This paper studies the effect of microlens front-face angle on the performance of an optical system consisting of a planar-graded refractive index (GRIN) lens pair facing each other separated by a free-space region. The planar silica microlens pairs are designed to facilitate low-loss optical signal propagation in the free-space region between the opposing optical waveguides. The planar lens is fabricated from a 38-μm-thick fluorine-doped silica layer on a silicon substrate. It has a parabolic refractive index profile in the vertical direction, which is achieved by controlled fluorine incorporation in the silica film to collimate the optical beam in the vertical direction. Horizontal beam collimation is achieved by incorporating a horizontal curvature at the front face of the lens defined by deep oxide etch. A generalized 3×3ABCDGH transformation matrix method has been derived to compute the coupling efficiency of such microlens pairs to take front-face angles that may be present due to fabrication variations or limitations and possible input/output optical fiber offset/tilt into considerations. Pairs of such planar GRIN lens with various free-space propagation distances between them ranging from 75 to 2500 μm and with front-face angles of 1.5 deg, 2 deg, and 4 deg have been fabricated and characterized. Beam propagation method simulations have been carried out to substantiate the theoretical and experimental results. The results indicate that the optical loss is reasonably low up to 1.5 deg of front-face angles and increases significantly with further increase in the front-face angle. Analysis shows that for a given system with specific microlens front-face angle, the optical loss can be significantly reduced by properly compensating the vertical position of the input and output fibers.
We present a simple technique to determine the design parameters of an optical interconnect system that uses integral planar lenses. The technique is based on the ABCD transformation matrix method. This analysis technique is significantly simpler and more efficient than the previously published methods for finding the design parameters and predicting the coupling efficiency of the system. The proposed method is applied to compute the coupling efficiency of single- and two-level optical systems.
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.