Extraordinary optical transmission in holographic and polycrystalline structures/Усиленное оптическое пропускание в голографических и поликристаллических наноструктурах тема диссертации и автореферата по ВАК РФ 01.04.03, кандидат наук Ушков Андрей Александрович

• Ушков Андрей Александрович
• кандидат наук
• 2021

Оглавление диссертации кандидат наук Ушков Андрей Александрович

Contents

Page

1. Introduction

Historical overview

Extraordinary optical transmission

EOT through subwavelength apertures

EOT through continuous metal films

Top-down and bottom-up fabrication approaches for EOT devices

Outline and objective of the thesis

2. Theory of Surface Plasmon Polaritons

2.1 Introduction

2.2 Scattering matrix theory

2.3 Eigenmodes calculation via scattering matrix

2.4 Electromagnetic modes in multilayer plane-parallel structures

2.4.1 Simulation algorithm

2.4.2 Metal-dielectric interface

2.4.3 Thin metal film

2.4.4 Waveguide on the metallic substrate

2.4.5 Fabry-Perot resonator

2.5 Conclusion

3. Theory of Diffraction Gratings

3.1 Introduction

3.2 Diffraction orders and Ewald's sphere

3.3 Numerical methods for gratings simulation

3.3.1 Introduction

3.3.2 Rigorous Coupled Wave Analysis

3.3.3 C-method

3.3.4 Generalized Source Method

3.4 Conclusion

4. Fabrication Methods

4.1 Introduction

4.2 Layer deposition methods

4.2.1 Spin coating

4.2.2 Magnetron sputtering

4.3 Methods of surface nanostructuring

4.3.1 Laser Interference Lithography

4.3.2 Colloidal Self-Assembly

4.4 Simulation of the resist development process

4.4.1 Isotropic development process

4.4.2 Simulations for Laser Interference Lithography

4.4.3 Simulations for Nanosphere Photolithography

4.5 Conclusion

5. Variable Depth Gratings

5.1 Introduction

5.2 Fabrication techniques for variable depth gratings

5.2.1 Resist reflow

5.2.2 Moving edge/slit

5.2.3 Moire patterns in the resist

5.3 Experimental observation of moire patterns

5.3.1 Two LIL exposures

5.3.2 Four LIL exposures

5.4 Conclusion

6. Transmission in Plasmonic Nanostructures

6.1 Introduction

6.2 Transmission through 1D gratings of constant depth

6.3 Transmission through 2D gratings of constant depth

6.3.1 Rectangular lattice

6.3.2 Hexagonal lattice

6.4 Transmission through 1D variable depth gratings

6.4.1 Introduction

6.4.2 Existence of optimal grating depth

6.4.3 Structure-induced color

6.5 Transmission through hexagonal nanohole arrays

6.5.1 Introduction

6.5.2 EOT in colloidal gratings with low and high disorder

6.5.3 Modelling of grating disorder via inverse space approach

6.5.4 Statistical study of polycrystalline structures

6.5.5 Depth-resolved EOT in colloidal gratings

6.6 Conclusion

Conclusion

References

List of figures

List of tables

Введение диссертации (часть автореферата) на тему «Extraordinary optical transmission in holographic and polycrystalline structures/Усиленное оптическое пропускание в голографических и поликристаллических наноструктурах»

1. Introduction Historical overview

Plasmonics is an intensively studied field of modern physics which combines nanotechnology, electronics and photonics [1]. One important center of attention in plasmonic research are Surface Plasmon Resonances (SPRs) - collective coherent oscillations of electrons at metal-dielectric interfaces. Despite the fact that the theoretical description was established in the early 1900s, plasmonic effects have been known for hundreds and thousands of years and were exploited by ancient glassmakers in their sophisticated masterpieces. A well-known example of "ancient nanotechnology"is the Lycurgus Cup (4th century) [2] which possesses different coloration in reflected and transmitted light, see Figs.1.1a-b. This dichroic effect is caused by incident light coupling with free electrons in small metallic nanoparticles embedded in glass [3]; their presence was revealed by analytical transmission electron microscopy [4]. Different metallic powders added to glass give various colors; it was widely used in medieval stained glass windows, see Fig. 1.1c.

