Enhanced optical Kerr effect method for a detailed characterization of the third order nonlinearity of 2D materials applied to graphene

Using an enhanced optically heterodyned optical Kerr effect method and a theoretical description of the interactions between an optical beam, a single layer of graphene, and its substrate, we provide experimental answers to questions raised by theoretical models of graphene third-order nonlinear optical response. In particular, we measure separately the time response of the two main tensor components of the nonlinear susceptibility, we validate the assumption that the out-of plane tensor components are small, and we quantify the optical impact of the substrate on the measured coefficients. Our method can be applied to other 2D materials, as it relies mainly on the small ratio between the thickness and the wavelength.Comment: 7 pages, 4 figure

Large nonlinear Kerr effect in graphene

Under strong laser illumination, few-layer graphene exhibits both a transmittance increase due to saturable absorption and a nonlinear phase shift. Here, we unambiguously distinguish these two nonlinear optical effects and identify both real and imaginary parts of the complex nonlinear refractive index of graphene. We show that graphene possesses a giant nonlinear refractive index n2=10-7cm2W-1, almost nine orders of magnitude larger than bulk dielectrics. We find that the nonlinear refractive index decreases with increasing excitation flux but slower than the absorption. This suggests that graphene may be a very promising nonlinear medium, paving the way for graphene-based nonlinear photonics.Comment: Optics Letters received 12/02/2011; accepted 03/12/2012; posted 03/21/2012,Doc. ID 15912

Optical modelling of 2D materials and multilayer systems: a complete picture

Bidimensional materials are, as their name suggests, ideally viewed as having no thickness. The advent of multilayer stacks of 2D materials and combinations of different materials in vertical van der Waals heterostructures highlights however that these materials have a finite thickness. In this article, we show how volume properties of stacked 2D layers can be calculated from boundary conditions and conversely. We introduce the layer, surrounded by vacuum, as a kind of transfer matrix with intrinsic parameters. This provides a link between continuous and discrete media, and a connection with the interface reflection and transmission coefficients calculated from microscopic models. We show how to model hybrid systems and identify in the zero-thickness limit the intrinsic parameters of the current sheet that represents the 2D material, namely the in-plane surface susceptibility $\chi^s$ and the out-of-plane parameter $\xi^s$ that corresponds to a displacement susceptibility. By considering anisotropic layers under the assumption that TE and TM modes are not coupled, we provide a unified vision of the different models used in optical characterization of 2D materials, including ellipsometry. We build on this to model 3D structures layer per layer and identify their effective permittivity and propagation constants. We show that our model fits existing ellipsometric data with the same reliability as the existing interface models, but with the advantage that multilayer and monolayer systems are described in a same way

Dispersive wave emission and supercontinuum generation in a silicon wire waveguide pumped around the 1550 nm telecommunication wavelength

We experimentally and numerically study dispersive wave emission, soliton fission and supercontinuum generation in a silicon wire at telecommunication wavelengths. Through dispersion engineering, we experimentally confirm a previously reported numerical study [1] and show that the emission of resonant radiation from the solitons can lead to the generation of a supercontinuum spanning over 500 nm. An excellent agreement with numerical simulations is observed.Comment: 4 pages, 4 figure

Anisotropy and effective medium approach in the optical response of 2D material heterostructures

2D materials offer a large variety of optical properties, from transparency to plasmonic excitation. They can be structured and combined to form heterostructures that expand the realm of possibility to manipulate light interactions at the nanoscale. Appropriate and numerically efficient models accounting for the high intrinsic anisotropy of 2D materials and heterostructures are needed. In this article, we retrieve the relevant intrinsic parameters that describe the optical response of a homogeneous 2D material from a microscopic approach. Well-known effective models for vertical heterostructure (stacking of different layers) are retrieved. We found that the effective optical response model of horizontal heterostructures (alternating nano-ribbons) depends of the thickness. In the thin layer model, well adapted for 2D materials, a counter-intuitive in-plane isotropic behavior is predicted. We confront the effective model formulation with exact reference calculations such as ab-initio calculations for graphene, hexagonal boron nitride (hBN), as well as corrugated graphene with larger thickness but also with classical electrodynamics calculations that exactly account for the lateral structuration

