A Uniform Plane Wave and Its Properties

Key Takeaways

• The uniform plane wave and its properties are of great practical importance, as any complicated wave type can be represented as the superposition of plane waves.

• When the electric (E) and magnetic (H) field vectors of a wave are in planes perpendicular to the direction of propagation, say the z-direction, this is called a plane wave. 

• A transverse electromagnetic wave (TEM) wave is an example of a plane wave. 

A uniform plane wave is the simplest type of electromagnetic wave

Electromagnetic waves have a wide variety of applications—communication systems, broadcasting, heating, cooking, and medical imaging all have electromagnetic waves, just to name a few. Time-varying currents and charges are responsible for the generation of electromagnetic waves, and, once generated, they propagate with a finite velocity independent of their source. 

Uniform plane waves are the simplest type of electromagnetic wave. The uniform plane wave and its properties are of great practical importance, as any complicated wave type can be represented as the superposition of plane waves. 

What Is a Uniform Plane Wave?

The time-varying electric and magnetic fields, which exist in an unbounded, homogeneous medium, generate uniform plane waves. A uniform plane wave can be defined using the magnitude of electric and magnetic fields. 

A Brief Summary of Uniform Plane Waves and Their Properties

The electromagnetic waves generating from sources are spherical. At large distances from the sources, they behave as plane waves. When the electric (E) and magnetic (H) field vectors of a wave are in planes perpendicular to the direction of propagation, say the z-direction, it is called a plane wave. Transverse electromagnetic waves (TEM waves) are an example of a plane wave. 

Plane waves have constant phase fronts and when their amplitudes are uniform, they form uniform plane waves. So, if the vectors E and H are constant at any of the planes at a given instant, then the plane wave turns into a uniform plane wave. 

In uniform plane waves, the orientation of the E field is perpendicular to the H field, and both are perpendicular to the direction of propagation of the wave. Consider a uniform plane wave propagating in the positive z-direction, with amplitude Eo. The electric field vector and magnetic field vector in the x-direction and y-direction of the uniform plane wave can be given by the following equations:

In uniform plane waves, the field vectors E and H satisfy the one-dimensional wave equation. The wave equation for the E field of the uniform plane wave  can be given  by the following equation (a similar equation applies for H as well):

Features of Uniform Plane Waves

Here are some key properties of uniform plane waves:

1. The vectors E and H are mutually perpendicular to the direction of propagation (z-direction). The fields  E and H have no dependence on the transverse coordinates x, y and are functions only of z, time(t).   

2. The direction of the Poynting vector is in the direction of propagation of the wave, in the z-direction. The Poynting vector is  the cross product of E and H and is given by the following equation: 

3. The magnitudes of E and H are the same in any individual plane normal to the direction of wave propagation (z-direction) at any given instant. 

4. The ratio of the magnitudes of E and H vectors are the same at all points at any given instant of time. The ratio is also called the intrinsic impedance of the medium in which the wave travels. In air or vacuum, it is equal to 377Ω.

5. The velocity of plane wave propagation in the air of vacuum can be given by the following equation:

The uniform plane wave and its properties are useful when defining complicated plane waves such as TEM waves, transverse magnetic (TM) waves, and transverse electric (TE) waves. Cadence's PCB Design and Analysis tools are advantageous when working on microwave and RF circuits handling TEM, TM, and TE waves.  

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