Scalar Coupled-mode Theory Research Articles

Frenet–Serret analysis of helical Bloch modes in N-fold rotationally symmetric rings of coupled spiraling optical waveguides

The behavior of electromagnetic waves in chirally twisted structures is a topic of enduring interest, dating back at least to the 1940s invention of the microwave travelling-wave-tube amplifier and culminating in contemporary studies of chiral metamaterials, metasurfaces, and photonic crystal fibers (PCFs). Optical fibers with chiral microstructures, drawn from a spinning preform, have many useful properties, exhibiting, for example, circular birefringence and circular dichroism. It has recently been shown that chiral fibers with N -fold rotationally symmetric (symmetry group C N ) transverse microstructures support families of helical Bloch modes (HBMs), each of which consists of a superposition of azimuthal Bloch harmonics (or optical vortices). An example is a fiber with N coupled cores arranged in a ring around its central axis ( N -core single-ring fiber). Although this type of fiber can be readily modeled using scalar coupled-mode theory, a full description of its optical properties requires a vectorial analysis that takes account of the polarization state of the light, which is particularly important in studies of circular and vortical birefringence. In this paper, we develop, using an orthogonal 2D helicoidal coordinate system embedded in a cylindrical surface at constant radius, a rigorous vector coupled-mode description of the fields using local Frenet–Serret frames that rotate and twist with each of the N cores. The analysis places on a firm theoretical footing a previous HBM theory in which a heuristic approach was taken, based on physical intuition of the properties of Bloch waves. After a detailed review of the polarization evolution in a single spiraling core, analysis of the N -core single-ring system is carefully developed step by step. Accuracy limits of the analysis are assessed by comparison with the results of finite element modeling, focusing in particular on the dispersion, polarization states, and transverse field profiles of the HBMs. We believe this study provides clarity into what can sometimes be a rather difficult field and will facilitate further exploration of real-world applications of these fascinating waveguiding systems.

Scalar coupled mode theory and variational analysis for planar SOI waveguide arrays: a detailed comparison

We present a detailed analytical comparison of two extensively used theories to study the coupled optical waveguide arrays. Various formulations of the scalar Coupled Mode Theory and the Ritz Galerkin variational analysis have been applied to 1-D SOI coupled waveguide arrays to study the TE modes of the structure having identical and non-identical waveguides. Equivalence between scalar Ritz Galerkin variational formulation and the coupled mode theory without any approximations is shown. Comparisons of various modal characteristics obtained from the different coupled mode and variational formulations have been shown along with the exact results obtained from the solution of the scalar wave equation. For the 1-D SOI array under consideration the non-identical waveguide configuration leads to stronger coupling which results in non-orthogonal supermodes using two of the coupled mode formulations. The excellent agreement with exact results and the much lower computational time compared to numerical techniques, make these analytical methods a preferred choice for the simulation of coupled waveguide arrays.

Power exchange in strongly coupled diffused channel waveguide arrays: an analyticalapproach

We present the modified scalar coupled mode analysis for an array ofN diffused channel waveguides. The study simulates the lateral evanescent field coupling inthe graded index channel waveguide array. In a two-step procedure, the propagationcharacteristics of individual waveguides are obtained first by the completely analytical,closed-form expressions obtained from the variational method. Consequent upon obtainingthe individual waveguide characteristics, the complete scalar coupled mode theory has beendeveloped that includes the non-orthogonality of the individual waveguide modes forstrongly coupled waveguides. The coupled mode equations are solved to obtain thesupermodes corresponding to the coupled waveguide configuration. Further to this, powerexchange in the graded index multi-waveguide systems has been studied. Complete powertransfer between the outside guides of the symmetric three-waveguide graded indexcoupler is reported when the condition of equispaced effective indices is met.

Rigorous vectorial coupled-mode theory for the isotropic waveguide with anisotropic disturbance

We present a rigorous vectorial coupled-mode theory (VCMT) for the isotropic waveguide structures with anisotropic disturbance by Maxwell equations and a modified dielectric tensor. The coupling coefficients are related to every element of a disturbed dielectric tensor. In the special case of isotropic disturbance and orthogonal mode coupling, our formulas can be reduced to the previous version of VCMT, in which the coupling coefficient does not include the polarization coupling term appearing in an earlier scalar coupled-mode theory with vector correction (SCMT-VC). The origin of the fundamental error found in the SCMT-VC is analyzed. Finally, we apply our theory to a special coupling between x- and y-polarized modes in a single-mode fiber.

