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The distance between successive wavefronts at 2π phase intervals is λo in the direction of propagation, and the distances separating these same wavefronts as measured along the x and z axes are equal or greater, as illustrated in Figure 9.2.1. For example: λ z = λo cos θ = 2π kz ≥ λo.
The simplest representation of Maxwell’s equations is in differential form, which leads directly to waves; the alternate integral form is presented in Section 2.4.3. The differential form uses the vector del operator ∇: ∇ ≡ xˆ ∂ + ∂x yˆ ∂ ∂ ∂y. + zˆ ∂z.
In other words, the polarization vector of the electric field, the polarization vector of the mag-netic field, and the direction k that the plane wave is propagating are all orthogonal. To see how much freedom there is left in the plane wave, it’s helpful to choose coordinates.
A beam linearly polarized along the x-axis and traveling in the positive z-direction can be represented by: E(z,t)=E0xöcos(kz"!t) (4.3) where xö is the unit vector along the x-axis. Of course, the choice of coordinate system is completely arbitrary. If we have a second coordinate system rotated by an angle θ, about the z-
Learning Objectives. By the end of this section, you will be able to: Describe the statistical interpretation of the wave function. Use the wave function to determine probabilities. Calculate expectation values of position, momentum, and kinetic energy.
21 Ιουν 2021 · The mode of Equations (12.1.6), Figure 12.1.2, is called a transverse electric mode, or a TE mode, because the electric field has no component along the guide axis, i.e. no component along the direction of propagation of the wave-guide mode.
θ0 = tan-1(X0/Z0). The waves crossing the x-y plane as seen here: The higher up the x-axis we go, the farther away from the source we find ourselves, so that the wavefront phase increases with increasing x. If φ0.is subtracted from the phase at x=0 (as usual), the phase increases linearly with x z θ0 d -p.2-
