Bismuth ferrite and silicon carbide harmonic nanoparticles: from characterization to tissue imaging

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Thesis

Reference

Bismuth ferrite and silicon carbide harmonic nanoparticles: from characterization to tissue imaging

ROGOV, Andrii

Abstract

Ce travail poursuit l'étude des propriétés physiques des nanoparticules harmoniques et leur utilisation comme biomarqueurs en microscopie multiphotonique. D'abord nous démontrons le potentiel du carbure de silicium (SiC) pour l'imagerie, qui vient de ses propriétés de génération de seconde harmonique et fluorescence à deux photons. SiC a une efficacité non linéaire élevée et la microscopie multiphotonique confirme la possibilité de détecter de SiC dans des cellules. Nous étudions ensuite des nanoparticules (NPs) de ferrite de bismuth (BFO) préparés par la méthode de combustion comme un marqueur potentiel de bio-imagerie pour la microscopie multiphotonique. Les nanoparticules de BFO sont des nouveaux marqueurs prometteurs combinant un signal non linéaire très élevé et une réponse magnétique modérée. Des études de cytotoxicité, hémolytique et le mécanisme d'internalisation suggèrent une bonne biocompatibilité et un grand potentiel de BFO pour l'imagerie biomédicale dans des applications diagnostiques. Dans le dernier chapitre, nous abordons la question des émissions endogènes harmoniques [...]

ROGOV, Andrii. Bismuth ferrite and silicon carbide harmonic nanoparticles: from characterization to tissue imaging. Thèse de doctorat : Univ. Genève, 2015, no. Sc. 4794

URN : urn:nbn:ch:unige-742002

DOI : 10.13097/archive-ouverte/unige:74200

Available at:

http://archive-ouverte.unige.ch/unige:74200

Disclaimer: layout of this document may differ from the published version.

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UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES Groupe de Physique Appliquée Professeur J.-P. WOLF Docteur L. Bonacina

Bismuth Ferrite And Silicon Carbide Harmonic Nanoparticles: From Characterization To Tissue Imaging

TH` ESE

présentée à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de Docteur ès Sciences, mention Physique

par

Andrii Rogov

de

Bilhorod-Dnistrovskyi (Ukraine)

Th`ese No 4794

GEN`EVE

Atelier de reproduction ReproMail 2015

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3 Curiosity does, no less than devotion, pilgrims make.

Abraham Cowle

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Remerciements

Il y a 4 ans, lorsque je cherchais un groupe où réaliser ma thèse, j’ai re¸cu pour conseils trois critères importants pour faire mon choix:

1. Les gens 2. Le sujet 3. l’´equipement

Parce que peu importe la qualité du matériel scientifique et combien est prometteur un sujet, rien de significatif ne peut se faire sans collègues qui vous fournissent un soutien, de l’expérience professionnelle et une main amicale dans les moments sont difficiles.

J’ai eu la chance de travailler au sein du Groupe de Physique Appliqu´ee avec des gens de diff´erents horizons, chacun d’eux rendant mon voyage de doctorat plus riche.

Tout d’abord je tiens à remercier mes superviseurs: Jean-Pierre Wolf et Luigi Bonacina. Luigi était la première personne que j’ai rencontrée au GAP- biophotonique, et il m’a aidé quotidiennement jusqu’à ma défense. Son ap- proche personnelle de la physique et de la science en général m’a formé en tant que chercheur et m’a aidé à comprendre comment de nouvelles connaissances sont créées. Merci à Jean-Pierre de m’avoir donné l’opportunité d’explorer différents projets au cours de ma thèse. Ma participation au concours éducatif MUST avec une expérience de stroboscope m’a aidé à développer mon ha- bileté à partager ma passion de la physique à un public non-technique.

Un merci en particulier à tous les francophones de notre groupe qui ont toléré et supporté mes tentatives pour apprendre la langue franaise. Merci beaucoup à Julien et Sylvain, qui m’ont aidé avec ce chapitre.

Je tiens à remercier les gens qui ont partagé avec moi le travaille en microcopie: Jérme Extermann qui était là au début de mon travail et qui m’a très patiemment et minutieusement conduit à travers les petits détails du travail avec des lasers, Thibaud et Sébastien pour notre travaille ensemble

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au laboratoire et le partage des différentes tches, et enfin Cédric pour la poursuite de la recherche multi harmonique, qui a commencé à la fin de ma thèse.

Merci à Denis Kiselev et Gustavo Sousa pour l’occasion de travailler avec la biobox et avoir partagé leur passion pour l’ingénierie, Jérme Kasparian - pour son recul par rapport aux connexions et similitudes entre dans les différents domaines de la physique, Wahb - pour des idées brillantes dans la compréhension fondamentale de la physique. Merci à Sylvain pour les conseils geek en Python et LateX. Merci à Marie, Debbie, Élise, Nicolas, Iris et Denis et d’autres pour les différents débats sur la physique et les choix de carrière et de soutien pendant ma période de recherche d’emploi. Merci

`

a Michel pour m’avoir aidé sur des questions d’ingénierie et pour m’avoir enseigné comment résoudre des problèmes avec une qualité Suisse, et non pas en utilisant seulement du ruban adhésif.

J’ai eu le privil`ege de travailler sur un grand projet interdisciplinaire:

NAMDIATREAM. Ce projet m’a donné une chance unique de voir la con- nexion entre les différents domaines de la science: physique, chimie, biologie, science des matériaux, médecine. Grce à Sebastien Swung, Daniel Rytz, San- drine Gerber, Davide Staedler, Solene Passemard, Julia Bode, Marie Iron- delle, Fernanda Ramos-Gomez, Frauke Alves, j’ai vu ce qui peut tre fait lorsque des professionnels avec une formation différente unissent leurs efforts sur la réalisation d’un objectif commun.

Grce à NAMDIATREAM j’ai rencontré des représentants de Nikon In- struments et grce à Daniel Ciepielewski eu l’occasion de voir la microscopie du point de vue de l’industrie.

Merci `a Isabel et Dragana pour leur aide dans les tches administratives et d’avoir rendu la partie bureaucratique de la recherche aussi lisse que possible.

Merci aux membres du jury Emmanuel Beaurepaire, Vladimir Lysenko et Daniel Rytz pour avoir consacré du temps, de l’énergie et de l’expertise afin d’évaluer mon travail et me fournir une rétroaction précieuse.

Ces années ont été non seulement une partie de ma carrière professionnelle mais aussi une partie importante de ma jeunesse. Mes amis en dehors de l’université m’ont apporté beaucoup de souvenirs et ma copine Elena a rendu

´etincelants et m´emorables nos voyages durant les vacances.

