Showing papers on "Equilibrium mode distribution published in 1974"

Mode conversion in planar dielectric separating waveguides

Abstract: Separating optical waveguides are expected to become important in integrated optics. They occur whenever a branching waveguide is used (Fig. 1a) or whenever two parallel waveguides in close proximity are separated (Fig. 1b). These situations will arise in virtually all applications of electrooptic switches and waveguide couplers that depend on evanescent coupling. Using quasi-normal modes and a step transition model we have studied theoretically the mode conversion behavior of separating planar dielectric waveguides as a function of taper slope and mode synchronism, which is adjusted by branch asymmetry. When the taper slope is large in a near symmetric structure, considerable mode conversion will occur and the structure will act as a power divider (Fig. 2b). Incident power concentrated in the upper and lower parts of the structure will end up in the upper and lower arms of the branch, respectively. This behavior is usually required for conventional evanescent couplers. However, in a more asymmetric structure with smaller taper slope, mode conversion is negligible and the structure will act as a mode splitter (Fig. 2a). Mode power is then transferred to one arm of the branch or the other. The transition boundary between a power divider and mode splitter (Fig. 3) is conveniently described approximately by: equation Here Δβ is the difference in mode propagation constant for large waveguide separation, θ is the taper slope, and γ is the decay constant of the field in the separating region. This result will allow quantitative design of mode splitters or power dividers, as desired, and should aid in the design of separating waveguides with minimum radiation losses.

Theory of the single-material fiber

Abstract: The term “single-material fiber” describes a dielectric optical waveguide made of only one type of glass. The theory of this waveguide is simplified by placing the structure between two perfectly conducting planes that have very little influence on the properties of the low-order modes. The field distribution and propagation constant of the lowest-order mode are investigated and compared to an approximate theory.

A technique for the study of mode cut-offs in multimode optical fibres

Abstract: We describe a technique of using a variable wavelength source to study mode cut-offs up to aV value of 20 for the optical fibre by means of the radiated (scattered) power leaving the fibre. This allows the identification of individual modes in a fibre carrying up to 80 or 100 modes in all and provides a non-destructive method for the study of the length and bend dependence of the energy carried by the highest order modes.

Analysis of the approach to the convection instability point

Abstract: A spectral analysis is presented of the fluctuations in a horizontal fluid layer subject to a downward directed temperature gradient, which, for a critical value, drives the system in a convective instability state. It is found that the external force resulting from the combination of the temperature gradient and the gravitation force gives rise to a coupling between the heat diffusion mode and a shear mode. As a result of this mode coupling the damping constant of the heat diffusion mode goes to zero when the temperature gradient increases towards its critical value, i.e. the heat diffusion mode behaves like a "soft mode". The implications of the mode coupling and of the ensuing softening of the heat diffusion mode on the light scattering spectrum are discussed.

A Simplified Mode Conversion Program for VLF Propagation in the Earth-Ionosphere Waveguide.

Abstract: : This report presents a variation of an earlier mode conversion program for numerically determining mode conversion coefficients and mode sums for a waveguide which is inhomogeneous along the direction of propagation (invariance normal to the transmitter receiver line is assumed and reflections due to the horizontal inhomogeneity are neglected). Although somewhat more approximate than the earlier program the present version has the advantage of not requiring a full wave fields program for the height gain calculations and can be implemented with about the same ease as a WKB program. It has one advantage over the WKB formulation and that is that mode numbering along the horizontal inhomogeneity is immaterial. The mode conversion program will yield mode conversion coefficients and a mode sum plot for ground based vertical dipole excitation of the vertical electric field at the ground as a function of distance from the transmitter. Since the mode conversion coefficients are independent of transmitter terminator distance, allowance has also been made for incrementing the latter distance and plotting mode sums for the incremented distances.