Optoelectronics: Photonic Materials and Devices
DT086/DT085
Ray Optics. Matrices of Cascaded Optical Components
Exercise #1
Tiny glass balls are often used as lenses to couple light into and out of optical
fibres. The fibre end is located at a distance f from the sphere. For a sphere of
radius a = 1 mm and refractive index n = 1.8 mm, determine f such that a ray
parallel to the optical axis at a distance y = 0.7 mm is focused onto the fibre,
as illustrated in Fig. 1.
f
2a
y
Lens
Fibre
Fig 1. Focusing light into an optical fibre with a spherical glass ball.
1. Applying the 2x2 Ray-Transfer Matrix technique, derive a transfer
matrix M for the given system of cascaded optical components, whose
elements are A, B, C, D, so that:
 y out   A B   yin 
   
 
 out  C D  in 
2.
3.
4.
5.
Assume, that the glass sphere can be decomposed into three
operations: an input refraction (at spherical boundary), an internal
translation, and an exit refraction.
Based on the derived transfer matrix, find the value of f (distance from
the sphere to the fibre end), that satisfies the condition of yout = 0, while
yin = y =0.7 mm and in = 0.
What is the value of out?
Based on the derived equation for the distance f, plot the dependence
of f versus refractive index n of the ball lens (assume it changes in the
range from 1 to 2.2). Comment on the results and graph plotted.
Based on the derived equation for the distance f, plot the dependence
of f versus radius a of the ball lens (assume it changes in the range
from 0.3 to 3 mm). Comment on the results and graph plotted.