This document discusses research on phononic crystals using photoelastic visualization techniques. Simulation results using FEM show negative refraction and focusing of waves passing through triangular arrangements of steel rods embedded in epoxy. The research aims to experimentally validate simulations by creating a solid-solid phononic crystal and using photoelastic methods to observe wave propagation. This will provide a better understanding of phononic crystal properties without limitations of computer simulation.

1. 1
Phononic Crystals
Propagation and Visualization of waves
Zhe Yi Soo, Dr. Ankit Srivastava
Illinois Institute of Technology
Phononic crystal has gained a lot of interested recently due to its ability to control, direct, and manipulate sound
waves. However, it requires a carefully design and manufacture process. Hence, a better underastanding on phononic
crystal is needed. In this paper, we are going to use stress analysis technique, Photoelastic method to observe propagation
of stress waves in phononic crystal. Experiments set up for photoelastic method and the theory behind it will be explained
in this paper.
A solid-fluid phononic crystal will be simulated through Fenics in this paper and a solid-solid phononic crystal will be
done in future experiments. The result will be compared to simulation results using Fenics. Negative refraction and
focusing will be the main topic that we will be experimenting in phononic crystal.
I. INTRODUCTION
The field of phononic crystals emerged over the past
two decades. The reason for the emerging interest towards
phononic crystals is due to phononic crystals are novel
material that provides exceptional control over phonons,
sounds, and mechanical waves [1].
Negative refraction and focusing are some of those
interesting topics in phononic crystals. These special
properties of elastic waves can only be achieved by phononic
crystals and could lead to a lot of great applications in
industry or even daily life. Sound proofing, sound cancelling,
and focusing sound are some of those important applications
for industry. Mechanical waves are waves that propagate as
an oscillation of matter and transfer energy while travelling
through a medium. Since we are able to control the
properties of mechanical waves using phononic crystals,
which means transfers of energy in mechanical waves are
being controlled. Hence, this research topic can be related to
Engineerng themes – Energy area.
However, it requires a precise and careful design in
order to control propagation of waves. This requires a great
understanding of how waves propagate in phononic crystals.
A lot of work has been done describing propagation of waves
in phononic crystals using calculation or Finite Element
Method (FEM) but we are focusing on visualization of waves
in phononic crystals using stress analysis method.
Photoelastic visualization technique has been chosen in
this experiment in imaging propagation of waves in
Phononic crystals. By using this technique, it provides us a
clear and detail image of the elastic waves. Hence, a better
understanding of the fundamental nature of wave
propagation in Phononic crystals can be achieved. This could
be very useful in future study of phononic crystal as we are
no longer restricted to computer simulation and analyzation
for observation of wave propagation in phononic crystals.
Besides, it can shorten the experiment time in observation of
wave propagation on phononic crystals. These can lead to an
easier designing and understanding of phononic crystals in
the future.
Photoelastic method has been used in many areas in
order to visualize stress waves. A quantitative evaluation of
ultrasonic waves in glass using photoelastic method has been
done. Principle of photoelastic and experiment set up details
is explained in this paper. This paper presented both 2D and
3D of sound pressure as a result of photoelastic method [2].
Photoelastic method is used to investigate sound field and
pressure that is generated using phased array transducer.
Phased array transducer provides an easier angle control,
more precise focal point control, and easier imaging
inspection result. Quarts glass is being chosen as the medium
in this experiment. Directivity measurement is done using
photoelastic method and is compared with the result using
Finite Element Method [3]. Image processing technique for
photoelastic method has been explained in this paper.
Residual stress is being eliminated using the image
processing technique and hence showing a clearer and better
result of propagation of ultrasonic waves [4].
Since photoelastic method requires a solid medium, a
solid-solid phononic crystal is needed in order to conduct the
experiment. A two dimensional solid-solid phononic crystal

2. 2
has been created by using epoxy and steel rods in this paper.
The phononic crystals is made of triangular arrangement f
steel rods embedded in an epoxy matrix. Epoxy is chosen
due to its viscosity and waves speed which made negative
fraction and focusing possible. The structure in this paper has
been chosen for our research project and we will use
photoelastic method to analyze the propagation of waves in
this phononic crystal.
II. METHODS
A simulation was done using Cygwin code. By setting
the domain and the orientation of the phononic crystal based
on the information below, simulation can be done using
Finite Element Method. The code is written based on the
calculation of how waves will propagate in solid-solid case
phononic crystal. Paraview is a data analysis and
visualization software that is used to visualize the result.
The phononic crystal is made of a triangular
arrangement of steel rods embedded in an epoxy matrix. The
diameter of the steel rods are 2mm and the lattice parameter
is 2.84mm. Thus the filling factor of the epoxy matrix is
equal to 0.45. There are a total of 420 rods which 40 rods on
base and a height of 20 rods. The density of the steel is 7800
kg/m^3, the longitudinal wave velocities are 6180 m/s and
the transverse wave velocities are 3245 m/s. The density of
the epoxy is 1150 kg/m^3, the longitudinal wave velocities
are 2440 m/s and the transverse wave velocities are 1130 m/s
[5].
The source of 780 kHz which is around 8 times larger
than the longitudinal wavelength in the epoxy is being used.
This design of phononic crystal is used for observation of
negative refraction.
The focus on this paper is observation of properties of
waves using photoelastic method. The result of the
photoelastic method will be compared with the simulation
result.
Photoelastic method is a non-destructive, whole field,
graphic stress analysis technique. The advantages of
photoelastic are as below.
1. Provides reliable full-field values of the
difference between the principal normal
stresses in the plane of the model.
2. Provides uniquely the value of the non-
vanishing principal normal stress along the
perimeter of the model, where stresses are
generally the largest.
3. Furnishes full-field values of the principal-
stress direction. (Sometimes called stress
trajectories.)
4. Is adaptable to both static and dynamic
investigations.
5. Requires only a modest investment in
equipment and materials or ordinary work.
6. It is fairly simple to use [6].
Figure 1 Experiment set up for photoelastic method.
The experiment set up for photoelastic method is shown
in figure 1. The photoelasticity method is based on the
properties of light. Stroboscope will be sending out pulsed
light with a fixed frequency that we require. A polarizer will
be converting randomly polarized light to plane polarized
light which in simple means filtering light and letting light
waves with specific direction to pass through. From figure 2,
the incoming light is resolved into two vector axis and one of
them passes through while the others are rejected [6].
Photoelastic materials which in here is the phononic
crystals are birefringent. This means that they are able to
refract light differently for different light-amplitude
orientation depending upon the state of stress in the material
[6]. As ultrasonic waves are mechanical waves, the state of
stress in the phononic crystal is changing according to the
waves emitted by probe.
In conclusion, the birefringent materials resolve
incoming light into two components which is parallel to the
principal stress axis. It retards the out coming light by an
amount that is proportional to the difference of principal
stresses [6].
Figure 2 Polarizer

3. 3
The analyzer works the same way as polarizer just in a
different orientation. Light coming out from the analyzer will
be focused by the lens and captured by the CCD camera.
Light captured will go through image processor and analyzed
using computer to show the propagation of waves in
phononic crystal.
The models of phononic crystals are made out by first
setting up the steel rods in triangular periodic arrangement in
order to obtain prism-shaped phononic crystals. Then, the
steel rods are embedded in liquid epoxy resin and a partial
vacuum is used during the hardening of resin in order to
avoid residual air bubbles in the phononic crystal [5].
III. RESULTS
Simulation of negative refraction and focusing has been
done using Fenics code.
Figure 3 Fenics simulation of negative refraction
As shown in the figure 3, it illustrates waves passing
through a 2D triangular arrangement or steel circular rods
embedded in water. A fluid solid case has been used in this
simulation. It shows a clear and detail negative refraction
phenomenon when the waves is coming out from the
triangular arrangement of steel rods. The wave is refracting
in a negative direction which is impossible for normal
refraction and hence called as negative refraction.
Figure 4 Fenics simulation of focusing
Simulation of focusing has been done using FENICS
code too. From figure 4, rectangular arrangements of steel
circular rods are embedded in water which acts like a lens.
The waves passing through the steel rods and focus in a short
distance from the end of the steel rods.
Solid-solid case which uses steel rods in epoxy matrix
requires more complex coding and still under
experimentation.
IV. DISCUSSION
The experiments has ensured that the simulation is
working correctly and will be used to simulate the solid-solid
case of phononic crystal. However, it requires more tuning
on the coding as it is more complex to simulate a solid-solid
case phononic crystal.
Figure 5 Positive refraction and negative refraction
According to Snell’s Law, waves will refract when
passing through a different median. As shown in figure 5,
when the waves are refracting to the other side of normal line,
it is positive refraction. However, it is negative refraction
when the waves refract on the same side of the normal line.
Figure 6 Explanation on Fenics simulation
From the simulation result, it is shown that the waves are
refracting at the same side of refraction and hence negative
refraction is achieved.
Using the properties of negative refraction, a better
focusing can be achieved which is shown in figure 7.

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Figure 7 Focusing using negative refraction property.
It is not possible for a conventional lens to produce an
image containing details that are finer than half of the
wavelength of the waves (diffraction limit). This loss in
detail is due to the non-propagating nature of evanescent
waves.
However, in lens made out of negative index material,
evanescent waves can propagate over small distances leading
to the preservation of detail. Negative refractive lens doesn’t
require a curved shape to focus the waves and, therefore,
leads to easier production.
V. CONCLUSION
Our research has done simulation on simpler case for
determining properties of phononic crystals such as negative
refraction and focusing. This established a good background
for us in future experiments on harder simulation which is on
solid-solid phononic crystal.
After simulation is done, we will be implementing the
model to hands on experiments which require techniques of
photoelastic method.
VI. ACKNOWLEDGEMENTS
This research is made possible through the help and
support from ACE Undergraduate Research Program. I
would also like to thank Yan Lu for providing technical
support in Fenics coding and simulation progress.
VII. REFERNCES
1. T. Gorishnyy, M. Maldovan, C. Ullal, E. Thomas,
(Dec 2005) Sound ideas. physics world: 1-7
2. K.Date,Y.Tabata*,H.Shjmada , A Quantitative
Evaluation Of Ultrasonic Wave in Solid By the
Photoelastic Visualization Method. Miyagi National
College of Technology, Medeshima Natori,
00900-560718710000- 1093, 1987 IEEE
3. Sho Washimori, Tsuyoshi Mihara and Hatsuzo
Tashiro (2012) Investigation of the Sound Field of
Phased Array Using the Photoelastic Visualization
Technique and the Accurate FEM. Materials
Transactions 53(4):631 to 635.
4. Kazuhiro Date, Yoshio Udagawa, Visualisation of
Ultrasonic waves in a solid by stroboscopic
Photoelasticity and Image Processing Techniques :
1755-1762
5. James W. Phillips, TAM 32, Experimental Stress
Analysis. University of Illinois at Urbana-
Champaign, 6.2-6.62.
6. A. Tinel, B. Dubus, J. Vasseur, and A.-C. Hladky-
Hennion (Feb 2011), Negative refraction of
longitudinal waves in a two-dimensional solid-solid
phononic crystal. Phys. Rev. B 83, 054301.