Enfin, je tiens à remercier ma famille: mon père qui m’a appris à compter et additionner des nombres avant de m’apprendre à lire, ma mère qui m’a donné la meilleure éducation possible et ma sœur, qui m’a soutenu pendant que je faisais mes études loin de ma maison.

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List of acronyms

A1R-MP Nikon multiphoton microscope BFO(BiFeO₃) Bismuth ferrite

BOA A prism compressor from Swamp optics DLS Dynamic light scattering

CLEM Correlative light electron microscopy FWHM Full width half maximum

GFP Green fluorescent protein HNPs Harmonic nanoparticles HRS Hyper Relay Scattering IRInfra-red

KTP(KTiOPO₄) Potassium titanyl phosphate

LASER Light amplification by stimulated emission of radiation MRIMagnetic resonance imaging

NA Numerical aperture

NDDNon-descanned detectors NIR Near-infrared

NPsNanoparticles PEG Polyethylene glycol PSFpoint spread function QDsQuantum dots

SEMScanning electron microscopy SHG Second harmonic generation SH Second harmonic

SiC Silicon carbide THP-1 Macrophages

TPEF Two-photon excited fluorescence UNPs Upconversion nanoparticles UV Ultraviolet

WD Working distance XRD X-ray diffraction

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Summary

This work continues the research started in our group of studying physical properties of harmonic nanoparticles and their use for biolabelling in multiphoton microscopy .

We first demonstrate imaging potential of silicon carbide (SiC) nanoparticles based on its second harmonic generation and two-photon excited fluorescence. SiC has a high nonlinear efficiency(17 pm/V) and multiphoton microscopy confirms the possibility of detection of SiC in cells. Simultaneous second harmonic generation and two-photon excited fluorescence emission of SiC nanoparticles allow multimodal detection for multiphoton microscopy.

We then investigate bismuth ferrite (BFO) nanoparticles(NPs) prepared by combustion method as a potential bioimaging label for nonlinear microscopy. BFO a high nonlinear efficiency measured at 79 pm/V. We demonstrate the bulk nature of the second harmonic process occurring within BFO particles, and show the possibility of determining the orientation of individual nanocrystals. Moreover, moderate ferromagnetic response is observed for BFO nanoparticles, allowing the BFO particles to be magnetically separated in solution. BFO nanoparticles are therefore new promising labels combining a very high nonlinear signal and a moderate magnetic response. The cytotoxicity, haemolytic response and internalization mechanisms evidence suggest good biocompatibility and a great potential for biomedical imaging in diagnostic applications.

In the last chapter we address the issue coming from harmonic endogenous emission of the tissue. We show that multi-harmonic emission of BFO NPs can be easily detected by multi-photon microscopy, using excitation >1100 nm. Based on this result, we demonstrate that the co-localization of second and third harmonic signals allow identifying with unprecedented selectivity NPs in a complex optical environment presenting endogenous sources of fluorescence and harmonic generation, an excised xenograft tumour tissue in our experiment. Moreover, by additional electron microscopy measurements, we show that BFO NPs could prospectively serve as localization fiduciaries in advanced correlative light electron microscopy studies.

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R´ esum´ e

Ce travail poursuit l’étude, qui a était commencée dans notre groupe, des pro- priétés physiques des nanoparticules harmoniques et leur utilisation comme biomarqueurs en microscopie multiphotonique.

D’abord nous démontrons le potentiel du carbure de silicium (SiC) pour l’imagerie, qui vient de ses propriétés de génération de seconde harmonique et fluorescence à deux photons. SiC a une efficacité non linéaire élevée (17 pm / V) et la microscopie multiphotonique confirme la possibilité de détecter de SiC dans des cellules. La génération simultanée de deuxèime harmonique et de fluorescence à deux photons par des nanoparticules de SiC permet la détection multimodale en microscopie multiphotonique.

Nous étudions ensuite des nanoparticules (NPs) de ferrite de bismuth (BFO) préparés par la méthode de combustion comme un marqueur potentiel de bio-imagerie pour la microscopie multiphotonique. BFO a une efficacité non linéaire élevée mesurée de 79 pm / V. Nous démontrons la nature volu- mique du processus de génération de deuxième harmonique survenant dans les particules de BFO, et montrons la possibilité de déterminer l’orientation de nanocristaux individuels. En outre, la réponse ferromagnétique modérée est observée pour les nanoparticules de BFO, permettant de les séparer magnétiquement en solution. Les nanoparticules de BFO sont donc des nouveaux marqueurs prometteurs combinant un signal non linéaire très élevé et une réponse magnétique modérée. Des études de cytotoxicité, hémolytique et le mécanisme d’internalisation suggèrent une bonne biocompatibilité et un grand potentiel de BFO pour l’imagerie biomédicale dans des applications diagnostiques.

Dans le dernier chapitre, nous abordons la question des émissions en- dogènes harmoniques du tissu. Nous avons utilisé comme modèle un tissu xénogreffe de tumeur présentant des sources endogènes de fluorescence et de génération d’harmoniques. Nous montrons que l’émission multi-harmonique de BFO NPs peut facilement être détectée par microscopie multi-photon, en utilisant une excitation λ > 1 100 nm. Sur la base de ce résultat, nous démontrons que la co-localisation de deuxième et troisième harmoniques per-

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mettent d’identifier des NPs avec une sélectivité sans précédent dans un en- vironnement optique complexe. En outre, par des mesures de microscopie

électronique supplémentaires, nous montrons que les NPs de BFO pourraient servir comme des marqueurs de localisation dans des études avancées de microscopie électronique et optique corrélatifs.

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List of Figures

2.1 Schematic representation of Second and Third harmonic gen-

eration process . . . 30

2.2 Two-photon absorption . . . 33

2.3 Evolution of the SHG conversion efficiency for perfect phase- matching and non phase-matching cases . . . 35

2.4 Epi-detected SH emission with respect to a particle size . . . 37

2.5 Polarization microscopy. The definition of the angles . . . 38

2.6 Polarization-resolved emission of BFO HNPs . . . 39

2.7 Imaging penetration depth. Results of numerical calculations 41 2.8 Absorption spectra of major tissue constituents . . . 41

2.9 An illustration of the Costes co-localization algorithm . . . 45

3.1 HNPs transmission electron microscopy images . . . 52

3.2 Signal photostability of HNPs emission . . . 56

3.3 Excitation wavelength flexibility of HNPs emission . . . 58

3.4 Orientation retrieval by defocused imaging . . . 62

3.5 Spectral phase sensitivity. Experimental and numerical defocused images of two adjacent nanoparticles . . . 64

3.6 Sensitivity to spectral phase. Images of individual KTP HNPs on a substrate obtained by 200 f and 13 fs pulses . . . 65

4.1 Experimental scheme of then TE300 nonlinear microscopy set-up 70 4.2 BOA single-prism pulse compressor. . . 71

4.3 A schematic representation of two detection arms (epi and forward) in the TE300 microscope . . . 72

4.4 The polarization response of the dichroic mirror in the TE300 setup . . . 73

4.5 Spectral calibration of the TE300 setup . . . 76

4.6 Photo of the TE300 setup. . . 77

4.7 Nikon A1R-MP microscope setup . . . 78 17

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4.8 4-channel episcopic Non-Descanned Detectors of the A1R-MP microscope. Quantum efficiency of the PMT photomultipliers 80 4.9 Schematics of Nikon’s spectral detection unit . . . 81 4.10 4-channel episcopic Non-Descanned Detectors of the A1R-MP+

microscope. Quantum efficiency of the GaAsP and normal PMT photomultipliers . . . 82 5.1 Photo and SEM image of SiC nanoparticles and SEM image

of SiC nanoparticles . . . 88 5.2 One-photon absorption and photo luminescence spectra of SiC

nanoparticles . . . 89 5.3 XRD pattern of SiC NPs and Dynamic light scattering mea-

surements of SiC NPs . . . 89 5.4 Non-linear microscopy image of SiC nanoparticles. Excitation:

720 nm . . . 92 5.5 Second harmonic microscopy images of SiC nanoparticles . . . 94 5.6 Second harmonic(excitation 970nm) and two-photon excited

fluorescence(excitation 720nm) spectra of SiC nanoparticles. . 95 5.7 Cells labeled with SiC P5 nanoparticles . . . 95 5.8 Co-localization of second harmonic and two photon excited

fluorescence(TPEF) of cells labeled with SiC nanoparticles . . 96 6.1 2D scan image of BFO nanoparticles and SHG spectrum of an

individual nanoparticle . . . 100 6.2 2D SHG image and polarization emission of BiFeO3 nanocrys-

tals (1) . . . 102 6.3 2D SHG image and polarization emission of BiFeO3 nanocrys-

tals (2) . . . 103 6.4 Room temperature magnetic hysteresis loops of BFO sample

and magnetic separation of BFO particles in water suspension 106 6.5 Uptake of uncoated BFO-NP by activated THP-1 cells . . . . 110 6.6 High throughput screening of BFO-NPs in humanderived cell

lines . . . 111 7.1 Bare BFO HNPs deposited on a substrate. SH: second har-

monic image. TH: third harmonic image. . . 117 7.2 Power dependence of the emission of a single BFO HNP mea-

sured at SH and TH frequency. Nonlinear axial PSF at SH and TH obtained with a 1.1 N.A . . . 118 7.3 Schematics of the two independent experimental approaches

used to determine the SH/TH ratio. . . 119

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LIST OF FIGURES 19 7.4 Experimental SH/TH ratio for two different excitation intensities119 7.5 Co-localization of the emission of bare BFO HNPs deposited

on a substrate . . . 121 7.6 A multiphoton image of an unlabelled tissue section of the

orthotopic breast tumour . . . 123 7.7 Effect of excitation wavelength and spectral detection filters

on relevant samples for this work. . . 124 7.8 Multiphoton images of the subcutaneous breast tumour tissue

labelled with BFO HNPs . . . 127 7.9 Multiphoton and SEM images of HeLa fixed cells labelled by

BFO HNPs . . . 128 A.1 Block diagram describing the main steps of the combustion

method used for BFO synthesis. . . 136 A.2 (Representative TEM image of BFO particles annealed at 600

°C. . . 137 A.3 DLS size distribution by intensity and by number and suspen-

sion image. SEM micrograph of the particles . . . 138 A.4 HRS intensity as a function of the concentration of nanopar-

ticles in suspension. . . 139 A.5 Interaction volume for backscattered electrons simulated for

for 5kV acceleration voltage. . . 147 A.6 Interaction volume for backscattered electrons simulated for

for 15kV acceleration voltage. . . 147

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List of Tables

2.1 Second order processes. . . 32 3.1 Nonlinear optical efficiency values and point groups for HNPs

nanomaterials . . . 54 4.1 List of objectives . . . 79 4.2 List of single-edge dichroic beamsplitters . . . 79 4.3 List of single-band bandpass filters . . . 79 4.4 List of single-edge dichroic beamsplitters and interferometric

filters used for A1R-MP+ microscope . . . 82 6.1 d tensor of BFO nanoparticles. Voigt notation . . . 104 6.2 Nonlinear coefficients d_ij (pm/V) values from the literature . 104

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Chapter 1 Introduction

Biophotonics includes development and application of optical techniques, particularly imaging, to the study of biological molecules, cells and tissue.

From the very beginning of biophotonics the development of new optical devices and imaging techniques allowed to make another step in discovery of new biological phenomena. A Dutch scientist Anton van Leeuwenhoek (1632-1723), one of the pioneers of microscopy, successfully developed new ways of polishing and grinding lenses and achieved a magnifying power of 270x. This technological achievement allowed him to be the first to see and describe bacteria, yeast plants, the teeming life in a drop of water, and the circulation of blood corpuscles in capillaries [1].

Nowadays, there are three well-known branches of microscopy: optical, electron, and scanning probe microscopy. While electron and scanning probe microscopes can achieve atomic resolutions [2,3], optical microscopes are lim- ited by diffraction limit to submicron resolution. On the other hand optical techniques allow to image relatively thick(up to 1mm [4]) living samples with no or minimal sample preparation. This work will focus on optical microscopes which use light to interact with matter in processes as fluorescence, second and third harmonic generation.

In 1960 the work of T.Maiman led to one of the major technological breakthroughs of the 20th century: the LASER [5]. The ability of lasers to deliver light with high intensities opened a door for observing nonlinear optical effects, such as second harmonic generation [6]. Predicted in 1931 by Maria Goppert-Mayer [7] the multiphoton excitation of a quantum system was a key physical effect, used in two-photon excited fluorescence microscopy introduced by Webb in 1990 [8]. Since then, the interest in this imaging techniques has grown exponentially. The origin of such success relays several advantages this approach presents with respect to its linear counter- part, including higher spatial resolution, deeper sample penetration, lower

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phototoxicity, better spectral separation between signal and excitation, and virtually no out-of-focus bleaching [9].

