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Self-assembled dielectric microsphere array enhanced Raman scattering for large-area and ultra-long working distance confocal detection

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Abstract

Here we report enhanced confocal Raman detection with large-area and ultra-long working distance by capping dielectric microsphere array. Microspheres have been found to provide three channels for Raman scattering enhancement, including localized photonic nanojets, directional antenna effects, and whispering-gallery modes. The maximum enhancement ratio of Raman intensity is up to 14.6 using 4.94-μm-diameter polystyrene (PS) microspheres. Investigation on the directional antenna effect of microsphere reveals that the microsphere array confines electromagnetic (EM) waves to a narrow distribution with small divergent angles, by which the signal-to-noise ratio is retained and the offset of focal plane position from sample surface can be up to ± 7.5 mm. The present work reduces the requirement of focusing in confocal Raman detection and hence makes the large-area detection possible via rapid mapping. It opens up a simple approach for high-sensitivity Raman detection of 3D-structured surface.

© 2015 Optical Society of America

1. Introduction

In recent years, dielectric micron-sized spheres have attracted increasing attention due to their unique optical properties, e.g. photonic nanojets [1–5], whispering gallery modes [6], directional antenna [7], etc. Photonic nanojets generated by high refractive index microspheres are non-evanescent and non-resonant beams that are focused in a subdiffractive lateral size (~λ/3) and can propagate a distance over a light wavelength. Several applications have been demonstrated via photonic nanojets, such as nano-particles detection [1], multiphoton-excited fluorescence/upconversion [8–10], sub-diffraction-limited resolution imaging [11–14], nano-patterning [15–17], etc. Whispering gallery modes (WGMs) are typically supported by dielectric microspheres in which waves are confined by continuous total internal reflection. WGMs were first observed in 1961 by Garrett et al. [6] and the ultrahigh-quality silica microspheres were first studied by Braginsky et al. [18]. The ultrahigh quality factor and small mode volume of dielectric microsphere resonator is best suited for strong-coupling cavity-QED, enhancement and suppression of spontaneous emission, novel laser sources, and dynamic filters in optical communications [19]. Microsphere WGM-guided transducers with ultimate detection limits have also been demonstrated for single molecule (including interactions) and nanoparticle sensing [20–23]. Furthermore, dielectric microspheres are highly directional optical antennae efficient over a wide range of frequencies, which can be combined with low NA objectives to form high performance optical system [7, 24, 25]. Wenger et al. fond that microspheres can increase the excitation intensity up to a factor of 2.2 and allow for collection efficiency up to 60% by redirecting the light emitted at large incidences toward the optical axis, which made the detection of single-molecule fluorescence possible [26]. Our previous work demonstrated a 10-fold enhancement of ZnO thin film photoluminescence in the UV band by microsphere directional optical antenna arrays [27].

