Development and application of 2D and 3D transient electromagnetic inverse solutions based on adjoint Green functions: A feasibility study for the spatial reconstruction of conductivity distributions by means of sensitivities

To enhance interpretation capabilities of transient electromagnetic (TEM) methods, a multidimensional inverse solution is introduced, which allows for a explicit sensitivity calculation with reduced computational effort. The main conservation of computational load is obtained by solving Maxwell's equations directly in time domain. This is achieved by means of a high efficient Krylov-subspace technique that is particularly developed for the fast computation of EM fields in the diffusive regime. Traditional modeling procedures for Maxwell's equations yields solutions independently for every frequency or, in the time domain, at a given time through explicit time stepping. Because of this, frequency domain methods are rendered extremely time consuming for multi-frequency simulations. Likewise the stability conditions required by explicit time stepping techniques often result in highly inefficient calculations for large diffusion times and conductivity contrasts. The computation of sensitivities is carried out using the adjoint Green functions approach. For time domain applications, it is realized by convolution of the background electrical field information, originating from the primary signal, with the impulse response of the receiver acting as secondary source. In principle, the adjoint formulation may be extended allowing for a fast gradient calculation without calculating and storing the whole sensitivity matrix but just the gradient of the data residual. This technique, which is also known as migration, is widely used for seismic and, to some extend, for EM methods as well. However, the sensitivity matrix, which is not easily given by migration techniques, plays a central role in resolution analysis and would therefore be discarded. But, since it allows one to discriminate features in the a posteriori model which are data or regularization driven, it would therefore be very likely additional information to have. The additional cost of its storage and explicit computation is comparable low disbursement to the gain of a posteriori model resolution analysis. Inversion of TEM data arising from various types of sources is approached by two different methods. Both methods reconstruct the subsurface electrical conductivity properties directly in the time domain. A principal difference is given by the space dimensions of the inversion problems to be solved and the type of the optimization procedure. For two-dimensional (2D) models, the ill-posed and non-linear inverse problem is solved by means of a regularized Gauss-Newton type of optimization. For three-dimensional (3D) problems, due to the increase of complexity, a simpler, gradient based minimization scheme is presented. The 2D inversion is successfully applied to a long offset (LO)TEM survey conducted in the Arava basin (Jordan), where the joint interpretation of 168 transient soundings support the same subsurface conductivity structure as the one derived by inversion of a Magnetotelluric (MT) experiment. The 3D application to synthetic data demonstrates, that the spatial conductivity distribution can be reconstructed either by deep or shallow TEM sounding methods

Design and optimisation of micro-structured waveguides in nonlinear crystals

Direct femtosecond laser inscription has emerged as one of the most efficient methods for direct three dimensional micro-fabrication of integrated optical circuits in dielectric crystals.Lithium niobate is one of the most widely used dielectric crystal for a wide range of optical functions. Using the direct femtosecond inscription technology, it is possible to produce almost circular tracks of 1-2:5μm diameters with negative refractive index changes up to -0:012 in lithium niobate crystals. Those tracks can be used as a cladding region to confine the propagating light inside a core region of a micro-structured waveguide. This dissertation is focused on the numerical investigation of the propagation properties of depressed-cladding,buried micro-structured waveguides in z-cut lithium niobate crystals which can be fabricatedby direct fs laser inscription method. First of all, we discuss how experimentally achievable parameters of cladding tracks such as their position, total number, refractive index contrasts between the low index cladding structure and the core region can be used to design buried micro-structured waveguides with good confinement properties and to achieve any control over the propagation properties of different polarisation modes specific to a wide range of applications of lithium niobate. Numerical analysis of micro-structured waveguides are implemented by using finite element method. The high nonlinear coefficient and wide transparency region of lithium niobate enable its use for frequency conversion applications towards mid-infrared wavelength ranges. In this thesis, optimisation of the guiding properties, specifically the confinement losses, of microstructured waveguides in lithium niobate is realised for both around telecom and mid-infrared wavelength regions. Optimisation is based on a practical approach which takes into account the variation of experimentally achieved track parameters over cladding region. It is shown that the spectral region where confinement losses are below 1 dB/cm can be extended up to a wavelength of 3:5μm. In recent years, a variety of design geometries for micro-structured waveguides has been a focus of research interest as a means of manipulating and controlling the properties of propagating light. The flexibility of writing tracks at various depths inside lithium niobatecrystals allows direct fabrication of micro-structured waveguides with advanced design geometries.The ability to write tracks at varying sizes by femtosecond laser inscription method enables the fabrication of micro-structured waveguides with highly complex spiral geometries. Here, we explore design issues of equiangular, Fermat and Archimedes spiral geometries in accordance with experimentally available track parameters. Optimisation of each geometry is separately implemented for telecom and mid-infrared wavelength ranges. The primary advantage of designing waveguides with spiral geometries is a much finer control and better manipulation of propagating light stemming from a higher number of parameters available for design. Also, it is found that the spectral region where confinement losses are below 1dB/cm can be further extended up to a wavelength of 3:66 μm

Light in correlated disordered media

The optics of correlated disordered media is a fascinating research topic emerging at the interface between the physics of waves in complex media and nanophotonics. Inspired by photonic structures in nature and enabled by advances in nanofabrication processes, recent investigations have unveiled how the design of structural correlations down to the subwavelength scale could be exploited to control the scattering, transport and localization of light in matter. From optical transparency to superdiffusive light transport to photonic gaps, the optics of correlated disordered media challenges our physical intuition and offers new perspectives for applications. This article reviews the theoretical foundations, state-of-the-art experimental techniques and major achievements in the study of light interaction with correlated disorder, covering a wide range of systems -- from short-range correlated photonic liquids, to L\'evy glasses containing fractal heterogeneities, to hyperuniform disordered photonic materials. The mechanisms underlying light scattering and transport phenomena are elucidated on the basis of rigorous theoretical arguments. We overview the exciting ongoing research on mesoscopic phenomena, such as transport phase transitions and speckle statistics, and the current development of disorder engineering for applications such as light-energy management and visual appearance design. Special efforts are finally made to identify the main theoretical and experimental challenges to address in the near future.Comment: Submitted to Reviews of Modern Physics. Feedbacks are welcom

Proceedings of the 19th Sound and Music Computing Conference

Proceedings of the 19th Sound and Music Computing Conference - June 5-12, 2022 - Saint-Étienne (France). https://smc22.grame.f