Mode characteristics in waveguides: match each mode category to its defining feature. List I (Mode category) A. Evanescent B. Dominant mode C. TM10 and TM01 in a rectangular waveguide List II (Characteristic) Rectangular waveguide does not support these TM modes No wave propagation (field decays exponentially) Lowest cutoff frequency among supported modes

Introduction / Context:
Waveguide modes determine whether signals propagate or decay. This question checks core understanding of evanescent fields, dominant modes, and which TM modes are disallowed in rectangular guides.

Given Data / Assumptions:

• Below cutoff, fields are evanescent: they decay along the guide.
• Dominant mode is the first mode to propagate as frequency increases.
• Boundary conditions in rectangular waveguides restrict permissible TM indices.

Concept / Approach:

Evanescent modes have β imaginary and cannot carry power over distance. The dominant mode in a rectangular waveguide is TE10, having the lowest cutoff frequency. TM10 and TM01 are not supported in rectangular guides due to boundary conditions requiring both integers nonzero for TM modes.

Step-by-Step Solution:

Verification / Alternative check:

From cutoff relations, β = √(k^2 − k_c^2). For f < f_c, β becomes imaginary, confirming evanescence. Rectangular waveguide mode tables list TE10 as dominant; TM_mn requires m and n both nonzero, excluding TM10 and TM01.

Why Other Options Are Wrong:

• Assigning “lowest cutoff” to evanescent modes is contradictory; evanescent means not above cutoff.
• Claiming TM10 propagates in rectangular guides violates boundary conditions for TM modes.

Common Pitfalls:

Confusing TE with TM naming and forgetting that “dominant” refers to the first allowed propagating mode, not the one with maximum field strength.

Final Answer:

A-2, B-3, C-1