A theory of optical pulse propagation in cascaded transmission systems that are based on the dispersioncompensating fiber technique is developed. The existence of two scales associated with fiber dispersion and system residual dispersion leads to a simple model for the averaged pulse dynamics. In the particular case of practical importance, the averaged pulse dynamics is governed by the nonlinear Schrödinger equation. The pulse transmission stability is examined.

We scrutinize the concept of integrable nonlinear communication channels, resurrecting and extending the idea of eigenvalue communications in a novel context of nonsoliton coherent optical communications. Using the integrable nonlinear Schrödinger equation as a channel model, we introduce a new approach-the nonlinear inverse synthesis method-for digital signal processing based on encoding the information directly onto the nonlinear signal spectrum. The latter evolves trivially and linearly along the transmission line, thus, providing an effective eigenvalue division multiplexing with no nonlinear channel cross talk. The general approach is illustrated with a coherent optical orthogonal frequency division multiplexing transmission format. We show how the strategy based upon the inverse scattering transform method can be geared for the creation of new efficient coding and modulation standards for the nonlinear channel.

We discuss a novel kind of nonlinear coupler with one channel filled with a negative index metamaterial. The opposite directionality of the phase velocity and the energy flow in the negative index metamaterial channel facilitates an effective feedback mechanism that leads to optical bistability and gap soliton formation.

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Resonant enhancement of electromagnetic waves propagating at oblique incidence in metamaterials, with dielectric permittivity and magnetic permeability linearly changing from positive to negative values, has been predicted and theoretically studied. This effect occurs for both TE and TM polarizations near the point where a refractive index changes its sign. Our model elucidates the unique features of the resonant enhancement in "positive-to-negative transition" metamaterials for a broad frequency range from microwaves to optics. Optical Society of America OCIS codes: 160.3918, 160.2710 The emergence of metamaterials has given rise to many unique electromagnetic (EM) phenomena, including negative index of refraction, which has never been found in nature, and enhanced interactions between materials and the magnetic field component of EM waves [1][2][3][4]. The unusual properties of negative-index materials (NIMs) are most prominently revealed at the interface of positive-and negative-index materials. Particularly, the right-handed triplet formed from the electric and magnetic fields and the wave vector ͑E , H , k͒ in the positive-index material (PIM) undergoes an abrupt change to form a left-handed triplet in the NIM, revealing a topologically critical phenomenon that leads to antiparallel directions of the wave and Poynting vectors in the NIM.To date, most of the studies in this area have been focused on abrupt transitions from PIMs to NIMs in homogeneous structures. However, recently it has been realized that inhomogeneous metamaterials open unparalleled opportunities for engineering space for wave propagation, thus enabling such fascinating functionalities as cloaking or wave concentrators [5][6][7][8][9][10][11][12]. In this Letter, we investigate the fundamental question of how EM waves propagate in an important class of inhomogeneous metamaterials, with material properties gradually changing from positive to negative values. We refer to these materials as transition metamaterials.We discovered that resonant field enhancement occurs near the zero refractive index point under oblique incidence of the EM wave on a transition metamaterial layer. This phenomenon appears to have an analog in plasma physics, where it is referred to as resonant absorption [13][14][15]. We discuss several unique features of resonant EM enhancement in metamaterials, demonstrating that transition metamaterials provide a novel platform for fundamental studies and potential applications of such EM enhancement phenomenon in a wide frequency range from microwaves to optical frequencies, with the important advantage of nearly unlimited flexibility in material parameter design.We consider light propagation in a medium consisting of a homogeneous PIM in the region x Ͻ 0 and a homogeneous NIM in the region x Ͼ 2h separated by a transition layer of width 2h, where both ⑀ and are real linear functions of the coordinate x along the normal to the interface such that ⑀͑x͒ = ⑀ 0 ͑1−x / h͒ and ͑x͒ = 0 ͑1−x / h͒ if 0 Ͻ x Ͻ 2h, as shown in Fig. 1 (wh...