How fast do evanescent fields decay?

The attenuation constant for an evanescent mode is alpha = (2 pi / lambda_c) times sqrt(1 minus (f/fc)^2), where lambda_c is the cutoff wavelength and fc is the cutoff frequency. Well below cutoff (f much less than fc), alpha approaches pi/a for TE10 mode, giving approximately 27.3 dB per guide width of attenuation. For WR-90 waveguide (a = 22.86 mm) at 5 GHz (below 6.56 GHz cutoff): alpha = 2 pi / (2 times 0.02286) times sqrt(1 minus (5/6.56)^2) = 91 Np/m = 790 dB/m. Even a few centimeters of below-cutoff waveguide provides enormous attenuation, which is exploited in waveguide attenuators.

What are evanescent-mode filters?

Evanescent-mode filters use below-cutoff waveguide sections loaded with resonant elements (capacitive screws, dielectric posts, or ridges) to create bandpass filters that are much more compact than conventional waveguide filters. The below-cutoff sections act as frequency-independent coupling elements (since alpha is nearly constant well below cutoff), while the resonant elements create the passband. Advantages: very compact (up to 80 percent smaller than conventional waveguide filters), wide spurious-free stopband (no higher-order mode resonances), and good power handling. Typical applications: satellite multiplexers, radar receivers, and test equipment preselector filters.

Do evanescent modes carry any power?

A purely evanescent mode stores reactive energy but transmits no real (time-averaged) power. The E and H fields are 90 degrees out of phase, so the time-averaged Poynting vector is zero. However, evanescent modes are physically real and play important roles at discontinuities: when a propagating wave encounters a step, slot, or iris, evanescent modes are excited to satisfy the boundary conditions. These modes store energy near the discontinuity and create the reactive (capacitive or inductive) behavior seen in the equivalent circuit model. In coupled-cavity structures, evanescent coupling between resonators determines the filter bandwidth and shape factor.

Waveguide Physics

Evanescent Mode

/eh-van-ess-ent mohd/

Mode below cutoff: fields decay exponentially, E ∝ e^−αz. α = (2π/λ_c)√(1−(f/f_c)²). Well below cutoff: α ≈ π/a = 27.3 dB per guide width. No real power transmitted (E,H 90° out of phase). Used in: evanescent-mode filters (80% smaller, spurious-free), waveguide attenuators, and coupling between resonator cavities.

Decay: e^−αz

α: 27.3 dB/a

Power: Zero (reactive)

Understanding Evanescent Modes

When a waveguide mode operates below its cutoff frequency, it cannot propagate. Instead of traveling as a wave, the electromagnetic fields decay exponentially with distance. This is not absorption (no energy is dissipated); rather, the fields store reactive energy and reflect all incident power back to the source. The propagation constant becomes purely imaginary, turning the wave equation solution from an oscillating function into an exponential decay.

While evanescent modes cannot transport power, they are not useless. RF engineers deliberately exploit them in evanescent-mode filters (achieving 80% size reduction), precision waveguide attenuators (attenuation is independent of frequency well below cutoff), and inter-cavity coupling in filter design. Understanding evanescent modes is also essential for analyzing waveguide discontinuities, where they are always excited.

Evanescent Mode Equations

Attenuation constant:
α = (2π/λ_c)√(1−(f/f_c)²)
= (π/a)√(1−(f/f_c)²) for TE₁₀

Well below cutoff (f<<f_c):
α ≈ π/a (frequency independent)
= 27.3 dB per guide width a

Field decay:
E(z) = E₀ e^−αz
Power: P(z) = P₀ e^−2αz

Poynting vector:
<S> = 0 (E and H 90° out of phase)

Evanescent Mode Applications

Application	Principle	Advantage	f Range	Example
EM filter	Loaded below-fc WG	80% smaller	1-40 GHz	Satellite mux
Attenuator	Calibrated decay	Freq-independent	DC-18 GHz	Piston attenuator
Coupling iris	Reactive coupling	BW control	All bands	Cavity filters
Mode suppressor	Higher modes decay	Mode purity	All bands	WG transitions
Near-field probe	Sub-λ aperture	Resolution	1-100 GHz	Scanning probe

Common Questions

Frequently Asked Questions

Decay rate?

α = (π/a)√(1-(f/fc)²). Well below cutoff: α≈π/a = 27.3 dB per guide width. WR-90 @ 5 GHz (fc=6.56): 790 dB/m. Few cm = enormous attenuation. Used in precision piston attenuators with frequency-independent calibration.

EM filters?

Below-cutoff WG loaded with capacitive screws/posts/ridges. Below-fc sections = frequency-independent coupling. Resonant elements create passband. 80% smaller than conventional WG filters. Wide spurious-free stopband (no higher-mode resonances). Satellite mux, radar, test equipment.

Power transmission?

Zero real power: E and H 90° out of phase, time-avg Poynting vector = 0. Stores reactive energy only. At discontinuities: evanescent modes excited to satisfy boundary conditions, create equivalent reactive (L or C) circuit elements. Inter-resonator coupling strength determines filter BW.

Related Terms

← E-Plane Far-Field →

Waveguide Design

Request a Quote

Need evanescent-mode filter design, waveguide attenuators, or EM analysis? Contact our team.

Get in Touch