It is well known that Raman scattering is extremely weak and hard to detect due to the small interactive cross section. Therefore, numerous studies have been performed in order to enhance the Raman signals for the past decades. The widely employed techniques include surface-enhanced Raman scattering (SERS), tip-enhanced Raman scattering (TERS), interference-enhanced Raman scattering (IERS), total internal reflection Raman scattering (TIRRS), resonance Raman scattering (RRS), near-field Raman microscopy (NORM), coherent anti-Stokes Raman scattering (CARS), stimulated Raman scattering (SRS), etc [28, 29]. Lu et al. first reported the enhancement of Raman scattering using self-assembly silica microspheres in 2007 and achieved an enhancement factor of 6 in the Raman scattering of Si wafer [28]. Du et al. observed a maximum Raman enhancement factor of ~11 for bulk Si by individual PS microspheres [30]. Then, the dependence of Raman enhancement ratio on objective NA, pump wavelength, size and refractive index of individual microsphere was studied by Bisht et al. [31]. They found that the enhancement ratio depended on matching of laser spot size with microsphere diameter and the short wavelength would result higher Raman scattering enhancement ratio, where the maximum enhancement ratio for Si wafers can be up to 16. Xiang et al. developed an approach for near-field Raman imaging using an optically trapped polystyrene (PS) microsphere to scan over the sample surface in water, by which the spatial resolution of ~80 nm was achieved [32]. Cardenas numerically simulated the light scattering by microspheres supported on Si thin film/metal/substrate structures and confirmed a strong confinement of light at the shadow side of the Si [33]. Furthermore, Alessandri et al. demonstrated the microsphere-enhanced Raman detection of ultra-thin films and coupled to metal- or all-oxide-based SERS active substrates to further boost Raman sensitivity for chemical and biochemical reactions [34]. Lombardi et al. employed a 2D array of silica particles as a SERS substrate for detection of crystal violet (CV), by which the enhancement ratio was up to the order of 104 when the CV molecules on the surface of the particle array [35]. In above-mentioned literatures, the mechanism of Raman scattering enhancement was attributed to the microsphere-generated photonic nanojets with a high light intensity on sample surface. Lu et al. further used silica microspheres to enhance the contrast in CARS imaging based on the low divergent angle of light wave distribution in the direction of propagation by microspheres [36]. Moreover, WGMs were found to have the capability for enhancement of Raman scattering in quantum dots, thin dye coating and molecules on microspheres [37–39]. However, the effect of WGMs on Raman scattering enhancement in bulk materials has not been reported.

In this work, we found new channels of Raman scattering enhancement by self-assembled dielectric microsphere array depositing on bulk materials. The microsphere array enhanced Raman confocal spectrometer has also demonstrated the capability for large-area and ultra-long working distance detection with high sensitivity.

2. Experimental

The Raman scattering signals were captured by a high resolution confocal Raman spectrometer (Horiba/Jobin-Yvon T64000). As shown in Fig. 1(a), the excitation source was an argon-ion laser with a wavelength of 514.5 nm. A 10x confocal objective with NA = 0.25 focused the excitation laser beam to around 40 μm. The Raman scattering signals were then collected by the same objective in backscattering configuration, in which the Rayleigh scattering was blocked by an edge filter. The direct single stage with a 640 mm focal length was employed to detect the Raman scattering signals in a wide spectral range through a liquid-nitrogen cooled CCD camera. A resolution of 1 cm−1 in Raman shift can be achieved through an 1800 lines/mm grating. The integration time was set as 1 s, 5 s, and 10 s. All data reported in this work were from sampling over 5 different areas for each type of microspheres. The enhancement ratios of Raman intensity (ERI) were calculated from averaging the 5 measurements. The focal plane position (fpp) was set from −10 mm to 10 mm, where the positive value meant the focal plane above the sample surface and the negative one indicated it inside the sample. The sample was tilted ranging from 0° to 20° in order to understand the effect of tiled angle on microsphere-based Raman scattering enhancement.

 figure: Fig. 1

Fig. 1 Experimental setup of microsphere array-enhanced Raman scattering. (a) Schematic of Raman spectrometer. (b)-(g) Surface morphologies of Si wafer capped with close-packed FS microspheres of (b) 1.49 μm, (c) 2.51 μm, (d) 5.04 μm, and (e) 7.27 μm diameters, as well as (f) 4.93-μm-diameter PS microspheres and (g) 5.50-μm-diameter PMMA microspheres.

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The c-axis orientated silicon wafers (001) were first cleaned by ultrasonic agitation in acetone, ethanol and deionized water for 5 mins, respectively. Hydrofluoric (HF) acid was then employed to remove the oxide layer and rinsed thoroughly in deionized water. After that, the microspheres were diluted by deionized water and the concentration of microspheres in suspension was 104-106 μL−1. The suspension was deposited onto a silicon wafer with a tiled angle of 10° by drop coating. After the suspension was air dried, a monolayer of hexagonally close-packed microspheres over an area of several mm2 was self-assembled. The morphologies of microspheres on the sample surface were observed by an optical microscope (Olympus LEXT-OLS-3100) fitted with a 50x/0.90 objective (MPLAPO). The dielectric microspheres used in this work included fused silica (FS) microspheres with diameters of 1.49 ± 0.01, 2.51 ± 0.02, 5.04 ± 0.03 and 7.27 ± 0.03 μm, polystyrene (PS) microspheres with a diameter of 4.93 ± 0.03 μm, and polymethylmethacrylate (PMMA) microspheres with a diameter of 5.50 ± 0.03 μm. Figs. 1(b)-1(g) demonstrates various microsphere arrays deposited onto Si wafers.

A finite difference time domain (FDTD) algorithm using the commercial software of COMSOL Multiphysics (licensed by COMSOL Co., Ltd.) was performed to simulate the electric fields both inside and outside the microsphere arrays, including focusing property, whispering-gallery mode and directional antenna effect, in order to understand the mechanism of enhanced Raman scattering via dielectric microsphere arrays.

3. Results and discussion

A typical Raman spectrum of the Si wafer is shown in Fig. 2(a). The strong Raman peak at ~520 cm−1 is assigned to the first order transverse optical (TO) mode. Microspheres with various diameters and refractive indexes were used in order to study the effects of microsphere diameter and refractive index on Raman scattering enhancement. All microspheres can enhance the Raman scattering [Figs. 2(a) and 2(b)]. It can also be found that the ERI of FS microspheres with 4-8 μm diameters were significantly higher than those in [28] and [31]. The ERI was dependent upon the microsphere diameter and refractive index. The microspheres with high refractive indexes (i.e. PS and PMMA where n = 1.60 and 1.49, respectively) can further improve ERI up to 11.8 by PMMA microspheres and 14.6 by PS microspheres, compared with 7.6 by FS microspheres with the similar diameter.

 figure: Fig. 2

Fig. 2 Enhancement of Raman scattering by microsphere arrays. (a) Raman spectra of bare and microsphere-capped Si wafers. (b) ERI for various microsphere arrays.

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According to the previous studies, the mechanism of Raman scattering enhancement was attributed to the photonic nanojets generated by the micron-sized spheres [28–35], in which only the enhancement of incident radiation (|Eloc(ωl)|2) was considered to contribute the Raman process. Actually, the radiation pattern can be altered by the directional antenna effect of microsphere [7], by which the radiation in the direction of detection would be further enhanced. Such a phenomenon is similar to the re-emission enhancement related to |Eloc(ωr)|2 in SERS [40]. Therefore, the primary mechanisms of microsphere-based Raman enhancement should be attributed to the local field enhancement (excitation) and the radiation enhancement (re-emission), which are assumed to be proportional to |Eloc(ωl)|2 and |Eloc(ωr)|2 [33]. When taken at a zero-Stokes shift (ωlωr) and assumed the focus spot as an emitting dipole, the ERI by microspheres can be estimated by | Eloc(ωl)|4 approximation as following

ERIsphere~02π0rs|Es(r)|4rdrdθπrs2×|E0|4=2×0rs|Es(r)|4rdrrs2×|E0|4
where Es is the electric field of the focused laser spot at the shadow side of the microsphere, rs is the microsphere radius, and E0 is the electric field of the raw laser beam. The distributions of electric fields focused by various microspheres were simulated by FDTD algorithm [Fig. 3]. Considering the reflectance of 38% and high absorption coefficient of 3952.6 cm−1 for silicon wafer at the wavelength of 514.5 nm, the Raman scattering was assumed to occur at the sample surface. Therefore, the material properties of substrate were ignored in this work and the distribution of electric field on the silicon surface (i.e. at the bottom of microsphere) was used to estimate the ERI [Eq. (1)]. Figure 3 illustrates the distributions of electric fields in the vicinity of different microspheres. It can be clearly seen that the incident laser was focused in a small area at the shadow side of microsphere and hence the laser intensity was enhanced dramatically. The calculated ERI for various microspheres by Eq. (1) are listed in Fig. 3 as well. The microspheres with larger diameters and refractive indexes were found to achieve higher ERI, which matched with the experimental results [Fig. 2(b)]. However, the experimental ERI generally showed 2~7.5 times higher than simulated ones for different microspheres. It indicates that other channels in addition to photonic jets should exist in microsphere-enhanced Raman scattering.

