An approximate analytical solution involving the evaluation of the overlap integral method has been developed to
estimate the coupled optical power in a multilevel optical system. The transmitter and receiver optics are located on
different planes, vertically separated by a distance Z. 45º micro-mirror pairs are used to facilitate out-of-plane reflection
of the optical beam in order for the transmitter and receiver components to be optically linked. The optical components
consist of planar waveguide focusing elements, involving a combination of graded-index effect and lens front curvature.
Optical signal in many active and passive optical devices can be well approximated by a Gaussian beam. The coupling
loss formulas have been derived to support elliptical and circular Gaussian beam analysis. Spot size mismatch, non-ideal
propagation distance, axial offset, mirror angular deviation and relative tilt between the two planes are major
contributors toward optical power loss in a multilevel optical system. The derived coupling loss formulas has been
applied to find the optimal coupling condition like micro-mirror positions, Z, relative distances of optical elements from
the micro-mirror, beam spot size, etc. for a prototype system. BPM simulation results are in good agreement with the
numerical results obtained by the approximate analytical solutions. The derived coupling loss formulas can be used to
estimate optimal optical power loss in a single level or multilevel optical system in MOEMS based optical circuits as
well as in a conventional optical system where paraxial approximation is assumed.