- Email: [email protected]
Real-space observation of photonic nanojet in dielectric microspheres
Physica E 61 (2014) 141–147
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Real-space observation of photonic nanojet in dielectric microspheres Cheng-Yang Liu n, Yung-Hsun Wang Department of Mechanical and Electro-Mechanical Engineering, Tamkang University, No. 151, Ying-chuan Road, Tamsui District, New Taipei City, Taiwan
H I G H L I G H T S
G R A P H I C A L
We present the real-space observation of photonic nanojet in microspheres. The photonic nanojets are measured by using a scanning optical microscope. The results provide a new tool to detect nano-objects in a far-field optical system.
We present the real-space observation of photonic nanojet in dielectric microspheres.
art ic l e i nf o
a b s t r a c t
Article history: Received 9 February 2014 Received in revised form 18 March 2014 Accepted 19 March 2014 Available online 27 March 2014
The three-dimensional real-space observation of photonic nanojet in different microspheres illuminated by a laser is reported. The finite-difference time-domain technique is used to perform the threedimensional numerical simulation for the dielectric microspheres. The key parameters of photonic nanojet are measured by using a scanning optical microscope system. We reconstruct the threedimensional real-space photonic nanojets from the collected stack of scanning images for polystyrene microspheres of 3 μm, 5 μm, and 8 μm diameters deposited on a glass substrate. Experimental results are compared to calculations and are found in good agreement with simulation results. The full width at half-maximum of the nanojet is 331 nm for a 3 μm microsphere at an incident wavelength of 633 nm. Our investigations show that photonic nanojets can be efficiently imaged by a microsphere and straightforwardly extended to rapidly distinguish the nano-objects in the far-field optical system. & 2014 Elsevier B.V. All rights reserved.
Keywords: Photonic nanojet Microsphere Microscopy
A B S T R A C T
1. Introduction The existence of diffraction limit is recognized by Ernst Abbe about 150 years ago using a conventional optical microscope [1,2]. The diffraction in the far field system results from the loss of evanescent waves that carry high spatial subwavelength information of an object. Moreover, when lightwave is focused by a traditional lens, the spot size cannot be infinitely sharpened due to diffraction. The dimension of light spot is usually calculated by the classic Rayleigh equation. In the recent years, several optical applications have been developed based on the research of dielectric microcylinders and microspheres.
n
Corresponding author. Tel.: þ 886 2 26215656x2061; fax: þ886 2 26209745. E-mail address: [email protected] (C.-Y. Liu).
http://dx.doi.org/10.1016/j.physe.2014.03.019 1386-9477/& 2014 Elsevier B.V. All rights reserved.
The phenomenon of photonic nanojets has been revealed by many scientific literatures [3–9]. The photonic nanojets appear as narrow and elongated spots with a high intensity of electromagnetic fields, if dielectric spherical micro-objects are well illuminated. Under theoretical and experimental investigations, these studies predict the appearance of a subwavelength-waist beam that emerges from the surface of the microsphere with low divergence. The excellent properties of photonic nanojets recommend nanojets as a useful implementation for high resolution nano-target detection [3,4], fluorescence microscopy improvements [10] and nano-patterning [11]. The more understanding of photonic nanojet is nevertheless needed to fully exploit the potential of microspheres as optical super-lens. The experimental demonstration of photonic nanojet is very important for nano-scale applications. An experimental observation of photonic nanojets created by single microsphere has been
142
C.-Y. Liu, Y.-H. Wang / Physica E 61 (2014) 141–147
performed using a fast scanning confocal microscope [12]. Detection of lightwave is achieved by an avalanche photodiode. The photonic nanojets in different diameters of microspheres with diameter ranging from 1 μm to 5 μm have been studied. It can be seen that photonic nanojets are efficiently imaged by a conventional optical microscopy system. Furthermore, Kim et al. have reported systematically how a modified and more complex illumination influences the properties of photonic nanojets [13]. The wavelength, the amplitude distribution, and the polarization of the illumination affect the localization and the shape of the photonic nanojets. Then, a novel approach is introduced to capture the optical virtual imaging at lateral resolution of 50 nm using microspheres and a white-light source [14,15]. The imaging mechanism in this optical system is related to photonic nanojets. However, the detailed imaging information of photonic nanojets should be studied further. In a simple optical microscope, an intensity enhancement has been obtained by focusing the incident lightwave with a silica microsphere for the green upconversion emission of a doped fluoroindate glass [16]. The experimental results offer an original method to enhance the upconversion emission intensity in biological specimens with rare earth doped particles that can be employed as nano-sensors. In this paper, we theoretically and experimentally demonstrate the three-dimensional (3-D) real-space observation of photonic nanojet in different microspheres illuminated by a laser at a wavelength of 633 nm. The finite-difference time-domain (FDTD) technique is used to perform the numerical simulation for the dielectric microspheres. The key parameters of photonic nanojet are measured by using a scanning optical microscope system. The three-dimensional real-space photonic nanojets are reproduced from the collected stack of scanning images for polystyrene microspheres of 3 μm, 5 μm, and 8 μm diameters deposited on a glass substrate. The 3-D numerical simulations of photonic nanojets are presented in Section 2. The experimental setup and measurement results are shown in Section 3. Finally, we summarize the remarks and discuss the potential applications of this study in Section 4.
