Showing papers on "Coupled mode theory published in 1993"
TL;DR: It is shown that discrete self-focusing may be realized in an array of coupled defocusing nonlinear waveguides and stable beam propagation corresponds to the case in which the electric field is equivalently distributed between two neighboring waveguide with relative phase difference π.
Abstract: It is shown that discrete self-focusing may be realized in an array of coupled defocusing nonlinear waveguides. Strongly localized self-focusing patterns are found, and it is pointed out that stable beam propagation corresponds to the case in which the electric field is equivalently distributed between two neighboring waveguides with relative phase difference π.
132 citations
01 Jun 1993
TL;DR: In this article, the authors developed a direct correspondence between a whispering gallery mode of a dielectric cylinder and a mode of an equivalent waveguide ring resonator, and the evanescent wave coupling characteristics of such modes can be simply modelled.
Abstract: By developing a direct correspondence between a given whispering gallery mode of a dielectric cylinder and a mode of an equivalent waveguide ring resonator, the evanescent wave coupling characteristics of such modes can be simply modelled. This also allows the conditions for resonant excitation of a single whispering gallery mode to be determined. The model needs a coupled mode theory which accurately describes the coupling between a straight waveguide and a curved waveguide to be developed. This theory is checked against BPM results.
130 citations
TL;DR: In this article, the modal properties of periodically segmented waveguides (PSWs) were analyzed by using the beam-propagation method and coupled-mode theory, and the results can be applied to the design of waveguide devices such as two-dimensional mode tapers and frequency selective couplers.
Abstract: Modal properties of periodically segmented waveguides (PSWs) are analyzed by using the beam-propagation method and coupled-mode theory. The modal effective indices in a PSW are shown to be equal to those of a continuous waveguide with an averaged Delta n. As a result, guided modes spread out, particularly those that are not strongly guided. The radiation loss is shown to oscillate with most of the waveguide parameters. In practical terms, this loss can be made negligible even for long periods. The results can be applied to the design of waveguide devices such as two-dimensional mode tapers and frequency-selective couplers. >
98 citations
TL;DR: In this paper, a coupled mode formalism is proposed to solve the nonlinear differential equations in the mean field approximation for nearly degenerate four-wave mixing in distributed feedback semiconductor lasers above threshold in investigated theoretically and experimentally.
Abstract: Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers above threshold in investigated theoretically and experimentally. The experimental results reveal an almost symmetric amplification of probe and conjugate fields versus frequency with respect to zero pump-probe detuning, in contrast with observations in traveling wave amplifiers. The result of the theory, based on the coupled mode formalism, is a set of nonlinear differential equations which are solved in the mean field approximation. The theory is shown to match well with the experimental results when the effect of the nonlinear gain compression is taken into account. >
54 citations
TL;DR: In this article, the space-time dynamical behavior of multistripe index-guided semiconductor laser arrays is studied by using an extension of the usual phenomenological laser model to include transverse diffraction of the counterpropagating optical fields and transverse diffusion of the excited carriers.
Abstract: The space–time dynamical behavior of multistripe index-guided semiconductor laser arrays is studied by using an extension of the usual phenomenological laser model to include transverse diffraction of the counterpropagating optical fields and transverse diffusion of the excited carriers. Our results confirm that evanescently coupled multistripe lasers are a fascinating manifestation of spatiotemporal complexity in spatially extended nonlinear systems. Stabilization of the laser output can be achieved by injection locking the array with a weak external injected signal, and we show that the stability of the externally driven array depends on the transverse profile of the injected signal. A numerical algorithm is presented that takes advantage of high-performance parallel computing architectures to solve the coupled partial differential equations describing the light–matter interaction in the laser structure. Both the model and the numerical algorithm are sufficiently flexible and modular to support arbitrary laser geometries and to allow for inclusion of important many-body semiconductor effects in future studies.
50 citations
TL;DR: It is found that the development of the phase-locked state is as fast as the onset of lasing without an evolutionary process and all predictions of optical instability in laser arrays need to be reexamined.
