Optical wavelength filter with tapered couplers

Optical wavelength filters based on tapered directional couplers are analyzed by nonorthogonal coupled-mode theory. The nonorthogonal coupled-mode formulation in general yields more accurate results than the conventional orthogonal coupled-mode theory. The focus is on the novel features of the tapered couplers used as wavelength filters. It is demonstrated that, in addition to reducing the crosstalk and suppressing the sidelobes, the tapered structure can also make the filtering response independent of the device length beyond a critical coupling length,.<>     

The extinction ratio in optical two-guide-coupler Delta beta switches with asymmetric detuning

Two-guide asymmetrically detuned Delta beta optical coupler switches with two equal-length sections that operate as on-off switches are examined by means of the exact eigenmodes of a slab waveguide model of the coupler. Two input/output configurations are analyzed, namely (1) where a single output guide is connected to the same guide of the coupler as the input guide, and (2) where a single output guide is connected to the coupled guide. For both cases, ideal switching, i.e. complete extinction in the off state, can be obtained in the two-section Delta beta coupler over a wide range of coupler lengths. The results differ from those of conventional coupled-mode theory in that when the two sections of the coupler are antisymmetrically detuned, i.e. delta = delta /sub 1/=- delta /sub 2/, complete extinction can be obtained only in a few special cases.<>     

Orthogonal Hybrid Waveguides: An Approach to Low Crosstalk and Wideband Photonic Crystal Intersections Design

A low crosstalk and wideband photonic crystal (PC) waveguide intersection design based on two orthogonal hybrid waveguides in a crossbar configuration is proposed. The finite-difference time-domain (FDTD) and coupled-mode theory (CMT) methods are used to simulate the hybrid waveguides of square lattice. The bandwidth (BW) and crosstalk of the intersection are investigated for various radii of the coupled cavities. It is shown that simultaneous crossing of the lightwave signals through the intersection with negligible interference is possible. The transmission of a 200-fs pulse at 1550 nm is simulated by using the FDTD method, and the transmitted pulse shows negligible crosstalk and very little distortion.     

A Frequency-Dependent Coupled-Mode Analysis of Multiconductor Microstrip Lines with Application to VLSI Interconnection Problems

The spectral Galerkin procedure is used to calculate the dispersion properties of multiple conductor microstrip lines. The resulting propagation constants are then used in a coupled-mode theory which demonstrates a frequency-dependent coupling of current in a five-conductor system. These results should he useful in the study of crosstalk between parallel microstrip lines used in VLSI interconnections.     

Performance and modeling of proton exchanged LiTaO3branching modulators

Proton-exchanged LiTaO₃ branching modulators are demonstrated experimentally and modeled using a normal mode coupled-mode theory. The normal modes are approximated by ordinary coupled-mode theory parameters which are experimentally obtained. Agreement between the model and the experimental results is demonstrated. Crosstalk in these linear branch devices is found to be linearly proportional to the voltage-length product, a result which leads to an analytic expression for the output power     

Coupled waveguide antennas

A structure consisting of two coupled waveguides is proposed as a leaky-wave antenna. The analysis of this device is based on coupled-mode theory. Previous coupled-mode treatments are extended, since radiative loss is not neglected and the asymmetry of the structure is taken into account. Two cases are considered: the coupling parameter constant with distancezalong the antenna and the coupling as a function ofz. In both, the radiative attenuation is maintained constant. It is found that the first case permits two "normal modes" to propagate and, if both modes are excited, the patterns may be superposed to produce desirable overall results. An example is given of an approximation to a pencil beam pattern. By means of the second method, essentially any of the common excitation functions may be produced. An example is given of an antenna to achieve a cosine-on-a-pedestal excitation. Experimental results are given and compared to theory. Suggestions are presented for further work.     

