KEYWORDS: Diffraction limit, Negative refraction, Metamaterials, Lamb Waves
Backward propagating waves, Focusing, Super-resolution, Ultrasonic
Imaging, Gradient Refractive Index.
The primary aim of this thesis is to develop novel techniques to focus ultrasonic waves
and demonstrate their applications. Focusing of waves improves the resolving
capability of the ultrasonic inspection system. Techniques to improve the resolution of
imaging systems beyond the diffraction limit are important to several clinical and
industrial applications, including underwater imaging, non-destructive evaluation, and
material processing. Apart from this, the conventional ultrasonic contact transducers
cannot focus ultrasonic waves inside a given bulk medium. In view of this, in this thesis,
focusing of ultrasound waves has been studied for two different applications; first, to

achieve a focal spot of subwavelength size which is then used to demonstrate super-
resolution, and second, to focus the ultrasound waves generated from a conventional

transducer to a predetermined location. The approaches developed are simple in design
and cost-effective.

The first approach is to design a lens, which can focus the ultrasound waves. The design
is based on the concept of negative refraction or backward propagating waves that exist
in plates. Certain Lamb wave modes exhibit backward wave propagation, in which the
phase velocity will be antiparallel to group velocity. The mode conversion from
forward to backward propagating wave mode will cause the waves to focus and this is
achieved by selecting two different materials, of same thickness. This novel lens is
named as material contrast lens. Materials are selected based on the mode conversion
from forward to backward propagating for a given thickness. Aluminium and
Molybdenum are chosen as two different materials as they exhibit mode conversion
phenomenon. The interface between the two metals causes the interaction of the

forward-propagating second symmetric Lamb mode S2 and converts into the backward-
propagating first symmetric S2b. Three-dimensional (3D) FE simulations are carried out

to observe the focal spot, and the results are validated experimentally. The output field is processed in the Fourier domain to establish the focal spot. Using the material
contrast lens the size of the focal spot obtained was 0.4 λ full width at half maximum
(FWHM), where λ is the operating wavelength, this is less than would be predicted by
the diffraction limit. This encouraged to use the proposed lens as a potential tool for
subwavelength imaging. Simulations are carried out to show the super-resolution
capability of the proposed lens.

For the second case of interest, design of a shell structure gradient refractive index
(GRIN) device is considered to focus the ultrasonic waves. The novel 'add-on' GRIN
device consists of multiple shells, arranged concentrically, to focus the ultrasonic
waves by leveraging dispersive behavior of the wave modes in hollow thin cylinders.
The design is demonstrated through longitudinal L(0,2) mode which propagates inside
the designed structure at a frequency of 500 kHz. The parameters of the shells such as
thickness and material of the shells, are chosen to focus the waves to a predetermined
focal spot. A two-dimensional (2D) axisymmetric finite element (FE) simulation is
performed, and validated through experiments. Varying the shell material or thickness
is shown to offer an elegant and straightforward way to achieve dynamic focusing
without advanced lenses or electronic steering.

This work proposes two novel approaches to focus the elastic waves efficiently and
demonstrates their application through subwavelength resolution and controlled wave
propagation within bulk medium. This research opens up the possibilities of developing
new lensing devices for integrating into medical imaging, nondestructive evaluation,
and sensing applications.