Abstract: The steady-state and transient dynamics of phase locking in a two-element Nd:YAG laser array have been studied. By creating two evanescent-coupled lasers in a Nd:YAG etalon using diode end pumping, the coupling strength between the laser elements in the array can be continuously varied by adjusting the positions of the pumping beams. This allows the observation of the phase-locking process over a wide range of coupling strength. We have found that the development of the phase-locked state is as fast as the onset of lasing without an evolutionary process. The instantaneous locking is also independent of the coupling strength once the coupling is strong enough to ensure phase locking. These phenomena disagree with the predictions based on the time-dependent coupled-mode theory of laser-array dynamics. Our experimental study and theoretical analysis have led to the conclusion that all predictions of optical instability in laser arrays need to be reexamined.
31 citations
TL;DR: In this article, a generalized coupled-mode model for multistripe index-guided laser arrays is developed that includes explicitly the influence of carrier-induced antiguiding, gain guiding, and carrier diffusion in the gain stripe.
Abstract: We develop a generalized coupled-mode model for multistripe index-guided laser arrays that includes explicitly the influence of carrier-induced antiguiding, gain guiding, and carrier diffusion in the gain stripe. As an illustration of an application of the model, stability criteria for two-element laser arrays are derived that show that the phase-locked solution is intrinsically unstable. We find that the phase-locked solution can be stabilized at a low external injection-locking power at the suitably chosen injection-locking frequency. We have tested our model in the large carrier-diffusion case and still find good qualitative agreement between the coupled-mode model and a full coupled partial differential equation model.
28 citations
TL;DR: In this article, an improved coupled-mode formulation based on the ideal modes of the coupled waveguides (ideal composite modes) is presented, which yields a more accurate grating period and coupling lengths.
Abstract: An improved coupled-mode formulation based on the ideal modes of the coupled waveguides (ideal composite modes) is presented. In comparison with the formulation based on the ideal modes of the individual waveguides (ideal waveguide modes), the formulation in terms of composite modes is more rigorous and yields a more accurate grating period and coupling lengths. In addition, the radiation loss due to input and output junctions can in the composite-mode formulation. A new to the coupled-mode equations is derived in which all the spatial harmonics generated by the periodic grating are taken into account. The power exchange between the waveguides is examined by considering the input and the output conditions. The phase-matching conditions and the coupling lengths are calculated and compared with the analysis in terms of the waveguide modes. The grating period predicted by the waveguide-mode formulation agrees very well with that by the composite-mode formulation; however, dramatically different coupling lengths are predicted by the two formulations. >
26 citations
TL;DR: In this paper, the coupled-mode equations describing the transduction characteristics of the inter-digital electrode transducer (IDT) are derived directly by the perturbation theory, and the parameters for the coupledmode equations are presented for quartz, LiTaO3 and LiNbO3 substrates.
Abstract: The coupled-mode theory is extremely useful for analysis of such periodic structures as grating reflector, resonator, and unidirectional transducer making use of electrode reflection as important constituent elements for the SAW devices. Here, the coupled-mode equations describing the transduction characteristics of the inter-digital electrode transducer (IDT) are derived directly by the perturbation theory. In addition, the parameters for the coupled-mode equations are presented for quartz, LiTaO3 and LiNbO3 substrates.
Next, based on the coupled-mode equations, the relationship among the quantities of the electrical port and two acoustic ports of the IDT is derived. The entire periodic structure was represented by a simple distributed equivalent circuit. The equivalent circuit analysis method is described for the analysis of the device characteristics. To show the usefulness of the present method, a backward-wave type trapped-energy SAW resonator and the resonator coupled filter are analyzed.
22 citations
TL;DR: An improved coupled-mode model to describe the dynamics of weakly index-guided semiconductor laser arrays is presented, derived from a partial differential equation model that includes the effects of carrier diffusion and gain guiding.
Abstract: We present an improved coupled-mode model to describe the dynamics of weakly index-guided semiconductor laser arrays. The model is derived from a partial differential equation model that includes the effects of carrier diffusion and gain guiding. Results from the two models are compared, and good qualitative and quantitative agreement is obtained.
TL;DR: In this paper, a model for the spatiotemporal dynamics of gain-guided semiconductor laser arrays is presented, which goes beyond coupled mode theory and treats the array as a single entity.
Abstract: A model is presented for the spatiotemporal dynamics of gain‐guided semiconductor laser arrays. The model goes beyond coupled mode theory and treats the array as a single entity. Numerical simulations of twin‐stripe gain‐guided arrays yield stable or pulsing outputs, depending on array parameters.
