Journal of Applied Mathematics and Physics, 2014, 2, 1105-1112
Published Online November 2014 in SciRes. http://www.scirp.org/journal/jamp
How to cite this paper: Bahrim, C., Raju, M.M., Khairuzzaman, M., Hsu, W.-T., Lanning, R.N. and Duplan, D. (2014) A New
Optoelectronic Switch: The Dielectric of a Capacitor Illuminated with a Laser Radiation. Journal of Applied Mathematics and
Physics, 2, 1105-1112. http://dx.doi.org/10.4236/jamp.2014.212128
A New Optoelectronic Switch: The Dielectric
of a Capacitor Illuminated with a
Cristian Bahrim*, Md Mozammal Raju, Md Khairuzzaman, Wei-Tai Hsu,
Robert Nick Lanning, Don Duplan
Department of Physics, La mar University, Beaumont, Texas, USA
Email: *cristian.bahrim@la mar.edu
Received August 2014
A dielectric changes its optical and electric characteristics when an external source provides
enough energy. We analyze the interaction between a laser beam and a dielectric surface placed
between two metal plates in a capacitor-type configuration. We show that a voltage applied across
the dielectric can shift the wavelength of the laser radiation as perceived by its electric dipoles.
The optical behavior of the dielectric in this arrangement recommends the device as a possible
optoelectronic switch which can be driven by a relatively small capacitor voltage.
Optoelectronic Devi ce, Las er-M atter Interact ion, Relative Perm i ttiv ity , Polarization of Light
A dielectric material is a collection of dipole molecules where the electronic charge forms an ellipsoid of rota-
tion and has two poles: a positive pole near the nuclei and a negative pole where there is a larger concentration
of electronic charge. When the dielectric is illuminated with radiation of low intensity, the electronic cloud has a
linear response and oscillates harmonically with respect to the equilibrium position, at the same frequency as the
incident radiation, or absorbs the radiation resonantly becoming opaque. In our experiment we will use dense
flint glass, which is a heavy silica-based glass doped with PbO molecules, irradiated with 532 nm from a diode
laser. In our experiment the dielectric is transparent to the radiation used because a laser beam of 532 nm has
much lower photon energy than what is needed for reaching the first excited state. Our flint glass becomes opa-
que in UV at 132.44 nm . The choice of using radiation of 532 nm is because the green light can be easily
observed by a normal human eye even when the light is dimmer, as it is the case in our measurements of Brew-
ster angle. We use a diode laser because it is more stable over a longer period of time as compared with other
The electric dipoles of the dielectric illuminated with 532 nm oscillate with a frequency of about 5.6 × 1014
C. Bahrim et al.
Hz and induce an electric field which propagates forward, in transmission. Each electric dipole oscillates as a
small antenna and passes the information about the incident light to the next dipole. The amplitude of oscillation
for all dipoles is the same for a dielectric with a linear response. However, each subsequent dipole in the dielec-
tric has a momentarily displacement which is slightly different than the previous one and the next dipole in the
direction of light propagation. The modulation of this gradual change of the dipoles’ displacement builds-up the
transmitted electric field (or ET-field).
Part of the radiation is also reflected back at an angle equal to the angle of incidence, according to the Fer-
mat’s Principle. This radiation forms the reflected electric field (or ER-field). The resonant interaction between
the electric field component of the incident radiation (or EI-field) and the electric dipoles induces a chain of di-
pole moments in the dielectric material which oscillates exactly in-phase with the incident field. A dipole
moment is the product of the electronic charge of one pole and its displacement . The electric dipoles build
together the net electric polarization of the dielectric, P which oscillates in-phase with the EI-field. The ratio of
these two fields defines the electric permittivity,
, of the dielectric:
where the absolute permittivity
0 is 0.00885 pF/mm. The relative permittivity
r of the dielectric indicates the
degree of polarization of the material’s dipoles with respect to vacuum:
The relative permittivity allows one to define the index of refraction of the dielectric as
This index of refraction represents a measure of the optical response of the material and indicates by how
much a radiation slows down when passing through it.
Reflection of light is a kind of back scattering at the dielectric surface that occurs whenever light experiences
a discontinuity in the incident medium. The plane of incidence is defined by the incident, reflected, and trans-
mitted rays, as shown in Figure 1. It is possible to polarize the reflected light at the interaction with a dielectric
surface. This happens at a precise angle of incidence called “Brewster angle”,
B. When light is incident at
there is no reflected component in the plane of incidence and all the light reflected is polarized in the plane per-
pendicular to the plane of incidence. Hence, the parallel component of the reflectance vanishes. The reflectance
is defined as the irradiance associated to the reflected light of the ER-field .
