- Email: [email protected]
Superenhanced photonic nanojet by core-shell microcylinders
Physics Letters A 376 (2012) 1856–1860
Contents lists available at SciVerse ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Superenhanced photonic nanojet by core-shell microcylinders Cheng-Yang Liu ∗ Department of Mechanical and Electro-Mechanical Engineering, Tamkang University, No. 151, Ying-chuan Road, Tamsui District, New Taipei City, Taiwan
a r t i c l e
i n f o
Article history: Received 15 January 2012 Received in revised form 30 March 2012 Accepted 16 April 2012 Available online 20 April 2012 Communicated by R. Wu Keywords: Photonic nanojet Microcylinder Power enhancement
a b s t r a c t The super-enhancement of photonic nanojets generated at the shadow side surfaces of core-shell microcylinders illuminated by a plane wave is reported. Using high resolution finite-difference timedomain simulation, the enhancements of photonic nanojet at resonance and off-resonance conditions of microcylinders are investigated. The intensity enhancement of photonic nanojet depends strongly on the thickness of metal shell. Under proper resonance condition, the photonic nanojet super-enhancement can be excited in the core-shell microcylinder. Even under off-resonance condition, the photonic nanojet from microcylinder is still strong enough. The results may provide a new technique to detect and image nanoscale objects below the diffraction limit. This could yield a new ultra-microscopy technique for using visible light to detecting nanoparticles, optical gratings, and single molecules. © 2012 Elsevier B.V. All rights reserved.
1. Introduction
Conventional optical microscopy is one of the most principal scientific instruments in the history of science development. The imaging resolution of a classical optical microscopy is constrained by diffraction limit to about half of the illuminating wavelength. Beating the diffraction limit has become one of the highlights of research in modern optics [1]. The light scattering from small particles is well described by Mie theory [2]. Mie theory solves Maxwell’s equations with a quasi-analytical solution rigorously. Recently, the phenomenon of photonic nanojets has been disclosed [3–8]. The photonic nanojets are obtained on the shadow side of a dielectric microcylinder under plane wave illumination. The most concern of photonic nanojets is that they have a subwavelength beam waist and propagate over several wavelengths with little divergence. The conventional focusing by an objective lens gives diffraction limited optical spots. Subwavelength optical resolution has become necessary for nanoscale applications. Hence, the direct applications of photonic nanojets for sensing and metrology, Raman spectroscopy [9], two-photon fluorescence enhancement [10], and optical trapping [11], and white-light nanoscope [12] have been discussed. Due to the particular features of photonic nanojets, Kong et al. have reported the photonic nanojet technique for detection of deeply subwavelength pits in a metal substrate [13]. It can be extended to optical wavelengths for high density data storage.
*
Tel.: +886 2 26215656 # 2061; fax: +886 2 26209745. E-mail address: [email protected].
0375-9601/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2012.04.035
On the hand, one of the interesting properties of the photonic nanojet is the backscattering of dielectric cylinder. Numerical and experimental studies show that backscattering can be enhanced by several orders of magnitude by placing nanoparticles within the photonic nanojets [14–18]. The backscattering enhancement shows a dependence on the location and dimension of the metal nanoparticle. As the results, nanoparticles as small as 10 nm can be detected when they are approaching a designed microcylinder. The detection of nanoparticles scattering are usually limited by the weak scattering intensities, because the scattering cross section of a nanoparticle with small radius is much smaller than the incident wavelength. Therefore, it would be critical to reduce this size dependence to improve the detection sensitivity in far field optical systems. The use of photonic nanojets offers an enhanced spatial resolution and a circumvention of the scattering cross section’s size dependence. Optical forces acting on a metallic nanoparticle are investigated when the nanoparticle is introduced within a photonic nanojet [11]. These findings are attractive because photonic nanojet may bridge the gap between a conventional micro-technology and a functional nano-device. In this Letter, we theoretically demonstrate the super-enhancement of localized photonic nanojets generated at the shadow side surfaces of core-shell microcylinders illuminated by a plane wave. Using high resolution finite-difference time-domain (FDTD) simulation, we have found that photonic nanojets have enhancement at resonance and off-resonance conditions of microcylinders. The intensity enhancement of photonic nanojet depends strongly on the thickness of metal shell. Under proper resonance condition, the super-enhancement of photonic nanojet can be excited in the coreshell microcylinder. Even under off-resonance condition, the photonic nanojet from microcylinder is still strong enough. The results
C.-Y. Liu / Physics Letters A 376 (2012) 1856–1860
Fig. 1. Schematic diagram of core-shell microcylinder for photonic nanojet.
