Propagation Constant Of Waveguide Research Articles

Restoring robust binary switching operation and exceptional point using long-period grating-assisted parity-time symmetric couplers

The impact of imbalance in waveguide propagation constants among parity-time symmetric coupled waveguides and/or of a complex-valued coupling coefficient is assessed. The narrow tolerance found implies that attempts to tightly control waveguide parameters appear to be elusive because of fabrication technology limitations, calling for more feasible mitigation avenues. It is shown that a grating-assisted parity-time symmetric coupler design restores both technologically robust binary switching operations and exceptional points. In addition, the proposed design is compatible with birefringence compensation techniques, providing polarization-independent operation as well as coupling and/or gain-loss profile modulation techniques that extend the control of switching operation in the parity-time symmetric phase. Using the wavelength as an additional tuning parameter near exceptional points opens promising avenues for manipulating the trajectory on Riemann sheets in topological photonics applications.

Variable propagation constant directional coupler

Variable propagation constant directional coupler is proposed and demonstrated. Compared with its conventional counterpart, the proposed coupler uses variable waveguide propagation constants as an extra degree of design freedom to achieve the required signal addition and cancellation. The operation principle is mathematically formulated and a step-by-step design methodology is presented. Two double-layer two-hole substrate integrated waveguide couplers: namely, one forward directional coupler and one backward directional coupler, are fabricated to validate the proposed concept. A coupling of −20 dB is achieved in both couplers and the maximum isolation of −47 and −52 dB are obtained by the forward and backward structures, respectively.

Efficient 2-D Finite-Element Solution of Vector Wave Equation in a Class of Curved Polygons

We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of waveguides filled with pieces of homogeneous materials. To apply the method, we first decompose the 2-D problem domain into a set of curved polygons of a specific characteristic. Then, we divide every polygon into a set of triangular elements with two straight edges. Finally, we introduce a set of hierarchical mixed-order curl-conforming vector basis functions inside every triangular element to discretize the vector wave equation. The advantages of the method are as follows. The curved boundaries of the elements are modeled exactly, and hence, there is no approximation in the geometrical modeling. The 2-D integrals of the matrix elements are reduced to 1-D integrals. Therefore, the matrix filling can be performed very fast. The total number of elements due to the discretization of a given domain is very small, and hence, the discretization of the problem domain takes up a very small percentage of the total computational time. We validate the method by comparing the results with those of the Ansoft High Frequency Structure Simulator simulator and investigate the accuracy and efficiency of the method through a numerical example.

Transmission, reflection, scattering, and trapping of traveling discrete solitons by $$\mathcal{C}$$ and $$\mathcal{V}$$ point defects

We study the interactions of moving discrete solitons in waveguide arrays with two types of point defects that are constructed by varying either the local linear coupling or local waveguide propagation constant at the center of the waveguide array. A broad discrete soliton is kicked toward the defect and interacts with it. Transmission, reflection, scattering, and trapping during the interaction between the soliton and the defect occur depending on the parameters. The detailed behavior of the soliton dynamics is analyzed numerically. A transmission window in the parameter domain is found and the behavior of this window for different parameters is studied. The dynamics of the soliton in the transmission window is found to have chaotic features under certain circumstances and the causes of these phenomena are identified and discussed.

Analog to electromagnetically induced transparency and Autler-Townes effect demonstrated with photoinduced coupled waveguides

It is shown that light transfer between two evanescently coupled optical waveguides can be interrupted when strong interaction with a third waveguide is induced. In the strong-interaction regime the transfer can be reactivated upon proper detuning of the waveguide propagation constants. These phenomena can be easily understood using the analog of Autler-Townes splitting and electromagnetically induced transparency from atomic physics. Experimental demonstration is provided using photoinduced reconfigurable waveguides.

Justification of the spectral method for calculating the propagation constants of waveguides and microstrip and slotted lines

The general scheme of the spectral method for determining the propagation constants of eigenmodes in a shielded slotted waveguide is presented. The method is justified, and the general properties of the spectrum of eigenmodes in the waveguide are established.

Novel Silica-Based Waveguide-Type Polarization Beam Splitters Using Trenches Filled With Low-Refractive-Index Material

We have proposed and fabricated two kinds of planar-lightwave-circuits-type polarization beam splitters (PBSs) using trenches filled with low-refractive-index material: a narrowband-type and a wideband-type. Both PBSs consisted of two 3-dB couplers and two waveguide arms with trenches of different lengths. A narrowband-type PBS used silica-based waveguides on silica substrates. On the other hand, a wideband-type PBS used silica-based waveguides on silicon. The local lateral refractive index difference (?) was increased by introducing a pair of trenches. Due to the local lateral enhanced optical confinement structure, the propagation constants of waveguides constructed using trenches filled with a low-refractive-index material depend strongly on the polarization. A narrowband-type PBS, which had the same arm lengths can have a high polarization extinction ratio, although the working bandwidth is restricted. However, a wideband-type PBS, which had the different arm lengths can function over a broad wavelength range, provided that the maximum polarization extinction ratio is acceptable. We optimized the structures of both types of PBS by carrying out simulations. In these simulations, the narrowband-type PBS exhibited a maximum polarization extinction ratio of -34.5 dB for the through-path at 1555 nm, -42.7 dB for the cross-path at 1545 nm, whereas the wideband-type PBS exhibited a -10 dB polarization extinction ratio bandwidth of 105 nm. Our fabricated narrowband-type PBS exhibited a -10 dB polarization extinction ratio bandwidth of 45 nm for both the through-path and the cross-path. At this bandwidth, the insertion loss was less than 9.0 dB. The maximum polarization extinction ratio was -28.9 dB for the through-path at 1570 nm, and -27.5 dB for the cross-path at 1535 nm.