These color effects arise from the excitation of localized surface plasmons, which are coupled states of light/free electrons at the surface of metallic nanoparticles embedded in a dielectric medium. A first step to explain plasmonic coloration effects was made in 1908 by Gustav Mie [5]. He mathematically showed that optical spectra of metallic particle colloids depend on particle size, the properties of metal precursor and dielectric matrix.

a) b) c)

Figure 1.1 — Examples of "ancient nanotechnologies"in pre-modern era: a) and b) The Lycurgus Cup in reflected and transmitted light, correspondingly. c) Multicolor medieval stained glass window. (Courtesy: NanoBioNet)

Another object of plasmonics are propagating surface waves at the metal/dielectric interface. In 1902 Wood experimentally observed uneven distribution of light in metallic grating spectra [6] (Wood's anomalies). Later, Zenneck (1907) [7] and Sommerfeld (1909) [8] obtained a specific solution of Maxwell's equations at radio frequencies propagating at the boundary between air and earth. Further research revealed that this solution in the form of surface waves is valid for propagating surface plasmons at dielectric/metal interfaces in visible range, too; it has led to the explanation of Wood's anomalies in the model of incident light/surface plasmons interactions, proposed by Fano in 1941 [9]. Ritchie considered surface plasmons in a thin metallic film and demonstrated that their energy depends on a film thickness [10]. In 1968 Kretschmann and Raether managed to excite the surface waves with visible light via a prism coupling [11], and the theory of surface plasmon polaritons was finally established.

Plasmonic modes are described by classical electrodynamics. However, due to their exceptional ability to concentrate the light in small subwavelength volumes in the vicinity of metallic surface plasmonic applications go far beyond the classical theory [12]. A growing interest in plasmonics in 1980s and 1990s is connected with surface-enhanced Raman scattering (SERS) discovered by Fleischmann in 1974 [13]; the giant enhancement of Raman scattering cross section of single molecules by factors up to 1014 was demonstrated [14; 15]. The prevailing mechanism

of SERS is believed to be the strong concentration of electric field at metallic surface due to plasmonic excitations. Positions and efficiencies of so-called hot spots of highly concentrated electric field can be controlled via a proper design of metallic substrates. Thus, plasmon-related applications stimulate the development of surface nanostructuring methods. Surface-enhanced Raman scattering with metallic nanoparticles and/or nanostructured metallic substrates were successfully used in label-free chemical detection for medical diagnostics [16] and in microbiological hazards detection for food safety [17].

Other applications such as surface-enhanced second harmonic generation [18; 19], four-wave mixing [20] and absorption [21] utilize the effect of plasmon local field enhancement, too. Plasmonic ability to confine the light in subwavelength volumes is promising for plasmonic subwavelength lithography [22], data storage and biophotonics [23]. SPR-based sensors have been applied for liquid refractive index detection [24] and gas sensing [25]. Other plasmonic devices are used for nonlinear optical conversion [26], light absorption in solar cells [27], heating [28] etc. An innovative plasmon-based microscope with the resolution beyond the diffraction limit was invented by Rothenhausler and Knoll [29]. All these intriguing applications made plasmonics one of the most populated field of optical research nowadays [30], see Fig. 1.2.

2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020

Year

Figure 1.2 — Number of research articles corresponding to the key word "plasmonic"published from 2000 to 2020 according to Google Scholar search

engine results.

Extraordinary optical transmission

We have considered above the general historical path of plasmonic research. Such distinctive properties of surface plasmons as energy concentration and subwavelength confinement defined the great attention to these modes and careful analysis of metal-dielectric interfaces. However, an interesting physics exists also in the direction perpendicular to surface, i.e. through the metal film. In 1998 Ebbesen et al. [31] was first who revealed unusual optical transmission peaks in rectangular arrays of perforations in a thin 200 nm silver layer. These peaks were orders of magnitude greater than predicted by a standard aperture theories, at the wavelengths which were larger than grating period (where no diffraction occurs) and ten times larger than the nanoholes diameter. At resonant wavelengths more light is transmitted through the single hole than incident on it, because the energy tunnels through the film via plasmonic modes. Since this pioneering work the effect of Extraordinary Optical Transmission (EOT) is intensively studied in a huge variety of diffraction systems while adopting it to applications. The subsequent sections constitute the overview of EOT in different setups.

