Quasi one-dimensional light beam generated by a graded-index microsphere

Generation of Photonic Nanojet Using Gold Film Dielectric Microdisk Structure

Due to their narrow beam waist size, high intensity, and long propagation distance, photonic nanojets (PNJs) can be used in various fields such as nanoparticle sensing, optical subwavelength detection, and optical data storage. In this paper, we report a strategy to realize an SPP-PNJ by exciting a surface plasmon polariton (SPP) on a gold-film dielectric microdisk. In detail, an SPP is excited by the grating-coupling method, then it irradiates the dielectric microdisk to form an SPP-PNJ. The characteristics of the SPP-PNJ, including maximum intensity, full width at half maximum (FWHM), and propagation distance, are studied by using finite difference time domain (FDTD) numerical solutions. The results demonstrate that the proposed structure can produce a high-quality SPP-PNJ, the maximum quality factor of which is 62.20, and the propagation distance of the SPP-PNJ is 3.08 λ. Furthermore, the properties of the SPP-PNJ can be modified flexibly by changing the thickness and refractive index of the dielectric microdisk.

Photonic Hooks Generated by a Concave Micro-Cylinder Based on Structure-Constrained Functions

Owing to its crooked trajectory and small full width at half-maximum, photonic hook (PH) has attracted wide attention since its inception and experimental confirmation. However, the present generation and regulation of PH are mostly dependent on the breaking of the symmetry of the system composed of the incident light and the regular structure particles, which inevitably limits the research of PH. In this work, the PH of the irregular particles is demonstrated with the help of a structure-constrained function (SCF). By varying the coefficients of the function, characteristic parameters of the PH, such as the bending angle, the effective length and the bending direction, can be effectively modulated. Meanwhile, high-quality PHs with a bending angle of up to 46∘ and an effective length of up to 11.90λ, as well as PHs with three bends, can be obtained using this method. The formation mechanism of the PH is revealed by simulating the distribution of the field intensity with the finite element method and analyzing with ray optics. This is the first time that we introduce a function into the investigation of PH, paving a new way for a more interesting exploration of PH.

Novel Bilayer Micropyramid Structure Photonic Nanojet for Enhancing a Focused Optical Field

In this paper, synthetically using refraction, diffraction, and interference effects to achieve free manipulation of the focused optical field, we firstly present a photonic nanojet (PNJ) generated by a micropyramid, which is combined with multilayer thin films. The theory of total internal reflection (TIR) was creatively used to design the base angle of the micropyramid, and the size parameters and material properties of the microstructure were deduced via the expected optical field distribution. The as-designed bilayer micropyramid array was fabricated by using the single-point diamond turning (SPDT) technique, nanoimprint lithography (NIL), and proportional inductively coupled plasma (ICP) etching. After the investigation, the results of optical field measurement were highly consistent with those of the numerical simulation, and they were both within the theoretical calculation range. The bilayer micropyramid array PNJ enhanced the interference effect of incident and scattered fields; thus, the intensity of the focused light field reached 33.8-times that of the initial light, and the range of the focused light field was extended to 10.08λ. Moreover, the full width at half maximum (FWHM) of the focal spot achieved was 0.6λ, which was close to the diffraction limit.

Photonic nanojets with ultralong working distance and narrowed beam waist by immersed engineered dielectric hemisphere