This phenomenon can simply and elegantly be explained by using the electric dipole oscillator model pro-
posed by Lorentz . Figure 1 shows an incident EI-field of amplitude E0I polarized parallel to the plane of in-
cidence. For an arbitrary angle of incidence,
I, the reflected ER-field of amplitude E0R and the transmitted ET-
field of amplitude E0T are also polarized in the same plane. Both directions of reflected and transmitted rays are
decided by the fact that light travels the path of least time (according to the Fermat’s Principle). Also, it is
well-known that an electric dipole cannot radiate energy along its axis of oscillation, but perpendicular on it.
When the direction of reflected light happens to be perpendicular on the direction of transmitted light, which is
for incidence at angle
B, then only the parallel component within the plane of incidence of the reflected light
vanishes. Using simple geometric reasoning one can find that
and using the Snell’s law we find the Brewster’s law 
In our data analysis we use a value of the refractive index for air (which is the incident medium), nI of
C. Bahrim et al.
Figure 1. The plane of incidence. The electric dipoles oscillate
perpen dicular on the transmitted ray. For incidence at Brewster
angle, only the perpendicular component on the plane of inci-
dence of the ER-field is reflected (open circles along the dotted
line), while the parallel component vanishes.
The purpose of our experiment is to use one laser source for modifying the Brewster angle and implicitly the
index of refraction of the dielectric according to Equation (5). This changes also the relative permittivity ac-
cording to Equation (3). The reason for such a variation of the optoelectronic characteristics is because the di-
electric’s dipoles perceive a shifted value of the wavelength of the incident radiation due to the presence of an
external source of energy which covers uniformly the dielectric surface.
In Section 2 we will describe the experimental setup and our experimental technique adopted for finding pre-
cise values of the Brewster angle from measurements of irradiances reflected (called hereafter “reflectances”) in
a region of a few degrees wide near the Brewster angle (called hereafter “Brewster region”). In Section 3 we
will present the theoretical interpretation, while the Conclusion will follow in Section 4.
2. The Experimental Method
2.1. Experimental Setup
Using the setup from Figure 2 we can observe the variation of the refractive index of the dielectric, nd, with the
change in the voltage applied across the capacitor that includes the dielectric. The capacitor has two parallel
aluminum plates placed on the top and bottom of the dielectric material. Several voltages have been applied in
order to produce different shifts of the laser’s wavelength as perceived by the dielectric, and implicitly a change
in the Brewster angle value and the relative permittivity of the dielectric.
We use a green diode laser of wavelength 532 nm incident on a dense flint glass. The laser radiation passes
through a beam splitter which splits the light into two parts: One part is sent to a monitoring branch for moni-
toring the stability of the probe laser and another part is sent through collimating slits incident on the dielectric
surface. The light reflected by the dielectric is further detected along the detector branch using a high sensitivity
light sensor. The incident light is attenuated to the desired intensity and next, polarized at 45˚ with respect to the
plane of incidence so that it has equal intensities in the parallel and perpendicular components defined with re-
spect to the plane of incidence (shown in Figure 1).
The light signal is carefully collimated before is incident on the dielectric surface and has the same diameter
where it impinges the surface throughout the experiment. Thus, on the dielectric surface the interaction between
the electric dipoles and the parallel and perpendicular components of the incident light is done evenly. Using a
linear polarizer on the detector branch we can separate the two components of the reflected light by the dielec-
tric surface. We observe that the parallel and perpendicular reflectances have different values . Finally, the
light detected by a high sensitivity photocell is transmitted to a computer interface for data processing, along
with the value of the angular position of the incident beam. In order to find the Brewster angle, we need to
scan a wider angular interval, of about 15˚, near the region where the parallel component of the reflectance
vanis he s.
C. Bahrim et al.
Figure 2. Th e experimental setup. The capacitor includes a dielectric placed
between two parallel metal plates.
2.2. Observables in Our Experiment
In our experiments, finding the Brewster angle requires to measure the parallel (R║) and perpendicular (R⊥)
components of the reflectance with respect to the plane of incidence. The analytic form for these two reflec-
tances can be derived using the Maxwell’s equations for electromagnetic waves incident on surfaces. The inte-
raction at surface imposes boundary conditions and generates the Fresnel’s equations (for details see ):
The major disadvantage of using these two components is that they do not have a simple variation near the
Brewster angle. Furthermore, the variation of the parallel component is very shallow near
B and makes the pre-
cision in finding its value to be very poor (It is about 0.1˚ in standard measurements with similar equipment ).
