Efficient Bragg waveguide-grating analysis by quasi-rigorous approach based on Redheffer's star product

Tervo, Jani; Kuittinen, Markku; Vahimaa, Pasi; Turunen, Jari; Aalto, Timo; Heimala, Päivi; Leppihalme, M.

doi:10.1016/s0030-4018(01)01530-9

Cited by 26 publications

(14 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is important to note that the combined scattering matrix typically does not have any symmetry so it becomes necessary to store all four scattering parameters in the combined matrices. Two scattering matrices can be combined as illustrated in Figure 4 using the Redheffer star product [16,26,42]. It is derived by writing Eq.…”

Section: Redheffer Star Productmentioning

confidence: 99%

“…Today, scattering parameters are so common that the terms "S 11 " and "S 21 " are often used synonymously for "reflection" and "transmission." Despite this strong and longstanding convention, the CEM community is adopting inefficient and unconventional formalisms for scattering matrices for use in semianalytical methods [7,16,[18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. The majority of the literature on this topic appears in optics journals, where the benefits of semianalytical methods are more pronounced and the use of scattering parameters in experiments is less common.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Rumpf¹

2011

PIER B

142

View full text Add to dashboard Cite

Abstract-The literature describing scattering matrices for semianalytical methods almost exclusively contains inefficient formulations and formulations that deviate from long-standing convention in terms of how the scattering parameters are defined. This paper presents a novel and highly improved formulation of scattering matrices that is consistent with convention, more efficient to implement, and more versatile than what has been otherwise presented in the literature. Semi-analytical methods represent a device as a stack of layers that are uniform in the longitudinal direction. Scattering matrices are calculated for each layer and are combined into a single overall scattering matrix that describes propagation through the entire device. Free space gaps with zero thickness are inserted between the layers and the scattering matrices are made to relate fields which exist outside of the layers, but directly on their boundaries. This framework produces symmetric scattering matrices so only two parameters need to be calculated and stored instead of four. It also enables the scattering matrices to be arbitrarily interchanged and reused to describe longitudinally periodic devices more efficiently. Numerical results are presented that show speed and efficiency can be increased by more than an order of magnitude using the improved formulation.

show abstract

Section: Redheffer Star Productmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Rumpf¹

2011

PIER B

142

View full text Add to dashboard Cite

show abstract

“…Both Fourier Modal Method (FMM) [16][17][18] and Finite Difference based mode solver, OptiMode by OptiWave [19,20], are used in this work to determine the optical mode profiles of the waveguides (slab or channels). In both cases a calculation window of 10 μm × 3.5 μm is taken into account with a mesh size of 20 nm in x-direction and 5 nm in y-direction.…”

Section: Methodsmentioning

confidence: 99%

“…The influence of the parameters, i.e., the thickness of the layers, is determined using a mode solver based on the Fourier Modal Method [16][17][18]. Accurate mode profiles and confinement factors are calculated by Finite Difference mode solver, OptiWave [19,20], in order to avoid ripples due to Gibbs phenomenon inherent to FMM.…”

Section: Horizontal Slot Waveguide Simulationsmentioning

confidence: 99%

Modal properties of a strip-loaded horizontal slot waveguide

Pélisset

Laukkanen

Kuittinen

et al. 2017

J. Eur. Opt. Soc.-Rapid Publ.

Self Cite

View full text Add to dashboard Cite

Background: Channel waveguides have been developed for years to comply with the need for smaller footprint and better integration in photonics circuits. However, they are still suffering from fabrication complexity and optical losses. These two limitations can be addressed by combining two types of channel waveguides, namely strip-loaded and slot waveguide.Methods: We present a systematic study of the geometrical parameters of a strip-loaded horizontal slot waveguide and their influence on the characteristics of the device. Simulations and experiments are carried out to understand the behavior of the electromagnetic field inside such a waveguide. In particular, the influence of the high and low refractive index layers and the loading-strip on the key characteristics of the structure, i.e., the confinement factor and the effective index, are investigated theoretically and compared with experimental values. Results: The main properties of this waveguide platform are a low lateral index contrast, a high vertical field confinement, and low-propagation losses (1.4 dB/cm). Conclusions: Our results show that this platform is highly versatile, easy to fabricate and low-losses. We also show that the geometry of the mode can be tuned to suit the application.

show abstract

“…In this case, not only the guided modes (which naturally vanish on both side of the boundary of the computational box), but also the radiation fields in the claddings which are attenuated in the perfectly matched-layers can be expanded into Fourier series. As a consequence, Method 2 can be used as an eigenmode solver for both guided and radiation modes, and in conjunction with an analytical integration in the z-direction by use of S-matrix scheme, 2 can solve many different problems related to the diffraction and propagation of guided wavwes by intricate non-periodic structures Silberstein et al 2001;Tervo et al 2001). For two-dimensional problems, this approach has been used to design short tapers which largely reduced out-of-plane radiation losses at the interface between conventional z-invariant slab waveguides and dielectric Bragg mirrors (Ctyroky et al 2002;Lalanne and Hugonin 2003), to study very low losses of photonic-crystal waveguides resulting from the light tunnelling through the finite thickness of the photonic crystal (Li and Ho 2004) or to compute Bloch waves of periodic grating waveguides (Cao et al 2002).…”

Section: Fourier Expansion Techniques For Implementing Mode Solversmentioning

confidence: 99%

Fourier modal methods for modeling optical dielectric waveguides

et al. 2005

View full text Add to dashboard Cite

This work contains new materials relative to the use of Fourier expansion techniques, also called plane-wave expansion techniques, for modelling normal modes of optical waveguides. Two rigorous fully vectorial methods are presented and benchmarked for a classical rib waveguide geometry well studied in the literature. The first method relies on a pole extraction and on a one-dimensional expansion scheme. A four-digit accuracy for the normalized propagation constant B is obtained for the dominant TE and TM modes of the benchmark problem and for a small number of retained Fourier harmonics. Better accuracy is anticipated for larger truncation ranks. The second method relies on a two-dimensional expansion scheme in Fourier space and provides a three-digit accuracy for the normalized propagation constant.

show abstract

Efficient Bragg waveguide-grating analysis by quasi-rigorous approach based on Redheffer's star product

Cited by 26 publications

References 23 publications

Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Modal properties of a strip-loaded horizontal slot waveguide

Fourier modal methods for modeling optical dielectric waveguides

Contact Info

Product

Resources

About