Second-harmonic generation in Mie-resonant dielectric nanoparticles made of noncentrosymmetric materials

Frizyuk, Kristina; Volkovskaya, Irina; Smirnova, Daria; Poddubny, Alexander N.; Petrov, Mihail

doi:10.1103/physrevb.99.075425

Cited by 83 publications

(84 citation statements)

References 59 publications

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“…According to [21,[25][26][27][28], the field E, which satisfies the Helmholtz equation ∇ 2 E + ε ω c 2 E = 0 with frequency ω in a medium with dielectric susceptibility ε, can be expanded into a series of vector spherical harmonics N p r mn ( √ ε ω c , r) (electric) and M p r mn ( √ ε ω c , r) (magnetic), introduced in [21,29]. They correspond to the electric field of electric and magnetic multipoles of the nth arXiv:1812.02988v3 [physics.optics]…”

Section: Derivation Of Selection Rulesmentioning

confidence: 99%

“…The superscript (3) means that the harmonic corresponds to a diverging wave [21]. In [29], using the multipole expansion of the Green's function [28,[30][31][32][33] it was shown that the coefficients D p i p r mn are proportional to the integral of the scalar product of the induced SH polarization P 2ω (r) =χ (2) E ω (r)E ω (r) and the vector harmonic with indices p i , p r , m, n over the nanoparticle volume: (2) E ω (r)E ω (r)] dV .…”

Section: Ordermentioning

confidence: 99%

“…Here N α are basis vectors of the Cartesian coordinate system which are proportional to electric vector harmonics with n = 1, taken at zero frequency [29], N x ∝ W −1111 (0), N y ∝ W −1−111 (0), N z ∝ W −1101 (0). Note that summation is performed over repeated indices, and the integral (3) is the sum of the integrals of three scalar products of vector spherical harmonics over all nonzeroχ (2) -tensor components.…”

Section: Ordermentioning

confidence: 99%

“…Thus, it is necessary to consider the behavior of vector harmonics with respect to the intersection of the particle's and lattice's groups, and to determine whether their product contains an invariant representation. Symmetry classification and irreducible representations of vector spherical harmonics for finite groups are given, for example, in [29,44].…”

Section: Ordermentioning

confidence: 99%

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Second-harmonic generation in dielectric nanoparticles with different symmetries

Frizyuk¹

2019

J. Opt. Soc. Am. B

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In this work we study second-harmonic generation a monocrystalline nanoparticle with a non-centrosymmetric crystalline lattice. It was shown that breaking the symmetry of the nanoparticle's shape can significantly affect the second harmonic radiation pattern. We propose a method for explaining and predicting the generated field for arbitrary nanoparticles and provide selection rules for nanoparticles with several different symmetries. IntroductionSecond-harmonic generation (SHG) by resonant nanoparticles has recently been actively studied both theoretically [1-5] and experimentally [6][7][8][9][10][11] in order to develop nanosized light sources. The absence of phase matching conditions at the subwavelength scales results in significant drop of the generation efficiency, making the exploitation of resonances in such nanoscale structures the only way to enhance SHG. During the last few decades, metallic nanostructures supporting localized surface plasmon esonances have been actively studied -while the lattice of typical plasmonic materials has a center of inversion, second harmonic (SH) generation is still possible by surface and nonlocal volume effects [12][13][14][15][16]. In more recent developments, nanoparticles from dielectrics and semiconductors with a non-centrosymmetric crystalline lattice and bulk second order non-linearity [17][18][19][20] have been extensively studied. Mie-resonances supported by these dielectric nanoparticles [21] can lead to several orders of magnitude increase in SHG efficiency compared to metal structures [22]. Despite the large number of studies in this area, the full physical picture explaining SHG enhancement in all-dielectric nanostructures has yet to be identified. Selection rules, i.e. rules that determine the correspondence between the modes excited at the fundamental frequency and the modes at the second harmonic, play one of the most important roles. Selection rules for SHG in nanoparticles from materials that do not have bulk nonlinearity, such as gold, silicon, etc., were studied in detail in [23] for spherical particles, and in [24] for particles of other shapes. Despite the many studies devoted to the investigation of SHG from nanoparticles with bulk nonlinearity, the nature of the multipole composition of the generated fields, as well as the effect of nanoparticle symmetry on it, has not been studied in detail. In most of the works, the results of the SH fields' multipole expansion numerical calculations are presented without an explanation of the physical nature of the appearance of certain modes in the spectrum. The goal of this work is to determine the selection rules for SHG by dielectric nanoparticles with arbitrary symmetries and with a nonlinear susceptibility tensor χ (2) . In particular, we will show that a violation of the symmetry can strongly affect the mode composition and, as a result, the radiation pattern of the SH. Derivation of selection rulesAccording to [21,[25][26][27][28], the field E, which satisfies the Helmholtz equation ∇ 2 E + ε ω c 2 E = 0 ...