Analysis of optical fiber directional coupling based on theHE11 modes. I. The identical-core case

For pt.II see ibid., vol.8, no.6, p.832-7 (1990). The directional coupling between two identical single-mode optical fiber cores is analyzed by using the coupled-mode theory in the vectorial form based on the exact HE₁₁ modes. Analytical expressions for the coupling coefficients and the butt coupling coefficient appearing in the conventional and the recently formulated new coupled-mode equations are presented. The effect of the different polarizations on the coupling is considered. The accuracy of the conventional and new theories as applied to the two-core system is examined by comparing the coupling coefficients with exact numerical values. It is shown that as long as the exact HE₁₁ modes are used, the coupled-mode calculations behave well in predicting the coupling strength beyond the weakly guiding regime, and that the simpler conventional theory can provide satisfactory results when applied in the vectorial form     

Coupling Between Dissimilar Waveguides

Investigators have used coupled-mode theory to analyze the coupling between identical waveguides; in such cases the coupling coefficients are found to be identical. If the waveguides differ, the coupling coefficients are asymmetrical and difficult to evaluate by strictly theoretical methods. An alternate approach to this case is considered in the present work. A pair of coupled-mode equations is first developed from a consideration of the permissible fields within the device. This clarifies the relationship between the coupled-mode theory and the more general classical electromagnetic theory by giving a careful definition of the coupled and the normal modes of a coupled structure. It is shown that the coupled-mode equations are an exact representation of the waveguide fields, although for engineering purposes it is often convenient to use approximate values of the coefficients of these equations. The mutual coupling coefficients are obtained from a two transmission-line model of the structure, with the actual coupling mechanism represented by a mutual impedance common to the two lines. For dissimilar lines, the ratio of the coupling coefficients is found to be equat to the ratio of the characteristic impedances. For the cases considered, this is the same as the ratio of the propagation constants of the uncoupled lines, which permits the coupling coefficients to be determined from relatively simple measurements. The adequacy of the theory has been confirmed by a series of experiments.     

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     

Coupled-Mode Analysis of an NRD-Guide Coupler Based on Singular Perturbation Technique

A coupled-mode formulation for an NRD-guide coupler is presented using the singular perturbation technique. The first-order and second-order perturbations are taken into account in the analysis and the coupled-mode equations based on the eigenmodes of each waveguide in isolation are derived. The propagation constants obtained by these equations are compared with those by the exact theory, conventional coupled-mode theory, and improved coupled-mode theory. The numerical results of present formulation are in good agreement with the exact theory and superior to those of the other formulations.     

Analysis of optical fiber directional coupling based on theHE11 modes. II. The nonidentical-core case

For pt.I see ibid., vol.8, no.6, p.823-31 (1990). The analysis of the directional coupling between two single-mode optical fiber cores based on the exact HE₁₁ modes is extended to the cases involving nonidentical fibers. The coupled-mode theory in the vectorial form is used, and analytical expressions for the coupling coefficients and the butt coupling coefficient appearing in the conventional and the coupled-mode equations are presented. The accuracy of the conventional and new theories as applied to the two-core system is examined by comparing the coupled-mode predictions with the exact numerical values for different core-radius ratios, waveguiding strengths, polarization states, and core separations. It is shown that the errors in the coupled-mode theories increase as the two cores become more dissimilar. As long as the dissimilarity between the cores is kept small, the coupled-mode calculations using the HE₁₁ modes in predicting the coupling strength can be of satisfactory accuracy even when the individual guides are not weakly guiding ones. It is found that the new theory may give relatively large errors in the touching-core case with distinctly different core radii     

用耦合模原理分析RLC串联电路

用两个状态变量构造的复数状态变量叫做耦合模。以耦合模为变量对电路或系统进行分析的方法叫耦合模分析。本文以RLC串联电路零输入响应和正弦稳态响应为例,入门性地介绍了耦合模原理在电路分析中的应用,包括耦合模的定义与性质,耦合模方程的列写与求解,耦合模方程的简化,以及用耦合模计算的元件储能和电路储能等。用数值计算方法给出了这些响应的波形,它们和用传统电路理论获得的波形完全一致。耦合模原理在分析模式耦合系统,并着眼于能量的传递时,具有特殊的用途,例如无线电能传输系统。     

Superimposed phase gratings in planar optical waveguides forwavelength demultiplexing applications