2. Numerical approach In order to procure precise numerical results for local electromagnetic field produced by the scattering of a homogeneous dielectric microsphere, the FDTD method has been selected to execute the 3-D calculations for photonic nanojets [17]. Recently, we have conducted two-dimensional and 3-D FDTD calculations with high resolution on photonic nanojets for microcylinders and microspheres [18–21]. The detailed enhancement analyses of localized elongated photonic nanojets generated by a core shell microcylinder and a graded-index microellipsoid are reported. Therefore, we study the internal and near external electromagnetic field distributions of plane wave illuminated
Fig. 1. Schematic diagram of a microsphere for photonic nanojet.
dielectric microspheres by using an FDTD algorithm under the perfectly matched layer boundary conditions. The computational domain is a cubic box in the 3-D simulations. The physical model consisted of four components: the light source, the dielectric microsphere, the surrounding medium (air), and the glass substrate. The centered finite difference expressions are used to the space and time derivatives that are estimated and second-order accurate in the space and time steps. The calculation step is 10 nm, which can ensure enough accuracy and high calculation speed. The propagation direction (x axis) of the illuminated light is normal to the surface of the glass substrate. For further details, refer to Ref. [17–21]. The calculation of FDTD approach is written in Matlab code. The personal computer used in the calculation has the central processing unit of Intel Core i7 and the random access memory of 24 GB. Fig. 1 depicts the several key parameters of a 3-D photonic nanojet. The four key parameters are defined in order to characterize the photonic nanojets. The maximum amplitude of the electromagnetic field in the photonic nanojet is the peak amplitude (p). The radial distance of the point of peak amplitude from the surface of the microsphere is the focal length (f). The radial distance from the point of peak amplitude at which the electromagnetic field decays to 1/e of the peak amplitude is the decay length (g). The double distance in the y direction of the point of peak amplitude to the points where the electromagnetic field decays to 1/e of the peak value is the nanojet width (w). The peak amplitude is the measurement of the focusing energy. The focal length is analogous to the working distance of a conventional lens. The diameter and the refractive index of microspheres are d and n1 ¼1.59. The refractive index of surrounding medium is n2 ¼1. A lightwave illumination at a wavelength of 633 nm in the x direction is incident from the left and impinges on the microspheres. Fig. 2 depicts the normalized power flow patterns of the photonic nanojets along the z axis for the microspheres at diameters d¼3 μm, d¼ 5 μm, and d¼8 μm. The dependence of intensity distributions has been explored by applying three different diameters. We observe that the nanojet size is directly proportional to the diameter of microsphere as it could be found in the focal spot of a conventional lens. Fig. 3 depicts normalized power flow patterns of the photonic nanojets along the x axis for the microspheres at diameters d¼3 μm, d¼ 5 μm, and d¼ 8 μm. This is easily intelligible as the photonic nanojet is a non-resonant phenomenon. The transverse full widths at half-maximum of nanojets are calculated to be 326 nm, 336 nm, and 346 nm for the diameters 3 μm, 5 μm, and 8 μm, respectively. Taking the ratio of nanojet size to diameter provides quantitatively comparable values.
