Generation of highly confined photonic nanojet using crescent-shape refractive index profile in microsphere
Introduction
Generation of photonic nanojet (PNJ) and controlled manipulation of its characteristics has attracted considerable current research interest. Photonic nanojet, characterized by high intensity, low divergence and sub wavelength lateral confinement, was first reported by Chen et al. in 2004 for the scattering of plane wave by lossless dielectric micro-cylinder and microsphere [[1], [2]]. Generation of photonic nanojet is a non-resonant phenomenon and has been shown to be relatively insensitive to the deformation and surface corrugations in the microspheres [[3], [4]]. Due to their unique characteristics, PNJ have found many applications in areas like Raman signal enhancement [[5], [6]], single molecule spectroscopy [7], fluorescence correlation spectroscopy [8], nano photolithography [[9], [10], [11]] and nanoscopy [[12], [13]] etc. Several approaches have been proposed for manipulating the length and confinement of photonic jet as many of aforesaid applications require control over the length and/or lateral dimension of the nanojet. The results reported in literature show that the length and full width at half maxima (FWHM) of photonic nanojet depend on size and shape of micro particle, refractive index of particle and that of the surrounding medium, wavelength, polarization and beam profile of the excitation light etc. [[14], [15]]. Apart from conventional shapes like sphere and cylinder, particles of other shapes such as axicon [16], micro cuboids [[17], [18]], micro discs [19], concentric graded index microsphere or ellipsoids [[20], [21]], core–shell microspheres [[22], [23]] and truncated microspheres [[24], [25]] etc. have also been explored in various studies to investigate tuning of PNJ characteristics. More recently Eti et al. have demonstrated controlled manipulation of photonic nanojet using controlled tuning of the refractive index in liquid crystals filled micro shells [26].
Wu et al. [9] have demonstrated mask-less lithography with a feature size of 250 nm () using a self-assembled planar structure of silica microsphere with a 400 nm centred ultraviolet (UV) broad band light source. McLeod and Arnold [10] have shown nano-lithography using photonic nano jet generated by optically trapped submicron size polystyrene microspheres with 355 nm laser source. A resolution of 102 nm () and 130 nm (/2.7), was shown for 0.5 m and 0.8 m sized polystyrene microspheres respectively. The approach followed by McLeod is however difficult to implement for practical applications due to inherent instability in trapping of small micro-spheres and associated Brownian motion. Using a bigger micro-sphere ( few micrometer diameter) can therefore be more useful for controlled nano photolithography if PNJ with narrow FWHM can be generated with such microspheres.
In this paper, we present the results of our studies on the variation of FWHM and length of PNJ generated from micro-spheres having crescent shape refractive index profile (CSRP). The results show that PNJ with FWHM down to /4.5 can be achieved in free space with multilayer CSRP lossless dielectric microsphere of 3 m diameter. In the presence of commonly used substrates with higher refractive index this would enables writing feature as small as /6.
Section snippets
Theory and simulations
A number of analytical and numerical approaches have been developed and applied to study the near as well as far field distribution of electromagnetic field in the photonic nanojet generated by microscopic dielectric objects. Analytical approach based on Mie theory and its suitable extension have been used to analyse the field distribution inside and outside the microsphere for concentric as well as eccentric inclusions [[22], [27], [28], [29]]. However, with increasing number of inclusions the
Results and discussion
Simulations were first performed for single microsphere of diameter while varying the refractive index ‘’ of microsphere from 1.3 to 2.0. The excitation wavelength was taken as 500 nm and the surrounding refractive index was taken as 1.0. A typical intensity distribution in the photonic nanojet and the variation of FWHM as a function of refractive index of micro-sphere are shown in Fig. 1. As the refractive index of microsphere increases the FWHM of photonic nanojet generated by
Conclusion
To conclude we have shown that extremely narrow PNJ with FWHM down to /4.5 in free space can be generated using the microspheres with multi-layer CSRP. The multi-layer CSRP microsphere allows confining PNJ well below the dimension that can be achieved using sub-micron sized microspheres and offer significant advantage in terms of ease in handling for various applications. For the applications requiring direct contact with microsphere the substrate refractive index was also
Acknowledgements
The authors would like to acknowledge the help received from Dr. J.T. Andrews, Department of Applied Physics, SGSITS, Indore, for help with numerical simulation using COMSOL and Dr. S.K. Majumder, Head, Laser Biomedical Applications Section, RRCAT, Indore, for his support. We thank Dr. T.K. Sharma, Head, Semiconductor Materials Lab. RRCAT, for critical reading of the manuscript.
