GRADUATE PROGRAM IN MATERIALS ENGINEERING AND NANOTECHNOLOGY
PILAR GREGORY VIANNA
METHODS TO ENHANCE THE NONLINEAR OPTICAL FREQUENCY CONVERSION IN TRANSITION METAL DICHALCOGENIDES
São Paulo 2022
METHODS TO ENHANCE THE NONLINEAR OPTICAL FREQUENCY CONVERSION IN TRANSITION METAL DICHALCOGENIDES
Thesis submitted to the Graduate Program in Materials Engineering and Nanotechnology of the Mackenzie Presbyterian University as a partial fulfillment of the requirements for the Degree of Doctor in Engineering.
SUPERVISOR: PROF. DR. CHRISTIANO JOSÉ SANTIAGO DE MATOS
São Paulo 2022
V617m Vianna, Pilar Gregory
METHODS TO ENHANCE THE NONLINEAR OPTICAL FREQUENCY CONVERSION IN TRANSITION METAL DICHALCOGENIDES [recurso eletrônico] / Pilar Gregory - Vianna.
20000 KB ; il.
Tese (Doutorado em Engenharia de Materiais e Nanotecnologia) - Universidade Presbiteriana Mackenzie, São Paulo, 2022.
Orientador(a): Prof(a). Dr(a). Christiano jose Santiago de Matos Referências Bibliográficas: f. 74 -86
1. 2d Materials. 2. Transition Metal Dichalcogenides. 3. Second- harmonic Generation. 4. Nonlinear Optics. 5. Epsilon-near-zero. I.
Matos, Christiano jose Santiago de, orientador(a).II. Título.
Bibliotecário Responsável: Maria Gabriela Brandi Teixeira - CRB 8/6339
Autor: Pilar Gregory Vianna
Programa de Pós-Graduação Stricto Sensu em Engenharia de Materiais e Nanotecnologia
Título do Trabalho: METHODS TO ENHANCE THE NONLINEAR OPTICAL FREQUENCY CONVERSION IN TRANSITION METAL DICHALCOGENIDES
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico FAPESP - Fundação de Amparo à Pesquisa do Estado de São Paulo
Instituto Presbiteriano Mackenzie/Isenção integral de Mensalidades e Taxas MACKPESQUISA - Fundo Mackenzie de Pesquisa
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PILAR GREGORY VIANNA
METHODS TO ENHANCE THE NONLINEAR OPTICAL FREQUENCY CONVERSION IN TRANSITION METAL DICHALCOGENIDES
Thesis submitted to the Graduate Program in Materials Engineering and Nanotechnology of the Mackenzie Presbyterian University as a partial fulfillment of the requirements for the Degree of Doctor in Engineering.
Approval date: Feb 11th, 2022
Prof. Dr. Christiano José Santiago de Matos Mackenzie Presbyterian University
Prof. Dr. Lucia Akemi Miyazato Saito Mackenzie Presbyterian University
Prof. Dr. Henrique Guimaraes Rosa Mackenzie Presbyterian University
Prof. Dr. Robert Murray Imperial College London
Prof. Dr. Anderson Stevens Leonidas Gomes Federal University of Pernambuco
A minha mãe, Katia Maria Gregory Vianna (in memoriam), por iluminar minha vida junto as estrelas. Ao meu pai, Jorge Alberto Vianna e irmão, Rodrigo Gregory Vianna, pela força, paciência e amor incondicionais.
To Professor Christiano José Santiago de Matos, my eternal gratitude for the patience. During the last 8 years, I’ve learned to think by myself and would never be able to mensurate how valuable your professional lead and true friendship have been.
To Professor James Hone, for receiving me so kindly at Columbia University and his family.
To my father, mother, and brother. I have no words to describe my love and admiration for you.
There’s nothing in my life purer than you.
My aunts Maria Cristina Gregory and Maria Valéria Fernandes, for the unvaluable help.
To all the colleagues from the Photonics Lab and MackGraphe, to whom this work wouldn’t have been possible without. Thank you for the fruitful discussions and endless support, most notably to Priscila Romagnoli, Carolina Tegon, Fernanda Cabrera, Henrique Bucker Ribeiro, Eduardo Aiub, Débora Morita, Danilo Nagaoka, Caroline Brambilla, Andressa Oliveira, Aline dos Santos, Anna Paula Godoy, Alexandre Samuel, Rodrigo Gerosa, Vinicius Alvarenga and Kamila and Bianca Tieppo.
To all the MackGraphe team, as well as, the Materials and Electrical Engineering Graduate Programs, Professors, technicians, and staff.
To Brunnely Bittencourt, Yopanan Rocha, and Débora Morita for saving my life so many times during the journey.
To CAPES (PRINT 88887.370132/2019-00) and the Brazilian Nanocarbon Institute of Science and Technology (INCT/Nanocarbon – 88887.195743/2018-00), CNPq, and FAPEMIG for the scholarships.
To the universe…
Desde o isolamento do grafeno, um número crescente de materiais 2D tem sido produzido, atraindo a atenção de pesquisadores das mais diversas áreas. O grafeno comporta-se como um semicondutor de gap zero, o que limita sua aplicabilidade em dispositivos fotônicos e optoeletrônicos. Já os dicalcogenetos de metais de transição (TMDs, do inglês, transition metal dichalcogenides), podem exibir diferentes fases, com energia de bandgap variável, importante para aplicações fotônicas como moduladores, fotodetectores e diodos emissores de luz. Além disso, os TMDs monocamada apresentam altas suscetibilidades ópticas não lineares, responsáveis por efeitos como a geração de segundo e terceiro harmônico (SHG / THG), importante para conversão de frequência totalmente óptica. No entanto, e apesar do enorme número de benefícios, a utilização dos TMDs para aplicações práticas ainda é um desafio. A espessura atômica desses materiais resulta em baixa interação luz-matéria, o que naturalmente leva a baixas eficiências de conversão de frequência (mesmo considerando a eficiência de conversão por unidade de espessura maior do que em materiais convencionais). Portanto, formas de aprimorar os processos e maximizar a interação não linear são cruciais para viabilizar aplicações práticas. Neste trabalho, propomos duas abordagens diferentes para aumentar a eficiência de conversão não linear em TMDs. A primeira estratégia foca na otimização do sistema por meio da influência do substrato. Demonstramos o uso de óxido de estanho dopado com flúor (FTO, do inglês fluorine-doped thin oxide), com a constante dielétrica próxima a zero (ENZ, do inglês epsilon-near-zero) próximo ao comprimento de onda de bombeio, para maximizar a eficiência de conversão não linear em TMDs monocamada. Medidas de SHG polarizado revelam uma intensidade uma ordem de magnitude maior em TMDs depositados em FTO do que em vidro. A segunda estratégia, apresentada como uma alternativa promissora é aumentar o comprimento da interação luz-matéria pela integração de materiais 2D em guias de onda. Exploramos a exfoliação assistida por ouro desses materiais a fim de obter monocristais macroscópicos de uma única camada, comparáveis em qualidade aos flakes microscópicos, que podem, em princípio, ser transferidos para estruturas de guias de ondas abrindo caminho para dispositivos fotônicos reais. Dessa forma, apresentamos o uso de diferentes técnicas de manipulação de TMDs e propomos o uso de diferentes substratos e plataformas para a obtenção de respostas ópticas não lineares otimizadas e mais eficientes.