Currently fluorescent dyes are the most widely used labels in microscopy.

The importance of fluorescent labels was highlighted by the 2008 Nobel Prize for chemistry awarded to O. Shimomura, M. Chalfie and R. Y. Tsien for the discovery and development of the green fluorescent protein, GFP. [10].

However these molecules suffer from a major drawback: photo-degradation.

Photo-degradation is an irreversible photon-induced chemical decay affecting fluorescent dyes, altering their signal over exposure. Bleaching occurs already after the emission of 10⁶−10⁸ photons in organic dyes [11] and<10⁵ photons in autofluorescent proteins. [12] The origin of bleaching is inherent to the excitation process of a quantum system involving real states.

Fluorescing semiconductor quantum dots(QDs) provide much higher photostability, but are known to suffer from blinking (strong fluorescence intensity variations over unpredictable timescales). [13]. It arises from the com- peting radiative and vibrational relaxation pathways, but efforts are made in order to prevent blinking in QD [14,15]. Another drawback of QDs is utiliza- tion of rare earth elements, meaning that use of QDs for biological research might be prevented because of low biocompatibility. Another type of labels are Upconversion nanoparticles (UNPs). Upconversion refers to nonlinear optical processes in which the sequential absorption of two or more photons leads to the emission of light at shorter wavelength than the excitation wavelength (anti-Stokes type emission). In contrast to other emission processes based on multiphoton absorption, upconversion can be efficiently excited even at low excitation intensities. The most efficient upconversion mechanisms are present in solid-state materials doped with rare-earth ions [16].

Furthermore, pulse excitation of noble metal NPs can exert surface plas- mon resonance, a strong local electro-magnetic field which can enhance the fluorescent response of molecular probes in their vicinity or also the non-linear signal such as second harmonic emission at surfaces and interfaces [17, 18].

A limiting factor for QD, metal NPs, UNPs and fluorescent labels is resonant nature of their emission, typically in the visible range. In recent years more and more attention is given to the IR region (with wavelength >

1µm), because of improved imaging tissue penetration [4].

The next type of imaging labels should be photostable, biocompatible, suitable for IR multiphoton excitation, and be easily detected even in pres- ence of endogenous emission of biological medium.

To address these requirements since 2006, several research groups world- wide have proposed a complementary approach, inherently nonlinear, based on the use of non-centrosymmetric metal oxide nanocrystals. Such particles lack an inversion symmetry center in their crystal structure and therefore

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25 present an efficient χ⁽²⁾ response. [19] Their second harmonic (SH) emission can be used as optical contrast mechanism for imaging applications. For this reason they are often referred to as harmonic nanoparticles (HNPs). SH emission from HNPs features a series of characteristics including orientation- dependent polarization patterns, coherent emission, and excitation wavelength tunability. This last property, which might seem counter-intuitive when thinking about frequency conversion in bulk phase-matched crystals, is directly stemming from the sub-coherence length dimensions of HNPs [20].

HNPs as imaging probes for biological samples have already been described. [21–23]. In our group the following non-linear nanomaterials have been studied: KNbO₃, LiNbO₃, BaTiO₃, KTP and ZnO [24]. The goal of this work was to study two new types of nanomaterials, SiC and BiFeO₃, and to advance bioapplications of HNPs from cell to tissue labelling.

After a theoretical introduction(Chapter 1) to the concepts of non-linear imaging and co-localisation of two optical signals, we present the review of HNPs for bioimaging. We then present the results concerning:

• Nonlinear properties of SiC

• Characterization of Bismuth Ferrite(BFO) nanoparticles

• Multiharmonic detection in tissues

Nonlinear properties of SiC HNPs SiC is known as a wide bandgap semiconductor with excellent electronic characteristics that allow this material to be used in high-temperature, high frequency, and high-power electronic devices. SiC is biocompatible and environmentally friendly, which gives this material a potential to be used in biomedical engineering and solar energy [25]. Both silicon and carbon are abundant on earth and SiC can be produced cost effectively.

Original optical properties of SiC nanostructures allowed their various promising applications as light emitting agents [26, 27], one-photon [28] and two-photon [29] bioimaging agents.

In this chapter, we investigate Second Harmonic Generation and Two- Photon Excited Fluorescence from SiC nanocrystals in order to describe their multimodal response for multiphoton microscopy. We show that SiC nanoparticles have high optical nonlinear efficiency, thus are suitable imaging probes for SH imaging and can benefit from the advantages related to this approach, i.e. signal photostability, wavelength flexibility, and narrow-band emission.

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Characterization of Bismuth Ferrite(BFO) nanoparticles In this chapter Second Harmonic Generation (SHG) from BiFeO₃(BFO) nanocrystals is investigated to determine their potential as biomarkers for multiphoton imaging. SHG properties are determined through Hyper Relay Scatter- ing(HRS) and nonlinear polarization microscopy. The high SHG efficiency confirms that BFO is a promising material for frequency conversion applications. We additionally demonstrated that the nanoparticles SHG properties are due to the bulk nature of the second harmonic process occurring within BFO particles. Moreover we retrieve the orientation of single nanocrystals by means of nonlinear polarization microscopy. In addition to nonlinear optical response moderate ferromagnetic response is observed for nanoparticles con- taining residualγ-Fe2O3 impurities, allowing the particles to be magnetically separated in solution. BFO nanoparticles are therefore new promising HNPs combining a very high SHG brightness and a moderate magnetic response.

The cytotoxicity, haemolytic response and internalization mechanisms evidence are reported for coated BFO-NPs suggested good biocompatibility and a great potential for biomedical imaging in diagnostic applications [30].

BFO-NPs must be coated with biocompatible polymers in order to stabilize the BFO-NPs suspensions in biological media and to increase their biocompatibility [31].

Multiharmonic detection in tissues Transition from cell to tissue imaging puts new challenges and opportunities for HNPs. In cellular imaging the second harmonic emission from nanoparticles is easily separable from endogenous fluorescence by using narrow-band interferometric filters. However when considering tissue imaging a new source of second harmonic endogenous emission(collagen) appears [32], thus making selective detection of HNPs more difficult.

The use of long wavelengths (>1µm), provided by the latest femtosecond sources, not only allow to gain in imaging penetration depth but also allow to record third harmonic signal, which was problematic before as the TH signal lies in UV region (opaque for conventional optics) when excited with with Ti:Sapphire oscillators in the range between 0.7 and 1.0 µm. Ability to record TH allows to add a new imaging modality for HNPs. Still the problem of separating HNPs signal from the background remains as tissue has endogenous sources of TH signal(lipid droplets) as well [33].