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Fig. 2. Focal length as a function of refractive index for dielectric (dashed line) and core-shell (solid line) microcylinders at d = 5 μm and t = 10 nm.
may provide a new technique to detect and image nanoscale objects below the diffraction limit. Details of the calculations and discussion of the results will be presented in the remainder of the Letter. 2. Numerical method In order to obtain highly accurate results for the photonic nanojet calculations, a proper selection with respect to numerical method is imperative. FDTD method [19] is a powerful, accurate numerical method that permits computer-aided design and simulation of photonic nanojets by microcylinders. Recently, we have conducted high resolution FDTD simulations on electro-optical resonant switching in side-coupled waveguide-cavity photonic crystal systems [20]. By using high resolution FDTD technique to solve Maxwell’s equations, we study the internal and near external field distributions of plane wave illuminated core-shell microcylinders. The perfectly matched layer (PML) absorbing boundary condition [21] is used to our FDTD simulations to terminate efficiently the outer boundary of the computational region. The center of microcylinders is laid out in the x– y plane. The propagation is along the x direction. The space steps in the x and y directions are x and y, respectively. The space lattice of FDTD has a uniform square cell size of 1 nm that is finer than 1/100 of an incident wavelength for all calculations. The sampling in time is selected to ensure numerical stability of the algorithm. The transverse electric wave propagation is considered in the present Letter wherein the incident electric field vector is in the propagation plane. The validation of the FDTD computational program has been reported by comparing with the exact solution for the light scattering of the microcylinders [22]. A more detailed treatment of the FDTD method is given in [19–22]. 3. Photonic nanojet enhancement Since photonic nanojet emission exists for a wide range of the microcylinder sizes, several papers have been reported for the spatial distributions of the internal and near external electromagnetic fields of plane wave illuminated dielectric cylinders [3–18]. These simulations have shown that high intensity photonic nanojets can exist in both the internal and near external fields along the incident axis. The location and the intensity of these near field photonic nanojets depend on the diameter of microcylinder and refractive index contrast between the microcylinder and its surrounding medium. The photonic nanojet can roughly be described with several parameters displayed in Fig. 1. The refractive indices of the core, metal shell, and surrounding medium are nd , nm ,
Fig. 3. Focal length as a function of shell thickness for dielectric (dashed line) and gold coating (solid line) microcylinders at nd = 1.5.
and ns , respectively. The focal length from the surface of the microcylinder to the point of maximum intensity of photonic nanojet is f . The diameter of microcylinder is d and the thickness of metal shell is t. The refractive index of the gold shell is 0.467 + 2.145i at the incident wavelength of 532 nm [23]. The microcylinder is surrounded by air medium (ns = 1). A plane wave at an initial wavelength of 532 nm is incident from the left and impinges on the microcylinder. These parameters will be precisely analyzed in the next paragraph. The numerical code permits the calculation of the total and scattered field throughout entire space when an incident lightwave interacts with a core-shell microcylinder. Fig. 2 depicts the focal length as a function of refractive index for dielectric and core-shell microcylinders at d = 5 μm and incident wavelength of 532 nm. The thickness of gold shell is t = 10 nm. The focal lengths for dielectric and core-shell microcylinders all decrease as refractive index increases. The core-shell microcylinders have no significant influence on the relation between focal length and refractive index. When the refractive index of the core of microcylinder is nd = 1.5, the photonic nanojets have a focal length of 526.3 nm for dielectric cylinder and 468.5 nm for gold shell microcylinder, respectively. In terms of intensity distribution, they all have a waist of about 250 nm. It is smaller than one-half wavelength. Fig. 3 shows focal length as a function of shell thickness for core-shell microcylinders at nd = 1.5. The focal length is reduced to 181.7 nm at t = 8 nm. The photonic nanojets are on the surface of cylinder when the
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C.-Y. Liu / Physics Letters A 376 (2012) 1856–1860
Fig. 4. Photonic nanojet intensity as a function of shell thickness for core-shell microcylinders with nd = 1.5.