EOT through subwavelength apertures

A great interest to EOT since the original Ebbesen paper in 1998 [31] is caused by both fundamental and applied reasons. On the one hand, the enhanced transmission is not predicted by the classical aperture theory, therefore an accurate theoretical model of this effect should be elaborated [32]. On the other hand, EOT is perspective for sensing [33], directional beaming [34], filters and polarizers [35]. These considerations motivate research groups to gain further insight into EOT.

In 2001, Krishnan et al. studied the transmission through a perforated metallic film sandwiched between a quartz substrate and a dielectric cover and demonstrated experimentally and numerically that the highest transmission occurs when both claddings have the same dielectric permittivity [36]. Further investigations concerned dispersion measurements under different incident polarizations [37], cylindrical

surface plasmons [38] and the influence of nanoholes shape and localized resonances on EOT [39—41].

If surface plasmon polaritons have a primary role for EOT, this effect should also exist for a metal film with a single perforation, surrounded by opaque periodical corrugations in order to excite SPPs near the hole. The effect of EOT was indeed demonstrated in such structures in 1999 for 2D square lattice of dimples with a single perforation [42] and in 2001 for a system of concentric grooves around the perforation (bull's eye structure) [43]. It is important to notice that in the latter work the influence of corrugations depth on EOT was taken into account, not only their periodicity. Finally, in 2004 Degiron [44] experimentally registered the enhanced transmission through a single subwavelength nanohole milled in optically thick and flat suspended silver film. In contrast to the classical Bethe's theory [45] of a hole in perfectly conducting screen of zero thickness, which predicts very small transmission for subwavelength hole diameters, Degiron showed that for real metals a localized surface plasmon mode excites on the aperture ridge allowing the resonant tunneling of light through this aperture.

Another direction of research is devoted to the effect of the nanoholes arrangement (linear chain of apertures [46], non-periodic structures [47]) and their number (nanoholes arrays of different sizes [48]).

EOT through continuous metal films

The progress in EOT research historically moved from structures with multiple nanoholes assembled in periodical lattices to single perforations surrounded by opaque corrugations. A natural continuation of those studies were attempts to completely remove these perforations from the design as they are experimentally difficult to produce, while conserving the plasmon-enhanced transmission. The general mechanism of EOT in this case is as follows: incident light couples to SPPs at metal-dielectric interface due to the metal periodical corrugations on the one side of metal film. If the metal is thin enough, the light tunnels through it via plasmonic mode and couples to the SPP on another side of the film, where it is re-emitted by metal surface corrugations.

Intuitively the decrease of metal thickness should always increase the transmission because of improved overlapping of SPPs at both film sides. However, Giannattasio showed in 2004 that there are two competing effects: the leakage radiation into the substrate and absorption, which lead to the existence of optimal metal thickness [49]. Hooper and Sambles investigated EOT in continuous metal films with dissimilar corrugations on the both sides [50], and the same year Wedge proposed to use undulated metal films to enhance the quantum efficiency of LEDs

[51].

Singh and Hillier in 2008 for the first time employed the effect of EOT in continuous metal films for a biosensor application [52]. Gratings obtained from DVD-Rs were coated with a thin film of gold with thicknesses between 20 nm and 50 nm, and different monolayers of hexanethiol, decanethiol and octadecanethiol were self-assembled on the top. The resonant wavelength of EOT was confirmed to be sensitive to the dielectric permittivity changes when the chain length of hydrocarbons varied. The next step toward industrial application of EOT for sensing was made by Yeh et al. [53]. In 2011 they proposed a novel diffraction-based method to register EOT through metallized gratings using a simple CCD camera, and monitored the adsorption, thin film formation and dielectric permittivity changes using a simple optical microscope setup.

Experimental measurements of plasmon-mediated transmission often give the values smaller than predicted theoretically. Tonchev and Parriaux showed [54] that it is caused by nanoclusters of overheated polymer at the grating surface, which introduce index and geometrical perturbations, and managed to experimentally recover the "lost photons".

