This document discusses optical losses associated with fiber optic joints. It describes losses from Fresnel reflection at the interface between fibers due to differences in refractive index. It also discusses losses from various types of geometric misalignments between fibers, including longitudinal offset, lateral offset, and angular misalignment. Finally, it examines losses from variations in optical parameters between fibers, such as core diameter, numerical aperture, and refractive index profile mismatches. Formulas are provided for calculating losses from many of these sources.

2. CONTENTS
Introduction
Losses due to Fresnel Reflection.
Losses due to Geometric and Optical Parameter
variations.
Multimode Fiber Joints.
Single Mode Fiber Joints.

3. INTRODUCTION
 Fiber splices: These are semipermanent or permanent joints which find
major use in most optical fiber telecommunication systems (analogous to
electrical soldered joints).
 Demountable fiber connectors or simple connectors: These are
removable
joints which allow easy, fast, manual coupling and uncoupling of fibers
(analogous to electrical plugs and sockets).
 A crucial aspect of fiber jointing concerns the optical loss associated with the
connection.
 A major consideration with all types of fiber–fiber connection is the optical
loss encountered at the interface.

4. Losses due to Fresnel
Reflection
A small proportion of the light may be reflected back into the
transmitting fiber causing attenuation at the joint. This phenomenon,
known as Fresnel reflection
Associated with the step changes in refractive index at the jointed
interface (i.e. glass–air–glass).
The magnitude of this partial reflection of the light transmitted
through the interface is given by equation 1.

5. Losses due to Fresnel
Reflection
The loss in decibels due to Fresnel reflection at a single interface is
given by equation 2.
Where n1 is the refractive index of the fiber core and n is the refractive
index of the medium between the two jointed fibers.
The effect of Fresnel reflection at a fiber–fiber connection can be
reduced by the use of an index-matching fluid between the gap.

6. Losses due to Geometric Variations
Misalignment may occur in three dimensions:
the separation between the fibers (longitudinal misalignment)
 the offset perpendicular to the fiber core axes (lateral
misalignment)
angle between the core axes (angular misalignment).

7. Losses due to Longitudinal & Lateral
misalignments

8. Losses due to Angular Misalignment

9. Losses due to Optical Parameter Variations
Losses at joints may occur due to the following reasons:
 variations in core and/or cladding diameters.
 variations in numerical apertures and/or relative refractive index
differences.
 variations in refractive index profiles.
 fiber faults (core ellipticity, core concentricity, etc.).

10. Losses due to Optical Parameter Variations

11. Multimode Fiber Joints
Lateral misalignment reduces the overlap region between the two
fiber cores.
The lateral coupling efficiency for two similar step index fibers (in a
multimode step index fiber) is given by equation 1.
The lateral misalignment loss in dB is given by equation 2.
where n1 is the core refractive index, n is the refractive index of the
medium between the fibers, y is the lateral offset of the fiber core
axes, and a is the fiber core radius.

12. Multimode Fiber Joints
Lateral misalignment loss in multimode graded index fibers is given
by equation 1.
Angular misalignment losses at joints in multimode step index fibers
is given by equation 2.
where θ is the angular displacement in radians and Δ is the relative
refractive index difference for the fiber.

13. Losses due to Geometric Variations
at a Multimode Fiber Joint
loss resulting from a mismatch of core diameters is given by equation
1.
loss caused by a mismatch of numerical apertures is given by equation
2.

14. Losses due to Geometric Variations
at a Multimode Fiber Joint
A mismatch in refractive index profiles results in a loss given by:
The total intrinsic losses obtained at multimode fiber–fiber joints
provided by the following equation: