Circular waveguides and symmetry: Which of the following circular waveguide modes are circularly symmetric (no azimuthal variation)?
-
ATE01
-
BTE02
-
Cboth (a) and (b)
-
Dneither (a) nor (b)
-
ETM11 only
Answer
Correct Answer: both (a) and (b)
Explanation
Introduction:Modes in circular waveguides are labeled TEmn or TMmn, where the first index m corresponds to azimuthal variations and the second index n corresponds to radial order. Recognizing which modes are circularly symmetric helps in low-loss transmission and mode conversion design.
Given Data / Assumptions:
- Circular metallic waveguide with air filling.
- TE0n modes have m = 0 (no dependence on azimuthal angle φ).
- We are considering TE01 and TE02 specifically.
Concept / Approach:
Azimuthal symmetry means the fields do not vary with φ. In circular guides, m = 0 satisfies this, so any TE0n or TM0n mode is circularly symmetric. Therefore, TE01 and TE02 are both circularly symmetric modes.
Step-by-Step Solution:
Identify the azimuthal index: m = 0 implies circular symmetry.Check modes: TE01 → m = 0, n = 1; TE02 → m = 0, n = 2.Conclude: both choices are circularly symmetric.Verification / Alternative check:
Field patterns for TE01 and TE02 show concentric rings with no angular variation, confirming circular symmetry useful for certain low-loss TE01 long-haul systems.
Why Other Options Are Wrong:
- Neither or a single mode only contradict m = 0 symmetry criterion.
- TM11 only: TM11 has m = 1, hence not circularly symmetric.
Common Pitfalls:
Confusing dominant mode (TE11) with symmetry; dominance relates to cutoff, not azimuthal variation.
Final Answer:
both (a) and (b)