Above we considered devices with a limited number of resonant wavelengths [52; 54; 55]. However, for the needs of biosensing, lasing and broadband filters multiple resonances are often required. In this context chirped gratings with spatial period variations are interesting substrates for EOT devices. In 2010 Yeh et al. investigated the visible-band transmission through chirped grating [56]. Due to the multiple resonances provided by the same sample, it expands the possibilities of plasmon-based sensing, for example, allowing the simultaneous monitoring of dielectric layer thickness and its refractive index. Another way to achieve multiple resonances are multi-pitched gratings, prepared via laser interference lithography [57], and plasmonic quasicrystals [58].

Top-down and bottom-up fabrication approaches for EOT devices

There exists a variety of fabrication methods for EOT devices. Since the pioneering work in 1998 [31], the Focused Ion Beam milling is intensively used to make subwavelength perforations of different size, shape [44] and arrangements [48]. The Electron-Beam Lithography has demonstrated approximately the same possibilities [59; 60]. Although these methods allow a high control over the geometry, they are still quite expensive for mass applications [61]. The principal difficulty of EOT geometry was the necessity to precisely perforate the metal screen, whereas the transmission is sensitive to the hole quality and size [44].

The situation is different for EOT through continuous metal films. As there are no perforations, the metal can be simply deposited on the top of periodically undulated dielectric gratings via, for example, thermal or magnetron sputtering [62; 63]. Here the processes of surface nanostructuring and metallization are separated, thus offering a wider choice of compatible fabrication techniques. One of the most popular techniques is Laser Interference Lithography (LIL, see Chapter 4), where the photosensitive material (resist) is exposed non-homogeneously in the interference field of coherent laser beams in order to perform spatial corrugations of resist surface after its development [64]. This method is flexible, stitching-free, produces nanopatterning over wafer-size areas and therefore is extensively used in plasmonics [57; 65; 66]. A modification of LIL which uses a single nanosecond pulse was introduced in 2018 [67], which sufficiently reduces the perturbations of interference field caused by mechanical and air instabilities. Among other possibilities there are gratings from commercially available DVDs [52], phase and amplitude masks for UV exposures [68] and master molds for Soft Imprint Lithography [69].

Fabrication techniques considered above correspond to the so-called top-down paradigm, where the material is initially bulk and it should be particularly deformed (Soft Imprint Lithography, [69]), dissolved (laser interference lithography, [64]) or perforated (Electron-Beam Lithography, [59]) in order to release the desired structure. In contrast, bottom-up paradigm considers the final geometry as the system of its structural elements; the process of fabrication in this case is a manipulation with small building blocks and their connection into a desired

framework. An approach which combines bottom-up and top-down fabrication steps and compatible with EOT research is the colloidal lithography [70].

The progress in colloidal research allowed to synthesize high-quality, stable nano/micro spheres made of silica, polymethyl methacrylate (PMMA) and polystyrene with a narrow diameter distribution [71—73]. The idea of colloidal lithography, first proposed by Fisher and Zingsheim in 1981 [74], is to form a monolayer of close-packed microspheres on the desired substrate via bottom-up self-assembly technique and utilize this film in subsequent top-down technological steps to transfer the colloidal hexagonal arrangement into the surface. These technological steps vary from one particular workflow to another and can include, for example, colloidal layer as a contact mask for metal deposition inside the interstices between spheres [75], protective layer for reactive ion etching [76] or various chemical processes [77; 78].

Concerning the EOT devices colloidal lithography is perspective primarily for its large structuring areas and industrial integration possibilities. Although the resulting hexagonal monolayers are polycrystalline, the plasmonic response was demonstrated in transmission studies [79; 80]. Recently, a plasmonic sensor based on colloidal monolayers was proposed [81]. In addition, colloidal lithography can replace expensive electron- or ion-beam lithographies in particular case of hexagonal arrays of nanoholes [82].

