Multiscale computational method for plasmonic nanoparticle lattices/Разномасштабный вычислительный метод для решеток плазмонных наночастиц тема диссертации и автореферата по ВАК РФ 01.04.05, кандидат наук Фрадкин Илья Маркович

• Фрадкин Илья Маркович
• кандидат наук
• 2022

Оглавление диссертации кандидат наук Фрадкин Илья Маркович

Contents

Page

Introduction

Chapter 1. Analytical review

Chapter 2. Hybrid computational approach for plasmonic lattices

2.1 Introduction

2.2 Effective polarizability

2.3 Scattering matrix calculation

2.4 Example: hybrid resonances

2.4.1 Homogeneous environment

2.4.2 Lattice in a waveguide

2.4.3 Lattice on a waveguide

2.4.4 Optical modes in waveguides of various thickness

2.5 Convergence and accuracy

2.5.1 Convergence

2.5.2 Accuracy

2.6 Conclusion

Chapter 3. Plasmonic lattices with complex unit cell

3.1 Introduction

3.2 Lattice with basis

3.3 Scattering matrix calculation

3.4 Example: routing plasmonic metasurface

3.5 Dipole toy model

3.6 Conclusion

Chapter 4. Stacks of plasmonic lattices

4.1 Introduction

4.2 Dipole approximation for a stack of plasmonic lattices

4.3 Thickness-independent resonance in a stack of plasmonic lattices

4.4 Spectra and near-field validation

Page

4.5 Conclusion

Chapter 5. Coupling the circularly-polarized light with waveguide

modes via plasmonic lattices

5.1 Introduction

5.2 Experimental and theoretical methods

5.3 Out-coupling QD emission from beneath the lattice

5.4 Out-coupling the guided modes

5.5 Conclusion

Conclusion

Nomenclature

Appendix A. Polarizability tensor calculation

A.l Scattered field formulation

A. 1.1 General formulation

A.1.2 Axially symmetrical case

A.2 Example of calculations

A.3 Resonant approximation for polarizability of individual particle

A.3.1 General formulation

A.3.2 Polarizability tensor calculation

A.3.3 Axially symmetrical case

A.4 Rotating a tensor

A.5 Analytical approach

A.6 Comparison of different approaches

A.7 Particles crossing the interface.....................Ill

Appendix B. Sum calculation

B.l Green's function filtering

B.2 Green's function near an interface

B.3 Convenient representation of M matrices

B.4 Analytical calculation of convolution for a homogeneous environment

B.5 Fast calculation of convolution

B.6 Calculation of generalized dynamic interaction constant

Page

Appendix C. Supplemental materials for Chapter

C.l Polarizability of golden nanobars

C.2 Details of practical calculations

C.3 Guided mode amplitude calculation

C.4 Photoluminescence measurements setup

References

Введение диссертации (часть автореферата) на тему «Multiscale computational method for plasmonic nanoparticle lattices/Разномасштабный вычислительный метод для решеток плазмонных наночастиц»

Introduction

Work relevance. Plasmonic materials play an important role in modern photonics. Most of their unique optical properties emerge from the negative value of the permittivity at the optical frequencies. It limits the penetration of electromagnetic fields in the metals but simultaneously confines them in the close vicinity of either plasmonic nanoparticles or plasmonic surfaces [1]. In particular, this results in an emergence of the famous Surface Plasmon Resonances (SPR) [2; 3], which correspond to the modes propagating along the metal/dielectric interfaces and Localized Surface Plasmon Resonances (LSPR) [4] in subwavelength plasmonic nanoparticles. Plasmonic modes allow us to overcome the diffraction limit, confine light at the subwavelength scale and enhance the light-matter interaction. Such opportunities found multiple application for Surface-enhanced Raman spectroscopy (SERS) [5 7], biosensors [8 11], hyperbolic [12; 13] and left-handed metamaterials [14; 15], optoelectronic [16; 17] and many other devices.

In the scope of this dissertation, special attention is paid to plasmonic metasurfaces, which are two-dimensional periodically-modulated structures made of metals. Plasmonic nanoparticles are very convenient constituents of corresponding lattices due to the disproportionally strong optical response of several-dozens-nanometers particles. These particles might be applied to design the structure that locally demonstrates the required optical response in terms of both amplitude and phase. This tool is widely applied for the purposes of flat optics [18 20], in holography [21 24] and other gradient metasurfaces. Moreover, plasmonic inclusions in some external photonic environments are often used to obtain the hybridized modes combining high field localization near the plasmonic nanoparticles with a relatively large quality factor ensured by the non-dissipative photons. Some of the structures demonstrate the effect of lattice plasmon resonance (LPR) [25 30], they are actively used for biosensors [9 11], enhancement and routing of the spontaneous emission [31 37], lasing [38 41] and other purposes [26; 29; 42; 43].

