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.
Hello everyone,
A simple ring resonator with a bus waveguide is described by:
$$ \begin{pmatrix} E_{t1}\\ E_{t2} \end{pmatrix} =
\begin{pmatrix} t & k\\ -k^* & t^* \end{pmatrix}
\begin{pmatrix} E_{i1}\\ E_{i2} \end{pmatrix} $$
I do not understand though why we have -k* and t*? Shouldn't...
I am interested in experimenting with AR lenses and one of the main technologies is a waveguide. They rely on total internal reflection, which needs light to go from a higher to lower refractive index medium. I am reading that current AR lenses use an outer layer with a lower refractive index to...
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...
Hey all,
I was citing a result from a review paper in my paper, and I think it's wrong. I would really appreciate an outside perspective if anyone has the time!
The result was for the electric field outside a metal rod (cylindrical waveguide, if you prefer) in vacuum. Here's the picture (you...
I pretend to use the ecuation twice, once for the interior and another for the vaccum, so if I use the cilindrical coordinates for \nabla_t^2 it results in two Bessel equations, one for the interior and another fot the vaccum.
In the vaccum, the fields should experiment a exponential decay, in...
Let's say I have three modes in a fiber that is elliptical cylinder shaped (cylinder with elliptical facet), as in the image below (the source:Optical Engineering, 46(4), 045003 (2007)) so what is the equations that describe these fields..
In Feynman's lectures, he explained the ##TE_{10}## mode of waveguide by considering a line source in the middle of waveguide as below:
since the adjacent sources are all out-of-phase, which means to have interference, the adjacent optical path would be about half of wavelength as below:
where...
I've seen these devices on shores as well as on ships , like a horizontal tube rotating slowly around it;'s axis.
Now from what I know it's a type of radar, and unlike phased array it rotates it's beam physically by means of using a motor to rotate the antenna itself , what I want to know is...
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...
Let's say that on the surface of the cladding we have evanescent field due to the total internal reflection between the core and the cladding. The refractive indices of the the core is 1.45 and the refractive index of the cladding is 1.4, and I want to use the gradient force of the evanescent...
Does the Silicon Nitride Waveguide (Si3N4) has a cladding ?! I read an article that they use the evanescent field of silicon-nitride waveguide.. If the answer yes it doesn't has a cladding then can I say that the evanescent field length in the surrounding medium is the mode field portion in that...
In the paper here, it says no matter what the waveguide structure is, if the smaller waveguide has a TM mode and the larger has a TE mode, then the coupling (Inner cross product \int\int_{S_{smaller-waveguide}} (E^{small}_{transverse} \times H^{large}_{transverse}) . \hat z dS, where z is the...
I claim that waveguides are resonators because a resonator is defined as a device which can produce you normal modes of some ' mathematical object' you're looking for, which in waveguide's case is Electromagnetic fields ( waveguide can produce normal modes called TE and TM ).
Am I right?
Hi. I'm having trouble with calculating
(8.59)
from (8.58)
(## \vec H_{//} ## is simply ## \vec H ## in Jackson, but that shouldn't matter.)
in Jackson. Specifically I think I'm not sure about parallel component of H field here.
For example, shouldn't I have two terms for the...
Hello!
I'm trying to simulate a connection between two 2-port devices via waveguide but calculated results do not agree with those, calculated in simulation software. All calculations are in the notebooks.
I took a two-port device and compared its S11 characteristic calculated using equivalent...
What actually is a mode of optical fiber propagation?Is it similar to modes which correspond to various configurations as in standing waves on a string ? Also How correct is it to consider no. of rays as no of modes?
Homework Statement
My electronics&physics lecture notes contain the following side note:
___
"A ladder transmission line comprises an alternating sequence of segments of two different transmission lines both of length $l$ with characteristic impedance $Z1$ and $Z2$. If the line is constructed...
Consider a waveguide with axis parallel to axis ##z##. Using cartesian coordinates the fields inside the waveguide can be written as
Where ##\alpha## is the wavenumber and ##k=\frac{\omega}{c}## .
The maxwell equations ##\nabla \times E=-\frac{\partial B}{\partial t}## and ##\nabla \times...