Among all colloidal-based surface nanostructuring methods a particular technique of Nanosphere Photolithography (NPL) [83] deserves a special attention. In contrast to techniques mentioned above, this one utilizes a colloidal monolayer in a more elaborated manner as an array of microlenses. Rigorous calculations [84] show that dielectric nano/microspheres can transmit the light into so-called nanojets - non-resonant, non-evanescent beams with propagation distances longer than the wavelength. If an array of dielectric colloidal particles, deposited on a photoresist, is illuminated by UV light, the resist is exposed non-homogeneously due to the array of nanojets. It leads to the fact that after colloidal particles removal and resist development nanoholes [85] or nanopillars [86] appear on the surface, in dependence on the resist type. The NPL approach is very flexible allowing various modifications such as tilted and multiple exposures [87; 88], 3D photolithography [89; 90], use of proximity effects [91], and therefore is perspective for the synthesis of complex plasmonic structures.

Extraordinary plasmon-mediated resonant transmission caused intensive studies in both experimental and theoretical directions; its possible applications in plasmonic sensing, energy transfer, lasing and optical filtering motivates optical society for the last decades to work at interdisciplinary level between nanofabrication methods, fundamental questions of electrodynamics and industry. Throughout the thesis a special attention is paid to the influence of depth on transmission effects. Despite the EOT has been known for two decades already [31], the number of articles is not very abundant. For example, Thio et al. measured the depth-resolved transmission spectra through a single subwavelength aperture [43], surrounded by periodical grooves of different depths. Concerning the EOT in continuous metal films the work of Cao et al. [67] should be mentioned. Their novel single-pulse nanosecond modification of LIL creates single-period structures with Gaussian modulation of depth due to the non-uniform energy distribution in a laser pulse. However, because of practical constraints the depth at the laser spot periphery does not change continuously. It led to the fact that only general features of EOT were noticed, for example the increasing of transmission with grating depth. Another interesting approach for grating apodization, based on surface buckling of elastomeric films, was introduced in [56]. The buckling results in 1D gratings where both pitch and depth vary simultaneously over the sample surface, thus pure depth-dependent effects cannot be studied. We believe that the little number of works originates from the lack of reliable yet inexpensive methods of grating depth apodization, that is why Chapter 5 of the present thesis is devoted to this issue.

Outline and objective of the thesis

Previous sections were devoted to the historical overview and recent progress in the broad research field of plasmonics. In the following, the contents of the thesis is outlined, which is devoted to both experimental and theoretical investigations of EOT in various diffractive structures including 1D, 2D holographic gratings and polycrystalline lattices of nanoholes.

Chapter 2 is devoted to the theory of Surface Plasmon Polaritons in conventional planar metal-dielectric structures. The systematic investigation of

plasmon-supporting geometries is based on eigenmodes calculation via scattering matrix method. In particular, an important relation between Fabry-Perot oscillations and plasmons is discussed.

In Chapter 3 principal concepts of diffraction grating theory are introduced as well as numerical methods of simulation, accompanied with mathematical explanations.

Chapter 4 contains the information about layer deposition methods and methods of surface nanostructuring utilized in the thesis. The process of resist development is studied in detail using numerical simulations for laser interference lithography and nanosphere photolithography.

In Chapter 5 we collected all fabrication techniques for grating depth modulation considered experimentally during the time of PhD and discussed their limits of applicability. We propose a novel moire-based method for grating apodization, which creates 1D and 2D structures with adiabatically varying depth, and introduce its theoretical and experimental verification.

Chapter 6 is devoted to systematic study of EOT in a variety of geometries, including 1D, 2D periodical holographic gratings, 1D variable depth gratings and polycrystalline arrays of nanoholes; an effective dimensionless coefficient of disorder is proposed to estimate the quality of polycrystalline substrates for EOT. The dependence of structural color on grating depth was experimentally demonstrated.

Finally, in Chapter 6.6 we draw the conclusions from the work and discuss perspectives for future research.

The work was accomplished in the Laboratory Hubert Curien (UMR CNRS 5516) in collaboration with CEA-Liten, and was funded by the SIS 488 doctoral school of Saint-Etienne, university of Lyon, France. The numerical simulations via rigorous Generalized Source Method (GSM) were performed by Dr. Alexey Shcherbakov.

