ECE 182

FIBER COUPLING AND ATTENUATION

OBJECTIVE: To study coupling efficiency as a function of numerical aperture for a fiber waveguide, and
find attenuation in 1km fiber spool.

BACKGROUND

Coupling of Light into a Fiber Using a Lens

Coupling of light into a fiber is not a simple task, especially for single-mode fiber having a
core diameter of a few microns. A simplified coupling setup is shown in Figure1. The most important
parameter of any coupling setup is a coupling efficiency. In the case where the light source is a
collimated laser beam of uniform intensity, the derivation for coupling efficiency is given below.

Fig. 1. Coupling of a uniform collimated light beam into a fiber using a lens.
F is lens focal distance and r is the radius of lens aperture.

The numerical aperture of the lens is defined by

NA (lens) = sinθ L (1)

For small θ L and n 0 = 1, the above becomes

NA (lens) ≅ θ L (2)

The dependence of the maximum acceptance angle θ F of the fiber is related to its critical angle φ c :

θF
n 0 sin= n12 − n 22 (3)

For small acceptance angle θ F :

NA (fiber) ≅ θ F (4)

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 The coupling efficiency is defined as the ratio of the light power accepted by the fiber core to
that incident on fiber. The light power gathered by the core can be described in terms of the fiber
acceptance angle by

P f = I i πx2 = I i π (F tanθ F )2 (5)

where I i is the incident light intensity. The total incident power is

P 0 = I i πr2 = I i π(F tanθ L )2 (6)

So, using equations above we can obtain the coupling efficiency:

2 2
Pf  tanθ F   NA (fiber) 
η =
= =
Po  tanθ L   NA (lens) 
(7)

When the light is coupled into the fiber using a lens, not only the angle of incidence of the
converging beam, but also the diameter of the incident light beam is restricted. The diameter of the
converging incident light beam has to be equal to or smaller than the core diameter for efficient
coupling of light to the fiber. Multimode fibers have a relatively large core, resulting in a high
coupling efficiency.

Fiber Loss

The loss in optical fibers is dominated by impurities in the silica-based materials that are used
for manufacturing fibers. The curve that represents loss versus wavelength in high-quality modern
silica fibers is shown in Figure 2. There are three regions of local minima in the fiber loss, near
0.85μm, 1.3μm and 1.55μm. At shorter wavelengths, the loss increases due to Rayleigh scattering. At
longer wavelengths, it increases due to infrared photon absorption. The typical low loss fiber has a
minimum loss less than 1dB/km at 1.55μm.

Fig. 2. Fiber loss versus wavelength

Light Attenuation in Fiber

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 Light propagating inside an optical fiber is governed by Beer’s law:

dP/dz = −αP (8)

where α is the attenuation coefficient. Although denoted by the same symbol as the absorption
coefficient, α includes not only material absorption but also other sources of attenuation. If P in is the
power launched at the input end of a fiber of length L, the output power P out from Eq. (8) is given by

P out = P in exp{-αL} (9)

Here attenuation coefficient α is measured in km-1. In telecommunication systems the attenuation

coefficient usually defined in units of dB/km:
𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜
𝛾𝛾 = 10𝑙𝑙𝑙𝑙𝑙𝑙 (10)
𝑃𝑃𝑖𝑖𝑖𝑖

Another effect that contributes to the attenuation of light is a light scattering arising from local
microscopic fluctuations in density. Density fluctuations lead to random fluctuations of the refractive
index. Light scattering in such a medium is known as Rayleigh scattering.
In practice, imperfections at the core-cladding interface (e.g., random core-radius variations)
can lead to additional losses which contribute to the net fiber loss. Bends in the fiber constitute
another source of scattering loss.

OPTICAL SETUP

The optical system starts with a low power HeNe laser. Its output beam is expanded with a spatial
filter, and collimated with a lens. An iris is used to control the size of the collimated beam. Following
the iris is an adjustable microscope objective mount. Objectives can be threaded into this mount. There
are transverse adjustments for centering the objective with respect to the input beam. This first mount will be
used to measure optical efficiencies of various objectives.
The next mount is a compound unit. The front part has a fixed-position objective mount for insertion
of objectives. The rear part has a fiber positioner that contains a fiber chuck with a short piece of fiber in it.
The positioner has x, y, and z movements to allow optimal positioning of the fiber tip with respect to the
focal spot of the particular objective used.
The final group of components consists of a compound mount with fiber chuck and a spool of
multimode fiber. The compound unit, as before, is used for coupling light into the fiber spool. The fiber
positioner is also used to hold the fiber chuck at the output end so that output power can be measured.
A power meter is used to measure the output powers. The fiber is a graded-index type with a core
diameter of 60µm. The fiber spool contains a 1km length of the fiber.

EXPERIMENTS

NOTE: The fiber tip must never come in contact with anything. In addition, when performing coupling of
light into the fiber using microscope objectives, monitor the distance between the fiber tip and the objective
lens surface, to prevent contact between the lens and the fiber, as this will damage both units.

Part A. Optical Efficiency of Microscope Objectives

- Check that the iris is open to pass the full width of the collimated beam.
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- Thread the NA=0.1 objective into the adjustable objective mount. Position the power meter detector
after the objective so that the expanded beam fills approximately 50% of the detector area.
- Adjust the transverse controls to center the objective with respect to the input beam in order to
maximize detected power.
- Slowly close the iris down until the output power drops 10%. Record the output power P0.
- Move the detector in front of the objective, and measure the input power P i .
- Calculate the optical efficiency of the objective as η 0 = P 0 / P i . Remove the objective.
- Repeat measurements for objectives with different NA= 0.25, 0.3, and 0.4. Note that Pi will vary
depending on the iris size set for each objective.

Part B. Fiber Coupling Efficiency as a Function of Numerical Aperture

The compound mount will be used for this part.

- Check that the fiber tip is protected. This is done by sliding the chuck itself until the fiber tip is shielded by
the metal chuck housing.
- Thread the NA=0.1 objective into the front part of the mount. Check the approximate focal distance for
this objective.
- Slowly slide the chuck until the fiber tip is located at the approximate focal distance away from the
objective lens. Gently lock the chuck in place with the lock-screw.
- On the screen observe the output spot from the fiber and adjust the x, y, and z controls to visually
maximize the output.
- Replace screen with detector. (Be careful do not break the fiber tip.)
- Maximize the detected output power by fine tuning the x, y, and z controls. Slowly close the iris down
until the output power drops 10%. Record this as the fiber output power P f .
- Move the detector in front of the objective, and measure the input power.
- Calculate the fiber coupling efficiency η f taking into account the power loses from part A for this
objective.
- Loosen the chuck lock-screw and slide the chuck so that the fiber tip is protected. Remove the
objective.
- Repeat measurements for objectives with different NA=0.25, 0.3, and 0.4.
- Plot the coupling efficiency η f vs. objective NA.

Part C. Linear Attenuation of the Fiber

- Using the objective with the highest coupling efficiency, couple light into the fiber spool.
- Place the detector close to the output fiber chuck. By fine tuning the x, y, and z controls maximize the
output power.
- Again close the iris down until the output power drops 10%. Record this as the fiber output power Pout.
- Move the detector in front of the objective, and measure the input power.
- Taking into account the power loses measured in parts A and B determine the power coupled into the
fiber as P in .
- Calculate fiber attenuation γ = 10log(Pout / Pin) dB/km. The fiber length is 1km.