TL;DR: Polarization dependence of grating-assisted waveguide Bragg reflectors is studied theoretically by use of a vectorial coupled-mode theory based on the ideal mode expansion and a criterion for choosing ideal waveguides is proposed.
Abstract: Polarization dependence of grating-assisted waveguide Bragg reflectors is studied theoretically by use of a vectorial coupled-mode theory based on the ideal mode expansion. A criterion for choosing ideal waveguides is proposed. Experimental results obtained from an ion-exchanged waveguide with an etched grating agree well with the theory.
TL;DR: In this article, a uniform, untapered, intermediate coupler structure which consists of a multimode waveguide is proposed, and the basic design rules for this coupler are worked out using coupledmode theory.
Abstract: Efficient coupling of light from a semiconductor waveguide to an optical fiber is difficult to achieve due to the inherent differences in the spot sizes. The problem is particularly severe in the vertical dimension. The use of a uniform, untapered, intermediate coupler structure which consists of a multimode waveguide is proposed. This structure has potential for integrating with the semiconductor waveguide. The basic design rules for this coupler are worked out using coupled-mode theory, and the detailed designs are based on direct calculation of the mode profiles in the coupler. A range of realistic examples is examined, and it is shown that the butt coupling efficiency from a typical semiconductor laser to an optical fiber can be improved by up to 5 dB. The dependence of performance on fabrication tolerances is also studied. >
TL;DR: In this article, the waveguides induced by interacting solitons (both bright and dark) are examined and expressions for the soliton separation throughout the interaction are obtained. And linear coupler theory is applied to these new expressions to calculate the behavior of small signal beams guided by one of the Solitons before the collision.
TL;DR: In this article, coupled-mode analysis of Cerenkov-radiation-type second-harmonic generation, using channel and fiber waveguides, is presented from the viewpoint of device design.
Abstract: Coupled-mode analysis of Cerenkov-radiation-type second-harmonic generation, using channel and fiber waveguides, is presented from the viewpoint of device design. Nonlinear coupled-mode equations generally applicable for various waveguide configurations are derived and solved by considering the effects of pump-power depletion, waveguide loss, and effects of nonlinear gratings. Analytical expressions for the conversion efficiency as well as the near- and far-field radiation patterns are given, and the physical implications are discussed. The approximate results calculated for typical device configurations are summarized in graphic form, with normalized parameters. Guidelines for optimum design are given. >
TL;DR: A generalized transfer matrix method to describe one-dimensional wave propagation in arbitrary linear lossless dielectrica is developed in this article, where coupled mode theory is derived as an approximation for weak periodic structures.
TL;DR: A theoretical formulation of coherent optical tunneling and the subsequent exchange of electromagnetic energy between two Mie-sized microspheres is presented and a useful analytical expression for the self- and mutual-coupling coefficients that are involved in the time-evolved coupled-mode equations is derived under a weakly coupling approximation.
Abstract: A theoretical formulation of coherent optical tunneling and the subsequent exchange of electromagnetic energy between two Mie-sized microspheres is presented. The coupled-mode theory of Debye potentials is used. A useful analytical expression for the self- and mutual-coupling coefficients that are involved in the time-evolved coupled-mode equations is derived under a weakly coupling approximation. Sample numerical results are shown for coupling between identical spheres.
TL;DR: The conventional and improved coupled-mode theories for the evanescent coupling of parallel dielectric waveguides are reexamined with a phenomenological perturbation analysis and a defect in the improved theory in the strong-coupling regime is brought out.
Abstract: The conventional and improved coupled-mode theories for the evanescent coupling of parallel dielectric waveguides are reexamined with a phenomenological perturbation analysis. A defect in the improved theory in the strong-coupling regime is brought out in a general manner.
01 Oct 1993
TL;DR: In this article, the differences between two distinct formulations of the coupled-mode method are analysed and justified, the difference, the mathematical basis of which is the different ways used to calculate the axial components of the electromagnetic field, is interpreted in terms of the continuity of the functions that affect the calculation of these components.
