This article is divided in five parts, the first one having nothing to do with tachyons. In fact, to prepare the ground, in part I (sect.2) we shall merely show that special relativity - even without tachyons - can be given a form such to describe both particles and antiparticles. Part II is the largest one: initially, after some historical remarks and having revisited the postulates of special relativity, we presnt a review of the elegant ''model theory'' of tachyons in two dimensions; passing then to four dimensions, we review the main results of the classical theory of tachyons that do not depend on the existence of Superluminal reference frames (or that are at least independent of the explicit form of the Superluminal Lorentz ''transformations''). In particular, we discuss how tachyons would look like, i.e. their apparent ''shape''. Last but not least, all the common causality problems are thoroughly solved, on the basis of the previously reviewed tachyon kinematics. Part III deals with tachyons in general relativity; in particular the question of the apparent Superluminal expansions in astrophysics is reviewed. Part IV shows the interesting, possible role of tachyons in elementary-particle physcis and in quantum theory. In part V, the last one, we face the (still open) problem of the Superluminal Lorentz ''transformations'' in four dimensions, by introducing, for instance, an auxiliary six-dimensional space-time, and finally present the electromagnetic theory of tachyons: a theory that can be relevant also from the ''experimental'' point of view.

Classical tachyons and possible applications

We analyze the nonlinear coupled differential equations for the nonlinear coherent coupler by extending the Stokes parameters formalism. The existence of bifurcation and instability phenomena is proved.

Stability analysis of nonlinear coherent coupling

We present the first experimental demonstration of spatial instability in the nonlinear evolution of the state of polarization of an intense light beam in a birefringent Kerr‐like medium. As the peak power crosses the threshold for the instability, we observed strong intensity‐dependent power transfer between the two counter‐rotating circularly polarized waves propagating along a birefringent optical fiber. The experimental results agree well with the theory.

Experimental observation of polarization instability in a birefringent optical fiber

Exact solutions for the evolution of the state of polarization along a nonlinear single-mode birefringent fiber are given by means of the Poincare sphere representation. This approach clearly shows the possibility of realizing a new class of devices, namely, a linear coherent amplifier–mixer and an optically activated polarization switch or a phase-sensitive optical discriminator with high fanout.

New all-optical devices based on third-order nonlinearity of birefringent fibers.

Hamiltonian chaos in nonlinear optical polarization dynamics

An exact, closed-form solution is presented for the propagation characteristics of an intense, arbitrarily polarized optical beam in an isotropic medium which is subjected to a dc electric field. The related phenomena of dc-electric-field-induced optical rectification and second-harmonic generation are examined as well as the propagation characteristics of a weak beam in an isotropic medium in the presence of both the intense optical and dc fields. One fundamental and noteworthy aspect of the results presented here is that both the formalism and the resulting solutions for these third-order nonlinear optical phenomena are given explicitly and entirely in terms of the set of real, observable Stokes parameters rather than in terms of the electric field amplitudes and phases.

Kenneth L. Sala

Papers

Nonlinear refractive-index phenomena in isotropic media subjected to a dc electric field: Exact solutions

Anticausal behavior in the imaging of a moving object: The implications for high-speed photography