Two-dimensional materials for tunable and nonlinear metaoptics

Fig. 1. (a) Electrons and holes bound into excitons for the 3D bulk and 2D materials. (b) The transition from 3D to 2D is expected to lead to an increase of both the bandgap and the exciton binding energy (indicated by the dashed red line). (c) Binding energy of excitons in some common 3D and 2D semiconductors. The yellow dotted line represents the thermal energy at RT. Panels (a) and (b) were reproduced with permission from Ref. 51 © 2014—APS, and panel (c) was reproduced with permission from Ref. 52 © 2022—AIP.

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Fig. 2. (a) Illustration of the exciton and trion. (b) Optical absorption spectrum of an h-BN-encapsulated ${WS}_{2}$ monolayer measured at $T = 5 K$ . (c) Experimental and fitted spectra for $n = 1$ states, where shaded green and blue regions represent the contributions from trions and excitons, respectively. (d) Zoomed-in view highlighting ( $n = 2$ ) excited state trions and excitons. (e) Cavity-enhanced exciton-trion resonance at RT. (f) ${WS}_{2}$ trion binding energy measured at RT. Panels (b)–(d) were reproduced with permission from Ref. 56 © 2019—APS, and panels (e) and (f) were reproduced with permission from Ref. 58 © 2023—Wiley.

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$Excitonic metaoptics working at low temperature. (a) Micrograph of the measured heterostructure. The MoSe2 monolayer is encapsulated between 33 nm (top) and 7 nm (bottom) thick h-BN layers. (b) Interaction of an incident field with a MoSe2 monolayer. (c) Gate voltage (Vg) dependence of the maximal extinction of transmitted light using the exciton resonance. (d) Schematic of the exciton-based TMDC metaoptics for dynamic beam steering. (e) Beam steering angle under the applied asymmetric voltage gradient. (f) Voltage and spectral dependence of the diffraction efficiency. Panels (a)–(c) were reproduced with permission from Ref. 59 © 2018—APS, and panels (d)–(f) were reproduced with permission from Ref. 61 © 2023—ACS.$

Fig. 3. Excitonic metaoptics working at low temperature. (a) Micrograph of the measured heterostructure. The ${MoSe}_{2}$ monolayer is encapsulated between 33 nm (top) and 7 nm (bottom) thick h-BN layers. (b) Interaction of an incident field with a ${MoSe}_{2}$ monolayer. (c) Gate voltage ( $V_{g}$ ) dependence of the maximal extinction of transmitted light using the exciton resonance. (d) Schematic of the exciton-based TMDC metaoptics for dynamic beam steering. (e) Beam steering angle under the applied asymmetric voltage gradient. (f) Voltage and spectral dependence of the diffraction efficiency. Panels (a)–(c) were reproduced with permission from Ref. 59 © 2018—APS, and panels (d)–(f) were reproduced with permission from Ref. 61 © 2023—ACS.

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Fig. 4. Excitonic metaoptics working at RT. (a) A Fresnel zone plate lens made on monolayer ${WS}_{2}$ . (b) Excitonic modulation of the light intensity in the focusing spot of the ${WS}_{2}$ zone plate lens. (c) A monolayer ${WS}_{2}$ free-space optical modulator based on a MOS capacitor configuration. (d) Modulation ratio (green) and absolute reflectance change (yellow) spectra. A 3 dB modulation ratio and a 10% reflectance change are observed in the experiment. (e) $Al / {Al}_{2} O_{3}$ cavity effect to enhance the excitonic resonance of monolayer ${WS}_{2}$ . (f) Dynamic phase and amplitude tuning with enhanced excitonic and trionic resonances in monolayer ${WS}_{2}$ . Panels (a) and (b) were reproduced with permission from Ref. 62 © 2020—Nature, panels (c) and (d) were reproduced with permission from Ref. 63 © 2023—Nature, and panels (e) and (f) were reproduced with permission from Ref. 58 © 2023—Wiley.

