A new coupled mode formulation for parallel dielectric waveguides is described. The results apply to any guided modes (TE, TM, or hybrid) in waveguides of arbitrary cross-section, dissimilar index, and nonidentical shape. Additional index perturbations not included within the waveguides are encompassed by the theory. Propagation constants and mode patterns for the coupled modes computed according to this theory are shown to agree very well with numerical solutions for the system modes when the latter can be determined. Moreover, the new results are more accurate than those obtained from prior coupled mode formulations. It is shown that even for Iossless guides the coupling coefficients from waveguide "b" to "a" and from "a" to "b," described by k ab and k ba respectively, are not related by their complex conjugates if the guides are not identical.

Coupled mode theory of parallel waveguides

Three classes of array modes of closely spaced antiguides are analyzed: coupled fundamental (element) modes, coupled first-order (element) modes, and modes adjacent to coupled fundamental modes. The behavior of coupled fundamental modes as a function of lateral index step is analyzed and explained from a ray-optics point of view. It is found that at resonance, for both coupled fundamental and first-order modes, the array-mode propagation constant is virtually identical to the propagation constant of the mode of a single, unperturbed antiguide. Several types of mode discrimination mechanisms are discussed. For devices with 3- mu m-wide antiguide cores and 1- mu m interelement spacing, intermodal discrimination values of 15-20 cm/sup -1/ can be achieved. Excellent agreement is found between experimental data and theoretical predictions based on the effective-index method. >

Phase-locked arrays of antiguides: model content and discrimination

Uniform linear arrays of antiguides have 100% optical transmission between elements when the interelement spacing is an integer number of leaky wave half‐wavelengths in the lateral direction. Resonant in‐phase‐mode and out‐of‐phase‐mode coupling occurs when the number of half‐wavelengths is odd and even, respectively. Such devices are called resonant optical waveguide (ROW) arrays. The discrimination between the resonant array mode and adjacent array modes reaches a maximum in close proximity to the resonance. An AlGaAs/GaAs ROW diode laser array operating close to resonance is demonstrated. Devices with virtually uniform near‐field intensity profiles operate in stable, diffraction‐limited in‐phase modes to drive levels in excess of three times threshold.

Resonant optical transmission and coupling in phase‐locked diode laser arrays of antiguides: The resonant optical waveguide array

The concepts, fabrication, and operating characteristics of monolithic two-dimensional, coherent AlGaAs laser arrays are presented. The arrays consist of 100 (10*10) active elements fabricated from a single-quantum-well graded-index separate-confinement heterostructure laser geometry. A surface relief grating is used for feedback and outcoupling. The elements of the array are index-guided ridge lasers with evanescent or Y coupling in the lateral direction and injection coupling longitudinally. The far field emanating from a 60- mu m*5-mm aperture, measures 0.01 degrees *1 degrees . These arrays emit more than 1 W peak power into a 2-AA wavelength interval. By adjusting the drive current to the electrically independent gain sections of these arrays, the angular position of the far-field beam can be steered. >

Two-dimensional coherent laser arrays using grating surface emission

Semiconductor diode lasers can be combined into monolithic phase-locked arrays that operate to continuous-wave (CW) powers in excess of 1 W and exhibit well-defined output beams to hundreds of mW. Applications of arrays include high-speed optical recording, high-speed printing, free-space communications, and efficient pumping of solid-state lasers. The authors review the current state of phase-locked array design with emphasis on the means for achieving fundamental mode operation. Models for understanding and predicting the behavior of phase-locked arrays are discussed, and the potential of various array structures to operate in a single, diffraction-limited output beam is evaluated.

Phase-locked arrays of semiconductor diode lasers

Experimental results of far-field patterns of semiconductor laser arrays with multiple contacts are reported. It is found that, by tailoring the distribution of the currents through the array elements, narrow single-lobe patterns—which are more useful in most applications—can be obtained from arrays that usually operate in a double-lobe mode. A diffraction-limited 1.8°-wide far-field pattern was obtained from a three-element array.

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Far-field distribution of semiconductor phase-locked arrays with multiple contacts

Supermode analysis of phase-locked arrays of semiconductor lasers: erratum

An integrated laser structure for paired stripe semiconductor lasers is provided with separate current control of each stripe laser. With optical coupling between the lasers, one of the lasers is operated below threshold and serves the longitudinal mode selection and tunability of the other laser, thereby to obtain a single longitudinal mode operation. Without coupling, the paired-laser structure operates as a source of two independent wavelengths.

Eli Kapon

Papers

Far-field distribution of semiconductor phase-locked arrays with multiple contacts

Supermode analysis of phase-locked arrays of semiconductor lasers: erratum

Paired, separately controlled, and coupled or uncoupled stripe geometry semiconductor lasers