3. Experimental measurement In our experiments, we investigate the emerging electromagnetic fields comprising photonic nanojets with a high sensitivity optical microscope. The mean diameters of the polystyrene microspheres, obtained from Duke Standards, are specified as 3.002 μm719 nm, 4.993 μm740 nm, and 7.979 μm775 nm. The refractive index of polystyrene microspheres is 1.59. The microspheres diluted in pure water and deposited on a cleaned microscope coverslip before air drying. The refractive index and thickness of borosilicate glass substrate are 1.51 and 150 μm, respectively. The concentration of microspheres is set to approach an average surface density of 1 bead per 50 50 μm2. Thus light scattering between neighboring microspheres is completely avoided. A high sensitivity optical microscope system to measure the characteristics of photonic nanojet from microspheres has recently been developed at the Tamkang University. Fig. 4 shows a schematic diagram of the experimental setup. A single mode stabilized Helium Neon laser (Melles Griot 25-STP-912-230, 633 nm) is used
C.-Y. Liu, Y.-H. Wang / Physica E 61 (2014) 141–147
143
Fig. 3. Normalized power flow patterns of the photonic nanojets along the x axis for the microspheres at diameters (a) d ¼3 μm, (b) d ¼ 5 μm, and (c) d ¼8 μm.
Fig. 2. Normalized power flow patterns of the photonic nanojets along the z axis for the microspheres at diameters (a) d ¼3 μm, (b) d¼ 5 μm, and (c) d ¼ 8 μm.
to investigate the generation of photonic nanojet in the visible spectrum. A beam splitter divides optical intensities to be sent in two beams with adjustable energy ratio. Half-waveplates and GlanThompson polarizers are used to adjust the optical intensities and to
optimize the contrast of the photonic nanojets. The specimen is mounted on a precision motorized stage in x and y directions. A high numerical aperture of the apochromatic objective (Olympus MPLAPON100XO) ensures high resolution of the nanojet measurements. The nominal lateral resolutions for the objective are calculated to be 226 nm and 352 nm with and without oil immersion at a wavelength of 633 nm. The objective is mounted on a piezo-actuator (Sigma Koki
144
C.-Y. Liu, Y.-H. Wang / Physica E 61 (2014) 141–147
Fig. 4. Schematic diagram of the experimental setup.
SFS-OBL-1) with z-scan range of 100 μm and a theoretical resolution of 1 nm. The piezo-actuator in z axis is used to precisely define the focal plane of interest at the highest resolution and observe the realspace nanojet from microspheres. The image detection is performed by a deep-cooling charge-coupled device (CCD) camera (FLI MLx205). Scanning and data acquisition are synchronized and commanded by a graphic user interface in computer. In order to prevent interreflections with the microspheres and other components, the beam passes through the microspheres and is absorbed by a beam dump. The optical system is located inside a light controlled darkroom. We measure the photonic nanojets from the different microspheres with linear polarized illumination. Fig. 5 shows measured intensity distributions of nanojets in the x–y plane from the 3 μm, 5 μm, and 8 μm microspheres. Serial x–y plane scans correspond to serial focal planes moving upwards by steps of 500 nm. The entire stack is made of 60 frames in this measurement, but we only select 20 frames around the best focusing plane for a better observation. The raw stack shows the concentrated enhancement of optical intensity for a couple of images, and concentric rings for the other images. The surrounding medium remains at a constant intensity
Fig. 5. Raw stack of real images along the z axis for the (a) 3 μm, (b) 5 μm, and (c) 8 μm microspheres illuminated at incident wavelength of 633 nm. The focal plane moves upwards by steps of 500 nm between each x–y plane scan.
C.-Y. Liu, Y.-H. Wang / Physica E 61 (2014) 141–147
and could assist in quantifying the regional enhancement of intensity. Fig. 6 shows real images along the x axis for the microspheres at different diameters. The expected focusing effect
145
is exhibited clearly. We observe excellent agreement of intensity distributions between the numerical and experimental representations. Fig. 7 shows intensity profile of photonic nanojet for different microspheres in simulation and measurement. The transverse intensity profile is sliced along y axis at the peak amplitude. The intensity profile appears a notable Gaussian lineshape as expected from theoretical calculations. We used the following profiles to estimate the full width at half-maximum of the best peak amplitude. The transverse full widths at halfmaximum of nanojets are measured to be 331 nm, 343 nm, and 352 nm for the diameters 3 μm, 5 μm, and 8 μm, respectively. Fig. 8 shows focal length as a function of diameter for photonic nanojets. The numerical modeling has been done for all diameters in the range 3–8 μm. The focal lengths of nanojet all increase as
Fig. 7. Intensity profile of photonic nanojet for different microspheres in (a) simulation and (b) measurement.
Fig. 6. Real images along the x axis for the microspheres at diameters (a) d ¼3 μm, (b) d¼ 5 μm, and (c) d ¼ 8 μm.
