Barbara Lunitz, Jürgen Jahns
Optical interconnections are of interest to solve the communication problems of digital computers. Planar optics is a systems technology to integrate free-space optics with interconnections as one possible application. Here we consider a planar optical clock distribution system, which is realized by a sequence of beam splitter gratings on a single wafer-size substrate [1]. In particular, we address the issue of fabrication and other tolerances that can affect the stability of the beam propagation. The sources for non-ideal beam propagation are substrate variations like thickness tolerances and non-parallelism of the substrate surfaces, a variation of the wavelength, or of the ambient temperature. These result in a lateral and angular offset of the output beam, which can potentially be severe for large wafers. To reduce this offset even for large variations of the substrate and the operating parameters, we use a tolerant design. In analogy to lens waveguides [2], we place a corrective lens system on one substrate surface (Fig. 1). Each lens has a focal length chosen to be equal to their separation along the path of the light beam.
Figure 1: Confocal lens system realized in planar optics.
Figure 2: Simulation results of a planar optical system with tolerances.
To analyze such a system we use ray tracing simulations. The curve above
(Fig. 2) show the results
of the simulations for the case of all four tolerances and deviations
mentioned above. On the
abscissa the lateral position of the beam is shown. On the ordinate the
lateral offset Ęs of the beam
position is given. This offset is shown for both, the uncorrected (dashed
line) and the corrected
system (solid line). The curve of the uncorrected system grows
exponentially because of the strong
influence of the wedge error. Although the other tolerances have a much
less drastic effect they, too,
can severely reduce the amount of light at the detector. For the
simulation the we chose
,
a wedge between the substrate surfaces of 1', 
nm,
and 
K.
For the corrected system, the error in the lateral position is
significantly reduced to
less than 350 
m.
In combination with suitable field lenses this is small enough to warrant
stable operation of the system.
[1] S. J. Walker and J. Jahns, "Optical clock distribution using integrated free-space optics", Opt. Comm. 90 (1992) 359-371
[2] J. Hirano and Y. Fukatsu, "Stability of a Light Beam in a Beam Waveguide", Proc. IEEE 52, (1964) 1284-1292