Palavras-chave: Materiais 2D; dicalcogenetos de metais de transição; geração de segundo harmônico; óptica não-linear; epsilon-near-zero (ENZ).
Since the isolation of graphene, an increasing number of 2D materials have been produced, attracting attention of researchers. Graphene, however, behaves as a zero-gap semiconductor, which limits its applicability in photonic and optoelectronic devices. 2D transition metal dichalcogenides (TMDs), on the other hand, can exhibit different phases, with tunable bandgap energy, enabling photonic applications including modulators, photodetectors, and light- emitting diodes. Furthermore, TMD monolayers present large nonlinear optical susceptibilities, which are responsible for effects such as second- and third-harmonic generation (SHG/THG), important for all-optical wavelength conversion. However, and despite the enormous number of benefits, direct TMD utilization for practical nonlinear optical applications is still an ongoing challenge. The atomic thickness of these materials results in reduced light–matter interaction, which naturally leads to low net frequency converted intensities (even if the conversion efficiency per unit thickness is higher than that in conventional materials). Therefore, ways to enhance the process and maximize the nonlinear interaction are crucial for making practical applications viable. In this work, we propose two different approaches for enhancing the nonlinear conversion efficiency in 2D TMDs. In our first strategy, we propose optimizing the overall system through the influence of the substrate. We demonstrate the use of fluorine- doped-thin-oxide (FTO) with an epsilon-near-zero point close to the pump wavelength to increase the nonlinear conversion efficiency in monolayer TMDs. Polarized SHG measurements reveal an intensity one order of magnitude higher on TMDs deposited on FTO than that on a bare glass substrate. Secondly, a promising alternative is to increase the light- matter interaction length by integration of 2D materials in on-chip waveguides. We exploit an exfoliation method to obtain macroscopic single-crystal monolayers, comparable in quality to microscopic flakes, which can in principle be transferred to waveguide structures, opening a path to real photonic devices. Thus, we present the use of different techniques to manipulate 2D TMDs and propose the use of different substrates and platforms to obtain optimized and more efficient nonlinear optical responses.
Key words: 2D materials; transition metal dichalcogenides (TMDs); second-harmonic generation (SHG); nonlinear optics; epsilon-near-zero (ENZ).
Figure 1. Bottom up and Top-down approaches for the preparation of 2D materials. ... 16 Figure 2. Deterministic transfer setup and process. (A) Experimental setup employed for the deterministic transfer process. (B) Steps involved in the transfer process. ... 18
Figure 3. (A) Electronic bandgaps of Graphene, TMDs and Black Phosphorus. (B) Approaches for 2D-material based optical modulation. Reproduced with permission [67].
Copyright 2020, De Gruyter. Licensed under CC BY 4.0. ... 19 Figure 4. Periodic table of elements highlighting the transition metals (M) and chalcogens (X), which combined form the MX2 structure of the TMDs. ... 21
Figure 5. Representation of the Armchair and Zigzag edges of MoS2. ... 22 Figure 6. Band structure variation of 2H-MoS2 ... 23 Figure 7. Absorption spectrum of mechanically exfoliated monolayer MoS2 at low temperature (solid green line) with two prominent resonances, known as the A and B excitons.
The blue dashed line shows the theoretical absorbance in the absence of excitonic effects.
Reproduced with permission [14]. Copyright 2016, Springer Nature. ... 25 Figure 8. Typical PL spectra for different multilayer TMDs at 300 K (top) and 4 K (bottom) on a SiO2 substrate. Reproduced with permission [90]. Copyright 2017, American Physical Society. Licensed under CC BY 4.0. ... 26
Figure 9. (a) Optical microscopy image of the MoS2 sample. (b) AFM image of the dashed triangle shown in (a), scale bar is 1 μm. (c) SHG image collected with a pump-laser at 800 nm (1.55 eV). Brighter colors mean stronger SHG intensity. Scale bar is 5 μm. (d) Intensity profile of the SHG image from the left to right at the yellow line shown in picture (c). Reproduced with permission [91]. Copyright 2013, American Physical Society. ... 27
Figure 10. (A) SHG characterization. Polar plot of the SHG intensity of a single-layer 2D material as a function of the pump linear polarization angle θ. Fitting the angular dependence, the armchair direction (dark blue arrow) of the sample is determined as the highest intensity.
The armchair direction is shifted by 30º from the zigzag direction (light blue arrow). (b) Optical image of the flakes. The axes are indicated as armchair (dark blue arrow) and zigzag (light blue arrow) and were determined by polarization-resolved SHG shown in (A). Reproduced with permission [93]. Copyright 2018, AIP Publishing LLC. Licensed under CC BY 4.0. ... 28
Figure 11. Polarized SHG measurements of different TMDs under varying uniaxial strain.
SHG measurements at the lowest and highest applied strain levels, purple and yellow, respectively. Fitted SHG curves at different strain levels. (bottom). Experimental measurements
Figure 12. Comparison of experimental and theoretical (A) |χ(2)| and (B) |χ(3)| for TMDs at 1560 nm excitation. Reproduced with permission [62]. Copyright 2018, American Physical Society. ... 30
Figure 13. Typical nonlinear optical effects and applications. Light blue, orange, pink and purple gradients represent different order nonlinear optics (NLO) susceptibility, nonlinear processes corresponding to different NL susceptibility, application, and further applications respectively. DFG: Difference frequency generation; TPEF: two-photon excitation fluorescence; SA: saturable absorption; HHG: high-harmonic generation; OPA: optical parametric amplification; OPO: optical parametric oscillation (OPO). Reproduced with permission [128]. Copyright 2020, MDPI. Licensed under CC BY 4.0. ... 34
Figure 14. Energy-level diagram for second- and third-harmonic generation. ... 35 Figure 15. Scheme of a monolayer treated as a nonlinear sheet susceptibility at the interface between air and the substrate. ... 37
Figure 16. AFM topography images for the original FTO substrate (A) and for the polished FTO substrate (B). ... 42
Figure 17: Simplified sample preparation process. 1) Bulk 2D material is placed onto the PDMS surface. 2) A Nitto tape is used to exfoliate the bulk flake until the monolayer limit. 3) The microscope slide with the PDMS/monolayer flake is turned upside down and gently pressed against the final substrate. The process is performed under an optical microscope and the microscope slide movement is controlled with an XYZ micropositioner. 4) The microscope slide is lifted, transferring the monolayer to desired substrate. ... 43
Figure 18: Optical microscope image of MoS2 and WS2 flakes deposited on the same FTO substrate. The red circle highlights the monolayer regions. ... 44
Figure 19: Optical characterization of MoS2 and WS2 on glass. Optical microscope images of MoS2 (A) and WS2 (C) deposited on glass. (B) & (D) Raman spectra obtained at the same color positions marked by a cross in (A) and (C), respectively. Raman data obtained at 532 nm with 0.5 s, 10 accumulations and 3.5 mW laser power for MoS2; and 2 s integration time, 10 accumulations and 1.15 mW laser power for WS2. ... 45
Figure 20: Optical characterization of MoS2 and WS2 on FTO. Optical microscope images of MoS2 (A) and WS2 (C) deposited on FTO. (B) & (D) Raman spectra obtained at the same color positions marked by a cross in (A) and (C), respectively. Raman data obtained at 532 nm
Figure 21. Dielectric function of FTO modeled by the Drude free electron model with parameters obtained by fitting experimental transmission spectra. ... 48
Figure 22. Experimental (black) and theoretical (red) transmittance for the p polarization at 0° (A) and 45° (B). ... 49
Figure 23. Experimental (black) and theoretical (red) transmittance for the s polarization at 0° (A) and 45° (B). ... 49
Figure 24. (A) Enhancement factor as functions of the wavelength and FTO thickness of the FTO-on-glass substrate. Blue dot indicates the experimental conditions. (B) Theoretical SHG enhancement factor as a function of the wavelength for a 520-nm FTO thickness. Dashed line shows the experimental wavelength. ... 52
Figure 25. (A) Transmittance T13ω, (B) Reflectance R13ω, and (C) Absorption A = 1 − R13ω − T13ω as functions of the fundamental wavelength and FTO thickness. The classical skin depth is represented as the black curve in each panel. ... 52
Figure 26. Experimental setup for SHG characterization of the samples. ... 54 Figure 27. Optical image of the flakes under red LED light illumination and the THG beam.