Engineered spherical micro-lens can manipulate light at sub-wavelength scale and emerges as a promising candidate to extend the focal length and narrow the focal spot size. Here, we report the generation of photonic nanojets (PNJs) with an ultralong working distance and narrowed beam waist by an immersed engineered hemisphere. Simulations show that a two-layer hemisphere of 4.5 µm radius exhibits a PNJ with the working distance of 9.6 µm, full width at half maximum of 287 nm, and length of 23.37 λ, under illumination of a plane wave with a 365 nm wavelength. A geometrical optics analysis indicated that the formed PNJ behind the immersed two-layer hemisphere results from the convergence of light of the outer-hemisphere fringe area, which refracts into and passes through the outer hemisphere and then directly leaves the outer-hemisphere flat surface. Thus the embedded hemisphere is comparable to an immersed focusing lens with high numerical aperture, which can promise both long working distance and narrowed beam waist. This is further demonstrated with the corresponding embedded-engineered single-layer hemisphere, whose spherical face is partly cut parallel to the hemispherical flat surface. In addition, the hemisphere is compatible with adjacent laser wavelengths. Finally, a spot size smaller than 0.5 λ is demonstrated in the lithography simulation. Due to these hemispheres low cost, they have potential in far-field lithography for pattern arrays with line width less than 0.5 λ.

Characteristics of photonic jets generated by a dielectric sphere illuminated by a Gaussian beam

Photonic jets (PJs) formed on the shadow side of micro-sized dielectric spheres excited by focused Gaussian beams are investigated within the framework of the generalized Lorenz-Mie theory (GLMT). The intrinsic advantages of rapidity and high accuracy of the GLMT in calculations enable us to conduct a systematic study of PJs at a low cost and a high reliability. To reveal the influence of beam parameters on the properties of PJs, numerical results concerning variations of key parameters of PJs, including the maximal intensity, the focal distance, which is linked to the position of maximal intensity, and longitudinal and transversal dimensions are presented with the change of the beam waist radius and the focal center location of the Gaussian beam. The results show that as the beam waist radius approaches the radius of the particle, the energy stream of the Gaussian beam contributes more efficiently to the formation of PJs. By properly tuning the location of the beam focal center, the PJ pattern can be efficiently engineered to a large extent.

All-dielectric concentration of electromagnetic fields at the nanoscale: the role of photonic nanojets

The photonic nanojet (PNJ) is a narrow high-energy beam that was originally found on the back side of all-dielectric spherical structures. It is a unique type of energy concentration mode. The field of PNJs has experienced rapid growth in the past decade: nonspherical and even pixelized PNJ generators based on new physics and principles along with extended photonic applications from linear optics to nonlinear optics have driven the re-evaluation of the role of PNJs in optics and photonics. In this article, we give a comprehensive review for the emerging sub-topics in the past decade with a focus on two specific areas: (1) PNJ generators based on natural materials, artificial materials and nanostructures, and even programmable systems instead of conventional dielectric geometries such as microspheres, cubes, and trihedral prisms, and (2) the emerging novel applications in both linear and nonlinear optics that are built upon the specific features of PNJs. The extraordinary features of PNJs including subwavelength concentration of electromagnetic energy, high intensity focusing spot, and lower Joule heating as compared to plasmonic resonance systems, have made PNJs attractive to diverse fields spanning from optical imaging, nanofabrication, and integrated photonics to biosensing, optical tweezers, and disease diagnosis.

Flexible Photonic Nanojet Formed by Cylindrical Graded-Index Lens

Photonic nanojets formed in the vicinity of the cylindrical graded-index lens with different types of index grading are numerically investigated based on the finite-difference time-domain method. The cylindrical lens with 1600 nm diameter is assembled by eighty-seven hexagonally arranged close-contact nanofibers with 160 nm diameter. Simulation and analysis results show that it is possible to engineer and elongate the photonic nanojet. Using differently graded-index nanofibers as building elements to compose this lens, the latitudinal and longitudinal sizes of the produced photonic nanojet can be flexibly adjusted. At an incident wavelength of 532 nm, the cylindrical lens with index grading = 2 can generate a photonic nanojet with a waist about 173 nm (0.32 wavelength). This lens could potentially contribute to the development of a novel device for breaking the diffraction limit in the field of optical nano-scope and bio-photonics.

