Manipulating Light-Matter Interactions in Two Dimensional Semiconductors Coupled with Plasmonic Lattices

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Publicly Accessible Penn Dissertations

2017

Manipulating Light-Matter Interactions In Two Dimensional Semiconductors Coupled With Plasmonic Lattices

Wenjing Liu University of Pennsylvania, [email protected]

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Recommended Citation Liu, Wenjing, "Manipulating Light-Matter Interactions In Two Dimensional Semiconductors Coupled With Plasmonic Lattices" (2017). Publicly Accessible Penn Dissertations. 2431. https://repository.upenn.edu/edissertations/2431

This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/2431 For more information, please contact [email protected]. Manipulating Light-Matter Interactions In Two Dimensional Semiconductors Coupled With Plasmonic Lattices

Abstract Understanding and tailoring light-matter interactions is critical to many fields, offering valuable insights into the nature of materials, as well as allowing a variety of applications such as detectors, sensors, switches, modulators, and lasers. While reducing the optical mode volume is critical to enhancing the light-matter interaction strength, plasmonic systems, with their extraordinary ability to confine the light far below the diffraction limit of light, provide intriguing platforms in boosting the light-matter interactions at nanoscale.

On the other hand, atomically thin semiconductors such as few-layered transition metal dichalcogenides (TMDs), a recently discovered class of materials, exhibit unique optical properties such as large exciton binding energies, tightly-bond trion excitations, and valley-spin locking, allowing the observations of interesting photonic and electronic phenomena including strong photon-exciton coupling, valley Zeeman and valley optical Stark effect, valley Hall effect, and spin light emitting, hence serve as great candidates to study light-matter interactions in two dimensional systems.

In this thesis, combining the two intriguing optical and material systems, we study light-matter interactions between 2D semiconductors and 2D plasmonic lattices, due to their compatibility with 2D semiconductors as well as strong and highly tunable plasmonic resonances. We investigated exciton- plasmon coupling by integrating MoS2 with plasmonic lattices of various geometrical designs and observed rich phenomena in different coupling regimes.

We will first present a detailed study of observing exciton-plasmon coupling in weak, intermediate and strong coupling regimes via different plasmonic lattice design. We’ve demonstrated large Purcell enhancement in weak coupling regime, and Fano resonances in intermediate coupling regime, and exciton-plasmon polariton formation in strong coupling regime. After that, we will discuss active tuning of the coupling strengths all the way across the weak and strong coupling regime via electrical gating. Finally, we will demonstrate chiral exciton-plasmon coupling by designing chiral plasmonic lattices.

Degree Type Dissertation

Degree Name Doctor of Philosophy (PhD)

Graduate Group Materials Science & Engineering

First Advisor Ritesh Agarwal

Keywords 2D semiconductors, exciton-plasmon coupling, light-matter interaction, plasmonic lattices, Plasmonics, polariton

Subject Categories Condensed Matter Physics | Optics | Physics

This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/2431 MANIPULATING LIGHT-MATTER INTERACTIONS IN TWO-DIMENSIONAL

SEMICONDUCTORS COUPLED WITH PLASMONIC LATTICES

Wenjing Liu

A DISSERTATION

Material Science and Engineering

Presented to the Faculties of the University of Pennsylvania

Partial Fulfillment of the Requirements for the

Degree of Doctor of Philosophy

2017

Supervisor of Dissertation

______

Ritesh Agarwal

Professor, Material Science and Engineering (MSE)

Graduate Group Chairperson

______

David J. Srolovitz, Joseph Bordogna Professor, MSE/MEAM

Dissertation Committee

Nader Engheta, H. Nedwill Ramsey Professor, ESE/BE/PHY/MSE

Cherie R. Kagan, Stephen J. Angello Professor, ESE/MSE/Chemistry

Jay Kikkawa, Professor, Physics and Astronomy

MANIPULATING LIGHT-MATTER INTERACTIONS IN TWO-DIMENSIONAL

SEMICONDUCTORS COUPLED WITH PLASMONIC LATTICES

2017

Wenjing Liu

This work is licensed under the

Creative Commons Attribution-

NonCommercial-ShareAlike 3.0

License

To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/us/

Acknowledgement

First of all, I’d like to thank my advisor, Prof. Ritesh Agarwal, who took me from the masters’ program, support me and guide me for my research. I had the most splendid five years working in his group, and none of these works would have been possible without him.

I really appreciate the helps from my committee members (past and present), Prof.

Engheta, Prof. Kagan, Prof. Cubukcu, and Prof. Kikkawa, whose insights and suggestions had a significant impact on this thesis.

I’d like to thank Dr. Mingliang Ren and Dr. Liaoxin Sun, who helped me a lot from the very beginning of my PhD study, taught me to do research and trained me on optical measurements. I’ve learnt so much from them, both academically and otherwise.

I would give my heartful thanks to Dr. Bumsu Lee and Dr. Joohee Park, my past groupmates and two of the main collaborators of this thesis. They’ve brought the whole research field of the 2D material and 2D plasmonics into the group and it would be impossible for me to accomplish this thesis without their hard work, great help and inspiration. I’d also thank Carl H. Naylor and Prof. A.T. Charlie Johnson, my collaborators of MoS2 monolayer sample growth, for growing MoS2 samples with excellent optical and electrical properties.

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I’d like to thank all my group mates and classmates, past and present, Sajal, Ee,

Brian, Chris, Carlos, Pavan, Rahul, Jacob, Daksh, Stephanie, Gerui, Zhurun, and Jian.

Thank you for your accompanies and helps during these years.

Finally, I would give my special thanks to my family, my parents and my husband.

Thank you for supporting me pursuing my PhD degree in every way. I love you all.

Abstract

Manipulating light-matter interactions in two-dimensional

semiconductors coupled with plasmonic lattices

Wenjing Liu

Ritesh Agarwal

Understanding and tailoring light-matter interactions is critical to many fields, offering valuable insights into the nature of materials, as well as allowing a variety of applications such as detectors, sensors, switches, modulators, and lasers. While reducing the optical mode volume is critical to enhancing the light-matter interaction strength, plasmonic systems, with their extraordinary ability to confine the light far below the diffraction limit of light, provide intriguing platforms in boosting the light- matter interactions at nanoscale.

In this thesis, combining the two intriguing optical and material systems, we study light-matter interactions between 2D semiconductors and 2D plasmonic lattices, due to their compatibility with 2D semiconductors as well as strong and highly tunable plasmonic resonances. We investigated exciton-plasmon coupling by integrating MoS2 with plasmonic lattices of various geometrical designs and observed rich phenomena in different coupling regimes.

We will first present a detailed study of observing exciton-plasmon coupling in weak, intermediate and strong coupling regimes via different plasmonic lattice design.

We’ve demonstrated large Purcell enhancement in weak coupling regime, and Fano resonances in intermediate coupling regime, and exciton-plasmon polariton formation in strong coupling regime. After that, we will discuss active tuning of the coupling strengths all the way across the weak and strong coupling regime via electrical gating.

Finally, we will demonstrate chiral exciton-plasmon coupling by designing chiral plasmonic lattices.

TABLE OF CONTENTS

Abstract ...... v

List of Tables...... xi

List of Illustrations ...... xii

Chapter 1. Introduction ...... 1

1.1 Light-matter interactions in nanocavities ...... 1

1.1.1 Weak coupling regime: Purcell enhancement ...... 1

1.1.2 Strong coupling regime and formation of exciton-polaritons ...... 3

1.2 Surface plasmon resonance and Plasmonic lattices ...... 10

1.2.1 Localized surface plasmon resonances ...... 12

1.2.2 Collective resonances in plasmonic lattices: Rayleigh-Wood’s anomaly

and surface lattice resonance ...... 14

1.3 Optical and electronic properties of monolayer MoS2 ...... 26

1.3.1 Structure, band structure and optical transitions of MoS2...... 26

1.3.2 Monolayer TMDs field-effect transistor ...... 28

1.3.3 Coupled spin and valley physics in monolayer MoS2 ...... 29

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1.4 Overview of the thesis ...... 31

Chapter 2. Plasmonic lattices and surface lattice resonances ...... 41

2.1 Plasmonic lattice fabrication and morphology characterization ...... 41

2.2 LSPR of the fabricated plasmonic lattices ...... 42

2.2.1 Nanodisks ...... 42

2.2.2 Nanorods ...... 45

2.2.3 Bowties ...... 46

2.3 Surface lattice resonance ...... 48

Chapter 3. Light-matter interaction between MoS2 and plasmonic lattices: weak and intermediate coupling regimes ...... 55

3.1 Motivation and Introduction ...... 56

3.2 Experimental methods ...... 57

3.3 Experimental results ...... 58

3.3.1 Surface-enhanced Raman scattering and surface-enhanced fluorescence

at room temperature ...... 58

3.3.2 Fano resonance at 77 K and towards strong exciton-plasmon coupling ...... 69

3.4 Conclusion ...... 74

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Chapter 4. Light-matter interaction between MoS2 and plasmonic lattices: strong coupling regime ...... 78

4.1 Motivation and Introduction ...... 79

4.2 Experimental method...... 81

4.3 Experimental result: observation and characterization of strong exciton-plasmon

coupling ...... 82

4.4 Temperature dependence of the exciton-plasmon coupling and strong coupling

at room temperature ...... 92

4.5 Conclusion ...... 96

Chapter 5. Active tuning of the exciton-plasmon coupling via electrical gating ...... 99

5.1 Motivation and Introduction ...... 99

5.2 Experimental methods ...... 101

5.3 Active tuning of the exciton-plasmon coupling strengths ...... 102

5.4 Conclusion ...... 112

Chapter 6. Chiral exciton-plasmon coupling in chiral plasmonic lattices ...... 116

6.1 Motivation and introduction ...... 116

6.2 Chiral plasmonic lattice design ...... 118

6.3 Chiral SLRs studied by reflectance measurement and FDTD simulation ...... 119

6.4 Chiral exciton-plasmon coupling between MoS2 and chiral plasmonic lattices ...... 126

6.5 Conclusion ...... 128

Chapter 7. Future directions and outlook ...... 131

7.1 Valley-selective strong exciton-plasmon coupling ...... 131

7.2 Active and electronically tunable metasurfaces...... 133

List of Tables

Table 4.1. Coupling constants obtained from fitting the experimentally measured polariton dispersion to a coupled oscillator model. All quantities are in units of meV.

List of Illustrations

Figure 1.1 Strong exciton-photon coupling in a two-level system. (a) polariton dispersions. Gray dotted line represents the photon dispersion, blue dotted line represents the exciton dispersion, and black solid lines represent the dispersions of the two polariton branches. (b) Hopfield coefficients calculated from (a).

Figure 1.2 Schematics of a metallic sphere in a uniform, static electric field.

Figure 1.4 Experimental observations of SLRs in different plasmonic lattices (a) Extinction spectra for several gold nanoparticle arrays at normal incidence. The average particle size was 123×85×35 nm for the main graph and 120×90×35 nm . Reprinted with permission from ref. 79. © 2006 American Physical Society. (b) Extinction spectra of an Au double-nanodisk array as a function of the angle of incidence. The electric field of the incident wave is perpendicular to the long axis of the double disk structure. Left inset: SEM image of the array. Right inset: A zoom of the extinction at 64o incidence. Reprinted with permission from ref. 80. © 2008 American Physical Society. (c) Extinction spectra as a function of k// for an Au nanorod array with rods sizes of 450×120×38 nm Inset shows the SEM image of the corresponding array. Reprinted with permission from ref. 81. © 2011 American Physical Society.

Figure 1.7 Structure and band structure of MoS2. (a) crystal structure and Brillouin zone of MoS2. Reprinted from ref.97. © 2011 Macmillan Publishers Ltd. (b) band diagram of bilayer (left) and monolayer (right) MoS2 with indirect and direct band gaps, respectively. Reprinted from ref.92. © 2010 American Chemical Society. (c) photoluminescence from monolayer and bilayer MoS2.Reprinted from ref.98. © 2010 American Physical Society.

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Figure 1.8 Optical transitions in monolayer MoS2. (a) Absorption spectrum of MoS2 showing A and B neutron excitons at 1.92 and 2.08 eV, respectively. (b) & (c) Absorption and photoluminescence spectra of monolayer MoS2 as a function of gate voltages showing in figure (b). Trion transition (A-) dominates at positive gate voltages while neutral exciton transition (A) is more evident at large negative gate voltages. Reprinted with permission from ref. 99. © 2012 Macmillan Publishers Ltd.

Figure 2.1 Fabrication processes of Ag plasmonic lattices

Figure 2.2 SEM images of Ag plasmonic lattices. (a) Bowtie array. (b) Nanodisk array. (c) Nanorod array.

Figure 2.3 Electric field profile of the dipolar LSPR of Ag nanodisk. Nano disk dimensions: r = 60 nm, h = 50 nm. Figure (a)-(c) show electric field polarized along (a) x, (b) y, and (c) z directions, respectively. (d) Magnitude of the total electric field. Inset: schematics of the system geometry.

Figure 2.4 Nanodisk LSPR mode position as a function of disk diameter.

Figure 2.5 (a) Far-field differential reflectance of six plasmonic lattices with nanodisk diameters ranging from 90-154 nm and 1000 nm lattice constant (uncoupled nanodisks). (b) LSPR wavelengths for the first and second order whispering gallery LSPR modes in individual silver nanodisks obtained by FDTD simulations along with the experimentally measured the dip positions from the reflectance spectra in (a)

Figure 2.6 Electric field profile of the LSPRs of a Ag nanorod. (a) Transverse mode. (b) Longitudinal mode. Nanorod dimensions: 170×110×50 nm

Figure 2.7 Electric field profile of the LSPRs of a Ag bowtie. (a) Transverse mode. (b) Longitudinal mode.

Figure 2.8 Schematic of the angle-resolved reflectance measurement setup

Figure 2.9 The angle-resolved differential reflectance spectra for five plasmonic lattices patterned on bare Si/SiO2 substrates with disk diameters ranging from 100-170 nm and 460 nm lattice constant. White dashed line represents the wavelength of the LSPR modes and the red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results obtained from a coupled-oscillator model.

Figure 2.10 The angle-resolved differential reflectance spectra for four plasmonic lattices patterned on bare Si/SiO2 substrates with lattice constant ranging from 380 to xiii

500 nm and 120 nm disk diameters. White dashed line represents the wavelength of the LSPR modes and the red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results obtained from a coupled-oscillator model.

Figure 3.1 Optical properties of monolayer MoS2-bowtie resonator array system at room-temperature. (a), Scanning electron microscope (SEM) image showing the silver bowtie array directly patterned on well-defined, stacked triangular flakes of mono- and bi-layer MoS2. Larger triangular flake of darker contrast corresponds to a single layer and smaller flake of lighter contrast to a bilayer. (b), Device schematic indicating the geometrical factors of a bowtie array: gap separation (g), thickness of the metal deposition (h), side length of a triangle (s), and unit cell dimension or pitch (p = (px, py)). (c), Raman scattering spectra of bare MoS2, bowtie array, and bowtie-MoS2. Geometrical factors: g = 20 nm; h = 50 nm; s = 100 nm; p = (500 nm, 300 nm). For all bowtie arrays studied throughout the paper, g = 20 nm and h = 50 nm. (d), PL spectra of bare MoS2, bowtie array, and bowtie-MoS2. Inset shows PL in log scale. (e), Calculated extinction of a single bowtie (g = 20 nm; h = 50 nm; s = 100 nm) with the inset displaying the E-field intensity profiles for TE and TM polarizations with respect to the long axis of a bowtie. (f), FDTD simulated E-field enhancements in the array of bowties (s = 100 nm) with four different unit cell lengths under normal plane wave incidence. Inset shows the E-field intensity profiles for TE or TM polarizations.

Figure 3.2 Polarization-dependent reflection spectra of the bowtie resonator array and photoluminescence spectra of MoS2 coupled with bowtie resonator array. (a) Normalized differential reflectivity (ΔR/R) spectra of experimental and calculated lattice-LSP modes in TE and TM polarizations for bowtie array on SiO2/Si substrate. Geometrical factors: s = 100 nm, p = (500 nm, 300 nm). (b) Average E-field enhancements for bowtie array on SiO2/Si calculated for the total area of the unit cell. (c) Experimental emission (PL and Raman) spectra for bowtie-MoS2 system. Inset; zoomed-in spectra near the Raman active region.

Figure 3.3 Polarization-dependent 2-D intensity scans. (a) Optical microscope image of bowtie arrays patterned in two orthogonal orientations on a MoS2 flake. (b) 2-D intensity scans measured at the Raman mode and A-exciton energies. Scanning area indicated in (a). Data in (e) shows different polarization response for Raman (horizontally patterned bowties) and A-exciton emission (vertically patterned bowties).

Figure 3.4 Spectral modification of MoS2 photoluminescence coupled with bowtie resonator arrays with different lattice-LSP dipole resonances at room temperature. (a) SEM images of four bowtie-array samples with different bowtie sizes and pitch values: (i) s = 100 nm, p = (400 nm, 500 nm) (ii) s = 100 nm, p = (400 nm, 300 nm) (iii) s = 100 nm, p = (300 nm, 200 nm) (iv) s = 170 nm, p = (500 nm, 800 nm). (b) ΔR/R spectra xiv

associated with the lattice-LSP modes of the four different bowtie patterns on SiO2/Si substrates. (c) PL spectra of bare MoS2 (black) and four different patterns. (d) Wavelength-dependent PL enhancements (ratios of PL obtained for bowtie-MoS2 sample to PL of bare MoS2) for the four patterns on monolayer MoS2. Inset shows the enhancement of A-exciton emission for all four patterns. (e) Normalized PL spectra of bare MoS2 (black) and the four different bowtie patterns on MoS2.

Figure 3.5 Calculated absorption spectra for bare MoS2 monolayer and bowtie-MoS2 system at room temperature. The calculated results are shown for sample (iii) in figure 3.4 (c). Bowtie geometrical factors: g = 20 nm, h = 50 nm, s = 100 nm, and p = (300 nm, 200 nm).

Figure 3.6 Fano resonance in the reflection spectrum of bowtie-MoS2 at 77 K. Bowtie geometry: TE mode, s = 100 nm, p = (300 nm, 200 nm). (a) and (b) Experimental and calculated ∆R/R spectra for bare MoS2, bowtie array, and bowtie-MoS2 system. Clear Fano resonances are observed at the A- and B-exciton spectral region. Inset in (b) shows the schematic for the mechanism of observed Fano resonance in the exciton-plasmon system. (c) Calculated absorption spectra for the bare MoS2 (black), bowtie array (blue), MoS2 in the combined bowtie-MoS2 system (green), and the bowtie in the combined bowtie-MoS2 system (red). The dotted circle highlights the region of MoS2 excitons where Fano resonances are observed in the refection spectra in (a)

Figure 3.7 Controlling Fano spectra of the bowtie-MoS2 system by tuning the plasmon- excitons detuning at 77 K. (a)-(c) Experimental ∆R/R spectra of bare MoS2, bowtie, and bowtie-MoS2 system for three different samples with the following excitation polarization and geometrical factors. TE polarization, s = 100 nm, p = (400 nm, 300 nm) (a) TM, s = 140 nm, p = (500 nm, 400 nm) (b) TE, s = 100 nm, p = (800 nm, 700 nm) (c) Clear Fano resonances are observed when the bowtie reflectance dips overlap with MoS2 excitons.

Figure 4.1 LSPR modes of individual (weakly-coupled) nanodisks patterned on Si/SiO2 substrate and on monolayer MoS2 with disks diameter of d = 140 nm and lattice constant, a = 1000 nm. (a) Far-field reflectance measurement of the Ag nanodisk array on Si/SiO2 substrate and on monolayer MoS2. The resonance position (reflectance dip) is redshifted from 640 nm to 695 nm due to the presence of MoS2. (b) The difference of the reflectance spectra between the array patterned on MoS2 and bare MoS2 from (a). The LSPR position (reflectance dip) can be clearly observed at 695 nm.

Figure 4.2 Strong exciton-plasmon coupling of silver plasmonic lattice-coupled monolayer MoS2 at 77K. (a)-(d) Angle-resolved differential reflectance spectra of four different silver nanodisk arrays with different disk diameters patterned on monolayer MoS2. The lattice constants of all four arrays are fixed at 460 nm while the disk xv

diameters are changed. White dashed lines correspond to the LSPR positions and yellow dashed lines represent the A (low energy) and B (high energy) excitons. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled- oscillator model. (e)-(h) Line cuts from the angle-resolved reflectance data taken from a constant angle represented by the vertical white dotted lines in (a)-(d), respectively. The dip positions are indicated by the blue triangles.

Figure 4.3 Composition of the four polariton branches for three representative LSPR- exciton detuning conditions in silver plasmonic lattice-coupled monolayer MoS2 at 77K. (a)-(c) A exciton fraction. (d)-(f) B exciton fraction. (g)-(i) lattice mode fraction. (j)-(l) LSPR fraction.

Figure 4.4 Strong exciton-plasmon coupling of silver plasmonic lattice-coupled monolayer MoS2 at 77K with disk diameter d = 110 nm and lattice constant a = 380 nm. (a) Angle-resolved reflectance spectrum of the Ag nanodisk array. (b) Angle-resolved reflectance spectrum of bare MoS2. (c) Angle-resolved reflectance spectrum of MoS2 coupled with Ag nanodisk array. (d) Line cuts from the angle-resolved reflectance data in (a)-(c) at k = 0. In (a)-(c), white dashed lines correspond to the LSPR positions and yellow dashed lines represent the A (low energy) and B (high energy) excitons. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled- oscillator model. Strong coupling between the LSPR and both the A and B excitons are clearly observed in (c) and (d) while the lattice resonance is detuned from the excitonic region, therefore highlights the critical role of the LSPR to enhance the exciton-plasmon coupling.

