MEMS, MOEMS, Nano, and Bionanotechnologies - Applied Optics Fundamentals and Device Applications - page 332

/
cos Ψ

c r

d
d

b
c

b
r

% Fiber
exposed Point

1 0 0 1.00 100

2 0.50 -0.44 0.91 95

FIGURE 7.6
Vertical misalignment (d b /d c ), height of fiber
core above chuck plane ( b/r ), and percent of
exposed fiber as functions of groove width to
fiber diameter ratio ( c/r ).

3 1.00 -1.38 0.59 80

4 1.53 -1.38 0 50

5 2.00 -1.38 -0.53 24

To obtain an idea of the actual sizes of the misalignment, we consider a
total groove width error of +0.5 μm. Then, the center of the fiber will be lower
than expected by −0.69 μm. This would be an important consideration for
direct integration of grooves and waveguides, considering a single-mode
core diameter of perhaps 4 μm; however, many efforts are directed toward
separately aligning the chuck and guides, so the real interest is in keeping a
consistent groove width among multiple grooves. One might expect a plus or
minus 0.1 μm variance between three grooves, and, therefore, the three fiber
cores would be aligned to ±0.14 μm.
Consider two fiber diameters of 80 and 125 μm. By aligning the core of the
smaller fiber with the chuck surface,

b > = 0 and therefore c

1
cos ψ

r =

Using the values r = 40 μm and ψ = 36°,

40 μ m

c = = 49 4 . μ m

cos 36

The critical values for both fibers are summarized in Figure 7.7.
Some representative V-groove chuck dimensions are shown at Figures 7.8
and 7.9. The groove width would be the critical dimension and would deter-
mine the groove depth by the crystal geometry. The groove width may be
96-100 μm as long as each of the three grooves is the same. The 200.6 μm
groove separation is also very important. This basic approach represents the
basis for a range of early silicon-bench optical-packaging devices.

Fiber-Dimensions V-Groove Values

Diameter Radius ( r ) c (μm) d (μm) c / r c (μm) b / r

80 μm 40 μm 49 67.4 1.225 0.6 0.015

125 μm 62-5 μm 49 67.4 0.789 38.9 0.620

FIGURE 7.7
Critical values for 80 and 125 μm diameter fibers.