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Fig. 5. Tunable graphene plasmon polaritons for mid-IR applications. (a) Schematic of tunable graphene plasmonic resonator for mid-IR radiation. (b) Carrier density dependence of the change in emissivity. (c) Conceptual view of tunable graphene plasmonic biosensor. (d) Extinction spectra of the sensor for bias voltages from $- 20$ to $- 130 V$ before (dashed curves) and after (solid curves) protein bilayer formation. (e) Graphene carrier density ( $n_{s}$ ) and Fermi energy ( $E_{F}$ ) were extracted from experimental IR extinction spectra at different voltages. (f) The permittivity of the protein bilayer extracted from the experimental IR spectra (solid red curves) compared with the permittivity extracted from IR reflection absorption spectroscopy (IRRAS) and ellipsometry measurements (dashed black curves). Panels (a) and (b) were reproduced from Ref. 80 with a CC license, and panels (c)–(f) were reproduced with permission from Ref. 82 © 2015—AAAS.

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Fig. 6. Tunable 2D plasmon polaritons in near-IR: (a) measurement configurations of tunable ${NbSe}_{2}$ plasmonics, (b) electrostatic-induced gating principle using ion gel. (c) Normalized electric field intensity as a function of the distance from the surface of ${NbSe}_{2}$ and ITO nanoribbons. (d) Tunable plasmonic resonance with varying gate voltage. (e) Schematic diagram of electron-excited MXene plasmon via EELS. (f) Diagram of the lattice structure and the chemical compositions of MXene. (g) High-angle annular dark-field transmission electron microscopy image of MXene film. (h) Experimental EELS spectra in MXene film. Panels (a)–(d) were reproduced with permission from Ref. 91 © 2021—Wiley, and panels (e)–(h) were reproduced with permission from Ref. 92 © 2022—AAAS.

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Fig. 7. Tunable PhPs. (a) Schematic of the s-SNOM measurements for gate-tuning PhPs in a square h-BN nanoantenna. (b) Near-field images of PhPs in an h-BN nanoantenna with different graphene Fermi levels. (c) Corresponding calculated images of PhPs. (d) Calculated near-field mid-IR spectra of the h-BN nanoantenna with different graphene Fermi levels. (e) Schematic of the graphene/ $α - {MoO}_{3}$ heterostructure on top of an $Au - {SiO}_{2} - Au$ in-plane sandwich substrate. (f) Isofrequency hybrid polaritons dispersion contours for Au and ${SiO}_{2}$ substrates at $910 {cm}^{- 1}$ . (g) Experimentally measured near-field amplitude image of hybrid polaritons showing partial focusing. (h) Experimentally measured hybrid PhP on a controlled Au substrate. Panels (a)–(d) were reproduced from Ref. 102 with a CC license, and panels (e)–(h) were reproduced from Ref. 103 with a CC license.

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Fig. 8. SHG from ${MoS}_{2}$ . (a) Schematic representation of the SHG using ${MoS}_{2}$ nanodisks. (b) Measured (dot) and calculated (curve) scattering spectra of ${MoS}_{2}$ nanodisk metasurface for different disk diameters (550 nm for blue and 300 nm for green). (c) Measured second-harmonic signal from a single nanodisk for different pump powers. (d) Mapping of second-harmonic intensity over the nanodisk array at a pump wavelength of 900 nm. (e) Measured scattering spectrum from a ${MoS}_{2}$ nanoparticle. (f) Measured second-harmonic signal from a ${MoS}_{2}$ nanoparticle shown in the inset of panel (e) for different pump powers at a wavelength of 884 nm. (g) Schematic representation of the SHG in 3R- ${MoS}_{2}$ nanodisks. (h) Measured second-harmonic spectrum of 3R- ${MoS}_{2}$ nanodisks with different disk diameters at a pump wavelength of 910 nm. Panels (a)–(d) were reproduced with permission from Ref. 141 © 2022—Wiley, panels (e) and (f) were reproduced with permission from Ref. 142 © 2023—Wiley, and panels (g) and (h) were reproduced from Ref. 143 with CC license.

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Fig. 9. HHG from TMD metasurfaces. (a) Concept of unidirectional SHG and THG using ${MoS}_{2}$ truncated cone metasurface. (b) Scanning electron microscope (SEM) image of the fabricated metasurface. (c) Measured transmission spectra of metasurface with different structural parameters. Measured wavelength-dependent generation of (d) THG and (e) SHG from the metasurface. (f) Schematic of ${WS}_{2}$ monolayer on a Fabry–Pérot (F-P) microcavity. (g) Measured second-harmonic intensity from the on and off cavity at an excitation wavelength of 800 nm. Panels (a)–(e) were reproduced from Ref. 145 under CC license, and panels (f) and (g) were reproduced with permission from Ref. 146 © 2022—ACS.