Fig. 8. Focal length as a function of diameter for photonic nanojets.
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Fig. 9. Decay length as a function of diameter for photonic nanojets.
Fig. 10. Full width at half-maximum as a function of diameter for photonic nanojets.
diameter increases for microspheres. The focal lengths are measured to be 167 nm, 335 nm, and 593 nm for the 3 μm, 5 μm, and 8 μm microspheres, respectively. Fig. 9 shows decay length as a function of diameter for photonic nanojets. The decay lengths of nanojet all increase as diameter increases for microspheres. The decay lengths are measured to be 1432 nm, 2315 nm, and 3676 nm for the 3 μm, 5 μm, and 8 μm microspheres, respectively. Fig. 10 shows full width at half-maximum as a function of diameter for photonic nanojets. For 3 μm microsphere, we obtained a best full width at half-maximum of nanojet, which is below the diffraction limit. The generation of photonic nanojet is based on a microsphere which provides highly confined electromagnetic fields to efficiently distinguish nanoscale characteristics. The values of focal length, decay length, and full width at half-maximum stand in good agreement with the tendency calculated in theoretical simulations. We reconstruct the threedimensional real-space photonic nanojets from the collected stack of scanning images for the microspheres of 3 μm, 5 μm, and 8 μm diameters as shown in Fig. 11. The intensity distribution at the 3 μm microsphere is clearly weaker because of the reduction of the microsphere diameter. This establishes a significant value that is widely exploited for nano-sensing and microscopy. In this paper, the material dispersion of microspheres is neglected. The absorption in the dielectric microspheres should be very small because the dimension of microspheres is small. The propagation losses of the dielectric microspheres include out-of-plane scattering loss and scattering loss from surface roughness [22–24]. The major source of propagation loss is the out-of-plane scattering and the surface roughness scattering appears from fabrication imperfections. The 3-D light scattering and diffusion investigations on photonic nanojet from various microspheres are currently being undertaken.
Fig. 11. Three-dimensional reconstructed photonic nanojets for the microspheres at diameters (a) d ¼3 μm, (b) d ¼ 5 μm, and (c) d ¼8 μm.
4. Conclusion The real-space observations of photonic nanojet have been theoretically and experimentally observed using a high sensitivity
C.-Y. Liu, Y.-H. Wang / Physica E 61 (2014) 141–147
optical microscopy system. The dielectric microspheres with diameter ranging from 3 μm to 8 μm, deposited on a glass coverslip have been studied the effects on confined electromagnetic fields. The intensity of photonic nanojet depends strongly on the diameter of microsphere. Comparison with theoretical calculation and experimental measurement shows a relative excellent qualitative agreement. Our experimental results show that photonic nanojets from microspheres can be efficiently imaged by a traditional microscopy system. The mechanism described here can be straightforwardly extended to picture a broad range of nanotargets. Further researches are required to bring this ultramicroscopy technique into realization.
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
Acknowledgments This work is funded by National Science Council of Taiwan under Grant number NSC 102-2221-E-032-009. References [1] H.C. van de Hulst, Light Scattering by Small Particles, Dover Publications, New York, 1981. [2] L. Novotny, B. Hecht, Principles of Nano-Optics, Cambridge University Press, New York, 2006. [3] Z. Chen, A. Taflove, V. Backman, Opt. Express 12 (2004) 1214. [4] X. Li, Z. Chen, A. Taflove, V. Backman, Opt. Express 13 (2005) 526.