Aim of the work

Aim of the dissertation is an experimental determination of optimal geometrical parameters for metallized metasurfaces working in EOT regime. Investigation of nanosphere photolithography method possibilities for EOT-based devices and the enhancement of resonant optical response of polycrystalline structures.

Scientific novelty All results are new. We proposed, theoretically established and experimentally validated the method for diffraction gratings fabrication with depth varying adiabatically in a wide range. This method can be considered as a new synthesis platform for advanced plasmonic elements working in resonant and non-resonant regimes.

Using the proposed approach the systematic study of plasmon-mediated transmission was conducted for the first time for a wide range of grating depths. An optimal grating depth for the highest resonant transmission was experimentally revealed.

For the first time the EOT was observed experimentally in metasurfaces fabricated via Nanosphere Photolithography (NPL).

We proposed a phenomenological model to take the polycrystallinity into account for numerical simulations of EOT in NPL-fabricated structures. In order to compare the quality of colloidal self-assembly regardless the particles' size a dimensionless parameter of disorder is proposed.

For the first time the effect of EOT recovery in disordered nanopore arrays due to their depth was observed experimentally. Using the theoretical model described above the theoretical EOT spectra were calculated, which are in a good agreement (within the 10% error) with experimental ones.

Scientific and practical importance

The proposed varying depth gratings fabrication method allows sufficiently reduce the time of structure experimental optimization.

Along with this, it can be considered as a novel synthesis platform for advanced plasmonic elements with resonant (i.e. frequency filters) and non-resonant (i.e. structure-induced color) working regimes.

In contrast to a standard procedure of colloidal self-assembly, nanosphere photolithography method is flexible in defining the geometry of periodically-arranged elements at large nanostructuring areas, which is prospective for industry of plasmonic substrates for biosensors.

For the first time a theoretical model is proposed for the calculation of EOT in polycrystalline samples, which can be used for periodically arranged elements of arbitrary shape on metasurfaces.

Propositions for the defense

1. A proposed method for subwavelength variable-depth gratings fabrication allows the controllable change of the EOT peak value up to 45%.

2. In metallized polycrystalline gratings fabricated via nanosphere photolithography it is possible to observe EOT with an intensity peak above 20% (a value comparable to the response of ideally periodic structures).

3. The proposed theoretical model for the optical response of two-dimensional plasmonic polycrystalline structures describes the influence of disorder on the resonant transmission peak.

4. The influence of disorder, manifested by a reduction of the maximum resonant transmission in plasmonic polycrystalline structures, can be partially compensated by the deeping of nanopores composing these structures.

Presentations and validation of research results

The results of the thesis were presented and discussed at conferences:

- 34th European Mask and Lithography Conference (EMLC-2018), Grenoble, France, 18-20 September 2018 (poster)

- METANAN0-2019, Saint-Petersburg, Russia, 15-19 July 2019 (oral)

- Journees Nationales sur les Technologies Emergentes (JNTE 2019), Grenoble, Grance, 25-27 November (oral)

- SPIE Photonics Europe 2020, 6-10 April 2020 (oral)

- 63 MIPT Scientific Conference, Dolgoprudny, Russia, 23-29 November 2020 (oral, best section paper award)

- PHOTOPTICS 2021, online conference, 11-13 February (oral, best conference paper award)

Publications

1. Ushkov A., Shcherbakov A. Temporal dispersion of Dyakonov modes induced by spatial dispersion in dielectric composites // AIP Conference Proceedings. — 2017. — t. 1874, № 1. — c. 040055.

2. Ushkov A., Shcherbakov A. Concurrency of anisotropy and spatial dispersion in low refractive index dielectric composites // Optics express. — 2017. — t. 25, №1. — c. 243—249.

3. Systematic study of resonant transmission effects in visible band using variable depth gratings / A. A. Ushkov [h gp.] // Scientific reports. — 2019. — t. 9, № 1. — c. 1—9.

4. Resonant TM transmission through metallized variable depth grating / A. Ushkov [h gp.] // Journal of Physics: Conference Series. — 2020. — t. 1461. — c. 012180.

5. Subwavelength diffraction gratings with macroscopic moire patterns generated via laser interference lithography / A. Ushkov [h gp.] // Optics Express. —

2020. — t. 28, № 11. — c. 16453—16468.