Fig. 6. Normalized field of core-shell microcylinders with t = 25 nm in (a) electric field and (b) power flow pattern at resonance condition.
Fig. 5. Normalized power flow patterns of core-shell microcylinders at shell thickness (a) t = 10 nm and (b) t = 15 nm under off-resonance condition.
shell thickness is t > 25 nm. The incident wavelength of 532 nm is chosen as an example. The focal length of the photonic nanojets is scalable in respect of the incident wavelength. The previous numerical studies [13–17] demonstrated a remarkable characteristic of photonic nanojets that they can significantly enhance the light backscattering by nanoparticles located
within the nanojets. In this Letter, we discuss the influences of shell thickness on intensity of photonic nanojets by core-shell microcylinders with d = 5 μm. Fig. 4 shows photonic nanojet intensity as a function of shell thickness for core-shell microcylinders with nd = 1.5. The all intensities for core-shell microcylinders are normalized to the intensity for the dielectric microcylinder. Under off-resonance condition, the maximum of intensity for photonic nanojet is 1.856 at t = 8 nm. Under resonance condition, the intensity of photonic nanojet by shell thickness of 25 nm is enhanced by two to three orders of magnitude. The optical intensity and resonance show strong thickness dependence. Fig. 5 shows the normalized power flow patterns of core-shell microcylinders at different shell thicknesses under off-resonance condition. It can be seen that the photonic nanojet from core-shell microcylinder is still strong enough even under off-resonance condition. Fig. 6 shows normalized field of core-shell microcylinders at t = 25 nm in electric field and power flow pattern. The photonic nanojet of microcylinder is excited state of resonance at the shell thickness of 25 nm. Fig. 6 depicts a highly resonant state where lightwave is emitted near the surface of a microcylinder. Fig. 7 shows normalized electric field of core-shell microcylinders at t = 30 nm. It denotes a stable state of resonance where lightwave is confined near the center of a microcylinder by total internal reflection. Recent studies have shown that optical forces between coupled metal nanoparticles can be enhanced when the nanoparticles are located at resonance condition [11]. In this Letter, the enhanced photonic nanojet is attributed to
C.-Y. Liu / Physics Letters A 376 (2012) 1856–1860
1859
Fig. 7. Normalized electric field of core-shell microcylinders with t = 30 nm at stable state of resonance.
increased thickness of shell at resonance condition, which essentially originates from the generation of a surface plasmon. Fig. 8 shows intensity profile of photonic nanojet for core-shell microcylinders at resonance and off-resonance condition. In terms of intensity distribution, they all have a waist of about 250 nm. It is smaller than one-half wavelength. The generation of photonic nanojet is based on a considerably large object which provides highly confined fields to efficiently image nanoscale features. The preparation of core-shell microcylinders can be achieved by a combination of standard procedures [24–26]. The thickness of shell can be varied from a few to several hundred nanometers. The optical properties of the dispersions of metal coating microcylinders with varying coating thickness agree extremely well with the predictions of Mie theory. In such core-shell microcylinders, the shell provides a physical barrier between the optically active core and the surrounding material that makes a strongly enhanced optical intensity. This effect is a fundamental requirement for the use of microcylinders in applications such as biological observation, light emitting devices, and optical microscopy which depend on their emission qualities. The waveguide propagation losses include out-of-plane leakage [27] and roughness scattering [28] in the microcylinder. Out-of-plane leakage provides the major source of propagation loss. Additionally, there is roughness scattering arising from fabrication imperfections. We are currently examining threedimensional FDTD simulations and measurements. The diffraction, diffusion, and scattering studies on the core-shell microcylinders are currently being undertaken. 4. Conclusion We have analyzed numerically the enhancement of localized photonic nanojets generated at the shadow side surfaces of coreshell microcylinders illuminated by a plane wave. Using high resolution FDTD simulation, the enhancements of photonic nanojet at resonance and off-resonance conditions of microcylinders are investigated. The intensity enhancement of photonic nanojet depends strongly on the thickness of metal shell. Under proper resonance condition, the photonic nanojet super-enhancement can be excited in the core-shell microcylinder. Even under off-resonance condition, the photonic nanojet from microcylinder is still strong enough. The enhancement of photonic nanojets promises to make a useful application for optical detecting, differentiating, and sorting nanoparticles. By analyzing intensity and distribution of enhanced photonic nanojets from core-shell microcylinders, this mechanism could be an important tool in the fields of nanotechnology and nano-biotechnology. Further theoretical investigations
Fig. 8. Intensity profile of photonic nanojet for core-shell microcylinders at (a) resonance and (b) off-resonance condition.
