MEMS, MOEMS, Nano, and Bionanotechnologies - Applied Optics Fundamentals and Device Applications - page 331

It is found that the variation of b > with changes in c is constant:

d
d

b
c

> = − 1

tan ψ

(7.6)

Figure 7.5 illustrates the form of Equations 7.3 and 7.6 for an arbitrary value
of ψ. This analysis shows that the vertical alignment improves for decreasing
values of c/r . On the other hand, it is found that the percent of exposed fiber,
expressed for convenience as the percent of the fiber diameter above the sur-
face of the chuck, decreases for increasing values of c/r . This percentage is a
parameter that can be indicative of the quality of the horizontal stability of
the fiber alignment, with lower values indicating better stability. It is seen
that better vertical alignment is obtained to some degree at the expense of
this horizontal stability.
As a numerical example, we use the value of ψ = 36°. This is the value for
the anisotropic etching angle in silicon for coupling chucks. The table at
Figure 7.6 provides results for several values of c/r . Point 1 shows that perfect
vertical alignment is only obtained with an infinite horizontal uncertainty
as there is of course no groove ( c = 0 = c/r ). At point 2, there is still a great deal
of the fiber above the plane of the chuck. Point 3 shows that, even when there
can be no further increase in the quality of vertical alignment, there is still
80% exposure. It therefore appears necessary to sacrifice some vertical accu-
racy in order to obtain a reasonable amount of horizontal stability. It appears
that the most reasonable value of c/r to use is in the vicinity of point 4 where
the fiber core is aligned near the surface of the chuck.

d b
d c

>

-1
tan Ψ

d b
d c

d b
d c

<

0

cos Ψ

( c / r )

FIGURE 7.5
Alignment error as a function of groove
dimension.

d b
d c

versus ( c / r )