(A) Attenuated red LED light. The yellow triangle delimits the monolayer TMDC flake. (B) Higher LED light intensity on the sample. ... 55
Figure 28. SHG spectrum, centred at 785 nm, obtained in the MoS2 sample. ... 56 Figure 29. Experimental SHG intensity as a function of pump polarization angle in the parallel polarization configuration for FTO (black), MoS2/FTO (red) and WS2/FTO (blue), normalized by the maximum measured SHG signal on the MoS2/glass sample. ... 57
Figure 30. Dependence of the SHG intensity on the pump power. ... 58 Figure 31. SHG intensity from FTO as a function of pump polarization angle in the parallel polarization configuration, measured at 4 different positions of the same substrate. ... 58
Figure 32. Experimental SHG intensity as a function of pump polarization angle in the perpendicular polarization configuration for MoS2/FTO (red) and MoS2/Glass (black). (B) Theoretical prediction for MoS2 on FTO (red) and Glass (black) in the perpendicular polarization. ... 59
Figure 33. Experimental SHG intensity as a function of pump polarization angle in the perpendicular polarization configuration for WS2/FTO (blue) and WS2/Glass (black). ... 60
Figure 34. Normalized PL for WS2 monolayers on PDMS (red curve) and after transferring to FTO (A) and Glass (B). ... 61
Figure 36. Schematic of a nonlinear material with domain engineering spatially modulated ... 64 Figure 37. (A) Schematic illustration of the layer-by-layer exfoliation procedure of bulk vdW single crystals. (B) Picture of six monolayer samples sequentially exfoliated on a SiO2/Si substrate.WSe2 bulk single crystal shown at the upper left corner. Reproduced with permission [50]. Copyright 2020, AAAS. ... 66
Figure 38. Schematic illustration of 20 waveguides on a chip and representation of a monolayer 2D material transferred to its surface (out of scale). ... 67
Figure 39. (A) MoS2 on template stripped gold supported by a thermal release tape (TRT).
The “pink” contrast region on the gold surface is an exfoliated monolayer MoS2 flake. Each full yellow line square on the green board has a size of 1 cm x 1 cm. (B) Monolayer MoS2
transferred to the SiO2/Si substrate. (C) MoS2 Raman characterization, with a wavenumber difference between the A1g to E12g modes of approximately 18.5 cm-1. ... 68
Figure 40. MoS2 monolayer flakes of different sizes on SiO2 substrate. ... 69 Figure 41. (A) Gold on a TRT. (B) Optical microscopy images of gold on a TRT. (C) Atomic force microscopy of gold o a TRT. RMS roughness of 1.05 nm. ... 69
Figure 42. (A) Gold on PDMS. (B-D) Optical microscopy images of gold on PDMS for different regions and magnifications. (A) Gold on 10:1 (base/curing agent) PDMS. (B-C) Atomic force microscopy for different regions of gold on PDMS. RMS roughness of 0.315 nm and 0.325 nm, for (B) and (C), respectively. ... 70
1 INTRODUCTION ... 12
2 TWO-DIMENSIONAL MATERIALS ... 15
2.12D MATERIALS’ MANIPULATION AND TRANSFER PROCESS ... 15
2.2TMDS: SUITABLE 2D MATERIALS FOR PHOTONIC APPLLICATIONS ... 18
2.3TRANSITION METAL DICHALCOGENIDES (TMDS) ... 20
2.3.1 Crystal Structure of TMDs ... 21
2.3.2 Optical Properties of TMDs ... 23
3 INTRODUCTION TO NONLINEAR OPTICS ... 32
3.1BRIEF HISTORY OF NONLINEAR OPTICS ... 32
3.2DEFINITION AND MODELS OF THE NONLINEAR RESPONSE ... 33
3.2.1 Second-harmonic generation ... 36
3.2.2 Third-harmonic generation ... 38
4 SHG ENHANCEMENT BY ENZ SUBSTRATES ... 40
4.1SAMPLE PREPARATION AND CHARACTERIZATION ... 41
4.1.1 FTO substrate characterization and processing ... 41
4.1.2 MoS2 and WS2 exfoliation and ENZ sample preparation ... 42
4.1.3 MoS2 and WS2 Raman and optical microscopy characterization ... 44
4.2NONLINEAR OPTICAL CHARACTERIZATION ... 46
4.2.1 Theoretical modeling of the second-harmonic generation ... 46
4.2.2 SHG Enhancement by ENZ substrates: experiments and analysis ... 53
5 LARGE AREA TMDS FOR DEVICE INTEGRATION... 63
5.1ENHANCED NONLINEAR INTERACTION ON WAVEGUIDES ... 63
5.2EXPERIMENTAL RESULTS ON LARGE AREA EXFOLIATION OF TMDS ... 67
6 CONCLUSION AND FUTURE WORKS ... 72
BIBLIOGRAPHY ... 74
SCIENTIFIC PRODUCTION ... 87
1 INTRODUCTION
The past decade has witnessed significant progress in the field of 2D materials.
A 2D material is a crystal in the form of a planar structure, which can be regarded as a 3D crystal with a negligible thickness. 2D materials present van der Waals (vdW) interactions between adjacent sheets, or monolayers, and strong covalent bonds providing in-plane stability, which allows the material’s thickness to be controlled at the atomic level [1]–[3]. Different thicknesses can be obtained from the exfoliation of their 3D counterparts, offering enormous possibilities.
Compared with the bulk and traditional thin-film materials, 2D materials hold a great advantage and competitiveness for device applications, including on-chip integration and next-generation technology such as spintronics, advanced nanoelectronics, nanosensing and many others [4]. The potential mainly comes from these materials’ game-changing properties, arising from the quantum confinement within their atomic thickness.
Such unique properties grant tremendous potential to the 2D materials in applications such as optical switching and modulators [5], [6], optoelectronics [3], [4], [7]–[16], energy storage [17]–[23], catalysis [24]–[33], ultrafast lasers [34]–[36], various types of sensing [37]–[44], and others. In terms of optical properties and photonic/optoelectronic applications, the thickness of mono- and few-atomic-layer 2D materials is much smaller than the wavelength of light, allowing the observation of a variety of new properties. Among them, most 2D materials present an optical response that is tuneable with the number of layers, attracting special interest, in particular for the practical applications previously mentioned.
