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1. THE FIBER FORUM
Fiber Optic Communications
JOSEPH C. PALAIS
PRESENTED BY

2. Joseph C. Palais 2.2 2
Section 2.2
Lenses
n
Consider a thin lens:
D
Fiber
f
P (Focal Point)
Focal Length
Index of Refraction

3. Joseph C. Palais 2.2 3
LENSES
R1 and R2 are the radii of curvature of the
lens.
R

4. Joseph C. Palais 2.2 4
LENSES
The focal point for a thin lens is found by
1 2
1 1 1
( 1)
n
f R R
f
f number of the lens
D
 
  
 
 
 
(2.4)

5. Joseph C. Palais 2.2 5
LENSES
If f (focal length) is large, then R1 and R2 must be
large making the lens a fairly flat surface.
If f (focal length) is small, then R1 and R2 must be
small. This limits the lens size, since Dmax = 2R.
Lenses are used to couple light sources to fibers and
in some connectors coupling light between fibers.

6. Joseph C. Palais 2.2 6
RAY TRACING RULES
1. Rays traveling through the center of the lens are
not deviated.
2. Incident rays traveling parallel to the lens axis
pass through the focal point after emerging from the
lens.
1
2
f
3
f focal plane
4
lens axis

7. 2.1 7
RAY TRACING RULES
3. An incident ray traveling parallel to a central
ray intersects that ray in the focal plane after
transmission through the lens.
4. An incident ray passing through the focal point
travels parallel to the lens axis after it emerges
from the lens.

8. Joseph C. Palais 2.2 8
CYLINDRICAL LENS
f
collimated beam
Focal Line
(Line Source)
Cylindrical lenses collimate rays from a line source.
Collimated means that all rays from the line source
emerge from the lens parallel to the lens axis.
lens axis

9. Joseph C. Palais 2.2 9
GRADED INDEX ROD LENS
(GRIN ROD LENS)
The refractive index is a function of radial position n = n(r) (decreases
with distance from its axis). Ray paths are sinusoidal.
P
P: The pitch is the length of one cycle
Sinusoidal ray paths
lens
axis
r

10. Joseph C. Palais 2.2 10
GRADED INDEX ROD LENS
P: Pitch
Consider a quarter pitch length of GRIN rod.
Collimation by a Quarter-Pitch Lens
Focusing by Quarter-Pitch Lens
rays
P/4

11. 2.1 11
GRADED INDEX ROD LENS
GRIN-rod lenses are used in many fiber devices.
The main purposes for which GRIN-rod lenses
are used are:
•To collimate light beams coming from a fiber
•To focus light beams onto a fiber
The GRIN-rod lens can have a small focal length.