and experimental efforts are needed to bring this mechanism into reality. References [1] L. Novotny, B. Hecht, Principles of Nano-Optics, Cambridge University Press, New York, 2006. [2] H.C. Van de Hulst, Light Scattering by Small Particles, Dover Publications, New York, 1981. [3] A.V. Itagi, W.A. Challener, J. Opt. Soc. Am. A 22 (2005) 2847. [4] C. Li, G.W. Kattawar, P. Zhai, Opt. Express 13 (2005) 4554. [5] P. Ferrand, J. Wenger, A. Devilez, M. Pianta, B. Stout, N. Bonod, E. Popov, H. Rigneault, Opt. Express 16 (2008) 6930. [6] A. Devilez, B. Stout, N. Bonod, E. Popov, Opt. Express 16 (2008) 14200. [7] K. Holms, B. Hourahine, F. Papoff, J. Opt. A: Pure Appl. Opt. 11 (2009) 054009. [8] M. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, H.P. Herzig, Opt. Express 19 (2011) 10206. [9] K.J. Yi, Y.F. Lu, Z.Y. Yang, J. Appl. Phys. 101 (2007) 063528. [10] S. Lecler, S. Haacke, N. Lecong, O. Crégut, J. Rehspringer, C. Hirlimann, Opt. Express 15 (2007) 4935. [11] X. Cui, D. Erni, C. Hafner, Opt. Express 16 (2008) 13560. [12] Z. Wang, W. Guo, L. Li, B. Lukyanchuk, A. Khan, Z. Liu, Z. Chen, M. Hong, Nat. Commun. 2 (2011) 218. [13] S. Kong, A. Sahakian, A. Taflove, V. Backman, Opt. Express 16 (2008) 13713. [14] Z. Chen, A. Taflove, V. Backman, Opt. Express 12 (2004) 1214. [15] X. Li, Z. Chen, A. Taflove, V. Backman, Opt. Express 13 (2005) 526. [16] Z. Chen, X. Li, A. Taflove, V. Backman, Appl. Opt. 45 (2006) 633. [17] A. Heifetz, J.J. Simpson, S. Kong, A. Taflove, V. Backman, Opt. Express 15 (2007) 17334. [18] S. Yang, A. Taflove, V. Backman, Opt. Express 19 (2011) 7084. [19] A. Taflove, S.C. Hagness, Computational Electrodynamics: The Finite Difference Time Domain Method, Artech House, Boston, 1998.
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[20] C.-Y. Liu, Phys. Lett. A 375 (2011) 3895. [21] J.-P. Berenger, J. Comput. Phys. 114 (1994) 185. [22] C. Li, G.W. Kattawar, P. Yang, J. Quant. Spectrosc. Radiat. Transfer 89 (2004) 123. [23] P.B. Johnson, R.W. Christy, Phys. Rev. B 6 (1972) 4370. [24] S.S. Park, B.Y.H. Liu, K.L. Rubow, Aerosol Sci. Tech. 16 (1992) 141.
[25] [26] [27] [28]
L.M. Liz-Marzán, M. Giersig, P. Mulvaney, Langmuir 12 (1996) 4329. P. Reiss, M. Protière, L. Li, Small 5 (2009) 154. G.R. Hadley, Photon. Technol. Lett. 14 (2002) 642. H. Benisty, C. Weisbuch, D. Labilloy, M. Rattier, C.J.M. Smith, T.F. Krauss, R.M. De la Rue, R. Houdré, U. Oesterle, C. Jouanin, D. Cassagne, J. Lightw. Technol. 17 (1999) 2063.