Figure 4.5 Temperature dependence of the strong exciton-plasmon coupling in silver plasmonic lattice-coupled monolayer MoS2 (a)-(b) Angle-resolved differential reflectance spectra of the silver nanodisk array coupled with MoS2 at 77 K and 300 K, respectively. The disk diameter is 120 nm with a lattice constant of 460 nm. White dashed lines correspond to the LSPR positions and yellow dashed lines represent the A (low energy) and B (high energy) excitons. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled-oscillator model. (c) The spectral line cuts taken from room temperature data in (b) with the incident angles θ ranging from 21.7o to 42.1o

Figure 4.6 Temperature dependence of the exciton-plasmon coupled system. (a) Temperature dependent differential reflectance spectra of bare MoS2. (b) Temperature dependent differential reflectance spectra of silver nanodisk array coupled with MoS2 obtained from the angle-resolved differential reflectance spectra at sin  0.37. The xvi

position of the line cut is shown in figure 4.4 (a) as a vertical white dotted line. (c) The wavelength of the A exciton and polariton branches 2 and 3 at sin  0.37 as a function of temperature, extracted from the dip positions in (a) and (b). (d) Exciton fractions of polariton branches 2 and 3 at sin  0.37 as a function of temperature, calculated from the COM with the temperature dependent exciton energies extracted from (a).

Figure 5.1 Schematics (a) and SEM images (b) of the MoS2-plasmonic lattice FET device.

Figure 5.2 Typical transconductance curve from a bare MoS2 FET device

Figure 5.3 Dispersion evolution of MoS2-plasmonic lattice system at different gate voltages. The yellow and orange dashed lines indicate the neutral exciton and trion energies measured from the bare region of the same MoS2 flake.

Figure 5.4 Line cuts of the angle-resolved reflectance spectra at different applied voltages. (a)-(c) Spectral line cuts. From bottom to up: sin = 0,0.15,0.3,0.4,0.5, respectively. (d)-(f) Zoomed-in spectra taken from the (a)-(c) with sin = 0.5 and corresponding Gaussian fitting for mode resolving. Yellow dashed line: A0 exciton, Orange dashed line: A- exciton (trion). Gray dashed line: mode positions extracted from the line cuts.

Figure 5.5 Evolution of the bare MoS2 reflectance with applied gate voltage.

Figure 5.6 COM fitting of the system dispersion and calculated exciton-LSPR coupling strengths.

Figure 5.7 Gate-voltage dependent exciton-plasmon coupling in the angle-resolved ΔR/R plots for three different silver nanodisks arrays with different resonance detuning values. (a)-(c), d = 110 nm. (f)-(h), d = 120 nm. (k)-(m). d = 140 nm. The position of uncoupled Ao, A- excitons, and LSPR are indicated as yellow-, orange- and white- dashed lines, respectively. (d), (i), (n), ΔR/R spectra obtained from line cuts (vertical white-dashed lines, sinθ = 0.35 in (a-c), sinθ = 0.30 in (f-h), and sinθ = 0.25 in (k-m), respectively) of the angle resolved spectra at different VG. Grey-dashed lines in (d), (i) and (n) trace the evolution of the system’s eigenstates upon carrier doping. (e), (j), (o) Comparison of the coupling strengths for Ao-LSPR and A—LSPR coupling obtained from the COM fitting as a function of the gate voltage.

Figure 6.1 SEM images of the tilt-nanorod lattices, with nanorod dimensions of 110×170 nm and lattice pitch of 450 nm. The tilting angle with respect to the vertical axis of the images are: (a) 0o (b) 30o (c) 45o and (d) 60o. Scale bars are 500 nm. xvii

Figure 6.2 Angle-resolved reflectance spectra of Ag nanorod lattices (110×170 nm nanorod and 450 nm lattice pitch) with different nanorod tilting angle and circular polarization illumination. (a)-(e): RCP illumination. (f)-(j) LCP illumination. (a)&(f): 0o rotation; (b)&(g): 30o rotation; (c)&(h): 45o rotation; (d)&(i): 60o rotation; (e)&(j): 90o rotation. The rotation angles are defined as the angle between the long axis of the nanorod and k//.

Figure 6.3 Spatial electric field distribution of a 110×170 nm Ag nanorod under (a) LCP and (b) RCP light illumination at 645 nm wavelength.

Figure 6.4 Phase difference between the longitudinal and transverse LSPR of a Ag nanorod (110×170 nm) at 640 nm. The nanorod is excited by a linearly polarized plane wave with its polarization indicated by the black arrow. At ωt=0, the electric field magnitude of the longitudinal mode reaches its maximum ((a)-(c)), and becomes nearly zero in the transverse mode ((d)-(f)). With an additional π⁄ 2 phase shift ((g)- (i)) in the transverse mode, the electric field interfere constructively along the bottom- left to up-right diagonal, and interfere destructively along the other, resulting in a diagonal mode.

Figure 6.5 Electric field profile of Ag nanorod lattice with 45o nanorod tilting illuminated by (a) LCP and (b) RCP light. Nanorod dimension: 110×170 nm, lattice pitch 450 nm.

Figure 6.6 Angle-resolved reflectance spectra calculated by FDTD simulation. Nanorod dimensions: 110×170 nm, lattice pitch 450 nm. Tilting angle 45o. (a) RCP illumination. (b) LCP illumination. (c) Circular Dichroism calculated from (a) and (b)

Figure 6.7 Angle-resolved reflectance spectra resolving both the input and output circular polarizations. (a)-(d) Lattice without nanorod tilting (0o tilting). (e)-(h) Lattice o with 30 tilting with respect to k//.

Figure 6.8 Strong exciton-plasmon coupling in co-polarization reflection. (a) LCP in- RCP out. (b) RCP in-LCP out. White dashed lines correspond to the LSPR positions and yellow dashed lines represent the A excitons. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled-oscillator model.

Figure 6.9 Strong exciton-plasmon coupling in co-polarization reflection. (a) RCP in- RCP out. (b) Line cuts from (a) taken from sin = 0.15 − 0.20. (c) LCP in-LCP out. (d) Line cuts from (c) taken from sin = 0.15 − 0.20.

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Figure 7.1 The (LCP) and (RCP) components of the LSPR of a nanorod excited by a LCP light. (a) Nanorod . (b) Nanorod .

Figure 7.2 Strong exciton-plasmon coupling in plasmonic metasurfaces coupled with monolayer MoS2. (a) Silver Pancharatnam–Berry phase metasurface with constant phase shift gradient patterned on monolayer MoS2. (b)&(c) Reflectance spectra under LCP and RCP illumination measured from the device in (a), showing SLRs and strong coupling with MoS2.

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Chapter 1. Introduction

1.1 Light-matter interactions in nanocavities

When light interacts with matter, in particularly, a direct bandgap semiconductor, a photon can be absorbed and excite an electron to the conduction band, leaving a hole in the valence band. This electron-hole pair can be strongly bond together via Columb interaction, and form a new quasiparticle named exciton. An exciton can then recombine radiatively and emit a photon, allowing energy transfers back and forth between the photon and the exciton. Studying and engineering such photon-exciton interactions in photonic and plasmonic nanocavities have drawn great attentions recently, as the energy transfer rate, or equivalently, the coupling strength can be greatly enhanced as the mode volume shrinks. Depending on the relation between the coupling strength and the dissipation rate of each resonance, the light-matter coupling can be classified into two regimes: the weak coupling regime, where perturbation theory can be used to describe the light-matter interaction processes, and strong coupling regime, where new eigenmodes are formed with the creation of new quasi-particles named exciton-polaritons.

1.1.1 Weak coupling regime: Purcell enhancement

In a two-level system, if coupling strength between the photon (plasmon) and the exciton is smaller than the average dissipation rate of the two states, the system is in

weak coupling regime:

| | < (1.1)

Where represents the exciton-photon coupling strength, γ and γ denote the decay rate of the exciton and the cavity photon, respectively. In weak coupling regime, the photon-exciton interactions can be described by perturbation theories, including emission and absorption of photons, lasing, and Purcell effect. In this dissertation, we will focus on the Purcell effect, which describes the enhancement of spontaneous emission rate by the presence of an optical cavity1. According to Fermi’s Golden rule, the transition rate of the system is proportional to the density of the final state, which can be enhanced by the presence of a cavity. The enhancement factor, i.e., the Purcell factor is given by:

= (1.2)

Where λ represents the wavelength in vacuum, n denotes the refractive index of the material, Q is the quality factor of the cavity and V is the mode volume.

The key quantity that determines the enhancement rate is hence the ratio between the cavity’s quality factor and the mode volume. Purcell effect has been extensively studied both theoretically and experimentally in photonic and plasmonic microcavities.

In photonic systems, high Purcell factor was pursued by either decreasing the mode volume or increasing the quality factor. In 1987, F. D. Martini et al.2 observed enhanced spontaneous emission rate of ~6 times of dye molecules placed in a Fabry-Perot cavity 2

with length equals to . Later, Gerard and coworkers showed 5-fold Purcell enhancement in quantum-dot embedded micropillar with quality factor of 2000 and cavity diameter of 1μm. Recently, several cavity geometries have been proposed or experimentally studied with quality factors up to 105 and/or mode volumes at the order

of , giving rise to a maximum Purcell factor of 190.4-6

On the other hand, plasmonic nanocavities are able to confine the light far beyond the diffraction limit (A formal description of plasmonic resonances and plasmonic systems is given in chapter 1.1.2), as a result, moderate Purcell factors of 10-100 can be observed in spite of the low quality factors of the plasmonic modes.7-12 Recently, in our group, Cho et al reported Purcell factor on the order of 103 in Ag-semiconductor nanowire core-shell structures.13 More interestingly, such exceptionally high Purcell enhancement allowed the observation of non-thermalized spontaneous emission, which enabled bright hot-luminescence from Si, an indirect band gap semiconductor. In another work, Russell et al. also reported Purcell factor of ~103 in an organic film sandwiched by a silver film and a silver nanowire.14

1.1.2 Strong coupling regime and formation of exciton-polaritons

In a two-level system, the strong coupling limit is reached once the photon-exciton coupling strength is greater than the average dissipation rate of the two particles:

| | ≫ (1.3)

Or more strictly,

≫ , (1.4)

In this regime, excitons and photons couple strongly, resulting in new eigenstates and quasiparticles with mixed excitonic and photonic characteristics named as exciton polaritons. The concept of polariton was first conceived by Tolpygo in 195015 and confirmed experimentally by Hopfield in 195816, followed by a series of works by

Hopfield and Thomas in 1950s and 1960s17-20. In this early stage, studies were carried out in bulk semiconductors such as CdS. An exciton-photon coupled system can be described by the coupled Schrodinger’s equation as:

ℏ = (1.5)

Where the Hamiltonian has the form:

− = (1.6) −

With and representing the energy of exciton and cavity photon, and

denoting their decay rates, and g as the coupling strength. These quantities are all functions of the wave vector k.

The two new eigenenergies, which are defined as polariton states, can hence be solved as:

E = + − + ± ±

4 + − + − (1.7) 4

To have polaritons as the new eigenstates, at zero detuning, i.e., where

∆ = − =0, the coupling strength g should at least satisfy:

| | > (1.8)

Physically, this criterion indicates that, for a new quasiparticle to form, an excitation should be able to coherently transfer between an exciton and a cavity photon multiple times before they decay.

The system reaches strong coupling limit if:

≫ , (1.9)

In this regime, equation (1.7) reduces to:

E = + ± 4 + − (1.10) ±

The E−k dispersion of the polariton modes given by equation for a dispersionless exciton (since the effective mass of excitons is much larger than of cavity photons, exciton dispersion is negligible in the region of interests) and linearly dispersed photon is plotted in figure 1.1 (a). As the result of the coupling, two new dispersion branches appear via an anti-crossing behavior centered at the resonance of the two uncoupled states. These two branches are termed as the upper and lower polariton branches, respectively. The minimum splitting of the two branches occurs at zero detuning, with the splitting value equals to 2g. This splitting is defined as Rabi

Splitting Ω , or normal-mode splitting, which serves as an indication of the light-

matter coupling strength of the system. Rabi splitting of a given system at the antinode of the cavity can be expressed as:

= (1.11)

Where n is the number of oscillators, Vm is the mode volume, and f denotes the oscillator strength, a dimensionless quantity representing the transition probability.

Therefore, in microcavities with small mode volume and high quality factors (small damping), Rabi splitting is expected to be significantly enhanced. The observations of strong coupling in microcavities were first succeeded in atomic systems in 1980s,21,22 and later in 1992, Weisbush et al. observed normal mode splitting in semiconductor quantum wells embedded in vertical cavity surface emitting lasers (VCSELs) microcavities.23 So far, strong coupling has been demonstrated in various microcavity systems, including distributed Bragg reflectors (DBR),24 whispering-gallery nanocavities,25,26 as well as semiconductor nanowires 27,28 and nanobelts.29

Polaritons can be represented by linear superpositions of the excitons and photons as:

Ψ, = + (1.12)

Ψ, = − + (1.13)

Hence, the matter and light fraction of the upper and lower polariton branches are determined by the modulus squared of X and C, and are termed as the Hopfield coefficients16:

∆ || = 1 + (1.14) ∆

∆ || = 1 − (1.15) ∆

Where ∆E represents the exciton-photon detuning − . At zero detuning,

∆E=0 , || = || = . Both the upper and lower polariton branches are exactly half-exciton half-photon. At positive detuning, the upper polariton is more exciton like while the lower polariton is more photon like, and vice versa. The Hopfield coefficients of the system in figure 1.1 (a) are plotted in figure 1.1 (b). The physical properties of polaritons, such as their effective masses, lifetimes, and dispersions, are fully controlled by the Hopfield coefficients, i.e., their exciton and photon fractions.

The unique half-matter-half-light nature of polaritons enables fascinating physical phenomena and novel photonic devices. For example, as polaritons not only have the characteristics of photons including small effective mass, fast propagation and long range spatial and temporal coherence, but also, via their matter fraction, possess strong inter-particle interactions that greatly enhances their nonlinear properties, they open the door of intriguing coherent phenomena: polariton Bose-Einstein condensation30,31 and polariton lasing30,32. Their enhanced nonlinearity also enables optoelectronic/all-optical circuit elements like polariton switches33, transistors34, and logic gates33,35,36, which are critical elements to photonic computation. Moreover, the dispersions of polaritons are strongly modified by their excitonic fraction, and can hence be significantly different from that of photons, which generates slow light that is advantageous for sensing37 and enhancing nonlinear processes38.

The concept of strong light-matter coupling and the formation of exciton-photon polaritons can be extended into relevant fields, such as intersubband polaritons39, 8

phonon polaritons40 or surface plasmon polaritons41. The system we will focus on in this thesis is the exciton-plasmon system, which has ultrasmall mode volumes at the expanse of high losses, compared with conventional photonic cavities. Although large coupling strength is required to overcome the high loss to reach the strong coupling regime, however, once it is reached, ultra large Rabi splitting can be expected due to the greatly enhanced light-matter interaction in highly confined cavities. Moreover, rich exciton-plasmon coupling phenomena such as Fano resonance42-44 and electromagnetic induced transparency (EIT)45,46 that are not generally accessible in photonic systems can also be observed in such highly lossy and strongly coupled systems. Currently, exciton-plasmon coupling becomes a significant field in nanophotonics and plasmonics, and strong exciton-plasmon coupling has been realized in various geometries including metallic nanoparticles47, gratings48 and lattices49-52. with giant Rabi splitting of up to several hundred meV48-52, at least one order of magnitude larger than ordinary photonic microcavities.

In general, the eigenstates of a coupled system with multiple resonances, both electrical and optical, can be treated by a coupled oscillator model (COM), where the system’s Hamiltonian is written as:

− … − … H= (1.16) − … ⋮ ⋮ ⋮⋱

Where and γ denote the energy and decay rate of each uncoupled states,

respectively, and represents the coupling strength between the ith and jth states.

The eigenstates of the coupled system and their compositions can then be found by solving the eigenstates and eigenvectors of the Hamiltonian matrix. The new eigenstates are linear superpositions of all uncoupled states, and their physical properties are determined by the fraction of each state.

1.2 Surface plasmon resonance and Plasmonic lattices

Surface plasmon resonances (SPRs) are electromagnetic excitations arising from collective oscillation of electrons of a metal at the metal-dielectric interface. Depending on the geometry, SPRs can be classified into two types: surface plasmon polaritons

(SPPs) that propagate along the interface of the metal-dielectric interface, and localized surface plasmon resonances (LSPRs) that are confined to plasmonic nanostructures.

SPRs produce subwavelength-scale confinement near the metal-dielectric interface and high local field enhancement, leading to strong light-matter interactions, and hence enabling the observation of surface enhanced Raman scattering (SERS) 53,54, giant enhancement of spontaneous emissions13, strong exciton-plasmon coupling with coupling strengths up to hundreds of meV48-52, and plasmon lasing at deep subwavelength scales55-57, which can find practical applications in quantum computing58,59, biosensing60,61, photothermal therapy62,63, and nanoscale light sources55,64.

Lately, there has been a growing interest in studying the plasmonic resonances and

their interaction with materials in a unique plasmonic system: plasmonic lattice.

Combining the advantages of both the strong field confinement of the local plasmonic modes and the high coherence of the propagating mode, plasmonic lattices serve as idea platforms in studying and manipulating the light-matter interactions in plasmonic systems. There are two distinct resonances exhibit in plasmonic lattices. Firstly, their building blocks, plasmonic nanostructures present localized surface plasmon resonances (LSPRs) that tightly confine and strongly enhance the electric field near their vicinity, resulting in ultrasmall mode volumes and hence ultrastrong light-matter interactions. The resonance energies, field enhancement, mode volumes and mode polarizations of LSPRs are highly sensitive to the sizes, shapes and local dielectric environments of the nanoparticles, and can hence be effectively controlled by design.

Secondly, when arranged into lattices, these nanostructures can couple coherently to the diffraction modes of the lattice via Raleigh-Wood’s anomaly65, and form a propagating lattice mode with relatively high quality factor and long spatial coherence. Finally, these two different types of resonances can couple strongly together and give rise to a unique type of plasmonic resonances named surface lattice resonances (SLRs). SLRs combine the best features of LSPRs and the diffraction modes, enable both strong light-matter interactions through the LSPR component, and allow distant materials to couple coherently via the propagating modes. Moreover, the LSRs are relatively simple to fabricate, and can be engineered with great freedom by tuning the LSPR and the diffractive mode individually via designing the geometries of the nanostructures and

the lattice arrangement.

1.2.1 Localized surface plasmon resonances

Localized surface plasmon is a non-propagating, fundamental excitation of the conduction electrons of metallic nanostructures coupled to the light field.41 When a subwavelength conductive nanoparticle is placed in an oscillating electromagnetic field, an effective restoring force arises from the curved surface of the nanoparticle, resulting in a resonance that amplify the electric field both inside and at the vicinity of the particle.

Such resonance is defined as localized surface plasmon resonance (LSPR). For noble metals, such as silver and gold, the LSPR wavelengths lie in the visible region, give rise to bright colors in both reflection and transmission, due to the resonantly enhanced scattering and absorption.

For a spherical nanoparticle with radius ≪λ, the wavelength of the light, the resonance problem can be solved by a quasi-static approximation. Suppose a sphere with a homogeneous dielectric constant ε located in a dielectric medium ε, and a static and uniform electric field E0 is applied, as shown in Figure 1.2.

Figure 1.2 Schematics of a metallic sphere in a uniform, static electric field. 12

The lowest order normal mode of the electrical potential inside and outside the sphere can be solved as:

φ =− cos (1.17)

φ =− cos + cos (1.18)

It can be seen that the electric field inside the sphere is uniform, while the outside field is a superposition of a uniform field and a dipolar field induced by a dipole moment located at the center of the particle. Therefore, the fundamental LSPR is a dipolar mode.

Hence, we can introduce the polarizability:

α=4π (1.19)

The resonance condition is thereby | +2| =0. At the resonance, the electric field can be tightly confined as well as greatly enhanced near the vicinity of a deep subwavelength metallic nanoparticle, which results in an ultrasmall mode volume, and allows for ultrastrong light-matter interactions.

The scattering and absorption cross sections are proportional to |α| and Im, respectively. As α is proportional to the volume of the nanoparticle, the absorption process is dominated in small nanoparticles while scattering process is dominated in large particles.

For larger particles with dimensions do not satisfy ≪λ , the quasi-static approximation is no longer valid due to the phase variation within the particle, and more

sophisticated theory is required. In 1908, Mie developed a complete theory to describe the resonance of a sphere, by expanding the electromagnetic field into a set of normal modes.66 According to Mie theory, a dipolar LSPR is damped by two competing processes: non-radiative decay process due to absorption via interband or intraband electron transitions; and radiative decay process of coherent electron oscillation into photons. Due to the high damping rate of both processes, LSPRs generally have short lifetimes of several femtoseconds, corresponding to a low quality factor of ~5-10. The radiative decay process starts to dominate as the particle size increases, leading to a further broadening of the resonance.

