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Micro-particle assisted nano-imaging has proven its success in the past few years since it can magnify the nano-objects, especially the metallic objects, into an image then collected by a conventional microscope. Micro-shell, which is a novel design of micro-particle in the configuration of a hemisphere with a hollow core region, is proposed and optimized in this paper in order to obtain a long photonic jet far away from its flat surface, thus increasing its working distance. Its dependence on the configuration and refractive index is investigated numerically. A micro-shell with the outer and inner radii of 5 and 2.5 µm and the refractive index of 1.5 can focus the incident light of 400 nm wavelength 2.7 µm away from the micro-shell flat surface, although the photonic jet intensity decreases to 25.8% compared to the solid hemisphere. Meanwhile, the photonic jet length of the micro-shell under the incident light of 400 nm and 1000 nm wavelengths are 1.7 µm and 4.3 µm, respectively, because its hollow core region tends to reduce the angle variation of the Poynting vectors in the photonic jet. With the long working distance and long photonic jet, the micro-shell could be used to scan over a sample to obtain a large area image when coupled with a conventional microscope, which is especially useful for the samples with the rough surfaces.
© 2015 Optical Society of America
1. Introduction
A conventional microscope resolves the objects with the feature size of around a half of the incident wavelength. To break the diffraction limit and improve the imaging resolution, a few methods have been developed, such as near field scanning optical microscope (NSOM), stimulated emission depletion (STED) microscopy, and photoactivatable localization microscopy (PALM) [1–3]. However, these techniques have their own limits, such as working with a single wavelength light source or in the near field, which employ complex designs as compared to the white light microscope. A nanoscope by utilizing micro-particles to enlarge the metallic nano-objects under the white light has been realized recently [4]. The image of dielectric nano-structures with the resolution of 25 nm was also demonstrated by using a confocal microscope [5]. Microsphere, which is the key component in the nanoscope setup, shows strong focusing effect, yielding the photonic jet outside the microsphere with high intensity [6]. Photonic jet has also found its applications in subwavelength nanopatterning and nanoparticle sensing as well [7–9]. However, it suffers from the disadvantage that the photonic jet is located near its surface, so that the microspheres are assembled on the sample surface and in direct contact with the sample. It is difficult to remove the microspheres and keeping the sample away from contamination. In the practical applications, the photonic jet of the micro-particle is desired to be kept far from its surface, and its configuration is expected to be as long as possible. Meanwhile, with a long photonic jet, even the samples are not mounted on the focusing spot with maximum intensity, a small position variation can still yield the similar results, keeping the system stable and consistent.
There are a few studies on the focusing effect of the microsphere and a few methods are proposed to optimize the photonic jet [10–13]. Multi-layer microsphere was studied theoretically to adjust the focusing intensity and photonic jet configuration [14, 15]. Microsphere immersed inside the liquid was also investigated numerically and experimentally. The refractive index contrast between the microsphere and the environment was tuned, so as to reduce the full width at half maximum (FWHM) and improve the imaging resolution [16, 17]. Recently, a double-layer dielectric microsphere was proposed, which can focus the incident light into an ultralong photonic jet, while the FWHM is 0.89 of the incident wavelength [18]. The FWHM of the photonic jet, which is a critical factor for imaging, is expected to be less than one half of the incident wavelength for super-resolution imaging.
In this paper, a novel micro-particle with the hemispheric shell configuration is proposed to generate an ultralong photonic jet far from its flat surface. This micro-particle is defined as ‘micro-shell’ in the following paragraphs. A unique advantage of this micro-shell design is that it is made by glass only and does not involve the other materials. Its dependence on the configuration and material are investigated. Through the glass micro-shell with the outer and inner radii of 5 μm and 2.5 μm, respectively, the incident light with the wavelength of 400 nm can be focused into a photonic jet 2.7 µm away from its flat surface with the length of 1.7 µm. Meanwhile, its FWHM kept below half of the incident wavelength, indicating the potential applications in super-resolution imaging.
2. Results and discussion
The micro-shell is with the outer and inner radii of R and r, respectively, as illustrated in Fig. 1(a). The hollow hemisphere and the shell share the same central point. The ratio between R and r is defined as the radius contrast ratio (R:r). When the light irradiates from the top, the photonic jet can be observed for micro-shell from both the Poyting vector distribution and the ray tracing in Figs. 1(b) and 1(c). The photonic jets formed for solid hemisphere and full sphere are shown in Figs. 1(d)-1(g) for comparison. The photonic jet is far away from the flat surface of solid hemisphere and micro-shell, while the photonic jet of full sphere is located near its surface. The photonic jet is tended to be elongated in micro-shell, which can be observed from Fig. 1(b) that the Poynting vectors around the focusing spot of micro-shell are parallel, instead of scattering outwards in solid hemisphere and microsphere in Figs. 1(d) and 1(f).
