Laser Light Is Incident on A Plastic Surface Lab Report

EEE341 Lab 1:Reection of Plane Waves1
Objective
Measure the reectance of polarized plane waves incident on the surface of a
material and observe the phenomenon of Brewster angle.
2
Introduction
When an electromagnetic plane wave (such as light) traveling in one medium,
such as air impinges on the interface of a second medium, such as water, the
wave is partially transmitted in the second medium and partially reected
back in the rst medium. The reectance (fraction of incident electromagnetic power that is reected at the interface) depends upon the angle of
incidence and the polarization of the wave as well as the indices of refraction
of the two media. The reection coecient (denoted by Γ) is the ratio Er /Ei ,
where Er is the electric eld of the reected wave and Ei is the electric eld of
the incident wave. Reectance (R) is the square of the reection coecient.
For a plane wave, the electric eld exists in a plane perpendicular to
the direction of propagation. As a result, any arbitrary polarization can be
specied as a superposition of two orthogonal base polarizations. These base
polarizations can be dened as being parallel to and perpendicular to the
plane of incidence.
Technical workers in optics use slightly dierent nomenclature and denitions of reection coecients for parallel and perpendicular polarizations
than workers in radio frequency and microwave electromagnetics. In this
lab, the optical nomenclature and denitions of reection coecients are
used whereas the textbook (Cheng) uses the radio frequency and microwave
electromagnetics nomenclature and denitions.
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iCourse: EEE341 Lab1
• The wave is said to be p-polarized if its E-eld is parallel to the
plane of incidence, as shown in Fig. 2.1. The reection coecient of
parallel-polarized waves is given by
Γp =
η1 cosθi − η2 cosθt
η2 cosθt + η1 cosθi
(2.1)
Notice that in Fig. 2.1 the incident and reected electric elds are in opposite directions when θi = 0. In contrast, in Fig. 8-21 in the textbook,
the incident and reected electric elds are in the same direction when
θi = 0. As a result, the equation for Γp is the negative of equation
(8-221) for Γk in the textbook. However, the reectance for parallel
polarization is the same for both conventions.
Rp = |Γp |2 = |Γk |2 = Rk
(2.2)
• The wave is said to be s-polarized if its E-eld is perpendicular to the
plane of incidence, as shown in Fig.2.2. The s in s-polarized comes from
the German word senkrecht , meaning perpendicular. The reection
coecient of perpendicular-polarized waves is given by
Γs =
η2 cosθi − η1 cosθt
η2 cosθi + η1 cosθt
(2.3)
Notice that in Fig. 2.2 the incident and reected electric elds are in
the same direction when θi = 0. Likewise, in Fig. 8-20 in the textbook,
the incident and reected electric elds are in the same direction when
θi = 0. As a result, the equation for Γs is the same as equation (8-206)
for Γ⊥ in the textbook. The reectance for perpendicular polarization
is the same for both conventions.
Rs = |Γs |2 = |Γ⊥ |2 = R⊥
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(2.4)
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iCourse: EEE341 Lab1
Figure 2.1: Parallel Polarization.
Figure 2.2: Perpendicular Polarization.
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iCourse: EEE341 Lab1
The plane of incidence is the plane that is normal to the surface of the
sample and contains the wave propagation vector. The intrinsic impedance
of a medium is
r
µ◦ µr
(2.5)
η=
◦ r
√
The refractive index is n = µr r . And the transmitted angle can be calcu-
lated by using Snell’s law as
sinθt
n1
=
sinθi
n2
3
(2.6)
Pre-Lab
Consider an experiment in which a polarized beam of laser light is incident on
a plastic surface. Assume the plastic has a relative permittivity of r2 = 2.3
and a relative permeability of µr2 = 1. Plot the theoretical reectance values
for both parallel and perpendicular polarizations: Rp vs θi and Rs vs θi ,
respectively, with θi in degrees. The range of the incident angle is set to be
0◦ ≤ θi ≤ 90◦ .
