Ivan Richter

Simulations of high-Q optical nanocavities with a gradual 1D bandgap

High-quality cavities in hybrid material systems have various interesting applications. We perform a comprehensive modeling comparison on such a design, where confinement in the III-V material is provided by gradual photonic crystal tuning, a recently proposed method offering strong resonances. The III-V cavity couples to an underlying silicon waveguide. We report on the device properties using four simulation methods: finite-difference time-domain (FDTD), finite-element method (FEM), bidirectional eigenmode propagation (BEP) and aperiodic rigorous coupled wave analysis (aRCWA). We explain the major confinement and coupling effects, consistent with the simulation results. E.g. for strong waveguide coupling, we find quantitative discrepancies between the methods, which establishes the proposed high-index-contrast, lossy, 3D structure as a challenging modeling benchmark.

Fourier Series-Based Bidirectional Propagation Algorithm With Adaptive Spatial Resolution

Recently we described the implementation of complex coordinate transformation as boundary conditions into a bidirectional eigenmode expansion propagation algorithm based on Fourier series expansion for modeling optical field distribution in waveguide devices. In this communication we report on the implementation of an additional coordinate transformation known as adaptive spatial resolution into this algorithm. It helps significantly reduce the number of expansion terms needed to reach required accuracy especially for photonics structures containing layers of very different thicknesses and/or optical properties, e.g., metal layers.

Comparison of 2D and 3D Fourier modal methods for modeling subwavelength-structured silicon waveguides

Frequency-domain Fourier modal methods have recently evolved into efficient tools for rigorous numerical modeling of a wide class of photonic and plasmonic structures and devices. In this contribution we describe the application of our 2D and 3D in-house tools, namely aperiodic rigorous coupled wave analysis (aRCWA) and bi-directional mode expansion propagation method using harmonic expansion (BEXX), on a recently described novel type of subwavelength grating (SWG) waveguides. They are created by means of periodically interlacing silicon segments with a superstrate material with a lower refractive index. It has been shown recently, both theoretically and experimentally, that for a suitable choice of SWG parameters such as grating period and duty cycle, the structure can support low-loss guided (Bloch) mode. Its effective index, mode profile and dispersion characteristics can thus be tailored to specific needs without the necessity of changing material composition. In our methods, either complex coordinate transformation or uniaxial anisotropic perfectly matched layers have been applied as efficient absorption boundary conditions. In order to reduce the number of expansion terms needed to reach required accuracy, the adaptive spatial resolution technique has been implemented. Structural symmetries of the devices can be fully utilized to this aim, too. Propagation constants of Bloch modes are also compared with those obtained with a full-vector film mode matching (FiMM) mode solver using the very simple effective medium theory (EMT).

Analysis of binary diffraction gratings: comparison of different approaches

Diffraction characteristics of periodic binary diffractive structures are studied using three different theoretical approaches. Namely rigorous coupled-wave analysis (RCWA), Kogelniks two-wave method, and the scalar method of transmittance have been applied to study diffraction characteristics and have been compared, and their applicability has been determined. For comparison purposes, a binary surface-relief grating made from an isotropic non-absorbing substrate in the planar diffraction regime, and a transverse electric polarized incident wave, are considered in this paper. Additionally, by calculating the diffraction efficiency of such gratings using the RCWA method, ith special respect to grating profile depth and period, it was possible to describe and explain the complex behaviour of diffraction efficiency, that is to find regions with typical diffraction regimes, of all gratings of a chosen kind, in this case given by the binary grating profile. Moreover, it has been shown ho the classical scalar transmittance method for analysis of thin diffraction gratings can be modified by an estimation of the propagation process through the grating depth in order to describe the volume phase synchronism dependence on the relative grating period.

Simulations of waveguide Bragg grating filters based on subwavelength grating waveguide

Subwavelength grating waveguides represent a flexible and perspective alternative to standard silicon-on-insulator nanophotonic waveguides. In such structures, waves propagate in the form of Bloch modes, in contrast to standard longitudinally uniform waveguides. Tunability of parameters of subwavelength grating structures possesses a great advantage of a broad variability of the (effective) refractive index and its dispersion, without significantly increasing fabrication complexity. A subwavelength grating structure is based on a (quasi)-periodic arrangement of two different materials, i.e. rectangular nanoblocks of silicon, embedded into a lower-index superstrate, with a period (much) smaller than the operational wavelength of the optical radiation. Clearly, by changing the filling factor, i.e., the duty-cycle of the subwavelength grating structure, its effective refractive index can be varied essentially between that of the superstrate and that of silicon. Our contribution is devoted to a detailed numerical analysis of Bloch modes in subwavelength grating waveguides and Bragg gratings based on subwavelength grating waveguides. Two independent versions of 3D Fourier modal methods developed within last years in our laboratories are used as our standard numerical tools. By comparison with results obtained with a 2D FDTD commercially available method we show that for reliable design of subwavelength grating waveguide devices of this kind, full-vector 3D methods have to be used. It is especially the case of Bragg gratings based on subwavelength grating waveguides, as analyzed in this paper. We discuss two options of a subwavelength grating modulation – designed by changing the subwavelength grating duty cycle, and by misplacement of Si blocks, and compare their properties from the point of view of fabrication feasibility.