As we show in this chapter the HNPs have a unique ability to simultaneously emit both second and third harmonic signals, which can be used for distinguishing their signal from endogeneous second and third harmonic emission of tissue.

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27 In this chapter we investigate the use of Bismuth Ferrite (BFO) nanoparticles for tumor tissue labelling in combination with infrared multi-photon excitation at 1250 nm. We report the efficient and simultaneous generation of second and third harmonic by the nanoparticles. On this basis, we set up a novel imaging protocol based on the co-localization of the two harmonic signals and demonstrate its benefits in terms of increased selectivity against endogenous background sources in tissue samples. Finally, we discuss the potential use of BFO nanoparticles as mapping reference structures for correlative light-electron microscopy.

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Chapter 2 Introduction of concepts used in this work

In the following section, we briefly describe the theoretical framework under- laying our experimental work. First we describe linear and non-linear polarization of the medium and second and third harmonic generation. Then we briefly describe the multiphoton microscopy and how it is different with respect to confocal microscopy. Finally we will describe the Costes colocal- ization algorithm which is useful for locating sources of multi(second and third) harmonic emission.

2.1 Linear and Non-linear Polarization

When an electromagnetic wave is propagating through a medium, the response of the medium can be expressed in term of macroscopic polarization P⃗. In the case of conventional (i.e., linear) optics, the induced polarization depends linearly on the electric field strength in a manner that can be described by the relationship

P⃗=₀χ⁽¹⁾⋅ ⃗E (2.1)

where the constant of proportionality χ⁽¹⁾ is the linear susceptibility and ₀ is the permittivity of free space. In nonlinear optics, the optical response can be described by generalizing Eq. 2.1 by expressing the polarization P⃗ as a Taylor series in the field strength E as:

P⃗=0(χ⁽¹⁾⋅ ⃗E

´¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¶

P⃗L

+χ⁽²⁾⋅ ⃗E²+χ⁽³⁾⋅ ⃗E³+ ⋅ ⋅ ⋅ +χ⁽ⁿ⁾⋅ ⃗Eⁿ+. . .

´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶

P⃗NL

) (2.2)

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ω=2ωexc

Ground state

Second Harmonic Generation (SHG) ωexc

ωexc

ω=3ωexc

Ground state

Third Harmonic Generation (THG) ωexc

ωexc

Figure 2.1: Schematic representation of Second and Third harmonic generation process

The quantities χ⁽²⁾ and χ⁽³⁾ are the second- and third-order nonlinear optical susceptibilities, and χ⁽ⁿ⁾ is the macroscopicn-th order dielectric susceptibility tensor of rank(n+1). The Eq. 2.2 is valid for lossless and disper- sionless media. As long as the field amplitudes remain small (< 10⁵ V/m), the polarization is linear (P⃗_L) but when the field amplitudes increase, the polarization become a nonlinear function of the electric fieldP⃗_NL. This nonlinear response will generate nonlinear optical effects, such as Kerr effect, generation of high harmonics, parametric amplification and multiphoton absorption. [34]

Sometimes the derivation of the polarization is more straightforward in the spectral domain. The Fourier relation between two representations of polarization is:

P⃗⁽ⁿ⁾(ω) = F [ ⃗P⁽ⁿ⁾(t)] = ₀ 2π∫

+∞

−∞

P⃗⁽ⁿ⁾(t)e^−iωtdt (2.3) Second harmonic generation

Let us consider the process of second-harmonic generation, which is illustrated schematically in Fig. 2.1. The incident electric field strength is represented as

E(t) =˜ Ee^−iωt+c.c. (2.4) wherec.c.stands for complex conjugate and the second-order susceptibility of a crystal χ⁽²⁾ is nonzero.

P˜⁽²⁾(t) =₀χ⁽²⁾E˜²(t) (2.5)

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2.1. LINEAR AND NON-LINEAR POLARIZATION 31 or explicitly as

P˜⁽²⁾(t) =2₀χ⁽²⁾EE^∗+ (₀χ⁽²⁾E²e^−i2ωt+c.c.) (2.6) In order to have a non-zero χ⁽²⁾ a material can not have a centrosymmetric structure. If the material possess an inversion symmetry a spatial transformation r⃗→ −⃗r is possible, and the components of Eq. 2.5 are mod- ified as follows: P⃗ → − ⃗P and E⃗ → − ⃗E. Under this transformation and in the light of Eq. 2.5, χ⁽²⁾→ −χ⁽²⁾. In conclusion, if the material possesses an inversion symmetry, Eq. 2.5 remains unchanged andχ⁽²⁾= −χ⁽²⁾=0. For material where inversion symmetry holds, no SHG signal is generated and more generally no even nonlinear processes from bulk medium are allowed. But at every interface inversion symmetry is broken and even nonlinear processes may occur.

According to the driven wave equation,

∆⃗E⃗(⃗r, t) − 1 c²

∂²E(⃗⃗ r, t)

∂t² =µ₀∂²P⃗(⃗r, t)

∂t² (2.7)

the second contribution in the right part of Equation 2.6 can lead to the generation of radiation at the second-harmonic frequency.

The first contribution in Eq. 2.6 does not lead to the generation of electromagnetic radiation (because its time derivatives vanish); it leads to a process known as optical rectification, in which a static electric field is created across the nonlinear crystal.

Sum- and difference frequency generation

The most general case of a second order nonlinear process is when the optical field incident upon a second-order nonlinear optical medium consists of two distinct frequency components, which we can represent in the form

E(t) =˜ E₁e^−iω¹^t+E₂e^−iω²^t+c.c. (2.8) The nonlinear polarization that is created in such a crystal is given according to Eq. 1.1.2 as P˜⁽²⁾(t) =₀χ⁽²⁾E˜²(t) or explicitly as

P˜⁽²⁾(t) =₀χ⁽²⁾(E₁²e^−2iω¹^t+E₂²e^−2iω²^t+E₁E₂e^−i(ω¹^+ω²^)t+ +2E1E₂^∗e^−i(ω¹^−ω²^)t+c.c.) +20χ⁽²⁾(E1E₁^∗+E2E₂^∗)

(2.9) We can express this result using the notation

P˜⁽²⁾(t) = ∑

n

P(ω_n)e^−iωⁿ^t (2.10)

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Under the supposition ω₁ ≥ω₂, we can summarize the second nonlinear order processes in Tab.2.1.

