The weighted index method: a new technique for analyzing planar optical waveguides

Robertson, M. J.; Kendall, P.C.; Ritchie, S.; McIlroy, P.W.A.; Adams, Matthew

doi:10.1109/50.41636

Cited by 43 publications

(9 citation statements)

References 11 publications

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“…Several methods exist that in certain respects might be viewed as improvements of the EIM; we mention the (Film) Mode Matching Method (MMM) (Peng and Oliner 1981;Sudbø 1993), in which the total field is expanded in the terms of O. V. Ivanova (B) · M. Hammer · R. Stoffer · E. van Groesen MESA + Institute for Nanotechnology, AAMP Group, University of Twente, P. O. Box 217, Enschede 7500 AE, The Netherlands e-mail: o.v.ivanova@math.utwente.nl the local slab modes and later matched across the interfaces, the Spectral Index Method (Vassallo and Wang 1990), in which the total field is put to zero at certain distances from the interfaces with strong refractive index contrast and later expanded in Fourier series, the Weighted Index Method (Robertson et al 1989), which using a variational procedure finds the modal field profile as the best separable solution of the wave equation and finally the Rigorous Effective Index Method (Benson et al 1992), which for rib waveguides with outer slices above cut-off, by variational means finds a simple transcendental equation for the propagation constant.…”

Section: Introductionmentioning

confidence: 99%

A variational mode expansion mode solver

et al. 2007

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A variational approach for the semivectorial modal analysis of dielectric waveguides with arbitrary piecewise constant rectangular 2D cross-sections is developed. It is based on a representation of a mode profile as a superposition of modes of constituting slab waveguides times some unknown continuous coefficient functions, defined on the entire coordinate axis. The propagation constant and the lateral functions are found from a variational principle. It appears that this method with one or two modes in the expansion preserves the computational efficiency of the "standard" effective index method while providing more accurate estimates for propagation constants, and well-defined continuous approximations for mode profiles. By including a larger number of suitable trial fields, the present approach can also serve as a technique for rigorous semivectorial mode analysis.

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Section: Introductionmentioning

confidence: 99%

A variational mode expansion mode solver

et al. 2007

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“…In this regard application of several techniques such as effective index method (Knox and Toulious 1970), spectral index method (Robson and Kendall 1990), weighted index method (Robertson et al 1989), perturbation method (Varshney and Kumar 1988), collocation method (Sharma and Banerjee 1989) etc. are well known.…”

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confidence: 99%

Analysis of arbitrary index profile planar optical waveguides and multilayer nonlinear structures: a simple finite difference algorithm

Chaudhuri

Roy

2007

Opt Quant Electron

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we present here a simple numerical method to obtain the mode effective indices as well as field distributions of modes of any arbitrary profile planar optical waveguide. The method is based on the solutions of scalar and semivectorial Helmoltz's equation by finite difference algorithm and devised with a field convergence technique. This approach is quite general and can be applied straightforwardly to calculate the guided as well as quasior leaky modes of any arbitrary planar structure without the need to solve any eigenvalue equation or any complex matrix formalism. Besides providing the ease of application, the algorithm is particularly useful for waveguides with any graded index profile or with irregular multilayered structure and multilayered waveguides with a localised arbitrary nonlinear film. The performance of our method is verified against typical problems with analytical solutions or having results known otherwise, and is shown to yield results with good accuracy.

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“…However, the waveguide simplification process is still a simple, applicable and useful way to gain insight on the operation of the structures of interest. This method and its variant, the weighted index method, 23 will be used in our later discussion on the single-mode operation cutoff in each structure.…”

Section: Effective Index Methods (Eim)mentioning

confidence: 99%

Analysis and structure design of distributed-feedback laser (DFB) and distributed Bragg reflector (DBR) laser using regrowth-free surface grating technology

Djie

Sookdhis

Dowd³

2001

SPIE Proceedings

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The realization of single-mode Distributed Feedback (DFB) and Distributed Bragg Reflector (DBR) lasers, based on surface grating structures is of considerable interest. Such devices offer a relatively simple grating fabrication process without complicated multistep-epitaxial growth or regrowth, as required in more conventional devices. This simplified processing could potentially reduce the fabrication cost for these lasers. A key concern for the surface grating lasers is designing the structure to provide sufficient feedback to achieve single mode operation with high yield and high quality as compared to conventional buried-grating DFB and DBR lasers. This paper reports numerical modelling of surface grating DFB and DBR lasers based on 1.55 µm wavelength InGaAs/InGaAsP/InP with graded-index separate confinement heterostructure multiple quantum well (GRINSCH-MQW) structures. Bragg wavelength operation of the DFB and DBR lasers may be satisfied by deeply etching fine surface gratings on both side portions and along top of the ridge stripe respectively. Sufficiently strong optical coupling between the corrugated structure and evanescent field can be achieved by controlling various parameters such as ridge width, etch depth, and grating width. The numerical results obtained allow optimum grating geometries to be developed to provide the desired feedback effect. Furthermore, the model has been used to investigate the influence on the device performance of fabrication errors and processing effects on the grating structures, prior to fabrication.

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The weighted index method: a new technique for analyzing planar optical waveguides

Cited by 43 publications

References 11 publications

A variational mode expansion mode solver

A variational mode expansion mode solver

Analysis of arbitrary index profile planar optical waveguides and multilayer nonlinear structures: a simple finite difference algorithm

Analysis and structure design of distributed-feedback laser (DFB) and distributed Bragg reflector (DBR) laser using regrowth-free surface grating technology

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