1.2.2 Collective resonances in plasmonic lattices: Rayleigh-Wood’s anomaly and surface lattice resonance

In 1902, Wood observed a striking phenomenon while measuring the reflectance from a gold grating: sharp drops appeared at certain incident angles (Figure 1.3), and named these spectra drops as ‘singular anomalies’.65 The first interpretation was proposed by Rayleigh67,68 that the anomaly occurs when the high-order diffractive light passes-off the surface of the grating. This diffractive beam can interact strongly with the SPPs of the metal grating, and thereby gives rise to an anomaly in the reflection spectrum. The resonance condition is therefore given by:

= sin ±1 (1.20)

Where n is an integer, λ is the wavelength of the light, d is the period of the grating, and θ refers to the angle of incidence. This equation denotes a linear dispersion in E− k or λ−sin space. This phenomenon was then named as Rayleigh-Wood’s anomaly.

Along with the lately rapid development of plasmonics, the concept was soon extended to plasmonic nanostructure 1D or 2D arrays. In these systems, the diffraction modes of the array couples strongly to the LSPR of individual nanostructures, giving rise to a new type of resonance named surface lattice resonance (SLR). The theoretical

prediction of SLRs were first proposed by Carron et al. in 1980s,69 and followed up by

Markel in 1990s70,71 and more recently Zou et al.72 In these works, the LSPR of periodically spaced nanoparticles are treated as coupled dipoles (coupled-dipole approximation, CDA), and sharp resonances arise near the Rayleigh-Wood’s condition, i.e., when a diffractive beam passes off the array plane, indicating the occurrence of collective oscillation mediated by the diffractive coupling of the LSPR. Alternatively, the dispersions of SLRs can be partially understood by more phenomenological models, including an extended Fano theory 73,74, or coupled oscillator model (COM) that has been widely applied to study the strong coupling of two states.

Experimentally, SLRs have been extensively studied in various plasmonic lattice geometries and via different experimental methods. Some earliest efforts were made by

Lamprecht et al. (2000)75, Haynes et al. (2003)76, Hicks et al. (2005)77 and Sung et al.

(2008)78. In these works, strong modification of the extinction spectra of a plasmonic array by the lattice pitch (interparticle spacing) were reported, thereby highlighting the role of the collective interactions between the nanoparticles. However, sharp resonances were not observed in these early stage approaches because of either an inappropriate choice of the lattice pitch or the lack of the angle resolution in illumination or observation. In 2008, Auguié et al. reported narrow peaks in extinction spectra of gold nanoparticle arrays at normal incidence, and successfully correlates the experimental observation with the SLRs predicted by the CDA (Figure 1.4 (a)).79 At the same time,

Kravets et al. observed sharp resonances in both reflectance and extinction spectra, in 16

Au single- and double-nanodisk arrays, with large angles of incidence (Figure 1.4 (b)).80

Later, Rivas and coworkers mapped out the SLR E − k dispersions experimentally in

Au nanorod arrays by keep changing the light’s incidence angle (Figure 1.4 (c)),81,82 and interpreted the observations by a COM to account for the strong coupling between

LSPR and the lattice diffraction mode. Recently, Fourier optics methods were also applied to study the dispersions SLRs in several works.51,83 These experimental studies allow deeper understandings of the SLRs in plasmonic lattices as well as enable the observations of tremendous light-matter interaction phenomena in this unique plasmonic system.

Figure 1.4 Experimental observations of SLRs in different plasmonic lattices (a) Extinction spectra for several gold nanoparticle arrays at normal incidence. The average particle size was 123×85×35 nm for the main graph and 120×90×35 nm. Reprinted with permission from ref. 79. © 2006 American Physical Society. (b) Extinction spectra of an Au double-nanodisk array as a function of the angle of incidence. The electric field of the incident wave is perpendicular to the long axis of the double disk structure. Left inset: SEM image of the array. Right inset: A zoom of the extinction at 64o incidence. Reprinted with permission from ref. 80. © 2008 American

Physical Society. (c) Extinction spectra as a function of k// for an Au nanorod array with rods sizes of 450×120×38 nm Inset shows the SEM image of the corresponding array. Reprinted with permission from ref. 81. © 2011 American Physical Society.

Arising from the coupling between the LSPR and diffraction modes, SLRs can combine the advantages of both individual components, including strongly amplified local E-field and small mode volume of the LSPR, as well as the enhanced quality factor, relatively long spatial coherence and high directionality of the propagating diffraction mode. Due to these unique properties, studying the light-matter interactions in plasmonic lattices nowadays becomes one of the most active areas in plasmonics.

Fluorescence enhancement, shaping and redirection were recently demonstrated;84-86

Plasmonic lattices based sensors were reported by utilizing the high sensitivity of the

SLRs to the local refractive environment;87 Directional Lasing from the SLR’s band edge was observed in plasmonic lattices in both near IR and visible regions;57,83,88

Strong exciton-plasmon coupling was realized in plasmonic lattices integrated with both organic and inorganic semiconductors with the coupling strengths over 1 order of magnitude higher than in conventional optical cavities;49-52 Polariton lasing, a phenomenon related closely to the Bose-Einstein condensation of polaritons, was reported in strongly coupled exciton-plasmon systems recently.89 In particular, among these great works, our group performed a series of systematic study on the exciton- plasmon coupling of plasmonic lattices coupled with newly discovered 2D semiconductors, including Purcell enhancement of photoluminescence and Fano resonances,90 strong exciton-plasmon coupling,91 and active tuning of the coupling strengths via electrical gating, which will be discussed in detail in the following chapters.

As mentioned earlier, there are mainly three approaches to understand the nature of the SLRs: coupled dipole approximation (CDA), coupled oscillator model (COM) for strong LSPR-lattice coupling, and Fano theory to study the resonance lineshapes.

Here, we will give a brief introduction on each of these three approaches.

1.2.2.1 Coupled dipole approximation (CDA)

The most accurate state of the art approach to calculate the SLRs is via the coupled dipole approximation (CDA). CDA predicts the system’s response by calculating the dipole moment induced by each nanoparticle in the presence of both the applied E-field and the dipole fields generated by other nanoparticles. Following derivation is reproduced with permission from ref.72 (© 2004 AIP Publishing). Suppose the ith particle in the array is located at and has the polarizability , then the dipole moment induced by this nanoparticle is:

= , (1.21)

Where , denotes the local field experienced by this particle, and it can be expressed as:

, = , + , = exp ∙ − ∑ ∙ (1.22)

Where is the dipole interaction matric and is written as:

× × ∙ A ∙ = + 1− (1.23)

Where is the vector from particle i to particle j. 19

From equation (1.21) & (1.22) we can get:

+ = exp ∙ (1.24)

For an array with N particles, there are N such linear equations, the polarization vectors can be obtained by solving these equations. After determining the polarization vectors, the extinction cross section can be calculated as:

∗ C = ∑ Im, ∙ (1.25) ||

For an array with infinite particles in vacuum, and with the wave vector normal to the array plane, it is possible to solve equation (1.24) analytically, resulting in the expression of the polarization of each particle as:

P= and C =4Im/ (1.26)

Where S is the dipole sum:

S= ∑ + (1.27)

With θ being the angle between and the incident light polarization. For small spherical plasmonic particles near its LSPR mode, by applying Drude model and equation (1.19), the polarizability of individual particles can be approximated to:

α= (1.28) ⁄

Where A is a positive real number, is the LSPR frequency, and γ is the Drude width. Substitute into equation (1.26) we get:

P= (1.29) ⁄

A sharp resonance appears when the imaginary part of the denominator vanishes, whose wavelength is slightly larger than the lattice spacing, indicating that the diffraction mode (with the wavelength exactly equals to the lattice spacing) interacts strongly to the LSPR of individual particles, and produces a strong and sharp new resonance-surface lattice resonance. Figure 1.5 shows the surface lattice resonances predicted by the CDA, with gold nanoparticles of 100 nm radius and various array period. It can be seen that the SLRs have strongly asymmetric lineshape, especially when they approach the LSPR of single particles. For realistic nanoparticles, Mie scattering or multipole expansion should be taken into account for higher order local fields.

Although the CDA approach provides deep physical insights and the most accurate prediction of the energies and lineshapes of the SLRs, it can only be readily applied to limited cases. In an inhomogeneous environment, or with inclined light incidence, the calculation based on CDA becomes very complicated, in these cases, alternative approaches can be applied to estimate the SLRs of the plasmonic lattices.

1.2.2.2 strong LSPR-Diffraction mode coupling by coupled oscillator mode (COM)

An alternative approach to calculate the SLR dispersion is the coupled oscillator model (COM). COM views different resonances as lossy oscillators, and induces a phenomenological term g as the coupling strength between these oscillators. Hence, analogous to the derivation in chapter 1.1.2, the system’s Hamiltonian (take a two-level system as a demonstration of concept) can be written as:

− = (1.30) −

Where E and γ denote the energy and damping of the uncoupled states, respectively.

The new eigenstates of the coupled system can be determined by solving the time- independent Schrodinger’s equation. As formally described in chapter 1.1.2, an anti- crossing behavior is expected in the dispersion when the two uncoupled oscillators are brought into resonance, which is also revealed in figure 1.5: away from the LSPR mode, the SLR follows nearly exactly the Rayleigh-Wood’s anomaly condition (in this case

λ=d), whereas when it approaches the LSPR position, it redshift from the Rayleigh’s conditions and broadened in linewidth, due to its coupling with the LSPR. This strong coupling behavior will be further discussed in detail in chapter 2 both experimentally and via COM fitting.

1.2.2.2 Extended Fano theory

Fano resonance is a type of resonance with an asymmetric lineshape resulted from the interference between a narrow resonance and a continuum. The narrow resonance changes its phase by π rapidly within its FWHM, while the background continuum remains nearly unchanged. Therefore, away from the continuum, the two resonances interfere constructively, and near the continuum, they interfere destructively, resulting in an asymmetric lineshape. The scattering cross-section calculated by the Fano theory is given by73:

σ≅ (1.31)

Where and denote the energy and damping of the narrow resonance, respectively, and q is the Fano parameter, characterized by the ratio of the resonant scattering to the background scattering. The lineshapes of the Fano resonance as functions of q are plotted in figure 1.6

More generally, an extended Fano theory was developed by Benjamin Gallinet et al.74 by taking into account the losses in both the narrow and broad resonances, and the

Fano lineshapes can be obtained by considering two coupled harmonic oscillators under

an external harmonic driving force. The equations of motion of the system can be written as:

− − = ⁄ ∙ (1.32) − −

In plasmonic lattices, the diffraction modes are in general much narrower than the

LSPR, hence the coupled resonance, SLR, can have highly asymmetric lineshapes

(figure 1.5) that can be described by the extended Fano theory. It is worth noting that the extended Fano theory is closely correlated to the coupled oscillator model described in the previous section. The only difference between these two approaches is that the

COM model focused on calculating the eigenstates of the system, while Fano theory emphasizes on the lineshapes of the coupled resonances.

In this thesis, the phenomenological COM method is applied to study the SLRs of the plasmonic lattices and further their coupling with active materials, for two reasons:

(1) The system has an inhomogeneous environment, and the light is incident with a high

N.A. objective which contains a wide range of incidence angle, hence CDA is not easily applicable. (2) COM is the standard model for studying the strong light-matter coupling, therefore, by applying COM, the coupling between all different resonances within the system, both photonic and electrical, can be consistently integrated into one physical model. In fact, COM has been extensively applied in plasmonic gratings and lattices to understand the light-matter coupling even in the cases CDA is applicable49, as it provides valuable physical insights into the coupling between different resonances. 25

Therefore, in this thesis, we will restrict our study to the COM method.

1.3 Optical and electronic properties of monolayer MoS2

Ever since the discovery of the first atomically thin, two-dimensional material: graphene, the studies on 2D materials become one of the most significant fields of the condensed matter physics. Among these new materials, monolayer transition metal dichalcogenides (TMDs), such as MoS2, are of special interests in nanophotonic, for several reasons. Firstly, unlike metallic graphene, they are direct band gap semiconductors with the band gap in the visible region, which can interact effectively with visible light.92 Secondly, they exhibit excitons with strong exciton binding energies,93,94 which may allow strong light-matter interactions that is robust to high temperature or high carrier densities. Thirdly, the different spins of the electrons are locked to the two degenerate valleys at the Brillouin zone edges, respectively, leading to valley dependent selection rules of the photon transition.95 These unique properties provide great opportunities in understanding and tailoring the light-matter interactions in 2D systems, including Purcell enhancement,90 exciton-photon and exciton-plasmon coupling 96 91, and spintronics, as well as pave the way for novel, ultrathin and flexible optoelectronic devices.

1.3.1 Structure, band structure and optical transitions of MoS2

MoS2 has a hexanol crystal structure with alternatively arranged Mo and S atoms

(figure 1.7 (a)). While bulk MoS2 is indirect band gap semiconductor, when thinned down to a monolayer, it becomes a direct band gap semiconductor with the direct band gaps located at the corners of the Brillouin zone, i.e., K and K’ points (figure 1.7 (a) and (b)). As a result, monolayer MoS2 exhibits significantly stronger PL than multilayers (figure 1.6 (c)).

Due to the strong spin-orbit coupling, the valence band of MoS2 splits into two bands, giving rise to two exciton transitions: A and B excitons at 1.92 and 2.08 eV, respectively at room temperature. As a result of the 2D quantum confinement as well as the reduced dielectric screening in a 2D geometry, the exciton binding energies are exceptionally strong in MoS2. The binding energy of A exciton is calculated to be ~0.85 eV by Cheiwchanchamnangij et al. and Ramasubramaniam93,94, more than one order of magnitude stronger than conventional three dimensional semiconductors. This unique

2D property also gives rise to tightly bound trion, a quasiparticle composed of two electrons and one hole. The first observation of trions was reported by K. F. Mak et al.99 via gate dependent optical absorption and photoluminescence measurement (figure 1.8), and the trion binding energy was calculated as ~20 meV. This observation is then confirmed by several followed up studies in MoS2 as well as other monolayer TMD materials. The relative strengths of neutral excitons and trions can be controlled by the doping level of the sample via electrical gating or optical injection.

Figure 1.8 Optical transitions in monolayer MoS2. (a) Absorption spectrum of MoS2 showing A and B neutron excitons at 1.92 and 2.08 eV, respectively. (b) & (c)

Absorption and photoluminescence spectra of monolayer MoS2 as a function of gate voltages showing in figure (b). Trion transition (A-) dominates at positive gate voltages while neutral exciton transition (A) is more evident at large negative gate voltages. Reprinted with permission from ref. 99. © 2012 Macmillan Publishers Ltd.

1.3.2 Monolayer TMDs field-effect transistor

Field-effect transistor (FET) is the essential building block of modern information, computation and communication technologies. Rapid improvement of FET performance and reduction of its size are critical to this important field. In contrast to graphene, monolayer and few-layered TMDs possess a bandgap, which is mandatory

for FET operation, hence become promising candidates for fabricating ultrathin and flexible FETs. The first monolayer MoS2 FET was demonstrated in 2011 by B.

Radisavljevic et al.,100 and soon attracted worldwide attention. Due to its relatively large bandgap (~2 eV) and ultrathin nature, a good switch on-off ratio of 108 was achieved with 4 V gate voltage. Subsequently, several followed up works were reported,

101-103 with monolayer or few-layered MoS2 obtained by exfoliation and CVD growth.

103,104 Recently, simple circuits with MoS2 FETs have also been realized.

Besides the potentials in generating practical electronic devices, monolayer or few- layered TMD FETs also attract great interests in optical physics, as the optical properties of these 2D semiconductors can be effectively controlled by gate voltages.

As mentioned in the previous section, at different doping levels, trion or neutral exciton transitions can be observed with tunable binding energies.99 Moreover, Zhang et al. realized electrically switchable chiral light-emitting transistors in WSe2 by utilizing its unique spin-valley physics, and pushing the system into ambipolar region by ion-gel gating.105 In addition, Yu et al. demonstrated gating induced second harmonic

106 generation in bilayer WSe2 via tuning the interlayer coupling. Here, in chapter 5, we will also discuss active tuning of the exciton-plasmon coupling strengths via electrical gating.

1.3.3 Coupled spin and valley physics in monolayer MoS2

In monolayer MoS2, the conduction band and valence band edges are located at the

two inequivalent K and K’ edges of the Brillouin zone with large separation in momentum space. The inversion symmetry breaking of MoS2 gives rise to the valley dependent selection rule: each valley corresponds to one circular polarization in both emitting and absorption processes. Moreover, MoS2 has a strong spin-orbit coupling

(SOC) originated from the d orbits of Mo, leading to coupled spin and valley physics and suppressing of spin relaxation via the valley degree of freedom. Such properties allow the manipulation of valley spins via optical, electric and magnetic methods. In

2012, Zeng et al. and Mak et al. have demonstrated controlling of valley polarization in MoS2 monolayers by optical helicity, in which ~30% circular polarization was observed in photoluminescence by circularly polarized laser excitation.107,108 In 2014 and 2015, valley selective Zeeman effect was discovered simultaneously by several groups,109-111 showing that magnetic field can induce valley splitting by a few meV via time-reversal symmetry breaking. Meanwhile, a large valley splitting corresponding to a magnetic field of ~60 T was achieved by ultrafast optical pulses via optical stark effect.112,113 Especially, currently, there has been a growing interest in studying the valley-polarization of exciton-polaritons.114,115 Enhanced valley polarization was observed with polariton formation that have been shown to be robust to high temperature and defects. These findings may pave the way for manipulating the valley degrees of freedom in strong coupling regime and enable polaritonic spintronic devices.

1.4 Overview of the thesis

Chapter 2 discusses the optical properties of the plasmonic lattices. LSPRs of Ag plasmonic nanostructures with different sizes and shapes were first studied by both finite-difference time-domain (FDTD) simulation and reflectance measurement. Then,

SLRs of plasmonic nanodisk lattices with different pitches and nanodisk sizes were characterized by angle-resolved reflectance measurement and COM fitting.

Chapter 3 demonstrates exciton-plasmon coupling phenomena in monolayer MoS2 integrated with Ag bowtie arrays in weak and intermediate coupling regime. In weak coupling regime, lager Photoluminescence enhancement up to 40-fold was observed when MoS2 is coupled to the plasmonic array, and the relationship between the PL enhancement and the plasmonic resonances was investigated by varying the geometrical factors of the plasmonic lattices. At low temperature, Fano-resonances were observed in reflectance spectra near the exciton energy when the plasmonic resonances was tuned to the excitonic region, indicating that the system reaches a stronger exciton-plasmon coupling regime.

Chapter 4 discusses strong exciton-plasmon coupling in the MoS2 coupled with Ag nanodisk lattice system. Strong coupling was first confirmed at 77 K by experimentally observed normal mode splitting in angle-resolved reflectance spectra and the coupling strengths were calculated by COM fitting. We will demonstrate that the strong coupling strengths, polariton compositions and dispersions can be effectively engineered by

plasmonic lattice design. Then we will show that the strong coupling phenomena survives at room temperature by measuring temperature dependent reflectance spectra, indicating possibilities of creating room temperature polaritonic devices.

Chapter 5 demonstrates active tuning across the weak and strong exciton-plasmon coupling regimes via electrical gating, by integrating the MoS2-plasmonic lattice system with a FET geometry. We show the decreasing and eventually complete vanishing of the exciton-plasmon coupling strengths while applying positive gate voltages, as well as the increasing of the trion-plasmon coupling strengths that approaches strong coupling regime at gate voltages up to 100 V. The implication of such findings in active polaritonic devices and magnetic plasmonics will be discussed.

Chapter 6 illustrates chiral exciton-plasmon strong coupling enabled by a chiral plasmonic lattice design. Square lattices composed of Ag nanorods with the nanorods tilted at a certain angle with respect to the lattice frame were applied in this research.

Chiral SLRs responded to different helicity of light in these lattices and the resulted chiral exciton-plasmon coupling will be studied via both FDTD simulation and reflectance measurement.

Finally, in chapter 7, we propose several future researches based on the work presented in this thesis. Firstly, we will discuss the possibility to achieve valley selective strong exciton-plasmon coupling by different plasmonic lattice designs, and studying the valley polarizations of the exciton-plasmon coupled system by lifting the valley

degeneracy via optical or magnetic fields. Secondly, we will propose active, electrically configurable metasurfaces design by coupling metasurfaces with monolayer MoS2.

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Chapter 2. Plasmonic lattices and surface lattice resonances

This chapter is reprinted in part with permission from “Liu, W., Lee, B., Naylor, C. H., Ee, H.-S.,

Park, J., Johnson, A. C. & Agarwal, R. Strong Exciton–Plasmon Coupling in MoS2 Coupled with

To understand and engineer the light-matter interactions in MoS2 integrated with plasmonic lattices, we first characterized the plasmonic resonances in these lattices. In this chapter, LSPRs, lattice diffraction modes, and SLRs in plasmonic lattices with different geometries will be discussed via FDTD simulation, experimental measurement, and COM fitting.

2.1 Plasmonic lattice fabrication and morphology characterization

Plasmonic lattices were patterned on SiO2 substrate with 300 nm thermally grown

SiO2. The substrate was first spin coated with one layer of PMMA 950 A2 at 2000 r.p.m for 60 seconds. Various plasmonic nanostructures were then defined by electron beam lithography with 5 nm resolution. After 1 min development in MIBK:IPA 1:3 solution,

50 nm silver was deposited by physical vapor deposition, and followed by a lift-off process. The fabrication procedure is shown in figure 2.1.

Figure 2.1 Fabrication procedure of Ag plasmonic lattices 41

The sizes and shapes of the plasmonic structures were characterized by scanning electron microscope (SEM) after the optical measurements. Figure 2.2 shows several examples of the SEM images for plasmonic bowtie, nanodisk, and nanorod arrays.