Process name Term

Optical Rectification (OR) P(0) =2₀χ⁽²⁾(E₁E₁^∗+E₂E₂^∗) Second Harmonic Generation (SHG) P(2ω1,2) =0χ⁽²⁾E_1,2²

Sum Frequency Generation (SFG) P(ω₁+ω₂) =₀χ⁽²⁾E₁E₂ Difference Frequency Generation (DFG) P(ω₁−ω₂) =₀χ⁽²⁾E₁E₂^∗

Table 2.1: Second order processes.

Third harmonic generation

We next consider the third-order contribution to the nonlinear polarization P˜⁽³⁾(t) =₀χ⁽³⁾E˜³(t).

In this case the nonlinear polarization becomes

P˜⁽³⁾=₀χ⁽³⁾(Ee^−iωt+c.c)³ =₀χ⁽³⁾E³e^−3iωt+3₀χ⁽³⁾∣E²∣Ee^−iωt+c.c (2.11) The first term in Eq. 2.11 describes a response at frequency 3ω that is created by an applied field at frequency ω. This term leads to the process of third-harmonic generation, which is illustrated in Fig. 2.1. According to the photon description of this process, shown in the right part of the figure, three photons of frequency ω are destroyed and one photon of frequency 3ω is created.

The second term in Eq. 2.11 describes a nonlinear contribution to the polarization at the frequency of the incident field; this term hence leads to a nonlinear contribution to the refractive index experienced by a wave at frequencyω, known as the Kerr effect.

Two-photon absorption

In the process of two-photon absorption, which is illustrated in Fig. 2.2, an atom makes a transition from its ground state to an excited state by the simultaneous absorption of two laser photons. The phenomenon was originally predicted by Maria Goeppert-Mayer in 1931, and it requires high excitation intensities as it occurs if the two photons are present together within a short time span.

Two-photon absorption is a χ⁽³⁾ process and it depends quadratically of the excitation intensity.

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2.1. LINEAR AND NON-LINEAR POLARIZATION 33

ω

Ground state Excited state

ω

Figure 2.2: Two-photon absorption

2.1.1 Second Harmonic Generation and Propagation

As we saw previously in Eq. 2.2χ⁽²⁾ is a third rank tensor with 27 elements.

Under certain conditions, called Kleinmans Symmetry conditions, the χ⁽²⁾ tensor can be simplified to 18 elements.

Kleinmans Symmetry Quite often nonlinear optical interactions involve optical waves whose frequencies ω_i are much smaller than the lowest resonance frequency of the material system. Under these conditions, the nonlinear susceptibility is largely independent of frequency [19]. Furthermore, under conditions of low-frequency excitation the system responds essentially instantaneously to the applied field.

Since the medium is necessarily lossless whenever the applied field frequencies ω_i are very much smaller than the resonance frequency ω₀, the condition of full permutation symmetry

χ⁽²⁾_ijk(ω3=ω1+ω2) =χ⁽²⁾_jki(−ω1 =ω2−ω3) (2.12) is valid under these circumstances. This condition states that the indices can be permuted as long as the frequencies are permuted simultaneously, and it leads to the conclusion that

χ⁽²⁾_ijk =χ⁽²⁾_jki =χ⁽²⁾_kij =χ⁽²⁾_ikj =χ⁽²⁾_jik =χ⁽²⁾_kji (2.13) These permutations are known as the Kleinman symmetry condition. The Kleinman symmetry condition is valid whenever dispersion of the susceptibility can be neglected.

Voigt notation When the Kleinman symmetry condition is valid, we can introduce the reduced tensord:

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d_ijk=χ⁽²⁾_ijk (2.14) We now assume that d_ijk is symmetric in its last two indices. This as- sumption is valid whenever Kleinmans symmetry condition is valid and in addition is valid in general for second-harmonic generation. We then sim- plify the notation by introducing a contracted matrix d_il according to the prescription

jk: 11 22 33 23, 32 31,13 12, 21

l: 1 2 3 4 5 6

The nonlinear susceptibility tensor can then be represented as a 3 × 6 matrix

d⁽²⁾_il =

⎡⎢

⎢⎢

⎢

⎢⎣

d11 d12 d13 d14 d15 d16

d₂₁ d₂₂ d₂₃ d₂₄ d₂₅ d₂₆ d₃₁ d₃₂ d₃₃ d₃₄ d₃₅ d₃₆

⎤⎥

⎥⎥

⎥

⎥⎦

(2.15) We can describe the nonlinear polarization leading to second-harmonic generation in terms of d_il by the matrix equation

⎡

⎢⎢

⎢⎣

Px(2ω) P_y(2ω) P_z(2ω)

⎤

⎥⎥

⎥⎦

=2₀

⎡

⎢⎢

⎢⎣

d11 d12 d13 d14 d15 d16

d₂₁ d₂₂ d₂₃ d₂₄ d₂₅ d₂₆ d₃₁ d₃₂ d₃₃ d₃₄ d₃₅ d₃₆

⎤

⎥⎥

⎥⎦

⎡⎢

⎢⎢

⎢

⎢⎢

⎣

E_x(ω)² E_y(ω)² E_z(ω)² 2E_y(ω)E_z(ω) 2E_x(ω)E_z(ω) 2E_x(ω)E_y(ω)

⎤⎥

⎥⎥

⎥

⎥⎥

⎦

(2.16)

Influence of Crystal Symmetry point group on the Second-Order Susceptibility tensor

Additional symmetry properties of a nonlinear optical medium can impose additional restrictions on the form of the nonlinear susceptibility tensor. By explicit consideration of the symmetries of each of the 32 crystal classes, one can determine the allowed form of the susceptibility tensor for crystals of that class [19]. For example, after applying the restrictions on a crystal of class 3m(the symmetry class of BiFeO₃, a material intensively studied in this work) the dil matrix simplifies to

d_il(3m) =

⎡⎢

⎢⎢

⎣

0 0 0 0 d₃₁ −d₂₂

−d22 d22 0 d31 0 0 d₃₁ d₃₁ d₃₃ 0 0 0

⎤⎥

⎥⎥

⎦

(2.17)

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0 2 4 6 8 10

z/um

0.0 0.5 1.0 1.5 2.0

SHG conversion efficiency, a.u.

1e 12

∆ k =0

∆ k 0

^0.0^0.00 ^0.05 ^0.10 ^0.15 ^0.20

0.5 1.0 1.5 2.0 1e 14

Typical size of a BFO nanoparticle

Figure 2.3: Evolution of the SHG conversion efficiency for perfect phase- matching case(∆k=0, green dashed line) and non phase-matching (∆k ≠0, blue solid line). Inset: enlargement for a nanometric non-centrosymmetric crystal of BFO(BiFeO₃, L_c = 1.67µm), where phase-matching condition is not any more valid.

