Final answer:
Linear combination of TEM modes results in superposing electric field vectors to produce dot patterns or equal intensity contours along respective axes of polarization. When analyzing TEM modes, the direction and magnitude of the electric fields are crucial, and the observed patterns depend on constructive or destructive interference of these modes.
Step-by-step explanation:
When dealing with the linear combination of TEM modes, the result is a superposition of the electric field vectors of each mode. The electric field patterns for TEM₁,₀ and TEM₀,₁ modes can be represented by dot patterns or contours of equal intensity. For TEM₁,₀, the electric field (E-field) is aligned along the y-axis (ay), with 'dots' or lines of equal intensity positioned in a grid-like pattern across the y-axis, indicating areas of equal E-field magnitude.
The direction of the E-field is perpendicular to the propagation direction with a linear polarization. Similarly, for TEM₀,₁, the E-field is aligned along the x-axis (ax), with the intensity pattern mirroring that of TEM₁,₀ along the x-axis. The resulting pattern from the combination depends on whether the modes are added constructively or destructively.
Additionally, according to Malus's Law, only the component of the EM wave parallel to the axis of a filter will pass through, and the intensity I of the transmitted wave is related to the incident wave by I = Io cos² 0, where Io is the intensity of the polarized wave before passing through the filter, and 0 is the angle between the direction of polarization and the axis of the filter.