Figure 2.2 SEM images of Ag plasmonic lattices. (a) Bowtie array. (b) Nanodisk array. (c) Nanorod array.

2.2 LSPR of the fabricated plasmonic lattices

As discussed in chapter 1, LSPRs of plasmonic nanostructures depend sensitively on their shapes, sizes and the local environment. In this section, we investigate LSPRs of three different nanostructure geometries: nanodisks, bowties, and nanorods via both finite-difference time-domain (FDTD) simulation and reflectance measurement.

2.2.1 Nanodisks

The LSPR modes of Ag nanodisks patterned on 300 nm SiO2/Si substrate were first studied by FDTD simulation. Figure 2.3 shows the E-field distribution of the 1st order

LSPR at the Ag-SiO2 interface of an Ag nanodisk with 120 nm diameter, excited by a plane wave polarized along x direction. The overall E-field distribution is two-fold

symmetric, hence this mode is termed as the dipolar mode. The dipolar mode contains strong local E-field in both in-plane (x and y) and out of plane (z) polarizations. While the in-plane components have monopolar (x) and quadripolar (y) characteristics, the out-plane E-field component oscillates as a dipole, hence allowing efficient far-field coupling.

Figure 2.3. Electric field profile of the dipolar LSPR of Ag nanodisk. Nano disk dimensions: r = 60 nm, h = 50 nm. Figure (a)-(c) show electric field polarized along (a) x, (b) y, and (c) z directions, respectively. (d) Magnitude of the total electric field. Inset: schematics of the system geometry.

The first and second order LSPR positions as functions of disk diameters are

determined by calculating the extinction cross section, and plotted in figure 2.4. The

LSPR position is positively correlated with the disk diameters as expected, and they scan across 560-700 nm wavelength region, the excitonic region of MoS2 and hence the wavelengths of interests of this thesis, with disk diameters of 100-170 nm.

Figure 2.4 Nanodisk LSPR mode position as a function of disk diameter.

The LSPR of the system was then studied experimentally, by measuring the far- field reflectance of fabricated arrays with lattice constant of 1000 nm. The interaction between nanodisks is weak in these lattices due to the large lattice constant, and measured dispersions via angle-resolved reflectance microscopy further confirmed that no or very weak lattice resonances were observed within 550 nm - 700 nm, the wavelength range relevant to the excitonic region of MoS2. Therefore, the measured resonances of these lattices can be approximately assumed to be the LSPRs of individual nanodisks. A dip in the differential reflectance (−/ , with

measured on the SiO2 substrate directly) spectra of the arrays was observed and found to redshift with increasing disk diameters (Figure 2.6 (a)). We found that the dip positions in the measured reflectance spectra matched well with the simulated wavelengths of the first order plasmonic mode (figure 2.6 (b)). Therefore, the reflectance dips can be correlated to the first order LSPR modes of the individual nanodisks.

2.2.2 Nanorods

Because of the asymmetric shape, the degeneracy of the LSPR modes of the two perpendicular polarizations is removed, hence, there exhibits two fundamental dipolar modes oscillating along the width and the length of the nanorods, respectively. Figure

2.6 shows the field profiles of the transverse and longitudinal dipolar LSPR, which are

analogous to the dipolar modes of nanodisks, while the resonance wavelengths are slightly redshifted compared with nanodisks of the same diameters.

Figure 2.6 Electric field profile of the LSPRs of a Ag nanorod. (a) Transverse mode. (b) Longitudinal mode. Nanorod dimensions: 170×110×50 nm

Nanorods provide additional degrees of freedom in the plasmonic lattice design by tuning their orientations and aspect ratios. Especially, As the phases change drastically near the LSPR wavelengths, at a certain wavelength close to the transverse or the longitudinal mode, an phase difference can be induced between the x and z polarized light, which makes the nanorods effectively a waveplate. This feature will be further discussed and exploited in chapter 6 in chiral plasmonic lattice design.

2.2.3 Bowties

Composed of two tip-to-tip metallic triangles, bowtie also exhibits two dipolar modes: the longitudinal and transverse modes (figure 2.7). Especially, the longitudinal mode (figure 2.7(b)) is a gap LSPR mode which tightly confine the electric field 46

between the two tips, leading to ultra-small mode volumes and potentially allowing strongly enhanced light-matter interaction. As a result, plasmonic bowties are widely applied in optical trapping1, fluorescence enhancement2,3, surface enhanced Raman scattering4, and plasmon lasing5 studies.

Figure 2.7 Electric field profile of the LSPRs of a Ag bowtie. (a) Transverse mode. (b) Longitudinal mode.

In this section, we discussed the LSPR of three different plasmonic nanostructures, in the following chapters, the three different geometries will be applied in different light-matter interaction studies according to their different properties. Nanodisks, with the simplest structure and high tunability of the LSPR wavelength, will be applied to systematically study and understand the SLRs of plasmonic lattices and strong exciton-plasmon coupling; Nanorods provide more degrees of control of the LSPR polarization, resonance wavelength and field profile, and hence will be utilized to design chiral plasmonic lattices and study chiral light-matter interaction; Bowties with

the highly-confined gap modes will be used to induce high Purcell enhancement of

MoS2 PL in weak coupling regime.

2.3 Surface lattice resonance

As introduced in chapter 1, when arranged into period arrays, the LSPR of individual nanostructures will couple strongly and coherently to the diffraction modes, producing a coupled mode named surface lattice resonance (SLR). Here, we experimentally investigated the lattice dispersions via angle-resolved reflectance measurement with various nanodisk sized and pitches.

The dispersions of the plasmonic lattices was measured by a home-built angle- resolved setup6 (figure 2.8) and a white light source. The white light beam was focused on the sample by a microscope objective (60×, NA = 0.7, Nikon) to a spot size that could be adjusted from ~5-10 μm. Collimated light reflected from the sample was focused at the back focal plane (Fourier plane) of the objective and a lens was used to project the Fourier plane onto the entrance slit of a spectrometer (Princeton

Instruments). The spectrometer CCD (2048 × 512 pixels) recorded both the wavelength of light and its spatial position at the entrance slit (angles of the reflected light) to extract the angle- and wavelength- resolved reflectance spectrum.

Figure 2.8 Schematic of the angle-resolved reflectance measurement setup

First of all, we fix the lattice pitch and vary the disk diameter (LSPR). Five different arrays contained 100 × 100 equally sized silver nanodisks arranged in a square lattice with the lattice constants of all arrays fixed to 460 nm were fabricated directly on the

SiO2/Si substrate. while the diameters of the nanodisks in different samples varied from

100 nm to 170 nm to allow their LSPR modes to span the 590 nm - 650 nm wavelength range, the excitonic region of MoS2. Sharp diffraction modes were subsequently observed due to the collective diffraction of the array in the measured angle-resolved reflectance spectra (figures 2.9 (a)-(e)) for all the five arrays. For all samples, the lowest energy lattice resonances, i.e., the (±1,0) diffraction modes were observed with the Γ point (in plane wave vector k|| = 0) near 560 nm. Significantly, as observed in figure 2.9

(b)-(d), for arrays with average disk diameters of 120 nm, 135 nm and 150 nm, we observed a pronounced anti-crossing of the dispersion curve near the LSPR

wavelengths (white dashed lines), which indicates strong coupling between the LSPR and the lattice resonances, implying that in the current system, the localized resonance of individual nanostructures can be coherently coupled to the collective diffraction of the lattices in these systems.

Secondly, to confirm the observation, we measured the dispersions of the lattices with fixed disk diameters d = 120 nm, while changing the lattice constant from 380-

500 nm (figure 2.10). In these cases, the diffraction modes redshift with increasing

lattice constants, while the anti-crossing region remained nearly unchanged near 600 nm, hence further illustrates the SLR formation leaded by the LSPR-diffraction mode coupling.

Figure 2.10 The angle-resolved differential reflectance spectra for four plasmonic lattices patterned on bare Si/SiO2 substrates with lattice constant ranging from 380 to 500 nm and 120 nm disk diameters. White dashed line represents the wavelength of the LSPR modes and the red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results obtained from a coupled-oscillator model.

The dispersion curves were then fitted to a coupled-oscillator model (COM), with the Hamiltonian given by:

ESS i  g  g SL 

H g E  i g  S  S SL  gSL g SL Ei LSPR  LSPR  where for the diagonal terms, E and γ denote the energy and the damping (half-width at

7 half-maximum ) of each mode and the subscripts S+, S- and LSPR stand for (+1,0), (-

1,0) diffraction mode and LSPR, respectively. The off diagonal term, g, represents the coupling strength between the two resonances. For simplicity, the arrays are assumed to be symmetric for positive and negative in-plane wave vector k||, hence the coupling strengths of LSPR to both the (+1,0) and (-1,0) diffraction modes were set to be the same as gSL. The system eigenstates were solved and fitted to the experimental data, with the linear E-k dispersions of (±1,0) diffraction modes obtained from the dispersions of array with detuned LSPR (figure 2.9 (e), d = 170 nm), and LSPR energies and coupling strengths used as fitting parameters. The fitted LSPR energies for all disk sizes agree well with both experimental data and FDTD simulation results for individual (uncoupled) nanodisks as shown in figure 2.5 (b). For the group of arrays with lattice constants of 460 nm, coupling strengths between LSPR and diffractive modes obtained from the COM are 95 meV, 110 meV and 125 meV, for average disk diameters of 120 nm, 135 nm and 150 nm, respectively. The lattice-LSPR coupling strength is positively correlated with the disk diameter likely due to the increase of the nanodisk polarizability with increasing diameter, which also explains the weaker lattice-LSPR coupling in array with smaller disk diameter as in figure 2.9 (a), where no pronounced strong lattice-LSPR coupling is observed. On the other hand, for the group of arrays with averaged disk diameters of 120 nm (figure 2.10), the lattice-LSPR coupling strengths are 120 meV, 110 meV, 95 meV and 95 meV for lattice constants of

380 nm, 420 nm, 460 nm and 500 nm, respectively, which are negatively correlated

with the lattice constants. Such correlation is probably because of both the enhanced interparticle interaction and the increased oscillator densities resulted from the reduced nanodisk spacing. The coupling strength between (+1,0) and (-1,0) diffraction modes, g±, was found to be negligible in all the measured arrays. The fitted polariton branches with negative k|| (figure 2.9 and 2.10, blue solid curves) show the dispersions and quality factors of the coupled lattice-LSPR modes change significantly as a function of lattice resonance-LSPR detuning. Away from the LSPR wavelengths, the coupled mode is dominated by the lattice resonance and therefore has a higher quality factor and a steeper dispersion, while near LSPR wavelengths, it becomes more LSPR-like with a lower quality factor and a nearly flat dispersion.

References:

1 Roxworthy, B. J., Ko, K. D., Kumar, A., Fung, K. H., Chow, E. K., Liu, G. L., Fang, N. X. & Toussaint Jr, K. C. Application of plasmonic bowtie nanoantenna arrays for optical trapping, stacking, and sorting. Nano Lett. 12, 796-801, (2012). 2 Kinkhabwala, A., Yu, Z., Fan, S., Avlasevich, Y., Müllen, K. & Moerner, W. Large single- molecule fluorescence enhancements produced by a bowtie nanoantenna. Nat. Photonics 3, 654-657, (2009). 3 Muskens, O., Giannini, V., Sánchez-Gil, J. A. & Gomez Rivas, J. Strong enhancement of the radiative decay rate of emitters by single plasmonic nanoantennas. Nano Lett. 7, 2871-2875, (2007). 4 Hatab, N. A., Hsueh, C.-H., Gaddis, A. L., Retterer, S. T., Li, J.-H., Eres, G., Zhang, Z. & Gu, B. Free-standing optical gold bowtie nanoantenna with variable gap size for enhanced Raman spectroscopy. Nano Lett. 10, 4952-4955, (2010). 5 Suh, J. Y., Kim, C. H., Zhou, W., Huntington, M. D., Co, D. T., Wasielewski, M. R. & Odom, T. W. Plasmonic bowtie nanolaser arrays. Nano Lett. 12, 5769-5774, (2012). 53

6 Sun, L., Ren, M.-L., Liu, W. & Agarwal, R. Resolving Parity and Order of Fabry–Pérot Modes in Semiconductor Nanostructure Waveguides and Lasers: Young’s Interference Experiment Revisited. Nano Lett. 14, 6564-6571, (2014). 7 Rodriguez, S. & Rivas, J. G. Surface lattice resonances strongly coupled to Rhodamine 6G excitons: tuning the plasmon-exciton-polariton mass and composition. Opt. Express 21, 27411-27421, (2013).

Chapter 3. Light-matter interaction between MoS2 and plasmonic lattices: weak and intermediate coupling regimes

This chapter is reprinted in part with permission from “Lee, B., Park, J., Han, G. H., Ee, H.-S.,

Naylor, C. H., Liu, W., Johnson, A. T. C. & Agarwal, R. Fano Resonance and Spectrally Modified

Photoluminescence Enhancement in Monolayer MoS2 Integrated with Plasmonic Nanoantenna

In this chapter, we will discuss the exciton-plasmon coupling between Monolayer

MoS2 and plasmonic bowtie arrays in weak and intermediate coupling regime. In weak coupling regime, the enhanced exciton-plasmon interaction in the plasmonic lattices enables profound changes in the emission and excitation processes leading to spectrally tunable, large photoluminescence enhancement via Purcell effect, as well as surface- enhanced Raman scattering at room temperature. Furthermore, intriguingly, at low temperatures, due to the decreased damping of MoS2 excitons interacting with the plasmonic resonances of the bowtie array, stronger exciton-plasmon coupling is achieved resulting in a Fano lineshape in the reflection spectrum, indicating that the system reaches an intermediate coupling regime. The ability to manipulate the optical properties of two-dimensional systems with tunable plasmonic resonators offers a new platform for the design of novel optical devices with precisely tailored responses.

3.1 Motivation and Introduction

Two-dimensional crystals such as transition metal dichalcogenides (TMDs) offer a unique material platform to investigate novel properties of strongly confined systems that can be further manipulated with heterogeneous integration with other low- dimensional systems1-5. However, their applications in fabricating photonic devices can be limited due to large nonradiative decay rates and small energy difference between different valleys with direct and indirect energy gaps, leading to extremely low photoluminescence (PL) quantum efficiency. Although increase in PL quantum

6 efficiency of MoS2 has been achieved via chemical functionalization and integration with photonic crystal cavities7, the reported enhancements have been low and also requiring large device footprints. In addition to achieving large enhancements in PL, it would also be desirable if the light-matter coupling in these systems can be tuned from weak to strong coupling limit, to enable a whole new suite of optoelectronic applications with precisely tailored responses.

Here, we will demonstrate a unique 2-D exciton-plasmon system composed of a monolayer of MoS2 integrated with a planar silver bowtie array to significantly tailor light-matter interactions in this system. As discussed in chapter 1&2, periodic patterning of bowties into an array leads to the coherent interactions between the LSPR and the lattice diffraction modes, resulting in further enhanced and much narrower surface lattice resonances (SLRs)8-11. By changing the geometrical parameters of the

bowtie array, we achieve broad spectral tunability of the SLRs. Through coupling of

MoS2 with the SLRs, PL and Raman scattering of MoS2 are drastically modified at room temperature. At low temperatures, due to the lower dephasing rate of excitons, much stronger exciton-plasmon coupling is realized, which is manifested as Fano resonances in the reflection spectra. These results demonstrate tunable optical modulation of the 2-D active medium induced by the plasmonic nanoresonators, leading to improvements in emission intensity and new optical properties based on interference between different excitation pathways of the exciton-plasmon system.

3.2 Experimental methods

MoS2 flakes were grown on SiO2/Si substrates by chemical vapor deposition

(CVD)12,13. 50 nm-thick silver bowtie arrays with varying geometrical factors were patterned directly on both SiO2 surfaces and the MoS2 flakes via electron-beam lithography (figure 3.1 (a)&(b)). Silver was used due to its strong plasmonic resonances as well as relatively low dissipation in the visible frequency range. Photoluminescence and Raman measurements were performed at room temperature on the NTEGRA

Spectra Probe system equipped with a 0.7 NA objective (~400 nm spatial resolution).

A c.w. 532 nm wavelength Ar ion laser focused to a spot size of 1 μm with an excitation power of 0.16 mW was used for all measurements. For reflectance measurements, the sample was excited by a white light source in our home-built optical microscopy setup with a 60X (0.7 NA) objective. The samples were loaded in an optical microscopy

cryostat (Janis ST-500) and cooled to 77 K with liquid nitrogen.

3.3 Experimental results

3.3.1 Surface-enhanced Raman scattering and surface-enhanced fluorescence at room temperature

-1 The Raman spectrum of the bare MoS2 sample displays modes at 384 cm and 403

-1 1 cm corresponding to the in-plane (E 2g) and out-of-plane (A1g) modes respectively

14 (figure 3.1 (c), black curve), that are fingerprints of a monolayer of MoS2 (ref. ).

Similarly, PL spectrum from bare MoS2 (figure 3.1 (d), black curve) displays peaks corresponding to A and B excitons at ~1.9 eV and 2.0 eV, respectively, that arise from

15,16 the direct band gap and strong spin-orbit coupling in monolayer MoS2 (ref. ).

Although the PL spectrum from the monolayer of MoS2 shows excitonic features at room temperature, the emission is not strong because of the low intrinsic emission efficiency in these systems, consistent with previous studies7,17.

However, both the Raman scattering and PL from the monolayer MoS2 integrated with silver bowtie array (refer to the figure captions for the bowtie geometrical factors) display enhancements of more than an order of magnitude compared to bare MoS2

(figure 3.1 (c)&(d), red curves). Typically, the mechanisms behind enhanced Raman scattering and PL emission are surface-enhanced Raman scattering (SERS) and surface- enhanced fluorescence (SEF) respectively, as observed in molecular systems placed in the vicinity of plasmonic nanostructures18,19. The enhanced emission at room 58

temperature is due to the local field increase at the position of the emitter arising from the lattice-LSPR of the bowtie array, suggesting weak coupling between the MoS2 excitons and lattice-LSPRs18.

(c), Raman scattering spectra of bare MoS2, bowtie array, and bowtie-MoS2. Geometrical factors: g = 20 nm; h = 50 nm; s = 100 nm; p = (500 nm, 300 nm). For all bowtie arrays studied throughout the paper, g = 20 nm and h = 50 nm. (d), PL spectra of bare MoS2, bowtie array, and bowtie-MoS2. Inset shows PL in log scale. (e), Calculated extinction of a single bowtie (g = 20 nm; h = 50 nm; s = 100 nm) with the inset displaying the E-field intensity profiles for TE and TM polarizations with respect to the long axis of a bowtie. (f), FDTD simulated E-field enhancements in the array of bowties (s = 100 nm) with four different unit cell lengths under normal plane wave incidence. Inset shows the E-field intensity profiles for TE or TM polarizations.

As discussed in chapter 2, single bowtie displaces two broadband dipolar LSPR

modes: the longitudinal and transverse modes, as shown in figure 3.1 (e). When the bowties are periodically patterned into a 2-D array, the plasmonic near-fields of individual bowties interact with each other, leading to collective coupling between the bowtie’s LSPRs and the lattice diffraction modes, produces SLRs8-11 with narrow resonance linewidths; for example, the calculated quality factor (Q) of a SLR at 1.9 eV

(figure 3.1 (f)) is 21, in comparison to a Q of 6 for a single-bowtie LSPR (longitudinal, figure 3.1 (e)). Furthermore, mode tunability of the SLRs improves significantly via tuning the pitch of the lattices, compared to single bowtie LSPRs, as represented in the calculated E-field enhancement profiles in figure 3.1 (f). Spatial E-field profiles (insets in figure 3.1 (e)&(f)) show that the plasmonic fields are mostly concentrated between the gaps or tips of the bowties with small optical mode volumes, hence, the exhibition of SLRs enhances the quality factor the plasmonic resonances without scarifying significantly the mode confinement, giving rise to strong PL enhancement via Purcell effect.

To understand the correlation between the SLRs and MoS2 PL and Raman scattering intensity, detailed spectroscopic characterization including polarization- dependent reflectance, PL and Raman spectra were performed on individual constituents and coupled MoS2-bowtie array system. To resolve the plasmonic modes, reflection spectra from the bowtie array patterned on 300 nm SiO2/Si substrate were measured in longitudinal and transverse polarizations (the polarization directions are defined with respect to bowtie’s long axis). Figure 3.2 (a) shows good agreement 60

between the experimental and calculated differential reflectance (ΔR/R = (Rsample ‒

Rbackground)/Rbackground) from the bowtie array on SiO2/Si substrates, which features broad dips for both polarizations. As discussed in chapter 2, in the plasmonic systems currently investigated, the plasmonic resonances correspond to the dips in the reflectance spectra. However, in this early stage of the study, resolving the dispersive

SLRs is hindered by the large NA of the objective, hence, only a broad dip was observed.

Nonetheless, as the SLRs present a strong anti-crossing centered at the LSPR energy with the flattening of the SLR dispersion, the reflectance dips in such angle-collective reflectance measurements can still manifest the LSPR energy, where strongest plasmonic mode and hence light-matter interactions may be observed. This argument can be confirmed by the simulated E-field enhancement spectra at normal incidence

(figure3.2 (c)), which shows that the reflectance dips still corresponds closely to the local E-field enhancement peaks. Moreover, as the PL measurement was also carried out with an objective of the same NA, the angle-collective reflectance spectra could be good enough to interpret the observed PL enhancement. Hence, here, we will restrict ourselves to the angle-collective reflectance spectra.