Propagation of second harmonic

Having derived an expression for the polarization (Eq. 2.2), we can substitute it into the wave equation (Eq. 2.7) and obtain:

∆⃗E⃗_SHG(⃗r) +k_SHG² E⃗_SHG(⃗r) = −16πω² c² [l1+

∇∇

k²_SHG] ⋅ ⃗P⁽²⁾(⃗r) (2.18) where l1 is the identity matrix of rank 3, k_SHG is the wave vector at 2ω, and E_SHG the field envelope at frequency 2ω. For this section, we apply the slowly varying amplitude approximation (SVAA), meaning we can neglect the second term of the right-hand side of Eq.2.18. Then, the equation can be expressed as [19]:

(∆+k²(ω)) E_SHGe^ik^SHG^z = − 16πω²

c² χ⁽²⁾E_ωE_ωe^i(k^ω^+k^ω^)z (2.19) where E_ω is the field envelope at the frequencyω.

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If we consider only the direction of propagation (z axis), we have:

∂E⃗_SHG

∂z =

iω²_SHGχ⁽²⁾ k_SHGc²

E⃗_ω²e^i∆kz (2.20) where ∆k=2k_ω−k_SHG is the wave vector mismatch or wave vector transfer.

The solution of this equation is:

E⃗_SHG(z) = iω²χ⁽²⁾

k_SHGc²E_ω²e^i∆kz−1

i∆k (2.21)

The last term introduces intensity modulation in the generation of SHG field. At a distance z, the intensity of the SHG field is expressed as [35]:

I_SHG(z) ∝ [E_SHG(z)]² ∝ [

e^i∆kz−1 i∆k ]

2

≡z²[sinc(

∆kz 2 )]

2

(2.22) The intensity of the SHG is a periodic function of the the distance z and is maximal when [sinc(x)]²=1, therefore:

I is maximal when{ ∆k=0, ∀z

size of z is in the order of the wavelength . (2.23) The former usually referred as phase-matching condition is verified for harmonic frequency conversion of laser pulses by bulk nonlinear crystals.

When we will study the SHG from non-centrosymmetric nanocrystals with a size smaller than the wavelength, only the second condition in Eq.2.23 applies. Defining L_c=π/∆k as the coherence length, we illustrate the SHG conversion efficiency in Fig. 2.3. The effect of the phase matching condition on the conversion efficiency of the medium is evident for propagation in a medium over a distance z > L_c/2. However, when we do not consider anymore a propagation regime, but a scattering regime, as in the case of small nonlinear object with a size z smaller or in the order of the excitation wavelength, the SHG conversion grows monotonically with the size of the sample and the phase-matching condition is not a constraint anymore.

For small objects observed in the focus of a medium or high N.A. objective, other consideration enter into play. By using the framework, developed by the Xie group [36], based on Green’s function formalism, one can show that epi detected SH oscillates as function of scatterer size. The Fig. 2.4 shows an example of such size dependence, calculated for 800nm laser excitation and NA = 0.6 (these parameters are relevant for the following chapter 6, where we describe second harmonic emission of BFO nanoparticles).

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0 100 200 300 400 500

Particle size/nm

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Epi emission signal, a.u.

1e10

second harmonic

60 80 100 120 140 0.0

0.5 1.0 1.5 2.0 2.5 3.0 1e9

Typical size of a BFO nanoparticle

Figure 2.4: Epi-detected SH emission with respect to a particle size, NA=0.6, λ_exc = 800nm. Inset: enlargement for a nanometric non-centrosymmetric crystal of BFO

2.1.2 Polarization resolved nonlinear microscopy

During polarization analysis of the nonlinear emiss ion of nanoparticles we used a framework developed in the group of J. Zyss (ENS, Paris) [37, 38].

Knowing the crystal tensor and having an excitation field with a well defined polarization, we can simulate the SHG response of the nanocrystals as a function of the linear polarization angle of the excitation. We will work out an analytical expression of the SHG intensity response recorded by the detector for two orthogonal polarizations of the detection. This will allow us in Chapter 6 to fit the experimental data and retrieve the spatial orientation of individual nanocrystals in the laboratory frame. In Fig. 2.5, we present a graphical illustration of the parameters used in this model.

Before considering the interaction between light and crystal, we first have to define its orientation in the laboratory frame. Usually a nonlinear susceptibility tensor d of a crystal is given in Voigt notation as d_ij 3 × 6 matrix, as was shown before. Before applying a rotation matrix we need to translate it to its original form d_ijk as 3 × 3 × 3 matrix. According to Fig. 2.5, we use rotation matrices S (with Euler’s angles φ, θ and ψ) to perform the change of the nonlinear susceptibility tensor orientation between the crystal (d^(2),C) and the laboratory frame (d^(2),L). Each tensor element d^(2),L_i,j,k can be

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X Z

Y

c - axis

φ

θ ψ

γ

E^ω

Figure 2.5: Polarization microscopy. The crystal orientation is expressed in the laboratory frame X,Y,Z by the Euler angles φ, θ, and ψ. The angleγ denotes the polarization of incident laser light on the sample plane.

expressed:

d^(2),L_ijk = ∑

¯i¯j¯k

d_¯^(2),C

i¯j¯k S_i¯iS_j¯jS_k¯k (2.24) corresponding to the tensorial notation:

d^(2),L=S⋅d^(2),C (2.25)

with the rotation matrixS given by:

S=

⎛

⎜

⎝

cosψcosθcosφ−sinψsinφ −sinψcosθcosφ−cosψsinφ sinθcosφ cosψcosθsinφ+sinψcosφ −sinψcosθsinφ+cosψcosφ sinθsinφ

−cosψsinθ sinψsinθ cosθ

⎞

⎟

⎠ (2.26) In the laboratory frame, we define the polarization as linearly varying overγ=360^○ in the transverse (XY) plane (Fig. 2.5). The excitation field is supposed to be ellipticity-free, having no variation of its intensity overα, and to be at normal incidence, with at most two nonzero in-plane components

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0

 4

 2 3

4



5 4

3 2

7 4

0

 4

 2 3

4



5 4

3 2

7 4

a) b)

Figure 2.6: Polarization-resolved emission of BFO HNPs. Each signal is analysed along two orthogonal directions: X (blue trace) and Y (red trace).

