A new variational method of incorporating loss in the analysis of coupled multiple-quantum well three-dimensional waveguides
TL;DR: In this paper, a simple method of calculating the imaginary part of the propagation constant in a lossy waveguide that closely follows the effective index method of finding the real propagation constant of a rectangular dielectric guide was developed.
Abstract: We have developed a simple method of calculating the imaginary part of the propagation constant in a lossy waveguide that closely follows the effective-index method of finding the real propagation constant of a rectangular dielectric guide. The method gives values much in agreement with the exact values obtained by the circular-harmonics method. The method has been used in the improved coupled-mode analysis of coupled-multiple-quantum-well waveguides developed by Tsang and Chuang. Three different configurations of coupled waveguides have been considered: slab, buried-channel, and strip-loaded waveguide directional couplers, where excitonic electrorefraction in multiquantum wells has been utilized to accomplish the switching. The output power-electric field curves calculated by using the above method agree closely in all three cases with similar curves obtained by using a complex propagation constant calculated by a numerical two-dimensional root-searching technique. The present method simplifies the design and optimization of coupled-waveguide devices and its application is illustrated in the case of multiple-quantum-well directional couplers. >
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TL;DR: In this article, a correction d'erreur dans light wave technologie, vol. 6, pp. 1051-1057, 1988, is presented.
Abstract: Correction d'erreur dans Light wave Technologie, vol. 6, pp. 1051-1057, 1988. Correction d'erreur dans light wave technologie, vol. 6, pp. 1058-1068, 1988
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TL;DR: Detailed calculations of the shift of exciton peaks are presented including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations ofexciton binding energy in a field.
Abstract: We report experiments and theory on the effects of electric fields on the optical absorption near the band edge in GaAs/AlGaAs quantum-well structures. We find distinct physical effects for fields parallel and perpendicular to the quantum-well layers. In both cases, we observe large changes in the absorption near the exciton peaks. In the parallel-field case, the excitons broaden with field, disappearing at fields \ensuremath{\sim}${10}^{4}$ V/cm; this behavior is in qualitative agreement with previous theory and in order-of-magnitude agreement with direct theoretical calculations of field ionization rates reported in this paper. This behavior is also qualitatively similar to that seen with three-dimensional semiconductors. For the perpendicular-field case, we see shifts of the exciton peaks to lower energies by up to 2.5 times the zero-field binding energy with the excitons remaining resolved at up to \ensuremath{\sim}${10}^{5}$ V/cm: This behavior is qualitatively different from that of bulk semiconductors and is explained through a mechanism previously briefly described by us [D. A. B. Miller et al., Phys. Rev. Lett. 53, 2173 (1984)] called the quantum-confined Stark effect. In this mechanism the quantum confinement of carriers inhibits the exciton field ionization. To support this mechanism we present detailed calculations of the shift of exciton peaks including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations of exciton binding energy in a field. We also calculate the tunneling lifetimes of particles in the wells to check the inhibition of field ionization. The calculations are performed using both the 85:15 split of band-gap discontinuity between conduction and valence bands and the recently proposed 57:43 split. Although the detailed calculations differ in the two cases, the overall shift of the exciton peaks is not very sensitive to split ratio. We find excellent agreement with experiment with no fitted parameters.
1,731 citations
TL;DR: In this paper, the authors studied the transmission properties of a guide consisting of a dielectric rod with rectangular cross section, surrounded by several dielectrics of smaller refractive indices.
Abstract: We study the transmission properties of a guide consisting of a dielectric rod with rectangular cross section, surrounded by several dielectrics of smaller refractive indices. This guide is suitable for integrated optical circuitry because of its size, single-mode operation, mechanical stability, simplicity, and precise construction. After making some simplifying assumptions, we solve Maxwell's equations in closed form and find, that, because of total internal reflection, the guide supports two types of hybrid modes which are essentially of the TEM kind polarized at right angles. Their attenuations are comparable to that of a plane wave traveling in the material of which the rod is made. If the refractive indexes are chosen properly, the guide can support only the fundamental modes of each family with any aspect ratio of the guide cross section. By adding thin lossy layers, the guide presents higher loss to one of those modes. As an alternative, the guide can be made to support only one of the modes if part of the surrounding dielectrics is made a low impedance medium. Finally, we determine the coupling between parallel guiding rods of slightly different sizes and dielectrics; at wavelengths around one micron, 3-dB directional couplers, a few hundred microns long, can be achieved with separations of the guides about the same as their widths (a few microns).
1,620 citations
TL;DR: In this article, a computer analysis of the propagating modes of a rectangular dielectric waveguide is presented, based on an expansion of the electromagnetic field in terms of a series of circular harmonics multiplied by trigonometric functions.
Abstract: This paper describes a computer analysis of the propagating modes of a rectangular dielectric waveguide. The analysis is based on an expansion of the electromagnetic field in terms of a series of circular harmonics, that is, Bessel and modified Bessel functions multiplied by trigonometric functions. The electric and magnetic fields inside the waveguide core are matched to those outside the core at appropriate points on the boundary to yield equations which are then solved on a computer for the propagation constants and field configurations of the various modes. The paper presents the results of the computations in the form of curves of the propagation constants and as computer generated mode patterns. The propagation curves are presented in a form which makes them refractive-index independent as long as the difference of the index of the core and the surrounding medium is small, the case which applies to integrated optics. In addition to those for small index difference, it also gives results for larger index differences such as might be encountered for microwave applications.
549 citations
TL;DR: In this paper, an improved coupled-mode equation for parallel dielectric waveguides was derived by using a newly found relationship that connects the propagation constants of the individual guides to the coupling coefficients via an overlap integral that measures the guides' proximity.
Abstract: An improved version of coupled-mode equations for parallel dielectric waveguides has been derived by using a newly found relationship that connects the propagation constants of the individual guides to the coupling coefficients via an overlap integral that measures the guides' proximity. The four parameters of these new coupled equations are simple functions of essentially one single quantity: the asynchronism of the individual guides properly normalized.
254 citations
TL;DR: In this article, a simple matrix method for obtaining propagation characteristics, including losses for various modes of an arbitrarily graded planar waveguide structure which may have media of complex refractive indices, is presented.
Abstract: We present here a simple matrix method for obtaining propagation characteristics, including losses for various modes of an arbitrarily graded planar waveguide structure which may have media of complex refractive indices. We show the applicability of the method for obtaining leakage losses and absorption losses, as well as for calculating beat length in directional couplers. The method involves straightforward 2 × 2 matrix multiplications, and does not require the solutions of any transcendental or differential equations.
244 citations