• Space harmonics are expansion of field similar to fourier expansion but are not power orthogonal due to mutual coupling

• Spatial harmonics converge easily in evaluating field integrals and helps in accurate estimation of properties of radiation pattern and thereby designing antenna

Floquet theoremTranslational symmetry of axially periodic structures in which mode is guided axially.

Cross-sectional complex field distribution of a periodic structure remains unchanged under an axial translation of observational point through period d , while amplitude multiplies itself by a complex constant

Macroscopic field Microscopic field

Fourier expansion of a Bloch wave indicates that field of a normal mode of axially periodic structure is expressible in terms of an infinite number of travelling waves

Each spatial harmonic has a phase velocity given by

For sufficiently large values of abs(n) all harmonics are axially slow n >= 0 forward travelling wavesLarge negative values if n backward travelling waves

Orthogonal polarization – end fire scanning possibleWave number – key for all radiation characteristicsLeakage – interruption of current flow by slots on top wall

Wide microstrip shorted by vias at edges to form SIWEasy integration with planar circuits as a promising antenna for integrated microwave and millimeter wave applications

[17] Collin, R. E., & Zucker, F. J. (1969). Antenna theory. 2 (1969). McGraw- Hill, ch. 19 and 20.

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