Wave Coupling by Warped Normal Modes

It has been shown by J.S. Cook that wave power may be transferred from one to another of two coupled waveguides through a variation of their phase constants. It is now clear that this is but one example of a new principle of coupling which is here called "nomal mode warping." Wave power inserted at one end of a coupled waveguide system may be made to appear at the other end with any desired power distribution by gradual warping of the normal mode field patterns along the coupler. In general, both variation of the coupling coefficient and phase constants are required. Much wider bands are theoretically possible than with any other distributed type of coupler. This principle may be applied to dielectric waveguides, birefringent media, and waveguides containing ferrite, to obtain both reciprocal and nonreciprocal couplers.     

A novel finite-element method for nonreciprocal magneto-photonic crystal waveguides

A new formulation of the finite-element method to analyze nonreciprocal waveguides in magneto-photonic crystals (MPCs) is proposed. Accurate solutions of light propagations for two different directions are obtained by the asymmetrical input condition. As numerical examples, the performance of a waveguide-type optical isolator in MPCs designed by the eigenmode analyses is confirmed by using this method. Subsequently, an effective way to enhance the nonreciprocity of the optical isolator is shown.     

A Proposal of Zero Leakage-Loss Passive Optical Combiner Based on Nonreciprocal Waveguide

In this letter, a zero-leakage-loss passive optical combiner based on nonreciprocal waveguides is proposed to remove the inherent 3-dB leakage loss in the conventional ones, which consists of a nonreciprocal waveguide grating-type isolator and circulator. The device concept is given, and the dispersion relation analysis and 3-D magnetooptical beam propagation method are employed to validate the feasibility and the device performance.     

Magnetooptical waveguides with polarization-independentnonreciprocal phase shift

Magnetooptical waveguides having nonreciprocal phase shift for both TE and TM modes can be prepared by properly adjusting the spatial variation of the Faraday rotation. Such waveguides are attractive to realize optical isolators. We investigate four concepts of magnetooptical waveguides which yield equal nonreciprocal phase shifts for the fundamental TE and TM modes. A polarization-independent Mach-Zehnder-type integrated optical isolator is presented. All the calculations are performed using material parameters typical for garnet films     

Simulation of polarization converter formed by poling-inducedpolymer waveguides

A polarization converter using electrooptic (EO) polymer waveguides is proposed and it is simulated by a full vectorial beam propagation method (VBPM) for anisotropic medium. First, an efficient structure of poling electrodes is proposed for the fabrication of TE-mode poling-induced waveguides in EO polymer. For given electrode structures of both TE-mode and TM-mode waveguides, poling-induced dielectric tensors are calculated by the finite-element method to provide refractive index distribution, data for VBPM simulation. It is shown numerically that the poled TE and TM mode waveguides work efficiently as the corresponding polarization filters. Then, new poling electrodes are suggested to fabricate a waveguide device formed by connecting the TE and TM mode waveguides adiabatically with a slowly varying structure. This waveguide device has the optic axis slowly rotating as one moves along the propagation direction, so that it will act as polarization converter. VBPM simulation shows that the polarization of the guided mode rotates following the optic axis distribution. Polarization conversion is demonstrated successfully with high conversion efficiency and low excess loss     

Phase-Matched Waveguide Using the Artificial Anisotropic Structure and its Application to a Mode Converter (Short Papers)

Phase matching by the artificial anisotropic structure and its application to a mode converter are proposed for millimeter-wave dielectric circuitry. A phase-matched dielectric planar waveguide is designed and mode conversion characteristics are studied. An experimental result of the nonreciprocal mode converter are presented to show the usefulness of the structure.     