In particular, atomically thin transition-metal dichalcogenides (TMDs) present extremely favorable physical properties for optical applications, such as monolayers featuring a direct band gap in the visible spectral range [45], which enables diverse photonic applications including modulators, photodetectors, and light-emitting diodes. Furthermore, TMD monolayers attracted additional attention due to their large nonlinear optical susceptibilities [46], which are responsible for effects such as second and third harmonic generation (SHG/THG), sum-frequency generation, four-wave mixing, high-harmonic generation and saturable absorption, which can be exploited for photonic applications such as all-optical wavelength conversion, ultrafast pulse shaping, optical imaging, quantum information processing, nano-scale light sources, among others.
Technically, effects such as harmonic generation are limited by the nonlinear optical response of traditional materials and their intrinsic nonlinear optical susceptibility [2],[3], usually presenting low conversion efficiencies. Also, symmetry plays a key role in nonlinear optics, with second harmonic generation only possible in materials without an inversion center, while odd-ordered nonlinear processes, such as third harmonic generation, can occur in all materials [49].
For photonic applications, the focus of this work, it is important to mention that TMDs are centrosymmetric in their bulk form, but TMD monolayers lack inversion symmetry, therefore, allowing the observation of nonlinear second order effects, such as SHG.
Additionally, from a nonlinear perspective, and given the atomic thickness of the materials, TMDs give rise to relatively high efficient frequency conversion. Also, the ultrasmall thickness waives the phase-matching requirement, as a single layer of material is hundreds of times smaller than the wavelength of light and the coherence length of the nonlinear process.
However, and despite the enormous number of benefits, direct TMD utilization for practical nonlinear optical applications is still an ongoing challenge. The atomic thickness of the 2D materials results in reduced light–matter interaction, which naturally leads to low net frequency converted intensities (even though the conversion efficiency per unit thickness is significantly higher than that in conventional materials). Therefore, ways to enhance the process and maximize the nonlinear interaction are crucial for making practical applications viable.
One possible means to obtain higher converted powers is to increase the conversion efficiency itself, which can be accomplished via optimizing the influence of the substrate. Another promising alternative is to increase the light-2D materials interaction length by integration with waveguides. However, for that, the quality, reproducibility, and scalability of TMD production methods must be accounted for, aiming at real device applications. While mechanical exfoliation is still considered the best method in terms of high-quality materials, yielding nearly-perfect single crystals that are essential for the efficiency and reproducibility in optical applications, it is also characterized by low scalability (low-throughput) and micron- size flakes.
In this work, we propose two different approaches for enhancing the nonlinear conversion efficiency in 2D TMDs. First, by exploiting the interaction with different substrates, and then by the maximization of the light-2D materials interaction length. Although several strategies have already been designed to enhance the nonlinear optical SHG process in TMDs
and other 2D materials, most methods rely on complex and time-consuming fabrication processes.
In our first strategy to increase the nonlinear frequency conversion efficiency in mechanically exfoliated monolayer TMDs, we propose and demonstrate the use of substrates presenting an epsilon-near-zero point close to the pump wavelength. As the nonlinear optical response in 2D materials strongly depends on a variety of factors, including the dielectric constant of the substrate, we use substrates with a low refractive index to maximize the pump electric field at the interface where the 2D material is located. The technique basically consists of acknowledging that, as the 2D material lies at the interface between two dielectrics, the pump field on it is given by the electromagnetic boundary conditions that arise from the reflection and refraction phenomena, tending to the maximum value if the refractive index tends to zero.
In parallel, for being able to obtain increased interaction lengths in on-chip waveguides, we exploit and improve an exfoliation method to obtain macroscopic single-crystal monolayers, which are comparable in quality to microscopic exfoliated flakes. For that, we use a nondestructive technique limited only by the sizes of the bulk crystals, exfoliating the TMD crystals on gold substrates yielding monolayers up to the centimeter scale. The monolayers with broken inversion symmetry and substantially enhanced nonlinear optical response [50] can be transferred, in the near future, to waveguide structures, opening a path to real photonic devices. That way, aiming at an enhanced light-matter interaction, we propose the large area TMD monolayers integration with waveguides for maximized nonlinear optical effects.
This thesis is organized as follows; Chapter 2 presents an overview on the current state-of-the-art 2D materials’ manipulation and sample preparation techniques, followed by their optical applications, focusing on the nonlinear optical literature directed to SHG in TMDs.
Chapter 3 introduces the theory behind nonlinear optics, while Chapter 4 presents theoretical and experimental results of improved SHG efficiency obtained with monolayer TMDs on ENZ substrates. Chapter 5 presents results obtained with the gold assisted exfoliation of large size monolayers and propose their integration with optical waveguides. Chapter 6 presents the conclusions and future perspectives.
2 TWO-DIMENSIONAL MATERIALS
Two-dimensional (2D) materials are a class of ultra-fine crystals with unique properties emerging from their nanometric dimensions and quantum confinement effects.
Graphene, the most famous 2D material was first isolated in 2004 by Geim and Novoselov[51]
and is the fundamental building block for a range of carbon materials with sp2 hybridization, such as graphite (3D), carbon nanotubes (1D), and fullerenes (0D) [52]–[54].
Since the isolation of graphene, an increasing number of 2D materials have been shown, attracting great attention due to their diverse breakthrough electrical, chemical, thermal, and optical properties. In particular, we highlight as especially interesting materials: hexagonal boron nitride (h-BN), black phosphorus (BP), 2D perovskites, silicene, and transition metal dichalcogenides (TMDs) [55][56].
This chapter presents a brief literature review on 2D materials manipulation and sample preparation techniques and their optical properties, with a focus on the nonlinear optical properties of TMDs, most specifically, second harmonic generation, the central topic of this work.
2.1 2D MATERIALS’ MANIPULATION AND TRANSFER PROCESS
2D materials are extremely sensitive to the substrate, impurities, contamination and other variables, and exfoliation (or growth) techniques and transfer processes are essential to the reproducibility and reliability of the studies employing these materials. Mechanical exfoliation, chemical vapor deposition (CVD), wet chemical synthesis, epitaxial growth and chemical self-assembly are only a few synthesis methods, some of which are more suitable for mass production than others [57][58]. These methods can be further expanded and categorized into bottom-up and top-down approaches, as shown in Figure 1.
Briefly, in the top-down methods, single- or few-layer 2D materials can be obtained from their bulk counterparts by breaking the van der Waals interaction between the stacked layers [59], [60]. Mechanical cleavage or exfoliation and liquid exfoliation are the most used techniques. In mechanical exfoliation, commonly referred to as the Scotch-tape method, a tape is used to peel off layers from the bulk crystal, repeating the process until the desired number of layers is reached, which is followed by the deposition of those exfoliated flakes on
the substrate. In the liquid exfoliation, from the bulk structure, 2D materials are obtained directly in solvents via sonication [59].