 figure: Fig. 3

Fig. 3 Numerical simulation of excitation laser focused by various microspheres and the corresponding ERI. The periodic boundaries were applied in order to simulate close-packed microsphere arrays. (a)-(f) The profiles of |E|4 at the shadow sides of (a) 1.49-μm-diameter, (b) 2.51-μm -diameter, (c) 5.04-μm-diameter and (d) 7.27-μm-diameter FS microspheres, as well as (e) 4.93-μm-diameter PS and 5.50-μm-diameter PMMA microspheres. The distributions of light intensities inside and in the vicinity of microspheres are demonstrated in the insets.

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It is well known that dielectric microsphere is an optical resonator trapping light by supported whispering-gallery modes (WGMs), by which the light-matter interaction can be strongly enhanced due to the modification of the optical density of states in the vicinity of microsphere. When the focused laser arrives on the Si wafer surface, a large amount of photons are scattered elastically (i.e. Rayleigh scattering). The scattered light could excite WGMs [Figs. 4(a) and 4(b)] when the microsphere radius (rs) is satisfied with the following condition [41]

rslλ2πn
where l is an integer indicating the light ray propagation of a distance ~2πrs in a round trip. If one round trip exactly equals l wavelengths (λ) in the microsphere with a refractive index of n, a standing wave (i.e. WGM) would occur. The calculated diameters of microspheres supporting WGMs are listed in Table 1. It was found that the integers exist for FS microspheres with diameters of 5.04 ± 0.03 and 7.27 ± 0.03 μm, PS microspheres with a diameter of 4.93 ± 0.03 μm, as well as PMMA microspheres with a diameter of 5.50 ± 0.03 μm under the wavelength of 514.5 nm. As a result, the Raman scattering cross-section can be dramatically increased by the standing waves trapped in these microsphere resonators. The enhancement ratio (Ef) of whispering gallery resonance is therefore estimated by Purcell effect [42]
Ef=34π2(λn)3(QV)
where Q and V are quality factor and mode volume of the microsphere, respectively. The Q factor is related to the microsphere diameter (Qrad), material absorption (Qmat), surface inhomogeneities (Qss) and surface contaminants (Qcont). In this work, only the radiative (curvature) losses (Qrad) were considered.

 figure: Fig. 4

Fig. 4 Microsphere-supported WGMs excited by excitation laser scattering. (a) Schematic of WGMs excitation in a microsphere. (b) A typical FDTD simulation of WGMs excited by a dipole scatterer in free space near the bottom of a 4.93-μm-diameter PS microsphere. (c) Comparison of theoretically calculated ERI with experimental results.

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Tables Icon

Table 1. The Nominal diameters and WGM-supported diameters of microspheres

By assuming azimuthal symmetry, the Q factors and mode volumes (V) of different microspheres are defined as [43]

