A guide to electric field propagation techniques for guided-wave optics

Yevick, David

doi:10.1007/bf00384672

Cited by 107 publications

(34 citation statements)

References 116 publications

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“…W AVE propagation in an optical waveguide can be analyzed by the beam propagation method (BPM) [1], [2]. The BPM's developed during the last two decades can be roughly categorized in terms of the discretization in the transverse direction, i.e., fast Fourier transform (FFT-BPM) [3], finite-difference (FD-BPM) [4]- [10], finite-element (FE-BPM) [11]- [14], and method of lines (Mol-BPM) [15].…”

Section: Introductionmentioning

confidence: 99%

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Shibayama

Matsubara²,

Sekiguchi³

et al. 1999

J. Lightwave Technol.

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Abstract-Efficient nonuniform schemes, based on the generalized Douglas (GD) scheme, are developed for the finite-difference beam propagation method (FD-BPM). For a two-dimensional (2-D) problem, two methods are presented: a computational space method and a physical space method. In the former, the GD scheme is employed, after replacing a nonuniform grid in the physical space with a uniform one in the computational space. In the latter, the GD scheme is directly extended to a nonuniform grid in the physical space. We apply these two methods to paraxial and wide-angle FD-BPM's. The fourth-order accuracy is achieved in the transverse direction, provided that the grid growth factor between two adjacent grids is r = 1 + O(1x). For the paraxial BPM, the reduction in the truncation error is demonstrated through modal calculations of a graded-index waveguide using an imaginary distance procedure. For the wide-angle BPM, the propagating field in a tilted waveguide is analyzed to show the effectiveness of the present scheme. As an application of the physical space method, an adaptive grid is introduced into the multistep method.Index Terms-Finite-difference methods, optical beam propagation, optical waveguides.

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Section: Introductionmentioning

confidence: 99%

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Shibayama

Matsubara²,

Sekiguchi³

et al. 1999

J. Lightwave Technol.

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“…This can be solved numerically by the beam propagation method (BPM) [10][11][12][13], which calculates the distribution of the field at the plane z m+1 = z m + Dz from the known field at the plane z m . In simulations, the finite difference algorithm has been used [11].…”

Section: Analysed Methodsmentioning

confidence: 99%

Comparison of numerical methods for light propagating in fibers with high steps of refractive index

Zegadlo

Karpierz

2012

Opto-Electronics Review

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Fast development of complex structures like microstructural fibers, photonic nanowires or slot waveguides requires numerical tools to predict a light propagation. There are many works concerning weakly guided case, but the microstructural fibers need algorithm for a high step of the refractive index. In this paper, three approximate methods are compared. The comparison concerns a structure consisting of circular cores surrounded by cladding for different values of the refractive index steps. Application of these methods in chromatic dispersion case is also presented. It is shown that certain conditions prefer two dimensional scalar algorithms (based on approximated methods) than three dimensional ones. This allows us to implement more efficient and less complicated methods.

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“…This method is applicable because the field amplitude slowly varies in the propagation direction [10]. Simple transparent boundary conditions were used [11] because they are most suited for highly multimode problems [12]. An additional absorbing layer with a width of 12.5 μm was added to ensure field falloff of the model.…”

Section: System Model Layoutmentioning

confidence: 99%

Optimal VIA Placement in Under Filled Embedded Multimode Waveguides

Riegel¹,

Howard²,

Middlebrook³

2013

OPJ

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The self-imaging property of multimode waveguides creates a challenging problem when finding the optimal placement position of an out-of-plane coupler for embedded waveguides. This problem is compounded when the waveguides are coupled using a small input such as a vertical cavity surface emitting laser (VCSEL) or a single mode fiber where only some of the modes are generated. When the waveguide system is under filled, the coupling efficiency for the optical vertical interconnect assembly (VIA) can vary by as much as 6.2 dB depending on the length of the proceeding waveguide due to different output fields from the self-imaging property. This requires sweeping each individual VIA over the entire range of possible coupler positions to find the total maximum coupling efficiency. This process increases in complexity when a VIA supports several parallel channels all having a different optical path length. If a VIA can be placed in a calculated position from the end of a terminated embedded waveguide dependent upon the modal structure then blind pick and place methods may be used. The optimal coupler placement was determined based on smallest average VIA attenuation, smallest attenuation variance, and worse-case alignment scenario.

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A guide to electric field propagation techniques for guided-wave optics

Cited by 107 publications

References 116 publications

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Comparison of numerical methods for light propagating in fibers with high steps of refractive index

Optimal VIA Placement in Under Filled Embedded Multimode Waveguides

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