Fig. 1 (a) Illustration of micro-shell with the outer and inner radii of R and r. The Poynting vectors distribution when the incident light transmits through (b) a micro-shell with refractive index of 1.5, outer and inner radii of 5 and 2.5 µm, (d) a solid hemisphere with the refractive index of 1.5 and radius of 5 µm, and (f) a sphere with refractive index of 1.5 and radius of 5 µm. Ray tracing when light transmits through (c) a micro-shell with refractive index of 1.5, outer and inner radii of 5 and 2.5 µm, (e) a solid hemisphere with the refractive index of 1.5 and radius of 5 µm, and (g) a sphere with refractive index of 1.5 and radius of 5 µm from the left.
Ray tracing results of a plane wave transmitting through the micro-shell is demonstrated in Fig. 1(c), which shows that the photonic jet is far away from the micro-shell flat surface as well. The ray tracing results of light transmission through solid hemisphere and microsphere are shown in Figs. 1(e) and 1(g), which agrees with the Poynting vector distribution well. In order to realize a long photonic jet at a far distance from the micro-shell flat surface, the dependence of the photonic jet of micro-shell on its configuration and material will be studied numerically by Lumerical 3D FDTD.
Figures 2(a)-2(j) shows the photonic jet dependence on the radius contrast ratio. The plane wave with the wavelength of 400 nm irradiates from the top onto the convex side of the micro-shell. The refractive index of the micro-shell and the outer radius are kept at 1.5 and 5 µm, respectively, while the radius contrast ratio is varied from 10:0 to 10:9. From the light intensity distribution, it is observed that the photonic jets formed by different micro-shells have different positions, lengths, FWHMs, and maximum intensities. The length of photonic jet is defined as the distance between the two points along the axis where the light intensity drops to 1/e of its maximum intensity. The FWHM is reduced gradually when the radius contrast ratio decreases, although the focusing intensity decreases. Meanwhile, the micro-shell with the lower radius contrast ratio yields a higher effective numerical aperture (NA). The effective NA is determined by the average focusing effect of the transmitted light through the micro-shell. In solid hemisphere (micro-shell with inner radius of 0), the light through the core region is focused with a less angle against the axis as compared to the light transmitting through the margin, due to the difference of the incident angle at the convex side of micro-shell. By removing the core material and increasing the inner radius, the light through the core region of the micro-shell tends to scatter outward, so that its contribution to focus is eliminated, yielding a less effective numerical aperture (NA). Meanwhile, the light transmitting through the margin with a larger focusing angle remains to form the photonic jet.
Fig. 2 Light intensity distributions when the light transmits through (a)-(j) the micro-shell with different radius contrast ratio, (k) microsphere (R = 5 μm) with n = 1.5, and (l) microsphere (R = 5 μm) with n = 1.3.
On the contrary, as the radius contrast ratio decreases, the transmitted light intensity becomes weaker as most of the light transmitting through the core region scatters outwards, which decreases the light intensity at the photonic jet. Therefore, although a larger inner radius results in a larger effective NA, the light intensity drops significantly as well. The balance between the effective NA and the light intensity at photonic jet is crucial. When the radius contrast ratio is less than 10:5, the FWHM is less than one half of the incident wavelength (λ = 400 nm), which is expected to break the diffraction limit for imaging. In this case, the maximum light intensity in the photonic jet drops to 25.8% of that in solid hemisphere. However, when the radius contrast ratio is less than 10:7, the focusing effect is too weak to be used in imaging or the other micro-particle assisted applications. It is also found that the focusing spot is getting closer to the micro-shell flat surface when the radius contrast ratio decreases. When the radius contrast ratio is 10:5, the FWHM is 182 nm and the distance from the micro-shell flat surface to the focusing spot is 2.7 µm. 2.7 µm is large enough as the working distance of the micro-shell assisted nano-imaging as compared to the size of nano-objects (< 200 nm). The photonic jets through microspheres (R = 5 μm) with the refractive indices of 1.5 and 1.3 are also simulated for comparison in Figs. 2(k) and 2(l). The FWHM of the photonic jet in microsphere with the refractive index of 1.5 is 208 nm, which is larger than that in micro-shell and its length is 0.8 μm. As the refractive index decreases to 1.3, although the photonic jet is elongated and far away from the microsphere surface, the FWHM increases to 325 nm, which cannot be used for super-resolution imaging.
