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Derivative free method for computing modes of multilayer planar waveguide

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Abstract

A technique to solve generalized dispersion equation of multilayer planar waveguide has been demonstrated to obtain all the expected guided modes. The solution is based on the derivative free method for computing the zeros of an analytical function in complex plane. The derivative free method extracts the roots which are very close to actual zeros of the function. Roots are further refined using the robust iteration method to achieve the desired accuracy. Application of the proposed method has been verified by solving the modes of a variety of structures including lossless structure, leaky structure, quantum well waveguide, active waveguide, ARROW waveguide and metal clad waveguide. The method is efficient and computes all modes of planar waveguide with high accuracy.

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References

  • Anemogiannis, E., Glytsis, E.G.: Multilayer waveguide: efficient numerical analysis of general structure. J. Lightwave Technol. 10(10), 1344–1351 (1992)

    Article  ADS  Google Scholar 

  • Anemogiannis, E., Gaylord, K.: Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: reflection pole method and wavevector density method. J. Lightwave Technol. 17(5), 929–941 (1999)

    Article  ADS  Google Scholar 

  • Chen, C.: Development and Implementation of Novel Numerical Techniques for Integrated Optics and Microwave Planar Structure. Master Thesis, University of Ottawa (May 2000)

  • Chen, C., Berini, P.: Efficient and accurate numerical analysis of multilayer planar optical waveguides in lossy anisotropic media. Opt. Express 7(8), 260–272 (2000)

    Article  ADS  Google Scholar 

  • Chilwell, J., Hodgkinson, I.: Thin film field transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguide. J. Opt. Soc. Am. A pp. 742–753(1984)

  • Dellnitz, M., Schutze, O., Zheng, Q.: Locating all the zeros of an analytical function in one complex variable. J. Comput. Appl. Math. 138, 325–333 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Delves, L.M., Lyness, J.N.: A numerical method for locating the zeros of an analytic function. Math. Comput. 21, 543–560 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  • Ghatak, A.K., Thyagarajan, K., Shenoy, M.R.: Numerical analysis of planar optical waveguide using matrix approach. J. Lightwave Technol. LT–5(2), 660–666 (1987)

    Article  ADS  Google Scholar 

  • Gillan, C.J., Schuchinsky, A., Spence, I.: Computing zeros of analytical functions in the complex plane without using derivative. Comput. Phys Commun. 175, 304–313 (2006)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  • Kravanja, P., Barel, M.V.: A derivative free algorithms for computing zeros of analytical functions. Computing 63(1), 69–91 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • Kravanja, P., Sakurai, T., Barel, M.V.: Error analysis of a derivative-free algorithms for computing zeros of holomorphic function. Computing 70(4), 335–347 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  • Kumar, A., Rastogi, V.: Multi-layer cladding leaky planar waveguide for high-power application. Appl. Phys. B pp. 577–583(2008)

  • Kwon, M.S., Shin, S.Y.: Simple and fast numerical analysis of multilayer waveguide modes. Opt. Commun. 233, 119–126 (2004)

    Article  ADS  Google Scholar 

  • Mehrany, K., Khorasani, S., Rashidian, B.: Variantional approach for extraction of eigenmodes in layered waveguide. J. Opt. Soc. Am. B 19(9), 1978–1981 (2002)

    Article  ADS  Google Scholar 

  • Ramadas, M.R., Varshney, R.K., Thyagarajan, K., Ghatak, A.K.: A matrix approach to study the propagation characteristics of a general nonlinear planar waveguide. J. Lightwave Technol. 7(12), 1901–1905 (1989)

    Article  ADS  Google Scholar 

  • Schlereth, K.H., Take, M.: The complex propagation constant of multilayer waveguide: an algorithm for personal computer. IEEE J. Quantum Electron. 26(4), 227–230 (1990)

    Article  Google Scholar 

  • Walpita, L.M.: Solution of planar optical waveguide equations by selecting zero elements in a characteristic matrix. J. Opt. Soc. Am. A pp. 595–602 (1985)

  • Ying, X., Katz, I.N.: A reliable argument principle algorithms to find the number of zeros of an analytical function. Numer. Math. 53, 143–163 (1988)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Instrument Research and Development Establishment, Dehradun, 248008, India

    Girish Semwal

  2. Department of Physics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Vipul Rastogi

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  1. Girish Semwal
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  2. Vipul Rastogi
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Correspondence to Girish Semwal.

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Semwal, G., Rastogi, V. Derivative free method for computing modes of multilayer planar waveguide. Opt Quant Electron 46, 423–438 (2014). https://doi.org/10.1007/s11082-013-9838-2

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  • DOI: https://doi.org/10.1007/s11082-013-9838-2

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