Dispersion study of even mode thin planar slab dielectric waveguide without computing d2β/d2k numerically

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 to d2β/d2k and need to be computed numerically. In this paper we have tried to compute analytical expressions for d2β/d2k in terms of β for the case of even modes of thin planar slab waveguide. To compute d2β/d2k accurately, β should be accurate enough up to ≈10−5 decimal point. This constraint sometimes generates the error in calculation of waveguide dispersion. Our study reveals that we can compute waveguide dispersion enough accurately for various modes by knowing only –β.