Plane-wave-spectrum approach for calculations of radiation pattern of junction lasers
01 Feb 1986-Journal of The Optical Society of America A-optics Image Science and Vision (Optical Society of America)-Vol. 3, Iss: 2, pp 264-267
TL;DR: In this paper, an analytical expression for mode-conversion coefficients at a laser-air interface is derived using plane-wave decomposition of the modal fields and the radiation pattern is explicitly expressed as function of Fresnel reflection coefficients of the interface and the incident mode spectrum.
Abstract: An analytical expression for mode-conversion coefficients at a laser–air interface is derived using plane-wave decomposition of the modal fields. Both the mode-conversion coefficients and the radiation pattern are explicitly expressed as function of Fresnel reflection coefficients of the interface and the incident mode spectrum.
Citations
More filters
TL;DR: In this paper, the dispersion equation of a strip-slab waveguide is derived from the condition of self-consistency of rays, and Green's function for the structure is derived by treating the modes as the superpositions of plane waves.
Abstract: The application of the plane-wave-spectrum method to strip–slab waveguides is described. The dispersion equation of the structure is first evaluated from the condition of self-consistency of rays. By treating the modes as the superpositions of plane waves, Green’s function for the structure is subsequently derived.
2 citations
TL;DR: In this paper, an analysis of the strip dielectric waveguide is presented using a plane-wave-spectrum approach, where the modes in the guide are viewed as superpositions of plane waves undergoing multiple reflections at the walls of the guides.
Abstract: An analysis of the strip dielectric waveguide is presented using a plane-wave-spectrum approach. The modes in the guide are viewed as superpositions of plane waves undergoing multiple reflections at the walls of the guides. The modal fields are evaluated at the residues of the integrand, which is a function of the transverse wavenumbers of the plane waves in the dielectric medium of the guide.
2 citations
TL;DR: In this paper, the authors studied the modes of a uniaxially anisotropic linear guide by a plane-wave spectrum approach and determined Green's function for Eymn and Exmn modes of the guide.
Abstract: We present the studies of the modes of a uniaxially anisotropic linear guide by a plane-wave spectrum approach. Starting with an arbitrary optical axis, the axial phase constants of the modes are evaluated for special cases. We conclude with the determination of Green’s function for Eymn and Exmn modes of the guide.
1 citations
TL;DR: A method for the determination of Green's function of Integrated optical directional coupler, using plane wave spectrum is presented in this paper, which gives better physical insight of the mechanism of wave propagation within the guide.
Abstract: A method for the determination of Green’s function of Integrated optical directional coupler, using plane wave spectrum is presented. The suggested method is straight forward and gives better physical insight of the mechanism of wave propagation within the guide.
References
More filters
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 paper, a solution of the laser fields, both inside and outside the laser, is given in terms of the mode-conversion coefficients and an integral equation for the radiation pattern.
Abstract: A solution of the laser fields, both inside and outside the laser, is given in terms of the mode-conversion coefficients and an integral equation for the radiation pattern. It is shown how very accurate analytic solutions can be obtained by what, at first sight, appear to be extremely crude approximations. The reason is that mode conversion is taken implicitly into account by using a multiplier, whose exact form does not appear to be very critical, as a weighting function to average two different formulas for the function representing the radiation; and with the correct form for it, all the mode-conversion and reflection coefficients can be legitimately ignored. A plane-wave formula for this multiplier is a good first approximation, and a number of existing expressions occurring in the literature are obtained in this way. It is also shown rigorously that the results of an earlier obliquity-factor analysis apply. Further refinements are introduced to allow for higher order discrete modes, and good approximate analytic forms for the mode-reflection and conversion coefficients are obtained. A check with a rather extreme example shows excellent agreement with Ikegami's numerical computation for the dominant-mode reflection at the laser-air interface. The methods of this paper are applicable to general laser structures of cylindrical geometry with either continuous or discontinuous variations in refractive index. Very accurate numerical solutions should be obtainable after only one iteration of the integral equation, starting with the reflection-modified form of Hockham's formula as initiating function.
56 citations
TL;DR: In this article, the mode reflectivity of a narrow stripe-geometry double heterostructure (DH) was computed taking into account lateral (parallel to the junction) confinement in addition to transverse confinement.
Abstract: The mode reflectivity of narrow stripe-geometry double heterostructure (DH) lasers is computed taking into account lateral (parallel to the junction) confinement in addition to transverse (normal to the junction) confinement. For most practical stripe width devices, the addition of lateral confinement insignificantly alters the reflectivity of the lowest order mode; calculations based upon transverse confinement alone (broad-area lasers) are analytically and numerically shown to provide an adequate description of the mirror reflectivities of most narrow stripe-geometry lasers.
18 citations
TL;DR: In this paper, the authors derived expressions for the reflectivity and conversion coefficients of modes reflected by the end facet of a laser with waveguiding both in the transverse and the lateral directions.
Abstract: Expressions are derived for the reflectivity and conversion coefficients of modes reflected by the end facet of a laser with waveguiding both in the transverse and the lateral directions. The modes are obtained by the effective-index method. The mathematical treatment takes into account the vectorial nature of the fields inside as well as outside the laser. It is assumed that Ex = 0, but all other field components do not vanish (TE-like modes). Expressions for the far-field pattern are also given, taking into account the reflectivity and mode conversion at the laser facet.
15 citations
TL;DR: In this paper, the two-dimensional reflectivity of transverse-magnetic-like modes (Hx = 0) is derived by means of the effective-index approximation, and mathematical expressions for the reflectivity and conversion coefficients are similar in form to those of Transverse-electric like modes, although the various functions and parameters in the equations are defined somewhat differently.
Abstract: Two-dimensional reflectivity of transverse-magnetic-like modes (Hx = 0) is considered. The modes are derived by means of the effective-index approximation. Mathematical expressions for the reflectivity and conversion coefficients are similar in form to those of transverse-electric-like modes, although the various functions and parameters in the equations are defined somewhat differently.
5 citations