Nevertheless, theoretical description of the described structures is rather difficult in practice. Indeed, plasmonic nanoparticle polarization generates the fields confined at a scale much smaller than both wavelength and period of a typical lattice. For this reason, such universal computational approaches as the finite element method (FEM) and finite-difference time-domain method (FDTD) require building

very dense meshes for the nanoparticles, which strongly limits their performance and operational speed. A similar situation appears for the Fourier modal method (FMM) [44; 45] based approaches specialized for the consideration of periodic structures. They require to take into account a huge number of spatial harmonics and become inefficient as well. For this reason, most of the studies devoted to plasmonic lattices that provide some theoretical analysis utilize the coupled/discrete dipole approximation (DDA) for the estimation of the optical spectra.

Currently, most of the developed dipole models consider simple lattices in homogeneous environment [10; 25; 26; 28 30; 34; 35; 39; 42; 43; 46]. Only recently, there were several advancements that consider lattices of more complicated design [32; 47 49] and even lattices in the multilayer environment [50; 51]. Nevertheless, there is still a need for a computational approach that allows one to put the plasmonic lattice in different environments and describe it in some universal way. Another actual problem is an accurate description of the lattice put onto an interface between two media. The desired computational approach should simplify the consideration and application of complex plasmonic lattices that are still studied to a very limited extent, and enable widespread, detailed analysis of stacked lattices and lattices with several particles in a unit cell.

The aim of the work is to develop multiscale computational method for consideration of plasmonic nanoparticle lattices, design prospective structures and study their optical properties.

To achieve these aims, the following tasks were formulated:

1. Derivation of the scattering matrix of simple plasmonic lattice in dipole approximation. Integration of the approach into Fourier modal method. Benchmarking and validation of the approach.

2. Expansion of the computational approach to the case of plasmonic lattices with complex unit cells. Demonstration of the method performance.

3. Application of the scattering-matrix-based approach to the study of stacked plasmonic lattices. Exploring the hybridization of lattice resonances.

4. Development of the plasmonic lattice design suitable for experimental realization. Validation of the theoretical approach by comparing the computed spectra with experimentally measured ones.

Propositions for the defence.

1. The developed approach allows derivation the scattering matrix of plasmonic lattice in dipole approximation, which strongly (more than

100 times in comparison with finite element method) accelerates the computation of corresponding optical spectra.

2. The computational approach is expanded and efficiently applied to the design of the plasmonic lattices with complex unit cells and study of their optical properties.

3. The computational approach paves the way for the consideration of stacked plasmonic lattices. The effect of the thickness-independent hybrid mode in a stack of two identical square lattices of plasmonic nanodisks is demonstrated.

4. The plasmonic lattice of golden nanobars is designed for the out-coupling of quantum dots emission from the GaAs waveguide. The estimated degree of circular polarization in the far-field is up to 80%, which makes the structure prospective for the application in integrated sources of circularly-polarized light.

The scientific novelty of the dissertation includes the following.

1. The developed theoretical approach allows derivation of the scattering matrices of plasmonic lattices in dipole approximation; in particular, the case of a lattice on an interface between two materials is rigorously studied.

2. The computational approach makes it possible to consider the lattices with complex unit cell of several nanoparticles; moreover, the proposed formulation allows integrating the plasmonic lattices in a complex dielectric environment and stacking them in a universal way.

3. Thickness-independent resonance is observed for the energy of Rayleigh anomaly resulting from the hybridization of modes in a stack of two identical plasmonic lattices.

4. Plasmonic grating of the proposed design demonstrates the feasibility to out-couple the quantum dots emission from the GaAs waveguide into a light beam of 80% degree of circular polarization.

The theoretical and practical value of the study is in the development and verification of the computational approach for effective consideration of the plasmonic lattices. Its fast computational speed and high precision pave the way for the design of still unexplored complex plasmonic lattices for different purposes.

Methodology. The main theoretical derivations presented in the dissertation are based on the formalism of the Fourier modal method in the form of the scattering matrices and discrete dipole approximation. The polarizabilities of the separate

particles are calculated based on the idea of scattered field formulation via finite-element-method-based computational packaged COMSOL Multiphysics. Validation of the results is conducted by comparison with the results provided by COMSOL Multiphysics and the classical Fourier modal method.