Bahrim and Hsu discovered in  that a normalization of the parallel (R║) and perpendicular (R⊥) components to
the total component generate two equations that can be fitted with a simple parabolic function in a region about
15˚ wide near
= =++ −
= =++ −
which leads to a theoretical minimum value of 0 for R║ (at
B) and a maximum value of 1 for R⊥ (at
er, experimentally does not exactly vanish at
B angle but it reaches a very small value that can be still resolved
with our detection system. This experimental choice is for practical reasons because we cannot know a priori the
exact value of the Brewster angle. First we need to perform the best parabolic fit using all the experimental data
points located both at lower and higher angular values than
B before we can find an accurate value for
Therefore our minimum value for R║ at
B has only a relative zero value.
C. Bahrim et al.
For stability purposes, throughout the experiment we have collected raw data for at least 15 seconds following
the conclusions previously published by Hsu and Bahrim in . Figure 3 shows a test case for the variation of
the angular value with the stability of the reflectance detected. Our studies indicated that we need to wait for
about 9 seconds before the signal detected reaches a plateau of stability. Hence we have to process data collected
only between 10 to 15 seconds. Our technique allows finding Brewster angles with a precision of 0.001˚ which
is 100 times better  than measurements using similar equipment .
3. Data Analysis
Varying the capacitor voltage from 0 V to 9 V, we were able to observe small changes of refractive indices, due
to the variation of the Brewster angle, with a similar precision as in other previous experiments where we have
used an isotropic energy source, such as a blackbody radiation . The present experimental method allows us
to generate accurate dispersive curves having a precision similar with other more sophisticated experimental
techniques, such as “the minimum deviation method” reported in .
3.1. Theoretical Model
In our present experiment, the dielectric is part of a capacitor configuration and therefore, the uniform voltage
applied across its surface supplies an extra energy U that can be simply added to the probe signal, E1, and thus,
produces another energy, E2, which is the one actually perceived by the dielectric’s oscillating dipoles:
E EU= +
Equation (10) is graphically represented in Figure 4.
The scalar addition of energies in Equation (10) is the consequence of the conservation of energy for our
closed system formed by the dielectric surface irradiated with light of
1 = 532 nm and having a voltage across it.
Using Planck-Einstein hypothesis regarding light as a photon E = hc/λ where hc is the product of Planck con-
stant and the speed of light in vacuum, the Equation (10) becomes
The change in the wavelength of the reflected light as perceived by the dielectric surface leads to a shifted
value of the index of refraction and the dielectric’s relative permittivity. In our experimental conditions, the la-
ser’s wavelength shifts from
1 of 532 nm at 3.0 V (where U = 0), to
2 of 518 nm at 4.0 V (where U = 0.0629
eV), 495 nm at 6.0 V (where U = 0.1742 eV) and 475 nm at 9.0 V (where U = 0.2797 eV).
3.2. Results and Interpretation
We illuminated the surface of a flint glass prism with radiation laser of 532 nm and varied the voltage across the
capacitor (hereafter called “capacitor vol t age”) from 0 to 9 V. We generated the plot shown in Figure 5. We
observe a decrease in the value of the Brewster angle with the increase of the capacitor voltage from 0 to 0.5 V,
followed by a quasi-linear increase above 1 V. This quasi-linear variation is consistent with Equation (10) for
the conservation of energy and also, with the ability of the dipoles to have a harmonic response to the presence
of an additional energy, U, distributed uniformly on the dielectric surface.
A linear trend of the Brewster angle indicates that both the laser and the capacitor voltage provide energies
which are weak enough so that the dielectric dipoles oscillate harmonically. In our experimental conditions the
dipoles have a linear elastic response under the action of the incident EI-field which is greatly helped by the very
small electronic inertial mass. This means that the net Coulomb force due to both the EI-field and the capacitor
voltage acts linearly on the dipoles closely follo wing the Hooke’s law: F = −kx, for a simple harmonic oscillator,
where x is the elongation of the dielectric dipoles and k is the spring constant of the electronic cloud.
From Figure 5 we observe that the result at 3V almost coincides with the value at 0V (where no voltage is
applied across the capacitor). In Figure 6 it is interesting to remark that a similar variation with the capacitor
voltage is obtained for the relative permittivity, after using subsequently Equations (5) and (3). This observation
reinforces the above interpretation with the linear response of the electric dipoles.
