In a rectangular waveguide, which TM mode exhibits the lowest cutoff frequency (i.e., the dominant TM mode)?

Introduction / Context:Rectangular waveguides support TE and TM modes with cutoff frequencies determined by the guide dimensions and mode indices m and n. Identifying the dominant TM mode is a classic exam task.

Given Data / Assumptions:

• For TM modes, both m and n must be nonzero (no TMm0 or TM0n).
• Cutoff frequency: fc(mn) = (c/2) * √[(m/a)^2 + (n/b)^2] for TMmn.
• Dimensions a ≥ b for standard guides.

Concept / Approach:Because TMm0 or TM0n are not permitted (Ez must vanish at the walls), the lowest indices allowed are m = 1 and n = 1. Thus TM11 is the TM mode with the lowest possible cutoff, making it the dominant TM mode (though overall guide dominant is TE10).

Step-by-Step Solution:

Verification / Alternative check:Textbook tables list TE10 as the overall dominant mode and TM11 as the dominant TM mode for a ≥ b rectangular guides.

Why Other Options Are Wrong:

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