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Publication# Phase-sensitive near field Investigation of Bloch surface wave propagation in curved waveguides

Elsie Barakat, Hans Peter Herzig, Liang Sun, Qing Tan, Jian Wang, Libo Yu

*European Optical Soc, *2014

Article

Article

Résumé

Bloch surface waves (BSWs) are electromagnetic surface waves excited in the band gap of a one dimensional dielectric photonic crystal. They are confined at the interface of two media. Due to the use of dielectric material, the losses are very low, which allows the propagation of BSWs over long distances. Another advantage is the possibility of operating within a broad range of wavelengths. In this paper, we study and demonstrate the propagation of light in ultra-thin curved polymer waveguides having different radii fabricated on a BSWs sustaining multilayer. A phase-sensitive multi-parameter near-field optical measurement system (MH-SNOM), which combines heterodyne interferometry and SNOM, is used for the experimental characterization. Propagating properties, bending loss, mode conversion and admixture are investigated. We experimentally show that when light goes through the curved part of the waveguide, energy can be converted into different modes. The superposition and interference of different modes lead to a periodically alternating bright and dark beat phenomenon along the propagation direction. Experimental optical phase and amplitude distributions in the curved waveguide show a very good agreement with simulation results.

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Maria-Pilar Bernal, Hans Peter Herzig, Myun Sik Kim

Lithium niobate (LN)-based devices are widely used in integrated and nonlinear optics. This material is robust and resistive to high temperatures, which makes the LN-based devices stable, but challenging to fabricate. In this work, we report on the design, manufacturing, and characterization of engineered dielectric media with thin-film LN (TFLN) on top for the coupling and propagation of electromagnetic surface waves at telecommunication wavelengths. The designed one-dimensional photonic crystal (1DPhC) sustains Bloch surface waves (BSWs) at the multilayer–air interface at 1550 nm wavelength with a propagation detected over a distance of 3 mm. The working wavelength and improved BSW propagation parameters open the way for exploration of nonlinear properties of BSW-based devices. It is also expected that these novel devices potentially would be able to modify BSW propagation and coupling by external thermal–electrical stimuli due to the improved quality of the TFLN top layer of 1DPhC.

2019Bloch surface waves (BSWs) are surface electromagnetic waves excited at the interface between a truncated periodic dielectric multilayer and a surrounding medium. This particular solution to the Maxwell equations in stratified media has been known since the late 1970s. However, few studies have been conducted till now on the manipulation and control of BSW propagation over 2D surfaces of photonic structures. There are several advantages provided by BSW propagation on almost flat surfaces. Due to the use of dielectric materials, losses are very low, thus allowing the propagation of BSWs over long distances. Another advantage in using BSWs is the possibility of operating within a broad range of wavelengths by properly designing a suitable multilayered structure. Furthermore, since the maximum intensity associated with BSWs can be tuned on the surface, a strong field intensity increased by several orders of magnitude can be achieved and can thereby enhance the field close to the structure's surface. This tunable localized field confinement is particularly attractive in fluorescence biosensing. In the following, we will use an exemplary BSW-sustaining multilayer as a general platform suitable for manipulating and controlling BSW propagation on its surface in the spectral range of telecom wavelengths. Several 2D optical photonic devices can be implemented starting from an ultra-thin (~ λ /15) polymer layer spun on the multilayer, which can be subsequently shaped as desired. The presence of the polymer modifies the local effective refractive index, enabling a direct manipulation of the BSWs. We experimentally and theoretically demonstrate that BSWs can be diffracted, focused, coupled and made resonating by locally shaping the geometries of 2D photonic devices—such as lenses, prisms, gratings, bended waveguides and waveguide couplers—on the multilayer. One of the main advantages is that these 2D photonic devices can have arbitrary shapes, which are difficult to obtain in 3D. The strong point of the platform concept is that a thin-film multilayer enables standard-wafer-scale production. The top surface can be modified to customize a 2D micro-system by, e.g., e-beam writing, optical lithography, stamping or other replication techniques. Since a BSW can be considered as a 2D wave and it is bounded at the surface of the multilayer, near-field imaging is one of the preferred tools to directly monitor and characterize the near field produced on the structured multilayered surface mentioned above. A multi-heterodyne scanning near-field optical microscope (MH-SNOM) developed in our lab (EPFL-OPT) makes near-field characterization possible. The operation wavelength is in the near infrared range (1460 nm–1580 nm). A polarization-retrieval method is developed in this thesis to measure and characterize the near-field polarization response for arbitrary polarization- sensitive photonic nano-devices, such as photonic crystal microcavities, waveguides, thin films, nanoparticles, spiral gratings and other near-field polarization-sensitive imaging applications. Polarization retrieval is easily accessible in far-field microscopy, but is challenging for the near field. This is because when a SNOM probe interacts with the near field and scatters the signal to the far field, the near-field polarization may be considerably altered. In this thesis, the developed method uses an isotropic region in the vicinity of the nanostructure as a calibration area, whose known polarization properties provide a global criterion to calibrate and quantify the polarization distortion induced by the detection system. It is then applied on the field measured above the structure of interest to compensate and reconstruct its complex field response. We experimentally show the effectiveness of the method on a silicon form- birefringent grating (FBG) with significant polarization diversity. Three spatial dimensional near-field measurements are in agreement with theoretical predictions obtained with rigorous coupled-wave analysis (RCWA). Pseudo-far- field (~10λ away from the surface) measurements are performed to obtain the effective refractive index of the FBG, emphasizing the validity of the proposed method. This reconstruction algorithm makes the MH-SNOM a powerful tool to analyze concurrently the polarization-dependent near-field optical response of any nanostructures with subwavelength resolution as long as a calibration area is available in close proximity.

