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

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

Nonlinear optics in graphene: Detailed characterization for application in photonic circuits

In the quest for ultrathin materials compatible with CMOS technology for all-optical signal processing applications in integrated photonics, graphene appears to be a promising candidate, with broadband1 optical properties and a high and broadband optical nonlinearity. However, researchers do not agree on the value of its nonlinear refractive index, and commonly used characterization methods do not provide a clear picture of the optical nonlinearity, in terms of its tensor nature or relaxation time. In the first part of this thesis, apart from the previously used Z-scan method, we have also used the ultrafast Optical Kerr Effect method coupled to Optical Heterodyne Detection (OHD-OKE) for the characterization of the third order optical nonlinearity of monolayer CVD graphene at telecom wavelengths. This method allows to separately measure the real and the imaginary part of the third-order nonlinearity, as well as their dynamics. With respect to the Z-scan method, OHD-OKE presents the major advantage of being robust against inhomogeneities of the sample. As such, we have demonstrated that graphene has a negative nonlinear refractive index, contrary to previously reported results. In addition, we have studied the real and imaginary part of graphene’s nonlinearity, when electrostatic gating is applied to change the chemical potential of graphene. Furthermore, we have proposed an enhanced version of the OHD-OKE method, together with the appropriate theoretical framework, in order to extract the tensor elements of the nonlinearity including the out-of-plane tensor elements. In particular, we have measured separately the time response of the two main tensor elements of the nonlinear susceptibility and we have experimentally verified that the out-of-plane tensor components are negligible. In the second part of this thesis, we have investigated, from an experimental point of view, the use of the nonlinear optical response of graphene for all-optical switching applications in integrated photonics. Namely, we have designed simple silicon nitride waveguide structures that constitute basic building blocks of switching devices, which were then fabricated and covered by graphene patches. Finally, we have experimentally tested the graphene-covered structures at low and high power levels and discussed the results.Doctorat en Sciences de l'ingénieur et technologieinfo:eu-repo/semantics/nonPublishe

Determination of Leaky Modes in Periodic Optical Devices

131 σ.Οι σύγχρονες εξελίξεις της οπτικής τεχνολογίας θέτουν στο επίκεντρο των προσδοκιών την οπτική ολοκλήρωση, στον τομέα των υπολογιστικών συστημάτων, και την επεξεργασία σήματος αποκλειστικά με οπτικά μέσα, στον τομέα των τηλεπικοινωνιών. Για την επίτευξη αυτών, είναι αναγκαίες οι περιοδικές οπτικές διατάξεις ή περιθλαστικά οπτικά στοιχεία τα οποία βασίζονται στα περιθλαστικά φράγματα. Στην παρούσα εργασία, για την θεωρητική μελέτη της περίθλασης ηλεκτρομαγνητικών κυμάτων στις περιοδικές οπτικές διατάξεις, αλλά και για τις προσομοιώσεις που έγιναν, χρησιμοποιήθηκε η μέθοδος συζευγμένων κυμάτων (RCWA) σε συνδυασμό με την ανάλυση διαρρέοντος ρυθμού (leaky-mode). Οι ρυθμοί διαρροής είναι πολύ σημαντικοί στη μελέτη των οπτικών διατάξεων και κυματοδηγών, καθώς χρησιμεύουν στην μαθηματική διατύπωση του ακτινοβολούντος πεδίου με πεπερασμένο πλήθος ρυθμών. Στόχος της εργασίας είναι η παρουσίαση δύο νέων μη αυστηρών αριθμητικών μεθόδων για την εύρεση των ρυθμών σε περιοδικές οπτικές διατάξεις. Οι δύο μέθοδοι, Μέθοδος Πλάτους Ανακλαστικότητας Ισχύος (RMM) και Μέθοδος Φάσης Συντελεστού Ανάκλασης (RCPM), χρησιμοποιούν τον συντελεστή ανάκλασης που προκύπτει από την ανάλυση RCWA και υπολογίζουν τους ρυθμούς γραφικά, μέσω Λορεντζιανών κατανομών. Οι προσομοιώσεις με την εφαρμογή των μεθόδων γίνονται για τέσσερις διατάξεις περιθλαστικών φραγμάτων (ολογραφικών φραγμάτων και φραγμάτων επιφανειακής χάραξης), σε πόλωση ΤΕ και ΤΜ. Για κάθε διάταξη, εξάγονται οι τιμές του συντελεστή διάδοσης καθώς και του συντελεστή σύζευξης, ενώ τα αποτελέσματα, που παρουσιάζονται αναλυτικά και σε σύγκριση με αποτελέσματα αυστηρής μεθόδου, οδηγούν σε χρήσιμα συμπεράσματα για την αξιολόγηση των δύο μεθόδων.The recent evolution in optical technology aims at the optical integration in the area of informatics, as well as the all-optical signal processing in the area of telecommunications. To this end, periodic optical devices and specifically Diffractive Optical Elements (DOEs) are necessary. DOEs are based on diffraction gratings. In this thesis, the Rigorous Coupled Wave Analysis (RCWA) combined with the leaky-mode approach are used both in the theoretical description of the diffraction of electromagnetic waves in periodic optical devices and in the simulation of this phenomenon. Leaky modes are very important to the study of optical devices and waveguides as they are used for the mathematical formulation of radiation field with a discrete finite sum of modes. The objective of this thesis is to present two new non-rigorous numerical methods for the determination of guided and leaky modes in periodic optical devices: The Reflectance Magnitude Method (RΜM) and the Reflection Coefficient Phase Method (RCPM); both these methods use the reflection coefficient resulting from RCWA to extract modes graphically from Lorentzian-type peaks. The application of these methods through the simulation of four different diffraction gratings (holographic gratings and surface-relief gratings) for both polarizations (TE and TM) is included. For each device, the values of transmission coefficient and coupling coefficient are extracted. The results are presented in detail, in comparison with those of rigorous methods (solving the dispersion equation in the complex plane) and finally lead to useful conclusions for the evaluation of the two numerical methods.Ευδοκία Χ. Δρεμέτσικ

Characterization of the 3rd order optical nonlinearity of graphene with the ultrafast Optical Kerr Effect method

info:eu-repo/semantics/nonPublishe

Characterization of nonlinear optical properties of graphene at telecommunication wavelength

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