# Combination of Characteristic Green’s Function Technique and Rational Function Fitting Method for Computation of Modal Reflectivity at the Optical Waveguide End-facet

### Abdorreza Torabi, Amir Ahmad Shishegar

#### Abstract

A novel method for computation of modal reflectivity at optical waveguide end-facet is presented. The method is based on the characteristic Green’s function (CGF) technique. Using separability assumption of the structure and rational function fitting method (RFFM), a closed-form field expression is derived for optical planar waveguide. The uniform derived expression consists of discrete and continuous spectrum contributions which denotes guided and radiation modes effects respectively. An optimization problem is then defined to calculate the exact reflection coefficients at the end-facet for all extracted poles obtained from rational function fitting step. The proposed CGF-RFFM-optimization offers superior exactness in comparison with the previous reported CGF-complex images (CI) technique due to contribution of all components of field in the optimization problem. The main advantage of the proposed method lies in its simple implementation as well as precision for any refractive index contrast. Excellent numerical agreements with rigorous methods are shown in several examples.

#### References

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#### Paper Citation

#### in Harvard Style

Torabi A. and Shishegar A. (2015). **Combination of Characteristic Green’s Function Technique and Rational Function Fitting Method for Computation of Modal Reflectivity at the Optical Waveguide End-facet** . In *Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 2: PHOTOPTICS,* ISBN 978-989-758-093-2, pages 14-21. DOI: 10.5220/0005332300140021

#### in Bibtex Style

@conference{photoptics15,

author={Abdorreza Torabi and Amir Ahmad Shishegar},

title={Combination of Characteristic Green’s Function Technique and Rational Function Fitting Method for Computation of Modal Reflectivity at the Optical Waveguide End-facet},

booktitle={Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 2: PHOTOPTICS,},

year={2015},

pages={14-21},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005332300140021},

isbn={978-989-758-093-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Photonics, Optics and Laser Technology - Volume 2: PHOTOPTICS,

TI - Combination of Characteristic Green’s Function Technique and Rational Function Fitting Method for Computation of Modal Reflectivity at the Optical Waveguide End-facet

SN - 978-989-758-093-2

AU - Torabi A.

AU - Shishegar A.

PY - 2015

SP - 14

EP - 21

DO - 10.5220/0005332300140021