# Waveguides Definition and 17 Discussions

A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities decrease according to the inverse square law as they expand into three dimensional space.
There are different types of waveguides for different types of waves. The original and most common meaning is a hollow conductive metal pipe used to carry high frequency radio waves, particularly microwaves. Dielectric waveguides are used at higher radio frequencies, and transparent dielectric waveguides and optical fibers serve as waveguides for light. In acoustics, air ducts and horns are used as waveguides for sound in musical instruments and loudspeakers, and specially-shaped metal rods conduct ultrasonic waves in ultrasonic machining.
The geometry of a waveguide reflects its function; in addition to more common types that channel the wave in one dimension, there are two-dimensional slab waveguides which confine waves to two dimensions. The frequency of the transmitted wave also dictates the size of a waveguide: each waveguide has a cutoff wavelength determined by its size and will not conduct waves of greater wavelength; an optical fiber that guides light will not transmit microwaves which have a much larger wavelength. Some naturally occurring structures can also act as waveguides. The SOFAR channel layer in the ocean can guide the sound of whale song across enormous distances.
Any shape of crossection of waveguide can support EM waves. Irregular shapes are difficult to analyse. Commonly used waveguides are rectangular and circular in shape.

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1. ### I Why is the electric field in y direction in a TE guided wave?

Hi, I have a fairly simple question, but the answer is probably not as simple. I'm not sure to understand why in a guided wave (TE), the electric field is in the y direction. I know ##E_z = 0##, but why ##E_x = 0, B_y = 0##?
2. ### Problem on Parallel Plate Waveguide

The Imgur Link of the Problem with the figure - Problem Link. I did not paste it here as the post upload quality seemed heavily pixelated for some reason. For this problem, what I did was to divide the waveguide into 2 sections of distinct permabilities to calculate the cutoff frequency. Since...
3. ### A Evanescent field of a waveguide

If we look to the figure, in several articles they mentioned that the part of the mode field, the tail of the mode field diameter, travel in the cladding, this maybe I can understand that because of a little change between the refractive indices of the core and the cladding, then the transverse...
4. ### Rearranging the equation for the cutoff condition in optical fibers

Hello! In Optical fibers, let ##k_1## and ##k_2## be respectively the propagation constants in core and cladding, ##\beta## the propagation costant of a mode along the direction ##z##, ##a## the radius of the fiber. Using the normalized quantities ##u=a \sqrt{k_1^2 − \beta^2}## and ##w=a...
5. ### A Dirichlet and Neumann boundary conditions in cylindrical waveguides

The book of Balanis solves the field patterns from the potential functions. Let say for TE modes, it is: F_z(\rho, \phi, z) = A_{mn} J_m(\beta_{\rho}\rho) [C_2 \cos(m\phi) + D_2 \sin(m\phi)] e^{-j\beta_z z} There is no mention of how to solve for the constant A_{mn} . Then, from a paper...
6. ### TE and TM modes in optical fibers

In a step-index optical fiber, considering Bessel functions of order ##\nu = 0## and no ##\phi## dependence, it is possible to obtain two separate sets of components, which generate respectively TE and TM modes. In the former case, only ##E_{\phi}##, ##H_r##, ##H_z## are involved; in the latter...
7. ### What is the difference between a waveguide/horn and regular metal pipes?

What is the difference between those horns/waveguides and regular metal pieces with a same geometry? Why the microwave companies sell those parts at hundreds and thousands dollars? Why we cannot buy some metal sheets or pipes on McMaster-Carr with very low price and make some microwave...
8. ### I Visualization of fields in waveguides

Can someone provide me intuitive visualization of how E or H field can be longitudinal in a waveguide (TM/TE)? TEM is easy to visualize, but how EM wave can behave like sound in a waveguide (constant phase and amplitude plane in the same direction)? [Moderator: large bold font removed. In the...
9. ### What is the attenuation below cut-off frequency for TE10?

It is not useful to talk about the attenuation below cut-off frequency, but I have this doubt about what happens to the wave below cut off for an electric conductor. As we know if we derive the propagation constant, it becomes imaginary saying that there should not be any wave propagating in the...
10. ### I Why different cutoff frequencies for TE and TM in a medium?

Today in my electro-magnetics class, we were told that the cut-off frequencies of TE and TM waves on a co-axial cable are different. As far as I understand, it says that if there is an electric field with one frequency projected on it and if we know that the problem can be simplified if we see...
11. ### Engineering Eigenfunctions of the vector Helmholtz equation

Hi everyone, I'm looking for a reference book that treats the theory behind the eigenfunctions solution of the so called vector Helmholtz equation and its Neumann and Dirichlet problems. I've already found a theory inside the last chapter of Morse & Feshbach's Methods of theoretical physics...
12. ### Transmission Lines

Homework Statement I am having problems with the second part of the question - proving that the relationship given is true. Homework Equations See question. The Attempt at a Solution Firstly, consider a single pair of transmission lines with characteristic impedances ##Z_{1}## and ##Z_{2}##...
13. ### Field frequency and angle of incidence in optical waveguides

Hello! In this previous post, most replies point out that it is not possible to predict the angle of refraction (and so the frequency) at a certain interface, given the wavelength of the original signal. In particular, But when dealing with optical waveguides, it seems to be different. I am...
14. ### Modes orthogonality in a dielectric slab

A typical mode in a dielectric slab like this, with propagation along x, uniformity along z and refractive index variation along y, is represented by the following function: f (y) = \begin{cases} \displaystyle \frac{\cos (k_1 y)}{\cos (k_1 d)} && |y| \leq d \\ e^{-j k_2 (y - d)} && |y| \geq d...
15. ### Transverse resonance method

The Transverse resonance method is used to determine the propagation constant of a wave in several waveguides, like the rectangular waveguide, or also dielectric waveguides. It takes advantage of the fact that a standing wave is present along a certain direction (transverse with respect to the...
16. ### Is pertubation a linear operation?

My question stems from a discussion I had with my colleague today. In Electomagnetic coupling , like in waveguide structures. We apply pertubation theory to find out the coupling between various modes that get coupled in the device. My colleague said that the coupling interaction was...
17. ### Solving Vector Modal Equation

I need help solving the vector modal equation for a step index fiber having a constant refractive index in the core and the cladding. (Under the conditions of zero dispersion and absorption.