Reliability of the obtained theoretical results is ensured by almost perfect match with the computations conducted via alternative widely-recognized computational approaches (see chapters 2-4) and agreement with the experimentally measured spectra (see Chapter 5). All the presented derivations are based on well-proven computational methods and approaches. The obtained results have been widely discussed at specialized seminars and conferences. The conclusions validity is additionally confirmed by publications in leading international peer-reviewed scientific journals.

Validation of the research results. The results obtained throughout the study were presented and discussed at the following scientific conferences, symposia, and seminars:

1. International Conference on Metamaterials and Nanophotonics METANANO 2018, Sochi, Russia, 17.09.2018

2. The 61st MIPT Scientific Conference, Dolgoprudny, Russia, 20.11.2018

3. Seminar on Solid State Theory, Department of Theoretical Physics named after I.E. Tamm, LPI RAS, 19.02.2019

4. IV International Conference on Metamaterials and Nanophotonics METANANO 2019, Saint-Petersburg, Russia, 16.07.2019

5. 9th German-Russian Week of the Young Researcher, Moscow, Russia,

24.09.2019

6. XXIV International Symposium "Nanophysics and Nanoelectronics Nizhny Novgorod, Russia, 12.03.2020

7. Low-dimensional Seminar of the Ioffe Physical-Technical Institute, on-line,

06.01.2020

8. METANANO Summer School on Nanophotonics and Metamaterials, online poster session, 06.07.2020, Best Poster Award

9. V International Conference on Metamaterials and Nanophotonics METANANO 2020, on-line, 17.09.2020

10. The 63rd MIPT Scientific Conference, Dolgoprudny, Russia, 24.11.2020

Personal contribution. All the results of the dissertation were obtained personally by the applicant or with his direct involvement. The applicant developed

the computational approach for plasmonic lattices and applied it to the design and theoretical study of all the structures considered in the dissertation. The applicant is the first author in all the main publications on the dissertation topic [Al A7]. Experimental part of the study [A4] described in chapter 5 was conducted by A.A Demenev, V.D. Kulakovskii and V.N. Antonov.

Publications. Based on the materials of the dissertation, 7 publications were published, including 7 papers in international journals indexed in Scopus and Web of Science.

Main Publications on the Dissertation Topic

Al. Fradkin, I. M. Fourier modal method for the description of nanoparticle lattices in the dipole approximation / I. M. Fradkin, S. A. Dyakov, N. A. Gip-pius // Physical Review B. 2019. Vol. 99, № 7. P. 075310.

A2. Fradkin, I. M. Nanoparticle lattices with bases: Fourier modal method and dipole approximation / I. M. Fradkin, S. A. Dyakov, N. A. Gippius // Phys. Rev. B. 2020. July. Vol. 102, issue 4. P. 045432.

A3. Fradkin, I. M. Thickness-Independent Narrow Resonance in a Stack of Plasmonic Lattices / I. M. Fradkin, S. A. Dyakov, N. A. Gippius // Physical Review Applied. 2020. Vol. 14, № 5. P. 054030.

A4. Plasmonic grating for circularly polarized outcoupling of waveguide-enhanced spontaneous emission, Editor's Pick / I. M. Fradkin [et al.] // Applied Physics Letters. 2022. Vol. 120, № 17. P. 171702.

A5. Fradkin, I. M. Light scattering by resonant nanoparticles in a 2D lattice. / I. M. Fradkin, S. A. Dyakov, N. A. Gippius // Journal of Physics: Conference Series. Vol. 1092. IOP Publishing. 2018. P. 012036.

A6. Fradkin, I. M. Scattering-matrix analysis of nanoparticle lattices in dipole approximation / I. M. Fradkin, S. A. Dyakov, N. A. Gippius // Journal of Physics: Conference Series. Vol. 1461. IOP Publishing. 2020. P. 012041.

A7. Fradkin, I. M. Dipole approximation for plasmonic lattices in layered structures / I. M. Fradkin, S. A. Dyakov, N. A. Gippius // AIP Conference Proceedings. Vol. 2300. — AIP Publishing LLC. 2020. — P. 020032.

Dissertation structure. Dissertation contains introduction, 5 chapters, conclusion and 3 appendices. It is written on 162 pages of typewritten text and includes 49 figures. The list of references includes 236 titles.

Список литературы диссертационного исследования кандидат наук Фрадкин Илья Маркович, 2022 год

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