The emission from bowtie-MoS2 exhibits distinct polarization dependence (figure

3.2 (c)) and is closely related to the corresponding E-field enhancement (figure 3.2(b)).

For example, in longitudinal polarization (red curves, figure 3.2 (b)&(c), the maximum

E-field enhancement at the A exciton energy corresponds to enhanced A exciton emission, while in transverse polarization (blue curves, figure 3.2 (b)&(c)), strong 61

Raman scattering intensity is consistent with the maximum E-field enhancement near these Raman modes. These are also confirmed in the polarization-dependent 2-D intensity scans measured at the Raman and A exciton energies (figure 3.3 (a)&(b)), consistent with the simulated enhancements (figure 3.2 (b)).

a Exp. (TE) 0

(a.u.) FDTD (TE)

Exp. (TM)  -2

FDTD (TM)

normalied -4

b 8 FDTD (TE) FDTD (TM)

2 - field enhancement -field E

c A

) 1g 3 A 5 1.5 1 ex Exp. (TE) E 2g 1.0

) 0.5 5

2 Intensity (x10 0.0 Exp. (TM) 2.26 2.28 2.30

Energy (eV)

1 Bex Intensity (x10 Intensity

0 1.6 1.8 2.0 2.2 2.4 2.6 Energy (eV) d Figure 3.2 Polarization-dependent reflection spectra of the bowtie resonator array and photoluminescence spectra of MoS2 coupled with bowtie resonator array. (a) Normalized differential reflectivity (ΔR/R) spectra of experimental and calculated lattice-LSP modes in TE and TM polarizations for bowtie array on SiO2/Si substrate. Geometrical factors: s = 100 nm, p = (500 nm, 300 nm). (b) Average E-field enhancements for bowtie array on SiO2/Si calculated for the total area of the unit cell.

(c) Experimental emission (PL and Raman) spectra for bowtie-MoS2 system. Inset; zoomed-in spectra near the Raman active region.

The effect of spectral tuning of the lattice plasmonic modes on modification of

MoS2 emission was studied by varying the geometrical factors of the bowtie array (four representative patterns are shown in figure 3.4 (a), labeled (i)-(iv)). In order to obtain the plasmonic mode positions and correlate them to the emission profiles, ΔR/R spectra were measured for the four patterns on SiO2/Si substrates (figure 3.4 (b)). The frequency-dependent emission enhancements of the monolayer MoS2 integrated with these four bowtie patterns (figure 3.4 (c)&(d)) show that the increase of the emission in the bowtie-MoS2 varies up to ~ 40× depending on the spectral positions of the plasmonic modes. When the plasmonic mode of the bowtie array is in resonance with

A or B excitons, as in pattern (iii) or (ii) respectively, the PL of the bowtie-MoS2 system increases at the corresponding spectral positions (figure 3.4 (c)&(d)). On the other hand, detuning of the plasmonic mode and the A or B exciton resonance leads to only minor

PL enhancement, as observed for pattern (i). These results prove our conclusion that the PL enhancement correlates closely to the reflectance dips and hence the plasmonic resonances at the PL wavelengths (final states of the photon emission), which is characteristic to the Purcell effect.

a (i) E (ii)

(iii) (iv)

b 0 (i) (a.u.) R

/ -2 (ii) R



(iii) -4

normalized (iv)

c bare MoS 20 2 (i) (ii) (iii) )

5 (iv)

10 PL PL(x10

d ) (iii) 60 (i) 15 (iv)

MoS2 (ii) I 10 (ii)

/ (iii)

(iv) ) enhancement (i)

ex 5 40 0 PL PL (A -0.1 0.0 0.1 0.2 bowtie+MoS2    ( )   LSP - Aex (I 20 enhancement 0 Trion A Bex

PL ex e 1.0 bare MoS2 (i) (ii) (iii) PL

(iv)

0.5 normalized

0.0 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 Energy (eV)

Figure 3.4 Spectral modification of MoS2 photoluminescence coupled with bowtie

resonator arrays with different lattice-LSP dipole resonances at room temperature. (a) SEM images of four bowtie-array samples with different bowtie sizes and pitch values: (i) s = 100 nm, p = (400 nm, 500 nm) (ii) s = 100 nm, p = (400 nm, 300 nm) (iii) s = 100 nm, p = (300 nm, 200 nm) (iv) s = 170 nm, p = (500 nm, 800 nm). (b) ΔR/R spectra associated with the lattice-LSP modes of the four different bowtie patterns on SiO2/Si substrates. (c) PL spectra of bare MoS2 (black) and four different patterns. (d)

Wavelength-dependent PL enhancements (ratios of PL obtained for bowtie-MoS2 sample to PL of bare MoS2) for the four patterns on monolayer MoS2. Inset shows the enhancement of A-exciton emission for all four patterns. (e) Normalized PL spectra of bare MoS2 (black) and the four different bowtie patterns on MoS2.

The normalized PL spectra from the four patterns in figure 3.4 (e) clearly show the modification in spectral shapes depending on the plasmonic mode positions. This feature, known as spectrally modified SEF, is typically observed in molecular systems coupled with plasmonic structures20-23. For spectrally modified SEF, the total fluorescence enhancement is given by, gtotal = gex · gem, where gex and gem are the excitation and emission rate enhancements, respectively. The increase in the excitation rate is due to the increased coupling between the incident light and the emitter, arising from the enhanced local field. In this case, the excitation rate enhancement depends only on the frequency of incident light (ωi), and should not affect the spectral shape.

For example, the calculated gex for sample (iii) (which shows maximum enhancement of the A exciton emission) is ~1.8 (figure 3.5), while the observed PL enhancement is much higher. This in addition to the observed spectral modification in the bowtie-MoS2 system cannot be explained only by the enhancement of the excitation rate, which is not very high because the laser excitation energy (2.33 eV) is considerably far away from the plasmonic modes. In addition, sample (i) shows a high-energy tail above the

B-exciton emission in the normalized PL spectrum (Fig. 3e, blue curve), corresponding to the lattice-LSP mode located at higher energy (Fig. 3b, blue curve), attributed to the emission from non-thermalized excitons, similar to the hot-exciton emission observed in plasmonically-coupled CdS nanowires24 demonstrated previously by our own group.

MoS 0.4 2

MoS2 in Bowtie-MoS2

0.2

Absorption

0.0 Laser excitation 1.6 1.8 2.0 2.2 2.4 2.6 2.8 Energy (eV)

The emission enhancement (gem) can be explained by the Purcell enhancement of the radiative decay rate and hence the quantum yield of the emitter in the presence of plasmonic resonators. The emission quantum yield (kr/(kr+knr)), where kr and knr are the radiative and the non-radiative decay rates, respectively, changes as both kr and knr change when the emitter is coupled with plasmonic resonators. The radiative decay rate

is affected mainly by the local plasmonic fields whereas the non-radiative decay rate depends on plasmonic losses and exciton quenching. Generally, in an electronic multi- level system, kr and knr are frequency dependent and depend on the competition between the intra- and inter-band relaxation rates. Therefore, our frequency-dependent PL enhancement (gtotal(ω)) can only be explained by the quantum yield increase (gem(ω)), which is frequency-dependent. For our bowtie-MoS2 (sample (iii)), the integrated fluorescence enhancement (over the entire spectrum) is ~25, which is an average enhancement over the measured area. Therefore, the actual enhancement inside the bowtie gap is expected to be much higher due to much higher fields inside the small mode volume of a bowtie. The average excitation rate enhancement in our system is only 1.8, which indicates that most of the fluorescence enhancement originates from the emission enhancement. This significant emission enhancement indicates effective coupling between 2-D excitons and plasmonic resonances and is in agreement with recent theoretical studies supporting the large increase in the radiative decay rate of an

25,26 emitter in the bowtie gap . Recently, minor increase in PL from MoS2 coupled with gold nanoantenna has been reported, but the mechanism for PL enhancement was attributed to in-coupling enhancement mediated by plasmons27. Further improvements in the emission yield in our system can be achieved by inserting a thin dielectric layer between MoS2 and metal structures to optimize the competition between exciton- quenching and plasmonic field enhancement at this interface.

3.3.2 Fano resonance at 77 K and towards strong exciton-plasmon coupling

To study how the bowtie-MoS2 coupled system responds at low temperatures when the exciton-dephasing rate is reduced, the far-field ∆R/R spectra for bare MoS2, bowtie array, and bowtie-MoS2 system were measured at 77 K (figure 3.6 (a)). Clear absorption dips associated with the A and B excitons in bare MoS2 appear at 1.92 eV and 2.1 eV

(black curve). ∆R/R of the bowtie array shows two broad dips (blue curve), with the plasmonic modes spectrally overlapping with the MoS2 excitons. In the combined bowtie-MoS2 system, however, an interesting phenomenon is observed; an asymmetric feature resembling Fano lineshape appears in the reflection spectra at the MoS2 exciton energies (red curve). The Fano lineshape is a result of the spectral interference between

28,29 a narrow discrete resonance and a broad continuum of states . In our case, the MoS2 excitons with a sharp resonance at 77 K couple with the broad continuum of plasmons.

Since the linewidth of the A exciton is much narrower than that of the B exciton, more distinct Fano lineshape was observed at the A exciton spectral region.

4 a bare MoS 2 Experiment bowties

bowtie-MoS2

2 R

R 

 A 0 ex Bex

b MoS2 Bowties (exciton) (LSP) FDTD dipole-dipole 6 e pi photon 4 g R

 2

bare MoS c 2 0.4 bowties FDTD MoS2 in bowtie-MoS2

bowtie in bowtie-MoS2

0.2 Absorption

0.0

1.6 1.8 2.0 2.2 2.4 2.6 Energy (eV)

Figure 3.6 Fano resonance in the reflection spectrum of bowtie-MoS2 at 77 K. Bowtie geometry: TE mode, s = 100 nm, p = (300 nm, 200 nm). (a) and (b) Experimental and calculated ∆R/R spectra for bare MoS2, bowtie array, and bowtie-MoS2 system. Clear Fano resonances are observed at the A- and B-exciton spectral region. Inset in (b) shows the schematic for the mechanism of observed Fano resonance in the exciton- plasmon system. (c) Calculated absorption spectra for the bare MoS2 (black), bowtie array (blue), MoS2 in the combined bowtie-MoS2 system (green), and the bowtie in the combined bowtie-MoS2 system (red). The dotted circle highlights the region of MoS2 excitons where Fano resonances are observed in the refection spectra in (a)

FDTD calculation simulating the ∆R/R response of the experimental system (figure

3.6 (b)) reproduces the reflection spectra of bare MoS2 (black curve) and the bowtie array (blue curve) as well as the Fano lineshape of the integrated bowtie-MoS2 system

(red curve). To further investigate the physical mechanism of the observed Fano features, the absorption spectra (figure 3.6 (c)) were calculated for bare MoS2, bowtie array, MoS2 in the combined bowtie-MoS2 system, and the bowtie array in the combined bowtie-MoS2 system. Bare MoS2 shows a sharp excitonic absorption (black curve) while the bowtie array shows broad plasmon absorption (blue curve), as expected. For the coupled bowtie-MoS2 system, absorption in MoS2 (green curve) shows absorption enhancement in comparison to the absorption of bare MoS2 due to the strong plasmonic field. However, absorption in the bowties (red curve) in the coupled system features complex interference at the MoS2 exciton energies compared to a typically broad plasmonic absorption. This demonstrates that the absorption in the bowtie array of the combined system exhibits Fano interference due to the strong interaction between MoS2 and the bowtie array.

The physical mechanism (figure 3.6 (b), inset) behind the measured Fano resonance in the bowtie-MoS2 system is the interference that occurs predominantly in the excitation process30-32; in the exciton-plasmon coupled system, the exciton life time is much longer than that of plasmons and therefore the excitation rate of excitons increases without any significant changes in the spectral shape or position due to the enhanced local plasmonic field (figure 3.6 (c), green curve). On the other hand, 71

absorption in the bowtie array can be significantly affected by the interference from the excitons with long lifetime via the exciton-plasmon dipole-dipole coupling. Thus, in the bowtie-MoS2 system, two major optical paths exist for the excitation of plasmonic modes31-33, i.e., direct excitation of the plasmons and their indirect excitation via the dipole-dipole coupling of MoS2 excitons and plasmons. The dipole-dipole interaction increases due to the local field enhancement arising from the surface plasmons and leads to exciton-plasmon coupling beyond the perturbative regime into an intermediate state between weak and strong coupling regime. The constructive and destructive interference between the two optical pathways leads to Fano resonance measured in our reflection spectra, consistent with the large PL enhancement addressed earlier (figure

3.4).

Fano shapes vary in our experimental ∆R/R measurements depending on the detuning between MoS2 excitons and tunable plasmonic modes (figure 3.7). Three representative samples are compared to examine their Fano spectral features by controlling their geometric factors and hence their plasmonic resonances. For a very small detuning of bowtie resonances (figure 3.7 (a)), much sharper Fano feature with more distinct asymmetry was observed in comparison to the samples with increasing detuning30,34,35 (figure 3.7 (b)&(c)). Moreover, no Fano response was observed in figure

3.7 (c) due to almost no overlap between the exciton and the plasmonic resonances, and small bowtie densities in a lattice with large lattice pitches. These observations strongly support the claim that our Fano features originate from the strong interaction between 72

MoS2 excitons and plasmonic resonances.

a b c bare MoS bare MoS bare MoS 0.5 2 0.5 2 0.5 2 bowties bowties bowtie bowtie-MoS bowties-MoS2 2 bowtie-MoS2

0.0 0.0 0.0 Aex Bex Aex B ex R A ex Bex R / R

R  R  R   

-0.5 -0.5  -0.5

-1.0 -1.0 -1.0

1.6 1.8 2.0 2.2 2.4 2.6 1.6 1.8 2.0 2.2 2.4 2.6 1.6 1.8 2.0 2.2 2.4 2.6 Energy (eV) Energy (eV) Energy (eV)

tuning detuning

Fano resonances appear in many systems ranging from autoionization of atoms to plasmonic nanostructures and metamaterials28,29,36-40. However, most observations are in passive systems with no involvement of electronic resonances36-40. Fano resonance has also been observed in gated bilayer graphene system, origin of which was due to coupling between discrete phonon and broadband graphene excitons41. Recently, Fano resonance and Rabi oscillations have been demonstrated in J-aggregate dye molecules coupled with metal nanostructures due to the enhanced interaction between the excitons

32,33,35,42 and LSPRs The bowtie-MoS2 system with very small mode volume, displays

Fano resonances due to the significantly enhanced optical coupling between the 2-D

MoS2 excitons and bowtie LSPR resonances, which can be modulated via the spectral

tuning of the plasmonic resonances.

Both originated from the interactions between coupled oscillators, Fano resonances in exciton-plasmon systems correlate closely to the strong exciton-plasmon coupling phenomenon. The observation of the Fano resonances in the system implies the potential of pushing the system into the strong coupling limit by optimizing the plasmonic lattice design and experimental technique, which was later achieved and will be discussed in the next chapter.

3.4 Conclusion

In conclusion, significant modification of the emission properties of monolayer

MoS2 was demonstrated upon its integration with silver bowtie nanoantenna arrays.

The strong plasmonic local field from lattice modified LSPR resonances in the bowtie arrays gives rise to enhanced Raman scattering and PL in MoS2 at room temperature.

Depending on detuning of MoS2 exciton and the plasmonic mode, spectrally modified

PL enhancement was exhibited. At low temperature, due to the strong dipole-dipole interaction between MoS2 excitons and plasmonic modes, quantum interference arises in the excitation process and is manifested as Fano-like asymmetric reflection spectra.

Since the Fano resonance lineshape and spectral position is very sensitive to local perturbations, it can be utilized to assemble optical switches and sensors45. Tailoring light-matter interactions between atomically thin semiconductor crystals and plasmonic nanostructures as demonstrated in this work will be critical to realize new physical

phenomena and fabricate novel optical devices with applications ranging from improved light sources, detectors, and sensors to photovoltaics.

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Chapter 4. Light-matter interaction between MoS2 and plasmonic lattices: strong coupling regime

This chapter is reprinted in part with permission from “Liu, W., Lee, B., Naylor, C. H., Ee, H.-S.,

Park, J., Johnson, A. C. & Agarwal, R. Strong Exciton–Plasmon Coupling in MoS2 Coupled with

After understanding the exciton-plasmon coupling between MoS2 and plasmonic lattices in weak and intermediate coupling regime, in this chapter, we will demonstrate strong exciton-plasmon coupling in silver nanodisk arrays integrated with monolayer

MoS2 via angle-resolved reflectance microscopy spectra of the coupled system. Strong coupling phenomenon is observed at both 77 K and room temperature by optimizing the lattice design, resolving the lattice dispersion via angle-resolved spectroscopy technique and a deeper understanding of the light-matter interaction of the system. The exciton-LSPR coupling strength up to 58 meV at was obtained. The strong coupling involves three types of resonances: MoS2 excitons, LSPR of individual silver nanodisks and lattice diffraction modes of the nanodisk array. Moreover, we will show that the exciton-plasmon coupling strength, polariton composition and dispersion can be effectively engineered by tuning the geometry of the plasmonic lattice, which makes the system promising for realizing novel two-dimensional plasmonic polaritonic devices.

4.1 Motivation and Introduction

Monolayer TMDs with large exciton binding energies1 are excellent candidates for achieving strong light-matter coupling2,3 for various applications including ultrathin, flexible polaritonic devices. In addition to the numerous intriguing physical phenomena observed in conventional polaritonic systems, polaritons in 2-D systems, in particular, due to translational symmetry breaking, have enhanced light-matter coupling strength due to the confinement of the excitons and the light field, and also enables exotic effect like superfluidity4 and emerging of topological polariton states5. Understanding and tailoring the coupling strength, composition and dispersion of the polaritons is critical to the realization of these effects and the development of 2D polaritonic devices.

In spite of the great progresses in understanding the strong coupling phenomenon, practical application of polaritonic devices is hindered by the limitation of the properties of traditional materials. The small exciton binding energies of conventional semiconductors like GaAs preclude the observation of polaritonic effects at room temperature, as is also the challenging in highly lossy plasmonic systems. Organic materials, on the other hand, have large exciton binding energies and are thus mostly applied to study strong coupling in plasmonic systems, but suffer from disorder

(inhomogeneous broadening) and photo-instability. At this stage, exploration of new exitonic materials suitable for practical devices is desired. TMDs have large exciton binding energies1 due to the 2D quantum confinement of the excitons6 as well as the

reduced dielectric screening7, which may overcome the high loss of the plasmonic systems and enable the robust exciton-plasmon coupling that is required for high temperature or high carrier density applications. Moreover, as crystalline semiconductors, they have significantly less inhomogeneous broadening and are highly photostable, and hence can be utilized for practical devices.

Here, we will study the strong exciton-plasmon coupling in MoS2 coupled with plasmonic lattices system, by further utilizing the supreme properties of SLRs including strong local field enhancement, relatively large quality factor, and high tuanbility via changing the nanoparticle and lattice geometries, which allows for greater freedom for tailoring the polariton composition and dispersion for engineering different properties in the system. Moreover, atomically thin TMDs coupled to planar plasmonic lattices with thickness as small as tens of nanometers may pave the way for ultrathin and flexible polaritonic devices.

In chapter 3, we demonstrated bowtie arrays coupled to monolayer MoS2, which in the weak coupling regime exhibited large Purcell enhancement at room temperature and in the intermediate coupling regime demonstrated Fano resonances due to the exciton-plasmon interaction at 77 K8. By a careful design of geometrical parameters of the plasmonic lattices and characterization of the resonance modes of the system dispersions by Fourier optics, in this chapter, we demonstrate the observation of strong coupling between the excitons in MoS2 and plasmons at both cryogenic and room

temperatures. We show that the coupling involves three types of resonances: excitons, lattice diffraction modes, and LSPRs, which can be effectively modulated by tuning the geometries of the plasmonic lattices to produce polaritons with different exciton/plasmon compositions and hence dispersions.

4.2 Experimental method

Same as the works demonstrated in previous chapters, MoS2 samples used in our experiments were grown by chemical vapor deposition (CVD) on Si substrates with

9 275 nm thermally grown SiO2. Silver nanodisks arrays with varying diameters and pitch (square, two-dimensional lattice) were then fabricated on both MoS2 monolayers and bare Si/SiO2 substrates via electron-beam lithography (see Chapter 2 for fabrication processes). Comparing with the MoS2-bowtie study discussed in chapter 3, we’ve made two optimizations to enable the observation of strong coupling: firstly, a home-built angle-resolved system was applied to study the SLR and exciton-plasmon polariton dispersions. Secondly, nanodisks were used in this work instead of bowties for two reasons: first, although exceptionally strong field enhancement can occur between the two apexes of the bowtie resonator, the precise fabrication of a homogeneous bowtie array is difficult due to the small gap width between the two apexes (~10-20 nm). In contrast, nanodisk arrays with a simpler cylindrical geometry and diameters of the order of 100 nm are more tolerant to the fabrication errors, which is advantageous for observing strong coupling by reducing the inhomogeneous broadening. Secondly, by

varying their diameters, the LSPRs of nanodisks can be more easily and precisely tuned to be in resonance with MoS2 excitons (A and B) to enable a systematic study of the effect of coupling of LSPR resonances with excitons and the resulting polariton dispersions.

4.3 Experimental result: observation and characterization of strong exciton- plasmon coupling

With the knowledge of the SLRs discussed in chapter 2, we will focus on the exciton-SLR coupling in this chapter. In order to study the exciton-plasmon coupling between MoS2 and the SLRs, plasmonic lattices with various lattice constants and disk diameters between 70-150 nm were patterned by e-beam lithography directly onto monolayer MoS2, which exhibit strong and tunable SLRs across the excitonic region of

MoS2. The experiment was first carried out at 77 K to reduce the exciton damping, while lowered temperature has little effect on plasmonic resonances. For arrays patterned on MoS2, the LSPR modes redshifts by ~50-60 nm due to the higher refractive

10 index of MoS2 , which is confirmed by reflectance measurements on uncoupled arrays, with and without MoS2 (figure 4.1).

Figure 4.1. LSPR modes of individual (weakly-coupled) nanodisks patterned on

Si/SiO2 substrate and on monolayer MoS2 with disks diameter of d = 140 nm and lattice constant, a = 1000 nm. (a) Far-field reflectance measurement of the Ag nanodisk array on Si/SiO2 substrate and on monolayer MoS2. The resonance position (reflectance dip) is redshifted from 640 nm to 695 nm due to the presence of MoS2. (b) The difference of the reflectance spectra between the array patterned on MoS2 and bare MoS2 from (a). The LSPR position (reflectance dip) can be clearly observed at 695 nm.

In Figure 4.2 (a)-(d), the angle-resolved differential reflectance spectra of MoS2 coupled with four different arrays are presented. Each array was designed with the same lattice constant of 460 nm but with different nanodisk diameters so that the LSPR wavelengths can be tuned across the excitonic region of MoS2 (590 nm - 650 nm). Bare monolayer MoS2 displays two reflection dips corresponding to A and B excitons at ~640 nm and 590 nm respectively, arising from its direct band gap and strong spin-orbit

11,12 coupling characteristics. For all nanodisk array coupled to MoS2 samples, anti- crossing of dispersion curves near both A and B excitons were observed, indicating strong exciton-plasmon coupling. The dispersion curves for all four different arrays

were fitted to a coupled oscillator model (COM, as described earlier) including five oscillators: A and B excitons, (+1,0) and (-1,0) diffractive orders (modes), and nanodisk

LSPR. The system’s Hamiltonian is represented by:

EAA- i 0 g AS g AS g AL  0E - i g g g  BB BS BS BL  H  gAS g BS E S- i S  0 g SL    gAS g BS0 ES- - i S- g SL    gAL g BL g SL gEi SL LSPR-  LSPR 

where the diagonal terms represent the uncoupled states: E and γ denote the energy and the damping (half-width at half-maximum) of each mode, and the subscripts A, B, S+,

S-, and LSPR stand for A- and B- excitons, (+1,0), (-1,0) diffraction mode and LSPR, respectively. The off-diagonal terms represent the coupling strength between each two resonances.

In the COM fitting, the energies of A and B excitons as measured from the reflectance spectra from the same MoS2 flake in the region without the nanodisk array were used; both lattice resonance dispersions and LSPR energies were treated as fitting parameters to account for the mode redshift caused by the presence of MoS2, with the dispersions of the lattice diffraction mode kept the same for all different lattices as they are solely determined by the lattice constants; coupling strengths between the A and B excitons, and between the two diffractive orders were set to zero, while other coupling

strengths were used as fitting parameters. The arrays are assumed to be symmetric for positive and negative in-plane wavevector k||, hence the coupling strengths of other resonances to both the (+1,0) and (-1,0) diffractive orders were set to be the same. The system’s eigenstates were then solved and fitted to the experimental data to obtain the coupling strength values.

Figure 4.2. Strong exciton-plasmon coupling of silver plasmonic lattice-coupled monolayer MoS2 at 77K. (a)-(d) Angle-resolved differential reflectance spectra of four different silver nanodisk arrays with different disk diameters patterned on monolayer MoS2. The lattice constants of all four arrays are fixed at 460 nm while the disk diameters are changed. White dashed lines correspond to the LSPR positions and yellow dashed lines represent the A (low energy) and B (high energy) excitons. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled-oscillator model. (e)-(h) Line cuts from the angle-resolved reflectance data taken from a constant angle represented by the vertical white dotted lines in (a)-(d), respectively. The dip positions are indicated by the blue triangles.

The system’s eigenstates, i.e. the polariton states, can be expressed as the linear combination of the five uncoupled states:

Pk    xXki i    i1 where P stands form the polariton state, Xi (i=1,2,3,4,5) stands for the five uncoupled states, and xi is the component of the eigenvector associated with each polariton state, analogous to the Hopfield Coefficient in the two-states strong coupling model13.

Table 4.1. Coupling constants obtained from fitting the experimentally measured polariton dispersion to a coupled oscillator model. All quantities are in units of meV.

Diameter A exciton B exciton LSPR Lattice d = 72 nm 9 13 90 resonance LSPR: 590 nm LSPR 45 43 -- Lattice d = 98 nm 16 11 97 resonance LSPR: 630 nm LSPR 58 40 -- Lattice d = 121 nm 17 16 116 resonance LSPR: 660 nm LSPR 44 26 -- Lattice d = 149 nm 15 9 133 resonance LSPR: 710 nm LSPR 35 17 --

The values for the LSPR wavelengths and coupling strengths as obtained from the

COM fitting are listed in table 4.1 The lattice-LSPR coupling strength is of the order of

100 meV and increases with increasing disk diameter, which is consistent with the observations from the arrays on bare Si/SiO2 substrate without MoS2. The exciton-

LSPR coupling is enhanced strongly with decreasing exciton-LSPR detuning, and the maximum coupling strength of 58 meV was found for the A exciton-LSPR coupling when the LSPR is nearly in resonance with the A exciton (d = 100 nm, LSPR ~630 nm).

The exciton-lattice diffraction mode coupling was found to be the weakest among the three types of coupling, with the coupling strengths of the order of 10-20 meV.

Therefore, in this MoS2-plasmonic lattice system, the exciton-plasmon strong coupling is mainly mediated by the LSPR which strongly couples to both A and B excitons and the lattice resonances14. Although LSPRs are highly localized, the presence of long- range lattice diffraction modes leads to coherent coupling of the MoS2 exciton-LPSR

“plexitonic” system at different regions, much beyond the length scales of the localized plasmons or excitons thereby increasing the oscillator strength of various coupled resonances.

Figure 4.3. Composition of the four polariton branches for three representative LSPR- exciton detuning conditions in silver plasmonic lattice-coupled monolayer MoS2 at 77K. (a)-(c) A exciton fraction. (d)-(f) B exciton fraction. (g)-(i) lattice mode fraction. (j)-(l) LSPR fraction.

The coupling between the five different resonances results in five polariton branches with different exciton and plasmonic contributions and hence dispersions

(figure 4.2). Since for all the four arrays, the highest energy polariton branch lies far above the excitonic region and does not show up in the wavelength range of the measurement, we will focus our discussion on the remaining four branches with lower energies. The fitting results of these four branches are plotted for negative k|| in figure

4.2 (a)-(d) (blue solid lines) and labeled as 1-4 from high to low energies. To further

understand the strong exciton-plasmon coupling behavior of the system, the fractions

2 of excitons and plasmons xi in the four polariton branches as functions of k|| were also calculated and plotted for the following three cases (figure 4.3): LSPR energy larger than the B exciton (d = 70 nm, see figure 4.2 (a)), LSPR energy between A and

B excitons (d = 100 nm, see figure 4.2 (b)), and LSPR energy lower than the A exciton

(d = 120 nm, see figure 4.2 (c)). Interestingly, the experimental and fitting results for arrays with different disk diameters illustrate that the strong exciton-plasmon coupling behavior of the system, including the polariton composition, dispersion, and coupling strength, can all be effectively tailored by changing the geometrical factors of the lattice, in this case the nanodisk diameter. First, the exciton and plasmon fractions of each polariton branches can be controlled by the relative spectral positions of LSPR and excitons. For the A exciton, when the LSPR is positively detuned from the A exciton (d

= 70 nm, figure 4.3 (a)), the A exciton is mainly distributed in branch 3 with ~0.9 exciton fraction at high k||, and in branch 4 with ~0.8 exciton fraction at low k||. As the

LSPR energy redshifts (d = 100 nm, figure 4.3 (b)) and becomes lower than the A exciton (d = 120 nm, figure 4.3(c)), the A exciton component gradually transfers into branch 2 with ~0.8 exciton fraction at high k|| and branch 3 with ~0.9 exciton fraction at low k||. For the B exciton on the other hand, while present in all four lattices, the proportion of the B exciton is mainly distributed in polariton branches 1 and 2, and as the LSPR-B exciton detuning changes from positive (d = 70 nm) to negative (d = 100 nm), the relative fractions of the B exciton and the LSPR in these two branches at high

k|| reverses from ~0.7 B exciton and ~0.3 LSPR to ~0.05 B exciton and ~0.95 LSPR

(Figure 4.3 (d)-(f)). Secondly, the dispersions of the polaritons changes drastically for different lattice designs. Among the three types of resonances, LSPRs have flat dispersions as they do not propagate; the effective masses of excitons are orders of magnitude larger than the lattice modes and hence also show nearly flat dispersions; therefore, the polariton dispersion is mainly determined by the fraction of the lattice diffraction resonances. For instance, in polariton branch 2, the dispersion is almost flat in the lattice with d = 70 nm where its lattice mode fraction is less than 0.2 for all k||

(figure 4.3 (g)). As the LSPR redshifts with increasing disk diameters, the LSPR fraction in this polariton branch decreases and the fraction of the lattice resonances increases, and hence the dispersion of this polariton branch becomes steeper. Finally, as discussed earlier, the exciton-plasmon coupling strength can be strongly enhanced when the LSPR mode is in resonance with the excitons, as shown in Table 1. In many cases, this change of coupling strength can also be characterized by the amount of splitting between the two polariton branches surrounding the excitons. For example, for the B exciton-plasmon coupling, when the LSPR is tuned close to the B exciton resonance, the splitting between polariton branch 1 and 2 is as large as 70 meV (d = 70 nm, figure 4.2 (a)). It decreases when the LSPR is gradually detuned from the B exciton, and finally reduces to 10 meV for d = 140 nm, corresponding to a large LSPR-B exciton detuning of 320 meV.

Figure 4.4. Strong exciton-plasmon coupling of silver plasmonic lattice-coupled monolayer MoS2 at 77K with disk diameter d = 110 nm and lattice constant a = 380 nm. (a) Angle-resolved reflectance spectrum of the Ag nanodisk array. (b) Angle-resolved reflectance spectrum of bare MoS2. (c) Angle-resolved reflectance spectrum of MoS2 coupled with Ag nanodisk array. (d) Line cuts from the angle-resolved reflectance data in (a)-(c) at k = 0. In (a)-(c), white dashed lines correspond to the LSPR positions and yellow dashed lines represent the A (low energy) and B (high energy) excitons. Red dots correspond to the dip positions obtained from the line cuts of the angle-resolved reflectance at constant angles. Blue solid lines are the fitting results from a coupled- oscillator model. Strong coupling between the LSPR and both the A and B excitons are clearly observed in (c) and (d) while the lattice resonance is detuned from the excitonic region, therefore highlights the critical role of the LSPR to enhance the exciton- plasmon coupling.

The significance of the LSPR in enhancing the exciton-plasmon coupling can be further addressed by the coupling between MoS2 and plasmonic lattice with the LSPR in resonance with the excitons and detuned lattice resonance (figure 4.4). Pronounced coupling phenomenon between the LSPR and both A and B excitons were observed in spite of the large exciton-lattice resonance detuning, which highlights the key role played by the LSPR in the observed strong exciton-plasmon coupling of the system.

The above results demonstrate that the tunable mode structure and distinct properties

of different resonances in a plasmonic lattice allow engineering of the exciton-plasmon coupling strength, polariton composition, and therefore their physical properties, which is crucial for polariton devices design tailored for specific applications. Specifically, the large exciton fraction increases the polariton lifetimes and enables stronger interparticle interaction, the large LSPR fraction enhances the coupling strength, and the lattice resonance fraction tailors the polariton dispersions, and its collective nature enable the coherent coupling for excitons within its coherence length (usually >10X lattice parameter). Proper tuning of these compositions by carefully designing the plasmonic lattices will allow for the development of polaritonic devices that are suitable for a variety of purposes.

4.4 Temperature dependence of the exciton-plasmon coupling and strong coupling at room temperature

Finally, to evaluate the robustness of the strong exciton-plasmon coupling of the system, we studied its temperature dependence by measuring the reflectance spectra for both silver array-coupled MoS2 (d = 120 nm, lattice constant 460 nm) and bare MoS2 monolayer as a function of temperature. For silver array-coupled MoS2, anti-crossing of the polariton dispersions at room temperature is not as evident as it is a 77 K (figure

4.5 (a) and (b)), which is due to increased exciton damping at high temperature indicated by the linewidth broadening of both A and B excitons (figure 4.6 (d)).

However, near the A exciton region (~660 nm), strong coupling can still be resolved in

the angle-selected reflectance spectra of MoS2 coupled to silver nanodisk array (figure

4.5 (c)). As seen in figure 4.5 (c), the reflectance dips for polariton branches 2 and 3 can be identified at the high- and low-energy sides of the A exciton, respectively. This finding demonstrates that strong exciton-plasmon coupling survives at room temperature, probably owning to the large exciton binding energy of MoS2 that is at least one order of magnitude larger than the thermal energy at the room temperature

(~26 meV). Fitting the measured angle-resolved reflectance to the coupled oscillator model with exciton energies and linewidths at room temperature gives an A exciton-

LSPR coupling strength of 43 meV and an A exciton-lattice resonance coupling strength of 11 meV, which is decreased only slightly from the values at 77 K (The B exciton-

LSPR coupling and the B exciton-lattice resonance coupling were ignored in this fitting). This result indicates that strong coupling is still robust at room temperature, and hence the system holds promise for room temperature plasmonic polaritonic devices in ultrathin semiconductors. It is also worth noting that this coupling strength value is much larger than the exciton-photon coupling strength of 23 meV reported in

2 MoS2 coupled with dielectric cavities at room temperature , and therefore highlights the strongly enhanced light-matter interaction strengths in plasmonic lattices.

For a more detailed study of the temperature dependence of exciton-plasmon polaritons, the wavelengths of the A exciton and the two polariton branches at sin  0.37 (white dashed vertical line in figure 4.5 (a)) as a function of temperature were extracted (figure 4.6 (c)). At low temperatures, the energy of polariton branch 2 at the selected angle is closer to the A exciton than polariton branch 3, and it also redshifts faster with increasing temperature. While at high temperatures, the rate of redshift of polariton branch 3 increases as its energy approaches the A exciton where the energy of branch 2 becomes nearly temperature independent.

Figure 4.6 Temperature dependence of the exciton-plasmon coupled system. (a)

Temperature dependent differential reflectance spectra of bare MoS2. (b) Temperature dependent differential reflectance spectra of silver nanodisk array coupled with MoS2 obtained from the angle-resolved differential reflectance spectra at sin  0.37. The position of the line cut is shown in figure 4.4 (a) as a vertical white dotted line. (c) The wavelength of the A exciton and polariton branches 2 and 3 at sin  0.37 as a function of temperature, extracted from the dip positions in (a) and (b). (d) Exciton fractions of polariton branches 2 and 3 at sin  0.37 as a function of temperature, calculated from the COM with the temperature dependent exciton energies extracted from (a).

The reason for this phenomenon is that the redshift of the A exciton changes the exciton-

LSPR detuning, and therefore changes the relative fractions of the exciton and plasmon of the polaritons. Quantitatively, the total exciton fraction can be calculated as the sum of the fraction of both A- and B- excitons:

2 2 2 xexciton xx A  B while the plasmon fraction can be represented by:

2 2 2 2 xplasmon xxx    LSPR where they satisfy,

2 2 xexciton x plasmon 1

As shown in the calculation results of the exciton fractions in Figure 4.6 (d), at the selected angle, polariton branch 2 contains 0.7 exciton fraction at 77 K and is more matter-like and temperature dependent, while at the room temperature, this proportion drops to 0.3, and it becomes more light-like and temperature independent. For polariton branch 3, on the other hand, the exciton fraction increases from 0.35 to 0.75 from 77 K to room temperature, therefore its temperature dependence shows the opposite trend.

This result further illustrates that the physical properties, in this case the temperature dependence, of the light-matter hybrids in emitter-coupled plasmonic lattices can be tailored by tuning the relative fractions of different resonances with different features, which will be helpful for designing polaritonic devices with precisely tailored responses.

4.5 Conclusion

To conclude, we have observed strong exciton-plasmon coupling in silver nanodisk arrays integrated with monolayer MoS2. Strong exciton-plasmon coupling was studied by angle-resolved reflectance measurement, FDTD simulations, and the coupled oscillator model. We show, for the first time, the evidence of strong coupling between surface plasmon polaritons and MoS2 excitons involving three types of resonances: excitons, plasmonic lattice resonances and localized surface plasmon resonances, with the ability to effectively tune the coupling strength and physical properties of plasmon- exciton polaritons by changing the diameter of the nanodisks. By combining the distinct

properties of LSPRs and long range diffraction modes of the plasmonic lattices and the unique properties of 2D semiconductors such as their large exciton binding energies and atomic thickness, unexplored coherent phenomena like plasmonic polariton Bose-

Einstein condensation as well as ultrathin and robust plasmonic polariton devices may become a reality.

References:

1 Qiu, D. Y., Felipe, H. & Louie, S. G. Optical spectrum of MoS 2: many-body effects and diversity of exciton states. Phys. Rev. Lett. 111, 216805, (2013). 2 Liu, X., Galfsky, T., Sun, Z., Xia, F., Lin, E.-c., Lee, Y.-H., Kéna-Cohen, S. & Menon, V. M. Strong light–matter coupling in two-dimensional atomic crystals. Nat. Photonics 9, 30- 34, (2015). 3 Dufferwiel, S., Schwarz, S., Withers, F., Trichet, A. A. P., Li, F., Sich, M., Del Pozo-Zamudio, O., Clark, C., Nalitov, A., Solnyshkov, D. D., Malpuech, G., Novoselov, K. S., Smith, J. M., Skolnick, M. S., Krizhanovskii, D. N. & Tartakovskii, A. I. Exciton-polaritons in van der Waals heterostructures embedded in tunable microcavities. Nat. Commun. 6, (2015). 4 Amo, A., Lefrère, J., Pigeon, S., Adrados, C., Ciuti, C., Carusotto, I., Houdré, R., Giacobino, E. & Bramati, A. Superfluidity of polaritons in semiconductor microcavities. Nat. Phys. 5, 805-810, (2009). 5 Karzig, T., Bardyn, C.-E., Lindner, N. H. & Refael, G. Topological polaritons. Phys. Rev. X 5, 031001, (2015). 6 Komsa, H.-P. & Krasheninnikov, A. V. Effects of confinement and environment on the electronic structure and exciton binding energy of MoS${}_{2}$ from first principles. Phys. Rev. B 86, 241201, (2012). 7 Chernikov, A., Berkelbach, T. C., Hill, H. M., Rigosi, A., Li, Y., Aslan, O. B., Reichman, D. R., Hybertsen, M. S. & Heinz, T. F. Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer ${\mathrm{WS}}_{2}$. Phys. Rev. Lett. 113, 076802, (2014). 8 Lee, B., Park, J., Han, G. H., Ee, H.-S., Naylor, C. H., Liu, W., Johnson, A. T. C. & Agarwal, R. Fano Resonance and Spectrally Modified Photoluminescence Enhancement in Monolayer MoS2 Integrated with Plasmonic Nanoantenna Array. Nano Lett. 15, 3646- 3653, (2015). 97

9 Han, G. H., Kybert, N. J., Naylor, C. H., Lee, B. S., Ping, J., Park, J. H., Kang, J., Lee, S. Y., Lee, Y. H., Agarwal, R. & Johnson, A. T. C. Seeded growth of highly crystalline molybdenum disulphide monolayers at controlled locations. Nat Commun 6, (2015). 10 Castellanos-Gomez, A., Agraït, N. & Rubio-Bollinger, G. Optical identification of atomically thin dichalcogenide crystals. Appl. Phys. Lett. 96, 213116, (2010). 11 Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS 2: a new direct- gap semiconductor. Phys. Rev. Lett. 105, 136805, (2010). 12 Splendiani, A., Sun, L., Zhang, Y., Li, T., Kim, J., Chim, C.-Y., Galli, G. & Wang, F. Emerging photoluminescence in monolayer MoS2. Nano Lett. 10, 1271-1275, (2010). 13 Hopfield, J. J. Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals. Phys. Rev. 112, 1555-1567, (1958). 14 Väkeväinen, A., Moerland, R., Rekola, H., Eskelinen, A.-P., Martikainen, J.-P., Kim, D.-H. & Törmä, P. Plasmonic surface lattice resonances at the strong coupling regime. Nano Lett. 14, 1721-1727, (2013).

Chapter 5. Active tuning of the exciton-plasmon coupling via electrical gating

Active control of light-matter interactions in semiconductors is critical for realizing next generation optoelectronic devices. In this chapter, we demonstrate electrical control of exciton-plasmon polariton coupling strength between strong and weak coupling regimes in a two-dimensional semiconductor integrated with plasmonic nanoresonators assembled in a field-effect transistor (FET) device. We show that the exciton-plasmon coupling strengths and hence the polariton dispersion can be altered dynamically with applied electric field by modulating the excitonic properties of monolayer MoS2 arising from many-body effects. In addition, strong coupling between charged excitons (trions) and plasmons was also observed upon increased carrier injection, suggesting a cornerstone of emergent spin-coupled plasmon systems, magnetoplasmons. The ability to dynamically control the respective optical properties with electric fields offers a new platform for the design of optoelectronic devices with precisely tailored responses.