Regarding the bottom-up methods, CVD growth is the most well-known among them. CVD is a high-temperature chemical synthesis process by which a desired material is deposited on substrates [57]. The process relies on the fact that a gaseous material will react in the vapor phase or on the surface of substrates, and thus form solid products that are deposited on the substrates. The number of layers, size, morphology and orientation, can be controlled by changing the growth parameters such as temperature, pressure, carrier gas flow rate, relative amounts of source materials, and source−substrate distance [61]. However, single crystal domains tend to be relatively small. Also, defects, such as vacancies, tend to be more frequent than in naturally grown crystals, and are usually associated to experimental conditions, such as the quality of the materials (precursors), growth rate and temperature, substrate properties, cleanliness of the overall system, among others.
Figure 1. Bottom up and Top-down approaches for the preparation of 2D materials.
Although extensive research progress has been achieved, challenges still remain and great efforts on pursuing precise control over the structures and properties of 2D materials for their application in practical devices are still ongoing. Specifically, to improve the existing
techniques and develop new methods with enough reproducible quality still requires enormous research efforts. Besides, obtaining precise control over their composition, lateral sizes, thicknesses, doping, defects, strain, and other properties becomes increasingly important to unveil the correlations between their structural features and properties [55].
Another important aspect is the possibility to manipulate and precisely transfer the materials, allowing for a fair comparison of their properties within the same conditions.
Autere et al. [62], for example, used micromechanically exfoliated MoS2, MoSe2, WS2 and WSe2 flakes transferred onto the same SiO2 substrate within tens to few hundreds of micrometers from one another. In that case, the sample preparation method was essential to allow for the precise deposition of the materials close enough to each other, guaranteeing a fair optical characterization and comparison. For that transfer, the authors used the deterministic transfer technique.
The all-dry deterministic viscoelastic stamping transfer process allows control and positioning of the 2D materials and facilitates their integration in different substrates and devices, which is useful for the exploration of their properties and the discovery of new phenomena with breakthrough potential in practical applications. The technique relies on the use of transparent viscoelastic stamps, through which light can pass, allowing for the precise visual positioning of the flakes under a microscope and, thus, a quick and efficient transfer [63].
Figure 2(A) shows the experimental apparatus employed to transfer the 2D materials with the deterministic viscoelastic technique [63]. The setup employed comprises an optical microscope, often supplemented with large working distance optical objectives, and a three- axis micropositioner to accurately move and position the stamp[63]. The system can also be improved by adding a goniometer for precise rotation and angle control between different flakes and automatizing the set-up, for example.
The detailed process is described in Figure 2(B) and starts with the micromechanical exfoliation of the bulk crystal with a scotch tape, which is then put in contact with the surface of a viscoelastic polymer, transferring the flakes. After the flakes are exfoliated and transferred to the viscoelastic polymer, the surface of the stamp is inspected under the optical microscope to select the materials to be used. Once a thin flake has been identified, the target substrate is fixed on the sample transfer stage, and the stamp attached to the three-axis manipulator with the flakes facing towards the sample. The great advantage of the technique is that, as the stamp is transparent, one can see the sample through, making it possible to align the
desired flake with the target surface. In order to transfer the flake to the surface, the stamp is gently pressed against the surface and slowly peeled off.
The working principle of the viscoelastic transfer is based on the fact that the stamp behaves as an elastic solid over short periods of time (by fast detaching the stamp, for example) while it will slowly flow over long timescales [64]. Therefore, by slowly peeling off the stamp from the surface of the substrate, it is possible to kinetically control the adhesion, detaching the elastomer and releasing the flakes that preferentially adhere to the substrate of choice. Different research groups have adapted the technique for different polymers, such as PDMS [63], PC[65] and PPC/PDMS [66], yielding slightly different processes, but all pertaining the same main idea. Depending on the polymer to be used, heating the substrate during the transfer process is necessary. By setting the temperature above the boiling point of water and the glass transition temperature of the polymer, flakes can be selectively picked up or dropped down and non-viscoelastic polymers can also be used [66].
Figure 2. Deterministic transfer setup and process. (A) Experimental setup employed for the deterministic transfer process. (B) Steps involved in the transfer process.
2.2 TMDS: SUITABLE 2D MATERIALS FOR PHOTONIC APPLLICATIONS
Strong interactions with light and their implications for photonic applications have been extensively demonstrated in atomically thin 2D materials. Graphene itself displays a sixfold rotational symmetry [63] with a single atomic layer absorbing 2.3% of the incident light in the visible to near-IR spectral range, associated to interband transitions [64]. Despite many unique features and all the early enthusiasm around the material, graphene behaves as a zero-
bandgap semiconductor, which can severely hinder its applicability on the fabrication of certain practical optical devices [57], [58] and for the semiconductor electronics industry [55].
That mentioned, the vast class of 2D materials and their versatile crystal structures allow for bandgap engineering. As shown in Figure 3(A), different materials present different bandgap energies, covering a wide spectral range and supporting the observation of different linear and nonlinear optical properties. Despite their similar layered structures, the properties of different 2D materials can be contrasting due to different compositions and structural arrangements. For example, complementary to graphene, which intrinsically has no bandgap [65], most TMDs present sizable bandgaps ranging from 1 to 2.5 eV. Black Phosphorus, also an interesting material, presents a bandgap between 0.3 to 1.5 eV (varying with the number of layers as in the TMDs), closing the gap between graphene and the TMDs.
Their unique structural features and outstanding properties render extremely attractive properties in a wide spectrum, as already mentioned [55][66][67].
Figure 3. (A) Electronic bandgaps of Graphene, TMDs and Black Phosphorus. (B) Approaches for 2D-material based optical modulation. Reproduced with permission [67]. Copyright 2020, De
Gruyter. Licensed under CC BY 4.0.
Additionally, the optical response of 2D materials can be further tailored by external fields or the environment, such as, electric fields, optical fields, magnetic fields, temperature, and pressure, with the most conventional approaches summarized in Figure 3(B).
In the case of 2D semiconductors, such as TMDs or black phosphorus, excitonic transitions also impact and influence optical properties [68]. These transitions lead to significant optical absorption, emission and nonlinear effects when the involved photons are close to resonance.
Excitons are bound pairs of an electron and a hole, obtained once the former is removed from the valence band due to an external perturbation, through the absorption of light, for example. Experimentally, the phenomena can be observed from the photoluminescence or the optical absorption spectrum, containing the fingerprints of excitons and their energies. In atomically thin materials, excitons are strongly bound and govern optical processes even at room temperature, and are crucial for nonlinear optics as they can resonantly enhance light- matter interaction by several orders of magnitude [80].
Among other nonlinear optical processes, SHG (and THG) are easily observable frequency conversion effects, where two (three) photons of identical energy combine into one photon of twice (three times) their energy [69]. The occurrence of SHG in a crystal is directly linked to its symmetry, where crystals with broken inversion symmetry can exhibit SHG, while crystals which are centrosymmetric cannot [69][70]. While black phosphorus is centrosymmetric regardless of its layer count, TMD monolayers have broken inversion symmetry and, therefore, allow for SHG signals.
Nonlinear optical characterization is also a powerful methods to allow for the comparison between the characteristics and possible device performance of materials.
