Transmission characteristics in plasmonic multimode waveguides

In this article, we examine spectral transmission characteristics based on the self-imaging effect in plasmonic multimode waveguides. For the analysis, we calculate the correlation between an input field and the field in the self-imaging plane. We perform full vectorial computations using the Method of Lines as numerical method. The resulting transmission profile is discussed with regards to the attenuation, the even and odd mode sets and for several structural parameters of the plasmonic waveguide. The introduced transmission characteristic may offer the opportunity for the implementation of filtering operations in plasmonic waveguides.     

Modification of the finite difference scheme for efficient analysis of thin lossy metallayers in optical devices

A method is proposed for the analysis of optical devices with lossy metal layer by including an analytical formulation into the finite difference expressions. Losses of TM0 mode in an electro-optic switch for wavelength 1523 nm, exhibiting a sharp maximum of 37 dB are computed by this method. The results show very good agreement with the data obtained by the Mode Matching Method and Finite Difference Beam Propagation Method.     

Analysis of curved bends in arbitrary optical devices using cylindrical coordinates

An extension of the beam propagation algorithm based on the method of lines (MoL–BPM) is proposed and substantiated for analysis of curved bends–constituent parts of complicated optical devices, connecting waveguides with different orientation. Cylindrical coordinates are introduced. The formulas are compatible with those in Cartesian coordinates for analysis of straight waveguides. So, in combination concatenations of curved bends and straight waveguides can be examined in a uniform way. For the purpose of analysis in cylindrical coordinates a suitable set of wave equations without any approximation and valid for a general hybrid case is derived. To prove the accuracy of the MoL–BPM in cylindrical coordinates applying the derived formulas, the curvature loss of a rib waveguide was computed and compared with other methods showing very good agreement. As an application of the method two straight waveguides are connected by a curved bend and the power flow is determined.     

Full vectorial band structure computation of photonic crystals with hexagonal lattice and a staircase approximation of the slanted unit cells

This paper describes band structure computations of photonic crystals with a hexagonal lattice. Particularly, the full vectorial three-dimensional case is considered. The unit cells are approximated with a staircase approximation. Due to their periodicity, fields inside the computational window can be related to those outside of this area. Numerical results are compared with those from the literature and show a very good agreement.     

Numerical stable determination of Floquet-modes and the application to the computation of band structures

Periodic structures like Bragg-gratings are important components of optical circuits. The analysis of these devices can be done very efficiently by combining eigenmode propagation methods with Floquet's theorem. A particular problem is the determination of the Floquet modes. Transfer matrix formulas are stable only in case of low losses and when the length of the periods is not too big. A stable method, also in the mentioned cases, is presented in this paper. Reflection coefficients are transformed from the output of a periodic segment to its input and the fields are computed in opposite direction. By this, the exponential increasing terms, which lead to the numerical problems are avoided. The formulas are applied to determine eigenmodes in various waveguide structures. Particular periodic structures are photonic crystals (PC), who have very promising features. For tailoring these PCs the knowledge of the band structure is required. With the Floquet modes that have been determined before this band structure has been calculated. A comparison with the literature showed a very good agreement.     

Numerical simulation of hollow waveguide arrays as polarization converting elements and experimental verification

In this paper we study the characteristics of hollow waveguides that are used as polarization converting elements. In particular, numerical simulations are compared with experiments where a good agreement is found. The numerical simulations are performed with the Method of Lines—an eigenmode propagation algorithm where the eigenmodes are computed after a discretization in the cross-section. Due to the vectorial 3D-problem, extensions of the standard algorithm were required to keep the numerical effort low. Particularly, only a reduced set of eigenmodes is used in the computations and inverting rectangular matrices is done with the help of left eigenvectors. Further, it is shown how these left eigenvectors can be determined with simple matrix vector products, i.e., at very low numerical cost. The fabrication of the device is very demanding because of a very high ratio between the metal width and its height. Here, direct electron-beam lithography is used for this task.     

A finite difference beam propagation algorithm based on generalized transmission line equations

A wide angle beam propagation algorithm is presented, which is based on generalized transmission line (GTL) equations. Besides the discretization, no further approximation is introduced. In principle, a full vectorial analysis is possible, and anisotropic material can be taken into account. The algorithm has been verified for planar 2D-waveguide devices. The wide angle characteristic has been examined by determining the propagation of tilted Gaussian beams in homogeneous media. Further studies were performed for tilted waveguides and for taper structures. Results for the latter devices were compared with other methods showing a very good agreement.     

Bragg waveguide grating as a 1D photonic band gap structure: COST 268 modelling task

Modal reflection, transmission and loss of deeply etched Bragg waveguide gratings were modelled by six European laboratories using independently developed two-dimensional (2D) numerical codes based on four different methods, with very good mutual agreement. It was found that (rather weak) material dispersion of the SiO₂/Si₃N₄ system does not significantly affect the results. The existence of lossless Floquet–Bloch modes in deeply etched gratings was confirmed. Based on reliable numerical results, the physical origin of out-of-plane losses of 1D or 2D photonic band gap structures in slab waveguides is briefly discussed.     

Analysis of a deep waveguide Bragg grating

Spectral properties of a very deep Bragg grating operating in a first diffraction order on a single-mode planar waveguide have been studied theoretically. It is shown that the scattering loss can be low (a few percent), the reflectivity very high (over 90%), the reflection band is shifted against the Bragg wavelength toward the shorter wavelengths, and its spectral shape is very different from that of a shallow grating. Inside a reflection band, a part of the input optical power penetrates through the grating even if it is infinitely long. These properties are predicted by modelling using two independent computer codes based on different modelling methods, namely the bi-directional mode expansion and propagation method (BEP), and a method of lines (MoL). The first method is discussed in some detail here. The work has been performed within the framework of European Action COST 240.