Efficient interface conditions for the semi-vectorial finite difference beam propagation method

F. Wijnands, F.H.G.M. Wijnands, T. Rasmussen, Hugo Hoekstra, J.H. Povlsen, A. Bjarklev, R.M. de Ridder

    Research output: Contribution to journalArticleAcademicpeer-review

    9 Citations (Scopus)
    39 Downloads (Pure)

    Abstract

    Efficient interface conditions (EICs) are derived for the propagation equation using the slowly varying envelope approximation for the dominant electric field component. At the interface between two different media, the two lateral second derivatives in the discretized propagation equation are adapted such that the discretized modal field equation is correct up to second order in the lateral grid spacing. Since the error term is then of the order of the lateral grid spacing, our EICs are first-order EICs. These interface conditions are compared with well-known zero-order EICs derived by Stern and Kim and Ramaswamy. It is shown that the first-order EICs yield faster convergence to the exact effective index value as the lateral grid spacing is decreased than do the zero-order EICs. It turns out that our EICs are very much like those derived by Vassallo. Using essentially the same method, he derived EICs of second and first order for the field component respectively parallel and perpendicular, to the interface. Hence the accuracy of his EICs is one order higher for the field component parallel to the interface, although it introduces an extra asymmetry in the propagation matrix.
    Original languageUndefined
    Pages (from-to)961-975
    JournalOptical and quantum electronics
    Volume27
    Issue number10
    DOIs
    Publication statusPublished - 1995

    Keywords

    • METIS-111520
    • IR-100090

    Cite this

    Wijnands, F., Wijnands, F. H. G. M., Rasmussen, T., Hoekstra, H., Povlsen, J. H., Bjarklev, A., & de Ridder, R. M. (1995). Efficient interface conditions for the semi-vectorial finite difference beam propagation method. Optical and quantum electronics, 27(10), 961-975. https://doi.org/10.1007/BF00558488
    Wijnands, F. ; Wijnands, F.H.G.M. ; Rasmussen, T. ; Hoekstra, Hugo ; Povlsen, J.H. ; Bjarklev, A. ; de Ridder, R.M. / Efficient interface conditions for the semi-vectorial finite difference beam propagation method. In: Optical and quantum electronics. 1995 ; Vol. 27, No. 10. pp. 961-975.
    @article{bcd26bcf2de9435a813b2160035fb869,
    title = "Efficient interface conditions for the semi-vectorial finite difference beam propagation method",
    abstract = "Efficient interface conditions (EICs) are derived for the propagation equation using the slowly varying envelope approximation for the dominant electric field component. At the interface between two different media, the two lateral second derivatives in the discretized propagation equation are adapted such that the discretized modal field equation is correct up to second order in the lateral grid spacing. Since the error term is then of the order of the lateral grid spacing, our EICs are first-order EICs. These interface conditions are compared with well-known zero-order EICs derived by Stern and Kim and Ramaswamy. It is shown that the first-order EICs yield faster convergence to the exact effective index value as the lateral grid spacing is decreased than do the zero-order EICs. It turns out that our EICs are very much like those derived by Vassallo. Using essentially the same method, he derived EICs of second and first order for the field component respectively parallel and perpendicular, to the interface. Hence the accuracy of his EICs is one order higher for the field component parallel to the interface, although it introduces an extra asymmetry in the propagation matrix.",
    keywords = "METIS-111520, IR-100090",
    author = "F. Wijnands and F.H.G.M. Wijnands and T. Rasmussen and Hugo Hoekstra and J.H. Povlsen and A. Bjarklev and {de Ridder}, R.M.",
    year = "1995",
    doi = "10.1007/BF00558488",
    language = "Undefined",
    volume = "27",
    pages = "961--975",
    journal = "Optical and quantum electronics",
    issn = "0306-8919",
    publisher = "Springer",
    number = "10",

    }

    Wijnands, F, Wijnands, FHGM, Rasmussen, T, Hoekstra, H, Povlsen, JH, Bjarklev, A & de Ridder, RM 1995, 'Efficient interface conditions for the semi-vectorial finite difference beam propagation method', Optical and quantum electronics, vol. 27, no. 10, pp. 961-975. https://doi.org/10.1007/BF00558488

    Efficient interface conditions for the semi-vectorial finite difference beam propagation method. / Wijnands, F.; Wijnands, F.H.G.M.; Rasmussen, T.; Hoekstra, Hugo; Povlsen, J.H.; Bjarklev, A.; de Ridder, R.M.

    In: Optical and quantum electronics, Vol. 27, No. 10, 1995, p. 961-975.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Efficient interface conditions for the semi-vectorial finite difference beam propagation method

    AU - Wijnands, F.

    AU - Wijnands, F.H.G.M.

    AU - Rasmussen, T.

    AU - Hoekstra, Hugo

    AU - Povlsen, J.H.

    AU - Bjarklev, A.

    AU - de Ridder, R.M.

    PY - 1995

    Y1 - 1995

    N2 - Efficient interface conditions (EICs) are derived for the propagation equation using the slowly varying envelope approximation for the dominant electric field component. At the interface between two different media, the two lateral second derivatives in the discretized propagation equation are adapted such that the discretized modal field equation is correct up to second order in the lateral grid spacing. Since the error term is then of the order of the lateral grid spacing, our EICs are first-order EICs. These interface conditions are compared with well-known zero-order EICs derived by Stern and Kim and Ramaswamy. It is shown that the first-order EICs yield faster convergence to the exact effective index value as the lateral grid spacing is decreased than do the zero-order EICs. It turns out that our EICs are very much like those derived by Vassallo. Using essentially the same method, he derived EICs of second and first order for the field component respectively parallel and perpendicular, to the interface. Hence the accuracy of his EICs is one order higher for the field component parallel to the interface, although it introduces an extra asymmetry in the propagation matrix.

    AB - Efficient interface conditions (EICs) are derived for the propagation equation using the slowly varying envelope approximation for the dominant electric field component. At the interface between two different media, the two lateral second derivatives in the discretized propagation equation are adapted such that the discretized modal field equation is correct up to second order in the lateral grid spacing. Since the error term is then of the order of the lateral grid spacing, our EICs are first-order EICs. These interface conditions are compared with well-known zero-order EICs derived by Stern and Kim and Ramaswamy. It is shown that the first-order EICs yield faster convergence to the exact effective index value as the lateral grid spacing is decreased than do the zero-order EICs. It turns out that our EICs are very much like those derived by Vassallo. Using essentially the same method, he derived EICs of second and first order for the field component respectively parallel and perpendicular, to the interface. Hence the accuracy of his EICs is one order higher for the field component parallel to the interface, although it introduces an extra asymmetry in the propagation matrix.

    KW - METIS-111520

    KW - IR-100090

    U2 - 10.1007/BF00558488

    DO - 10.1007/BF00558488

    M3 - Article

    VL - 27

    SP - 961

    EP - 975

    JO - Optical and quantum electronics

    JF - Optical and quantum electronics

    SN - 0306-8919

    IS - 10

    ER -

    Wijnands F, Wijnands FHGM, Rasmussen T, Hoekstra H, Povlsen JH, Bjarklev A et al. Efficient interface conditions for the semi-vectorial finite difference beam propagation method. Optical and quantum electronics. 1995;27(10):961-975. https://doi.org/10.1007/BF00558488