Woodward et al. [46] used SHG and THG imaging for evaluating the nonlinear optical susceptibilities, χ(2) and χ(3), of MoS2. Direct experimental comparison between graphene and MoS2 showed ∼3.4x stronger third-order nonlinearity in the monolayer TMD. As expected from the inversion symmetry of its atomic structure, SHG was not observed in graphene [46].
The fact that the TMDs allow for second order nonlinear optical processes is, therefore, an additional benefit of this class of materials. This is the reason why we focus on their utilization for frequency conversion applications.
2.3 TRANSITION METAL DICHALCOGENIDES (TMDS)
For photonic applications, the focus of this work, 2D TMDs are of special importance due to the reduced dimensionality of the materials leading to a significant impact on the electronic band structure. During the following sessions, we approach the TMDs crystal structure and introduce different linear and nonlinear optical characteristics of these 2D materials together with a review of the state-of-the-art literature.
2.3.1 Crystal Structure of TMDs
2D TMDs are atomically thin materials of the type MX2, where M refers to a transition metal (M) from the groups 4 to 10 of the periodic table and (X) to a chalcogen, such as sulfur (S), selenium (Se), or tellurium (Te). In general, TMDs involving transition metals from groups 4 to 7 have a layered structure, while those involving groups 8 to 10 have non- layered structures. In Figure 4 it is possible to observe the allowed combination of elements to form the structure of TMDs. Typically, each layer has an approximate thickness of 6 ~ 7 Å, interlayer stacked by weak van der Waals forces [71].
Figure 4. Periodic table of elements highlighting the transition metals (M) and chalcogens (X), which combined form the MX2 structure of the TMDs.
TMDs present two basic edge structures, namely zigzag and armchair, as shown in Figure 5. Different types of crystal arrangements can be observed from the stacking layers of TMDs: trigonal prismatic thermodynamically stable (2H and 3R) phases, and an octahedral (1T) metastable phase with a metallic behavior [57], [82], [83]. Between 2H and 3R phases, the layers’ arrangement is different, with the former containing two layers per unit cell stack in the hexagonal symmetry and the latter three layers per unit cell in the rhombohedral symmetry, both with trigonal prismatic coordination [72][73]. Therefore, TMDs exhibit diverse properties dependent on their phase and composition, and can be observed as semiconductors (2H-MoS2, 2H-WS2), metals (1T-MoS2, 1T-WS2, NbS2, VSe2), semimetals (Wte2, TiSe2), and even superconductors (NbSe2, NbS2, TaS2, TaSe2) at low temperatures (1.7 to 7 K) [56]. The
properties of TMDs can, thus, be tailored according to their crystalline structure, the number of layers and, their stacking sequence [74].
Figure 5. Representation of the Armchair and Zigzag edges of MoS2.
Molybdenum disulfide (MoS2), for example, is one of the materials presenting a semiconductor character (2H-MoS2) and a metallic character (1T-MoS2) based on different crystalline structure conformations, therefore, showing completely different electronic properties. Unique electrical and optical properties also arise from the quantum confinement, responsible for the changes in the band structure of 2H-MoS2 with decreasing thickness. The positions, in wavevector space, of the valence and conduction band edges change as observed in Figure 6, with the indirect bandgap semiconductor in the bulk form turning into a direct bandgap semiconductor in the monolayer [75]–[77]. The arrows in Figure 6 indicate the lowest energy interband transition (between the maximum of the valence band and the minimum of the conduction band), from which it is possible to confirm the change from an indirect to a direct bandgap.
The calculated values for the bandgap energies of bulk and monolayer MoS2 are 0.88eV and 1.71 eV, respectively[75]. Experimentally, variations to the monolayer bandgap values can be observed mainly due to different measurement techniques/conditions and sample
preparation methods, leading to a range that spans from 2.16 eV, in MoS2 combined to other materials (heterostructures) [78], to ~1.8 eV in an isolated monolayer [79].
Figure 6. Band structure variation of 2H-MoS2
with decreasing thicknesses. Reproduced with permission [75]. Copyright 2017, Springer Nature.
The transition from indirect to direct bandgap in monolayer TMDs is responsible for the emergence of strong photoluminescence[80]. Such a feature shows that quantum confinement in materials like MoS2 and other TMDs provides new opportunities for engineering the electronic structure, as well as the optical properties, of matter at the nanoscale[81].
2.3.2 Optical Properties of TMDs
The optical properties of atomically thin 2D semiconductor TMDs are dominated by confinement effects related to carriers, excitons, and charged excitons that influence and can help to maximize linear and nonlinear interactions, also at room temperature, significantly contributing to the performance of TMDs in photonic devices. The following sessions are devoted to the linear and nonlinear optical properties of these materials.
2.3.2.1 Linear Optical Properties of TMDs
In monolayer TMDs, the direct bandgap increases the emission and absorption efficiency of photons with an energy equal to the bandgap, whereas indirect bandgap materials require additional phonon absorption or emission to compensate for the difference in momentum [82]. The stronger light-matter interaction in monolayer TMDs, therefore facilitates their use in diverse photonic applications.
Mak et al. [83] were the first to experimentally demonstrate the change of the bandgap in MoS2 with varying thicknesses through characterization by photoluminescence, absorption and photoconductivity spectroscopy. For mechanically exfoliated monolayer MoS2, the measured bandgap was of 1.84 eV. Other 2D semiconductor TMDs, such as WS2, WSe2
and MoSe2, with the same prismatic trigonal structure as MoS2, also exhibit direct bandgap for a single atomic layer and indirect bandgap for two layers or more. For MoS2, MoSe2, MoTe2, WS2 and WSe2, the usual direct optical bandgap values for a monolayer are of 1.9 eV, 1.57 eV, 1.08 eV, 1.97 eV, and 1.65 eV, respectively[84].
As previously mentioned, theoretical-experimental differences in the bandgap energy values tend to occur both due to the precision of the adopted computational methods and due to specific experimental conditions. The optical bandgap may vary with the used substrate and other experimental factors such as the quality and level of contamination of the materials. Thus, the choice of substrate and the use of clean and precise techniques for manipulation and synthesis of the 2D TMDs are of key importance so that the studies of its properties are reproducible and conclusive at the nanoscale.
For photonic applications based on linear optical effects, 2D TMDs are especially attractive because, despite the atomic thickness, they present strong electron-photon interaction[3], [85] especially at excitonic resonances[86], [87]. The strong interaction with light can be understood through the nature of the electronic and excitonic states of the material.
Singularities in the density of electronic states of TMDs ensure a strengthening of light-matter interactions, leading to an increase in photon absorption[3]. TMDs absorb more than 15% of the incoming light at the lowest excitonic resonance energy[88] despite their atomically thin character. Considering their thickness of 6 ~ 7 Å, they achieve one order of magnitude larger sunlight absorption than GaAs and Si, for example[89].
Excitonic resonances consist of energetically localized states, which enable the maximization of not only the linear but also the nonlinear optical effects. In the absence of
excitonic effects, the expected absorption for a monolayer MoS2 would be as shown by the blue (theoretical) curve in Figure 7. The experimental absorbance of a mechanically exfoliated MoS2
monolayer, however, presents characteristic and well-defined peaks as shown by the green line in the same figure. Two peaks, one at 1.92 eV and the other at 2.08 eV are associated with the formation of excitons known as A and B, respectively [14], [80]. Luminescence peaks associated with the recombination of these excitons are also observed in the PL spectrum.
