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We describe propagation in a uniaxially anisotropic medium by relying on a suitable plane-wave angularspectrum representation of the electromagnetic field. We obtain paraxial expressions for both ordinary and extraordinary components that satisfy two decoupled parabolic equations. As an application, we obtain, for a particular input beam (a quasi-Gaussian beam), analytical results that allow us to identify some relevant features of propagation in uniaxial crystals.

The problem of prediction of the equilibrium state in an isolated composite system with an adiabatic internal wall is a delicate problem, whose solution is easily seen to be not entirely determined in the frame of elementary thermodynamics. We show how this indeterminacy can be removed by introducing a suitable kinetic model, in which the influence of the finite velocity of the wall on the change of momentum of the gas molecules impinging on it plays a relevant role. An interesting feature of the entropy behavior of the system is discussed.

Soliton propagation in a multimode optical fiber in the presence of an intensity-dependent refractive index is investigated by means of a set of nonlinear coupled equations derived in the frame of coupled-mode theory. In particular, the conditions on modal amplitudes and modal dispersion necessary for soliton existence are derived.The possibility of propagating distortion-free pulses (envelope solitons) in optical waveguides by taking advantage of the quadratic nonlinearity of the refractive index in order to balance material dispersion was pointed out several years ago.' Subsequently, this problem has been the object of a renewed interest that has led to a better understanding of the role of the waveguide structure 2 and of the finite coherence time of the carrier. 3Following the above investigations and after the recent experimental observation of solitons 4 concerning single-mode optical fibers, it is natural to look for a generalization of the previous results to the case in which more than one mode is present. Along this line, the possibility of exploiting nonlinear-mode interaction in a multimode fiber for optical pulse confinement and the conditions under which it can take place have been stated. 5 We write here, relying on the coupled-modetheory approach to nonlinear propagation, a general set of coupled equations describing pulse evolution in a multimode optical fiber in the presence of an intensity-dependent refractive index. We specialize this system of equations to investigate soliton propagation, thus enabling us to derive the conditions under which it can be achieved.In the frame of the coupled-mode formalism, the evolution of a multimode optical pulse is studied by identifying the departure of the refractive index from ideality, which is responsible for coupling, with the presence of a nonlinear part in the refractive index itself.Assuming that the fiber material is isotropic and that the fast-responding electronic processes dominate the nonlinear response, the nonlinear polarization pNL takes the form 7 bitrary mode takes place over few centimeters and on the hypothesis of weakly guiding fiber allowing one to neglect the longitudinal field component with respect to the transverse ones.The analytic field Xx can be written as (3) where r = (xy) represents the transverse coordinates, the Er's are the modal transverse configurations, 0, is the propagation constant of the vth mode, and the (,(z,t)'s are the slowly varying mode amplitudes, having allowed for the various modes to be centered on slightly different frequencies wt. Equation (2) implies a total dielectric constant of the form E(r,z,w) = ei(r,co) + E 2 1Rx(r,z,t)12, Ex (r,z,t) = E E^(r) exp[icowt -if,(w,)z]4'i(Z~t),where El(r,co) is the fiber linear dielectric constant, so that E 2 1l-12 can be regarded as the fiber deviation from ideality giving rise to mode coupling. By taking advantage of the results of coupled-mode theory, 6 one is able to obtain the following set of coupled equations:wherewhich implies a nonlinear contribution to the di...