This paper describes a theoretical design of an integrated optical geodesic lens using a noncircular overlay to correct spherical aberrations. The corrected lens design can achieve diffraction-limited performance for an on-axis beam with an aperture equal to 90% of the lens diameter. The paper also contains an analysis of the tolerances, which must be met during the fabrication of such a lens to maintain a diffraction-limited spot and prescribed focal length. This analysis showed that the most sensitive parameter is the thickness of the overlay.
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Description of Lenses on which Error Analysis was Performed and Focal Spot Changes due to Errors in Depression Fabrication Entries Represent the Ratio of Change in Focal Spot to Change in a Lens Parameter
Location change varies; magnitude is near 1 for most cases
Signs refer to effect of increase in depth, shift in the +y direction
Table II
Changes in Focal Spot due to Errors in Fabricating the Overlay. Entries Represent the Ratio of Change in Focal Spot to Change in a Lens Parameter Except for the Nrel Column
Thickness Error Causing 1μm Size Increase, both Causes Considered
A
1.01
a
3.6 × 10−6
.014 μm−1
0.12 Å
15 Å
2.6 Å
B
1.02
b
6.6 × 10−6
.0015 μm−1
2.3 Å
330 Å
44 Å
C
1.02
b
1.0 × 10−5
.0015 μm−1
11.0 Å
480 Å
67 Å
D
1.04
c
1.8 × 10−5
.16 μm−1
0.20 Å
8.2 Å
1.1 Å
J
1.04
c
6.1 × 10−5
.16 μm−1
0.33 Å
50 Å
3.8 Å
E
1.08
d
3.2 × 10−5
.014 μm−1
4.5 Å
360 Å
23 Å
In units of change in relative index per micron of thickness.
Tables (5)
Table I
Description of Lenses on which Error Analysis was Performed and Focal Spot Changes due to Errors in Depression Fabrication Entries Represent the Ratio of Change in Focal Spot to Change in a Lens Parameter
Location change varies; magnitude is near 1 for most cases
Signs refer to effect of increase in depth, shift in the +y direction
Table II
Changes in Focal Spot due to Errors in Fabricating the Overlay. Entries Represent the Ratio of Change in Focal Spot to Change in a Lens Parameter Except for the Nrel Column