The coupled-mode theory (CMT) for optical waveguides is reviewed, with emphasis on the analysis of coupled optical waveguides. A brief account of the recent development of the CMT for coupled optical waveguides is given. Issues raised in the debates of the 1980’s on the merits and shortcomings of the conventional as well as the improved coupled-mode formulations are discussed. The conventional coupled-mode formulations are set up in a simple, intuitive way. The rigorous CMT is established on the basis of a linear superposition of the modes for individual waveguides. The cross-power terms appear logically as a result of modal nonorthogonality. The cross power is necessary for the self-consistency of the CMT for dissimilar waveguides. The nonorthogonal CMT, though more complicated, yields more-accurate results than the conventional orthogonal CMT for most practical applications. It also leads to the prediction of cross talk in directional couplers. The conventional orthogonal CMT is, however, reliably accurate for describing the power coupling between two weakly coupled, nearly identical waveguides. For dissimilar waveguides, a self-consistent orthogonal CMT can be derived by a redefinition of the coupling coefficients, and it predicts the coupling length and therefore the power exchange between the waveguides accurately if the two waveguides are far apart. Three typical coupler configurations—the uniform, the grating-assisted, and the tapered—are examined in detail. The accuracy, scope of validity, limitations, and extensions of the coupled-mode formulations are discussed in conjunction with each configuration. To verify the arguments in the discussions, comparisons with the exact analytical solutions and the rigorous numerical simulations are made.

Coupled-mode theory for optical waveguides: an overview

An optical coupler, for coupling two optical waveguides (50, 60), and an optical switch based on the optical coupler. The indices of refraction of parallel sections of the two waveguides (50, 60) are reversibly perturbed periodically in space by imposing a mechanism (58, 68, 59, 69) to couple low order modes in the two waveguides via a high order mode common to the two waveguides. The waveguides are thus coupled with a beat length that may be five or more orders of magnitude shorter than it would be without the periodic perturbations.

Intermediate-state-assisted optical coupler

Solutions to problems involving the scattering and guiding of waves by multilayered grating configurations can be phrased in rigorous modal terms. We show that such a modal solution can be represented by electrical transmission-line networks, which are generalized forms of simpler conventional circuits. This approach brings considerable physical insight into the grating diffraction process and facilitates the derivation of the fields everywhere. In particular, the transmission-line representation can serve as a template for computational algorithms that systematically evaluate dispersion properties, radiation effects, wave coupling and other characteristics that are not readily obtained by other methods. Examples illustrating the application of the present approach are given for waves guided by grating configurations encountered in optoelectronic devices.

Modal transmission-line theory of multilayered grating structures

We report the first demonstration of broadly electrically tunable (215 A), narrow‐band (∼20 A full width at half maximum), wavelength selective, grating‐assisted coupling between vertically stacked buried rib InGaAsP/InP channel waveguides. This current injection tuned device is suitable for integration in a variety of photonic devices and integrated circuits including broadly tunable extended cavity lasers, amplifier/filter, and demultiplexer/detector circuits.

Broadly tunable InGaAsP/InP buried rib waveguide vertical coupler filter

A grating-assisted directional coupler is investigated using an improved coupled-mode formulation for multi-waveguide systems with longitudinal perturbation. This approach is capable of handling three-dimensional structures as well as a complex index of refraction and nonisotropic media. The case of two coupled channel waveguides is closely examined, and a numerical analysis is carried out for several cases of slab structures. >

Coupled mode formulation for directional couplers with longitudinal perturbation

The spectral properties of grating-assisted directional couplers are studied using an improved coupled mode formulation. Key parameters for the design of these structures, such as the grating period, the coupling length, and other structural parameters, are calculated. The frequency response, the filter bandwidth, and the tuning range are analyzed. The technique is used to examine a specific case of InGaAsP-InP tunable filters, and the results are compared to a prior experiment. >

Frequency response and tunability of grating-assisted directional couplers

A monolithic integration of a double barrier AlAs/GaAs resonant tunneling diode and a GaAs/AlGaAs quantum well laser is reported. Negative differential resistance and negative differential optical response are observed at room temperature. The device displays bistable electrical and optical characteristics which are voltage controlled. Operation as a two‐state optical memory is demonstrated.

Monolithic integration of a resonant tunneling diode and a quantum well semiconductor laser

Tunable, single longitudinal mode spectrum of a novel monolithic, laterally coupled semiconductor stripe laser has been demonstrated. A tuning range of 14.2 nm, which is the widest observed so far in a monolithic device, has been achieved.

Single‐mode very wide tunability in laterally coupled semiconductor lasers with electrically controlled reflectivities

Frequency selectivity of a novel type of multielement, multisection laterally coupled semiconductor laser array is studied using the round-trip method. It is found that such a structure should lead to a strong frequency selectivity owing to a periodic dependency of the threshold gain on the frequency. A gain-guided two-coupled-cavity device was fabricated. The experimental results show excellent agreement with the theoretical prediction.

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Giora Griffel

Papers

Coupled mode formulation for directional couplers with longitudinal perturbation

Frequency response and tunability of grating-assisted directional couplers

Monolithic integration of a resonant tunneling diode and a quantum well semiconductor laser

Single‐mode very wide tunability in laterally coupled semiconductor lasers with electrically controlled reflectivities

Frequency control using a complex effective reflectivity in laterally coupled semiconductor laser arrays.