Contents lists available at SciVerse ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Superenhanced photonic nanojet by core-shell microcylinders Cheng-Yang Liu ∗ Department of Mechanical and Electro-Mechanical Engineering, Tamkang University, No. 151, Ying-chuan Road, Tamsui District, New Taipei City, Taiwan
a r t i c l e
i n f o
Article history: Received 15 January 2012 Received in revised form 30 March 2012 Accepted 16 April 2012 Available online 20 April 2012 Communicated by R. Wu Keywords: Photonic nanojet Microcylinder Power enhancement
a b s t r a c t The super-enhancement of photonic nanojets generated at the shadow side surfaces of core-shell microcylinders illuminated by a plane wave is reported. Using high resolution finite-difference timedomain simulation, the enhancements of photonic nanojet at resonance and off-resonance conditions of microcylinders are investigated. The intensity enhancement of photonic nanojet depends strongly on the thickness of metal shell. Under proper resonance condition, the photonic nanojet super-enhancement can be excited in the core-shell microcylinder. Even under off-resonance condition, the photonic nanojet from microcylinder is still strong enough. The results may provide a new technique to detect and image nanoscale objects below the diffraction limit. This could yield a new ultra-microscopy technique for using visible light to detecting nanoparticles, optical gratings, and single molecules. © 2012 Elsevier B.V. All rights reserved.
1. Introduction
Conventional optical microscopy is one of the most principal scientific instruments in the history of science development. The imaging resolution of a classical optical microscopy is constrained by diffraction limit to about half of the illuminating wavelength. Beating the diffraction limit has become one of the highlights of research in modern optics [1]. The light scattering from small particles is well described by Mie theory [2]. Mie theory solves Maxwell’s equations with a quasi-analytical solution rigorously. Recently, the phenomenon of photonic nanojets has been disclosed [3–8]. The photonic nanojets are obtained on the shadow side of a dielectric microcylinder under plane wave illumination. The most concern of photonic nanojets is that they have a subwavelength beam waist and propagate over several wavelengths with little divergence. The conventional focusing by an objective lens gives diffraction limited optical spots. Subwavelength optical resolution has become necessary for nanoscale applications. Hence, the direct applications of photonic nanojets for sensing and metrology, Raman spectroscopy [9], two-photon fluorescence enhancement [10], and optical trapping [11], and white-light nanoscope [12] have been discussed. Due to the particular features of photonic nanojets, Kong et al. have reported the photonic nanojet technique for detection of deeply subwavelength pits in a metal substrate [13]. It can be extended to optical wavelengths for high density data storage.
*
Tel.: +886 2 26215656 # 2061; fax: +886 2 26209745. E-mail address: [email protected].
0375-9601/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physleta.2012.04.035
On the hand, one of the interesting properties of the photonic nanojet is the backscattering of dielectric cylinder. Numerical and experimental studies show that backscattering can be enhanced by several orders of magnitude by placing nanoparticles within the photonic nanojets [14–18]. The backscattering enhancement shows a dependence on the location and dimension of the metal nanoparticle. As the results, nanoparticles as small as 10 nm can be detected when they are approaching a designed microcylinder. The detection of nanoparticles scattering are usually limited by the weak scattering intensities, because the scattering cross section of a nanoparticle with small radius is much smaller than the incident wavelength. Therefore, it would be critical to reduce this size dependence to improve the detection sensitivity in far field optical systems. The use of photonic nanojets offers an enhanced spatial resolution and a circumvention of the scattering cross section’s size dependence. Optical forces acting on a metallic nanoparticle are investigated when the nanoparticle is introduced within a photonic nanojet [11]. These findings are attractive because photonic nanojet may bridge the gap between a conventional micro-technology and a functional nano-device. In this Letter, we theoretically demonstrate the super-enhancement of localized photonic nanojets generated at the shadow side surfaces of core-shell microcylinders illuminated by a plane wave. Using high resolution finite-difference time-domain (FDTD) simulation, we have found that photonic nanojets have enhancement at resonance and off-resonance conditions of microcylinders. The intensity enhancement of photonic nanojet depends strongly on the thickness of metal shell. Under proper resonance condition, the super-enhancement of photonic nanojet can be excited in the coreshell microcylinder. Even under off-resonance condition, the photonic nanojet from microcylinder is still strong enough. The results
C.-Y. Liu / Physics Letters A 376 (2012) 1856–1860
Fig. 1. Schematic diagram of core-shell microcylinder for photonic nanojet.
