APh 24
Experiment No. 1
Spring 2012
BASIC OPTICAL COMPONENTS
I. Brief Overview
This experiment introduces you to a variety of optical phenomena and components: Lenses, Brewster's
angle, total internal reflection, polarization, polarizers, and waveplates. You will also learn to efficiently
couple light into optic fiber.
Background (fiber only)
Optical fibers are now the primary terrestrial telecommunications medium. The low
inherent cost per unit bandwidth has made this a reality over the past five years. Major
installations of optical fibers for long haul lines have been made by all carriers (e.g. ATT,
GTE, Sprint, etc.). Undersea fiber optic cables have also been installed between the major
continents. Local telephone companies have installed high–bandwidth links between
central switching offices. The cost and attenuation of glass fibers have both dropped
dramatically in the past two decades as a result of the research and development
undertaken by Nippon Electric Co., Bell Labs, and the Corning Glass Works among others.
For example, single–mode, step–index glass fibers are available from Corning with an
attenuation less than 1 dB/km at a wavelength of 1.3 µm and a bandwidth capability of
several GHz for about 30 cents per meter. (Can you imagine looking through a glass
window one kilometer thick with about 15% loss of light?) Losses less than 0.2 dB/km are
obtained at the more optimum wavelength of about 1.55 µm. The next major step will be
the installation of optical fiber networks to bring broadband telecommunications to
individual households.
For many applications, optical fiber has replaced coaxial electrical cable so it was
necessary for equipment manufacturers to develop optical fiber connectors that serve the
same function as coaxial cable connectors (such as the BNC type connector we are all
familiar with). The technical challenge of a fiber–optic connector is that the core diameter
of a fiber is extremely small (see problem 2 below) so the mechanical alignment accuracy
requirement is very daunting especially for a single–mode fiber. A small misalignment
between two connectors could add a very large loss to an optical fiber network.
F many experimental situations, it is necessary to efficiently couple a laser beam into the
end of an optical fiber with a lens. Say we are focusing a beam of diameter D with a lens
of focal length F. Geometrical optics would predict an infinitely small beam diameter at F,
as shown by the dashed lines in the figure below. According to this, any sized laser beam
with any lens could couple into any fiber no matter how small the fiber core! For a more
accurate description, it is necessary to describe the beam as having a Gaussian intensity
profile.
As you may recall from APh 23, the intensity distribution I(r,z) of a Gaussian beam is
given by:
1
1/ 2
  z 2 
Po
 2r 2
  ,
I (r, z)  2
exp(
) and ( z)  0 1  
2
2


R
(z)
(z)
  RG  
2
where  0 is the 1/e2 radius and R RG   0 /  is the Rayleigh range. Unfortunately, the
Gaussian character of a laser beam places a limit on the smallest beam diameter
attainable with a given lens. This is represented by the solid lines in the figure below,
which show of the 1/e2 points of the beam as it focuses. Fortunately (actually
fundamentally), there is an additional property: beam size does not change much over the
Rayleigh range RRG of the beam, so there is a certain tolerance in how accurately we need
to locate the focus, e.g., when aligning a fiber in the focal direction relative to a coupling
lens.
For the moment ignore the left side of the figure above and follow the beam as it
propagates away from the focus. As you may also recall, a Gaussian laser beam with an
initial 1/e2 diameter of d=2  0 will diffract and in the far field will have an angular spread
 gaus s  4 /   / d  ,
given by:
where gauss is the full angle traced out by the 1/e2 points of the laser intensity profile. This
is shown on the right side of the figure above. Outside of the Rayleigh range, the angular
spread of a Gaussian beam is the same as the angular spread of the limiting geometrical
rays (the dashed lines of the figure). We can use this fact to find the real focal spot
diameter d produced by a lens of focal length F for a collimated input beam of diameter D.
A lens of focal length F will bend parallel geometric rays separated by D by the full angle
geom:


 geom   2 tan1
D D
  F.
2F 
Since  g a u ss  g eo m, we find:
d
4
 g eo m

4F
.
D
Thus, we can calculate d by knowing F and D or by measuring . We can ensure that d is
small enough in order to couple into a small micron-scale sized fiber core.
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II. Preparation
Review Hecht, Sections 4.6.3 (Fresnel Equ.), 4.7 (TIR), 5.2.3 (Thin lenses), 5.5.1 (Prisms), 8.1–8.2
(Polarization), 8.6–8.8 (Waveplates), your APh 23 class notes, and the "Newport Tutorial" on the
subjects mentioned above (http://www.newport.com/content/default.aspx?id=812#Optics). Then answer
the following questions in your notebook. Read through the lab procedure.
Prelaboratory Questions:
1. (Prism, 20pts) A ray is incident on a 60° equilateral prism, which has an index of refraction “n”.
The ray makes an angle of incidence of  i 1 with the prism’s first surface. See Hecht Figure 5.56.