Analytical expressions for power exchange in multiwaveguide systems

We present a complete analysis of power exchange in multiple coupled waveguides, using the modified scalar coupled-mode theory and give generalized expressions for power exchange between any two waveguides of a multiple-waveguide system. We thus obtain a reciprocity principle applicable to power exchange between any two waveguides. Completely generalized and accurate analytical expressions for all coupling coefficients, all perturbation correction terms, and all nonorthogonality terms involved in the analysis are presented.

Analytical expressions for effective indices in a three-waveguide coupler

We present analytical expressions for the effective indices of a three-waveguide directional coupler, using the modified scalar coupled-mode theory. Our analysis takes into account all perturbation correction terms, all coupling coefficients, and all overlap integrals and leads to a simple analytical condition for maximum power transfer between the two outside guides.

Polarization rotation in periodic loaded rib waveguides

Polarization rotation in an asymmetric periodic loaded rib waveguide is analyzed by a scalar coupled-mode theory with vector correction. The scalar modes of the dielectric loaded rib waveguide are calculated by using a simple variational method. The polarization rotation is found to be caused by a geometric effect due to the asymmetric loading of the waveguide. By phase-matching the two polarized modes through the periodic loading, complete polarization rotation can be achieved. >

A scalar coupled-mode theory with vector correction

A coupled-mode formulation based on scalar modes is developed for guided-wave devices in optoelectronics and fiber optics. In the formulation, the vector property of the electromagnetic field is represented as additional coupling to the coupling due to the refractive-index perturbations. The nonorthogonality of the scalar modes in the individual waveguides is taken into account. The theory is applied to directional couplers made of parallel slabs, rectangular channel waveguides, and circular fibers. Comparisons with the exact solutions available demonstrate very good agreement. Within the framework of the simple scalar analysis, the theory may be applied to the modeling and analysis of propagation and coupling of the vector electromagnetic waves in a broad range of practical optical guided-wave devices. >

Modeling and analysis of fiber-optic mode transducers: single fiber with periodic perturbations

The fiber-optic LP/sub 01/ from or to LP/sub 11/ mode transducers are analyzed by a scalar coupled-mode theory with vector correction. The authors deal with fiber-optic mode transducers made of a single fiber with periodic perturbations due to microbends, acoustic waves, or a photoinduced index grating. Both the couplings caused by the index perturbations and by the vector property of the fields (polarization effect) are taken into account in the analysis. Approximate analytical solutions to the coupled-mode equations are obtained. The power exchange among the modes along the fiber and spectral properties of the mode transducers are examined. The functions of the mode transducers used as wavelength filters and polarizers are studied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Variational coupled-mode theory of optical couplers

A scalar coupled-mode theory is developed from the variational principle. The formulation is variational in the sense that the mode parameters are adjustable and can be optimized subject to the coupling between the guides. The theory is applied to slab and fiber couplers. In comparison with the conventional scalar coupled-mode theory in which only the amplitudes of the modes in the individual guides are adjustable, the variational scalar coupled-mode theory predicts more accurate propagation constants and field patterns of the normal modes of the couplers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comparison between strong coupling theory and experiment for three-arm directional couplers in Ti:LiNbO/sub 3/

The derivation of scalar coupled mode theory for TEM waveguide arrays is examined. It is demonstrated that four previously published methods are identical at this level of approximation. The accuracy of the theory and its application to a slab-waveguide model of a three-arm coupler is considered. It is shown that the coupled mode equations require modification for slowly varying arrays. Analytic expressions for the matrix coefficients are presented, and it is demonstrated that device input-output transitions have significant effect on the response. The model is compared with experimental measurements of three-arm couplers fabricated in Ti:LiNbO/sub 3/, and excellent qualitative agreement is obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Explanation of asymmetric switch response of three-arm directional couplers in Ti:LiNbO 3 using strong coupling theory

Previous experimental measurements of switch response of strongly-coupled three-arm integrated optic directional couplers in Ti:LiNbO 3 have shown a marked asymmetry with voltage. This effect is not predicted by simple coupled mode theory. Good agreement with the experimental measurements may however be obtained using a modified scalar coupled mode theory, including the effects of modal overlap and correct description of the bend sections.