5.1 Motivation and Introduction

The strongly confined 2D excitons in monolayer TMD semiconductors lead to several interesting optical features such as large exciton binding energy1-4 and oscillator strength5,6, and the observation of higher-order excitations such as charged excitons

(trions)7,8. The optical properties of 2D excitons can be significantly altered when coupled to an external cavity, leading to various physical phenomena in different light- matter coupling regimes. In previous chapters, with carefully chosen and designed 2D plasmonic lattices, we demonstrated exciton-plasmon coupling in weak, intermediate and strong coupling regimes. Here, we utilize the advantages of the plasmonic lattices at different aspect: they offer unique opportunities for tailoring light-matter interactions in 2D materials owning to their ease of integration and open geometry, which is also compatible with electrical injection or gating device configuration.

Owning to the atomically thin nature of the monolayer TMD semiconductors and the associated significantly reduced screening of the charge carriers, their optoelectronic properties can be effectively controlled via electrostatic doping induced by the gate electric field in a FET geometry. As a result, novel findings have been reported including the modulation of exciton binding energies9,10, observation of charged trions8,11, and valley-contrast second-harmonic generation12. Here, by combining a plasmonic lattice coupled with monolayer MoS2 configured in a FET device, we demonstrate active control of the coupling strengths between the MoS2 excitons and SLRs, with continuous and reversible transition between the strong and weak exciton-plasmon coupling regimes achieved by electron injection or depletion in the active MoS2 monolayer. In contrast to conventional bulk semiconductors, 2D TMD semiconductors provide simultaneously both tightly-bond excitons from its extreme 2D confinement, as well as efficient and complete modulation of its excitonic properties 100

upon electrostatic doping, enabling the excitons to couple and decouple to plasmons effectively. Furthermore, under certain doping conditions, strong coupling between trions and plasmons was also observed, giving rise to a new type of fermionic polaritons.

Therefore, the spin classification of the exciton-plasmon system can be switched back and forth between bosonic (neutral exciton-plasmon) or fermionic (trion-plasmon) spin states by simple application of the external electric field to the system, offering novel opportunities in quantum optoelectronic devices.

5.2 Experimental methods

Figure 5.1 Schematics (a) and SEM images (b) of the MoS2-plasmonic lattice FET device.

Plasmonic lattices and source/drain electrodes are fabricated simultaneously onto the as grown monolayer MoS2 flakes via e-beam lithography (figure 5.1). A 285 nm-thick thermally grown SiO2 layer sandwiched between MoS2 and highly doped Si substrate produces a metal-oxide-semiconductor FET with a capacitance of ~ 12 nF/cm2.

Charge carriers are injected or depleted from the electrical contacts depending on the gate electrostatic potential (VG) with respect to MoS2. For example, a VG of ~ 100 V

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12 2 can lead to a carrier density of ~ 8×10 /cm in the MoS2 monolayer, estimated from the capacitance of the device. As a result, the chemical potential (Fermi level) of MoS2 can be altered by ~ 50 meV depending on the carrier density. Figure 5.2 shows a typical transconductance curve obtained from a bare MoS2 FET device, displaying n-type channel performance. The plasmonic lattices were fabricated with the diameters of the silver nanodisks varied between 110 and 140 nm, with constant thicknesses and pitches of 50 nm and 460 nm, respectively, to allow strong exciton-plasmon coupling. To characterize the evolution of the exciton-plasmon coupling strengths, the dispersions of the coupled MoS2 exciton-SLR system were measured by a home-built angle-resolved reflection microscopy setup13 while tuning the gate voltage.

Figure 5.2 Typical transconductance curve from a bare MoS2 FET device

5.3 Active tuning of the exciton-plasmon coupling strengths

Figure 5.3 (a)-(e) shows evolution of the MoS2-plasmonic lattice dispersion upon applying positive gate voltages. When gate voltage was applied, clear dispersion

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changes can be observed. At VG=0 (figure 5.3 (a)), clear anti-crossing behavior can be observed centered at the A exciton energy (640ish nm, yellow dashed line), indicating strong exciton-plasmon coupling. With increasing gate voltages, such anti-crossing feature gradually diminished, instead, an additional spectral feature appeared near 650 nm, matching the trion energy (figure 5.3 (c), orange dashed line). At VG = 80 V, the highest gate voltage applied (Figure 5.3 (e)), the anti-crossing corresponding to A exciton completely vanished, while trion-SLR coupling could still be observed, indicated by the kink-like feature in the dispersion curves near the trion resonance.

The exciton-plasmon and trion-plasmon coupling can be better visualized by plotting the line cuts extracted from different angles of the angle-resolved spectra at different applied gate voltages, as shown in figure 5.4 (a)-(c). Five line cuts taken from sin = 0 (bottom black curve) to sin = 0.5 (top green curve) were plotted for

VG=0, 40 and 80 V, respectively. These ΔR/R spectra show clearly resolved exciton-

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plasmon polariton dispersions originated from both Ao and A- exciton-plasmon coupling at different gate voltages. At VG = 0 V, distinct polariton branches resulting from strong Ao exciton-plasmon coupling can be observed, as indicated by the grey dash lines. The strong Ao exciton-plasmon coupling and the absence of A- exciton polariton features indicate that the sample was lightly doped. As the carrier concentration increased upon applying positive VG = 40 V, new polariton mode (~ 650 nm) corresponding to A- exciton-plasmon appeared in the ΔR/R spectra (figure 5.4 (b)), accompanied by a slight blue-shift of the preexisting polariton branches. Upon

o increasing VG to be 80 V (figure 5.4 (c)), the polariton modes originating from A exciton-plasmon coupling vanished while the A- (trion) polariton gained oscillator strength, resulting in more enhanced reflection features and mode splitting. To better resolve the exciton-plasmon coupling at each applied gate voltages, figure 5.4 (d)-(f) present the zoomed-in reflectance spectra of the line cuts taken at sin = 0.5 (green curves in (a)-(c)), where the SLR of the fabricated lattice has nearly zero detuning with

A exciton. At all VG, mode splitting was observed, and two or three modes can be resolved as indicated by the Gaussian fitting of the reflectance curves, suggesting that the system changed progressively from strong Ao exciton-plasmon coupling to strong

A- exciton (trion)-plasmon coupling regime with increasing carrier concentration.

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Figure 5.4 Line cuts of the angle-resolved reflectance spectra at different applied voltages. (a)-(c) Spectral line cuts. From bottom to up: sin = 0,0.15,0.3,0.4,0.5 , respectively. (d)-(f) Zoomed-in spectra taken from the (a)-(c) with sin = 0.5 and corresponding Gaussian fitting for mode resolving. Yellow dashed line: A0 exciton, Orange dashed line: A- exciton (trion). Gray dashed line: mode positions extracted from the line cuts.

These experiments demonstrate that plasmon coupling to the excitonic resonances can be finely tuned between the weak and strong coupling limits via electric control of charge carrier density in the active medium of 2D semiconductors. In addition, the possibility of creating trion-plasmon polaritons, a unique type of fermionic light- matter hybrids, in which the spin structure of the trion can effectively couple to the plasmon, can enable a new class of magnetoplasmonic systems.

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The observed coupling tuning is attributed to the modulation of the exciton oscillator strengths via carrier injection/depletion. Figure 5.5 shows the reflectance spectra measured from the bare region of the same MoS2 flake. With increasing gate voltages, Ao exciton displayed a slight blue shift in its resonance energy and linewidth broadening in the ΔR/R arises from the many-body effects upon carrier doping14, which are consistent with our observation of the evolution of the exciton-plasmon coupling with increased doping, and will be discussed later in more detail.

Figure 5.5 Evolution of the bare MoS2 reflectance with applied gate voltage.

In order to quantitatively characterize the observed tuning phenomena of the exciton-plasmon coupling, the angle-resolved spectra were fitted to a coupled oscillator model (COM) to calculate the exciton-plasmon coupling strengths as a function of VG, as shown in figure 5.6. The COM fitting results are in excellent agreement with the experimental data, capturing all the features of the recorded dispersions over large wavelength and angle ranges at different applied VG. The VG-dependent exciton-LSPR 106

coupling strengths are presented in figure 5.6 (f), while the exciton-diffraction mode coupling strengths are found to be nearly negligible in this device. At VG = 0 V, only the Ao exciton-plasmon strong coupling was observed in the reflectance spectrum, as indicated by clear anti-crossing behaviors of the dispersion curves, with a coupling strength of 63 meV. As the carrier concentration increased upon applying positive VG,

Ao exciton gradually decoupled from the SLRs, and eventually disappeared in the dispersion spectra. Upon increasing the positive gate voltage, an additional polariton branch emerged (figure. 5.6 (b)), resulting from the splitting of the initial polariton branch 2 at the A- exciton state, indicating A--plasmon coupling. With a further increase in VG (figure 5.6 (c)-(d)), the new polariton branch 2 progressively blue shifted, suggesting increased mode splitting between the polariton branches 2 and 3 near the A- state (increase in A- plasmon coupling), and decreased mode splitting between polariton

0 o branches 1 and 2 near the A state (decrease in A plasmon coupling). At VG = 80 V

(figure 5.6 (e)), the polariton branches 1 and 2 merged into one branch, which indicates that the coupling between Ao excitons and the lattice-LSP modes vanished, owing to the collapse of their oscillator strengths under high doping conditions. The evolution in the exciton-plasmon coupling strengths is simulated by the COM fitting. Upon applying

0 positive VG, the A exciton-LSP coupling strength undergoes a large change from 63 meV to almost zero, while the coupling between trions and lattice-LSP modes gradually increased with increased doping and reached a maximum coupling strength of 42 meV at VG = 80 V, caused by a partial transition of the oscillator strengths from neutral

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excitons to negatively charged trions.

Figure 5.6 COM fitting of the system dispersion and calculated exciton-LSPR coupling strengths.

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Lower value in the maximum coupling strength of the A- exciton can be explained by its weaker oscillator strength than Ao exciton. However, given that the typical oscillator strength of trions found in 2D quantum wells or bulk materials is more an order of magnitude lower than that of the neutral excitons7,15, this finding is intriguing since the magnitude of the trion-plasmon coupling strength is comparable to neutral exciton-plasmon coupling, which further illustrates the enhanced interaction between excitons and charged carriers due to significantly reduced screening, and large overlap between electron and hole wave functions from their extreme 2D confinement16.

The Fermionic nature of the trion-plasmon hybrid modes can lead to very different quantum properties than the bosonic exciton-plasmon polaritons. For instance, in exciton-polariton systems, coherent phenomena such as Bose-Einstein condensation can arise at high polariton densities from their bosonic nature, while in a fermionic polariton system, completely different behavior would be expected. The modulation between the exciton-plasmon and trion-plasmon coupled system also suggests an attractive platform for the strongly coupled spin and plasmon systems, magnetoplasmons, in which the combination of plasmonics and magnetism enables the control of the plasmonic properties via magnetic field and gives rise to novel magneto- optical responses in the materials.

To further study the modulation of light-matter coupling of the system and its active control via external fields, nanodisk arrays with different disk diameters (d =120

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and 140 nm) on the same MoS2 flake were measured. LSPR arising from different sized silver disks resulted in different coupling strengths with Ao and A- excitons (figure 5.7) due to different LSPR-exciton detuning17. Silver nanodisks with diameters of d = 120 and 140 nm have their LSPR at 670 nm and 685 nm (figure 5.7 (f)-(h) and (k)-(m), white dashed lines) respectively. Unlike the previous device with the LSPR nearly in resonance with the A- excitons, the LSPR of the d=140 nm device is largely detuned from the excitonic region (> 150 meV detuning). In all devices, the tuning of the exciton-plasmon coupling (figure 5.7 (f)-(h) and (k)-(m)) with different VG was observed, with qualitatively similar trends, but very different coupling strength values negatively correlated with the exciton-LSPR detuning, which is consistent with our previous studies17. The different LSPRs in these different arrays not only quantitatively changed the exciton-plasmon coupling strengths, but more importantly, altered the nature of the exciton-plasmon coupling of the system. Figures 5.7 (d), (i)&(n) show the series of line-cuts obtained at different VG, extracted from the angle-resolved spectra of the three lattices at the angles where the SLRs have zero detuning with the Ao exciton

(sinθ=0.34, 0.32, and 0.27 for d=110, 120 and 140 nm, respectively). For d=110 nm device, mode splitting was resolved at all VG, with their evolution indicated by grey- dashed lines, suggesting that the system changed progressively from strong Ao exciton- plasmon coupling to strong A- exciton-plasmon coupling regime. In contrast, the d=140

nm device (Fig. 5.7 (n)) showed two polariton modes observed at VG =0 V gradually merged into one broad dip with increasing VG, indicating that the system evolved from

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strong to weak coupling regime. The d=120 nm lattice is in the intermediate regime between the strong- and weak- coupling of trions. These results, consistent with other similar devices, also provide more insights about design strategies for obtaining precisely tailored optoelectronic responses in 2D polaritonic devices.

Figure 5.7. Gate-voltage dependent exciton-plasmon coupling in the angle-resolved ΔR/R plots for three different silver nanodisks arrays with different resonance detuning values. (a)-(c), d = 110 nm. (f)-(h), d = 120 nm. (k)-(m). d = 140 nm. The position of uncoupled Ao, A- excitons, and LSPR are indicated as yellow-, orange- and white- dashed lines, respectively. (d), (i), (n), ΔR/R spectra obtained from line cuts (vertical white-dashed lines, sinθ = 0.35 in (a-c), sinθ = 0.30 in (f-h), and sinθ = 0.25 in (k-m), respectively) of the angle resolved spectra at different VG. Grey-dashed lines in (d), (i) and (n) trace the evolution of the system’s eigenstates upon carrier doping. (e), (j), (o) Comparison of the coupling strengths for Ao-LSPR and A—LSPR coupling obtained from the COM fitting as a function of the gate voltage.

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Enhanced many-body effects are one of the unique characteristics of highly confined TMD monolayers even at moderate doping levels, which can be easily

4,7,9,10 achieved from Si/SiO2 back-gated FET devices . Greatly reduced screening due to the lack of large bulk polarization leads to increased Coulomb interaction and scattering process, which along with phase-space filling (Pauli blocking) effect influences the exciton oscillator strength and binding energy9,10,18. The increased charge carrier concentration under positive electrostatic gating results in the reduction of the Ao oscillator strength due to exciton bleaching, giving rise to weaker interactions between excitons and plasmons, which drives the system towards weak coupling regime. On the contrary, the depletion of charge carriers makes MoS2 more intrinsic, resulting in stronger exciton-plasmon coupling. in TMD monolayers, continuous and reversible switching between strong and weak exciton-plasmon coupling regimes can be achieved in response to the variation of charge carrier concentration (Fermi level shift), which can be easily controlled by external fields, owing to the unique attributes of the 2D excitonic systems.

5.4 Conclusion

In summary, we demonstrated active control of the coupling strengths between

2D MoS2 excitons and plasmonic lattices integrated in an FET device, via charge carrier injection/depletion. Continuous and reversible transition between the strong and weak exciton-plasmon coupling regimes was achieved by tuning the gate voltage.

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Furthermore, we also showed that the trion resonances could also couple with the lattice plasmons at high electron doping concentration, showing their own dispersion properties. Our work demonstrates that unique opportunities exist in 2D monolayer semiconductors to electrically control light-matter interactions, owing to the lack of bulk polarization in these ultrathin materials, which reduces carrier screening, and hence leads to extraordinarily strong exciton oscillator strengths and binding energies, as well as enhanced many body effects. Electrical control of light-matter interactions in photonic devices is very attractive for designing modulators, switches, sensors, and other functional polaritonic devices. Furthermore, stronger trion-plasmon coupling can be an attractive platform for studying the strongly coupled spin and plasmon systems, i.e., magnetoplasmons, in which the combination of plasmonics and magnetism can enable the control of plasmonic properties by magnetic fields, giving rise to novel magneto-optical responses in these class of materials.

References:

1 He, K., Kumar, N., Zhao, L., Wang, Z., Mak, K. F., Zhao, H. & Shan, J. Tightly bound excitons in monolayer WSe 2. Phys. Rev. Lett. 113, 026803, (2014). 2 Chernikov, A., Berkelbach, T. C., Hill, H. M., Rigosi, A., Li, Y., Aslan, O. B., Reichman, D. R., Hybertsen, M. S. & Heinz, T. F. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS 2. Phys. Rev. Lett. 113, 076802, (2014).

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3 Ye, Z., Cao, T., O’Brien, K., Zhu, H., Yin, X., Wang, Y., Louie, S. G. & Zhang, X. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214-218, (2014). 4 Ugeda, M. M., Bradley, A. J., Shi, S.-F., Felipe, H., Zhang, Y., Qiu, D. Y., Ruan, W., Mo, S.- K., Hussain, Z. & Shen, Z.-X. Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor. Nat. Mater. 13, 1091-1095, (2014). 5 Zhang, C., Wang, H., Chan, W., Manolatou, C. & Rana, F. Absorption of light by excitons and trions in monolayers of metal dichalcogenide Mo S 2: Experiments and theory. Phys. Rev. B 89, 205436, (2014). 6 Robert, C., Lagarde, D., Cadiz, F., Wang, G., Lassagne, B., Amand, T., Balocchi, A., Renucci, P., Tongay, S. & Urbaszek, B. Exciton radiative lifetime in transition metal dichalcogenide monolayers. Phys. Rev. B 93, 205423, (2016). 7 Mak, K. F., He, K., Lee, C., Lee, G. H., Hone, J., Heinz, T. F. & Shan, J. Tightly bound trions in monolayer MoS2. Nat. Mater. 12, 207-211, (2013). 8 Ross, J. S., Wu, S., Yu, H., Ghimire, N. J., Jones, A. M., Aivazian, G., Yan, J., Mandrus, D. G., Xiao, D., Yao, W. & Xu, X. Electrical control of neutral and charged excitons in a monolayer semiconductor. Nature Communications 4, 1474, (2013). 9 Chernikov, A., van der Zande, A. M., Hill, H. M., Rigosi, A. F., Velauthapillai, A., Hone, J. & Heinz, T. F. Electrical tuning of exciton binding energies in monolayer WS 2. Phys. Rev. Lett. 115, 126802, (2015). 10 Gao, S., Liang, Y., Spataru, C. D. & Yang, L. Dynamical Excitonic Effects in Doped Two- Dimensional Semiconductors. Nano Lett. 16, 5568-5573, (2016). 11 Liu, X., Galfsky, T., Sun, Z., Xia, F., Lin, E.-c., Lee, Y.-H., Kéna-Cohen, S. & Menon, V. M. Strong light–matter coupling in two-dimensional atomic crystals. Nat. Photonics 9, 30- 34, (2015). 12 Seyler, K. L., Schaibley, J. R., Gong, P., Rivera, P., Jones, A. M., Wu, S., Yan, J., Mandrus, D. G., Yao, W. & Xu, X. Electrical control of second-harmonic generation in a WSe2 monolayer transistor. Nat. Nanotechnol. 10, 407-411, (2015). 13 Sun, L., Ren, M.-L., Liu, W. & Agarwal, R. Resolving Parity and Order of Fabry–Pe rot Modes in Semiconductor Nanostructure Waveguides and Lasers: Young’s Interference Experiment Revisited. Nano Lett. 14, 6564-6571, (2014). 14 Auguié, B. & Barnes, W. L. Collective resonances in gold nanoparticle arrays. Phys. Rev. Lett. 101, 143902, (2008). 15 Combescot, M. & Tribollet, J. Trion oscillator strength. Solid State Commun. 128, 273- 277, (2003). 16 Gan, X., Gao, Y., Fai Mak, K., Yao, X., Shiue, R.-J., van der Zande, A., Trusheim, M. E., Hatami, F., Heinz, T. F. & Hone, J. Controlling the spontaneous emission rate of monolayer MoS2 in a photonic crystal nanocavity. Appl. Phys. Lett. 103, 181119, (2013). 17 Liu, W., Lee, B., Naylor, C. H., Ee, H.-S., Park, J., Johnson, A. C. & Agarwal, R. Strong Exciton–Plasmon Coupling in MoS2 Coupled with Plasmonic Lattice. Nano Lett. 16, 1262-1269, (2016).

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18 Schmitt-Rink, S., Chemla, D. & Miller, D. Linear and nonlinear optical properties of semiconductor quantum wells. Adv. Phys. 38, 89-188, (1989).

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Chapter 6. Chiral exciton-plasmon coupling in chiral plasmonic lattices

6.1 Motivation and introduction

Studying of chirality, a key molecular structural concept, has become an active research field in optical physics ever since it was introduced into metamaterial and metasurface design. These artificial structures can exhibit orders of magnitude stronger chirality than natural chiral media via careful design, hence giving rise to potential applications such as chiral biomolecule sensing1-3, polarization sensitive metasurfaces4-

6 and holograms7,8. Chiral light-matter interactions in these artificially designed structures have also been extensively studied, including tailoring the chiral emission9 and lasing10, or in nonlinear optics for chiral second harmonic generation11. However, previous works were only limited in weak coupling regime, and the chirality of strong light-matter coupling has never been reported. In conventional microcavities, polaritons are spin degenerate, with the spin projection along the microcavity axis couples directly to circularly polarized light. Polariton’s spin carries a quantum bit of information, making spin-based polaritonic devices extremely promising for quantum information processing, and polariton spin switches12, transistors 13,14, and memories15 have been recently experimentally demonstrated or proposed. Our study on chiral strong coupling allows the manipulation of polaritons’ spin degrees of freedom, may pave the way of novel chiral polaritonic devices, as well as contribute to the researches of polariton spin 116

dynamics.

