Ray traces in a distributed-index planar microlens.
In this paper ray-optical treatment in a planar microlens with 3-D distributed refractive index is presented. An integral form of the ray equation has been derived when the index distribution is expressed by the sum of decomposed functions of radial distance r and axial distance z as in actual fabricated devices. The integral equation is solved independently with respect to r and z, and an analytic form of the ray trace has been obtained in some cases. By applying the result to a planar microlens with index distribution which can be almost approximated by the profile assumed here, its optical properties such as focal length, numerical aperture, and spherical aberration have been estimated.
Iga
K
K
Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama 227, Japan.
Oikawa
M
M
Banno
J
J