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[23] [24]
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A.V. Itagi, W.A. Challener, J. Opt. Soc. Am. A 22 (2005) 2847. C. Li, G.W. Kattawar, P. Zhai, Opt. Express 13 (2005) 4554. A. Devilez, B. Stout, N. Bonod, E. Popov, Opt. Express 16 (2008) 14200. K. Holms, B. Hourahine, F. Papoff, J. Opt. A: Pure Appl. Opt. 11 (2009) 054009. H. Guo, Y. Han, X. Weng, Y. Zhao, G. Sui, Y. Wang, S. Zhuang, Opt. Express 21 (2013) 2434. S. Lecler, S. Haacke, N. Lecong, O. Crégut, J. Rehspringer, C. Hirlimann, Opt. Express 15 (2007) 4935. W. Guo, Z.B. Wuang, L. Li, D.J. Whitehead, B.S. Luk’yanchuk, Z. Liu, Appl. Phys. Lett. 90 (2007) 243101. P. Ferrand, J. Wenger, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, H. Rigneault, Opt. Express 16 (2008) 6930. M. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, H.P. Herzig, Opt. Express 19 (2011) 10206. Z. Wang, W. Guo, L. Li, B. Lukyanchuk, A. Khan, Z. Liu, Z. Chen, M. Hong, Nat. Commun. 2 (2011) 218. A. Darafsheh, G.F. Walsh, L. Dal Negro, V.N. Astratov, Appl. Phys. Lett. 101 (2012) 141128. C. Pérez-Rodríguez, S. Ríos, I.R. Martín, L.L. Martín, P. Haro-González, D. Jaque, Opt. Express 21 (2013) 10667. A. Taflove, S.C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method, Artech House, Boston, 1998. C.-Y. Liu, Phys. Lett. A 376 (2012) 1856. C.-Y. Liu, Phys. Lett. A 376 (2012) 3261. C.-Y. Liu, Prog. Electromagn. Res. Lett. 37 (2013) 153. C.-Y. Liu, J. Mod. Opt. 60 (2013) 538. H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C.J.M. Smith, T.F. Krauss, R.M. De La Rue, R. Houdr´e, U. Oesterle, C. Jouanin, D. Cassagne, J. Lightw. Technol. 17 (1999) 2063. W. Kuang, W. Kim, A. Mock, J. O’Brien, IEEE J. Sel. Top. Quantum Electron. 12 (2006) 1183. A. Di Falco, M. Massari, M.G. Scullion, S.A. Schulz, F. Romanato, T.F. Krauss, IEEE Photonics J. 4 (2012) 1536.
Contents lists available at ScienceDirect
Physica E journal homepage: www.elsevier.com/locate/physe
Real-space observation of photonic nanojet in dielectric microspheres Cheng-Yang Liu n, Yung-Hsun Wang Department of Mechanical and Electro-Mechanical Engineering, Tamkang University, No. 151, Ying-chuan Road, Tamsui District, New Taipei City, Taiwan
H I G H L I G H T S
G R A P H I C A L
We present the real-space observation of photonic nanojet in microspheres. The photonic nanojets are measured by using a scanning optical microscope. The results provide a new tool to detect nano-objects in a far-field optical system.
We present the real-space observation of photonic nanojet in dielectric microspheres.
art ic l e i nf o
a b s t r a c t
Article history: Received 9 February 2014 Received in revised form 18 March 2014 Accepted 19 March 2014 Available online 27 March 2014
The three-dimensional real-space observation of photonic nanojet in different microspheres illuminated by a laser is reported. The finite-difference time-domain technique is used to perform the threedimensional numerical simulation for the dielectric microspheres. The key parameters of photonic nanojet are measured by using a scanning optical microscope system. We reconstruct the threedimensional real-space photonic nanojets from the collected stack of scanning images for polystyrene microspheres of 3 μm, 5 μm, and 8 μm diameters deposited on a glass substrate. Experimental results are compared to calculations and are found in good agreement with simulation results. The full width at half-maximum of the nanojet is 331 nm for a 3 μm microsphere at an incident wavelength of 633 nm. Our investigations show that photonic nanojets can be efficiently imaged by a microsphere and straightforwardly extended to rapidly distinguish the nano-objects in the far-field optical system. & 2014 Elsevier B.V. All rights reserved.
Keywords: Photonic nanojet Microsphere Microscopy
A B S T R A C T
1. Introduction The existence of diffraction limit is recognized by Ernst Abbe about 150 years ago using a conventional optical microscope [1,2]. The diffraction in the far field system results from the loss of evanescent waves that carry high spatial subwavelength information of an object. Moreover, when lightwave is focused by a traditional lens, the spot size cannot be infinitely sharpened due to diffraction. The dimension of light spot is usually calculated by the classic Rayleigh equation. In the recent years, several optical applications have been developed based on the research of dielectric microcylinders and microspheres.
n
Corresponding author. Tel.: þ 886 2 26215656x2061; fax: þ886 2 26209745. E-mail address: [email protected] (C.-Y. Liu).
http://dx.doi.org/10.1016/j.physe.2014.03.019 1386-9477/& 2014 Elsevier B.V. All rights reserved.
The phenomenon of photonic nanojets has been revealed by many scientific literatures [3–9]. The photonic nanojets appear as narrow and elongated spots with a high intensity of electromagnetic fields, if dielectric spherical micro-objects are well illuminated. Under theoretical and experimental investigations, these studies predict the appearance of a subwavelength-waist beam that emerges from the surface of the microsphere with low divergence. The excellent properties of photonic nanojets recommend nanojets as a useful implementation for high resolution nano-target detection [3,4], fluorescence microscopy improvements [10] and nano-patterning [11]. The more understanding of photonic nanojet is nevertheless needed to fully exploit the potential of microspheres as optical super-lens. The experimental demonstration of photonic nanojet is very important for nano-scale applications. An experimental observation of photonic nanojets created by single microsphere has been
142
C.-Y. Liu, Y.-H. Wang / Physica E 61 (2014) 141–147
performed using a fast scanning confocal microscope [12]. Detection of lightwave is achieved by an avalanche photodiode. The photonic nanojets in different diameters of microspheres with diameter ranging from 1 μm to 5 μm have been studied. It can be seen that photonic nanojets are efficiently imaged by a conventional optical microscopy system. Furthermore, Kim et al. have reported systematically how a modified and more complex illumination influences the properties of photonic nanojets [13]. The wavelength, the amplitude distribution, and the polarization of the illumination affect the localization and the shape of the photonic nanojets. Then, a novel approach is introduced to capture the optical virtual imaging at lateral resolution of 50 nm using microspheres and a white-light source [14,15]. The imaging mechanism in this optical system is related to photonic nanojets. However, the detailed imaging information of photonic nanojets should be studied further. In a simple optical microscope, an intensity enhancement has been obtained by focusing the incident lightwave with a silica microsphere for the green upconversion emission of a doped fluoroindate glass [16]. The experimental results offer an original method to enhance the upconversion emission intensity in biological specimens with rare earth doped particles that can be employed as nano-sensors. In this paper, we theoretically and experimentally demonstrate the three-dimensional (3-D) real-space observation of photonic nanojet in different microspheres illuminated by a laser at a wavelength of 633 nm. The finite-difference time-domain (FDTD) technique is used to perform the numerical simulation for the dielectric microspheres. The key parameters of photonic nanojet are measured by using a scanning optical microscope system. The three-dimensional real-space photonic nanojets are reproduced from the collected stack of scanning images for polystyrene microspheres of 3 μm, 5 μm, and 8 μm diameters deposited on a glass substrate. The 3-D numerical simulations of photonic nanojets are presented in Section 2. The experimental setup and measurement results are shown in Section 3. Finally, we summarize the remarks and discuss the potential applications of this study in Section 4.
2. Numerical approach In order to procure precise numerical results for local electromagnetic field produced by the scattering of a homogeneous dielectric microsphere, the FDTD method has been selected to execute the 3-D calculations for photonic nanojets [17]. Recently, we have conducted two-dimensional and 3-D FDTD calculations with high resolution on photonic nanojets for microcylinders and microspheres [18–21]. The detailed enhancement analyses of localized elongated photonic nanojets generated by a core shell microcylinder and a graded-index microellipsoid are reported. Therefore, we study the internal and near external electromagnetic field distributions of plane wave illuminated
Fig. 1. Schematic diagram of a microsphere for photonic nanojet.
dielectric microspheres by using an FDTD algorithm under the perfectly matched layer boundary conditions. The computational domain is a cubic box in the 3-D simulations. The physical model consisted of four components: the light source, the dielectric microsphere, the surrounding medium (air), and the glass substrate. The centered finite difference expressions are used to the space and time derivatives that are estimated and second-order accurate in the space and time steps. The calculation step is 10 nm, which can ensure enough accuracy and high calculation speed. The propagation direction (x axis) of the illuminated light is normal to the surface of the glass substrate. For further details, refer to Ref. [17–21]. The calculation of FDTD approach is written in Matlab code. The personal computer used in the calculation has the central processing unit of Intel Core i7 and the random access memory of 24 GB. Fig. 1 depicts the several key parameters of a 3-D photonic nanojet. The four key parameters are defined in order to characterize the photonic nanojets. The maximum amplitude of the electromagnetic field in the photonic nanojet is the peak amplitude (p). The radial distance of the point of peak amplitude from the surface of the microsphere is the focal length (f). The radial distance from the point of peak amplitude at which the electromagnetic field decays to 1/e of the peak amplitude is the decay length (g). The double distance in the y direction of the point of peak amplitude to the points where the electromagnetic field decays to 1/e of the peak value is the nanojet width (w). The peak amplitude is the measurement of the focusing energy. The focal length is analogous to the working distance of a conventional lens. The diameter and the refractive index of microspheres are d and n1 ¼1.59. The refractive index of surrounding medium is n2 ¼1. A lightwave illumination at a wavelength of 633 nm in the x direction is incident from the left and impinges on the microspheres. Fig. 2 depicts the normalized power flow patterns of the photonic nanojets along the z axis for the microspheres at diameters d¼3 μm, d¼ 5 μm, and d¼8 μm. The dependence of intensity distributions has been explored by applying three different diameters. We observe that the nanojet size is directly proportional to the diameter of microsphere as it could be found in the focal spot of a conventional lens. Fig. 3 depicts normalized power flow patterns of the photonic nanojets along the x axis for the microspheres at diameters d¼3 μm, d¼ 5 μm, and d¼ 8 μm. This is easily intelligible as the photonic nanojet is a non-resonant phenomenon. The transverse full widths at half-maximum of nanojets are calculated to be 326 nm, 336 nm, and 346 nm for the diameters 3 μm, 5 μm, and 8 μm, respectively. Taking the ratio of nanojet size to diameter provides quantitatively comparable values.
