Transducer diffraction theory and development of an ultrasonic tomogram

The work described in this thesis is the development of an ultrasonic tomogram to provide outlines of cross-sections of the ulna in vivo. This instrument, used in conjunction with X-ray densitometry previously developed in this department, would provide actual bone mineral density to a high resolution. It was hoped that the accuracy of the plot obtained from the tomogram would exceed that of existing ultrasonic techniques by about five times. Repeat measurements with these instruments to follow bone mineral changes would involve very low X-ray doses. A theoretical study has been made of acoustic diffraction, using a geometrical transform applicable to the integration of three different Green's functions, for axisymmetric systems. This has involved the derivation of one of these in a form amenable to computation. It is considered that this function fits the boundary conditions occurring in medical ultrasonography more closely than those used previously. A three dimensional plot of the pressure field using this function has been made for a ring transducer, in addition to that for disc transducers using all three functions. It has been shown how the theory may be extended to investigate the nature and magnitude of the particle velocity, at any point in the field, for the three functions mentioned. From this study. a concept of diffraction fronts has been developed, which has made it possible to determine energy flow also in a diffracting system. Intensity has been displayed in a manner similar to that used for pressure. Plots have been made of diffraction fronts and energy flow direction lines.

Nonlinear diffraction in sub-critical femtosecond inscription

Material processing using high-intensity femtosecond (fs) laser pulses is a fast developing technology holding potential for direct writing of multi-dimensional optical structures in transparent media. In this work we re-examine nonlinear diffraction theory in context of fs laser processing of silica in sub-critical (input power less than the critical power of self-focusing) regime. We have applied well known theory, developed by Vlasov, Petrishev and Talanov, that gives analytical description of the evolution of a root-mean-square beam (not necessarily Gaussian) width RRMS(z) in medium with the Kerr nonlinearity.

Nonlinear diffraction in sub-critical femtosecond inscription

Material processing using high-intensity femtosecond (fs) laser pulses is a fast developing technology holding potential for direct writing of multi-dimensional optical structures in transparent media. In this work we re-examine nonlinear diffraction theory in context of fs laser processing of silica in sub-critical (input power less than the critical power of self-focusing) regime. We have applied well known theory, developed by Vlasov, Petrishev and Talanov, that gives analytical description of the evolution of a root-mean-square beam (not necessarily Gaussian) width RRMS(z) in medium with the Kerr nonlinearity.

Sub-critical regime of femtosecond inscription

We apply well known nonlinear diffraction theory governing focusing of a powerful light beam of arbitrary shape in medium with Kerr nonlinearity to the analysis of femtosecond (fs) laser processing of dielectric in sub-critical (input power less than the critical power of selffocusing) regime. Simple analytical expressions are derived for the input beam power and spatial focusing parameter (numerical aperture) that are required for achieving an inscription threshold. Application of non-Gaussian laser beams for better controlled fs inscription at higher powers is also discussed. © 2007 Optical Society of America.

Sub-critical regime of femtosecond inscription

We apply well known nonlinear diffraction theory governing focusing of a powerful light beam of arbitrary shape in medium with Kerr nonlinearity to the analysis of femtosecond (fs) laser processing of dielectric in sub-critical (input power less than the critical power of selffocusing) regime. Simple analytical expressions are derived for the input beam power and spatial focusing parameter (numerical aperture) that are required for achieving an inscription threshold. Application of non-Gaussian laser beams for better controlled fs inscription at higher powers is also discussed. © 2007 Optical Society of America.

Experiments and analysis of combined diffraction and self diffraction effects in a nematic liquid crystal cell

The potential for nonlinear optical processes in nematic-liquid-crystal cells is great due to the large phase changes resulting from reorientation of the nematic-liquid-crystal director. Here the combination of diffraction and self-diffraction effects are studied simultaneously by the use of a pair of focused laser beams which are coincident on a homeotropically aligned liquid-crystal cell. The result is a complicated diffraction pattern in the far field. This is analyzed in terms of the continuum theory for liquid crystals, using a one-elastic-constant approximation to solve the reorientation profile. Very good comparison between theory and experiment is obtained. An interesting transient grating, existing due to the viscosity of the liquid-crystal material, is observed in theory and practice for large cell-tilt angles.

Experiments and analysis of combined diffraction and self diffraction effects in a nematic liquid crystal cell

The potential for nonlinear optical processes in nematic-liquid-crystal cells is great due to the large phase changes resulting from reorientation of the nematic-liquid-crystal director. Here the combination of diffraction and self-diffraction effects are studied simultaneously by the use of a pair of focused laser beams which are coincident on a homeotropically aligned liquid-crystal cell. The result is a complicated diffraction pattern in the far field. This is analyzed in terms of the continuum theory for liquid crystals, using a one-elastic-constant approximation to solve the reorientation profile. Very good comparison between theory and experiment is obtained. An interesting transient grating, existing due to the viscosity of the liquid-crystal material, is observed in theory and practice for large cell-tilt angles.