Dots correspond to experimental data, while solid lines represent the best fit, giving following angle values: a) θ = 150°, φ = 281°, ψ = 275°, b) θ = 141°, φ = 69°, ψ = 330°

[38]. Therefore it is defined at the fundamental frequency as [37]:

E(γ, ω⃗ ) =E(ω)

⎡⎢

⎢

⎢⎢

⎢⎣ cosγ sinγ

0

⎤⎥

⎥

⎥⎥

⎥⎦

(2.27) where E(ω) is the field in the frequency domain.

Simplifying the expression by removing the terms including E(z, ω) =⃗ 0, we express the SHG polarization in the laboratory frame as:

P⃗⁽²⁾(γ, ω) =2₀d^(2),L

⎛

⎜⎜

⎜

⎜⎜

⎜

⎝

cos²γ sin²γ

0 0 0 2 sinγcosγ

⎞

⎟⎟

⎟

⎟⎟

⎟

⎠

(2.28)

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In order to calculate P⃗⁽²⁾(γ, ω) we need to translate χ^(2),L into 3 × 6 matrix, using Voigt notation. The radiation of the SHG field is obtained by introducing the nonlinear dipole moment P⁽²⁾ in the expression for a radiat- ing field perpendicular to ⃗k and the square of the field gives the expression of the radiated intensity:

E⃗_radiated ∝ ⃗k× ( ⃗P⁽²⁾× ⃗k) I⃗_radiated = ∣ ⃗E_radiated∣

2 (2.29)

As in our measurements we did not use a high NA objective( an objective with NA 0.6 was used) there was no need to integrate the radiated signal over the collection angle of the objective, like it was done by the group of J. Zyss ( [37], Appendix C). It allowed to derive the analytical expressions for the two projections of I⃗_radiated as a function of γ: f_x^γ and f_y^γ. These expressions can be found in A.1.4.

The examples of polarization resolved nonlinear response of BiFeO3nanocrys- tals are presented in Fig. 2.6.

2.1.3 Nonlinear microscopy

Started in 1990 by W.Denk and W.Webb nonlinear microscopy as compared to linear fluorescence microscopy, its features increased imaging depth, no out-of-focus bleaching, and spatial resolution comparable to confocal techniques without compromise in sensitivity [39].

Spatial Resolution

Having a point-like source object, the image obtained on a detector will be the convolution of the source object with the system’spoint spread function (PSF, also called system’s impulse response). Its gives a measure of the qual- ity of the imaging system by quantifying the spread of a point source [40].

The complete derivation of the point spread function can be found in [41].

The field radiated by a planar object is related to its corresponding source image plane distribution via a Fourier transform relation. In addition, a uniform function over a circular area in one Fourier domain corresponds to the Airy function in the other Fourier domain. It means that if a converg- ing uniform spherical wave passes through an uniformly-illuminated circular aperture it yields an Airy function image at the focal plane.

The point spread function in the image plane for a dipole oriented along

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10^-10 10^-9 10^-8 10^-7 10^-6 10^-5 10^-4 10^-3 10^-2 10^-1 10⁰

Normalized Epi-Detected HNP Signal

500 400 300

200 100

HNP position [µm]

800 nm 1064 nm 1320 nm 1550 nm

Figure 2.7: Imaging penetration depth. Results of numerical calculations, showing the expected normalized epi-detected SH signal generated by HNPs embedded in murine liver tissue at different depths for various excitation wavelengths. The calculations fully take into account the optical properties of the tissue (absorption, scattering) and the detection geometry. [22]

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

wavelength/um 10⁰

10¹ 10² 10³

Abs. Coeff. [cm−1]

10⁰ 10¹ 10²

Red. Scatt. Coeff. [cm−1]

melanin

red.

scatt.

coeﬀ.

water

Hb

HbO2

water protein

Figure 2.8: Absorption spectra of major tissue constituents (dotted lines, left axis, logarithmic scale) and scattering properties of skin (red solid line, right axis, logarithmic scale).

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the x axis can be represented as:

∣E(x, y, z =0)∣² ∝ [

2J₁(2πρ)˜ (2πρ)˜ ]

2

(2.30) where ˜ρ =NAρ/M λ and M is the transverse magnification. From 2.30, we can extract the width of the PSF ∆x = 0.6098M λ/NA which correspond to the distance between the maximum and the first minimum of the PSF (Eq. 2.30).

Intuitively the distinction between two different emitters will be possible when the distance between the two PSF will be equal to the width of the PSF.

The spatial resolution of a system can be expressed by the Abbe’s formula:

∆r=0.6098 λ

NA (2.31)

Another quantity which is to related to the spatial resolution is a full width half maximum (FWHM) of the PSF, which is equal to

FWHM=0.51 λ

NA (2.32)

In confocal microscopy, the spatial resolution depends on the size of the pinhole inserted in the conjugated plane of the objective. The theoretical limit of spatial resolution is given by the diameter of the Airy disc and is very hard to attain experimentally. [42] Contrarily, in nonlinear microscopy, the only limitation is the fulfilling of the back aperture of the objective and the theoretical limits can be reached. [42]

Nonlinear microscopy can obtain the resolution comparable to confocal microscopy by exploring properties of a nonlinear excitation process, which is proportional to the n-th power of the process nonlinear order (i.e. square in the case of second order processes and two-photon absorption). Therefore, the intensity needed to generate a two-photon process will be available in a very restricted volume compared to the one-photon process. This confine- ment will enhance the spatial resolution, and it becomes [9]

FWHM(2 photon)=

√

2ln2⋅0.32 λ

NA =0.44 λ

NA (2.33)

In comparison with confocal microscopy multiphoton microscopy uses longer wavelengths which gives an advantage in terms of increased penetration depth because of lower scattering. Extermann et al.showed by an experiment and a Monte Carlo simulation(shown in Fig. 2.7) that low scattering plays a more important role compared to absorption for deep tissue

Bismuth ferrite and silicon carbide harmonic nanoparticles: from characterization to tissue imaging

Thesis

Reference

Bismuth ferrite and silicon carbide harmonic nanoparticles: from characterization to tissue imaging

Bismuth Ferrite And Silicon Carbide Harmonic Nanoparticles: From Characterization To Tissue Imaging

TH` ESE

Andrii Rogov

Remerciements

List of acronyms

Contents

Summary

R´ esum´ e

List of Figures

List of Tables

Chapter 1 Introduction

Chapter 2

Introduction of concepts used in this work

2.1 Linear and Non-linear Polarization

2.1.1 Second Harmonic Generation and Propagation

z/um

SHG conversion efficiency, a.u.

∆ k =0

∆ k 0

2.1.2 Polarization resolved nonlinear microscopy

X Z

Y

φ

θ ψ

γ

a) b)

2.1.3 Nonlinear microscopy