Conical refraction and nonlinearity.

We study conical refraction in crystals where both diffraction and nonlinearity are present. We develop a new set of evolution equations. We find that nonlinearity induces a modulational instability when it is defocussing as well as focussing. We also examine the evolution of incident beams which contain analytic singularities, and in particular optical vortices, which do not feel the effect of conical refraction.

Fast and efficient computer modeling of ferromagnetic seed arrays of arbitrary orientation for hyperthermia treatment planning.

PURPOSE: Effective hyperthermia treatment planning requires an ability to predict temperatures quickly and accurately from an arbitrary distribution of power. Our purpose was to design such a fast executing computer code, MGARRAY, to compute steady-state temperatures from ferromagnetic seed heating, allowing seeds to have arbitrary orientations and to be curved to permit more realistic modeling of clinical situations. We further required flexibility for the tissue domain, allowing inhomogeneity with respect to thermal conductivity and blood perfusion, as well as an arbitrary shaped boundary. METHODS AND MATERIALS: MGARRAY uses multigrid methods and a finite volume discretization to solve the Pennes bioheat transfer equation in three dimensions. We used MGARRAY to compare temperature distributions that result from an array of straight, parallel seeds and from an array of seeds that were curved and tilted randomly by 13 degrees. RESULTS: On a personal workstation the Central Processing Unit (CPU) time of MGARRAY was under 4 min. We found that the median temperature in a predetermined target volume was approximately 0.8 degrees C higher in the straight array than in the curved array. At specific locations within the target volume temperature differed by approximately 0.5-0.9 degrees C, but could differ by up to several degrees, depending on proximity to a seed and the level of blood perfusion. CONCLUSION: These differences can impact on retrospective analyses whereby temperatures at a few locations are used to infer the overall temperature field and blood perfusion levels. The flexibility and computational speed of MGARRAY could potentially lead to a substantial improvement in both retrospective and prospective hyperthermia treatment planning.

A new computer method to quickly and accurately compute steady-state temperatures from ferromagnetic seed heating.

A new, very fast, yet accurate program, MGSEED, has been developed that computes steady-state temperatures from the three-dimensional bioheat transfer equation due to heating by a ferromagnetic seed. Seeds have a self-regulating power absorption characteristic such that their temperatures remain within a few degrees of their Curie transition point. The code is also very flexible, being able to model a seed of any orientation embedded in a tissue domain that can be inhomogeneous with respect to blood perfusion or thermal conductivity. MGSEED uses multigrid (or multilevel) programming techniques as well as a finite volume discretization that exploits knowledge of the approximate shape of the temperature solution very near to a seed. These techniques allow the code to sample the seed very coarsely, requiring only one or two nodes to cross the seed. With these coarse samplings MGSEED calculated very accurate temperatures in under 3 min of CPU time on a Sun Sparcstation 2. The accuracy of MGSEED is demonstrated at different levels of perfusion by comparing its solution in a perpendicular plane that bisects the seed with the known analytical solution. The speed of MGSEED is compared to other methods of solution and it is found that MGSEED performs 14 times faster than successive over relaxation and conjugate gradient methods, and 2.5 times faster than a preconditioned (modified block incomplete Cholesky) conjugate gradient method. It is concluded that the techniques for discretization and solution incorporated into MGSEED can greatly improve the flexibility and speed of hyperthermia treatment planning, which could ultimately lead to an increased level of control over treatment outcome.

Propagation-induced adiabatic following in a semiconductor amplifier.

A propagation-induced transition from linear amplification into an adiabatic following regime is predicted for femtosecond pulses in an inverted semiconductor medium. This process is accompanied by considerable pulse shortening.