Variational analysis of diffused planar and channel waveguides and directional couplers

Sharma, Anurag; Bindal, Pushpa

doi:10.1364/josaa.11.002244

Cited by 11 publications

(8 citation statements)

References 10 publications

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“…Subject to an incident light source, wave propagating in the diffused channel with the refractive index described above will be predicted. In Table I, the magnitudes of k 0 n e predicted at different grids agree well with 10.666679 shown in [10]. In addition, the predicted amplitude profile in Figure 3 is also seen to have the similar profile predicted in the work of [8].…”

Section: Numerical Resultssupporting

confidence: 79%

“…The first three‐dimensional problem under current investigation is the optical wave propagation in the diffused channel schematic in Figure 2. The refractive index profile in this waveguide is the result of diffusing Ti +2 into LiNbO 3 in the x – y plane, thereby yielding the graded profile given below 10 where and g ( x ) = exp(− x 2 /2 D 2 ). The notation ‘ erf ’ denotes the error function.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The predicted spatial rate of convergence for the two-dimensional analytic test problem chosen for the validation sake. The computed value of k 0 n e in [10] is 10.666679. Table II.…”

Section: Numerical Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Development of a convection–diffusion–reaction model for solving Maxwell's equations in frequency domain

Sheu¹,

Lin²,

Li³

2011

Numerical Methods in Fluids

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SUMMARY We propose in this study a numerically accurate and computationally efficient convection–diffusion–reaction finite difference scheme to discretize the full‐vector and semi‐vector optical waveguide equations. The scheme formulated in a grid stencil of five nodal points for solving the three‐dimensional waveguide equations employs the locally analytic solution. In this three‐dimensional study, calculations were carried out for the investigation of wave propagation in diffused channel, rectangular and rib types of optical waveguide. Copyright © 2011 John Wiley & Sons, Ltd.

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Section: Numerical Resultssupporting

confidence: 79%

Section: Numerical Resultsmentioning

confidence: 99%

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Development of a convection–diffusion–reaction model for solving Maxwell's equations in frequency domain

Sheu¹,

Lin²,

Li³

2011

Numerical Methods in Fluids

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“…Furthermore, if the weakly guiding approximation is assumed in the whole interest domain, then we can neglect polarization dependence to obtain the scalar wave equation 5that considerably reduces the computational time. For three-dimensional (3-D) structures, we only compute a diffused channel waveguide in this paper, which has been solved by Sharma and Bindal [20] assuming scalar approximation. In two-dimensional (2-D) structures such as planar waveguides, the derivatives with respect to in (3) and (4) are zero if the infinite extension is along the -direction.…”

Section: Mathematical Formulations Of Wave Equationsmentioning

confidence: 99%

An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

Huang

Yang²

2003

J. Lightwave Technol.

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An accurate and efficient solution method using spectral collocation method with domain decomposition is proposed for computing optical waveguides with discontinuous refractive index profiles. The use of domain decomposition divides the usual single domain into a few subdomains at the interfaces of discontinuous refractive index profiles. Each subdomain can be expanded by a suitable set of orthogonal basis functions and patched at these interfaces by matching the physical boundary conditions. In addition, a new technique incorporating the effective index method and the Wentzel-Kramers-Brillouin method for the a-priori determination of the scaling factor in Hermite-Gauss or Laguerre-Gauss basis functions is introduced to considerably save computational time without experimenting with it. This method shares the same desirable property of the spectral collocation method of providing a fast and accurate solution but avoids the oscillatory solutions and improves the poor convergence problem of the simple spectral collocation method with single domain where regions of discontinuous refractive index profiles exist. Applications to several two-and three-dimensional waveguide structures having exact or accurate approximate solutions are given to test the accuracy and efficiency; all the results are found to be in excellent agreement. Index Terms-Discontinuous refractive index profiles, domain decomposition, optical waveguides, orthogonal basis function, scaling factor, spectral collocation method. I. INTRODUCTION R ECENTLY, there has been growing interest in developing integrated optics devices in optical communication systems. The fundamental operating principle and optimal design of optical devices such as modulators, switches, filters, fibers, and semiconductor lasers are often based on the comprehension of optical waveguide theory [1]. Hence, solving the optical waveguide problems is an essential way to clearly realize these devices. However, only a limited number of waveguides, which have simple geometry and specific refractive index profiles (RIPs), have analytic solutions [1], [2]. Consequently, employing

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“…1 Recently, for example, Sharma and Bindal applied such a technique to optimize diffuse planar and channel waveguides. 2 Another approach that considerably simplifies this analysis is the well-known ray-tracing technique. 3 Ray trajectories are solutions from the eikonal approach to the partial differential equation for the electromagnetic field propagating inside an optical medium.…”

Section: Introductionmentioning

confidence: 99%

Light propagation in optical waveguides: a dynamic programming approach

Calvo

Lakshminarayanan

1997

J. Opt. Soc. Am. A

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We apply techniques of optimal-control theory, namely, the methods of dynamic programming, to the problem of light propagation in optical waveguides. This formulation is equivalent to the resolution of an eikonal equation. We illustrate this optimization technique for the case of an ideal parabolic refractive-index-profile distribution. We discuss the possibility of extending this procedure to other types of optical waveguides and optical media.

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Variational analysis of diffused planar and channel waveguides and directional couplers

Cited by 11 publications

References 10 publications

Development of a convection–diffusion–reaction model for solving Maxwell's equations in frequency domain

Development of a convection–diffusion–reaction model for solving Maxwell's equations in frequency domain

An efficient method for computing optical waveguides with discontinuous refractive index profiles using spectral collocation method with domain decomposition

Light propagation in optical waveguides: a dynamic programming approach

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