The uniform EC-field associated to the capacitor voltage establishes a uniform source of energy for all dipoles
C. Bahrim et al.
Figure 3. An example of the variation of Brewster angle with the time of
detection at VC = 3V . A threshold of stability is reached for any voltage after
about 9 - 10 seconds..
Figure 4. A schematic energy diagram associated to Equation (10).
0 is the
opacity wavelength, which is 132.44 nm for a dense flint glass illuminated
with 532 nm .
Figure 5. The variation of
B with VC.
on the dielectric’s surface and creates an even attraction of their poles towards the plates of opposite polarity due
to the Coulomb force. Due to the capacitor voltage the dipoles become more polarized (or elongated) on the di-
electric surface and the degree of polarization increases with the voltage. On the other hand the incident laser
radiation is linearly polarized at 45˚ from the plane of incidence and will also tend to align the dipoles along
the direction of polarization of the EI-field according to the Lorentz model described in the Introduction. When
both fields are acting simultaneously on the dipoles a competition occurs that can explain the variation of the
C. Bahrim et al.
Figure 6 . The variation of
R with VC.
relative permittivity with the capacitor voltage reported in Figure 6.
Thus, for very small capacitor voltages, lower than 0.5 V in our case, the electric dipoles on the dielectric
surface align themselves along the EI-field of the laser beam which is tilted 45˚ from the plane of incidence, thus
providing a polarization-like effect which reduces the net charge on the capacitor’s plates and implicitly the ca-
pacitance. When the capacitor voltage slightly exceeds 0.5 V the electric field of the probe laser does not man-
age to align alone the dipoles anymore and the dipoles’ orientation starts to be gradually dominated by the
EC-field of the capacitor, thus working in increasing the charge on the plates for the same capacitor voltage (VC)
and also the capacitance according to the relationship C = Q/VC. The competition between the two electric fields
at 3V makes the flint glass illuminated with a laser beam of 532 nm and 2 mm in diameter to generate the same
dielectric response as for the case without voltage across the dielectric. With a further increase of the capacitor
voltage the orientation of the electric dipoles is strongly dominated by the EC-field associated to VC. Due to an
additional energy, U, from the capacitor voltage, the dipoles on the dielectric will oscillate linearly at higher
frequencies, as indicated by Equation (11). This is causing a lower inertial resistance, and therefore, higher rela-
The general trend in the variation of the relative permittivity with the change in the capacitor voltage shown in
Figure 5 for the test case of a dense flint glass illuminated with a laser radiation of 532 nm is expected to be al-
most the same for any type of dielectric. However, the actual voltages for the minimum value of the relative
permittivity (for flint is at 0.5 V) and for the resetting to the initial conditions at no capacitor voltage (for flint is
at 3 V) will certainly be different. The reason appears clear from the actual meaning of the relative permittivity,
which represents a measure of the degree of polarization of the dielectric material according to Equation (2). A
material with larger net atomic polarization, P, will have larger relative permittivity,
r, as indicated by equation
(2) and will most likely require a larger capacitor voltage for the alignment of the electric dipoles along the
EC-field. Also the intensity of the laser field and the waist of the laser beam are two important factors that need
to be considered. The region of transition in the dielectric polarization property from a polarization driven by the
EI-field of the laser to the EC-field of the capacitor voltage can make this device when illuminated with laser
radiation to function as an optoelectronic switch.
 Bahrim, C. and Hsu, W.-T. (2009) Precise Measurements of the Refractive Indices for Dielectrics Using and Improved
Brewster Angle Method. American Journal of Physics, 77, 337-343. http://dx.doi.org/10.1119/1.3056583
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Journal of Physics, 69, 1166-1168. http://dx.doi.org/10.1119/1.1397457
 Hsu, W.-T. and Bahrim, C. (2009 ) Accurate Measurements of Refractive Indices for Dielectrics in an Undergraduate
Optics Laboratory for Science and Engineering Students. European Journal of Physics, 30, 1325-1336.
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 Bahrim, C., Duplan, D., Hsu, W.-T. and Lanning, R. (2012) Measuring the Curve of Dispersion for Dielectrics Using a
Low-Energy Laser and a Thermal Source of Radiation. Bulletin of the American Physical Society, APS March Meeting
2012, Boston, 27 February-2 March 2012, B32.00013.
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