Dominant mode in rectangular waveguides: Which mode is the first to propagate (lowest cutoff) in a standard air-filled rectangular waveguide?

Introduction:
Every rectangular waveguide has a dominant mode: the mode with the lowest cutoff frequency, which therefore propagates first as frequency increases. Identifying it is essential for single-mode operation and component design.

Given Data / Assumptions:

• Air-filled rectangular waveguide of width a and height b (a > b).
• Standard boundary conditions on perfectly conducting walls.
• TE/TM cutoff relationships apply: fc ∝ sqrt((m/a)^2 + (n/b)^2).

Concept / Approach:

For TE_mn and TM_mn modes, the lowest combination is m = 1, n = 0 in TE family for a typical guide with a > b. This gives TE10 as the dominant mode. Its cutoff frequency is fc = c / (2a), which is lower than other combinations for the same geometry.

Step-by-Step Solution:

Verification / Alternative check:

Waveguide charts and standards (WR series) are based on TE10 dominance, ensuring single-mode bandwidth between TE10 cutoff and the next higher-order mode cutoff.

Why Other Options Are Wrong:

• TE01, TE20, TE11, TM11 have higher cutoff frequencies for a standard aspect ratio.

Common Pitfalls:

Confusing dominant with circular-guide dominance (TE11 is dominant in circular guides). In rectangular guides, TE10 is dominant.

Final Answer:

TE10