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Waveguide dispersion can be tailored but not the material dispersion. Hence, the total dispersion can be shifted at any desired band by adjusting the waveguide dispersion. Waveguide dispersion is proportional tod  2    β    d    k  2${{{d^2}\beta} \over {d{k^2}}}$    and need to be computed numerically. In this paper, we have tried to compute analytical expression ford  2    β    d    k  2$ {{{d^2}\beta} \over {d{k^2}}}$    in terms ofβ   $ \beta $    for the case of an asymmetric planar slab. To computed  2    β    d    k  2${{{d^2}\beta} \over {d{k^2}}}$    accurately with numerical technique,β   $\beta $    should be accurate enough up to≈    10   −  5$ \approx {10^{- 5}}$    decimal point. This constraint sometimes generates the error in calculation of waveguide dispersion. To formulate the problem we will use the graphical method. Our study reveals that we can compute the waveguide dispersion enough accurately for various modes by knowing –β   $\beta $    only.

journal of optical communications

Exact Dispersion Study of an Asymmetric Thin Planar Slab Dielectric Waveguide without Computing            d  2    β    d    k  2        ${{{d^2}\beta} \over {d{k^2}}}$    Numerically