Contra-directional Coupling Research Articles

Elliptical normal modes and stop band reconfiguration in multimode birefringent one-dimensional magnetophotonic crystals

This study examines photonic stop band reconfiguration upon magnetization reversal in multimode elliptically birefringent Bragg filter waveguides. Magnetization reversal in longitudinally magnetized magneto-optic waveguides affects the character of the local orthogonal elliptically polarized normal modes, impacting the filter's stop band configuration. Unlike the standard case of circular birefringence in magneto-optic media, opposite helicity states do not transform into each other upon magnetization reversal for a given propagation direction. Rather, helicity reversals yield new and different normal modes with perpendicularly oriented semimajor axes, corresponding to a north-south mirror reflection through the equatorial plane of the Poincar\'e sphere. For asymmetric contradirectional coupling between different-order waveguide modes in multimode magnetophotonic crystals, this symmetry breaking, namely, the obliteration of normal modes upon magnetization reversal, allows for strongly reconfigured stop bands, through the hybridization of the elliptically polarized states. The effect of Bloch mode reconfiguration on the stop band spectral profile contributes to the magnetic response of the filter. In such elliptically birefringent media, input polarization helicity reversal also becomes a powerful tool for optical transmittance control. Both magnetization and helicity reversals can thus serve as useful tools for the fabrication of on-chip magnetophotonic crystal switches.

Localization of electromagnetic energy by a pair of parallel waveguides with contradirectional coupling

The contradirectional coupling between a pair of planar dielectric waveguides, whose guiding layers are respectively a negative index medium and a positive index medium (PIM, i.e., the conventional medium), is theoretically investigated using the coupled mode theory. It is shown that, by tapering the middle segment of the PIM guiding layer to introduce a certain phase shift, the energy flow circulation can be established based on the contradirectional coupling effect, and, thus, the electromagnetic energy is localized in the waveguide system. This phenomenon is further verified numerically with the finite-difference time domain method. The quality factor of this open waveguide cavity is also discussed.

Spontaneous Emission and Coupled-Mode Theory in Multimode 1-D Systems With Contradirectional Coupling

By means of source terms and coupled-mode theory, the essential features of spontaneous emission in multimode waveguides with counterdirectional feedback, such as corrugated and photonic crystal waveguides, are described in a heuristic manner. These multimode source terms generalize a similar approach evoked in multilayer structures. We account for features such as the “mini-stopband,” and the “stripe of minigaps” of broad photonic crystal waveguides, modeling previous experimental data. The result holds in several situations for which the differences in source terms for the uncoupled waveguide modes are not important. The approach yields significant results through a simple path.

Ultra-short plasmonic splitters and waveguide cross-over based on coupled surface plasmon slot waveguides

Composite metal-dielectric-metal (MDM) surface plasmon polariton (SPP) structures are first proposed to realize the ultra-short optical splitters with simplified designs. The operation mechanism is based on the contra-directional coupling achieved in composite plasmonic slot waveguides. In certain cases, the switching function can also be realized. It is further shown that based on the same physical mechanism multi-dielectric-core composite MDM structures could serve as a novel plasmonic waveguide crossover component with low cross talk and high throughput.

Bloch surface wave excitation based on coupling from photonic crystal waveguide

In this paper, a way to excite a Bloch surface wave by coupling from the photonic crystalwaveguide is presented. The Bloch surface mode in a two-dimensional photonic crystalappears in the bandgap by changing the size of surface rods. The dispersion relation ofsurface modes will be affected when altering the radius of surface rods. The co-directionaland contra-directional couplings between these modes are also discussed. The coupledmode theory is used to study the coupling between the waveguide mode andsurface mode of photonic crystals. Finally, finite element simulations are alsopresented.

Ultrasonic waveguide with square wave surface grating

The effect of spatial harmonics of a square-wave surface grating on the multiband frequency response of ultrasonic SH waves in an elastic plate is investigated. Stopbands are found to occur under simultaneous occurrence of first-order and higher-order Bragg resonances together with co-directional and/or contra-directional mode coupling conditions. The odd harmonic nature of the structure causes stopbands to appear above the cutoff frequencies of the odd-numbered modes. The attenuation within stopbands is found to be greatest when all propagating modes are coupled and reflected. The simultaneous resonance conditions for higher order stopbands must contain at least one co-directional mode coupling condition. The analysis is performed according to the multiple scales scheme, leading to the derivation of coupled mode equations, which are solved numerically using the fundamental matrix method.

Blue-shifted contra-directional coupling between a periodic and conventional dielectric waveguides

The interaction between a periodic and conventional dielectric waveguides is investigated theoretically for a two-dimensional model system. A modified coupled-mode theory is formulated for the considered system and found to agree well with rigorous numerical calculations. It is shown that in a certain wavelength range the contra-directional coupling between the two waveguides can be achieved with high efficiency. But the spectrum of the coupling efficiency is blue-shifted and thus the strongest coupling does not occur in the case when two individual waveguides have the same propagation constant. For such a contra-directional coupling system, the coupling efficiency grows with the coupling length and it tends to 100% (excluding insertion loss) when the coupling length is larger than a certain value, and the coupling window can be largely broaden by reducing the distance between the coupled waveguides.

Emission control in broad periodic waveguides and critical coupling

Broad periodic channel waveguides, with a corrugation on their edge, exhibit a remarkable structure in their dispersion diagram, in the form of stripes of minigaps, whose hyperbolic shape is demonstrated. Around the Brillouin zone edge, the contra-directional feedback borrows the geometry of Littrow diffraction. Spontaneous emission from a large subset of modes then acquires a strong modulation. Lasing on these modes, the so-called “Littrow lasing”, offers also the lowest lasing threshold of the open resonator system. Reviewing our recent studies of this system, we discuss slow light and critical coupling phenomena: for a properly adjusted contra-directional coupling, the bands become substantially flat in a sizable area of the dispersion diagram, opening various perspectives. The band engineering tools to master these phenomena and the physical implications in other domains are briefly reviewed.

Backward Guiding of Terahertz Radiation in Periodic Dielectric Waveguides

The guiding properties of periodic dielectric waveguides (PDWGs) are investigated theoretically at terahertz frequencies for both two- and three-dimensional model systems. It is shown that in a PDWG there may exist several bound modes, and among them often occur backward modes with antiparallel phase velocity and energy flow. The backward guiding behavior of the PDWG is demonstrated by its contra-directional coupling with a conventional dielectric waveguide (CDWG). For the coupler formed by a PDWG and a CDWG, the coupling direction of energy flow is selectable, since the PDWG supports either a forward or a backward mode at different frequencies.

Contradirectional Coupling Between III–V Stacks and Silicon-On-Insulator Corrugated Waveguides for Laser Emission by Distributed Feedback Effect

We propose a distributed-feedback laser design that takes advantage of Bragg contradirectional coupling between a III-V stack and a silicon-on-insulator corrugated waveguide. This particular coupling scheme enables an equal share of the optical field between the III-V stack and the silicon waveguide, therefore providing an optimum tradeoff between modal gain and coupling efficiency. Numerical simulations indicate that a coupling constant of the order of 12 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> could be achieved for a 200-nm III-V stack-waveguide spacing, relaxing the constraints toward the integration technology.

Effects of three coupling coefficients on the spectrum characteristics of superstructure fiber grating

For the superstructure fiber grating (SFG) consisting of fiber Bragg grating (FBG) and long-period fiber grating (LPFG), there exist three kinds of coupling: the contra-directional coupling between forward propagating core mode and backward propagating core mode, the contra-directional coupling between core mode and cladding mode, and the co-directional coupling between core mode and cladding mode. By using the similarity transformation method for the coupled mode equations, the effects of three coupling coefficients κcoL, κclL, and κSL on the transmission and reflection spectra of SFG have been investigated. The simulations show that the overall intensity of the transmission spectrum of SFG is decided by LPFG, that the main lobes of the transmission and reflectivity spectra of SFG are decided by coupling coefficients κcoL an κSL, and that the side lobes of the transmission and reflectivity spectra are decided by coupling coefficients κclL and κSL.

Optical coupling between a long-period fiber grating and a parallel tilted fiber Bragg grating

We experimentally demonstrate the contradirectional optical coupling between two parallel fibers that contain a long-period fiber grating and a tilted fiber Bragg grating, respectively. Strong coupling occurs between the cladding modes of the same order over the overlapped resonance bands of the two gratings. By optimizing the coupling conditions, we achieve a peak coupling efficiency of approximately 80% at approximately 1,534 nm with a 3 dB bandwidth of approximately 0.12 nm and a side-mode suppression ratio of approximately 16 dB, regardless of which fiber light is launched into. This coupler configuration can be explored for the development of narrow-band all-fiber optical components.

Light wheel confined in a purely dielectric composite waveguide

A properly designed composite waveguide consisting of a one-dimensional photonic crystal waveguide and a conventional dielectric waveguide is proposed for the realization of a localized "light wheel". Light confinedly rotating between the two waveguides is numerically demonstrated and explained physically in detail. A delocalized "light wheel" is found at the band gap edge caused by contra-directional coupling between the two waveguides. Because of this delocalized "light wheel" , the composite waveguide can be used to trap light as a cavity, and a quality factor of 9 x 10(3) is achieved as an example. The present structure is completely dielectric and thus easy to realize with a low loss.

Bandgap formation and selective suppression of Bloch states in birefringent gyrotropic Bragg waveguides

Birefringent magnetophotonic crystals are found to exhibit degeneracy breaking for asymmetric contradirectional coupling in planar waveguides. Fundamental to high-order local normal mode coupling leads to partially overlapping gyrotropic bandgaps inside the Brillouin zone and partial suppression of Bloch mode propagation. A large magneto-optically active reorientation in polarization state is found for allowed Bloch modes at bandgap edges.

An Integrative Biosensor Based on Contra-Directional Coupling Two-dimensional Photonic Crystal Waveguides

We propose an integrative biochemical sensor utilizing the dip in the transmission spectrum of a normal single-line defect photonic crystal (PC) waveguide, which has a contra-directional coupling with another PC waveguide. When the air holes in the PC slab are filled with a liquid analyte with different refractive indices, the dip has a wavelength shift By detecting the output power variation at a certain fixed wavelength, a sensitivity of 1.2 × 10−4 is feasible. This structure is easy for integration due to its plane waveguide structure and omissible pump source. In addition, high signal to noise ratio can be expected because signal transmits via a normal single-line defect PC waveguide instead of the PC hole area or analyte.

Phase Shaping to Control the Performance of a Contra-Directional Grating-Assisted Coupler

We propose a method of improving the performance of a planar grating-assisted contra-directional coupler for use as a photonic switch. By means of a nonuniform Bragg grating, rapid phase jumps are introduced within the reflection spectra of coupler supermodes. This creates a reflection peak of steep slopes, flat top, and desired width. Sample numerical results are given for realistic material and device parameters. A discrete layer-peeling method is employed for the synthesis of the Bragg grating.

Volumetric negative-refractive-index medium exhibiting broadband negative permeability

In this article, a broadband, volumetric, negative-refractive-index metamaterial is presented and its operation is explained. The structure achieves a negative permeability bandwidth of 60% using a periodic cage of backward-wave transmission lines. The permeability is negative over a broad bandwidth due to contradirectional coupling between a backward wave guided by a transmission line and a forward, free-space wave. Negative permittivity is realized using an array of inductively loaded wires. Propagation within the infinite negative-refractive-index (NRI) medium as well as transmission through finite slabs of the NRI medium is presented. The results demonstrate that the proposed NRI medium exhibits a refractive index equal to −1 at 2.45 GHz and is well matched to free space throughout the NRI bandwidth.

Generalized Coupled-Mode Approach of Metamaterial Coupled-Line Couplers: Coupling Theory, Phenomenological Explanation, and Experimental Demonstration

A generalized coupled-mode approach of metamaterial coupled-line couplers is presented. This approach is an extension of the traditional coupled-mode theory (CMT) to the cases of arbitrary types of conventional or metamaterial couplers with lines represented by the most general composite right/left-handed (CRLH) transmission line models. The proposed approach is completely rigorous and applicable to any type of coupler, symmetric or asymmetric, conventional or metamaterial. The CRLH generalized CMT is thoroughly derived and closed-form results for both the complex propagation constants and scattering parameters are provided. Simplified formulas based on a quasi-TEM approximation (exact in the perfectly TEM limit) are derived for contra-directional couplers, which are the most common types in microwaves. The phenomenology of both symmetric CRLH-CRLH and asymmetric conventional CRLH metamaterial coupled-line couplers is completely explained from the proposed approach. The theoretical predictions and phenomenological explanations are validated by experimental demonstration, accompanied by ideal circuit simulation, for the case of a symmetric conventional coupler, a symmetric CRLH coupler, and an asymmetric conventional CRLH coupler

2D photonic crystal cavity-based WDM multiplexer

We designed a multiport two-dimensional (2D) photonic crystal (PhC) multiplexer based on contra-directional coupling and standing-wave resonators. The device is composed of PhC filters with up to 12 cavities in the same micro-patterned structure: adjacent strips with different periods contain a single cavity, and by selecting the proper lattice constants we tune the dropped frequency of each cavity. Each filter has 1.16 nm bandwidth, at a central wavelength 1550 nm, and the channels are 10 nm spaced. The variations in the local lattice period are very small, and the mismatch between two adjacent structures does not affect the propagation of the beam in the bus channel. The PhC structure has been analyzed by using the plane wave expansion method and the device performance has been investigated with the finite-difference time-domain technique. The transmittance of each drop filter is about 74%, with a non-uniformity between channels less than 5%. The overall longitudinal dimension of the multiplexer is less than 20 μ m.

Inverse Scattering in Multimode Structures

We consider the inverse scattering problem associated with any number of interacting modes in one-dimensional structures. The coupling between the modes is contradirectional in addition to codirectional and may be distributed continuously or in discrete points. The local coupling as a function of position is obtained from reflection data using a layer-stripping-type method, and the separate identification of the contradirectional and codirectional coupling is obtained using matrix factorization. Ambiguities are discussed in detail, and different a priori information that can resolve the ambiguities is suggested. The method is exemplified by applications to multimode optical waveguides with quasi-periodical perturbations.