Figure 7. Absorption spectrum of mechanically exfoliated monolayer MoS2 at low temperature (solid green line) with two prominent resonances, known as the A and B excitons. The blue dashed line shows the theoretical absorbance in the absence of excitonic effects. Reproduced with permission [14].
Copyright 2016, Springer Nature.
Cadiz et al. [90] also experimentally demonstrated how the strong light-matter interaction in TMDs behaves as a function of the temperature by photoluminescence measurements. The typical spectra for multi-layer TMDs deposited on a SiO2 substrate at room temperature can be observed in Figure 8(A). It is observed that MoS2 has the broadest PL emission at 300K, while WS2 multi-layer exhibit the narrowest emission. Figure 8(B) shows the PL spectra for the same TMDs at cryogenic temperature. While at room temperature the PL spectra of TMDs are determined by a broad peak corresponding to bright exciton transitions, at low temperatures a series of additional spectrally narrow resonances appears. These resonances can be ascribed to excitons trapped in local potential wells, due to the presence of impurities
and/or strain in realistic TMD samples. They vanish at higher temperatures, where the thermal energy is sufficient to overcome the trapping potential [88].
Figure 8. Typical PL spectra for different multilayer TMDs at 300 K (top) and 4 K (bottom) on a SiO2 substrate. Reproduced with permission [90]. Copyright 2017, American Physical Society.
Licensed under CC BY 4.0.
2.3.2.2 Nonlinear Optical Properties of TMDs
Another optical effect arising from light-matter interactions is second harmonic generation (SHG), the focus of this work, which is characterized by the conversion of incident light with a frequency ω, into 2ω. SHG is the lowest-order frequency conversion nonlinear optical process and plays an important role in frequency conversion devices. Third harmonic generation (THG) and high harmonic generation (HHR) are also important nonlinear optical processes, following the same frequency conversion principle under intense laser light illumination. Several studies have shown that TMDs are extremely promising in terms of efficiency for SHG and other nonlinear processes. In this section we will focus on the literature review of the nonlinear optical properties of TMDs; the theory behind SHG will be presented in the next chapter.
The thickness of TMDs (and other 2D materials) is smaller than the wavelength of the incident light, thus, eliminating the need for phase matching between the pump and the
second-harmonic radiation [91]. Despite the atomic thickness, resonant excitation and other enhancement mechanisms can be used to increase the nonlinear optical effects. Naturally, nonlinear processes also depend on the intrinsic symmetry of the 2D crystals, the strength of the involved oscillators, and as previously mentioned, the excitation wavelength. Thus, TMDs have an advantage over graphene, as they are not centrosymmetric for odd numbers of layers.
That is, TMDs with 1, 3, 5 layers, and so on, present second order nonlinearity.
Indeed, Malard et al. [91] observed efficient second-harmonic generation from odd-layered MoS2 crystals. Figure 9(A) shows the optical image of a sample of mono- and few- layer MoS2, which are more easily distinguishable by the AFM image in the Figure 9(B). Figure 9(C) presents the sample second-harmonic image for the same area in Figure 9(A), showing well-defined regions where the second-harmonic intensity varies, with significant signal only observed for regions with an odd number of layers. Figure 9(D) shows the intensity profile of the SHG image from the left to right along the yellow line shown in Figure 9(D). Li et al. [92]
also observed strong SHG in MoS2 with an odd number of layers.
Figure 9. (a) Optical microscopy image of the MoS2 sample. (b) AFM image of the dashed triangle shown in (a), scale bar is 1 μm. (c) SHG image collected with a pump-laser at 800 nm (1.55 eV).
Brighter colors mean stronger SHG intensity. Scale bar is 5 μm. (d) Intensity profile of the SHG image from the left to right at the yellow line shown in picture (c). Reproduced with permission [91].
Copyright 2013, American Physical Society.
The crystalline orientation of 2D materials can be obtained by analyzing the dependence of the SHG intensity with the pump polarization. Since the nonlinear susceptibility is a tensor dependent on symmetry, a strong dependence of the harmonic intensity with the direction of the incident electric field is obtained[92]. In Figure 10, for example, the crystallographic orientation of a monolayer TMD is indicated by the dark blue arrow (armchair axis) in the optical microscopy image of Figure 10(B). The analysis was obtained by verification of the second-harmonic intensity with incident linearly polarized light as a function of the excitation angle, as shown in Figure 10(A). The SH intensity peaks correspond to the armchair axes of the crystal, with the zig-zag axes at an angle of 30° from the maximum, indicated by the arrows in both Figure 10 (A) and (B). The same characterization can be used and applies to other 2D semiconductor TMDs such as MoS2, WS2 and WSe2.
Figure 10. (A) SHG characterization. Polar plot of the SHG intensity of a single-layer 2D material as a function of the pump linear polarization angle θ. Fitting the angular dependence, the armchair direction (dark blue arrow) of the sample is determined as the highest intensity. The armchair direction
is shifted by 30º from the zigzag direction (light blue arrow). (b) Optical image of the flakes. The axes are indicated as armchair (dark blue arrow) and zigzag (light blue arrow) and were determined by polarization-resolved SHG shown in (A). Reproduced with permission [93]. Copyright 2018, AIP
Publishing LLC. Licensed under CC BY 4.0.
The SHG technique can also be used to probe strain in TMDs [49], [94]. Based on the fact that mechanical strain tends to alter the symmetry of a crystal, even the smallest levels can have a huge impact on the SHG intensity of atomically thin materials. Strain can break the crystal symmetry along different polarization directions and therefore, change the nonlinear susceptibility tensor [49]. Mennel et al. [49] measured SHG for different TMDs and analyzed the mechanical deformation as a function of the polarized SHG intensities. In Figure
11 we can observe the lowest and highest applied strain levels as the purple and yellow plots, respectively. In most samples, the six-fold SHG symmetry is broken even without externally applied strain, attributed to the TMDs exfoliation and transfer processes.
Figure 11. Polarized SHG measurements of different TMDs under varying uniaxial strain. SHG measurements at the lowest and highest applied strain levels, purple and yellow, respectively. Fitted SHG curves at different strain levels. (bottom). Experimental measurements are shown in the top row and theoretical predictions in the bottom row. Reproduced with permission [49]. Copyright 2018, AIP
Publishing LLC. Licensed under CC BY 4.0.
Furthermore, literature reports on the observation of SHG in a variety of TMDs such as MoS2 [46], WS2[81], WSe2[82], MoSe2[80][83], ReS2[84] and others. Autere et al. [62], for example, showed strong SHG and THG in semiconductor TMD monolayers. In this case, the authors deposited different TMDs (MoS2, MoSe2, WS2 and WSe2) on the same substrate for a direct comparison between the materials, since the substrate can have critical impact on the measured intensities, as already mentioned. The SHG and THG for the flakes were excited by a 1560 nm mode-locked fiber laser. The nonlinear optical susceptibility χ(2) of MoSe2 is found to be approximately two to six times larger than that of the other TMDs analyzed, which is attributed to the resonant enhancement of the SHG in MoSe2. The energy of the A exciton in MoSe2 (∼790 nm) matches closely with the wavelength of the SHG signal (780 nm), causing an SHG ~4 to 40 times larger than that from the other materials. The third-order nonlinear susceptibility χ(3) of all four materials was found to be comparable to that of graphene, with the
largest value observed for MoS2. The |χ(2)| and |χ(3)| values measured and calculated by the authors are presented on Figure 12 (A) and Figure 12 (B), respectively.