6. Moire effects in subwavelength gratings: apodized structures for visible band optical applications / A. A. Ushkov [h gp.] // Integrated Photonics Platforms: Fundamental Research, Manufacturing and Applications. — 2020. — t. 11364. — c. 112—119.

7. Compensation of disorder for extraordinary optical transmission effect in nanopore arrays fabricated by nanosphere photolithography / A. Ushkov [h gp.] // Optics Express. — 2020. — t. 28, № 25. — c. 38049—38060.

8. Nanosphere Photolithography: The Influence of Nanopore Arrays Disorder on Extraordinary Optical Transmission / A. Ushkov [h gp.] // 9th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS). —

2021.

Personal contribution

All the original results presented in this thesis were obtained by the author personally or with his direct involvement.

Thesis structure

The thesis consists of six chapters and list of 238 references. The full volume of the dissertation is 180 pages, including 86 figures and 4 tables.

Заключение диссертации по теме «Радиофизика», Ушков Андрей Александрович

Conclusion

Diffractive structures realized via various fabrication approaches play a crucial role in modern optical research. Diffraction orders provided by a structural periodicity together with a proper design of the elementary cell suggest wide possibilities for light manipulations. One of the research areas benefiting from surface nanotexturing is plasmonics, which works at the interdisciplinary level between fundamental questions of electrodynamics, nanofabrication methods, and industry. In the present thesis a systematic study of plasmonic effects in various diffraction devices was performed concerning both experimental and theoretical aspects. The main topic connecting all presented research is Extraordinary Optical Transmission (EOT) through thin metallic films via plasmonic modes excitations.

In Chapter 1 a historical overview of plasmonic studies was given with a special attention to the EOT effect, discovered about 20 years ago. We formulated the objectives of the thesis, using the information about EOT in different sample designs and recent progress in this field. Important EOT applications include sensing, optical security/authentication elements and structure-induced color.

In the following Chapter 2 the principal elements of the scattering matrix theory and the calculation of eigenmodes were introduced. Based on this approach, we considered the electromagnetic modes in a number of plane-parallel structures with a detailed analysis of plasmons. The systematic study then moved from single metal-dielectric interfaces to more complex geometries like a waveguide on a metallic substrate supporting multiple resonances. The understanding of electromagnetic mode behavior in these structures is helpful for the introduction of diffraction gratings in Chapter 3, where we discussed the advantages of gratings for optical coupling over other methods, obtained the main analytic properties and explained principles of rigorous simulation methods for gratings.

While Chapters 2 and 3 constituted the theoretical basis for the thesis, the following Chapter 4 concerned the utilized fabrication methods. As the thesis is devoted to EOT in ideal and polycrystalline structures, we paid special attention to Laser Interference Lithography (LIL) and Nanosphere Photolithography (NPL) as techniques capable to realize these geometries. In addition, we considered in detail

the process of isotropic resist development for both of these techniques, presented algorithms and performed simulations of the development steps in LIL and NPL.

The following two chapters 5 and 6 presented the results obtained during the PhD work. In the Introduction we highlighted the importance of the grating depth for plasmonic excitations control. In analogy with chirped gratings of varying period, which can tune the spectral position of plasmons, variable depth gratings continuously change the coupling coefficient at a fixed resonant wavelength and thus are perspective for the control of the EOT magnitude in a single sample. Additionally, the variable depth design might be promising for structural color generation and developing of all-dielectric abnormal reflection gratings. Consequently, the ability to easily produce variable depth gratings using a cheap and time-effective fabrication approach is highly desirable. In the Chapter 5 we proposed and experimentally verified a number of such techniques based on different principles. We proposed a model explaining the moire pattern generation of different forms in resist. The effect was studied experimentally and numerically, and demonstration samples with depth variations at microscopic and macroscopic scales were prepared.

