What are Waveguides?

A Waveguide is a specialized structure that is used to direct electromagnetic waves from one point to another with minimal signal loss, at high frequencies. Unlike the traditional transmission lines, waveguides do not have a central conductor. Instead, they are hollow and rely on the reflections from the inner walls of the tube to guide the waves and transmit power from one point to another. They are widely used in microwave and RF communications, optical systems, and radar applications. 

A rigid rectangular waveguide 

The structure of the waveguide is an important parameter that determines how the wave will propagate through it. It makes the waveguide highly efficient for high-frequency signals. Waveguides are generally hollow metallic tubes or dielectric structures with retangular, circular or elliptical cross-sectional shape. The metallic waveguides have conductive walls which help in reflecting the electromagnetic waves, whereas in the dielectric waveguides a high-refractive index core is surrounding by a lower-index cladding for total internal reflection of the signal. 

The waveguides can be classified on a lot of parameters like structure, material, operating mode, frequency of operation, etc. Based on the shape, the waveguides are classified as rectangular and circular. The rectangular waveguides have cross-section of rectangular shape and circular waveguides have a cross-section that is circular in shape.

Modes of Operation

In waveguide theory, the terms TE (Transverse Electric) and TM (Transverse Magnetic) refer to the two primary operating modes of electromagnetic waves propagating through a waveguide. These modes define the behavior of the electric and magnetic fields inside the waveguide and determine how the wave travels through it.

Transverse directions w.r.t the direction of signal propagation in a Waveguide 

TE Mode (Transverse Electric Mode) 

In TE mode, the electric field is entirely transverse to the direction of propagation (see image above), meaning it has no component along the direction of the wave propagation, whereas the magnetic field will have components in all three directions, including the direction of propagation of wave. There are infinite number of solutions for the wave equation corresponding to the magnetic fields. The solutions are disguised using the mode indexes, and the modes are represented as TE(m,n), where ‘m’ represents the number of half-wavelength variations of the electric field along the x-direction and ‘n’ represents the number of half-wavelength variations of the electric field along the y-direction. The ‘m’ and ‘n’ values can be 0,1,2.. and must satisfy the relationship m ≠ n. Each mode is associated with a cut-off frequency, below which no TE propagation occurs in rectangular waveguides. The mode of propagation with the lowest cut-off frequency is called the dominant mode. TE10 is the dominant mode in rectangular waveguides.  

Different TE modes showing the variations in electric filed with change in value of ‘m’  

TM Mode (Transverse Magnetic Mode) 

In TM mode, the magnetic field has no component in the direction of propagation, meaning it is entirely transverse to the direction of propagation, i.e. it lies in the cross-sectional plane of the waveguide. Whereas the electric field has component along the direction of propagation (the waveguide axis). When Maxwell’s equation or wave equation for the electric fields in the rectangular waveguide is solved, and infinite solutions can be distinguished using the mode indexes. The value of m or n can never be equal to zero, but unlike TE mode, m can be equal to n, making the dominant mode in the rectangular waveguide is TM11. 

 TM11 Mode

The lowest operating mode in a rectangular waveguide is the TE10 mode and the cutoff frequencies of the TE and TM mode depend on the dimension of the waveguide. In a circular waveguide, the cross-section of the waveguide is circular. They support both the TE and TM modes, but typically allow more complex mode patterns as compared to rectangular waveguides. The dominant mode in circular waveguides is often the TE11 mode, while higher-order models can also propagate.

Characteristics of Waveguides 

1. Cutoff Frequency of Waveguides: The cutoff frequency for each mode in a waveguide is the specific frequency, below which the mode cannot propagate. This frequency is determined by the waveguide’s dimensions and the mode of operation. For rectangular waveguides, the cutoff frequency fc for the dominant TE10 mode can be calculated by the equation below. You can also use our calculator to calculate the cutoff frequency for rectangular waveguides.

For circular waveguides, the cutoff frequency fc  for the dominant mode can be calculated by the equation below. You can also use our calculator to calculate the cutoff frequency for circular waveguides.

Click here to learn more about Waveguide Cutoff Frequencies. 

2. Impedance and Losses: The characteristic impedance of a waveguide depends on the operating mode and the frequency. As the frequency increases, the impedance changes, which affects the efficiency of the energy transfer. There are two loss mechanisms that occur in the waveguides - conductor losses and dielectric losses.

Conductor losses occur due to surface resistance in the waveguide walls, which is more visible at high frequencies. Dielectric losses are found in dielectric-filled waveguides, where the energy is absorbed by the material. 

3. Phase Velocity: The phase velocity refers to the speed at which a specific phase of a wave (e.g., a crest) propagates through a medium. The phase velocity of waves in a waveguide may be higher than the speed of light in free space. However, this does not violate the principles of relativity, as the group velocity, which represents the speed at which the overall shape or the envelope of the wave (carrying energy or information) moves, is below the speed of light.

 The phase velocity is given as: 

where λ_c is the wavelength of light.

4. Wavelength: In a waveguide the effective wavelength of an electromagnetic wave differs from its free-space wavelength due to the constraints imposed by the geometry of waveguide. This difference is explained by the phase velocity and cutoff frequency which lead to a longer wavelength inside the waveguide. This effect becomes significant as the operating frequency approaches the waveguide’s cutoff frequency.

Where λ_g is the waveguide wavelength, λ_o is the free-space wavelength, and ‘a’ is the broad dimension of the waveguide.