Analysis of polarization independent Mach-Zehnder-type integratedoptical isolator

This paper proposes, for the first time, an integrated optical isolator independent of light polarization. A Mach-Zehnder interferometer (MZI) with two nonreciprocal phase shifters, one for transverse electric (TE) modes and another one for transverse magnetic (TM) modes can be adjusted so that it blocks the fundamental modes of the waveguides constituting the interferometer propagating in one direction and is transparent for the modes propagating in the opposite direction. If the interferometer branch waveguides are in single mode regime, the performance of the device will not depend on the polarization of incoming light. The nonreciprocal phase shifters can be realized on structures with magnetization tangential to the propagation direction. Three geometries of nonreciprocal phase shifters are discussed and tolerances are estimated     

Analysis of Periodic Ferrite Slab Waveguides by Means of Improved Perturbation Method

Periodic ferrite slab waveguides are analyzed by means of an improved perturbation method, and nonreciprocal leakage phenomena are shown theoretically. As an application of these phenomena, new planar isolators and circulators are proposed. Numerical examples are also provided.     

Coupled modes of multiwaveguide systems and phased arrays

A new theory describing coupled mode propagation in an array of arbitrary optical waveguides is developed. The formulation unambiguously accounts for real and/or imaginary index perturbations and its solutions yield supermode patterns and propagation constants. Several examples of coupled TE slab waveguides are evaluated and the results are shown to compare very favorably with exact solutions. The calculated propagation constants and mode patterns differ quantitatively and qualitatively from those derived from the prior theory. In particular, the supermode gains derived according to the new theory agree very well with exact solutions and predict different supermode ordering and splitting than those derived by the prior theory.     

Numerical method for the calculation of mode fields and propagation constants in optical waveguides

The scalar wave equation for optical waveguides with arbitrary refractive index profiles is solved using a numerically stable integration method. The mode fields and the corresponding propagation constants are determined iteratively. Results for waveguides based on different well-known fabrication techniques are shown and the design of a new sensitive integrated optical switch is proposed.     

Pumping planar waveguide amplifiers using a coupled waveguidesystem

A novel scheme is presented that can be used to efficiently pump optical waveguide amplifiers. It is based on the coupling between two adjacent waveguides, where pump light is gradually coupled from a nonabsorbing pump waveguide into the amplifier waveguide. The coupling between the waveguides in such a configuration is calculated using an improved coupled mode theory (CMT). The proposed distributed coupling scheme can enhance the optical gain in systems that exhibit a reduced pumping efficiency at high pump power. A numerical example is given for a sensitized neodymium-doped polymer waveguide amplifier, in which the optical gain increases from 0.005 dB to 1.6 dB by changing from conventional butt-coupling to distributed coupling     

Tapered polymer single-mode waveguides for mode transformation

This paper presents a tapered polymer waveguide structure for coupling light between optical waveguides with differing geometries. Optical fibers, lasers, and other photonic integrated circuit components can be coupled with tapered waveguides. The polymer waveguide performs a mode transformation between different mode shapes and sizes. For example, the mode transformation can be from an elliptical laser diode mode to that of a circular optical fiber mode. The input and output of a tapered waveguide structure are analyzed, for the case of laser to fiber coupling, in order to determine the effect of misalignments on the coupling efficiency. Adiabaticity in waveguide propagation is discussed. The fabrication of our polymer waveguides is also described     

Mode orthogonality in reciprocal and nonreciprocal waveguides

Using a general reciprocity theorem as a basis, the orthogonality relations for lossy reciprocal and nonreciprocal waveguides are discussed. To obtain a useful orthogonality relation which can extract a particular mode from a general mode expansion, a reciprocal waveguide must be bidirectional. A nonreciprocal waveguide, however, must be mutually bidirectional with its complementary waveguide (obtained by reversing the DC magnetic field applied to the gyrotropic media). For these bidirectionally conditions to be met, a waveguide must possess at least one of three symmetries: reflection, 180° rotation, or rotary reflection symmetry. In those cases warranted by the structure symmetry, simplified forms for the orthogonality relations are presented. The orthogonality relations for the special case of lossless reciprocal or nonreciprocal waveguides are discussed     

Collinear acoustical TM-TE mode conversion in proton exchangedTi:LiNbO3 waveguide structures

