Chapter One - Metasurfaces from [formula omitted]-materials

<p indent="0mm">Lithium niobate (LiNbO₃, LN) crystal has a large second-order nonlinear coefficient (<italic>d</italic>₃₃=25.2 pm/V@1064 nm), wide transparent window (0.35–5 μm), and stable periodic microdomain structure preparation, which is a good platform for the study and application of second-order nonlinear optical effects. Lithium niobate thin film (LNTF) is regarded as a promising integrated photonics platform due to its excellent linear and nonlinear optical properties. As the basic unit of an integrated optical system, lithium niobate micro/nano waveguide has been studied as a transmission and control device, and it shows excellent second-order nonlinear optical characteristics. The second-order nonlinearity plays an important role in modern optics, including second-harmonic generation (SHG), sum- and difference-frequency generation, parametric down conversion, and parametric oscillation. Efficient and compact wavelength converters based on second-order nonlinearity are key components for a wide range of applications, including entangled photon sources, optical parametric oscillators, and optical parametric amplifiers. The second-order nonlinear polarization intensity is proportional to the square of the electric field intensity. Micro/nano optical waveguides can improve the light intensity in the device through the local characteristics of the spatial light field, to improve the conversion efficiency of the nonlinear processes. And significantly enhanced electric field strength makes the normalized nonlinear conversion efficiency of LNTF waveguides exceed that of the reverse proton<bold> </bold>exchange lithium niobate waveguides (frequency conversion efficiency 150% W^–1 cm^–2@1550 nm) by one order of magnitude. The nonlinear conversion efficiency of LNTF micro/nano waveguides can be further improved through mode phase matching (MPM) or quasi-phase matching (QPM) to optimize the spatial overlap between the eigenmodes involved in the nonlinear process. The detailed theory, fabrication and application were demonstrated in the manuscript as follows: (1) The theory of second harmonic generation. As an example of second-order nonlinear process, the factors affecting the conversion efficiency of second harmonic generation were analyzed, and can be summarized as nonlinear coefficient, mode special overlap, mode area and phase-matching condition. (2) The fabrication of periodically poled lithium niobate waveguides and periodically poled technics. Based on the micro fabrication processes such as electron beam lithography, dry etching and chemico-mechanical polishing, the propagation loss could be reduced to <sc>0.027 dB/cm.</sc> With the combination of low loss waveguides and the electrode polarization process, periodically poled lithium niobate microstructures and the detailed fabrication processes were discussed in the manuscript. (3) Efficient second harmonic generation based on MPM and QPM. It was reported that the normalized efficiency can reach 1000% W^–1 cm^–2, and we described broadband and tunable SHG in detail. (4) Spontaneous parametric down conversion. With the development of quantum information technology and its application in the fields of secure communication and precision measurement, quantum photon sources with high speed, high brightness and high purity have attracted more and more attention. Due to the strong optical confinement, the micro/nano waveguides reduce the pump power and improve the quality of generated photon pairs, which is helpful to realize the integrated optical path of quantum information processing. In summary, this paper reviews the recent development of second-order nonlinear optical effects in LNTF micro/nano waveguides. Firstly, the theory of second harmonic conversion is introduced, and then the fabrication and periodically poled techniques of LNTF micro/nano waveguides are discussed. As an example, the efficient SHG and parametric down conversion of LNTF waveguides were detailedly demonstrated. The processes of mode phase matching and quasi-phase matching technics, tunable SHG and wideband frequency doubling effect were emphatically investigated.

Second-order nonlinearity in solids gives rise to a plethora of unique physical phenomena ranging from piezoelectricity and optical rectification to optical parametric amplification, spontaneous parametric down-conversion and the generation of entangled photon pairs. Monolayer transition metal dichalcogenides, such as MoS2, exhibit one of the highest known second-order nonlinear coefficients. However, the monolayer nature of these materials prevents the fabrication of resonant objects exclusively from the material itself, necessitating the use of external structures to achieve the optical enhancement of nonlinear processes. Here we exploit the 3R phase of a molybdenum disulfide multilayer for resonant nonlinear nanophotonics. The lack of inversion symmetry—even in the bulk of the material—provides a combination of massive second-order susceptibility, extremely high and anisotropic refractive index in the near-infrared region (n > 4.5) and low absorption losses, making 3R-MoS2 highly attractive for nonlinear nanophotonics. We demonstrate this by fabricating 3R-MoS2 nanodisks of various radii, which support resonant anapole states, and observing substantial (>100-fold) enhancement of second-harmonic generation in a single resonant nanodisk compared with an unpatterned flake of the same thickness. The enhancement is maximized at the spectral overlap between the anapole state of the disk and the material resonance of the second-order susceptibility. Our approach unveils a powerful tool for enhancing the entire spectrum of optical second-order nonlinear processes in nanostructured van der Waals materials, thereby paving the way for nonlinear and quantum high-index transition metal dichalcogenide nanophotonics.

We present an analytical method involving the nonlinear polarizability tensor for calculating the second harmonic generation (SHG) intensity for a nonlinear sandwich metasurface. The theoretical model is that a nonlinear meta-atom can be considered as a nonlinear electric- and magnetic-dipole, which allows the nonlinear polarizability tensors to be calculated from the far-field of the scattered SHG. The results suggest that the simultaneous excitation of electric and magnetic plasmonic resonances improves the SHG intensity, which is quantitatively consistent with the ones by the finite-difference time-domain method. Therefore, various nonlinear metasurfaces can be designed for applications in nonlinear micro-nano photonic devices.

Metasurfaces are artificial two-dimensional (2D) planar surfaces that consist of subwavelength ‘meta-atoms’ (i.e. metallic or dielectric nanostructures). They are known for their capability to achieve better and more efficient light control in comparison to their traditional optical counterparts. Abrupt and sharp changes in the electromagnetic properties can be induced by the metasurfaces rather than the conventional gradual accumulation that requires greater propagation distances. Based on this feature, planar optical components like mirrors, lenses, waveplates, isolators and even holograms with ultrasmall thicknesses have been developed. Most of the current metasurface studies have focused on tailoring the linear optical effects for applications such as cloaking, lens imaging and 3D holography. Recently, the use of metasurfaces to enhance nonlinear optical effects has attracted significant attention from the research community. Benefiting from the resulting efficient nonlinear optical processes, the fabrication of integrated all-optical nano-devices with peculiar functionalities including broadband frequency conversions and ultrafast optical switching will become achievable. Plasmonic excitation is one of the most effective approaches to increase nonlinear optical responses due to its induced strong local electromagnetic field enhancement. For instance, continuous phase control on the effective nonlinear polarizability of plasmonic metasurfaces has been demonstrated through spin-rotation light coupling. The phase of the nonlinear polarization can be continuously tuned by spatially changing the meta-atoms’ orientations during second and third harmonic generation processes, while the nonlinear metasurfaces also exhibit homogeneous linear properties. In addition, an ultrahigh second-order nonlinear susceptibility of up to 104 pm V−1 has recently been reported by coupling the plasmonic modes of patterned metallic arrays with intersubband transition of multi-quantum-well layered substrate. In order to develop ultra-planar nonlinear plasmonic metasurfaces, 2D materials such as graphene and transition metal dichalcogenides (TMDCs) have been extensively studied based on their unique nonlinear optical properties. The third-order nonlinear coefficient of graphene is five times that of gold substrate, while TMDC materials also exhibit a strong second-order magnetic susceptibility. In this review, we first focus on the main principles of planar nonlinear plasmonics based on metasurfaces and 2D nonlinear materials. The advantages and challenges of incorporating 2D nonlinear materials into metasurfaces are discussed, followed by their potential applications including orbital angular momentum manipulating and quantum optics.

Second-order nonlinear χ2 processes hold the key to realizing various promising classical and quantum applications. Only conventional non-centrosymmetric materials like aluminium nitride (AlN) and lithium niobate (LN) exhibit a strong second-order nonlinearity. While germanium (Ge) has the advantage of mature foundry processing due to its complementary metal-oxide-semiconductor (CMOS) compatibility compared to conventional χ2 materials, it has a weak second-order nonlinearity owning to its inversion symmetry. It is predicted that exploiting micro-scale strain gradients induced by silicon nitride (SiN) stressors can break the inversion symmetry of Ge and enable more efficient second harmonic generation (SHG) in mid-infrared (MIR). We herein demonstrate SHG in visible and telecom S-band ranges by pumping our germanium-on-insulator (GOI) sample with a tunable femtosecond pulse laser. The signature quadratic power dependence curve of SHG has also been experimentally observed. In this report, we also propose a novel approach to breaking the inversion symmetry of Ge, which can amplify its weak second-order nonlinearity. We designed a Ge micro-bridge with a periodically changing nano-scale strain gradient that is orders of magnitude higher than the previously proposed structures utilizing SiN stressors. This results in a 3-orders of magnitude enhancement in χ2 according to both a classic anharmonic model and density potential theory. Our work paves the way toward a CMOS compatible and high χ2 nonlinear material for integrated photonic applications.

Monolayer transition metal dichalcogenides (TMDs) are widely used for integrated optical and photoelectric devices. Owing to their broken inversion symmetry, monolayer TMDs have a large second-order optical nonlinearity. However, the optical second-order nonlinear conversion efficiency of monolayer TMDs is still limited by the interaction length. In this work, we theoretically study the second harmonic generation (SHG) from monolayer tungsten sulfide (WS2) enhanced by a silica microsphere cavity. By tuning the position, size, and crystal orientation of the material, second-order nonlinear coupling can occur between the fundamental pump mode and different second harmonic cavity modes, and we obtain an optimal SHG conversion efficiency with orders of magnitude enhancement. Our work demonstrates that the microsphere cavity can significantly enhance SHG from monolayer 2D materials under flexible conditions.

We propose a simple scheme of degenerate spontaneous parametric down-conversion (SPDC) in nonlinear metasurfaces or photonic crystal slabs with quasi-guided modes. It employs a band crossing between even- and odd-parity quasi-guided mode bands inside the light cone (above the light line) and a selection rule in the conversion efficiency of the SPDC. The efficiency can be evaluated fully classically via the inverse process of noncollinear second-harmonic generation (SHG). As a toy model, we study the SPDC and SHG in a monolayer of noncentrosymmetric spheres and confirm that the scenario works well to enhance the SPDC.

In this thesis, I overcome the challenges and fill the gaps in knowledge for the design and analysis of photonic crystal slab waveguides (PCSWs) as spontaneous parametric down-conversion (SPDC) sources of photon-pairs, as well as to investigate their potential for engineering the properties of the photon-pair quantum state. I have developed the required formalism for analyzing both the quantum process of SPDC and its classical counterpart of second-harmonic generation (SHG). In studying SHG, I verified my formalism through comparing its results with direct nonlinear simulations. In these formulations, special attention was given to treating lossy modes, as they prove to be an inherent part of the SPDC designs in PCSWs. Moreover, I have found a practical set of PCSW designs, phase-matched for three-wave-mixing processes, while demonstrating that PCSWs can offer a strong control over the phase-matching configuration. This includes reaching phase-matching between modes of different propagation directions, reaching simultaneous phase-matching between multiple processes, and controlling the group velocity of the modes at the point of phase-matching. These capabilities proved to be the key to discovering the unique strength of PCSWs for the SPDC application. Through the use of various phase-matching configurations, I showed how compact SPDC sources can be designed using PCSWs that are capable of creating entanglement and tuning its extent in different degrees of freedom, with specific examples for path and spectral degrees of entanglement, all in a fully integrated way and directly at the generation step. This work also includes my experimental results on characterizing lithium niobate nanostructured ridge waveguides, demonstrating phase-matched SHG. Finally, I propose the concept of atom-mediated SPDC, for interfacing a single-emitter source with a photon-pair source, relying on the bandgap evanescent modes of a periodic waveguide.

Electrically reconfigurable nonlinear metasurfaces provide dynamic control over nonlinear phenomena such as second-harmonic generation (SHG), unlocking novel applications in signal processing, light switching, and sensing. Previous methods, like electric-field-induced SHG in plasmonic metasurfaces and Stark-tuned nonlinearities in quantum well metasurfaces, face limitations due to weak SHG responses from metals and mid-infrared constraints of quantum wells, respectively. Addressing the need for efficient SHG control in the visible and near-infrared ranges, we present a novel approach using the electro-optic (EO) effect to modulate SHG. By leveraging the exceptional EO and SHG properties of lithium niobate (LN), we integrate the EO effect with SHG within a metasurface framework for the first time. Our LN metasurface achieves an 11.3% modulation depth in SHG amplitude under a ±50 V alternating voltage. These results open new avenues for reconfigurable photonic applications. including tunable nonlinear light sources, quantum optics, and nonlinear information processing.

Lithium niobate is a critical material extensively used in nonlinear optics. The recent development of nanophotonic lithium niobate devices further extends their importance with enhanced nonlinearity and scalability. However, the performance of nonlinear optical processes in lithium niobate is influenced by the photorefractive effect. In this work, we study the impact of the photorefractive effect on second-order nonlinear optical processes in nanophotonic lithium niobate waveguides. We simulate the parametric down-conversion for squeezed light generation and second-harmonic generation in nanophotonic lithium niobate waveguides, considering the photorefractive effect. The squeezing generation with parametric down-conversion only experiences a constant wavelength shift as the refractive index change remains constant. On the other hand, the second-harmonic generation spectrum is distorted, and a decrease in nonlinear efficiency is observed. This is because the strength of the photorefractive effect varies along the waveguide. We further show that the ideal efficiency of second-harmonic generation can be recovered by the adapted poling technique, where the phase matching condition change caused by the photorefractive effect is compensated by adjusting the poling period of lithium niobate waveguides. Eventually, we analyze the cascaded process of second-harmonic generation and parametric down-conversion for squeezed light generation, and show that squeezing level up to 17.6 dB can be realized using 10 mW power with current performance of nanophotonic lithium niobate devices.

We present a detailed theoretical and numerical analysis on the temporal-spectral-spatial evolution of a high-peak-power femtosecond laser pulse in two sets of systems: a pure lithium niobate (LN) plate and a periodically poled lithium niobate (PPLN) plate. We develop a modified unidimensional pulse propagation model that considers all the prominent linear and nonlinear processes and carried out the simulation process based on an improved split-step Fourier transformation method. We theoretically analyze the synergic action of the linear dispersion effect, the second-order nonlinearity (2nd-NL) second-harmonic generation (SHG) effect, and the third-order nonlinearity (3rd-NL) self-phase modulation (SPM) effect, and clarify the physical mechanism underlying the peculiar and diverse spectral broadening patterns previously reported in LN and PPLN thin plate experiments. Such analysis and discussion provides a deeper insight into the synergetic contribution of these linear and nonlinear effects brought about by the interaction of a femtosecond laser pulse with the LN nonlinear crystal and helps to draw a picture to fully understand these fruitful optical physical processes, phenomena, and laws.