References (40)
Photonic nanojet shaping of dielectric non-spherical micro particles
Physica E
(2014)- et al.
Geometric effect on photonic nanojet generated by dielectric micro-cylinders with non-cylindrical cross-sections
Opt. Commun.
(2016) - et al.
Synthesis of composite eccentric double-shelled hollow spheres
Polymer
(2009) - et al.
Facile microfluidic production of composite polymer core–shell microcapsules and crescent-shaped microparticles
J. Colloid Interface Sci.
(2017) - et al.
Photonic nanojet enhancement of backscattering of light by nanoparticles: a potential novel visible-light ultramicroscopy technique
Opt. Express
(2004) - et al.
Optical analysis of nanoparticles via enhanced backscattering facilitated by 3-D photonic nanojets
Opt. Express
(2005) - et al.
On-and off-optical-resonance dynamics of dielectric micro-cylinders under plane wave illumination
J. Opt. Soc. Am. B
(2015) - et al.
Persistence of photonic nanojet formation under the deformation of circular boundary
J. Opt. Soc. Am. B
(2015) - et al.
Enhanced Raman scattering by self-assembled silica spherical micro particles
J. Appl. Phys.
(2007) - et al.
Enhancement of Raman scattering by two orders of magnitude using photonic nanojet of a microsphere
J. Appl. Phys.
(2011)
Strong electromagnetic confinement near dielectric microspheres to enhance single-molecule fluorescence
Opt. Express
Multi-focus parallel detection of fluorescent molecules at picomolar concentration with photonic nanojets arrays
Appl. Phys. Lett.
A deep sub-wavelength process for the formation of highly uniform arrays of nanoholes and nanopillars
Nanotechnology
Fabrication of plasmonic nanodiscs by photonic nanojet lithography
Appl. Phys. Express
Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope
Nature Commun.
Locomotion of microspheres for super-resolution imaging
Sci. Rep.
Photonic nanojet
J. Comput. Theor. Nanosci.
Engineering photonic nanojets
Opt. Express
Localized EM and photonic jets from non-spherical and non-asymmetrical dielectric mesoscale objects: Brief review
Ann. Phys. (Berlin)
Cited by (11)
Photonic nanojet of a Gaussian beam illuminated low refractive index microsphere in air: A comprehensive variation of parameters
2022, Journal of Quantitative Spectroscopy and Radiative TransferCitation Excerpt :These investigations were somewhat expanded by Dong and Su [43], who concluded that the PNJ position can be changed by varying the beam-sphere distance, and Geynts et al. [44] who concluded that the optimal PNJ properties can be achieved when the incident beam size is similar to the microsphere size. Further complexity of the spherical case was achieved by including a spherical inclusion [45], and going over to layered spheres [46], elipsoids [47,48], crescent layered spheres [49], or core-shell spheres [50], all limited to a small range of parameters. Most recently, a broader range of parameters was presented by Mandal and Dantham [51], however the influence of the GB position was not investigated along other variations, and only the scattered component of the electrical field was taken into account.
Photonic nanojet beam shaping by illumination polarization engineering
2020, Optics CommunicationsCitation Excerpt :Later in 2014, Han et al. studied Gaussian beam [36] and zero-order Bessel beam [37] scattering by micro-spheroids. Patel [47] also used Gaussian beam to generate highly confined PNJs from a crescent-shape refractive index profile in microsphere. In addition, the polarizations of the incident beams also have an impact on the generated PNJs.
T-matrix methods for electromagnetic structured beams: A commented reference database for the period 2014–2018
2019, Journal of Quantitative Spectroscopy and Radiative TransferCitation Excerpt :The approach computed the quantities of interest directly from surface currents with no need ever to compute the scattered electromagnetic fields. Patel et al. [300] dealt with the generation of highly confined photonic nanojets using crescent-shape refractive index profile (CSRP) in microspheres (Crescent shapes may be defined as multilayered spheres which are nonconcentric with a common point of attach on the external surface). The results showed that photonic nanojets with FWHM down to ∼λ/4.5 can be achieved in free space with multilayer CSRP lossless dielectric microspheres of 3 µm diameter.
Surface optical sensitivity enhanced by a single dielectric microsphere
2022, Optics ExpressPhotonic Jets and Single-Photon Emitters
2022, Advanced Photonics Research