Curved Wave Guides Research Articles

弯曲波导上的光学调控与应用

弯曲波导上的光学调控与应用

Photonic systems with two-dimensional landscapes of complex refractive index via time-dependent supersymmetry

We present a framework for the construction of solvable models of optical settings with genuinely two-dimensional landscapes of refractive index. The solutions of the associated non-separable Maxwell equations in paraxial approximation are found with the use of the time-dependent supersymmetry. We discuss peculiar theoretical aspects of the construction. Sufficient conditions for existence of localized states are discussed. Localized solutions vanishing for large $|\vec{x}|$, that we call light dots, as well as the guided modes that vanish exponentially outside the wave guides are constructed. We consider different definitions of the parity operator and analyze general properties of the $\mathcal{PT}$-symmetric systems, e.g. presence of localized states or existence of symmetry operators. Despite the models with parity-time symmetry are of the main concern, the proposed framework can serve for construction of non-$\mathcal{PT}$-symmetric systems as well. We explicitly illustrate the general results on a number of physically interesting examples, e.g. wave guides with periodic fluctuation of refractive index or with a localized defect, curved wave guides, two coupled wave guides or a uniform refractive index system with a localized defect.

A General S-bend Approximation by Cascading Multiple Sections of Uniformly Curved Waveguides

Curved waveguides are an important wave guiding structure and have been widely used in building integrated photonics circuits with various functions including directional couplers, modulators, ring resonators, and Mach-Zehnder interferometers etc. However, curved structure always leads to attenuation of the guided mode as it propagates through the bend region. In practice the bending loss may be negligible if the radius of curvature is large, but the loss increases rapidly at small radii. Amongst curved waveguide structures the S-bend has been widely used, because it is relatively easy to design and can provide a low transition loss between parallel offset waveguides. In this paper we present a new general approach to S-bend optical waveguides by cascading multiple sections of uniformly curved waveguides. The aims are to offer maximize structure that can be used in more powerful beam propagation methods to estimate the loss in bends of continuously-varying curvature. We approach the S shaped bend waveguide by multiple sections such as 2, 6, 14 and 30 sections back to back and calculate the total loss. The convergence of resulting curvature variation are very rapid and the overall loss calculation found good agreement with analytical calculation based on low slope approximation.

Band-gap structures for matter waves

Spatial gaps correspond to the projection in position space of the gaps of a periodic structure whose envelope varies spatially. They can be easily generated in cold atomic physics using finite-size optical lattice, and provide a new kind of tunnel barriers which can be used as a versatile tool for quantum devices. We present in detail different theoretical methods to quantitatively describe these systems, and show how they can be used to realize in one dimension matter wave Fabry-Perot cavities. We also provide experimental and numerical results that demonstrate the interest of spatial gaps structures for phase space engineering. We then generalize the concept of spatial gaps in two dimensions and show that this enables to design multiply connected cavities which generate a quantum dot structure for atoms or allow to construct curved wave guides for matter waves. At last, we demonstrate that modulating in time the amplitude of the periodic structure offers a wide variety of possible atom manipulations including the control of the scattering of an incoming wave packet, the loading of cavities delimited by spatial gaps, their coupling by multiphonon processes or the realization of a tunable source of atoms. This large range of possibilities offered by space and time engineering of optical lattices demonstrates the flexibility of such band gap structures for matter wave control, quantum simulators and atomtronics.

Finite-Difference Mode Solver for Curved Waveguides With Angled and Curved Dielectric Interfaces

A finite-difference scheme for accurately analyzing step-index dielectric waveguides with angled and curved dielectric interfaces has been proposed by Chiang Here, this formulation is generalized to take into account a possible curvature of the entire waveguide along the propagation direction, and it is shown how Perfectly Matched Layers can be incorporated in order to accurately compute the bending or curvature loss of dielectric waveguides with step-index profiles of arbitrary shape. Furthermore, the formulation of the interface equations that relate the fields and their derivatives on both sides of a dielectric interface has been simplified, so that their implementation no longer requires any further explicit conversions between coordinate systems.

Echelle grating – curved wave-guide demultiplexer for photonic integrated circuits

A grating spectrometer integrated with curved output wave guides was designed and fabricated in GaAs–AlGaAs waveguide structure for use in the 1 μm wavelength range. By incorporating curved wave guides, a larger separation between output facets was obtained. This is desirable for future integration. High-quality patterns were fabricated by focused ion beam lithography and reactive ion etching. Eight outputs with a channel spacing of 2 nm were obtained. The potential of the structure for integration with active components is discussed.

Modelling of circular wave guides

In many circumstances the design of interconnects in a photonic integrated circuit can be simplified by using low loss curved wave guides in the shapes of circular arcs. Radiative losses associated with the curvature have been computed as a function of the radius of curvature. The technique takes advantage of the effective index method to reduce the problem from two dimensions to one dimension (1D) and uses a change of coordinate that transforms an arc of circle into a straight line. This transformation results in a monotonous increase of the refractive index as function of r (the distance from the centre of the circle) for original constant index regions. The new system is solved by discretizing this varying effective index onto many small layers of constant index over a window large enough to contain the region where the field is not negligible. A multilayer algorithm in 1D is then used to find complex propagation constants in which the imaginary part is related to the fundamental energy loss owing to the curvature. The solution also gives the shape of the field necessary to match the mode profiles at the junction between the straight and curved part of the wave guide. The basic change of variable has been extended to the finite difference solution of the scalar wave equation and to the beam propagation method.

A Decoupled Formulation of the Vector Wave Equation in Orthogonal Curvilinear Coordinates, with Application to Ferrite-Filled and Curved Waveguides of General Cross Section

The introduction of a double complex-number system and the combining of the transverse field components into a compact composite structure enable the wave equation to be expressed in a form in which certain mathematical combinations of field components appear as entities completely decoupled from each other. Hence the equations can be solved for these combinations and ultimately for the components themselves. The method appears limited to guides of constant cross section and of either 1) isotropic medium and curved axis, or 2) axially anisotropic nonreciprocal medium and straight axis.

Propagation of TE01Waves in Curved Wave Guides

TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> waves transmitted through curve wave guides lose power by conversion to other modes, especially to TM <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</inf> . This power transfer to coupled modes is explained by the theory of coupled transmission lines. It is shown that the power interchange between coupled lines and their propagation constants can be derived from a single coupling discriminant. Earlier calculations of TE <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</inf> conversion loss in circular wave guide bends are confirmed and extended to S-shaped bends. Tolerance limits for random deflections from an average straight course are given.

On Curved Wave Guides

On Curved Wave Guides