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The axis is the unit vector (unique except for sign) which remains unchanged by the rotation. The magnitude of the angle is also unique, with its sign being determined by the sign of the rotation axis. The axis can be represented as a three-dimensional unit vector and the angle by a scalar θ.
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.
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.
Any disturbance that complies with the wave equation can propagate as a wave moving along the x-axis with a wave speed v. It works equally well for waves on a string, sound waves, and electromagnetic waves. This equation is extremely useful. For example, it can be used to show that electromagnetic waves move at the speed of light.
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.
We find H0 = (ωμ0)−1 (k × E0), that is, the magnetic field vector is perpendicular to the electric field vector and the wavevector k. Let us consider a plane wave with real amplitude E0 and propagating in direc-tion of the z axis. This plane wave is represented by E(r, t) = where k = |k| = ω/c.
