Maria Bayard Dühring - Solid Mechanics

4 Chapter 2 Time-harmonic propagating waves
propagates near the surface of a half space. The Lamb wave is a type of wave that
propagates in plates. The solid crystals are in general anisotropic such that their
properties, as elastic, thermal, electric and optical properties, depend on the crystal
direction. If the material is piezoelectric the elastic wave will be accompanied by
an electric field. Apart from direct mechanical impact the elastic waves can be generated
in different ways, for instance by the thermal-elastic effect by laser pulses,
or by applying an electric field to transducers connected to a piezoelectric material
were a wave is generated by the inverse piezoelectric effect.
Audible waves were the first known types of waves. At the end the 19th century,
it was known that seismic waves can propagate as bulk waves in the earth and in
1885 it was discovered by Lord Rayleigh that also surface waves are generated by
seismic activity [4]. The piezoelectric effect was discovered in 1880 [5] and it was
employed in the first sonar that were tested during the 1st World War. The waves
were generated by transducers and launched in the water to detect submarines.
This was the first application of elastic waves and they have ever since been studied
in both fluids and structures. An increasing number of applications have emerged
such as oscillators, filters, delay lines and ultrasound scanning in medicine and nondestructive
testing. An important condition for realizing these applications and
making them efficient was the intensive study of new piezoelectric materials and
their fabrication, as ceramics and single crystals, that started in the middle of the
20th century. This made it possible to transform electric energy efficiently into
acoustic energy through bulk wave transducers for high frequencies around 1 GHz.
In 1965 it was shown by White and Voltmer [6] that Rayleigh waves can be excited
by interdigital transducers, which consist of arrays of electrode fingers deposited on
the surface of a piezoelectric material. The electrode fingers define the wavelength
and the width of the wave beam. This method is now the most common way to
generate and detect acoustic waves, and Rayleigh waves are used extensively in
electromechanical bandpass filters and resonators in telecommunication, television
and mobile phones [7] as well as in oscillators and sensors [8, 9, 10]. With the
modern fabrication techniques it is possible to make interdigital transducer that
generates SAWs with frequencies up to a few GHz. A new application of SAWs is
in optoelastic devices where optical waves are modulated, see subsection 2.1.3.
2.1.2 Optical waves
The other type of waves treated here are electromagnetic waves, which can propagate
both in vacuum and in solid media, see [11] for an introduction to this field. The
electric and magnetic fields have the same phase and are polarized perpendicular to
each other and perpendicular to the propagation direction. Electromagnetic waves
were first suggested by Maxwell in the 1860s [12], where he combined the laws of
electricity and magnetism in Maxwell’s equations. Electromagnetic waves are fully
described by these vector equations, which give the electric and the magnetic fields
for general elliptic polarized waves in structured medias. They can be reduced