{Q=Re(k)2Im(k)V=VQε(r)|E(r)|2d3rmax[ε(r)|E(r)|2]
where k is the complex eigenvalue (wavenumber) of the resonant cavity mode, ε(r) is the dielectric constant, |E(r)| is the electric field strength and VQ is the integration volume. The WGM-supported microspheres (i.e. 5.04-μm-diameter and 7.27-μm-diameter FS microspheres, 4.93-μm-diameter PS microspheres, as well as 5.50-μm-diameter PMMA microspheres) demonstrated high Q values (~105) compared to other microspheres (~101). As a result, Raman scattering can further be enhanced by Purcell effect provided by microsphere-supported WGMs in addition to the photonic nanojets and directional antenna effect. The WGM-enhanced ERI is therefore rewritten as
ERI=ERIsphere+(1β)×Ef
where β is the coupling loss for WGMs excitation. According to the numerical calculation, it was found that the theoretical ERI was in good agreement with experimental results when β = 0.98 [Fig. 4(c)]. It meant that only 2% of scattered light energy was coupled into the microsphere for excitation of WGMs. It was attributed to the phase mismatching in scattering-based coupling in free space. However, the additional enhancement ratios with 2-7.5 times can still be achieved due to the high Q factors and small mode volumes of the microsphere resonators. As a prospect, the ERI can further be increased as the coupling efficiency is improved. According to FDTD simulation, the diameter greater than 4 μm and the large refractive index were found to benefit for microsphere resonators with high Q-factors due to the low radiative losses. Hence, the high refractive microspheres with diameters > 4 μm are recommended to enhance Raman scattering. Moreover, there is a possibility for tunnelling of photons from one microsphere to neighbour ones via the evanescent coupling in the microsphere array. The tunnelling effect of adjacent microspheres on Raman scattering enhancement was ignored in this work.

In addition, microspheres also demonstrated the capability of long working distance (WD) detection [Fig. 5(a)]. Compared with the bare wafer (where WD = ± 0.5 mm), the WD of microsphere-capped wafer was dramatically increased up to ± 3.5 mm using 4.93-μm-diameter PS microspheres. In a confocal Raman spectrometer, it is well known that the high signal-to-noise ratio (SNR) is due to the confocal pinhole filtering scattered light out of the focal point. The focal plane position (fpp) is therefore a key parameter affecting intensity of Raman signals. In general, the signal intensity of light scattering away from the focus is exponentially reduced by the confocal pinhole, resulting in a short WD detection. However, the confocal pinhole cannot block the scattered light that is close to the optical axis [Fig. 5(c)]. Figures 5(d)-5(j) illustrate the divergent EM waves from a dipole in free space and close to various microspheres. It can be seen that the microspheres are natural directional antenna that confined EM waves to a narrow distribution with small divergent angles (<15°). Especially for the large diameter and high refractive microspheres (i.e. 4.93-μm-diameter PS microspheres), the confined EM waves were close to parallel propagation waves. The scattered light can then pass through the confocal pinhole even fpp≠0 [Fig. 5(c)]. As a result, the long WD detection can be achieved. Figure 5(b) illustrates that the WD was increased with increasing the integration time of Raman signal acquisition, where the maximum WD was up to ± 7.5 mm under a fair integration time (i.e. 10 s). The ultra-long WD detection provides a new approach to achieve confocal Raman rapid mapping of 3D-structured surfaces without focus adjustment.

 figure: Fig. 5

Fig. 5 Ultra-long working distance Raman scattering detection by microspheres. (a) Microsphere-enhanced Raman scattering intensities for various microspheres and fpps. (b) The effect of integration time on maximum Δfpp for detection. (c) Schematic of confocal configuration and scattered light collection under different fpps. (d) The electric field intensity and angular distribution of EM waves emitted from a dipole in free space. (e)-(j) The electric field intensities and angular distributions of EM waves emitted from a dipole close to (e) 1.49-μm-diameter FS, (f) 2.51-μm-diameter FS, (g) 5.04-μm-diameter FS, (h) 7.27-μm-diameter FS, (i) 4.93-μm-diameter PS, and (j) 5.50-μm-diameter PMMA microspheres. The blue dash lines indicate the angle of the maximum cone of light that can be collected by the objective.