Abstract: In the paper, the differences between two distinct formulations of the coupled-mode method are analysed and justified. The difference, the mathematical basis of which is the different ways used to calculate the axial components of the electromagnetic field, is interpreted in terms of the continuity of the functions that affect the calculation of these components. The original formulation of the coupled-modes method is shown to converge in a more efficient way than the Ogusu formulation, although it is less efficient from a numerical viewpoint. Results of the propagation constant in isotropic dielectric waveguides are presented which confirm the better convergence of the original formulation. Applying this formulation in conjunction with the modal matching method allows an improvement in the accuracy of the analysis of dielectric discontinuities between materials of high permittivity. Then, this formulation is useful for designing between materials of high permittivity. Then, this formulation is useful for designing isotropic dielectric structures as mode launchers or filters, as well as nonreciprocal elements constructed with ferrites.
TL;DR: In this article, a coupled mode theory is extended to give a solution that exactly satisfies the boundary condition on a range-varying rigid basement, achieved by transforming the coordinate system so that at each range the basement coincides with a coordinate surface, and the partial separation of variables is construed with respect to the coordinate that is normal to that surface.
Abstract: Previous coupled mode approaches to acoustic propagation in ocean waveguides either (1) apply strictly to the case where interfaces other than the (free) ocean surface are range‐independent, or else (2) they satisfy the boundary conditions at such interfaces approximately. In this paper coupled mode theory is extended to give a solution that exactly satisfies the boundary condition on a range‐varying rigid basement. This is achieved by transforming the coordinate system so that at each range the basement coincides with a coordinate surface, and the partial separation of variables is construed with respect to the coordinate that is normal to that surface. Related work by other researchers is discussed, and the numerical implementation of the theory is described. Results for basements exhibiting both upsloping and downsloping regions are presented, and the exchange of radiated power between the modes is investigated for these cases.
TL;DR: In this paper, the second harmonic generation in the Cerenkov configuration in planar waveguides in LiNbO3 has been analyzed using coupled mode theory, taking into account the propagation loss in the waveguide, which shows an exponential behaviour with waveguide length, in contrast to a linear relation obtained by neglecting pump depletion.
Abstract: Second harmonic generation (SHG) in the Cerenkov configuration in planar waveguides in LiNbO3 has been analysed using coupled mode theory. Taking into account the propagation loss in the waveguide, we have derived an expression for the SHG efficiency which shows an exponential behaviour with waveguide length, in contrast to a linear relation obtained by neglecting pump depletion. We have also presented results of measurements on waveguide-length dependence of second harmonic power in proton-exchange LiNbO3 waveguides in the Cerenkov configuration which are consistent with the theory.
TL;DR: In this paper, a brief analysis of recent experimental data reported for radiation-induced responses in directional coupler waveguides is presented, and the experimental data are compared with the coupled mode theory for the case of non-synchronous coupling.
Abstract: A brief analysis of recent experimental data reported for radiation-induced responses in directional coupler waveguides is presented. The data are compared with the coupled mode theory for the case of non-synchronous coupling. This analysis is important in understanding undesirable radiation-induced responses in guided wave devices such as cross talk and optical signal attenuation. The radiation-induced responses are examined and shown to be attributal to the alteration of the waveguide propagation and coupling constants. The magnitude of the refractive index change experienced by a directional coupler, which is exposed to a transient electron exposure, is determined from electro-optic theory and found to be consistent with theoretical predictions.
TL;DR: In this article, the authors show that the results obtained in a simplified approximation are as accurate as those obtained by a more complex algebra retaining all terms, and that the apparent accuracy of the conventional coupledmode results is due to the neglect of two significant terms which affect the result in opposite ways.
Abstract: Various approximations involved in scalar coupledmode theory for parallel guides based on the basis of linear combination of fields of individual wave guides have been investigated in detail. First, the propagation constants of supermodes have been obtained by direct substitution of trial field in wave equation retaining all terms; then effect of neglecting the \"small\" terms to obtain the approximate forms has been studied. We show that the results obtained in a simplified approximation are as accurate as those obtained by a more complex algebra retaining all terms. Further, the accuracy at each step of approximation is obtained and the apparent accuracy of the \"conventional\" coupledmode results is shown to be due to the neglect of two significant terms which affect the result in opposite ways.
TL;DR: In this article, two coupled-mode theories based on individual waveguide modes and compound system modes, respectively, are reviewed with proper modification and new comments, and the relation between these two theories is built and it is found that one theory is actually an efficient approximation of the other.