Figure 12. Comparison of experimental and theoretical (A) |χ(2)| and (B) |χ(3)| for TMDs at 1560 nm excitation. Reproduced with permission [62]. Copyright 2018, American Physical
Society.
Moreover, the diversity of TMDs, their combination and different excitation wavelength conditions means that bandgap engineering and a wide range of resonances are potentially accessible for nonlinear device implementation and optimization, including those based on SHG, THG and other nonlinear optical phenomena at the telecom wavelengths. Seyler et al. [95] showed a mechanism to electrically control second-order optical nonlinearities in monolayer WSe2. The intensity of second-harmonic generation at the A-exciton resonance was tuned by over an order of magnitude at low temperature and by nearly a factor of four at room temperature through electrostatic gating in a field-effect transistor [95]. Khan et al. [96] showed that the SHG response is highly sensitive to temperature modulation in 2D TMDs, with an effect enhanced by 25.8% in monolayer MoSe2 only by temperature increase, whereas the nonlinear effect is found to be quenched in the case of 3L, 5L, and 7L MoSe2 [96]. In this case, the temperature study is not related to excitonic resonances, but to the different thermal expansion behavior for different layers, leading to variable interband and intraband lattice symmetries triggered by a temperature variation between -120°C and 120°C. Different structures, such as MoS2 nanoscrolls [97], pyramid-like WS2 [98], and heterostructures[99] have also been used to enhance the second-harmonic intensity based on the superposition of the involved fields.
Another promising class of methods to enhance the nonlinear optical effects is the combination of 2D materials with different field enhancement platforms, including
plasmonic nanostructures for localized surface plasmon excitation[100]–[104], hybrid dielectric structures[105], [106], metallic and dielectric metasurfaces governed by bound states in the continuum[107]–[113], photonic crystal nanocavities[114], [115], optical microcavities[116], [117] and waveguides[118].
Although these methods have proven to enhance the SHG fields, complex and time-consuming fabrication processes are required[119]. Plasmonic metal nanostructures, for example, require that the fundamental or the frequency-converted field be overlapped with the resonance spectrum of the nanostructures, thus demanding specific nanofabrication techniques to appropriately tune the plasmon resonance[105]. Also, it is well known that noble metal structures exhibit strong optical loss in the visible band, which greatly influences the nonlinear response[104], [120]. Metasurfaces, in turn, demand structuring with high spatial resolution and often require fabrication by electron-beam lithography, imposing scalability and cost drawbacks to practical manufacturing of nonlinear optical devices. The same applies to photonic crystal nanocavities, which rely on high-definition lithographic methods, which are essential for the design of superior quality resonance structures in which mode coupling is required.
A simpler approach to field-enhancement, however, seems to have been so far ignored. In Chapter 4, we propose and demonstrate the use of substrates presenting an epsilon- near-zero point close to the pump wavelength to increase the nonlinear frequency conversion efficiency in mechanically exfoliated monolayer TMDs [119]. Additionally, waveguides allow for extended interaction length, further promoting the enhancement of the nonlinear optical effects and on-chip applications, to be discussed in Chapter 5.
3 INTRODUCTION TO NONLINEAR OPTICS
The purpose of this chapter is to introduce the basic concepts of nonlinear optics, especially regarding second-harmonic generation, which is described in the case of bulk and sheet nonlinearities.
3.1 BRIEF HISTORY OF NONLINEAR OPTICS
Nonlinear optical phenomena are nonlinear in the sense that they occur when the response of a material to an applied optical field depends nonlinearly on the strength of the optical field [121]. While the nonlinear optical effects are often considered weak compared to the linear effects of similar physical origin, they become important when the involved electric fields are a significant fraction of the electric fields existing within the material. That said, the development of nonlinear optics as a field of study originated in the early 1960’s with the development of the laser, simultaneously reported by Maiman[122] and Collins et al.[123].
Lasers are sources of coherent light, characterized by a high degree of monochromaticity, high directionality, and high intensity or brightness [124].
Nonlinear optics was finally endorsed with the discovery of optical second- harmonic generation in crystalline quartz by Franken et al. [125] in 1961, commonly recognized as the greatest milestone for the establishment of the field[126]. His work was only possible with the development of pulsed ruby lasers, allowing for large electric fields. Subsequently, several other optical frequency-mixing effects were demonstrated based on the application of lasers, including sum-frequency generation (1962), third-harmonic generation (1962), optical rectification (1962), optical difference-frequency generation (1963), and optical parametric amplification and oscillation (1965) [126].
In the beginning, nonlinear optics primarily revolved around harmonic generation, as it is often the most straightforward effect. However, the principles of other fundamental nonlinear electromagnetic effects, such as saturable absorption and two-photon absorption (TPA) were already known before the invention of lasers. Saturable absorption was earlier observed in radio(microwave)-frequency spectroscopy and TPA was theoretically described in the early 1930’s [126].
Nowadays, nonlinear optics has developed into many different categories. The growth of research in the field is closely related to the rapid technological advances that have
occurred in related areas, such as ultra-fast phenomena, fiber optics, and optical communications [127]. It is also important to highlight the critical impact of nonlinear effects for the operation of lasers. With dye lasers, it is possible to cover the range of wavelengths from 350 to 950 nm, for example, including the entire visible spectrum. A variety of nonlinear processes, including harmonic generation, parametric down-conversion, and stimulated Raman effects, allow to extend the range for coherent sources throughout the infrared and ultraviolet [124].
With lasers, spectroscopy and sensing being so crucial to a wide range of fields, nonlinear optics has become of high importance in today’s research, used in a wide variety of applications including sensors, data storage and information transfer. With its ubiquitous use and great potential, the field of nonlinear optics remains a high priority for investigation. The concepts and methods penetrate actively into other fields, while it now spans from the micrometer to the nanometer scale and from classical to quantum, increasingly becoming an interdisciplinary field of research with many concepts that cross different discipline boundaries [127].
3.2 DEFINITION AND MODELS OF THE NONLINEAR RESPONSE
In linear optics, when light travels along a material, the electric field, 𝐸̃, induces a polarization 𝑃̃ in the medium, often described by [121]:
𝑃̃(𝑡) = 𝜖0𝜒(1)𝐸̃(𝑡). (3. 1) Here, the polarization 𝑃̃ and electric field 𝐸̃ are presented as scalar quantities, for simplicity.
The tilde symbol, “∼”, denotes a quantity that varies rapidly in time; 𝜖0 is the permittivity of free space. The term χ(1) is a constant of proportionality known as the linear susceptibility and describes the linear optical effects, such as absorption, refraction, dispersion, and birefringence.
That is, the induced polarization varies linearly with the incident electric field; a dependence with quadratic or higher order components of the electric field would, thus, indicate a nonlinear response.
In nonlinear optics, the optical response of a material to the applied optical field can be expressed by expanding the resulting polarization, 𝑃̃, as a power series in terms of the electric field, 𝐸̃, as follows[121]:
