Third-Order Optical Nonlinearity in Two-Dimensional Transition Metal Dichalcogenides

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer twodimensional (2D) transition-metal dichalcogenides (TMDCs), having the formula MX2 with M = Mo, W and X = S, Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semi-classical perturbation analysis of response functions. We numerically calculate the linear chi((1))(mu nu) (-omega;omega) and nonlinear surface susceptibility tensors chi mu nu zeta eta((3)) (-omega(Sigma);omega(r),omega(s),omega(t)) with omega(Sigma) = omega(r)+ omega(s) +omega(t) . Both non-degenerate and degenerate cases are studied for thirdharmonic generation and nonlinear refractive index, respectively. Computational results obtained with no external fitting parameters are discussed regarding two recent reported experiments on MoS2 , and thus we can confirm the extraordinarily strong optical nonlinearity of TMDCs. As a possible application, we demonstrate generation of a pi/4-rotated squeezed state by means of nonlinear response of TMDCs, in a silica micro-disk resonator covered with the 2D material. Our proposed method will enable accurate calculations of nonlinear optical response, such as four-wave mixing and highharmonic generation in 2D materials and their heterostructures, thus enabling study of novel functionalities of 2D photonic integrated circuits.

Experimental and numerical investigation of two-dimensional photonic crystals for application in integrated optics

David Leuenberger

Two-dimensional (2D) photonic crystals (PhCs) at near-infrared wavelengths are promising candidates for novel integrated optics applications. The main focus being on 'all PhC' monolithically integrated optical circuits. Because of well established fabrication technologies particular emphasis is on 'quasi' 2D PhCs where a 2D lattice of air holes is etched through a planar step-index waveguide providing the optical confinement in the third dimension. This approach has been successfully demonstrated both in GaAs and InP-based systems. We have studied vertical low-index-contrast structures both in GaAs and InP. These structures suffer inherently from radiation losses that are strongly affected by the air hole depth and shape. A semi-analytical 'ε"-model' enables out-of-plane scattering to be described by an effective imaginary dielectric constant in the air-holes which can be used in 2D finite difference time domain (FDTD) calculations. The model, once validated by 3D FDTD, allows us to deduce from optical simple slab transmission measurements the structural parameters (e.g. size, depth and form of the hole). The experimental transmission spectra are obtained with the so-called 'internal light source technique' (ILS), which allows for quantitative normalised transmission measurements, thus eliminating the uncertainties due to the in-out coupling arising in alternative characterisation techniques, i.e. end-fire. The ILS technique proved to be a versatile method without stringent limits for assessing the fabrication parameters (air-filling factor and loss) but also proved to be suitable for testing building blocks. In this thesis different building blocks were fabricated in the GaAs system and analysed using diverse modeling techniques (e.g. plane wave expansion, FDTD and coupled mode theory). The first building block was used to study contra-directional coupling of the fundamental mode with higher-order modes in channel waveguides. It is an extension of the work on waveguides with symmetric periodic corrugation to the case of multi periodicity. We showed that by breaking the translational symmetry in these structures referred to as hybrid waveguides, the number of mini-stopbands is increased and not, as one could have expected, decreased. A second building block analysed to guide light around the corner, are cavity resonant bends (CRBs). As our analysis showd that CRBs work best with non-degenerate cavity modes, different low-symmetry order cavities were studied with differ coupling coefficients between cavity and waveguides. Unfortunately, the resulting peak transmission and overall performance was below our expectations. An important building block in integrated optics are directional couplers. They have a potential for applications such as 3dB-intensity splitting or channel add-drop filtering. To reduce the coupling length, transmission measurements of a series of coupler structures of different lengths were taken. In the case of two W3 waveguides separated by a single row, the coupling length proved to be very dependent on the hole diameter in the single row. For this case the experimentally determined coupling length, which has been validated by both PWE and FDTD simulations, was of the order of 350 periods which corresponds to an absolute length of about 80 μm, a value that is small for conventional optics, but rather large for the domain of PhC optics where due to the unusually high propagation losses the integrated circuit has to be kept small. This value could, however, be reduced by a factor of at least three when reducing the ratio between the barrier hole and the nominal hole radius to 0.5. Finally we studied the waveguides needed to connect the different building blocks. The standard solution are channel waveguides, line-defects obtained by omitting a number of rows of holes. An alternative approach are coupled cavity waveguides (CCWs). They not only offer the potential for waveguiding but may also be used for non-linear optics by exploiting the special dispersion properties of CCWs (e.g. low group-velocity). A tight-binding model has been set-up that describes the interaction between the neighbouring cavities and that allows one to deduce the dispersion properties of the chain from the single cavity field distribution.

EPFL2004

Accordabilité de la réponse optique des cristaux photoniques par infiltration de matériaux organiques

Pascale El-Kallassi

Photonic crystals are stuctures in which the refractive index varies periodically on the wavelength scale in one, two or three dimensions. Due to interference effects, these structures can forbid light propagation over a large spectral range called "the photonic bandgap". Integrated optics is one of the potential applications of photonic crystals in which the information can be treated as a light signal that propagates through photonic crystal-based devices, such as filters, lasers, waveguides, bends and multiplexers. The photonic crystals structures studied for integrated optics applications consist of periodic arrays of holes etched through classical semiconducteur-based planar waveguides. For any practical application, the optical properties of the fabricated components have to be tuned by external means. In this thesis, we explore a possible approach to photonic crystal tuning : the infiltration of photoactive organic materials in the holes of these photonic structures. First we considered liquid crystals, which exhibit anisotropic optical properties like birefringence due to their long-range orientational order. This latter molecular organization can be modified by external factors, i.e. temperature and electric field. Nematic liquid crystals were infiltrated in the holes of the photonic crystals to tune their properties by changing the temperature and applying an electric field. Moreover, the organization of liquid crystals in the nanometric holes were studied by optical techniques. The demand for all-optical tunable devices in integrated optical circuits led us to consider the possibility of optically tuning the response of photonic crystal structures. For this purpose, we used photo-induced phase transitions of a liquid crystal blend doped with azobenzene photochromic molecules. Since the phase transitions in these mixtures depend on the concentration of the photochromic compound and on the temperature, we studied in detail the phase diagram of the blend. The last part of this thesis focused on one of the most innovative aspects in the domain of photonic crystal tuning : selective infiltration to locally modify the optical properties of the photonic structures. We used the photopolymerization of acrylate monomers by ultraviolet laser irradiation. Finally, with three clear examples, this thesis shows that organic photoactive materials are well-adapted to be combined with photonic crystals. We demonstrated that the obtained hybrid structures are very promising for integrated optics applications.

EPFL2009

Nanofluidic tuning of photonic crystal circuits

Demetri Psaltis

By integrating soft-lithography-based nanofluidics with silicon nanophotonics, we demonstrate dynamic, liquid-based addressing and high Δn/n (∼0.1) refractive index modulation of individual features within photonic structures at subwavelength length scales. We show ultracompact tunable spectral filtering through nanofluidic targeting of a single row of holes within a planar photonic crystal. We accomplished this with an optofluidic integration architecture comprising a nanophotonic layer, a nanofluidic delivery structure, and a microfluidic control engine. Variants of this technique could enable dynamic reconfiguration of photonic circuits, selective introduction of optical nonlinearities, or delivery of single molecules into resonant cavities for biodetection.