Precise formula for calculating spot size in optical waveguides and its accuracy

Spot size is a fundamental parameter that expresses the degree of spreading of the transverse electric field distribution of a guided mode. This quantity is used when there is offset loss between different guided wave elements. It is extremely important to determine an accurate spot size value in the design of an optical integrated circuit containing a number of guided wave devices. the goal to derive a highly precise spot size requires a least square approximation of a transverse electric field distribution of the guided wave in terms of the electric field of a Gaussian beam. The transverse electric field distribution of the fundamental mode propagating in an optical waveguide was expanded orthogonally in terms of Hermite‐Gaussian functions. With a 0th‐order expansion coefficient as the maximum, an approximate equation suitable for highly accurate numerical computation was derived. the present equation does not change its equation form by Fourier transform and has mathematical validity. Fur ther, when the approximate equation is used in the present study, the junction loss of the offset axes of the waveguides can be approximated best by that of the Gaussian beam waves. This paper uses as an example the TE mode in a three‐layered slab waveguide in studies of approximation accuracy for the defined spot size value. With the present approximate equation, the spot size can be derived accurately by a successive approximation. It was demonstrated with an actual successive approximation that accuracy improves significantly and is better than the one obtained from a conventional equation.