1857
Fig. 2. Focal length as a function of refractive index for dielectric (dashed line) and core-shell (solid line) microcylinders at d = 5 μm and t = 10 nm.
may provide a new technique to detect and image nanoscale objects below the diffraction limit. Details of the calculations and discussion of the results will be presented in the remainder of the Letter. 2. Numerical method In order to obtain highly accurate results for the photonic nanojet calculations, a proper selection with respect to numerical method is imperative. FDTD method [19] is a powerful, accurate numerical method that permits computer-aided design and simulation of photonic nanojets by microcylinders. Recently, we have conducted high resolution FDTD simulations on electro-optical resonant switching in side-coupled waveguide-cavity photonic crystal systems [20]. By using high resolution FDTD technique to solve Maxwell’s equations, we study the internal and near external field distributions of plane wave illuminated core-shell microcylinders. The perfectly matched layer (PML) absorbing boundary condition [21] is used to our FDTD simulations to terminate efficiently the outer boundary of the computational region. The center of microcylinders is laid out in the x– y plane. The propagation is along the x direction. The space steps in the x and y directions are x and y, respectively. The space lattice of FDTD has a uniform square cell size of 1 nm that is finer than 1/100 of an incident wavelength for all calculations. The sampling in time is selected to ensure numerical stability of the algorithm. The transverse electric wave propagation is considered in the present Letter wherein the incident electric field vector is in the propagation plane. The validation of the FDTD computational program has been reported by comparing with the exact solution for the light scattering of the microcylinders [22]. A more detailed treatment of the FDTD method is given in [19–22]. 3. Photonic nanojet enhancement Since photonic nanojet emission exists for a wide range of the microcylinder sizes, several papers have been reported for the spatial distributions of the internal and near external electromagnetic fields of plane wave illuminated dielectric cylinders [3–18]. These simulations have shown that high intensity photonic nanojets can exist in both the internal and near external fields along the incident axis. The location and the intensity of these near field photonic nanojets depend on the diameter of microcylinder and refractive index contrast between the microcylinder and its surrounding medium. The photonic nanojet can roughly be described with several parameters displayed in Fig. 1. The refractive indices of the core, metal shell, and surrounding medium are nd , nm ,
Fig. 3. Focal length as a function of shell thickness for dielectric (dashed line) and gold coating (solid line) microcylinders at nd = 1.5.
and ns , respectively. The focal length from the surface of the microcylinder to the point of maximum intensity of photonic nanojet is f . The diameter of microcylinder is d and the thickness of metal shell is t. The refractive index of the gold shell is 0.467 + 2.145i at the incident wavelength of 532 nm [23]. The microcylinder is surrounded by air medium (ns = 1). A plane wave at an initial wavelength of 532 nm is incident from the left and impinges on the microcylinder. These parameters will be precisely analyzed in the next paragraph. The numerical code permits the calculation of the total and scattered field throughout entire space when an incident lightwave interacts with a core-shell microcylinder. Fig. 2 depicts the focal length as a function of refractive index for dielectric and core-shell microcylinders at d = 5 μm and incident wavelength of 532 nm. The thickness of gold shell is t = 10 nm. The focal lengths for dielectric and core-shell microcylinders all decrease as refractive index increases. The core-shell microcylinders have no significant influence on the relation between focal length and refractive index. When the refractive index of the core of microcylinder is nd = 1.5, the photonic nanojets have a focal length of 526.3 nm for dielectric cylinder and 468.5 nm for gold shell microcylinder, respectively. In terms of intensity distribution, they all have a waist of about 250 nm. It is smaller than one-half wavelength. Fig. 3 shows focal length as a function of shell thickness for core-shell microcylinders at nd = 1.5. The focal length is reduced to 181.7 nm at t = 8 nm. The photonic nanojets are on the surface of cylinder when the
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C.-Y. Liu / Physics Letters A 376 (2012) 1856–1860
Fig. 4. Photonic nanojet intensity as a function of shell thickness for core-shell microcylinders with nd = 1.5.
Fig. 6. Normalized field of core-shell microcylinders with t = 25 nm in (a) electric field and (b) power flow pattern at resonance condition.
