Integrated Optics - Applied Optics Fundamentals and Device Applications - page 284

It is seen that point B, the beginning of the curved section, divides q into
two sections, and Γ represents the percentage of this division. The radius of
curvature is found to be

( 1 Γ

θ

− ) q

R = (5.34)

tan

R
q tan

Γ = − 1 θ

The center of curvature C is located at distances t and s relative to point D . In
order to find t and s we first find x and y

Γ q

x R + =

tan β

or

Γ q ( 1 − Γ

θ

) q

x = −

tan β tan

and

= cos β y

or

cos
tan

β
θ

cos
tan

β
θ

y = Γ q − ( 1 − Γ ) q

then

t = sin β

or

) sin
tan

β
θ

⎡
⎢

⎤
⎥

t = q Γ cos β − ( 1 − Γ

and

Γ q

δ = − y

sin β