The demand for the transmission of information has rapidly increased as the recent popularization of personal computers and the recent development of the internet and as a result, there has gradually been used optical transmission system having a high transmission velocity. The optical waveguide has been used in such an optical transmission system as an optical interconnection means. When this optical waveguide (core) has a curved shape such as a sigmoidally curved shape or S-shape, the central axis of the light-propagation mode causes a deviation with respect to the geometrical central axis of the core at the sigmoidally curved portions whose curvature is discontinuously changed and this in turn results in the generation of an optical loss. It would be necessary for the reduction of this optical loss to form a portion (offset) having an axially deviated structure (axis-deviation structure), wherein the central axis of the core is deviated, in a part of the sigmoidally curved region. However, the extent of axis-deviation should be determined depending on the refractive indexes of the core and the clad as components of such an optical waveguide, the dimension of the core and the wavelength of light passing through the same and also due to production tolerance, it is quite difficult to establish any optimum axis-deviation structure and this leads to the generation of an optical loss. Accordingly, it would generally be preferred that the optical waveguide is free of any such axis-deviation structure. Moreover, this technique likewise suffers from a problem such that it is impossible to form an axis-deviation structure having any degree of axis-deviation optimum for wavelengths falling within a wider range since the extent of axis-deviation should be determined depending on the wavelength of light.
In this connection, the general explanation of such an axis-deviation structure for the optical waveguide is disclosed in literature (see, for instance, “Kouha-Kougaku (Technology of Light Waves)”, KOKUBUN Yasuo, published by Kyoritsu Publishing Co., Ltd., p. 250).
In this respect, there have been known functions in some CAD softwares, which are used for creating a curved shape of optical waveguides and the like. By way of example, one of the curved shapes prepared by the function has a shape that is formed by connecting two circular arcs which have a radius of curvature equal to R so that the directions of two circular arcs opposite to one another (hereunder referred to as “arc-connected shape”). In such an arc-connected shape, the curvature thereof is discontinuously changed at the connected point and therefore, it is necessary to form an axis-deviation structure at the connected point of these arcs as has been described above (see, FIG. 5D).
In addition, there has also been known a shape depicted using the following cosine function (in the CAD software, this is referred to as “S-bent cosine shape”) and it is not necessary, in this shape, to arrange the foregoing axis-deviation structure in the middle of the curve:
  y  =            1      2        ⁢          (              1        -                  cos          ⁢                                          ⁢          π          ⁢                                          ⁢          z                    )      
However, the curvatures at the both ends of an optical waveguide having an arc-connected shape are finite and accordingly, the optical waveguide having such an arc-connected shape should be connected to a linear optical waveguide through an axis-deviation structure incorporated into the former (see FIG. 5C).
Furthermore, in case of an optical waveguide having such a shape which makes use of the following sine function (in the CAD software, this is referred to as “S-bent sine shape”), it is not necessary to arrange the foregoing axis-deviation structure in the middle of the curve and the radius of curvature thereof is infinite (or the curvature is equal to zero) at the both ends thereof, in other words, when connecting the optical waveguide having such a shape to a linear optical waveguide, the central axis of the former is completely in agreement with that of the latter and therefore, the connection of these waveguides never requires the use of any axis-deviation structure at all (FIG. 5B):
  y  =      z    -                  1                  2          ⁢          π                    ⁢      sin      ⁢                          ⁢      2      ⁢      π      ⁢                          ⁢      z      