Abstract: Two coupled-mode theories based on individual waveguide modes and compound system modes, respectively, are briefly reviewed with proper modification and new comments. The relation between these two theories is built and it is found that one theory is actually an efficient approximation of the other. Also, the reason why the results obtained with the first more accurate than those obtained with the second is found. The constraint on both approaches is shown. >
11 Oct 1993
TL;DR: In this article, a quasi-optical mode converter was designed to transform the TE/sub 22,6/ cylindrical waveguide mode at 110 GHz to a Gaussian beam in free space.
Abstract: A quasi-optical mode converter has been designed to transform the TE/sub 22,6/ cylindrical waveguide mode at 110 GHz to a Gaussian beam in free space. The converter consists of an irregular cylindrical waveguide section followed by a step-cut launching aperture and several focussing reflectors in an open mirror transmission line. The irregular waveguide section, which was designed with coupled mode theory, is used to bunch the radiation into Gaussian bundles prior to the launch. The reflectors that follow were designed with Gaussian optics and diffraction theory. A rigorous diffraction theory has been developed to analyse the converter system. The converter was built and a preliminary test on a MW power level pulsed gyrotron has been completed. A symmetric Gaussian beam output with the predicted beam waist of 0.9 cm was observed. Experimental results are compared to diffraction theory simulations and very good agreement is obtained.
02 Aug 1993
TL;DR: In this paper, a coupled mode theory for electron wave directional couplers is presented, which includes the dephasing effect on electrons due to temporally random phase destroying collisions.
Abstract: In this paper, a coupled mode theory for electron wave directional couplers is presented. The theory includes the dephasing effect on electrons due to temporally random phase destroying collisions. Using this scheme, the switching characteristics of the electron wave directional coupler is studied. >
TL;DR: In this paper, a coupledmode theory for parallel electron waveguide structures is developed and presented, which takes the nonorthogonality between the modes belonging to different electron waveguides, which is neglected in the first-order theory, into consideration and reflects this fact by including the modal overlap integral terms in the resultant coupledmode equations.
Abstract: A coupled‐mode theory for parallel electron waveguide structures is developed and presented. This theory takes the nonorthogonality between the modes belonging to different electron waveguides, which is neglected in the first‐order theory, into consideration and reflects this fact by including the modal overlap integral terms in the resultant coupled‐mode equations. Various numerical examples are presented, using this improved theory and the first‐order theory, and are compared with those of the exact calculations. It is shown that the improved theory can give more accurate results than the conventional first‐order theory. Therefore, it is very useful for analyzing the quantum field‐effect directional couplers and similar quantum interference devices.
TL;DR: In this article, the accuracy and scope of validity of different coupled-mode formulations for a tapered optical waveguide coupler are assessed by comparison with the beam propagation method (BPM), and it is demonstrated that the coupledmode theory based on local modes is valid only for small tilt angles, whereas an improved formulation that takes into account the wavefront-tilt effect yields highly accurate results for relatively large tilt angles.
Abstract: The accuracy and the scope of validity of different coupled-mode formulations for a tapered optical waveguide coupler are assessed by comparison with the beam propagation method (BPM). It is demonstrated that the coupled-mode theory (CMT) based on local modes is valid only for small tilt angles, whereas an improved formulation that takes into account the wavefront-tilt effect yields highly accurate results for relatively large tilt angles. The radiation loss at the input and the output junctions can also be estimated by a simple mode-matching method combined with the improved CMT. The coherent coupling between two junctions,which is neglected in the coupled-mode formulations, is observed in the BPM simulations. >
TL;DR: In this article, an improved coupled mode theory of the nonlinear directional coupler based on the supermodes of the coupler was proposed and the predicted value of the switching intensity agreed well with recent experimental data.
Abstract: We present an improved coupled mode theory of the nonlinear directional coupler based on the supermodes of the coupler and show that the predicted value of the switching intensity agrees well with recent experimental data. The theory relates to couplers constructed from semi-conductor materials and makes use of the plasma theory to express the dependence of the dielectric function on the field intensity. The analysis accounts for both the time dependence of the incident laser pulse and the spacial variation of the laser field in the direction transverse to the propagation direction.