Consider the three following cases:
(a) At  i 1 , the ray passes through the first surface and undergoes total internal reflection (TIR) at the
second incident surface (the side opposite point A in Figure 5.56). Find the value of  i 1 where the
ray is just at the critical angle for TIR at the second surface.
(b) Find the value of  i 1 , where the deviation angle,  (Figure 5.56), is a minimum.
(c) Assume the ray is polarized parallel to the plane–of–incidence. Find the value of  i 1 where the light
reflected from the first surface is minimized. (What is this angle called?)
*Note how each of these three angles can be used to determine the index of refraction of the prism.
2. (Waveplates, 20 pts) Suppose you wanted to rotate the axis of a linearly polarized beam by 45 with
a wave plate. Which type of wave plate would you use? How should the wave plate’s axes be oriented
with respect to the original linear polarization axis? Suppose you wanted to produce a circularly
polarized beam. Which type of wave plate would you use? How should the wave plate’s axes be
oriented with respect to the original linear polarization axis? Assume you have a polarized light source, a
polarizer, and two unlabelled wave plates. The axes of the waveplates are unlabelled. However, you can
rotate the waveplates relative to the polarization of the light source. You are told one wave plate is a half
wave plate and the other is a quarter wave plate. Describe a procedure to tell the wave plates apart.
4. (Isolator, 20 pts) Explain in your own words how you can make an optical isolator from a quarter
wave plate and polarizer. Can you do the same thing with a half wave plate with 45 rotation.
5. (Laser beam size, 20 pts) A knife edge is often used to determine a laser beam size in a given
direction. A common practice is to mount a knife edge on a translation stage and use it to cut through the
laser beam under measurement while measuring the transmitted beam power. Explain how you would
æ 2r 2 ö
determine a laser beam diameter 20 with a Gaussian intensity profile I0 expç- 2 ÷. Can you do it with
è w0 ø
only two measurements, and which two points would you suggest. (Hint: the total transmitted power
æ 2r 2 ö
¥
a
with a knife edge at y =a is given by P(a) = ò dx ò dyI0 expç- 2 ÷).
-¥
-¥
è w0 ø
6. (Fiber numerical aperture, 20 pts) The term numerical aperture (N.A.) characterizes the range of
angles that an optical system can emit or accept light. For a lens, the N.A. is then NA=n sin , where n is
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the index of refraction the lens works in and  is the maximum half angle sustained by an object or
image point (Hecht p.215). Understanding the meaning of the N.A., what will be the numerical aperture
of a light waveguide (fiber optic) with core index nf and cladding index nc? For a fiber of NA=0.12, what
is the maximum acceptance angle max? Bonus: Most of the fibers we use are so called single mode
fiber. Assuming light that propagates in and outside of a single mode fiber is Gaussian, how would you
define the NA of the single mode fiber?
III. Experiment Procedure
Note: There are several parts to this experiment, so it is important to pace yourself. The total estimated
time is 200 min.
1. Start up: Identify the collection of optical components set out on the optical table (there is a list on
the table). Have your TA show you how to set up and adjust the components. Turn on the laser.
Optical component list: glass plate, prism, polarizer, waveplate#1, waveplate#2, mirror, and 2 lenses.
You also have a power meter for measuring laser power.
2. Laser’s Polarization Direction: (Estimated time - 10 minutes; 10 pts) With the laser clamped on the
table, use the tilting glass plate, examine qualitatively the magnitude of the Fresnel reflection as the plate
orientation is changed. Cast the reflection on the wall or target screen. You can rotate the laser in its
mount to change the polarization direction. Loosen the large socket–head screw. (But don't over–tighten
this screw!) Adjust the polarization direction of the laser and the plate orientation to demonstrate
Brewster's angle. (This is a common technique to determine the direction of polarization of a laser.) If
you can't find Brewster's angle in 5 minutes, call in your TA for help. Estimate Brewster’s angle.
Based on the angle, what is the index of refraction of the black glass plate?
3. Total Internal Reflection and Brewster’s angle: (Estimated time – 30 minutes; 30 pts) There is an
equilateral 60° prism mounted in a rotation stage. Place the stage in the beam path, so that one of the
sides is normal to the laser beam. Check that the laser is p-polarized with respect to the prism. Measure
Brewster’s angle. What is the uncertainty of this measurement? Based on the measured angle, what is
the index of refraction of the prism? Notice where the light first undergoes total internal reflection (TIR).
Rotate the stage until light just emerges instead of undergoing TIR. Think about how you would
accurately measure the critical angle with this equipment. (Which part of the prism should the light hit?
How should the prism be mounted relative to the rotation stage? Does it matter?). Measure the angle of
incidence. Based on the measured angle, what is the index of refraction of the prism?
4. Angle of Minimum Deviation: (Estimated time - 20 minutes; 20 pts) With the same setup, study the
minimum deviation effect and measure the angle–of–incidence which produces minimum deviation.