3. Experimental measurement In our experiments, we investigate the emerging electromagnetic fields comprising photonic nanojets with a high sensitivity optical microscope. The mean diameters of the polystyrene microspheres, obtained from Duke Standards, are specified as 3.002 μm719 nm, 4.993 μm740 nm, and 7.979 μm775 nm. The refractive index of polystyrene microspheres is 1.59. The microspheres diluted in pure water and deposited on a cleaned microscope coverslip before air drying. The refractive index and thickness of borosilicate glass substrate are 1.51 and 150 μm, respectively. The concentration of microspheres is set to approach an average surface density of 1 bead per 50 50 μm2. Thus light scattering between neighboring microspheres is completely avoided. A high sensitivity optical microscope system to measure the characteristics of photonic nanojet from microspheres has recently been developed at the Tamkang University. Fig. 4 shows a schematic diagram of the experimental setup. A single mode stabilized Helium Neon laser (Melles Griot 25-STP-912-230, 633 nm) is used
C.-Y. Liu, Y.-H. Wang / Physica E 61 (2014) 141–147
143
Fig. 3. Normalized power flow patterns of the photonic nanojets along the x axis for the microspheres at diameters (a) d ¼3 μm, (b) d ¼ 5 μm, and (c) d ¼8 μm.
Fig. 2. Normalized power flow patterns of the photonic nanojets along the z axis for the microspheres at diameters (a) d ¼3 μm, (b) d¼ 5 μm, and (c) d ¼ 8 μm.
to investigate the generation of photonic nanojet in the visible spectrum. A beam splitter divides optical intensities to be sent in two beams with adjustable energy ratio. Half-waveplates and GlanThompson polarizers are used to adjust the optical intensities and to
optimize the contrast of the photonic nanojets. The specimen is mounted on a precision motorized stage in x and y directions. A high numerical aperture of the apochromatic objective (Olympus MPLAPON100XO) ensures high resolution of the nanojet measurements. The nominal lateral resolutions for the objective are calculated to be 226 nm and 352 nm with and without oil immersion at a wavelength of 633 nm. The objective is mounted on a piezo-actuator (Sigma Koki
144
C.-Y. Liu, Y.-H. Wang / Physica E 61 (2014) 141–147
Fig. 4. Schematic diagram of the experimental setup.
SFS-OBL-1) with z-scan range of 100 μm and a theoretical resolution of 1 nm. The piezo-actuator in z axis is used to precisely define the focal plane of interest at the highest resolution and observe the realspace nanojet from microspheres. The image detection is performed by a deep-cooling charge-coupled device (CCD) camera (FLI MLx205). Scanning and data acquisition are synchronized and commanded by a graphic user interface in computer. In order to prevent interreflections with the microspheres and other components, the beam passes through the microspheres and is absorbed by a beam dump. The optical system is located inside a light controlled darkroom. We measure the photonic nanojets from the different microspheres with linear polarized illumination. Fig. 5 shows measured intensity distributions of nanojets in the x–y plane from the 3 μm, 5 μm, and 8 μm microspheres. Serial x–y plane scans correspond to serial focal planes moving upwards by steps of 500 nm. The entire stack is made of 60 frames in this measurement, but we only select 20 frames around the best focusing plane for a better observation. The raw stack shows the concentrated enhancement of optical intensity for a couple of images, and concentric rings for the other images. The surrounding medium remains at a constant intensity
Fig. 5. Raw stack of real images along the z axis for the (a) 3 μm, (b) 5 μm, and (c) 8 μm microspheres illuminated at incident wavelength of 633 nm. The focal plane moves upwards by steps of 500 nm between each x–y plane scan.
C.-Y. Liu, Y.-H. Wang / Physica E 61 (2014) 141–147
and could assist in quantifying the regional enhancement of intensity. Fig. 6 shows real images along the x axis for the microspheres at different diameters. The expected focusing effect
145
is exhibited clearly. We observe excellent agreement of intensity distributions between the numerical and experimental representations. Fig. 7 shows intensity profile of photonic nanojet for different microspheres in simulation and measurement. The transverse intensity profile is sliced along y axis at the peak amplitude. The intensity profile appears a notable Gaussian lineshape as expected from theoretical calculations. We used the following profiles to estimate the full width at half-maximum of the best peak amplitude. The transverse full widths at halfmaximum of nanojets are measured to be 331 nm, 343 nm, and 352 nm for the diameters 3 μm, 5 μm, and 8 μm, respectively. Fig. 8 shows focal length as a function of diameter for photonic nanojets. The numerical modeling has been done for all diameters in the range 3–8 μm. The focal lengths of nanojet all increase as
Fig. 7. Intensity profile of photonic nanojet for different microspheres in (a) simulation and (b) measurement.
Fig. 6. Real images along the x axis for the microspheres at diameters (a) d ¼3 μm, (b) d¼ 5 μm, and (c) d ¼ 8 μm.
Fig. 8. Focal length as a function of diameter for photonic nanojets.
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Fig. 9. Decay length as a function of diameter for photonic nanojets.
Fig. 10. Full width at half-maximum as a function of diameter for photonic nanojets.
diameter increases for microspheres. The focal lengths are measured to be 167 nm, 335 nm, and 593 nm for the 3 μm, 5 μm, and 8 μm microspheres, respectively. Fig. 9 shows decay length as a function of diameter for photonic nanojets. The decay lengths of nanojet all increase as diameter increases for microspheres. The decay lengths are measured to be 1432 nm, 2315 nm, and 3676 nm for the 3 μm, 5 μm, and 8 μm microspheres, respectively. Fig. 10 shows full width at half-maximum as a function of diameter for photonic nanojets. For 3 μm microsphere, we obtained a best full width at half-maximum of nanojet, which is below the diffraction limit. The generation of photonic nanojet is based on a microsphere which provides highly confined electromagnetic fields to efficiently distinguish nanoscale characteristics. The values of focal length, decay length, and full width at half-maximum stand in good agreement with the tendency calculated in theoretical simulations. We reconstruct the threedimensional real-space photonic nanojets from the collected stack of scanning images for the microspheres of 3 μm, 5 μm, and 8 μm diameters as shown in Fig. 11. The intensity distribution at the 3 μm microsphere is clearly weaker because of the reduction of the microsphere diameter. This establishes a significant value that is widely exploited for nano-sensing and microscopy. In this paper, the material dispersion of microspheres is neglected. The absorption in the dielectric microspheres should be very small because the dimension of microspheres is small. The propagation losses of the dielectric microspheres include out-of-plane scattering loss and scattering loss from surface roughness [22–24]. The major source of propagation loss is the out-of-plane scattering and the surface roughness scattering appears from fabrication imperfections. The 3-D light scattering and diffusion investigations on photonic nanojet from various microspheres are currently being undertaken.
Fig. 11. Three-dimensional reconstructed photonic nanojets for the microspheres at diameters (a) d ¼3 μm, (b) d ¼ 5 μm, and (c) d ¼8 μm.
4. Conclusion The real-space observations of photonic nanojet have been theoretically and experimentally observed using a high sensitivity
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optical microscopy system. The dielectric microspheres with diameter ranging from 3 μm to 8 μm, deposited on a glass coverslip have been studied the effects on confined electromagnetic fields. The intensity of photonic nanojet depends strongly on the diameter of microsphere. Comparison with theoretical calculation and experimental measurement shows a relative excellent qualitative agreement. Our experimental results show that photonic nanojets from microspheres can be efficiently imaged by a traditional microscopy system. The mechanism described here can be straightforwardly extended to picture a broad range of nanotargets. Further researches are required to bring this ultramicroscopy technique into realization.
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