to the research on random lasers. However the two phenomena are very different from our situation. In random lasers, the enhancement is not specific to the two-photon excitation process, but is due to a feedback effect which occurs in multiple scattering regime. The sphere concentrations are several orders of magnitude larger than in our experiment [23, 24] and no lasing effect is observed at a concentration of Rhodamine lower than 1×10^-4M [24]. Another fluorescence enhancement using dielectric spheres considers the case when the molecules are inside the particle [9, 10], which is again not the case here.

Figure 4 shows the measured fluorescence intensity as a function of sphere concentration and for different excitation powers. The fluorescence enhancement reaches a maximum (around 35 %) for relatively small sphere concentrations (4 – 6× 10¹¹ spheres/L). For higher concentrations (> 1 × 10¹² spheres/L), the fluorescence is still larger than in sphere-less samples, but the enhancement is less prominent most probably because of light scattering effects. Extinction by light scattering is not specific to the two-photon experiment, of course [25] and could have been reduced when working with a thinner sample. Rather the intensity increase at lowest concentrations is a two-photon effect. This behavior is again distinctly different from the one reported for the rhodamine fluorescence in TiO ₂ suspensions (random laser) [23, 24]. The latter increases only for sphere concentration larger than (> 1 × 10¹² spheres/L), and is accompanied by drastic changes in the shape and in the peak position of the emission spectra. In our case, spectral shifts induced by the addition of spheres are less than < 1.5 nm, and the spectral width of the fluorescence remains unchanged. As presented in figure 4, the relative fluorescence increase does not depend on the laser intensity. This suggests that the enhancement is not due to a multi-photon photochemistry process.

 

Fig. 3. Two photon excited fluorescence of Rhodamine B with and without micro-spheres (5 × 10¹¹ spheres/L). Excitation wavelength is λ_o = 795 nm, with 115 mW average power. Inset: Excitation power dependence of the spectrally integrated fluorescence of a sample with silica spheres (7 × 10¹¹ spheres/L). The spectrum is observed with small deformation due to the BG39 filter. See text for details.

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5. Discussion

Following the above arguments, the observed fluorescence enhancement occurs in a regime very different from the one required for random lasing [23, 24] or pre-threshold fluorescence increase. In variance with the latter, we observe an enhancement only under two-photon excitation, and at much smaller sphere concentrations. Given the large inter-sphere distance of the order of 10 μm, our experiments are actually performed in the single scattering regime, and not under multiple scattering conditions. We therefore turn our attention to alternative explanations. The observed fluorescence increase could be due to a possible binding between chro-mophores and negatively charged spheres that would result in an enhancement of fluorescence efficiency. Using time-correlated single photon counting, we measured the fluorescence decay under one-photon excitation at 480 nm of sphere-free samples and of samples with 7 and 14 × 10¹¹ spheres/L, and found that the transients perfectly superpose. The fluorescence quantum efficiency is thus unchanged by the presence of spheres. Could there be a local increase of the chromophore density ? If chromophore binding occurs, it must be weak as we do not observe sizeable spectral shifts or broadening in absorption and emission. This is not unexpected given the relatively large size and low mobility of the rhodamine cations compared to protons in the solution. The latter will therefore neutralize most of the SiO anions on the spheres.

 

Fig. 4. Spectrally integrated fluorescence of Rhodamine as a function of sphere concentration for three incident powers. Fluorescence has been normalized to one when there is no sphere. Excitation wavelength is λ_o = 795 nm. Average power are 170 (o), 115 (.) and 4.6 (+) mW. The continuous line is a guide-to-the-eye. Inset: optical density per millimeter of rhodamine with (7×10¹¹ spheres/L) and without spheres.

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We would like to stress that Coumarin 4 (Umbelliferone 47) displays a sphere concentration dependence of the fluorescence enhancement very similar to the one of rhodamine B, although the effect is somewhat smaller, between 5 and 10%. As the enhancement is observed with comparable concentration of spheres for two different molecular species and as alternative explanations do not seem to apply (see above), we suggest that it is a manifestation of the intensity concentration by photonic jets. In order to estimate an upper boundary for the fluorescence enhancement for the present low sphere concentrations, we can consider the spheres as being independent and use the calculated field distribution (Fig. 1). Such estimations predict only 2–3 % maximum signal increase, which is clearly lower than the effect observed for rhodamine B, but of the right order of magnitude for Coumarin 4. The main conclusion, however, from these calculations is that forthcoming experiments should work in better conditions such as an optimized sphere size and reduced extinction due to scattering so as to maximize the fluorescence enhancement.

6. Conclusions

We have shown in this work that two-photon absorption in molecular dyes is enhanced in solution when adding a suspension of micrometric dielectric spheres. The observation of a fluorescence increase, while the fluorescence yield remains constant, suggests that the enhancement is brought about by an increased photon density (photonic jets) in the vicinity of the spheres. While the present report is a first step in the right direction, further work should be directed towards maximizing the effect by optimizing the dielectric sphere diameter or the index of refraction difference. Also would it be worthwhile exploring different experimental conditions such as to measure in the backward direction in order to minimize loss due to light scattering. Another motivation resides in the reversibility principle, due to which spheres may behave as lenses collecting fluorescence and collimating it into the backward direction [9].

Finally, interesting new effects can be envisioned when the optical properties of the micrometric spheres are combined with other functions such as bio-chemical recognition or magnetism.

The authors are grateful to E. Piémont (Faculté de Pharmacie, Inst. G. Laustriat, UMR 7034, ULP Strasbourg) who performed the time-resolved fluorescence experiments. The work was funded by the CNRS and the University Louis Pasteur Strasbourg.