In Chapter 6 the results concerning the observation of EOT were presented. We studied the plasmon-mediated transmission in a systematic manner for a wide range of diffractive structures. Using the well-known 1D case for introducing principal theoretical and experimental aspects, we also considered 2D gratings with different symmetry and a 1D grating with adiabatically varying depth fabricated via the proposed method. In all these cases a big attention was paid to the existence of an optimal grating depth for the highest EOT, which was around 40% in the 0th transmission order. In addition, we observed the structural color induced by different depths in a single sample. The extraordinary transmission was for the first time also observed in polycrystalline arrays of nanopores fabricated via NPL. Here, besides the grating depth influence, the additional effect of disorder affects the plasmonic transmission. We proposed a phenomenological model adapted for the 2D case which takes into account the presence of multiple domains and introduced a dimensionless parameter of disorder which characterises real samples. Based on the developed numerical approach, we found a non-trivial interplay between the disorder and grating depth in the context of EOT. Numerical simulations were confirmed by experimental transmission measurements.

The presented results covering a wide range of possible EOT-supporting geometries pave the way towards promising experimental and theoretical research. The effect of EOT is perspective for highly sensitive all-optical detection devices, spectral filtering and plasmon lasing, because it can improve the signal-to-noise ratio and simplifies experimental setups. In contrast to reflection-based schemes, the transmission regime does not require precise adjustments of optical elements as they are aligned along one straight line.

Nowadays complex designs with a geometry varying across the surface is intensively studied for information-rich all-optical bio- and chemical sensors [56; 185; 230]. The LIL setup modification proposed in the thesis introduces additional degrees of freedom for grating apodization. The fabricated variable-depth metallized gratings demonstrate prominent dependence of EOT on depth, which can be utilized to improve the signal-to-noise ratio and control the EOT magnitude in transmission-based plasmonic sensors. Additionally, these samples showed a significant color change induced by the structure and can be considered as a platform for optical protection elements [137].

As an outlook, there is a possibility to adapt the mentioned LIL modification for creating bi-harmonic gratings with a varying phase between Fourier components across the surface. It is known [231; 232] that diffraction gratings can produce plasmonic band gaps (PBGs) which are used in light-matter interaction studies, light-emitting diodes and optical circuits; in this context the variable-phase geometry could provide an effective control of PBGs via the phase.

It was discussed in Chapter 4 that the nanosphere photolithography suggests wide possibilities for industrial low-cost nanotexturing of large planar and non-planar substrates, where the ideal ordering of elements is not a crucial factor. The performed experiments confirmed the feasibility of NPL-based EOT devices. The effect of disorder on optical behavior was studied for a number of 1D and 2D structures [227; 233—235]. Depending on the fabrication workflow various types of disorder can be brought into the geometry, which require their own statistical models. In our investigations special attention was paid to the polycrystallinity of NPL-fabricated samples. We believe that the dimensionless parameter of disorder proposed in the thesis, which depends on the average number of elements in a single domain, is well adapted and perspective for future EOT research.

Another promising research direction of NPL-based plasmonic structures might be the moire patterns generation via multiple UV exposures. A recently introduced concept of moire nanosphere lithography [236] is compatible with the NPL approach. Moreover, NPL offers wide opportunities for moire geometry optimizations, because close-packed colloidal monolayers with a small angular shift between them can be deposited sequentially in a simple manner, while multiple UV exposures record the total quasicrystalline topography in the resist. Metallic na-nostructures obtained by this approach have potential applications in all-optical or SERS-based sensors and surface-enhanced spectroscopy. Another promising application are surfaces with strong diffusive properties in the visible range due to disordered nanotexturing.

Concerning the fabrication, a perspective and innovative future work within the scope of NPL is the use of soluble thin films which capture the close-packed monolayers of colloidal particles. These flexible layers can be applied to planar and non-planar surfaces, relax the requirements on substrate hydrophilicity and perform the surface nano/micro structuring, acting as a transfer mask and avoiding the microsphere self-assembly step on a liquid-air interface. First promising results (not presented in the thesis) concerning the NPL with soluble thin colloidal films were obtained during the period of this PhD in collaboration with CEA-Liten, Grenoble. The idea of light focusing via arrays of microspheres utilized in NPL can also be further developed for laser surface micro/nanopatterning [237; 238] which removes fabrication steps related to photosensitive materials.

Список литературы диссертационного исследования кандидат наук Ушков Андрей Александрович, 2021 год

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