A theoretical analysis of superimposed phase gratings in planar optical waveguides for wavelength demultiplexing applications is developed. Using coupled-mode theory, it is shown that the coupling between the gratings affects diffraction characteristics for output beams of close angular or wavelength separation. Nevertheless, taking into account the coupling effects and adjusting critical parameters, high-performance devices are found to be achievable in carefully designed structures. The authors predict that wavelength demultiplexers having efficiencies larger than 95%, angular and wavelength separation smaller than 0.2° and 20 Å, respectively, and crosstalk attenuation lower than -40 dB are possible     

A comparison of beam propagation and coupled-mode methods:application to optical fiber couplers

We analyze the instantaneous power in the local normal modes of an optical fiber coupler with both various three-dimensional paraxial electric field propagation methods and coupled-mode theory. Our calculations show that large improvements in speed result if a low-order, split-operator, finite-difference propagation algorithm is substituted for the standard split-step fast Fourier transform technique. Further, as field evolution procedures incorporate higher-order modes, the calculated power transfer ratios agree far better with experiment than the corresponding coupled-mode predictions. The coupled-mode results however, can be improved by taking into consideration the exact shape of the refractive index profile and higher-order modes, while the approach is simple to program, and yields qualitatively correct predictions for performance trends     

A unified approach for the coupled-mode analysis of nonlinearoptical couplers

A unified approach for the coupled-mode analysis of nonlinear optical couplers is proposed. This approach is basically an extension of the work of [Haus, vol. 5, p. 16, 1987] to include optical nonlinearity. After the nonlinear coupled-mode theory is established, various basis functions are used as trial fields to derive coupled-mode equations. It is found that two published coupled-mode theories can in fact be deduced from the proposed one with individual linear or nonlinear waveguide modes serving as trial fields, thus making the coupled-mode equations from variational principle and reciprocity theorem equivalent. Coupled-mode equations based on system modes are also presented. Furthermore, analytical and/or numerical methods for solving coupled-mode equations are included. More research and discussion can be conducted based on the knowledge addressed in this paper     

A new approach to grating-assisted couplers

A novel approach to the analysis and design of grating-assisted directional couplers is proposed. Power exchange between the waveguides is maximized through phase matching of two power-orthogonal modes of the parallel coupler. It is shown that either complete power transfer or zero crosstalk can be achieved at two different coupling lengths even when the two wavelengths are strongly coupled and/or close to synchronism. An analytical solution to the coupled-mode equations is obtained for the grating of rectangular shape. A grating-assisted coupler made of two slab waveguides is examined as an example to illustrate the salient features of the scheme     

Latch-up and image crosstalk suppression by internal gettering [in CMOS]

Internal gettering can be used to reduce crosstalk in imagers and latchup susceptibility in CMOS circuits. The internal gettering process forms defects in the bulk of the silicon wafers that are effective recombination sites for minority carriers in the substrate. Experimental and theoretical results are presented for crosstalk reduction obtained in an area imager. The current gain /spl beta/ of the parasitic lateral n-p-n transistors formed in the substrate in CMOS circuits was considerably lower for the internally gettered wafers. The trigger current needed to initiate latch-up in the n-p-n-p structures increased as 1//spl beta/, in accordance with the theory. A Monte Carlo method was developed to calculate the expected transistor current gain. The calculated /spl beta/s are in excellent agreement with the measured values.     

Calculated wavelength sensitivity of lithium niobate switches

A method is presented for calculating the wavelength sensitivity for electrooptic guided-wave stitches that work by mode interference, including directional-coupler and balanced-bridge switches. The method relies on a coupled-mode theory, using measured wavelength sensitivity of the coupling. Crosstalk is taken as the bandwidth-limiting property and is calculated by expanding in bandwidth. It is found that the wavelength sensitivity depends on the coupler gap, the amount of coupling, and the electrode configuration. Numerical examples show that switches with proper design can exhibit better than 25 dB of crosstalk with a 100-μm bandwidth. Modulators have a still wider bandwidth     

Self-consistent vector coupled-mode theory for tapered opticalwaveguides

A nonorthogonal coupled-mode theory for nonparallel waveguides is derived. An orthogonal coupled-mode theory is developed based on the exact local array modes. The relation between the two formulations is established. Closed-form solutions are obtained for the two-guide synchronous tapered coupler. The formalism obeys power conservation