Efficient numerical method for analyzing photonic crystal slab waveguides

Yuan, Lijun; Lu, Ya Yan

doi:10.1364/josab.28.002265

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…Of course, it is still necessary to calculate the propagating modes of the PhC waveguide. This can be done efficiently using the DtN formalism [18,19], even for 3D waveguides [20]. Besides, the boundary condition (6) involves only the propagation constants of these modes.…”

Section: Dtn Map Methods and Boundary Conditionsmentioning

confidence: 99%

Simple boundary condition for terminating photonic crystal waveguides

Zhen

2012

J. Opt. Soc. Am. B

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Many photonic crystal (PhC) devices are non-periodic structures due to the introduced defects in an otherwise perfectly periodic PhC, and they are often connected by PhC waveguides that serve as input and output ports. Numerical simulation of a PhC device requires boundary conditions to terminate PhC waveguides that extend to infinity. The rigorous boundary condition for terminating a PhC waveguide is a non-local condition that connects the wave field on the entire surface (or line in two-dimensional problems) transverse to the waveguide axis, and it is relatively difficult to use, especially for realistic devices, such as those in PhC slabs. In this paper, a simple approximate boundary condition involving a few points in the waveguide axis direction is introduced. The new boundary condition is used with the Dirichlet-to-Neumann map method to take advantage of the lattice structures and identical unit cells in PhC devices. Comparisons with the rigorous non-local boundary condition indicate that the simple boundary condition gives accurate solutions if the computational domain is enlarged by a few lattice constants in each direction.

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Section: Dtn Map Methods and Boundary Conditionsmentioning

confidence: 99%

Simple boundary condition for terminating photonic crystal waveguides

Zhen

2012

J. Opt. Soc. Am. B

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“…In earlier works [14,15], the VMEM has been used to analyze dielectric slabs with air holes, where the incident wave is a propagating mode of the slab. The method has also been used to analyze photonic crystal slab waveguides [16]. In [13], the VMEM was formulated for scattering problems with general incident waves, and applied to analyze the transmission of light through a circular aperture in a metallic film.…”

Section: Introductionmentioning

confidence: 99%

“…In [13], the VMEM was formulated for scattering problems with general incident waves, and applied to analyze the transmission of light through a circular aperture in a metallic film. Since only circular holes are involved in these studies [13][14][15][16], cylindrical wave expansions are used to represent the solutions to the 2D Helmholtz equations.…”

Section: Introductionmentioning

confidence: 99%

Vertical mode expansion method for analyzing elliptic cylindrical objects in a layered background

Shi

2015

J. Opt. Soc. Am. A

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The vertical mode expansion method (VMEM) [J. Opt. Soc. Am. A31, 293 (2014)] is a frequency-domain numerical method for solving Maxwell's equations in structures that are layered separately in a cylindrical region and its exterior. Based on expanding the electromagnetic field in one-dimensional vertical modes, the VMEM reduces the original three-dimensional problem to a two-dimensional (2D) problem on the vertical boundary of the cylindrical region. However, the VMEM has so far only been implemented for structures with circular cylindrical regions. In this paper, we develop a VMEM for structures with an elliptic cylindrical region, based on the separation of variables in the elliptic coordinates. A key step in the VMEM is to calculate the so-called Dirichlet-to-Neumann (DtN) maps for 2D Helmholtz equations inside or outside the ellipse. For numerical stability reasons, we avoid the analytic solutions of the Helmholtz equations in terms of the angular and radial Mathieu functions, and construct the DtN maps by a fully numerical method. To illustrate the new VMEM, we analyze the transmission of light through an elliptic aperture in a metallic film, and the scattering of light by elliptic gold cylinders on a substrate.

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“…Recently, a vertical mode expansion method (VMEM) was developed for analyzing circular or elliptic cylindrical objects in a layered background [17,18]. The method is related to the earlier work of Boscolo and Midrio [19] and its further extensions [20,21] for photonic crystal slabs, and it has been used to analyze light transmission through apertures in metallic films and scattering of light by metallic nanoparticles.…”

Section: Introductionmentioning

confidence: 99%

Efficient vertical mode expansion method for scattering by arbitrary layered cylindrical structures

Shi¹,

Lu²

2015

Opt. Express

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A relatively simple and efficient numerical method is developed for analyzing the scattering of light by a layered cylindrical structure of arbitrary cross section surrounded by a layered background. The method significantly extends an existing vertical mode expansion method (VMEM) for circular or elliptic cylindrical structures. The original VMEM and its extension give rise to effective two-dimensional formulations for the three-dimensional scattering problems of layered cylindrical structures. The extended VMEM developed in this paper uses boundary integral equations to handle the two-dimensional Helmholtz equations that appear in the vertical mode expansion process. The method is applied to analyze the transmission of light through subwavelength apertures in metallic films and the scattering of light by metallic nanoparticles.

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Efficient numerical method for analyzing photonic crystal slab waveguides

Cited by 8 publications

References 16 publications

Simple boundary condition for terminating photonic crystal waveguides

Simple boundary condition for terminating photonic crystal waveguides

Vertical mode expansion method for analyzing elliptic cylindrical objects in a layered background

Efficient vertical mode expansion method for scattering by arbitrary layered cylindrical structures

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