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Section: Derivation Of Selection Rulesmentioning

confidence: 99%

Section: Ordermentioning

confidence: 99%

Section: Ordermentioning

confidence: 99%

Section: Ordermentioning

confidence: 99%

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Second-harmonic generation in dielectric nanoparticles with different symmetries

Frizyuk¹

2019

J. Opt. Soc. Am. B

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“…Moreover, the nanoparticles of larger sizes comparable to the wavelength can also be considered that will increase the efficiency of SPDC process. This way, one should take into account the excitation of the higher-order multipolar components in the nanoparticle and their consequent decay into the other modes preserving particular symmetry rules typical for the second-order nonlinear processes [25,26]. This renders the considered scheme as a general recipe for the symmetry-based nonlinear generation of N00N-states with nanoparticles.…”

Section: Introductionmentioning

confidence: 99%

Generating Quantum States of Surface Plasmon-Polariton Pairs with a Nonlinear Nanoparticle

Olekhno

Petrov

Iorsh

et al. 2019

2019 Conference on Lasers and Electro-Optics Europe &Amp; European Quantum Electronics Conference (CLEO/Europe-EQEC)

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We consider a generation of two-particle quantum states in the process of spontaneous parametric down-conversion of light by a dielectric nanoparticle with χ (2) response. As a particular example, we study the generation of surface plasmon-polariton pairs with an AlGaAs nanoparticle located at the silver-air interface. We show that for particular excitation geometries, N00N-states of surface plasmon-polariton pairs could be obtained. The effect can be physically interpreted as a result of quantum interference between pairs of induced sources, each emitting either signal or idler plasmon. We then relate the resulting N00N-pattern to the general symmetry properties of dyadic Green's function of a dipole emitter exciting surface waves. It renders the considered effect as a general way towards a robust generation of N00N-states of surface waves using spontaneous parametric down-conversion in χ (2) nanoparticles. arXiv:2002.05268v1 [physics.optics]

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Spectral Tuning of High‐Harmonic Generation with Resonance‐Gradient Metasurfaces

Jangid,

Richter,

Tseng

et al. 2023

Advanced Materials

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High‐index dielectric subwavelength structures and metasurfaces are capable of enhancing light‐matter interaction by orders of magnitude via geometry‐dependent optical resonances. This enhancement, however, comes with a fundamental limitation of a narrow spectral range of operation in the vicinity of one or few resonant frequencies. Here we tackle this limitation and introduce an innovative and practical approach to achieve spectrally tunable enhancement of light‐matter interaction with resonant metasurfaces. We design and fabricate resonance‐gradient metasurfaces with varying geometrical parameters that translate into resonant frequencies dependence on one of the coordinates of the metasurface. The metasurfaces are composed of bone‐like nanoresonators which are made of germanium, and they support high‐Q optical resonances in the mid‐IR spectral range. We apply this general concept to observe the resonant enhancement of the 3rd and 5th harmonics generated from the gradient metasurfaces being used in conjunction with a tunable excitation laser to provide a wide spectral coverage of resonantly‐enhanced tunable generation of multiple optical harmonics.This article is protected by copyright. All rights reserved

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Second-harmonic generation in Mie-resonant dielectric nanoparticles made of noncentrosymmetric materials

Cited by 83 publications

References 59 publications

Second-harmonic generation in dielectric nanoparticles with different symmetries

Second-harmonic generation in dielectric nanoparticles with different symmetries

Generating Quantum States of Surface Plasmon-Polariton Pairs with a Nonlinear Nanoparticle

Spectral Tuning of High‐Harmonic Generation with Resonance‐Gradient Metasurfaces

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