The two-photon state with spatial entanglement is an essential resource for testing fundamental laws of quantum mechanics and various quantum applications. Its creation typically relies on spontaneous parametric downconversion in bulky nonlinear crystals where the tunability of spatial entanglement is limited. Here, we predict that ultrathin nonlinear lithium niobate metasurfaces can generate and diversely tune spatially entangled photon pairs. The spatial properties of photons including the emission pattern, rate, and degree of spatial entanglement are analyzed theoretically with the coupled mode theory and Schmidt decomposition method. We show that by leveraging the strong angular dispersion of the metasurface, the degree of spatial entanglement quantified by the Schmidt number can be decreased or increased by changing the pump laser wavelength and a Gaussian beam size. This flexibility can facilitate diverse quantum applications of entangled photon states generated from nonlinear metasurfaces.

The optical nonlinear effects can provide different advanced electromagnetic functionalities, such as wave mixing and phase conjugation, which can be applied in a variety of new applications. However, these effects usually suffer from extremely weak nature and require high input intensity values in order to be excited. Interestingly, the large third order nonlinearity of graphene, along with the strong field confinement stemming from its plasmonic behavior, can be utilized to enhance several relative weak nonlinear effects at infrared (IR) and terahertz (THz) frequencies. Towards this goal, various nonlinear graphene metasurfaces are presented in this work to effectively increase the efficiency of different optical nonlinear effects and, as a result, decrease the required input intensity needed to be excited. In particular, we will show that the efficiency of four-wave mixing (FWM) can be improved by several orders of magnitude by using a nonlinear metasurface composed of patterned graphene ribbons, a dielectric interlayer, and a metallic reflector acting as substrate. We also demonstrate that the self-phase modulation (SPM) nonlinear process can be enhanced by using an alternative graphene nonlinear metasurface, operating as coherent perfect absorber, leading to a pronounced shift in the resonant frequency of the coherent perfect absorption (CPA) effect of this structure as the input intensity of the impinging incident waves is increased. This property will provide a robust mechanism to dynamically tune and switch the CPA process. Furthermore, it will be presented that strong negative reflection and refraction can be achieved by a single graphene monolayer film due to the enhancement of another nonlinear process, known as phase conjugation. This nonlinear process is envisioned to be used in the construction of a perfect imaging device with subwavelength resolution.

3D polarization structures have received growing interest due to their unique optical properties and extra information‐carrying capacity. Although the second harmonic generation (SHG) from nonlinear optical metasurfaces has enabled advanced polarization control, the realization of 3D polarization structures has not been reported. This study proposes and experimentally demonstrates a nonlinear metasurface approach to simultaneously generate SHG beams and create 3D polarization structures. Upon the illumination of a linearly polarized fundamental wave (FW), the efficacy of this method is exemplified through the simulation and experimental demonstration of various SHG polarization structures ranging from rings to 3D polarization knots. The SHG polarization distributions on these structures can be further modulated by continuously changing the linear polarization state of the FW. The 3D polarization control with nonlinear metasurfaces offers a new approach to generate SHG beams with customized 3D polarization distributions, which are promising for high‐dimensional optical information processing and encryption.

Metasurfaces are highly effective at manipulating classical light in the linear regime; however, effectively controlling the polarization of nonclassical light generated from nonlinear resonant metasurfaces remains a challenge. Here, we present a solution by achieving polarization engineering of frequency-nondegenerate biphotons emitted via spontaneous parametric down-conversion in GaAs metasurfaces, utilizing quasi-bound states in the continuum (qBIC) resonances to enhance biphoton generation. Through comprehensive polarization tomography, we demonstrate that the emitted photons' polarization directly reflects the qBIC mode's far-field properties. Furthermore, we show that both the type of qBIC mode and the symmetry of the meta-atoms can be tailored to control each single-photon polarization state, and that the subsequent two-photon polarization states are nearly separable, offering potential applications in the heralded generation of single photons with adjustable polarization. This work provides a significant step toward utilizing metasurfaces to generate quantum light and engineer their polarization, a critical aspect for future quantum technologies.