An ultranarrow photonic nanojet formed by an engineered two-layer microcylinder of high refractive-index materials

A photonic nanojet (PNJ) is a tightly focused beam that emerges from the shadow surface of microparticles. Due to its high peak intensity and subwavelength beam waist, the PNJ has increasingly attracted attention, with potential applications in optical imaging, nanolithography, and nanoparticle sensing. A variety of ways have been demonstrated to further shrink the beam waist of PNJs, such as engineering the microparticle geometry and optimizing a multilayer structure. In this simulation work, we report the realization of an ultranarrow PNJ, which is formed by an engineered two-layer microcylinder of high refractive-index materials. Finite element analysis shows that under 632.8 nm illumination, the full width at half maximum of the beam waist can reach 87 nm (~λ/7.3). As far as we know, this is the narrowest PNJ ever reported. Using the backscattering intensity as a contrast mechanism, we also demonstrated the imaging resolution and capability of the ultranarrow PNJ through numerical simulations. We anticipate that this ultranarrow PNJ will open new possibilities in a variety of research areas, including nanoparticle detection, biomedical imaging, and nanolithography.

Numerical Study of Tunable Photonic Nanojets Generated by Biocompatible Hydrogel Core-Shell Microspheres for Surface-Enhanced Raman Scattering Applications

Core-shell microspheres have been applied in various research areas and, in particular, they are used in the generation of photonic nanojets with suitable design for photonic applications. The photonic nanojet is a narrow and focused high-intensity light beam emitting from the shadow-side of microspheres with tunable effective length, thus enabling its applications in biosensing technology. In this paper, we numerically studied the photonic nanojets brought about from biocompatible hydrogel core-shell microspheres with different optical properties. It was found that the presence of the shell layer can significantly affect the characteristics of the photonic nanojets, such as the focal distance, intensity, effective length, and focal size. Generally speaking, the larger the core-shell microspheres, the longer the focal distance, the stronger the intensity, the longer the effective length, and the larger the focal size of the generated photonic nanojets are. The numerical simulations of the photonic nanojets from the biocompatible core-shell microspheres on a Klarite substrate, which is a classical surface-enhancing Raman scattering substrate, showed that the Raman signals in the case of adding the core-shell microspheres in the system can be further enhanced 23 times in water and 108 times in air as compared in the case in which no core-shell microspheres are present. Our study of using tunable photonic nanojets produced from the biocompatible hydrogel core-shell microspheres shows potential in future biosensing applications.

Optimization of photonic nanojets generated by multilayer microcylinders with a genetic algorithm

We employ a genetic algorithm coupled with Mie theory to optimize the magnetic field intensity profile of photonic nanojets (PNJs) generated by multilayer microcylinders at visible wavelengths in free space. We first optimize five-layer microcylinders to elongate the PNJs. We show that a properly designed five-layer microcylinder structure can generate an ultra-long PNJ with a beam length ~ 107.5 times the illumination wavelength λ₀. We then optimize five-layer microcylinders to narrow the waist of PNJs. We show that a PNJ with a full-width at half maximum waist of ~ 0.22λ₀ can be obtained outside the surface of the optimized microcylinder. In addition, curved PNJs with subwavelength waist are also obtained. We finally optimize the five-layer structures for refractive index sensing based on the beam length of PNJs. The estimated minimum detectable refractive index variation when using this sensing method is ultra-small. Our results could potentially contribute to the development of a new generation of devices for optical nanoscopy and biophotonics, and greatly promote the practical applications of PNJs.

Ultralong photonic nanojet formed by dielectric microtoroid structure

A photonic nanojet (PNJ) is a highly confined light beam formed by a transparent particle under light wave illumination. Here, we propose and numerically investigate the PNJ formed by a dielectric circular toroid with micro dimensions and a homogenous refractive index. Three-dimensional finite-difference time-domain (FDTD) simulations are conducted and demonstrate that ultralong PNJs can be formed by the doughnut-like structure. Besides, microtoroid structures can allow high-index materials (n=3.5) for PNJ generation. Various PNJ properties, including the focal distance, PNJ length, full width at half-maximum, and maximum intensity, can be flexibly tuned by modifying the geometry of the proposed structure.

Side-lobes-controlled photonic nanojet with a horizontal graded-index microcylinder

A photonic nanojet generated by the transparent dielectric microparticle (microsphere or microcylinder) is a sub-wavelength focused beam. The properties of the photonic nanojet have been modified by changing the refractive index and structure of the micropaticles. In this Letter, a super-narrow photonic nanojet with a full width at half-maximum waist of approximately 116.6 nm (λ/4.3, with 500 nm excitation wavelength) is obtained by a horizontal graded-index microcylinder, which is divided by multilayers parallel to the direction of light propagation. The method for side lobes controlling by the waves' superposition from the modified graded refractive index and that of the center layer is proposed and discussed. Also, a structure with the composition of different height plates approaching the desired circular section is suggested for decreasing the difficulties in fabrication, and generates a similar photonic nanojet.

Direct imaging of tunable photonic nanojets from a self-assembled liquid crystal microdroplet

We report the direct experimental observation of electrically tunable photonic nanojets (PNJs) generated from self-assembled liquid crystal (LC) microdroplets formed by dispersing nematic LCs in polymer matrix. Optical measurements were performed with a home-built laser-scanning confocal microscope system. PNJs with subwavelength beam waists were successfully obtained from LC microdroplets of 5 μm diameter, similar to those from SiO₂ microspheres of the same size. By applying external voltage of a few volts, some of major properties of PNJs, such as beam length and brightness, are tuned. Electro-tunable PNJs from self-assembled LC microdroplets may open the way for the development of novel micro-optical devices.

Spatial control of photonic nanojets

For a long time, light focusing from microspheres has been intensively researched. The microsphere has been shown to be capable of generating a high intensity beam with sub-wavelength width, known as a photonic nanojet (PNJ). In this article, we present a detailed report on the properties of a new asymmetrical microstructure, consisting of a supporting stage and a spherical cap, and demonstrate precise engineering of the PNJ characteristics by simply selecting its geometrical dimensions. More importantly, we find that a single asymmetrical microstructure can generate an ultra-elongated PNJ on the shadow side and the cascade of two asymmetrical elements can generate a PNJ with a full width at half maximum (FWHM) waist down to 0.27λ. In addition, because of the presence of energy convergence regions within the second element, an ultra-narrow PNJ can be generated even when the length of the second element in the cascade is many orders of magnitude greater than the wavelength or deviates somewhat from the optimal dimensions. This offers design flexibility and manufacturing tolerance, which has not been demonstrated in the conventional microsphere design or its derivatives. We believe that these remarkable performance features make the asymmetrical structure and its cascade attractive in numerous applications.

Photonic jets from Babinet's cuboid structures in the reflection mode

In this Letter, we demonstrate applicability of Babinet's principle of complementary diffractive structures for the formation of near-field photonic jets in the reflection mode. Structures, complementary to dielectric cuboids, are characterized with additional geometric and electromagnetic parameters compared to initial cuboids and, for this reason, offer more opportunities for the design of photonic jets with required properties. Babinet's structures allow control of such parameters of photonic jets as the focus length, width, length, maximal field intensity, and ellipticity of jets.

Direct imaging of optimal photonic nanojets from core-shell microcylinders

We first experimentally evaluate the direct imaging of photonic nanojets from core-shell microcylinders. The optimal photonic nanojet with long length, a high intensity spot, and low divergence is observed at the designed gold-silver-coating microcylinder. A special microcylinder consists of multilayered metallic shells (gold, silver, and copper) and a dielectric core (polydimethylsiloxane) at a diameter of 5 μm and a height of 6 μm. The electromagnetic distributions inside and outside the core-shell microcylinders are calculated by using the finite-difference time-domain method. The direct-imaging measurements for photonic nanojets are performed with a scanning-optical-microscope system. Such core-shell microcylinders provide new pathways for high-resolution optical imaging, which are useful for biophotonics, plasmonics, and optical data storage.

Tunable photonic nanojet formed by generalized Luneburg lens

Nanojet has been emerging as an interesting topic in variety photonics applications. In this paper, inspired by the properties of generalized Luneburg lens (GLLs), a two-dimensional photonic nanojet system has been developed, which focal distance can be tuned by engineering the refractive index profile of GLLs. Simulation and analysis results show that the maximum light intensity, transverse and longitudinal dimensions of the photonic nanojet are dependent on the focal distance of the GLLs, thereby, by simply varying the focal distance, it is possible to obtain localized photon fluxes with different power characteristics and spatial dimensions. This can be of interest for many promising applications, such as high-resolution optical detection, optical manipulation, technology of direct-write nano-patterning and nano-lithography.

Photonic nanojets in Fresnel zone scattering from non-spherical dielectric particles

We experimentally and numerically study near-field and far-field visible light scattering from lithographically defined micron scale dielectric particles. We demonstrate field confinement and elongated intensity features known as photonic nanojets in the Fresnel zone. An experimental setup is introduced which allows simultaneous mapping of the angular properties of the scattering in the Fresnel zone and far-field regions. Precise control over the shape, size and position of the scatterers, allows direction control of the near-field intensity distribution. Intensity features with 1/3 the divergence of free space Gaussian beams of similar waist are experimentally observed. Additionally the direction and polarization of the incident light can be used to switch on and off intensity hot spots in the near-field. Together these parameters allow a previously un-obtainable level of control over the intensity distribution in the near-field, compared to spherically and cylindrically symmetric scattering particles.

Modulation of photonic nanojets generated by microspheres decorated with concentric rings

A novel design of decorating microsphere surface with concentric rings to modulate the photonic nanojet (PNJ) is investigated. By introducing the concentric ring structures into the illumination side of the microspheres, a reduction of the full width at half maximum (FWHM) intensity of the PNJ by 29.1%, compared to that without the decoration, can be achieved numerically. Key design parameters, such as ring number and depth, are analyzed. Engineered microsphere with four uniformly distributed rings etched at a depth of 1.2 μm and width of 0.25 μm can generate PNJ at a FWHM of 0.485 λ (λ = 400nm). Experiments were carried out by direct observation of the PNJ with an optical microscope under 405 nm laser illumination. As a result, shrinking of PNJ beam size of 28.0% compared to the case without the rings has been achieved experimentally. Sharp FWHM of this design can be beneficial to micro/nanoscale fabrication, optical super-resolution imaging, and sensing.

Photonic jet with ultralong working distance by hemispheric shell

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.

Super-long photonic nanojet generated from liquid-filled hollow microcylinder

Photonic nanojet (PNJ) from liquid-filled hollow microcylinder (LFHM) under a liquid immersion condition is numerically investigated based on the finite element method and physically analyzed with ray optics. Simulation and analysis results show that, by simultaneously introducing the immersed liquid and filled liquid, the propagation beam is greatly flattened, and super-long PNJs with decay length more than 100 times the illumination wavelengths are obtained in the outer near-field region of the LFHM. With the variation of the refractive index contrast between the filled and immersed-liquids, the properties of the PNJs, such as the focal distance, decay length, full width at half-maximum, and maximum light intensity can be flexibly tuned.

Photonic nanojets generated using square-profile microsteps

We have shown experimentally that square-profile microsteps on a silica substrate, with square sides of 0.4, 0.5, 0.6, and 0.8 μm and height of 500 nm, illuminated through the substrate by a linearly polarized laser beam of wavelength λ=633  nm, produce, near the surface, enhanced-intensity regions (termed photonic nanojects), with their intensity being six times higher than that of the incident light and their respective full width at half-maximum diameters being 0.44λ, 0.43λ, 0.39λ, and 0.47λ, which is below the diffraction limit of 0.51λ. It is worth noting that when the step side is smaller than the wavelength, the focus is found within the step; otherwise the focus is outside the step, which is similar to an optical candle.

Ultralong photonic nanojet formed by a two-layer dielectric microsphere

A photonic nanojet is a highly focused optical beam with a subwavelength waist on the shadow side of the sphere. Successful far-field applications require long nanojets that extend afar. Using the exact Mie theory, we show that ultralong nanojets can be generated using a simple two-layer microsphere structure, using conventional optical materials that are readily available. In particular, we show that for a glass-based two-layer microsphere, the nanojet has an extension of 22 wavelengths. We also show that long nanojets can be formed using semiconductors at infrared frequencies in free space.

Photonic nanojet-enhanced nanometer-scale germanium photodiode

A design challenge for photodiodes yielding both high speed and responsivity is the necessity to concentrate incident light into a subwavelength active volume region. Photonic nanojets have been reported in the literature as a means to focus an incident plane wave to a subwavelength-waist propagating beam with applications ranging from next-generation DVDs to characterizing subwavelength features within dielectric targets. In the present work, a new application of photonic nanojets is proposed, focusing electromagnetic energy into a photodiode. Three-dimensional finite-difference time-domain solutions are conducted to determine the advantages of photonic nanojet-enhanced photodiodes at near-infrared wavelengths (1310 nm). We find that photonic nanojets provide a factor of 26 increase in the volume-integrated electric field within the subwavelength active volume of the photodiode of size 0.0045 μm³. Furthermore, this increase is achieved independent of the incident polarization and over a broad bandwidth. Photonic nanojets may thus serve as an attractive alternative to plasmonics for some applications.

Elongated Photonic Nanojet from Truncated Cylindrical Zone Plate

Previously (Chen et al., 2004), it was shown that dielectric cylinder can form focal spots with small diameters and long depth. This type of focal spot was called photonic nanojet. In this paper, it was shown that dielectric cylinder of radius 595 nm (1.12 of wavelength) forms near the surface a photonic nanojet with diameter equal to 0.31 of wavelength and depth of focus equal to 0.57 of wavelength. Adding truncated concentric rings with radiuses equal to radiuses of zone plate to the cylinder increases the depth of focus to 1.18 of the wavelength. The diameter and intensity of focal spot near the cylinder surface remain unchanged.

Wavelength-scale lens microscopy via thermal reshaping of colloidal particles

Lenses are by far the most simple tools for visualization. Although they are intrinsically limited in resolution, recent efforts have aimed at focusing visible light in micro-scale lenses with subwavelength resolution, triggering an intense interest in further improving and understanding their performances. Herein, we report on a distinctive library of wavelength-scale solid immersion lenses facilitated the self-assembly of polystyrene colloidal particles. The thermally activated structural changes in polystyrene colloidal spheres directly impact the optical performance of the obtained lenses. Similar melting dynamics is observed for spheres of various size spheres at different temperatures. This allows precise control of the contact angle spanning a broad range from 180° to <20°. The fabricated lenses display deviations from the ray optics, allowing us to resolve features as small as 180 nm using a simple microscopy setup. We succeed in proper self-assembly of the colloidal lenses that enables large-area optical nanoscopy through simple and reliable experimental protocols. The limitations and the artifacts of the present technique are discussed.

Detection of embedded ultra-subwavelength-thin dielectric features using elongated photonic nanojets

Photonic nanojets have been previously shown (both theoretically and experimentally) to be highly sensitive to the presence of an ultra-subwavelength nanoscale particle within the nanojet. In the present work, photonic nanojets elongated by almost an order of magnitude (relative to the latest previously published work) are found to possess another key characteristic: they are sensitive to the presence of ultra-subwavelength nanoscale thin features embedded within a dielectric object. This additional characteristic of photonic nanojets is demonstrated through comparisons between fundamentally different 3-D and corresponding 1-D full Maxwell's equations finite-difference time-domain (FDTD) models.