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Meanwhile, the intensity of Raman scattering became sensitive to the tilting angle of sample due to the directional EM waves confined by microspheres. Figure 6(a) shows the effect of tilting angle on intensity of Raman scattering. It can be seen that the Raman scattering intensity was nearly constant for the bare Si wafer whereas the ones from microsphere-capped substrate were gently reduced with increasing the tilting angle. When the tilting angle was greater than a threshold (as the dash lines indicated in Fig. 6(a)), the Raman intensities were dramatically reduced. Figure 6(b) illustrates the mechanism of Raman intensity reduction related to the tilting angle. Figure 5 shows that the main lobe of directional EM waves (k0) perpendicular to the substrate surface contains the most energy that can enter the objective as the substrate is horizontal. When the substrate is tilted, some EM wave vectors would be out of the objective and hence the intensity of collectable Raman scattering is mild reduced. Further increasing the tilting angle greater than the NA of objective, the k0 cannot be collected by the objective resulting in a significant reduction of Raman intensity. Therefore, the tilting angle of substrate α should be satisfied with the following condition in order to obtain an acceptable Raman scattering intensity,

αsin1(NAn0)
where n0 is the refractive index of ambient media. In this work, α should be lower than 14.5°. It should also be noted that the amount of change in intensity with tilting angle is significantly varying with the diameter of refractive index of the microspheres. For the microspheres with large diameters and high refractive indexes, the EM waves can be confined closer to parallel propagation waves [Figs. 5(e)-5(j)]. The corresponding Raman scattering intensities are therefore more sensitive to the tilting angle of substrate and reduced dramatically when α>14.5°. The prediction is in good agreement with the experimental results [Fig. 6(a)].

 figure: Fig. 6

Fig. 6 The effect of substrate tilting angle on Raman scattering intensity. (a) The effect of tilting angle on Raman scattering intensity for various microspheres. (b) The collection of EM waves under various tilting angles. (c) An application of microsphere-based large-area and ultra-long WD confocal Raman detection of 3D-structured surface.

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According to above discussion, it can be found that the microsphere array provides a new way to achieve enhanced confocal Raman detection with ultra-long working distance and large area via rapid mapping. Although the Raman intensity is sensitive to the tilting angle of microsphere-capped sample surface, the Raman scattering intensity keeps flat [Fig. 6(a)] when the tilting angle is lower than the threshold [Eq. (6)]. As a practical application, microspheres can be applied onto a 3D-structured surface for Raman detection [Fig. 6(c)], in which adjustment of fpp is inessential during mapping and the contaminant signals can be rapidly captured owing to the high ERI.

4. Conclusions

In this work, we presented self-assembled dielectric microsphere array-enhanced Raman scattering for large-area and ultra-long working distance confocal detection. It was observed that the Raman peaks were significantly enhanced by capping microsphere arrays. The roots of Raman scattering enhancement come from three channels, i.e. localized photonic nanojets, directional antenna effects and whispering gallery modes supported by the microspheres. The enhancement ratio of Raman intensity can be dramatically increased as the microsphere diameter and refractive index are satisfied with the condition supporting WGMs. The maximum enhancement ratio was up to 14.6. Moreover, the microsphere array demonstrated the capability of ultra-long working distance for confocal Raman detection, which can be attributed to the directional antenna effect of microsphere. The scattered light is confined by microsphere to a narrow distribution with small divergent angle, by which the scattered light can pass through the confocal pinhole even the scatterer out of the objective focus. The maximum working distance was up to ± 7.5 mm under the integration time of 10 s. The confocal Raman detection without focus adjustment is therefore achieved for the first time. Although the sensitivity to tilting angle of sample surface is the major drawback of microsphere-enhanced Raman scattering, we found that the Raman intensity was nearly constant when the tilting angle was lower than a threshold dominated by the NA of objective (e.g. 14.5° in the configuration of this work). The present work opens up new opportunities for Raman detection of 3D-structured surfaces by capping dielectric microsphere arrays. The high sensitivity is guaranteed by microsphere-enhanced Raman scattering and confocal setup of the spectrometer, whereas the free of focusing is beneficial to rapid mapping. Raman detection with large-area and ultra-long working distance can therefore be achieved.