New materials for nonlinear optical applications : the nonlinear refractive index of colloidal PbSe quantum dots

We present a detailed study of the nonlinear optical properties of colloidal PbSe quantum dot (Q-PbSe) suspensions and thin films. The nonlinear refractive index n2 has been measured with the Z-scan technique as a function of wavelength (1.20 -- 1.75 textmum), optical intensity and nanocrystal volume fraction. The n2-spectra show negative resonances near the Q-PbSe optical transitions. We attributed the high n2 to biexciton creation within the Q-PbSe. The n2 of a close-packed thin Q-PbSe film is 6 orders of magnitude larger than values for bulk Si of GaAs at telecom wavelengths, suggesting that Q-PbSe might be a promising material for all optical signal processing.info:eu-repo/semantics/publishe

Anisotropy and effective medium approach in the optical response of two-dimensional material heterostructures

Two-dimensional (2D) materials offer a large variety of optical properties, from transparency to plasmonic excitation. They can be structured and combined to form heterostructures that expand the realm of possibility to manipulate light interactions at the nanoscale. Appropriate and numerically efficient models accounting for the high intrinsic anisotropy of 2D materials and heterostructures are needed. In this article, we retrieve the relevant intrinsic parameters that describe the optical response of a homogeneous 2D material from a microscopic approach. Well-known effective models for vertical heterostructure (stacking of different layers) are retrieved. We found that the effective optical response model of horizontal heterostructures (alternating nanoribbons) depends on the thickness. In the thin layer model, well adapted for 2D materials, a counterintuitive in-plane isotropic behavior is predicted. We confront the effective model formulation with exact reference calculations such as ab initio calculations for graphene, hexagonal boron nitride (hBN), as well as corrugated graphene with larger thickness but also with classical electrodynamics calculations that exactly account for the lateral structuration.</p

Impact of nonlocal interactions in dissipative systems: towards minimal-sized localized structures

In order to investigate the size limit on spatial localized structures in a nonlinear system, we explore the impact of linear nonlocality on their domains of existence and stability. Our system of choice is an optical microresonator containing an additional metamaterial layer in the cavity, allowing the nonlocal response of the material to become the dominating spatial process. In that case, our bifurcation analysis shows that this nonlocality imposes a new limit on the width of localized structures going beyond the traditional diffraction limit.Comment: 4 pages, 4 figure

Nematicon-driven injection of amplified spontaneous emission into an optical fiber

We investigate experimentally the interaction between amplified spontaneous emission (ASE) and a soliton, which are both generated in a dye-doped nematic liquid crystal (LC) cell. A light beam is injected through an optical fiber slid into the cell to form a soliton beam. ASE is then automatically collected by this self-induced waveguide and efficiently coupled into the same optical fiber, in the backward direction. We demonstrate that the presence of the soliton improves the ASE collection by one order of magnitude. We also show that the ASE is highly polarized in the plane of the LC cell and that the ASE spectrum depends on the pump stripe orientation with respect to the LC director. The origin of the spectral anisotropy of the gain curves is determined with the help of femtosecond pump-probe spectroscopy.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Electrodynamic models of 2D materials: can we match thin film and single sheet approaches?

The electromagnetic properties of 2D materials are modeled either as single sheets with a surface susceptibility or conductivity, or as thin films of finite thickness with an effective permittivity. Their intrinsic anisotropy, however, has to be fully described to reliably predict the optical response of systems based on 2D materials or to unambiguously interpret experimental data. In the present work, we compare the two approaches within the transfer matrix formalism and provide analytical relations between them. We strongly emphasize the consequences of the anisotropy. In particular, we demonstrate the crucial role of the choice of the thin film's effective thickness compared with the parameters of the single sheet approach and therefore the computed properties of the 2D material under study. Indeed, if the isotropic thin film model with very low thickness is similar to an anisotropic single sheet with no out-of-plane response, with larger thickness it matches with a single sheet with isotropic susceptibility, in the reasonable small phase condition. We illustrate our conclusions on extensively studied experimental quantities such as transmittance, ellipsometry and optical contrast, and we discuss similarities and discrepancies reported in the literature when using single sheet or thin film models