# Optical Phenomena in Mesoscale Dielectric Particles

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Optical Optical Whirlpools, Nano-Vortices, Optical Hearts

## 3. Fano Resonances in Dielectric Mie Resonance Mesophotonics

^{4}–10

^{7}. In this respect, super-resonances demonstrate the appearance of the magnetic photonic jets and giant magnetic fields in dielectric microspheres with high refractive index of ~4, that may be attractive to many photonic applications.

## 4. Giant Magnetic Field Generation in Mesoscale Particles

_{l}= Φ = ∇E/E. The high K

_{l}values can be created, for example, in free-space optics, including vortices and point vortices. This results from the uncertainty principle ΔEΔt ≥ ℏ/2, which in terms of the number of photons and photon phase can be reformulated as ΔNΔΦ ≥ 1/2. Differentiation of this relation results in K

_{l}~∇N/N

^{2}, i.e., the high wavenumbers can be reached in the vicinity of the optical vortex representing a singularity (zero-intensity point) with the phase of the field circulating round this point [7]. For example, for superresonance condition (Figure 2) the local ratio of wave vectors in singular points near the outer surface of a particle can reach K

_{0}/K

_{l}~10

^{−2}, where K

_{0}is a wavevector of incident wave. So the giant magnetic fields can be created inside the dielectric particle due to creating subwavelength optical vortices with large phase gradients in the vicinity of singularities.

^{5}tesla, which approaches the interatomic magnetic fields [7]. The disadvantages of the high magnetic field generated by higher order resonances are highly sensitive to the mesoscale particle material losses. Note that such a magnetic field is comparable with magnetic cumulative generators [11,12]. With such magnetic fields, magnetic nonlinear optics effects can be expected when the refractive index is changed by the magnetic effects only. This magnetic nonlinear optics can however be implemented under two conditions: (1) rather low dissipation, (2) magnetic nonlinear response significantly exceeds the electric nonlinear response due to nonlinearity, viz. ε = ε(E) [7].

^{2}near the shadow side of the cube is almost 400 higher than that of the plane wave incident on the cube (for a sphere with the size parameter q~5.38 and the overlapping of multiple resonance modes E

^{2}(max)~40). It should be noted that in dielectric mesoscale particles, the maximum field intensity is close to the particle boundary in contrast to plasmonic particles, where the maximum field intensity is observed on its surface. However, a detailed analysis of the electric and magnetic field structures for non-spherical particles is beyond the scope of this paper and will be discussed elsewhere.

## 5. Photonic Nanojets

#### Photonic Jet: Electric or Magnetic?

^{2}distribution with the field enhancement H

^{2}for a spherical particle, the high refractive index n~1.5 and the size parameter q~10. One can see that in the localized radiation area, the maximum magnetic-field intensity is about two times higher than the electric-field intensity.

^{4}~10

^{5}stronger than the magnetic dipole transitions. However, unlike plasmonic particles, the first resonance of the dielectric spherical particles is a magnetic dipole resonance, which occurs when the light wavelength in the particle equals the diameter, viz. λ/n~2R. In this case, the electric field polarization is antiparallel at the opposite boundaries of the sphere, that provides a strong connection with circulating displacement currents, whereas at the center, the magnetic field vibrations are directed up and down [40].

## 6. Anomalous Apodization Effect

## 7. Tangential Electric Field Component Control

## 8. Terajets

_{1}= 0.1λ and d

_{2}= 0.25λ metal particles, respectively [56]. The use of metamaterials for mesoscale particles provides new effects, for example, the photonic jet birefringence [26]. In this early research [26], we present the results of the photonic jet formation based on 2D photonic crystals (PhC) with the high-index (n = 3.32) dielectric cylindrical rods in air host medium. We show that the high-intensity peaks localize in a small volume of the PhCs within the rods, that cannot be predicted by the Bloch-waves theory. Since the photonic jet length in the transverse magnetic (TM) mode is about two times shorter than that of the TM mode, the photonic jet is birenfringent. According to Khodzitsky et al. [59], there are another two types of the heterogeneous metamaterial structure based on photopolymer-perforated cuboid, namely the rectangle with circle holes in homogenious dielectric and the alternating layers. The smallest beam waist of ~0.2λ is observed for the TM-polarized wave in polylactic acid photopolymer. It is thus possible to separate photonic jets in space for transverse-electric- and TM-polarized waves [26].

## 9. Anomalous Gouy Phase Shift

## 10. Waveguide Systems Based on Dielectric Particles Chain

## 11. Specular-Reflection Photonic Nanojet

## 12. Overcoming the Diffraction Limit and Image Quality Improvement

^{−}

^{4}reduces the intensity by four orders of magnitude. The similar effect of resonance super-resolution imaging is considered in [96]. It is interesting to note that 0.27 × 0.6λ focal spot for the linear polarization of the illuminating wave can be obtained in an off-resonance frequency mode for a specific configuration of a zone plate [97] with a low level of the side lobes, but at a maximum field intensity, which is 1000 times lower. This is shown in Figure 7.

## 13. Nanostructured Particles with Refractive Index near 2

## 14. Structured Fields in the Form of Photonic Hooks and Loops

## 15. Low-Dimensional Systems. Plasmonic Jets and Hooks

_{3}N

_{4}) was investigated in [144] using the solution of Maxwell’s equations. The idea of a waveguide based on the cubic particle chains [79] provided the increase in the propagation length of the localized plasmonic wave [145].

## 16. Acoustic Jets and Hooks

## 17. Conclusions

_{3}C

_{2}nanoparticles are used in the photonic hook [124].

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Three-dimensional view of Poynting vectors at critical points. Particle size parameter: q = 22.24159. PVH - Poynting vector hotspot. Adapted from [6].

**Figure 2.**Distribution of the maximum field intensity for a spherical Teflon particle (refractive index n = 1.43) depending on the size parameter q at different absorption coefficient of the particle material k (

**a**). Dependence of the field localization width on the size parameter q at different absorption coefficient in the particle material k (

**b**). Electric (

**c**) and magnetic (

**d**) field intensities at the resonance value of the size parameter q = 28.64159 and absorption indices k = 0 and k = 1.7 × 10

^{–3}. Adapted from [8].

**Figure 3.**Intensity distribution in {x-z} plane: electric field E

^{2}(

**a**), magnetic field H

^{2}(

**b**), for spherical particle (n~1.5 and q~10). Adapted from [15]. The temporally averaged normalized values of the electric u

_{E}(

**c**,

**d**) and magnetic u

_{H}(

**e**,

**f**) energy densities for a low loss cubic Teflon particle illuminated by a plane wave with linear polarization E

_{x}.

**Figure 4.**E

^{2}field enhancement distribution in {x-z} plane for axially illuminated circular-column particle-lens 3λ in size (

**a**), cubic (

**b**), and spherical particle (

**c**) without/with the mask apodization.

**Figure 6.**Generation of photonic jet for spherical particle (n = 1.077) positioned on dielectric substates: (

**a**) n

_{1}= 3.83, (

**b**) n

_{1}= 4.08.

**Figure 7.**Formation of localized radiation for spherical particle at resonance frequency (

**a**) and zone plate with immersion cone on off-resonance frequency (

**b**) at linear polarization.

**Figure 8.**Field intensity distribution for truncated segment resonance and its fragments. Plane front incidents from bottom to top. Adapted from [101].

**Figure 9.**Formation of photonic hook for cubic particle with lateral mask (

**a**); image contrast of test object in photonic jet radiation (dotted curve) and photonic let (solid curve) (

**b**).

**Figure 10.**Structured fields in the form of photonic hook (

**a**) and bottle-like region of localized field (

**b**) based on a pair of dielectric rods. (

**c**) optical trapping in standing wave region, (

**d**) concept of the structured light in the form of photonic hook in step-index medium.

**Figure 11.**Vortices in the Rexolite (density: 1049 kg/m

^{3}, axial sound velocity: 2337 m/s, transverse sound velocity: 1157 m/s) particle and hotspot generation in off-resonance (

**left**) and near-resonance (

**right**) modes.

**Figure 12.**Acoustic jet in non-resonant mode for particle with q~2π (

**a**) and resonance scattering of acoustic wave on a spherical Rexolite particle located in water depending on Mie parameter (

**b**). Inset: hotspot structure on the particle shadow-side surface at the resonant frequency. Maximum intensity at points 1–3 are: 325 (1), 325,000 (2), 1000 (3) in units of the acoustic wave intensity incident on the particle.

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Minin, O.V.; Minin, I.V.
Optical Phenomena in Mesoscale Dielectric Particles. *Photonics* **2021**, *8*, 591.
https://doi.org/10.3390/photonics8120591

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Minin OV, Minin IV.
Optical Phenomena in Mesoscale Dielectric Particles. *Photonics*. 2021; 8(12):591.
https://doi.org/10.3390/photonics8120591

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Minin, Oleg V., and Igor V. Minin.
2021. "Optical Phenomena in Mesoscale Dielectric Particles" *Photonics* 8, no. 12: 591.
https://doi.org/10.3390/photonics8120591