Collinear acoustooptic TM-TE mode conversion is experimentally investigated in proton exchanged Ti:LiNbO₃ optical waveguides. Their birefringence is adjusted by an appropriate annealing to allow phase matching at surface acoustic wave frequencies of about 90 MHz and 180 MHz, respectively. A planar mode converter with an efficiency of up to 90 percent is presented (87 MHz, 175 MHz). Furthermore, a combined acoustical/optical strip waveguide structure is developed as mode converter, leading to strongly reduced power requirements; only 0.3-mW acoustic power is sufficient to achieve a conversion efficiency of 50 percent     

脊形波导耦合的光纤阵列设计

分析了单模光纤与脊形波导的耦合模理论,讨论了其模式特点、最佳耦合条件.在此基础上,计算并设计出满足最佳耦合条件的光纤阵列V-型槽宽度.所设计的光纤阵列在对光纤提供高精度定位的同时,又能保证其与脊形波导的高效率耦合.     

Analysis of polarization independent optical amplifiers and filtersbased on polarization rotation in periodically asymmetricwaveguides

Polarization rotation in periodically asymmetric passive and active waveguides is described theoretically. The analysis is based on the vector wave equation and analysis of the coupled mode equations. It is shown that these periodically asymmetric active waveguides can be employed as polarization-independent optical amplifiers, and that strictly polarization-independent amplifiers require a rotation of an integer multiplier of π radians. An illustrative example of such an amplifier with a buried waveguide structure suitable for monolithic integration is analyzed. Polarization-insensitive passive Bragg filters employing, in addition to the ordinary grating, a periodically asymmetric perturbation are also considered, and polarization rotation in a distributed feedback laser filter is discussed     

Coupled-mode theory

The authors give a brief historic perspective of the coupled mode theory. The development and applications of the theory in microwaves in early years and in optoelectronics and fiber optics in recent years are described. They then consider lossless coupling of two modes in time. Two coupled resonance circuits, or two coupled microwave or optical resonators, are the physical examples. The start-up of a parametric oscillator is another example. Then they look at the formal derivation of coupled mode theory and consider the more general case when the modes are not energy-orthogonal and the energies are not necessarily positive. A more detailed account of the nonorthogonal coupled mode theory developed in the last five years for optical waveguides is given     

Low-loss twists in oversized rectangular waveguide

The unwanted mode conversion from twists in overmoded waveguides is calculated from numerical integration of the coupled-mode equations, considering simultaneous coupling of the five lowest-order modes coupled in a twist. Twists with tapered or linearly varying rates of twist are shown to be superior in medium- or broad-band applications to those with uniform twist rate. Measurements consistent with these theoretical calculations are discussed for uniform twists in WR90 waveguide at 60 GHz and for an electroformed twist having a linearly tapered rate of twist in WR187 waveguide from 15.7 to 17.7 GHz. The coupling coefficients needed in the calculations are derived and are compared with the results of other work, including a modal expansion of the dominant mode in twisted waveguide. The work also considers the transmission through an oversized waveguide with a mode converter generating a trapped unwanted mode, and the result for the dependence of the resonance depth on the mode conversion and the attenuation of the trapped mode is found     

Coupled GaAs multiple-quantum-well channel waveguides includingquadratic electrooptic effect

Two coupled channel waveguides using GaAs multiple quantum wells are investigated using an improved coupled-mode theory for anisotropic waveguides and the effective index method. The quadratic electrooptic effect in the multiquantum-well structures is taken into consideration. It is shown that only a moderate electric field for multiquantum-well waveguides is necessary to achieve the optical power switching compared with that required for a bulk GaAs waveguide     

Non-evanescent adiabatic directional coupler

A directional coupling mechanism based on an adiabatic coupling between three optical modes is suggested. The optical power transfer between two waveguides which are far apart is mediated by adiabatic coupling between zero-order optical modes of the individual waveguides and a high-order intermediate mode. The analytical model for an adiabatic three-mode coupling based on a scalar wave equation is presented. The directional coupling via the adiabatic mode coupling between copropagating modes is described and compared with a nonadiabatic directional coupling assisted by periodic perturbation. It is shown that adiabatic directional coupling has much less sensitivity to the mode parameters and to the wavelength