The refractive index of the shell material also influences the photonic jet formation. Figure 3 shows the light intensity distribution by the micro-shell with different refractive indices, corresponding to different materials. The refractive index is changed from 1.3 to 2.0, which corresponds to silica, most of the polymer materials, and Barium Titanate widely available in nature. The wavelength of the incident light is also chosen to be 400 nm. The inner and outer radii are 2.5 and 5 µm, keeping the optimal radius contrast ratio obtained from the previous study. As the refractive index increases, the photonic jet length ranges from 2.9 µm to 1.1 µm for the micro-shell with the refractive index of 1.3 – 2.0. When the refractive index increases, although the length of the photonic jet decreases and the distance between the photonic jet and the micro-shell flat surface shrinks, the advantage is that the FWHM decreases significantly. With the higher refractive index, the micro-shell tends to focus the light more efficiently, resulting in a smaller FWHM, which is an important factor to determine the imaging resolution. As the refractive index is larger than 1.7, the critical angle becomes smaller and the internal reflection inside the micro-shell dominates while less light transmits through the micro-shell. When the refractive index is 1.5 or 1.6, the corresponding FWHM is 182 or 159 nm, which are significantly lower than one half of the incident wavelength (λ = 400 nm). This indicates the potential to realize a super-resolution imaging by using the micro-shell with the refractive index of 1.5 or 1.6.
Fig. 3 Light intensity distribution when the light transmits through the micro-shell with different refractive indices from 1.3 to 2.0.
In the practical application, the micro-particle is coupled with a conventional white light microscope to realize a nanoscope with high resolution. The light distribution through the optimized micro-shell (R = 10 μm, r = 5 μm, and n = 1.5) at different incident wavelengths was investigated as well. As observed in Figs. 4(a)-4(d), the photonic jet length ranges from 1.7 μm to 4.3 μm under different incident wavelengths from 400 to 1000 nm. As the incident wavelength increases, the photonic jet length also increases accordingly. At each incident wavelength, the photonic jet length is about 4 times of the incident wavelength, indicating the micro-shell can work over a broadband from visible to near infrared. The location of photonic jet is shifted far away from the micro-shell as the incident wavelength increases. The FWHMs under 400, 600, and 800 nm incidence are all below a half of the incident wavelength, which shows that micro-shell works in visible spectrum for super-resolution imaging. The light intensities under 4 different incident wavelengths are summed up to approximate the case of white light incidence as shown in Fig. 4(e). The FWHM is 245 nm, which is smaller than a half of the average incident wavelength of 700 nm. The intensity along the dash line in Fig. 4(e) is extracted and shown in Fig. 4(f). The photonic jet length is 1.5 μm under white light incidence with the maximum intensity 2.5 μm away from the flat surface. In practical application, when the micro-shell is used in imaging combined with a conventional white light microscope, the incident beam through the objective lens is a Gaussian beam instead of plane wave [19]. In this case, the FWHM is expected to reduce as the micro-shell could converge the incident light further, yielding an even higher resolution in imaging.
Fig. 4 (a)-(d) Light intensity distribution at different incident wavelengths from 400 to 1000 nm through micro-shell with outer and inner radii of 5 and 2.5 μm, refractive index of 1.5. (e) Photonic jet under white light by combining the light intensity under 4 different incident wavelengths 400, 600, 800, and 1000 nm. (f) The light intensity distribution along the axis (dash line) of micro-shell in (e).
Although the micro-particle assisted imaging is mainly used to increase the lateral resolution in x-y dimension, the axial resolution along z direction is also an important factor to be considered. To extract the information of sample fine structures encoded in the evanescent wave is the key step to determine the resolution. The micro-particle can convert the evanescent wave to propagation wave and then magnify the image, so as to realize the super-resolution imaging [5]. For evanescent wave, according to the relation among the wave vectors along different directions in Eq. (1), the effective wavelength of evanescent wave will decrease as the effective wavelength in lateral direction decreases [20].
where n is the refractive index of the environment, k0 the incident wave vector in vacuum, kx and ky wave vectors in x-y dimension, and kz the wave vector of evanescent wave in z direction. The resolution in x-y dimension improved due to the effective wavelength in x-y dimension decreases. Meanwhile, the effective wavelength in the evanescent wave in z direction will also decrease according to Eq. (1). The shorter effective wavelength can detect the smaller object, so that theoretically both the resolutions in x-y dimension and z direction will be increased concurrently.3. Conclusions
In this paper, micro-shell is designed and investigated to realize a long photonic jet far away from its flat surface. The configuration and the material of the micro-shell structure are optimized via numerical simulation. A photonic jet with the length of 1.7 µm and full width at half maximum of 182 nm is obtained when the inner and outer radii are 2.5 and 5 µm and the refractive index is 1.5 under the incident wavelength of 400 nm. The photonic jet under the other incident wavelength ranging from visible to near infrared is also studied. Over a broadband, the photonic jet through the micro-shell is with the length of about 4 times of the incident wavelength. The long photonic jet is attributed to the energy flow near the focal spot is essentially parallel to the light propagation direction to generate a small angular deviation. The optimal micro-shell has the unique advantages that it consists of a single material and operates in ambient air. Most importantly, the photonic jet is far away from the micro-shell flat surface, which promises the large area imaging even for a sample with the rough surface by scanning.
Acknowledgments
This research is supported by the National Research Foundation, Prime Minister’s Office, Singapore under its Competitive Research Programme (CRP Award No. NRF-CRP 10-2012-04).
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