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Fig. 10. Quasi-BIC h-BN metasurface. (a) SEM images of the fabricated metasurface unit cell on h-BN with an increasing scaling factor and (b) the corresponding excited high-Q quasi-BIC resonance from 400 to 100 nm with an increasing scaling factor. (c) Measured second-harmonic signal from quasi-BIC metasurface. This figure is reproduced with permission from Ref. 148 © 2023—Wiley.

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Table 1. 2D materials and their nonlinear optical responses.

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Table 1. 2D materials and their nonlinear optical responses.


2D material	Nonlinear effect^a	Nonlinear coefficient^b	Emission wavelength (nm)^c	Thickness^d
Graphene	THG	42,000	263 to 1030	ML
FWM	14,000	360 to 1566	ML; FL
${MoS}_{2}$	SHG	10,000	370 to 780	ML; BL; FL
THG	2.4	520 to 660	ML
FWM	—	430 to 450	FL
${MoSe}_{2}$	SHG	5	600 to 900	ML
THG	2.2	520	ML
FWM	—	750	ML
${WS}_{2}$	SHG	900	415 to 660	ML
THG	2.4	520	ML
${WSe}_{2}$	SHG	1000	400 to 795	ML; BL
THG	1	520	ML
GaSe	SHG	240	400 to 800	ML; FL
THG	1600	520	FL
GaTe	SHG	0.115	760	7 to 57 nm
THG	2000	520	7 to 57 nm
BP	THG	1.6	520	10 nm; 1L to 4L
FWM	—	1550	4.3 nm; 18 nm
${MoTe}_{2}$	SHG	5	500	FL
${ReS}_{2}$	THG	53	505	ML
InSe	SHG	—	530	9 to 25 nm
hBN	SHG	200	405	ML; BL; FL

Table 2. 2D materials preparation methods. We summarize the key features of the common top-down approaches in 2D materials preparation for (a) exfoliation and (b) nanopatterning.

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Table 2. 2D materials preparation methods. We summarize the key features of the common top-down approaches in 2D materials preparation for (a) exfoliation and (b) nanopatterning.


Method	Typical size	Key features	Pros	Cons	Ref.
(a)
Mechanical exfoliation	nm to $μ m$	Use adhesive tapes to delaminate bulk materials, ideal for research	High-quality flakes, preserving material intrinsic properties	Limited scalability, being labor intensive, and miniature flake sizes	175–177
Liquid-phase exfoliation	nm to $μ m$	Use adhesive tapes to delaminate bulk materials, ideal for scalable production	High versatility and scalability	Reduced flake quality from solvent residue	178–180
Electrochemical exfoliation	Up to hundreds of $μ m$	Use electric fields to exfoliate materials either in solution or on electrodes, ideal for device fabrication	Large size samples, high scalability and tunability, limited environmental impact	Limited throughput	91, 181, and 182
(b)
Lithography (UV and DUV, e-beam) and etching	From $μ m$ to 10 nm	Pattern creation via lithography and etching, can achieve high resolution and integration	Being compatible with existing semiconductor processes; high precision	Potential damage from etching processes; photoresist residues	24, 37, 61, and 62
Tip or ion-assisted direct patterning	Sub-100 nm	Direct pattern writing with tip or ion offers customization and clean surfaces	Avoiding photoresist residues; enabling customized patterning	Generally slower process; higher cost for high-resolution patterns	22 and 26
Optical direct patterning	Down to 100 nm	Direct pattern writing by high-power laser offers customization and clean surfaces	Avoiding photoresist residues; enabling customized patterning	Lower resolution compared with the other two methods	23

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Zeng Wang, Kandammathe Valiyaveedu Sreekanth, Meng Zhao, Jinpeng Nong, Yincheng Liu, Jinghua Teng, "Two-dimensional materials for tunable and nonlinear metaoptics," Adv. Photon. 6, 034001 (2024)

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Paper Information

Category: Reviews

Received: Dec. 13, 2023

Accepted: Apr. 18, 2024

Published Online: May. 22, 2024

The Author Email: Teng Jinghua (jh-teng@imre.a-star.edu.sg)

DOI:10.1117/1.AP.6.3.034001

CSTR:32187.14.1.AP.6.3.034001

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