Moreover, earlier studies on chiral plasmonic nanoresonators were mostly focused on the chirality induced by the asymmetry of individual plasmonic nanoantennas, however, the lattice resonances and their interactions with the LSPRs can play critical roles in the system’s chirality as well. Recently, Cotrufo et al.9 studied chiral emission from dye molecules coupled with plasmonic lattices composed of chiral nanoantennas, by taking into account both the chiral LSPRs and the lattice modes; Z. Wang et al16 showed circular dichroism in plasmonic metasurfaces controlled by both the LSPR and the lattice constant. Nevertheless, in these works, the chirality was still induced by chiral plasmonic nanostructures, and the relatively complex nanostructures generate complicated LSPR modes, which may hinder the observation and understanding of the light-matter interactions of the system. Moreover, lattice resonances are essential in studying the light-matter interactions in plasmonic lattices. In weak coupling regime, lattice resonances possess tunable dispersions, and induce collective interactions between the emitters, hence enable modifications of the emission spectrum, directional emission and lasing. Furthermore, with relatively high quality factors and allowing distant excitons to couple coherently, the existence of lattice resonances can help overcome the high losses of the plasmonic system and push the system into strong coupling regime, leading to the formation of exciton-plasmon polaritons. However, these intriguing phenomena have not yet been fully explored in plasmonic chiral structures. 117

6.2 Chiral plasmonic lattice design

Here, to further emphasize the significance of the lattice effect, i.e., the collective interactions between the plasmonic nanoantennas, in both inducing chirality and enhancing the light-matter interaction, we systematically investigated the chirality of the plasmonic lattices composed of achiral silver nanorods, with the rods tilted by a certain angle with respect to the lattice frame (Figure 6.1). In these lattices, the chirality results solely from the strong interactions between the LSPR of the nanorods and the lattice resonances. Furthermore, we integrated these chiral plasmonic lattices with

MoS2 and realized, for the first time, helicity dependent strong exciton-plasmon coupling. It should be addressed that unlike the complicated nanoresonators generally applied in chiral planer structures, the nanorods in the current design possess simple but strong dipolar LSPRs, which is critical to observe and understand the strong exciton-plasmon coupling of the system. Moreover, such simple design also avoids complicated fabrication processes and may allow chiral functionalities at very short wavelength ranges.

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6.3 Chiral SLRs studied by reflectance measurement and FDTD simulation

First of all, we measured the helicity dependent angle-resolved reflectance from five lattices composed of nanorods tilted by 0o, 30o, 45o, 60o and 90o, with the rotation angles defined as the angle between the long axis of the nanorod and the in-plane wave vector k// determined by the measurement. The lattice constants were kept at 450 nm and the nanorod sizes are 110×170 nm for all lattices. As expected, the achiral 0o and 90o lattices (figure 6.2 (a)&(f), (e)&(j)) response identically to the LCP and RCP

o o input light. The lattice dispersions were observed in both 0 and 90 lattices but with different characteristics. Because the lattice modes appeared within the current wavelength range are TE modes, they couple strongly to the LSPR oscillating

o perpendicular to the in-plane wave vector k// and form SLRs. As a result, the 0 lattice

(figure 6.2 (a)&(f)) couples to the transverse LSPR (LSPR corresponding to the width of the nanorod, see chapter 2 for more discussion) located near 640 nm and present an anti-crossing in its dispersion, while in the 90o lattice, the correspondent longitudinal

LSPR (LSPR corresponding to the nanorod length) is located near 750 nm, outside the wavelength range of the measurement, hence the dispersion follows the linear diffraction modes. On the contrary, the lattices with 30o, 45o, and 60o nanorod tilting all show pronounced chirality. While with both input circular polarizations, the dispersions translate progressively from 0o to 90o with increasing tilting angle, the dispersion obtained with RCP light input is always more 90o-tilting like, and the dispersion with the LCP light input is more 0o-tilting like. In addition, the lattice with 45o tilting angle 119

is in fact an achiral lattice, the chirality observed here results from the selection of the direction of k//. Hence, the chirality measured in this lattice is extrinsic chirality, and

o the LCP and RCP responses reverses if k// is rotated by 90 .

To understand the mechanism of the observed chirality, FDTD simulation was performed on both single nanorod and the nanorod lattices. The simulation shows that,

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when excited by a circularly polarized light, at the resonance wavelength, the LSPR oscillates along one of the diagonal of the nanorods, as shown in figure 6.3. This is because that at a given wavelength, the longitudinal mode and the transverse mode exhibit a phase difference. At the resonant wavelength (around 640 nm), such phase shift is nearly π⁄ 2 (figure 6.4 (a)-(c) and (d)-(f)) at the near field, which makes it effectively a quarter waveplate. Therefore, when the nanorod is excited by a circularly polarized light, an additional π⁄ 2 phase difference is added between the two linear polarizations of the incident beam, hence the phase difference between the longitudinal and transverse mode becomes 0 or π, resulting a linearly polarized near field resonance.

Depending on the helicity of the light, these two modes interfere distractively along one diagonal, and constructively along the other diagonal, producing two degenerate diagonal LSPR modes.

Figure 6.3 Spatial electric field distribution of a 110×170 nm Ag nanorod under (a) LCP and (b) RCP light illumination at 645 nm wavelength.

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Figure 6.4 Phase difference between the longitudinal and transverse LSPR of a Ag nanorod (110×170 nm) at 640 nm. The nanorod is excited by a linearly polarized plane wave with its polarization indicated by the black arrow. At ωt = 0 , the electric field magnitude of the longitudinal mode reaches its maximum ((a)-(c)), and becomes nearly zero in the transverse mode ((d)-(f)). With an additional π⁄ 2 phase shift ((g)-(i)) in the transverse mode, the electric field interfere constructively along the bottom-left to up- right diagonal, and interfere destructively along the other, resulting in a diagonal mode.

When arranged into lattices, the two degenerate diagonal modes polarized along

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different directions with respect to the lattice frame, resulting in different LSPR- diffraction mode coupling, hence giving rise to different SLR dispersions (figure 6.5).

Figure 6.5 Electric field profile of Ag nanorod lattice with 45o nanorod tilting illuminated by (a) LCP and (b) RCP light. Nanorod dimension: 110×170 nm, lattice pitch 450 nm.

Although the actual mechanism is complicated, the difference between the LCP-

SLR and the RCP-SLR can be qualitatively understood by the simulation result: the

RCP-LSPR corresponds to a dipole with the tilting angle larger than the nanorod itself, hence the RCP-SLR is more 90o-tilting like, and vice versa. The far-field angle-resolved reflectance spectra under circularly polarized light excitation were also calculated by

FDTD simulation (figure 6.6 (a) and (b)), showing perfect agreement with the experimental data. The circular dichroism (CD), defined as (RLCP-RRCP)/(RLCP+RRCP) is calculated as a function of both incident angle and wavelength (Figure 6.6 (c)).

Pronounced CD only appears near the SLR dispersion lines, which further proves that the CD results solely form the LSPR-lattice coupling. 123

These lattices were further studied by resolving both the input and output circular polarizations via decomposing the reflected light from the sample into LCP and RCP components by placing a second quarter wave plate and a polarizer in the reflected light path. For an isotropic surface, such as SiO2, under normal illumination of a circularly polarized light, the phase difference of the two perpendicular polarization directions is maintained in the reflected beam, while the propagation direction is reversed. Hence the handedness of the reflected beam is reversed. On the contrary, the reflected beam from the designed plasmonic lattices illuminated by a circularly polarized light can contain both the LCP and RCP components, as the lattices serve as waveplates that rotate the polarization of the incident light. Figure 6.7 shows the measured reflectance spectra of the 0o and 30o tilting lattices with different input and output helicities.

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For the achiral 0o lattice, as expected, the L in-R out and the R in-L out (co-polarization reflection, figure 6.7 (b)&(c)), as well as the L in-L out and the R in-R out (cross- polarization reflection, figure 6.7 (a)&(d)) spectra show identical dispersions, indicating no chirality in this lattice. In contrast, for the chiral 30o lattice, while the two co-polarization reflection spectra (figure 6.7 (f)&(g)) remained nearly identical,

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significant chirality appears in the cross-polarization reflection spectra (figure 6.7

(e)&(h)): The R in-R out reflectance present clear, strong lattice modes, while the L in-

L out spectrum only shows weak dispersions. Moreover, whereas only the lattice diffraction modes were observed in cross-polarization reflection spectra, the co- polarization reflection spectra exhibit strong LSPR-diffraction mode coupling induced by the diagonal LSPR mode appeared near 640 nm. Such Fano-type coupling results in a peak-like feature near the original diffraction mode’s dispersion lines. Therefore, the reflectance intensities of the co- and cross- polarizations display nearly opposite features, i.e., a peak in the co-polarization reflectance corresponds closely to a dip in the cross-polarization reflectance.

6.4 Chiral exciton-plasmon coupling between MoS2 and chiral plasmonic lattices

After assigning the SLRs in the Ag nanorod arrays with different circular polarizations, we studied the chirality in exciton-plasmon coupling by patterning the nanorod arrays on top of monolayer MoS2. Here, we still decompose the reflected beam into the LCP and RCP components while illuminating the sample with LCP and RCP lights, analogous to what we did in figure 6.7. The nanorods are tilted by 30o with respect to k//, and their dimensions were chosen to be 100×160 nm, to account for the redshift of the LSPR when the lattice is coupled to MoS2 (see chapter 3), while the lattice pitches were kept at 450 nm. Plotted in figure 6.8 (a) and (b), both the co- polarization reflectance spectra show similar and pronounced strong coupling with A

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excitons, and the dispersions can be nicely fitted to a COM with a single LSPR located at ~645 nm, which is consistent with the observations in bare plasmonic lattices. In both cases, the exciton-LSPR and exciton-diffraction mode coupling strengths are ~50 meV and ~10 meV, respectively, while the LSPR-diffraction mode coupling strengths are

~120 meV.

Interesting contrast occurs in the cross-polarization reflectance spectra (figure 6.9).

While in the R in-R out spectrum (figure 6.9 (a)), strong coupling was observed

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between the A exciton and SLRs, as indicated by the normal mode splitting near the A exciton in the dispersion (figure 6.9 (b)), the L in-L out polarization (figure 6.9 (c)) only results in weak coupling, as no anti-crossing was observed near the A exciton position.

Therefore, the chirality of the designed lattice not only leads to quantitative coupling strengths change, but also changes the nature of the exciton-plasmon coupling. The exciton-diffraction mode coupling strength in figure 6.9 (a) is calculated to be ~25 meV.

6.5 Conclusion

To conclude, we designed and studied chiral plasmonic lattices composed of achiral plasmonic nanorods and with significant chirality induced by the LSPR-lattice coupling.

We then coupled these chiral plasmonic lattices with monolayer MoS2 and observed, for the first time, chiral exciton-plasmon coupling, with the coupling strengths

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effectively controlled by the lattice design, and the circular polarizations of the input and output light, which tunes the coupling into either weak or strong coupling regimes.

By addressing the light-matter coupling in planar chiral structures, this study may shed lights on novel active and tunable chiral metasurface device designs, as well as opens new possibilities in manipulating the polaritons spin degree of freedom.

References:

1 Zhao, Y., Askarpour, A., Sun, L., Shi, J., Li, X. & Alù, A. in CLEO: QELS_Fundamental Science. FM3K. 6 (Optical Society of America). 2 Maoz, B. M., Chaikin, Y., Tesler, A. B., Bar Elli, O., Fan, Z., Govorov, A. O. & Markovich, G. Amplification of chiroptical activity of chiral biomolecules by surface plasmons. Nano Lett. 13, 1203-1209, (2013). 3 Hendry, E., Mikhaylovskiy, R., Barron, L., Kadodwala, M. & Davis, T. Chiral electromagnetic fields generated by arrays of nanoslits. Nano Lett. 12, 3640-3644, (2012). 4 Yu, N., Aieta, F., Genevet, P., Kats, M. A., Gaburro, Z. & Capasso, F. A broadband, background-free quarter-wave plate based on plasmonic metasurfaces. Nano Lett. 12, 6328-6333, (2012). 5 Zhao, Y. & Alù, A. Manipulating light polarization with ultrathin plasmonic metasurfaces. Phys. Rev. B 84, 205428, (2011). 6 Gansel, J. K., Thiel, M., Rill, M. S., Decker, M., Bade, K., Saile, V., von Freymann, G., Linden, S. & Wegener, M. Gold helix photonic metamaterial as broadband circular polarizer. Science 325, 1513-1515, (2009). 7 Ye, W., Zeuner, F., Li, X., Reineke, B., He, S., Qiu, C.-W., Liu, J., Wang, Y., Zhang, S. & Zentgraf, T. Spin and wavelength multiplexed nonlinear metasurface holography. Nature Communications 7, (2016). 8 Khorasaninejad, M., Ambrosio, A., Kanhaiya, P. & Capasso, F. Broadband and chiral binary dielectric meta-holograms. Science advances 2, e1501258, (2016). 9 Cotrufo, M., Osorio, C. I. & Koenderink, A. F. Spin-Dependent Emission from Arrays of Planar Chiral Nanoantennas Due to Lattice and Localized Plasmon Resonances. ACS Nano 10, 3389-3397, (2016). 129

10 Kopp, V. I., Zhang, Z.-Q. & Genack, A. Z. Lasing in chiral photonic structures. Progress in Quantum Electronics 27, 369-416, (2003). 11 Valev, V., Smisdom, N., Silhanek, A., De Clercq, B., Gillijns, W., Ameloot, M., Moshchalkov, V. & Verbiest, T. Plasmonic ratchet wheels: switching circular dichroism by arranging chiral nanostructures. Nano Lett. 9, 3945-3948, (2009). 12 Amo, A., Liew, T., Adrados, C., Houdré, R., Giacobino, E., Kavokin, A. & Bramati, A. Exciton–polariton spin switches. Nat. Photonics 4, 361-366, (2010). 13 Shelykh, I., Johne, R., Solnyshkov, D. & Malpuech, G. Optically and electrically controlled polariton spin transistor. Phys. Rev. B 82, 153303, (2010). 14 Johne, R., Shelykh, I., Solnyshkov, D. & Malpuech, G. Polaritonic analogue of Datta and Das spin transistor. Phys. Rev. B 81, 125327, (2010). 15 Cerna, R., Léger, Y., Paraïso, T. K., Wouters, M., Morier-Genoud, F., Portella-Oberli, M. T. & Deveaud, B. Ultrafast tristable spin memory of a coherent polariton gas. Nature communications 4, (2013). 16 Wang, Z., Wang, Y., Adamo, G., Teh, B. H., Wu, Q. Y. S., Teng, J. & Sun, H. A Novel Chiral Metasurface with Controllable Circular Dichroism Induced by Coupling Localized and Propagating Modes. Advanced Optical Materials 4, 883-888, (2016).

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Chapter 7. Future directions and outlook

In this thesis, we investigated light-matter interactions in MoS2 integrated with plasmonic lattices in different exciton-plasmon coupling regimes, and shown the manipulation of the exciton-plasmon coupling in exciton-plasmon lattices via lattice design, external field, and inducing chirality. Here, we will propose two possible future directions to further understand the exciton-plasmon coupling phenomena, to utilize the unique valley physics of 2D TMDs and to move towards practical polaritonic devices:

(1) Study the valley-selected strong exciton-plasmon coupling in different plasmonic lattices to engineer the valley physics of MoS2. (2) Active and electrically tunable metasurfaces based on strongly coupled MoS2-plamsonic lattice system.

7.1 Valley-selective strong exciton-plasmon coupling

As discussed in chapter 1, resulted from the inversion symmetry breaking and strong spin-orbit coupling, monolayer TMDs exhibit spin-valley locking, whereas each valley couples to only one helicity of light. This unique property draws a great deal of attention recently and leads to the emerging of a new research area named valleytronics1,2. In strong coupling regime, in particular, exciton-polaritons have been shown to enhance the valley polarization, and exotic quantum phenomena such as optical valley Hall effect, the formation of spatial valley-polarized domains via polariton-polariton scattering, has been recently proposed. 3

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As we demonstrated in chapter 6, plasmonic lattices provide unique opportunities in manipulating polaritons spin degree of freedom, which is not easily accessible in conventional photonic cavities. Here, focusing on near-field plasmonic resonances and exciton-plasmon interaction, we propose valley-selected exciton-plasmon coupling.

More specifically, by plasmonic lattice design, it may be possible to excite plasmonic resonances with different near field polarizations under circularly polarized light illumination, which can allow strong exciton-plasmon coupling involving only one valley, or with both valleys coherently. The nanorods discussed in Chapter 6, for example, exhibit diagonal LSPR modes with nearly linear polarization, which contain nearly equal contributions of and spins. On the other hand, different nanostructure designs may result in LSPR with circularly polarized near field.

Therefore, plasmonic lattices composed of these two types of nanostructures are expected to lead to very different valley-exciton-plasmon coupling phenomenon. More sophisticated lattice designs may allow chiral valley-exciton coupling, e.g., strong coupling with one valley and weak coupling with the other, to further the valley degree of freedom in strong coupling regime. Such phenomenon can be investigated via examining the dispersion evolution while lifting the valley degeneracy by, e.g., valley

Zeeman effect or valley optical Stark effect, which, by the way, can be interesting topics by themselves in strong coupling regime.

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Figure 7.1 the (LCP) and (RCP) components of the LSPR of a nanorod excited by a LCP light. (a) Nanorod . (b) Nanorod .

7.2 Active and electronically tunable metasurfaces.

Metasurfaces refer to a type of ultrathin artificial planar structures that can shape the electromagnetic wave fronts by inducing abrupt and controllable changes of the optical phases, magnitudes and polarizations near their surfaces4, which enable various flat optical components including waveplates5, lenses6 and holograms7. Tunable metasurfaces are of high demand to realize real time manipulation of optical response, and tunability realized by mechanically stretching8 and phase change materials9 have been lately experimentally demonstrated or theoretically proposed. Here, we propose active metasurfaces that can be electrically modulated by integrating the metasurfaces with monolayer MoS2.

Our group has recently studied Pancharatnam–Berry phase metasurfaces10 based on plasmonic nanoantenna arrays. A plasmonic nanoantenna can lead to a certain local phase discontinuity depending on its shape and orientation, therefore, by designing the

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arrangement and orientation of the nanoantennas, optical functionalities such as lenses and holograms can be realized. Figure 7.2 (a) shows an example of a metasurface designed to induce a constant gradient of phase jump. Interestingly, when we pattern these metasurfaces on MoS2 monolayer and measure the angle-resolved dispersion, they present clear SLRs and can couple strongly to the MoS2 excitons (Figure 7.2

(b)&(c)).

Figure 7.2 Strong exciton-plasmon coupling in plasmonic metasurface coupled with monolayer MoS2. (a) Silver Pancharatnam–Berry phase metasurface with constant phase shift gradient patterned on monolayer MoS2. (b)&(c) Reflectance spectra under LCP and RCP illumination measured from the device in (a), showing SLRs and strong coupling with MoS2.

These results open up the possibilities of fabricating active metasurfaces in strong coupling regime, and manipulate their optical responses electrically via applying gate voltages, analogous to what we demonstrated in Chapter 5. The tuning of the coupling strength and hence the system’s dispersion leads to pronounced change of the effective refractive index, which may ultimately control the phase shift and/or efficiency of the

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metasurface. If necessary, MoS2 can be etched into several electrically isolated regions to allow independent electrical control of each region, hence realizing greater tunability of the metasurface functionalities.

References:

1 Schaibley, J. R., Yu, H., Clark, G., Rivera, P., Ross, J. S., Seyler, K. L., Yao, W. & Xu, X. Valleytronics in 2D materials. Nature Reviews Materials 1, 16055, (2016). 2 Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS 2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802, (2012). 3 Bleu, O., Solnyshkov, D. & Malpuech, G. Optical Valley Hall Effect based on Transitional Metal Dichalcogenide cavity polaritons. arXiv preprint arXiv:1611.02894, (2016). 4 Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139-150, (2014). 5 Yu, N., Aieta, F., Genevet, P., Kats, M. A., Gaburro, Z. & Capasso, F. A broadband, background-free quarter-wave plate based on plasmonic metasurfaces. Nano Lett. 12, 6328-6333, (2012). 6 Aieta, F., Genevet, P., Kats, M. A., Yu, N., Blanchard, R., Gaburro, Z. & Capasso, F. Aberration-free ultrathin flat lenses and axicons at telecom wavelengths based on plasmonic metasurfaces. Nano Lett. 12, 4932-4936, (2012). 7 Ni, X., Kildishev, A. V. & Shalaev, V. M. Metasurface holograms for visible light. Nature communications 4, (2013). 8 Ee, H.-S. & Agarwal, R. Tunable metasurface and flat optical zoom lens on a stretchable substrate. Nano Lett. 16, 2818-2823, (2016). 9 Wang, Q., Rogers, E. T., Gholipour, B., Wang, C.-M., Yuan, G., Teng, J. & Zheludev, N. I. Optically reconfigurable metasurfaces and photonic devices based on phase change materials. Nat. Photonics 10, 60-65, (2016). 10 Lin, D., Fan, P., Hasman, E. & Brongersma, M. L. Dielectric gradient metasurface optical elements. Science 345, 298-302, (2014).

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