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Minin, I.V. Mesoscale Dielectric Particles: Unusual Optical Effects. Encyclopedia. Available online: (accessed on 07 December 2023).
Minin IV. Mesoscale Dielectric Particles: Unusual Optical Effects. Encyclopedia. Available at: Accessed December 07, 2023.
Minin, Igor V.. "Mesoscale Dielectric Particles: Unusual Optical Effects" Encyclopedia, (accessed December 07, 2023).
Minin, I.V.(2021, December 30). Mesoscale Dielectric Particles: Unusual Optical Effects. In Encyclopedia.
Minin, Igor V.. "Mesoscale Dielectric Particles: Unusual Optical Effects." Encyclopedia. Web. 30 December, 2021.
Mesoscale Dielectric Particles: Unusual Optical Effects

Mesoscale dielectric particles are mesostructures comprising both wavelength-scaled (i.e. dimensions comparable to wavelength) particles and particle chains or arrays. These particles are made of low loss dielectric materials having relatively low refractive index, namely the refractive index less than two. The main unusual optical effects in such structures are discussed below.

mesoscale particle optical effects Fano superresonance Giant magnetic field optical vortices

1. Optical Optical Whirlpools, Nano-Vortices, Optical Hearts

The anomalous light scattering possesses the number of interesting and unusual properties such as a complex structure of the near field, which may include optical vortices, optical whirlpool and other specific traits of the nanoscale level [1]. For example, the term optical whirlpool was introduced in [2] by Bashevoy et al., who show that near the plasmonic resonance of the metal particle, nanosized optical vortices are observed, which resemble an optical whirlpool. Luk’yanchuk et al [3]. describe the optical vortices with the specific heart size, significantly lower than the diffraction limit for particles with a low size parameter q < 1. It is also found that near-field optical vortices appear at points matching the symmetric quadrupole resonance and forward and back scattering.
Another interesting effect connected with the optical vortices is a possibility of three-dimensional subwavelength confinement of light outside the dielectric particle with q~10 parameter, known as a photonic jet. This is associated with the vortex formation in the near field, namely the field squeeze due to the optical vortices occurring at the particle boundary, near the formation of the photonic jet [4].
Based on the Lorenz-Mie theory, it was found in [5] that spherical mesoscale particles with definite size parameters could cause substantially great field strength in singularities and form two extreme hotspots near the particle poles. Thus, the increase in the field intensity in the hotspots corresponded to 438 and 514 values for the size parameters of q = 22.24159 and q = 28.64159 of the Teflon sphere, respectively. Additionally, a surprisingly large circulation was discovered for the three-dimensional Poynting vector in the form of heart (see Figure 1), which was impossible to predict by a conventional two-dimensional analysis.
Figure 1. Three-dimensional view of Poynting vectors at critical points. Particle size parameter: q = 22.24159. PVH - Poynting vector hotspot. Adapted from [5].
These new physical phenomena allow explaining such interesting effects as the formation of the photonic jet and hotspots.

2. Fano Resonances in Dielectric Mie Resonance Mesophotonics

The crucial role in the formation of Fano resonances play magnetic dipole resonances of isolated dielectric particles. The magnetic dipole mode of the dielectric particle excited at the wavelength of the magnetic resonance can be stronger than the electric dipole response, thereby contributing to the scattering effectiveness. Luk’yanchuk et al. [6] show that low-scattering mesoscale dielectric microspheres can produce high-order Fano resonances associated with the internal Mie modes. It follows from this that the regions associated with such a superresonance can be located inside a spherical particle and the field structure has no whispering gallery mode. These resonances observed at a certain size parameter yield the magnetic field enhancement of the order of magnitude of 104–107. 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.
Yue et al. [7] identified the super-enhancement focusing of Teflon spheres with the certain size parameters and the refractive index n < 2, which rendered the field enhancement about 4000 times stronger than that of the downward radiation and demonstrated the possibility of overcoming the diffraction limit despite the high sensitivity to losses in the particle material. The Teflon spheres were characterized by a unique arrangement of hotspots at the poles of the sphere and were stipulated by a specific behavior of the Mie modes [7]. The manifestation of the super resonance effect is clearly seen in Figure 2. This figure also shows the effect of transformation of hot spots at the poles of the sphere in the absence of the photonic jet losses when small losses are introduced into the sphere material. With increasing losses in the sphere material, the maximum intensity of the electric and magnetic fields was compared for the size parameter q = 22.24159. At q = 28.64159, the magnetic field intensity was approximately two times higher than that of the electric field, in the absence of the particle material losses. The size decrease in the field localization (hotspots) down to less than the diffraction limit was observed after the introduction of small losses into the sphere material, which could be even less than in the ideal case of the particle material without losses (Figure 2b).
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 [7].

3. Giant Magnetic Field Generation in Mesoscale Particles

A new physical effect of the optical super-resonance in mesoscale dielectric spheres is conditioned by the high-order Fano resonance [6][7] and can become a new method of achieving super-high magnetic fields. This is conditioned by the following factors. The high-order Fano resonances in such particles are characterized by the high degree of the field localization, that exceeds the diffraction limit both inside the particle and on its surface. The latter is associated with the formation of regions having high values of the local wavenumber vectors by analogy with the superoscillation effects [8][9]. In accordance with this theory, the local wavenumber vector is a local phase gradient, viz. Kl = Φ = ∇E/E. The high Kl 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 Kl~∇N/N2, 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 [6]. 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 K0/Kl~10−2, where K0 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.
Optical vortices occur in dielectric mesoscale particles, when the size parameter q exceeds a certain value depending on its high refractive index [4]. Accordingly, the ring currents create magnetic fields in accordance with the Biot–Savart law. In accordance with this law, the coil radius must be reduced to increase the H field amplitude. Thus, the minimum radius of the respective equivalent coil is limited by the size of the order of one wavelength. Inside the dielectric particle, the magnetic field can be enhanced by more than four orders, resulting in the magnetic field of about 105 tesla, which approaches the interatomic magnetic fields [6]. 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 [10][11]. 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) [6].
An effect similar to the resonances noted above is also observed for particles of a different shape, other than a sphere or a cylinder. For example, for a cubic particle with a side of about 2λ (q~2π) and n = 1.59, for linear polarization and under conditions of the geometric resonance, the hot spot intensity E2 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 E2(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.
These effects of high-order Fano super-resonances are very attractive for such promising directions as, for example, the improvement of absorption effects, ablation induced by the magnetic pressure, and others.


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Subjects: Optics
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