Multicasting is becoming increasingly important in today's networks. In optical networks, optical splitters facilitate the multicasting of optical signals. By eliminating the transmission of redundant traffic over certain links, multicasting can improve network performance. However, in a wavelength-division multiplexed optical network, the lack of wavelength conversion necessitates the establishment of a single multicast circuit (lighttree) on a single wavelength. On the other hand, establishing several unicast connections (lightpaths) to satisfy a multicast request, while requiring more capacity, is less constrained in terms of wavelength assignment. The objective of this paper is to evaluate the tradeoff between capacity and wavelength continuity in the context of optical multicasting. To this end, we develop accurate analytical models with moderate complexity for computing the blocking probability of multicast requests realized using lighttrees, lightpaths, and combinations of lighttrees and lightpaths. Numerical results indicate that a suitable combination of lighttrees and lightpaths performs the best when no wavelength conversion is present.

A plume consisting of vapour and ionized particles of the workpiece is usually formed during various types of laser materials processing. The characteristics of this plume depend on a large number of parameters such as the laser power, spot size, scanning speed, material properties and shielding gas. The height, radius, temperature and absorption coefficient of the plasma are calculated for various values of process parameters. The surface temperature of the melt pool and the vaporization rate are also calculated on the basis of the Stefan condition at the liquid-vapour interface. The absorption coefficient of the plasma given by the Kramers-Unsöld relation and the ionization fraction given by the Saha-Eggert equation are used to model the laser beam propagation through the plasma. A detailed analysis of the plasma stability indicates that absorption of the laser beam by the plasma affects the melt-pool surface temperature nonlinearly.

A plume consisting of vapour and ionized particles from the workpiece is commonly formed during various types of laser materials processing. The process parameters such as the laser power, spot diameter, scanning speed, material properties and shielding gas affect the properties of the vapour-plasma plume. A mathematical model is presented in this paper to predict the plasma properties, such as its temperature and absorption coefficient, and the partitioning of laser energy between the plasma and workpiece for different process parameters. The effect of plasma on the surface temperature of the liquid metal and the vaporization rate are modelled using the Stefan condition at the liquid-vapour interface. A new experimental technique named as the pinhole experiment is presented in this paper to measure the partitioning of laser energy between the plasma and the workpiece.

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