Ambiguous Refractive Index Sensitivity of Fano Resonance on an Array of Gold Nanoparticles

We investigate the optical response to refractive index changes of a Fano resonance occurring in a random array of gold nanoparticles supported on a glass substrate. The Fano resonance results from the interference between localized surface plasmon on a gold nanoparticle and the light reflected at the boundary of the glass substrate. We demonstrate that the sensitivity of the resonance to the refractive index of the surrounding medium is highly dependent on the excitation geometry and can assume either positive or negative values. We furthermore present a theoretical analysis explaining this behavior based on the rigorous coupled wave analysis (RCWA) as well as the island film theory.

Analysis of couplers between photonic nanowires and subwavelength grating waveguides

Subwavelength grating (SWG) waveguides offer the freedom of (effective) refractive index variation in the design of integrated optical components and devices in silicon-on-insulator waveguides without significantly increasing fabrication complexity. An SWG waveguide is formed by a subwavelength (quasi)-periodic structure consisting of short segments of silicon embedded into a lower-index superstrate. As a result, to the first approximation, the SWG waveguide behaves as a channel waveguide with its core refractive index determined by the filling factor of silicon in the superstrate. By changing the filling factor, i.e., the duty-cycle of the SWG structure, its (effective) refractive index can be varied essentially between that of the superstrate and that of silicon. Here we present a numerical analysis of light coupling between a conventional silicon nanowire waveguide and a periodic SWG waveguide by means of a tapered SWG coupler. The coupler function is to facilitate the smooth and low-loss transition from a conventional mode of a photonic nanowire to a Bloch mode of a periodic SWG waveguide, both propagating with different group velocities. To increase the reliability of numerical simulations, two independent 3D numerical codes based on different formulations of a Fourier modal method (FMM) are used for the analysis. Results of modeling of tapered SWG couplers of different lengths confirm excellent optical properties of these couplers, including very low coupling and return losses.

Synthetic diffractive elements for security applications realized on an enhanced integral dot-matrix system

One of the important fields of application of synthetic diffractive structures is optical document security. Several methods of security enhancement of diffractive elements for security applications are presented, namely, high carrier-frequency cryptograms and noise-covered elements are introduced. Structures are designed with respect to the fabrication on special enhanced integral dot-matrix system.

Design of binary phase-only diffractive optical elements for laser beam shaping

This contribution concentrates on a study and comparison of non- iterative design methods (error diffusion methods) based on a hardclip approach with iterative methods, namely iterative Fourier transform algorithm (IFTA), in designing binary phase-only diffractive optical elements (BPDOEs) for laser beam shaping. Two error diffusion methods as a non-iterative methods were considered, implemented and used for designing BPDOEs: the classical algorithm of error diffusion (ED) and the signal window minimum average error algorithm (SWMAE). Also, different schemes and approaches of IFTA algorithm were analyzed, implemented, and compared. The methods together with the simple hardclip method were analyzed for both diffusive and fan-out type objects: the signal-to-noise ratio and the diffraction efficiency dependencies on both the spatial-bandwidth product and on the signal-window position were obtained, enabling to determine the optimum design parameters and constraints within each method. As for the IFTA method, the role and a proper shape of the scale factor were analyzed, and a new way of characterization of the algorithm convergence was introduced, using the spectrum representation. The practical realization using e-beam lithography technology shows a good qualitative agreement with designed types of elements.

Design of narrowband Bragg spectral filters in subwavelength grating metamaterial waveguides

Properties of reflection and transmission spectral filters based on Bragg gratings in subwavelength grating (SWG) metamaterial waveguides on silicon-on-insulator platform have been analyzed using proprietary 2D and 3D simulation tools based on Fourier modal method and the coupled-mode theory. We also demonstrate that the coupled Bloch mode theory can be advantageously applied to design of Bragg gratings in SWG waveguides. By combining different techniques, including judiciously positioning silicon loading segments within the evanescent field of the SWG waveguide and making use of its dispersion properties, it is possible to attain sub-nanometer spectral bandwidths for both reflection and transmission filters in the wavelength range of 1550 nm while keeping minimum structural features of the filters as large as 100 nm. Numerical simulations have also shown that a few nanometer jitter in the size and position of Si segments is well tolerated in our filter designs.