Nonlinear dispersion in a coupled-resonator optical waveguide

The propagation of an optical pulse in a coupled-resonator optical waveguide may be calculated nonperturbatively to all orders of dispersion, in the conventional tight-binding approximation, even though the dispersion relationship is nonlinear. Working in this framework, we discuss limits of the physical parameters and approximations to the exact formulation that highlight the conditions under which pulse distortion can be minimized. The results are fundamental to the design of coupled-resonator optical waveguides and are also relevant to other applications of the tight-binding method

Nonlinear multiplexing in optical fiber communications

The nonlinear evolution of a dispersion-managed soliton admits a novel nonlinear multiplexing scheme for optical communications. Information is coded onto the canonical parameters (chirp and width) characterizing the pulse. It is shown that in dispersion-managed fiber communication channels, there exists the possibility of a nonlinear multiplexing scheme, with no linear analog, that effectively multiplies the bit-rate throughput several-fold. Alternatively, the same bit-rate is achieved while relaxing the requirements on the pulse width, so that slower modulation speeds and narrowband in-line filters may be used without paying a penalty in the information-transfer rate. In addition, the scheme is insensitive to minor variations in the multiplexing parameters. The analysis is based on a Hamiltonian reduction of the dispersion-managed nonlinear Schrodinger equation, and is corroborated with direct numerical simulations

Coupled-resonator optical waveguides: Q-factor and disorder influence

Coupled resonator optical waveguides (CROW) can significantly reduce light propagation pulse velocity due to pronounced dispersion properties. A number of interesting applications have been proposed to benefit from such slow-light propagation. Unfortunately, the inevitable presence of disorder, imperfections, and a finite Q value may heavily affect the otherwise attractive properties of CROWs. We show how finite a Q factor limits the maximum attainable group delay time; the group index is limited by Q, but equally important the feasible device length is itself also limited by damping resulting from a finite Q. Adding the additional effects of disorder to this picture, limitations become even more severe due to destructive interference phenomena, eventually in the form of Anderson localization. Simple analytical considerations demonstrate that the maximum attainable delay time in CROWs is limited by the intrinsic photon lifetime of a single resonator.Comment: Accepted for Opt. Quant. Electro

Matrix analysis of microring coupled-resonator optical waveguides

We use the coupling matrix formalism to investigate continuous-wave and pulse propagation through microring coupled-resonator optical waveguides (CROWs). The dispersion relation agrees with that derived using the tight-binding model in the limit of weak inter-resonator coupling. We obtain an analytical expression for pulse propagation through a semi-infinite CROW in the case of weak coupling which fully accounts for the nonlinear dispersive characteristics. We also show that intensity of a pulse in a CROW is enhanced by a factor inversely proportional to the inter-resonator coupling. In finite CROWs, anomalous dispersions allows for a pulse to propagate with a negative group velocity such that the output pulse appears to emerge before the input as in “superluminal” propagation. The matrix formalism is a powerful approach for microring CROWs since it can be applied to structures and geometries for which analyses with the commonly used tight-binding approach are not applicable

Analysis of Optical Pulse Propagation with ABCD Matrices

We review and extend the analogies between Gaussian pulse propagation and Gaussian beam diffraction. In addition to the well-known parallels between pulse dispersion in optical fiber and CW beam diffraction in free space, we review temporal lenses as a way to describe nonlinearities in the propagation equations, and then introduce further concepts that permit the description of pulse evolution in more complicated systems. These include the temporal equivalent of a spherical dielectric interface, which is used by way of example to derive design parameters used in a recent dispersion-mapped soliton transmission experiment. Our formalism offers a quick, concise and powerful approach to analyzing a variety of linear and nonlinear pulse propagation phenomena in optical fibers.Comment: 10 pages, 2 figures, submitted to PRE (01/01

Spatial optical solitons in nonlinear photonic crystals

We study spatial optical solitons in a one-dimensional nonlinear photonic crystal created by an array of thin-film nonlinear waveguides, the so-called Dirac-comb nonlinear lattice. We analyze modulational instability of the extended Bloch-wave modes and also investigate the existence and stability of bright, dark, and ``twisted'' spatially localized modes in such periodic structures. Additionally, we discuss both similarities and differences of our general results with the simplified models of nonlinear periodic media described by the discrete nonlinear Schrodinger equation, derived in the tight-binding approximation, and the coupled-mode theory, valid for shallow periodic modulations of the optical refractive index.Comment: 15 pages, 21 figure

Robust optical delay lines via topological protection

Phenomena associated with topological properties of physical systems are naturally robust against perturbations. This robustness is exemplified by quantized conductance and edge state transport in the quantum Hall and quantum spin Hall effects. Here we show how exploiting topological properties of optical systems can be used to implement robust photonic devices. We demonstrate how quantum spin Hall Hamiltonians can be created with linear optical elements using a network of coupled resonator optical waveguides (CROW) in two dimensions. We find that key features of quantum Hall systems, including the characteristic Hofstadter butterfly and robust edge state transport, can be obtained in such systems. As a specific application, we show that the topological protection can be used to dramatically improve the performance of optical delay lines and to overcome limitations related to disorder in photonic technologies.Comment: 9 pages, 5 figures + 12 pages of supplementary informatio

Lyapunov exponent of the random Schr\"{o}dinger operator with short-range correlated noise potential

We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schr\"{o}dinger equation with the white noise potential can be expressed through the Lyapunov exponent $\gamma$ which we determine explicitly as a function of the noise intensity \sigma and the frequency \omega. We find uniform two-parameter asymptotic expressions for $\gamma$ which allow us to evaluate $\gamma$ for different relations between \sigma and \omega. The value of the Lyapunov exponent is also obtained in the case of a short-range correlated noise, which is shown to be less than its white noise counterpart.Comment: 20 pages, 4 figure