Concepts associés (16)

Bloch's theorem

In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves modulated by periodic functions. The theorem i

Waveguide

A waveguide is a structure that guides waves, such as sound (acoustic waveguide), light (optical waveguide), radio waves (radio-frequency waveguide) or other electromagnetic waves, with minimal los

Cristal photonique

Les cristaux photoniques sont des structures périodiques de matériaux diélectriques, semi-conducteurs ou métallo-diélectriques modifiant la propagation des ondes électromagnétiques de la même manière

The design and minaturization of microwave circuits involves the analysis and optimization of a large varity of structures, which, in general, are based on arbritrary objects embedded in also arbritary media. The most common situation is found when optimizing terminal antennas, whose main constraint is the antenna's volume, which must be fitted into a specified space, which in general is the phone or laptop case. This kind of antennas can also include stratified media, oblique metallizations, dielectric objects, waveguide components, in their definition making their analysis more difficult from the numeric point of view. The complete treatment of this kind of problems has been performed traditionally using Finite Differences or Finite Elements software, while it is more rare to find Method of Moments implementations for the solution of this kind of general problems. The Method of Moments has a certain number of advantages as the inclusion of radiation conditions or stratified media in the Green's function of the problem. Due to this it is possible to mesh only the surfaces or boundary conditions that are not included in the Green's function definition, obtaining, for instance, a more natural radiation boundary condition compared to other fullwave methods. The other big concern is the optimization of this kind of structures. In general the structures we are dealing with in this work can have very irregular shapes, in order to fit within the required volume constraints. The traditional optimizations techniques based on the gradient or conjugated gradient are not efficient when optimizing functions containning multiple minima and a large search space, which is the case in the optimization of terminal antennas. When miniaturizing terminal antennas or just a simple microstrip filter, the number of unknowns can be very large, and the different optimization variables can vary within wide limits in the search space. In this situation the Genetic Algorithms are ideal for seeking the global optimum solution of our problem. This work covers the analysis and optimization of microwave circuits, including antennas and filters in microstrip and waveguide technologies, paying more attention to the implementation of the Method of Moments (MoM) in conjugation with the Mixed Potential Integral Equation (MPIE) and Electric/Magnetic Field Integral Equation (EFIE/MFIE). The work has been split into 3 main goals: The analysis of 3 dimensional structures in stratified media, including arbritary shaped dielectric bodies using the Method of Moments, (MPIE,EFIE,MFIE). The analysis of shielded environments and more precisely the analysis of retangular waveguide cavities with the Method of Moments. The implementation of several optimization techniques, emcompassed in the frame of genetic algorithms, for the design and miniaturization of terminal antennas and microstrip filters. Some relevant examples linked to the efficiency and accuracy of the different methods and techiques explained in this work are included in each chapter, yielding to practical results suitable to be used in real life design problems. The main contributions of this work can be summarized as follows: In Chapter 2 we have developed the interpolation of 3D Green's function to the general solution of dielectric objects embedded in multilayered media. The interpolation method itself is preceeded by a spectral extraction of the quasi-static terms. This technique, very often applied in complex images techniques, has been applied to our specific Green's function problem yielding very good results in terms of accuracy and Green's function computation time. Another contribution, also emcompassed in Chapter 2, is the integration of the static part of the field dyadic G̿EM, performed by splitting the field dyadic into TM and TE components, allowing then an analytical integration of the dyadic terms in stratified media. In the frame of shielded environments in Chapter 3, the most important contribution is the extension of Ewald's acceleration technique to full electric and magnetic problems, allowing the acceleration of the field dyadic G̿EM and thus permit the extension of the MoM to the simulation of arbritary metallic shapes coupled to apertures through Ewald's approach. In Chapter 4 the most important contribution is the implementation of a Bayesian optimiser based on the estimation of probability made by dependencies trees. The dependency tree based method found in [1] and later in [2] has been adapted to the terminal antenna miniaturization yielding to excellent results in optimisation time and quality of the solution provided by the optimiser. Our implementation of the dependency tree method was found to be better than the traditional method used in this kind of problems. Chapter 4 contains also an implementation of the growing cells method presented in [3] for the specific problem of optimising pseudo periodic structures, like microwave filters, yielding to a powerful interpolating method which accelerates the optimisation process of microwaves devices whose fitness response is very time consuming.