One-dimensional Photonic Lattices Research Articles

Defect solitons in photonic lattices

Nonlinear defect modes (defect solitons) and their stability in one-dimensional photonic lattices with focusing saturable nonlinearity are investigated. It is shown that defect solitons bifurcate out from every infinitesimal linear defect mode. Low-power defect solitons are linearly stable in lower bandgaps but unstable in higher bandgaps. At higher powers, defect solitons become unstable in attractive defects, but can remain stable in repulsive defects. Furthermore, for high-power solitons in attractive defects, we found a type of Vakhitov-Kolokolov (VK) instability which is different from the usual VK instability based on the sign of the slope in the power curve. Lastly, we demonstrate that in each bandgap, in addition to defect solitons which bifurcate from linear defect modes, there is also an infinite family of other defect solitons which can be stable in certain parameter regimes.

Observation of lower to higher bandgap transition of one-dimensional defect modes

We demonstrate one-dimensional optically-induced photonic lattices with a negative defect and observe linear bandgap guidance in such a defect. We show that a defect mode moves from the first bandgap to a higher bandgap as the lattice potential is increased. Our experimental results are in good agreement with the theoretical analysis of these effects.

Discrete interband mutual focusing in nonlinear photonic lattices

We study nonlinear coupling of mutually incoherent beams associated with different Floquet-Bloch waves in a one-dimensional optically-induced photonic lattice. We demonstrate experimentally how such interactions lead to asymmetric mutual focusing and, for waves with opposite diffraction properties, to simultaneous focusing and defocusing as well as discreteness-induced beam localization and reshaping effects.

Defect modes in one-dimensional photonic lattices

Linear defect modes in one-dimensional photonic lattices are studied theoretically. For negative (repulsive) defects, various localized defect modes are found. The strongest confinement of the defect modes appears when the lattice intensity at the defect site is nonzero rather than zero. When launched at small angles into such a defect site of the lattice, a Gaussian beam can be trapped and undergo snake oscillations under appropriate conditions.

Discrete Diffraction and Spatial Self-Action of Light Beams in One-Dimensional Photonic Lattices in Lithium Niobate

Features of the behavior of light beams in one-dimensional photonic lattices in iron-doped lithium niobate have been experimentally studied. It is demonstrated that bright discrete spatial solitons and bright gap solitons can be formed in this system using 633 nm radiation on a microwatt power level. © 2005 Pleiades Pub- lishing, Inc.

Aperiodic lattices for photonic bandgap engineering

ABSTRACTA new method is presented, based on the discrete Fourier Transform, for the design of aperiodic lattices to be used in photonic bandgap engineering. Designing an aperiodic lattice by randomly choosing defects is unlikely to result in useful optical transmission characteristics. By contrast, this new method allows an aperiodic lattice to be designed directly from the desired optical characteristic. The use of this method is illustrated with a design for a structure to realise two transmission wavelengths in the stopband of a one-dimensional photonic lattice. This design has been fabricated in silicon-on-insulator and some optical characteristics are given.

Large photonic band gap's in one-dimensional multilayer structures

A one-dimensional photonic lattice constructed from a material possessing a higher value of dielectric constant has been studied under the consideration of photonic band gap, filling fraction, and the competition of different transmission mechanism of the incoming electromagnetic waves. A special attention has been paid to the localized state introduced by the introduction of defect in our multilayer structure.

Bloch analysis of photonic lattices that incorporate vertical cavity surface-emitting laser arrays

We analyzed one-dimensional photonic lattices that incorporate mirror-modulated vertical cavity surface-emitting laser arrays utilizing the Bloch formalism. First, infinitely long arrays are considered. The in-phase mode (with a main central lobe at the far field) and antiphase mode (with two main symmetrically-located lobes at the far-field) are examined. A comparison of the modal losses of the in-phase and the antiphase modes, resulted in the discovery of regimes in which the in-phase mode is dominant. Considering lattices of finite length, we compared the results of the Bloch model to the exact solutions. It is shown that the boundary conditions in these lattices select a specific mode from the continuous spectrum in the infinite case. Consequently, the lattice's length affects the eigenmodes and the corresponding eigenvalues in a periodic manner.

Field distribution inside one-dimensional random photonic lattices

The electromagnetic field distribution inside a one-dimensional random photonic lattice has been studied by using the transfer matrix method. We have considered incident waves at frequencies both within and outside the photonic bandgap. It is shown that in the vicinity of a Bragg remnant frequency, a random photonic lattice manifests a local maximum of the field intensity ensemble average inside the structure. The width of this maximum is much larger than a unit cell of the lattice.

Defects and Photonic Wells in One-Dimensional Photonic Lattices

The concept of local photonic lattice (PL) is introduced in 1D photonic lattices (PL's) to interpret the defects as donor-like or acceptor-like within any band gap of the host PL. Based on the concept of the local PL, an analysis is presented on the tunability of a movable defect which would be used as a tunable frequency filter. By further extending the local PL, we introduce a 1D photonic well composed of the well-like 1D PL sandwiched by the barrier-like 1D PL's. Similarity is investigated between the 1D photonic wells and the semiconductor quantum wells (QW's). It is shown that the bound states are well described by the effective “mass” approximation in analogy to the QW's. These bound states appear as sharp peaks in the transmission spectrum of the finite size 1D photonic well.

Competition of different scattering mechanisms in a one-dimensional random photonic lattice

A one-dimensional random photonic lattice is studied both by the plane-wave method and by the transfer matrix approach for arbitrary contrast in its dielectric permittivity. The roles and competition of different scattering mechanisms such as Bragg diffraction, single-scatterer resonances, and Bragg remnants are investigated. The localization length, band-gap width, and middle-gap frequency are analyzed for both random and regular lattices in the higher-frequency bands. An analytical expression allowing the prediction of the existence of band-gap closing is obtained. It is shown not only that strong localization results from Bragg diffraction and disorder in the scatterers’ distribution but also that Bragg remnants produce localization for a medium with small contrast.