Acknowledgments

The authors acknowledge the support of National Natural Science Foundation of China (NFSC) (11504012, 51475014), Scientific Research General Program of Beijing Municipal Commission of Education, and Doctoral Research Startup Fund of Beijing University of Technology.

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Figures (6)

Fig. 1
Fig. 1 Experimental setup of microsphere array-enhanced Raman scattering. (a) Schematic of Raman spectrometer. (b)-(g) Surface morphologies of Si wafer capped with close-packed FS microspheres of (b) 1.49 μm, (c) 2.51 μm, (d) 5.04 μm, and (e) 7.27 μm diameters, as well as (f) 4.93-μm-diameter PS microspheres and (g) 5.50-μm-diameter PMMA microspheres.
Fig. 2
Fig. 2 Enhancement of Raman scattering by microsphere arrays. (a) Raman spectra of bare and microsphere-capped Si wafers. (b) ERI for various microsphere arrays.
Fig. 3
Fig. 3 Numerical simulation of excitation laser focused by various microspheres and the corresponding ERI. The periodic boundaries were applied in order to simulate close-packed microsphere arrays. (a)-(f) The profiles of |E|4 at the shadow sides of (a) 1.49-μm-diameter, (b) 2.51-μm -diameter, (c) 5.04-μm-diameter and (d) 7.27-μm-diameter FS microspheres, as well as (e) 4.93-μm-diameter PS and 5.50-μm-diameter PMMA microspheres. The distributions of light intensities inside and in the vicinity of microspheres are demonstrated in the insets.
Fig. 4
Fig. 4 Microsphere-supported WGMs excited by excitation laser scattering. (a) Schematic of WGMs excitation in a microsphere. (b) A typical FDTD simulation of WGMs excited by a dipole scatterer in free space near the bottom of a 4.93-μm-diameter PS microsphere. (c) Comparison of theoretically calculated ERI with experimental results.
Fig. 5
Fig. 5 Ultra-long working distance Raman scattering detection by microspheres. (a) Microsphere-enhanced Raman scattering intensities for various microspheres and fpps. (b) The effect of integration time on maximum Δfpp for detection. (c) Schematic of confocal configuration and scattered light collection under different fpps. (d) The electric field intensity and angular distribution of EM waves emitted from a dipole in free space. (e)-(j) The electric field intensities and angular distributions of EM waves emitted from a dipole close to (e) 1.49-μm-diameter FS, (f) 2.51-μm-diameter FS, (g) 5.04-μm-diameter FS, (h) 7.27-μm-diameter FS, (i) 4.93-μm-diameter PS, and (j) 5.50-μm-diameter PMMA microspheres. The blue dash lines indicate the angle of the maximum cone of light that can be collected by the objective.
Fig. 6
Fig. 6 The effect of substrate tilting angle on Raman scattering intensity. (a) The effect of tilting angle on Raman scattering intensity for various microspheres. (b) The collection of EM waves under various tilting angles. (c) An application of microsphere-based large-area and ultra-long WD confocal Raman detection of 3D-structured surface.

Tables (1)

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Table 1 The Nominal diameters and WGM-supported diameters of microspheres

Equations (6)

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ER I sphere ~ 0 2π 0 r s | E s ( r ) | 4 rdrdθ π r s 2 × | E 0 | 4 = 2× 0 r s | E s ( r ) | 4 rdr r s 2 × | E 0 | 4
r s lλ 2πn
E f = 3 4 π 2 ( λ n ) 3 ( Q V )
{ Q= Re( k ) 2Im( k ) V= V Q ε( r ) | E( r ) | 2 d 3 r max[ ε( r ) | E( r ) | 2 ]
ERI=ER I sphere +( 1β )× E f
α sin 1 ( NA n 0 )
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