4
Procedure
Equipment:
• Laser module.
• Pohtometer.
• Polarizers(parallel and perpendicular).
• Sample disk.
• Optical bench.
In this lab, electric and magnetic elds of high frequency electromagnetic
waves can’t be measured directly. However, the incident and reected powers
can be measured and then used in the following relation to calculate the
measured reectance values.
Pr = RPi
(4.1)
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1. Setup the experiment on the optical bench as shown in Fig.4.1.
Figure 4.1: A diagram of experiment setup.
2. At a given position, the electric eld of an unpolarized laser beam
varies randomly in time, while the electric eld of a linearly polarized
beam traces a straight line. A wave can be polarized by letting it pass
through a polarizing glass. The small round polarizing glass provided
in this lab has a notch on its edge that is used to identify the direction
of the polarized E-eld. The E-eld of the polarized wave is in a direction normal to a line passing through the notch and the center of the
circular glass. The laser beam must be polarized in this lab experiment
by judiciously utilizing a proper polarizer in parallel or perpendicular
polarization.
3. Using the protractor and the plastic disc to measure the angle of incidence. The disc has lines on it with 5-degree increments. Remember
that the angles are always measured from the normal on the surface of
the sample.
4. Using the photometer to measure transmitted and reected powers.
The sensitivity of the meter will be taken into account during the experiment. Therefore, a judicious scale or multiplier should be used.
During the measurement, the photometer sensor will have to be held
steady with your hand so that the laser spot is incident on the black
square inside the sensor cap. To get consistent results, discuss a plan
with lab partners on how to read the power properly from the deection
of the meter.
5. The polarization of the light beam from the laser module varying slowly
with time. Therefore, whenever the reected power is measured, the
incident power should also be measured. Moreover, try to reduce the
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iCourse: EEE341 Lab1
time elapsed between measuring Pi and Pr . This will help to normalize
the eect of any uctuations in power.
6. You will take measurements at dierent angles of incidence. The angle of reection is the same as the angle of incidence from the law of
reection.
7. First, align a proper polarizer to produce a parallel-polarized beam and
measure the incident and reected powers at dierent angles of incidence. Record the measurements in the table along with the calculated
Rp . Did you recognize the Brewster angle while scanning the angles?
8. Next, align a proper polarizer to produce a perpendicular-polarized
beam and measure the incident and reected powers at dierent angles
of incidence. Record the measurements in the table along with the
calculated Rs .
9. Overlap measurement data of Rp and Rs on the corresponding plots
which were obtained from pre-lab section. Adjust the value of r2
slightly in the equations to produce new graphs of Rp and Rs which
would better t the measurement data. What is the better t value of
r2 ? Include the graphs produced with this new r2 .
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Post-Lab
1. A right-hand circularly-polarized wave in free space (η1 ) impinges on a
PEC (Perfect Electrical Conductor) object (η2 ) with perfectly smooth
and at surface. The surface area is assumed to be electrically large
compared to the wavelength of incidence. How do you dene the sense
of rotation from the reected wave on that surface?
2. A laser beam with unknown polarization is traveling over the air in a
specic direction. How can you determine the polarization of the beam
by using a Plexiglas sample?
3. A laser beam (operating at 1013 Hz) is normally incident on the surface
of salt water. Salt water has the following parameters: r = 80, µr = 1,
σ = 20 × 103 (S/m).
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(a) Is water a good dielectric or a good conductor in this case? Why?
(b) Calculate the magnitude of the reection coecient.
4. For which type of polarization does the Brewster angle exist for nonmagnetic materials? At the Brewster angle of incidence, what is the
angle made by the refracted ray with the reected ray?
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Lab Report
Compile your report template into a single PDF le, and submit it using the
link provided in Canvas. The format of the le name is EEE341_ your last
name_ Lab1.pdf.
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