Propagation vectors Subject

Equation 10.14 deseribes the TPA transition amplitude for a molecule subjected to two light beams with arbitrary electric field vectors and propagation vectors. A particularly useful application of TPA in gas phase spectroscopy employs two counterpropagating laser beams with k2 = — ki k2. In this case, a molecule traveling with velocity parallel to k2 will experience Doppler shifts... 

In a lattice-gas the individual cells are the structural units of a D-dimensional regular lattice. Each cell is defined by its position vector r on the discrete space, a finite number of states s(r ) and a set of transition rules E that map the state of the cell at time t into the state at time t + 1. A finite number of particles reside in each cell. A discrete velocity c, with / = 1,..., k is associated to each particle. This velocity is chosen such that the particle can propagate to a neighboring cell in unit time. Each velocity direction is subject to an exclusion principle of utmost single occupancy. The combinations of occupancies define the set of possible states associated with each cell. The configuration of each cell is defined by the Boolean field... 

These vector wave equations are a restatement of Maxwell s equations for an arbitrary refractive index profile. Subject to the requirements that the modal fields are bounded everywhere and decay sufficienfly fasf af large distances from the waveguide, these equations contain all of the information necessary to determine the modal fields and propagation constants of all the guided modes of the waveguide. 

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