The Generation of Standing Waves in the Dielectric Medium

Key Takeaways

• When waves possess E and B fields of the same magnitude and phase in planes perpendicular to the direction of propagation, they can be called uniform plane waves.

• When a plane electromagnetic wave travels in free space, its speed is equal to the speed of light. 

• The normal incidence of a plane wave at an interface between perfectly dielectric and perfectly conducting mediums generates standing waves in the dielectric medium. 

When a plane electromagnetic wave travels in free space, its speed is equal to the speed of light

Electromagnetic waves are composed of both electric (E) and magnetic (B) fields. When waves possess E and B fields of the same magnitude and phase in planes perpendicular to the direction of propagation, they can be called uniform plane waves. 

When a plane electromagnetic wave travels in free space, its speed is equal to the speed of light. However, not only the speed changes when it interfaces two mediums while in propagation; the complete behavior of the plane wave changes. When the traveling wave encounters two different mediums, it may either get partly reflected or transmitted, depending on the characteristics of the mediums. The normal incidence of a plane wave at an interface between perfectly dielectric and perfectly conducting mediums generates standing waves in the dielectric medium.  

The Normal Incidence of a Plane Wave at the Media Boundary

Consider a plane wave traveling from bounded perfect dielectric medium 1 to perfectly conducting medium 2 with permittivity, permeability, and conductivity  , respectively. Medium 1 is a perfect dielectric,  and medium 2 is a perfect conductor, . In this case of an incident plane wave, the reflection coefficient  and transmission coefficient (T) are as follows:

The values of the reflection and transmission coefficients indicate that no wave is transmitted to the conducting medium. The incident wave gets reflected completely at the interface of the mediums. The electric field of the resultant wave in medium 1 is the sum of electric fields of the incident wave and the reflected wave as given by equation (3). The electric field of the incident and reflected waves in medium 1 are given by equations (4) and (5), respectively. The resultant wave is composed of both electric and magnetic fields and it is given by equations (6) and (7), respectively. 

Standing Waves in the Dielectric Medium

From the above equations, it is clear that the incident wave is a forward traveling wave and the reflected wave is a backward traveling wave when measured from the boundary of the mediums. The boundary of the two mediums is assumed to be at z=0. The superposition of the forward and backward traveling waves creates a standing wave in dielectric medium 1. 

From equations (6) and (7), we can see that the electric field and magnetic field vector of the standing wave vary sinusoidally, with distance measured from z=0. In the standing wave, E is maximum when H is zero. E and H are 90 degrees out of phase with each other in both time and space. 

Understanding the characteristics of standing waves in the dielectric medium is useful when working with dielectric resonators. In the case of an impedance mismatch, standing waves are generated inside dielectric waveguides. In addition to understanding standing wave characteristics, having some basic knowledge about the electric and magnetic fields present in  standing waves  is helpful when working with waveguide structures and cavities.

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