Adaptive Wavelet Collocation Method for Simulation of Time Dependent Maxwell's Equations

This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field at that time instant. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fields are sparse, there will be less grid points. On the adapted grid, update schemes with high spatial order and explicit time stepping are formulated. The method has high compression rate, which substantially reduces the computational cost allowing efficient use of computational resources. This adaptive wavelet collocation method is especially suitable for simulation of guided-wave optical devices

Simulations of vertically-coupled microdisk-resonators by 3-D vectorial coupled mode theory

Fully vectorial 3D frequency-domain simulations of vertically coupled integrated-optical microdisk-resonators are described. The 'rigorous' coupled mode theory model combines numerically computed bend modes of the cavity disk and guided modes of the straight bus waveguides

COMPARATIVE PHYSICO-CHEMICAL AND PHYTO-CHEMICAL ANALYSIS OF TALISADI CHURNA WSR TO DIFFERENT MARKET SAMPLES

Talisadi Churna is a compound herbal formulation extensively used in disorders of upper respiratory tract and Gastro-intestinal tract. Formulation has greater demand due to its simple combination, therapeutic efficacy and methods of preparation and packaging due to which multiple companies prepare the formulation with due precision and safety evaluation. A current study was taken to evaluate in-house prepared sample of Talisadi Churna as per the AFI protocol and was compared to 3 different market samples. All the samples of Talisadi Churna were subjected to physico-chemical, preliminary phyto-chemical analysis and TLC. The study reveals that there is a significant difference is seen in the physico-chemical analysis and TLC, but there is no significant difference is seen in the preliminary phyto-chemical analysis

Interaction of whispering gallery modes in integrated optical micro-ring or -disk circuits: Hybrid CMT model

Whispering gallery modes supported by open circular dielectric cavities are embedded into a nonparametric two-dimensional frequency domain hybrid coupled mode theory framework. Regular aggregates of these cavities, including straight access channels, are investigated. The model enables convenient studies of the guided wave scattering process, the response of the circuit to guided wave excitation. Transmission resonances can be characterized directly in terms of resonance frequency and linewidth by computing supermodes of the entire composite circuits, comprising both cavities and bus waveguides. Examples of single ring and disk filters, a coupled-resonator optical waveguide, and a three-cavity photonic molecule in a reflector configuration allow the approach to be assessed

Splitting of Whispering Gallery Modes by Nanoparticles Embedded in High Q Microcavities

ABSTRACT Effects of perturbations of the whispering gallery modes (WGMs) in cylindrical microcavity resonators by embedded nano size particles are studied by the finite difference time domain modeling. Apart from the foreseeable effects of spectral shift and broadening of WGM resonances, we also observed a key feature of splitting of the WGM peaks. This splitting occurs as a result of formation of symmetric and antisymmetric standing waves inside the cavity. It is demonstrated that magnitude of the splitting reaches several angstroms for 5 µm cavities with index 1.59 supporting moderately high quality (Q≈10 5 ) WGMs. We show that this effect allows developing biomolecular sensors based on measuring this splitting in porous cavities or in cavities with liquid cores. Keywords: resonators, optical confinement, sensors, whispering gallery modes, optics at surfaces, particles scattering INTRODUCTION Due to high quality (Q) factors of whispering gallery modes (WGMs) in spherical, cylindrical or toroidal cavities they are widely used [1-3] in lab-on-chip and sensor applications. In such cavities WGMs circulate thousands of times inside the cavity that increases their interaction length with the nanoparticles such as DNA, molecules, colloidal particles, or quantum dots located in the vicinity of resonators' surface. The conventional spectroscopic sensors operate based on measurements of a spectral shift or broadening of the corresponding WGM resonance. One of particularly interesting effects reported for ultra-high Q microspheres In this work we show by using numerical modeling that the sensor devices can be built on a principle based on measurements of a fine splitting of the WGM peaks caused by the embedded nanoparticles. We show that by placing the nanoparticle in an optimal position inside the cavity [8] the WGM splitting can be increased by several orders of magnitude compared to the previously studied cas

SIMULATIONS OF VERTICALLY-COUPLED MICRODISK-RESONATORS BY 3-D VECTORIAL COUPLED MODE THEORY

Fully vectorial 3D frequency-domain simulations of vertically coupled integrated-optical microdisk-resonators are described. The “rigorous ” coupled mode theory model combines numerically computed bend modes of the cavity disk and guided modes of the straight bus waveguides

Cylindrical integrated optical microresonators: Modeling by 3-D vectorial coupled mode theory

A spatially three-dimensional (3-D), fully vectorial coupled mode theory model for the interaction between several straight or bent dielectric optical waveguides, each supporting multiple modes, is described. The frequency domain model is applied to the coupler regions of cylindrical microresonators, here considered for applications as integrated optical filters. For simple test cases, comparisons with results of beam propagation calculations and of a rigorous system mode analysis provide some validation of the approach. By combination of two coupler representations one obtains a complete 3-D vectorial microresonator description without any free parameters, that permits a convenient investigation of the influence of geometrical parameters on the spectral response. When applied to a microring resonator with pronouncedly hybrid cavity modes, the model reveals the manifold features that may appear in the spectra of these devices

Comparison of coupled mode theory and FDTD simulations of coupling between bent and straight optical waveguides

Analysis of integrated optical cylindrical microresonators involves the coupling between a straight waveguide and a bent waveguide. Our (2D) variant of coupled mode theory is based on analytically represented mode profiles. With the bend modes expressed in Cartesian coordinates, coupled mode equations can be derived in a classical way and solved by numerical integration. Proper manipulation of the propagation matrix leads to stable results even in parameter domains of compact and/or radiative structures, which seemed unsuitable for a perturbational approach due to oscillations of the matrix elements along the propagation. Comparisons with FDTD calculations show convincing agreement

Analytical Approaches to the Description of Optical Microresonator Devices

Optical ring resonators are commonly discussed on the basis of a frequency‐domain model, that divides a resonator into coupler elements, ring cavity segments, and the straight port waveguides. We look at the assumptions underlying this model and at its implications, including remarks on reciprocity/symmetry arguments, the general power transfer characteristics, the resonance condition, the spectral distance and width of the resonances, the quantities that describe the resonator performance, and a few remarks about tuning. A survey of bend mode properties and a coupler description in terms of coupled mode theory fills the abstract notions of the model. As an example for devices that rely on a standing wave principle, in contrast to the traveling waves found in the microrings, we consider in less detail microresonators with square or rectangular cavity shapes. Also here a frequency domain coupled mode theory can be applied that opens up simple possibilities to characterize resonant configurations