Fig. 5. Normalized power flow patterns of core-shell microcylinders at shell thickness (a) t = 10 nm and (b) t = 15 nm under off-resonance condition.
shell thickness is t > 25 nm. The incident wavelength of 532 nm is chosen as an example. The focal length of the photonic nanojets is scalable in respect of the incident wavelength. The previous numerical studies [13–17] demonstrated a remarkable characteristic of photonic nanojets that they can significantly enhance the light backscattering by nanoparticles located
within the nanojets. In this Letter, we discuss the influences of shell thickness on intensity of photonic nanojets by core-shell microcylinders with d = 5 μm. Fig. 4 shows photonic nanojet intensity as a function of shell thickness for core-shell microcylinders with nd = 1.5. The all intensities for core-shell microcylinders are normalized to the intensity for the dielectric microcylinder. Under off-resonance condition, the maximum of intensity for photonic nanojet is 1.856 at t = 8 nm. Under resonance condition, the intensity of photonic nanojet by shell thickness of 25 nm is enhanced by two to three orders of magnitude. The optical intensity and resonance show strong thickness dependence. Fig. 5 shows the normalized power flow patterns of core-shell microcylinders at different shell thicknesses under off-resonance condition. It can be seen that the photonic nanojet from core-shell microcylinder is still strong enough even under off-resonance condition. Fig. 6 shows normalized field of core-shell microcylinders at t = 25 nm in electric field and power flow pattern. The photonic nanojet of microcylinder is excited state of resonance at the shell thickness of 25 nm. Fig. 6 depicts a highly resonant state where lightwave is emitted near the surface of a microcylinder. Fig. 7 shows normalized electric field of core-shell microcylinders at t = 30 nm. It denotes a stable state of resonance where lightwave is confined near the center of a microcylinder by total internal reflection. Recent studies have shown that optical forces between coupled metal nanoparticles can be enhanced when the nanoparticles are located at resonance condition [11]. In this Letter, the enhanced photonic nanojet is attributed to
C.-Y. Liu / Physics Letters A 376 (2012) 1856–1860
1859
Fig. 7. Normalized electric field of core-shell microcylinders with t = 30 nm at stable state of resonance.
increased thickness of shell at resonance condition, which essentially originates from the generation of a surface plasmon. Fig. 8 shows intensity profile of photonic nanojet for core-shell microcylinders at resonance and off-resonance condition. In terms of intensity distribution, they all have a waist of about 250 nm. It is smaller than one-half wavelength. The generation of photonic nanojet is based on a considerably large object which provides highly confined fields to efficiently image nanoscale features. The preparation of core-shell microcylinders can be achieved by a combination of standard procedures [24–26]. The thickness of shell can be varied from a few to several hundred nanometers. The optical properties of the dispersions of metal coating microcylinders with varying coating thickness agree extremely well with the predictions of Mie theory. In such core-shell microcylinders, the shell provides a physical barrier between the optically active core and the surrounding material that makes a strongly enhanced optical intensity. This effect is a fundamental requirement for the use of microcylinders in applications such as biological observation, light emitting devices, and optical microscopy which depend on their emission qualities. The waveguide propagation losses include out-of-plane leakage [27] and roughness scattering [28] in the microcylinder. Out-of-plane leakage provides the major source of propagation loss. Additionally, there is roughness scattering arising from fabrication imperfections. We are currently examining threedimensional FDTD simulations and measurements. The diffraction, diffusion, and scattering studies on the core-shell microcylinders are currently being undertaken. 4. Conclusion We have analyzed numerically the enhancement of localized photonic nanojets generated at the shadow side surfaces of coreshell microcylinders illuminated by a plane wave. Using high resolution FDTD simulation, the enhancements of photonic nanojet at resonance and off-resonance conditions of microcylinders are investigated. The intensity enhancement of photonic nanojet depends strongly on the thickness of metal shell. Under proper resonance condition, the photonic nanojet super-enhancement can be excited in the core-shell microcylinder. Even under off-resonance condition, the photonic nanojet from microcylinder is still strong enough. The enhancement of photonic nanojets promises to make a useful application for optical detecting, differentiating, and sorting nanoparticles. By analyzing intensity and distribution of enhanced photonic nanojets from core-shell microcylinders, this mechanism could be an important tool in the fields of nanotechnology and nano-biotechnology. Further theoretical investigations
Fig. 8. Intensity profile of photonic nanojet for core-shell microcylinders at (a) resonance and (b) off-resonance condition.
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