(See Hecht eqn. 5.54.) Determine the refractive index of the prism from this angle. Which of the three
previous methods for determining the index of refraction do you think has the highest accuracy? Which
is the lowest? Explain.
5. Polarizers: (Estimated time - 15 minutes; 15 pts) Place an optical polarizer in the laser beam path.
Measure and plot the transmission power as a function of the orientation angle, taking only enough data
points to produce a reasonable plot, but take a bit more data around the minimum and maximum
transmission points. Normalize the plot to the maximum value. Does it look like the theoretical
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function? (See Hecht Section 8.2.1) What is the actual transmission at best? The transmission is the ratio
of the maximum transmitted power to the incident power. You will probably have to turn the room lights
off when measuring the transmission minimum.
6. Waveplate Set-up and Identification: (Estimated time – 20 minutes; 20 pts) You are given
waveplate 1 and waveplate 2 and a linear polarizer. Determine which wave plate is the half-wave plate
and which is the quarter-wave plate. Record what your procedure and observations.
7. The Half-wave Plate: (Estimated time - 15 minutes; 15 pts) Measure the angles of the wave-plate
axes according to the angular scale of the wave-plate holder. Rotate the wave plate holder until the
polarization is rotated by 90 degrees. How does this agree with your theoretical expectations?
8. The Quarter-wave Plate: (Estimated time - 15 minutes; 15 pts) Measure the angles of the wave-plate
axes according to the angular scale of the wave-plate holder. Set the waveplate to make a circularly
polarized beam. Pass your circularly polarized beam through a linear polarizer. If you rotate the axis of
the linear polarizer, how should the transmitted power vary for a perfectly circularly polarized beam?
What do you actually find? Express you finding in terms of the ratio of the maximum to minimum
amount of power transmitted. Can you tweak the waveplate a little to make the beam more circularly
polarized? (Some applications benefit from using un-polarized light. It is difficult to “un-polarize” a
previously polarized light source. Circular polarization is frequently used to mimic un-polarized lightdo you see why?)
9. Optical Isolator: (Estimated time - 20 minutes; 20 pts) Using a polarizer and the quarter-wave plate
from 8, make your own optical isolator. Describe what you did. Place the isolator ~1.5 m from the laser,
to the other side of the table. Place and adjust a mirror so that the reflected beam returns back through
the optical isolator toward the laser. Slightly angle the reflected beam so that it can be measured with a
power meter. Determine the ratio of the returned beam intensity to the transmitted beam intensity. There
is a preassembled optical isolator in the lab. Set it down on the metallic tabletop. Observe the way the
light passes through the isolator. Flip the isolator over. Try the same thing on a target screen. Why is
there a difference? (This same type of isolator will be used in later experiments to prevent laser
frequency instability from retro-reflections.)
10. Laser beam expander: (Estimated time – 25 minutes; 25 pts) You will be given two positive lenses
of different focal lengths. (a) Use the knife-edge method to roughly determine the focal lengths of the
lenses. For this, you only need to determine qualitatively the location of the focal point by looking at the
projected beam on a screen after the knife edge. Observe what happens to the projected beam when the
knife edge is before, after, and at the focal point. The beam from the HeNe laser is assumed collimated.
(b) Set up a laser beam expander use the two lenses. (c) Use the knife-edge method to determine the
input and output beam sizes, and compare them with your prediction from the lens properties.
11. Fiber coupling (Estimated time– 30 minutes; 30 pts) Check out the overall fiber coupling setup first
and read through this part of the procedure. Ask TA’s help if you do not understand what we are
expected to accomplish in this part of the lab. Direct the beam into the 5-axis fiber positioning mount.
Remove the fiber from the 3-axis stage by loosening the setscrew and sliding out the copper barrel. Be
very careful as not to damage the fiber and the fiber tip. Place the fiber end in a safe location, making
sure that the end doesn’t become dirty or damaged. You should see a diverging beam emerging from the
coupling lens (a microscope objective). Use the knife-edge technique to measure the incident laser beam
size. Width given lens focal length, determine the laser spot size at the focal point. Does this size match
well with the fiber core size to be coupled? Use the power meter to measure the laser power before the
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lens. Record this value. Re-attach the fiber mounting plate and fiber to the power meter. You will now
align the fiber. Adjust the stage to maximize the light through the fiber to the power meter. Remember
to iterate between focal length Z and X-Y spatial positioning of the fiber mount. Calculate the relative
transmitted power. A coupling efficiency of greater than 50% should be attainable. Call in a TA if you
can’t get a very high intensity after 10 minutes. Slowly back out the fiber in the Z (axial) direction. At
which distance does the transmitted power fall to half the peak power? How does this compare to the
Rayleigh range of the laser beam?
If there are more time left, you can experiment with different microscope objectives and optimal
coupling efficiency you can achieve.
11. Turn off the laser. Clean up the lab and put away all optics as you find them before you leave. (You
will suffer penalty points if you don’t.)
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