Solid state microcavity dye lasers fabricated by nanoimprint lithography

We present a solid state polymer microcavity dye laser, fabricated by thermal nanoimprint lithography (NIL) in a dye-doped thermoplast. The thermoplast poly-methylmethacrylate (PMMA) is used due to its high transparency in the visible range and its robustness to laser radiation. The laser dye is Rhodamine 6G ClO4. This dye is shown to withstand temperatures up to 240 °C without bleaching, which makes it compatible with the thermal nanoimprint lithography process. The 1.55 μm thick dye-doped PMMA devices are fabricated on a SiO2 substrate, yielding planar waveguiding in the dye-doped PMMA with two propagating TE–TM modes. The laser cavity has the lateral shape of a trapezoid, supporting lasing modes by reflection on the vertical cavity walls. The solid polymer dye lasers emit laterally through one of the vertical cavity walls, when pumped optically through the top surface by means of a frequency doubled, pulsed Nd:YAG laser. Lasing in the wavelength region from 560 to 570 nm is observed from a laser with a side-length of 50 μm. In this proof of concept, the lasers are multimode with a mode wavelength separation of approximately 1.6 nm, as determined by the waveguide propagation constant(s) and cavity dimensions. The stamps used in this work were fabricated by UV-lithography, limiting the lateral dimensional control of the devices. The resolution of NIL is ultimately limited by the quality of the stamps. Using electron beam lithography for stamp fabrication, the NIL process presented here offers the possibility for adding mode-selecting elements, e.g., diffractive- or sub-wavelength optical elements.

Substantiation of the Spectral Method for Calculating Propagation Constants for Waveguides with Microstrip and Slit Lines

We prove the spectral method for calculating the propagation constants of normal waves in screened waveguides with an irregular cross-section and a nonhomogeneous filling. The problem is reduced to the nonlinear spectral problem for operator-functions in a Hilbert space. Existence theorems are proved for spectral points and the cutoff method is substantiated.

Pulse distortion in optical fibers and waveguides with arbitrary chromatic dispersion

We present a complete end-to-end characterization of Gaussian pulse propagation through optical fibers and waveguides with an arbitrary dispersion profile. Our model takes into account the possible chirping of the source and it also encompasses the influence of the source linewidth. We modeled the arbitrary dispersion by taking as much of the coefficients from the Taylor series representing the fiber and waveguide propagation constant as desired. The model is used to study the impact of higher-order dispersion terms in the propagated pulse shape and rms time width. Also outlined are applications to the calculation of capacity limits in optical communications systems limited by high-order dispersion terms and to other fields such as the calculation of aberrations in temporal imaging systems and spatial diffraction.

Measurement of propagation constant in waveguides with wideband coherent terahertz spectroscopy

A quasi-optical technique for characterizing micromachined waveguides is demonstrated with wideband time-resolved terahertz spectroscopy. A transfer-function representation is adopted for the description of the relation between the signals in the input and output port of the waveguides. The time-domain responses were discretized, and the waveguide transfer function was obtained through a parametric approach in the z domain after describing the system with an autoregressive with exogenous input model. The a priori assumption of the number of modes propagating in the structure was inferred from comparisons of the theoretical with the measured characteristic impedance as well as with parsimony arguments. Measurements for a precision WR-8 waveguide-adjustable short as well as for G-band reduced-height micromachined waveguides are presented.

On the use of linear-prediction techniques to improve the computational efficiency of the FDTD method for the analysis of resonant structures

Linear-prediction (LP) techniques are used to accurately and efficiently compute the frequencies and damping factors of microwave resonant structures from their transient response, which was previously obtained by using the finite-difference time-domain (FDTD) method. The LP equations are formulated in terms of a total least squares (TLS) problem and are solved by using the singular-value decomposition (SVD) algorithm. This approach confers robustness to the LP method, improves the spectral resolution, and provides a simple criterion for selecting the order of the LP model. We illustrate these characteristics of the LP method by applying it to two types of problems: the determination of the propagation constants of waveguides loaded with lossy dielectrics, and the calculation of the resonant frequencies of cylindrical cavities loaded with dielectric ring resonators.

A treatment of magnetized ferrites using the FDTD method

The finite-difference-time-domain (FDTD) method is extended to include magnetized ferrites. The treatment of the ferrite material is based on the equation of motion, using Gilbert's approximation of the damping term. The validity of the formulation is verified by applying it to the calculation of propagation constants in waveguides containing ferrites with transverse magnetization. The results for a rectangular waveguide filled with ferrites and those for a rectangular waveguide loaded with a centered ferrite slab are compared with the exact results, showing good agreement.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Highly accurate vector correction for optical waveguide propagation constants

A vector correction is derived to the propagation constants obtained from a polarised analysis of graded-index optical waveguides. This general formula is reduced to a form suitable for use with semiconductor rib and strip-loaded waveguides. Corrected propagation constants calculated for a range of semiconductor rib waveguide structures coincide with available results from a full vector approach. Moreover, the vector correction term is always small, underpinning the accuracy of this simple and fast polarised approach for the first time.

Demonstration of Dispersive Optical Bistability With a Third Order Nonlinear Optically Active Polymer

ABSTRACTDispersive optical bistability in a Fabry-Perot (F-P) cavity with a third order nonlinear optical polymer was demonstrated. This effort involved the development of several nonlinear optical polyimides and an evaluation of their linear optical and nonlinear optical properties. These Materials were processed into waveguiding films having good homogeniety and optical properties. Several of these films were shown to have desirable third order nonlinearities, while exhibiting good mechanical and environmental stability. Characterization of these materials involved the measurement of their absorption profiles, film thicknesses, optical waveguide propagation constants and nonlinear optical susceptibilities. Based on the measured results, a specific polyimide was chosen and used to demonstrate an all-optical instrinsic bistable device operating at a wavelength of 1.06 μ. Using ∼ 100 ps input pulse widths at 1.06 μ, dispersive optical bistability originating from the induced refractive index change, δn, due to an electronic nonlinearity of the polyimide was observed.

A perturbation analysis for modes in graded waveguides by hypervirial and Hellmann-Feynman theorems

The algebraic formulas for calculating modes and propagation constants in waveguides with an arbitrary index profile are derived with the use of hypervirial theorems (HVT) and Hellmann-Feynman theorem (HFT). Formulas and numerical results for a gaussian index profile are obtained and compared with those obtained by WKB or ray technique and earlier perturbation approaches. The method is simple to apply, and the results are very accurate.

Use of a variational moment method in calculating propagation constants for waveguides with an arbitrary index profile

A variational moment method is used to calculate propagation constants of 1-D optical waveguides with an arbitrary index profile. The method is applicable to 2-D waveguides as well, and the index profiles need not be symmetric. Examples are given for the lowest-order and the next higher-order modes and are compared with exact numerical solutions.

New results for rib waveguide propagation constants

The propagation constants of dielectric rib waveguides for optoelectronics are calculated by new methods designed either as an advance on typical existing methods, or for comparison with them. The classical variational methods agree with each other, but are somewhat pessimistic in that they underestimate the value of the propagation constant. Vector and scalar finite element or finite difference methods fall into a pattern of agreement with each other. Overall, there is a remarkable consensus between the values and the differences between them which highlights their advantages and disadvantages. The implications for directional couplers are briefly discussed.

Transmission line models for lossy waveguide interconnections in VLSI

At high frequencies the waveguide nature of interconnections in VLSI circuits becomes important. Moreover, losses in interconnection are a major feature, not a perturbation. Here it is shown that even for such lossy waveguide structures an exactly equivalent RLGC transmission line can be found. Equations are given determining these transmission line parameters in terms of the waveguide propagation constant and complex average power, and also in terms of integrals over the electric and magnetic field varibles. The resulting L , C , and G parameters differ from the usual static values when losses are important, and R is not restricted to the usual formula based upon a perturbation treatment of the skin effect. Consequently, semiconductor substrates can be treated. Current and are found to have an abstract meaning in the equivalent transmission line. For a waveguide in a medium where conductivity and permittivity vary with position (such as a many-layered medium) an explicit formula relating current and to weighted averages of transverse waveguide fields is given. A brief discussion of the reformulation of Thevenin equivalent circuit parameters in terms of reflection coefficients avoids terms such as open circuit voltage that are difficult to interpret for the equivalent transmission line. The framework presented allows construction of equivalent circuits for lossy waveguide interconnections, drivers, and terminations that provide correct spatial dependence in the direction of propagation and correct power relations despite the abstract nature of current and in these lines.

Formulation of variational principles via Lagrange multipliers

Recent work on variational principles in mathematical physics enables one to construct, in a novel and systematic way, stationary expressions for a wide class of functionals P(E), where E is an unknown (vector) function whose defining equation cannot be solved exactly. The method involves the use of Lagrange multipliers, which can be a constant λ, a function F(x,y,z), and a dyadic operator Γ, to account for each of the equations (constraints) that define E. As illustrations, we consider vector and scalar scattering problems, and eigenvalue problems such as the determination of resonant frequencies and propagation constants of waveguides.