We report on the enhanced light output of GaN-based flip-chip light-emitting diodes (LEDs) fabricated with SiO2/TiO2 distributed Bragg reflector (DBR) on mesa sidewall. At the wavelength of 400 nm, five pairs of SiO2/TiO2 DBR coats on the GaN layer showed a normal-incidence reflectivity as high as 99.1%, along with an excellent angle-dependent reflectivity. As compared to the reference LED, the LED fabricated with the DBR-coated mesa sidewall showed an increased output power by a factor of 1.32 and 1.12 before and after lamp packaging, respectively. This could be attributed to an efficient reflection of the laterally guided mode at the highly reflective mesa sidewall, enhancing the subsequent extraction of light through the sapphire substrate.

The averaged-Lagrangian method is applied to wave-wave interactions in an infinite, homogeneous, collisionless, warm magnetoplasma. The amplitudes of the waves are assumed to vary slowly in time and space, due to coupling between them. Euler-Lagrange equations are obtained from the contributions to the averaged microscopic Lagrangian second and third order in perturbation, by variation with respect to the wave amplitudes. These are the coupled-mode equations. The phase variation yields the action transfer equation. As applications of the method, coupled-mode equations are derived in explicit forms for all possible interactions among waves propagating nearly parallel, and among those propagating exactly perpendicular, to the static magnetic field. Some of the coupling coefficients are new. Where comparisons with previous iterative analyses are possible, the advantages of the method are discussed. INTRODUCTIONThe linear theory developed in Part 1 of this three-part paper assumes that an arbitrary perturbation can be expressed as a superposition of non-iteracting eigenmodes. A characteristic result of nonlinearity is the occurrence of coupling among these modes. If the coupling is weak, then arbitrary perturbations may still be expressed approximately as a superposition of eigenmodes, but whose amplitudes are now assumed to vary slowly in time and space. By 'slowly' we mean that the scale of the variation due to the wave-wave interaction is much longer in time and space than the period and wavelength. We shall assume that this scale •s comparable to the ratio of the amplitude of a perturbation to that of the zero-order quantity, and denote it by a small parameter E. We shall also assume that interaction occurs coherently, i.e., at this point we shall not treat interaction in the random phase approximation. We shall consider all possible types of three-wave interactions in the infinite, collisionless, warm magnetoplasma, with an immobile ion background, considered in Part 1. The procedure to be followed is similar to that used in the analysis of nonlinear wave interaction in a cold plasma [Dougherty, 1970;Dysthe, 1974]. The averaged-Lagrangian is first obtained in section 2 for waves propagating at an oblique angle to the static magnetic field. It was demonstrated in Part Copyright (•) 1977 by the American Geophysical Union. 1, section 3, that action is conserved in the linear theory. When nonlinear interaction occurs, action is exchanged among waves due to the wave coupling. The action-transfer equations, and the coupled-mode equations, are derived in section 3. In section 4, these equations are specialized to the case of waves propagating nearly parallel to the static magnetic field. In section 5, interactions among longitudinal and ordinary cyclotron harmonic waves propagating perpendicular to the static magnetic field are considered. (Coupled-mode equations for these cases are presented in explicit forms suitable for computation in appendix A.) A comment on general solutions to the coupled mode equations is made ...

The purpose of this study is to compare predictions of the backscatter spectrum, including effects of ionospheric inhomogeneity, with experimental observations of incoherent backscatter from an artificially heated region. Our calculations show that the strongest backscatter echo received is not from the reflection level, but from a region some distance below (about 900 m for an experiment carried out at Arecibo).By taking the standing wave pattern of the pump into account properly, the present theory explains certain asymmetrical features of the upshifted and down-shifted plasma lines in the backscatter spectrum, and the several satellite peaks typically accompanying them.

The averaged-Lagrangian method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic Lagrangian treated in papers 1-3 is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfv6n wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic Lagrangian density. (1977a), Microscopic Lagrangian description of warm plasmas, 1, Linear wave propagation, Radio Sci., 12, 941-951. Kim, H., and F. W. Crawford (1977b), Microscopic Lagrangian description of warm plasmas, 2, Nonlinear wave interactions, Radio Sci., 12, 953-963. Kim, H., and F. W. Crawford (1982), Macroscopic Lagrangian description of warm plasmas, 2, Applications to wave-wave interaction, submitted to Radio Sci. Peng, Y.-K. M., and F. W. Crawford (1982), Macroscopic Lagrangian description of warm plasmas, 1, Formulation of the Lagrangian, submitted to Radio Sci.

This three-part paper describes linear and nonlinear plasma wave phenomena in an infinite, homogeneous, collisionless, warm magnetoplasma by means of a microscopic Lagrang/an. Part 1 derives the dispersion relation for all modes of linear wave propagation. To do so, the charged particle position vectors and the fields are first expanded in terms of sinusoidal perturbations from equilibrium. The contribution to the microscopic Lagrang/an, expanded to second order in the perturbations, is then averaged over space and time to remove rapidly varying terms. The Euler-Lagrange equations, obtained from variations of the Lagrangian with respect to the amplitudes of the perturbation parameters, are the first-order Maxwell equations and the perturbed particle trajectory. Variation with respect to the phase gives the equation of conservation of action. The Lagrangian is specialized to waves propagating nearly parallel, and exactly perpendicular, to the static magnetic field, and familiar wave dispersion relations are obtained. In Part 2, the nonlinear coupling of these waves is studied. In Part 3, both wave-wave and wave-particle interactions are taken into account. INTRODUCTIONThe conventional iterative analysis of nonlinear plasma wave phenomena involves direct use of Maxwell's equations and the equations describing the particle dynamics, i.e., the Vlasov equation for the microscopic treatment of warm plasmas, the moment equations for the macroscopic approximation, and the single-particle equation of motion for cold plasmas. This approach leads to formidable theoretical and algebraic complexities, especially for warm plasmas Crawlord, 1968, 1969;Stenflo, 1970;Kim et al., 1971]. As an effective alternative, the Lagrangian method familiar in analytical dynamics may be applied. The purpose of this paper is to demonstrate how it may be used in the microscopic description of small-signal wave propagation (Part 1), and in nonlinear wave-wave (Part 2) and wave-particle interactions (Part 3), in a warm magnetoplasma.A suitable averaged-Lagrangian method has already been developed for cold plasmas; the procedure is as follows [Dougherty, 1970;Dysthe, 1974]. First, the plasma perturbation parameters (the charged particle position vectors and the fields) are expanded in terms of a sum of sinusoidal perturbations from equilibrium whose amplitudes, frequencies, and wave vectors are assumed to vary slowly in space and time due to the nonlinearity. The Lagrangian is then expanded in terms of these perturbations, and averaged over space and time so as to remove rapidly varying terms [Sturrock, 1961;Whitham, 1965;Bretherton and Garrett, 1968;Simmons, 1969;Dewar, 1970; Galloway and Crawford, 1970; Galloway and Kim, 1971; Zielke, 1975]. The Euler-Lagrange equations derived from the zeroth-order Lagrangian yield the dynamical equations for the equilibrium state. The first-order Lagrangian vanishes. Variations of the second-order Lagrangian with respect to the amplitudes and phases give the small-signal equations and the equation of action ...