Hello there,
I was wondering if the power profile of a single mode waveguide can be changed? I mean, a wave that travels through the waveguide will have a harmonic shape, right? Is it possible to get a different shape of the power profile?
Thank you :)
Hello,
I'm looking for some insightfull answers for the following topic:
I have a (slotted) waveguide where multiple (50) antennas (for sending and receiving) are located in a slot that runs along the waveguide (200 meters long). On both ends of the waveguide are probes located for the wireless...
I am a little confused about the difference between TE and TM waves in a waveguide. Let's say a monochromatic plane wave is incident on a wave guide. Then will this result in both TE and TM waves such that the sum of the guided waves at the entrance of the waveguide agrees with the plane wave?
Homework Statement
In a rectangular waveguide, b = a/2, find the section, if exists, in which the magnetic field is circularly polarized (TE10 mode).
Homework Equations
Rectangular waveguide equations for TE10 mode (referencing Pozar book).
Circular polarization (π/2 out of phase and same...
The problem states that the wavelength and frequency in a waveguide are related by:
##\lambda = \frac{c}{\sqrt{f^2 - f_0^2}}##
then asks to express the group velocity ##v_g## in terms of c and the phase velocity ##v_p = \lambda f##
Solution:
Given that ##\omega = 2\pi f##,
## \omega(k) =...
Hi, I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\^{e}_z$ comes from in the following equation:
##
\frac{\partial{\vec{E}_t}}{\partial{z}}+i\frac{\omega}{c}\hat{e}_z\times \vec{B}_t=\vec{\nabla}_tE_z
##
Homework Statement
The shielding efficiency of an aperture depends on e−αd, where α is the frequency-dependent attenuation constant of the aperture and d is the thickness of the material (or the cutoff waveguide) at frequencies below cutoff.
where ωc=2πfc.
Calculate α for an air-vent...
I just read some words from the book Optical Waveguide Theory by Snyder, Allan W., p226. It says that
"However, although it is possible for the phase velocity of a mode to exceed the maximum speed of light in the cladding (of waveguide), c/n_cl, this cannot occur without losing power to...
Has anyone considered the iron core of a transformer to act as a transmission line or waveguide, where it conveys energy from primary to secondary? The core seems to resemble a "magnetic version" of the single wire Goubau line.
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...
Microwave wave guide
Davenn stated: as a rule of thumb, the width of a wave guide needs to be of the same order of magnitude as the wavelength of the guided wave.
Will a 100+GHz wave guide fit down a 6 inch pipe? what shape would it be? Round, Square, Other?
Homework Statement
1)Find the EM fields that go through a coaxial waveguide (inner radius equals a, outer radius equals b) filled with a dielectric material where both TE and TM modes propagates.
2)Find the cutoff frequency.
3)Find the cutoff frequency if we close both ends of the waveguide...
Hi
I have a waveguide that is rectangular and multimode that I but-couple to a standard telecom SMF28 fiber. I have imaged the output of the waveguide and the fiber with a 25X microscope objective onto the chip of an IR-camera. Usually the mode overlap is calculated by cross-correlation of the...
Homework Statement
Homework Equations
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The Attempt at a Solution
[/B]
Hello
As you see my solution I found TM(5 , 2.5) that is incorrect because n should be integer not float number.In Addition when I check book solution I found TM mode is TM(2,1)
what is my mistake?
I trying to formulate a new project based on waveguides (~1 cm long) for sensing with the evanescent field. In all papers I've seen on similar topics they all aim for single mode (SM) waveguides, but I never understood the reason.
Is there a quick answer?
How did they derive equation (6)?
I don't like how they say -Φm instead of Φm, but that aside, I get that both rays 1A and 2A' travel the same distance, but AC incurs a phase change due to total internal reflection (-Φm) and it travels AC from there. Meanwhile, A'C is the distance the other...
Dear PF:
I'm currently working in a problem that has had me stranded for several weeks now. The problem reads as follows:
(See attachment)
Consider a beam of quantum particles (that is, the particles are small enough to exhibit non-negligible quantum effects) that propagates through a...
I am trying to simulate a Gaussian beam through an optical waveguide having a circular cross-section in matlab. I am familiar with the theory of modes in an optical fiber and can analytically calculate the evolution of the beam by breaking down the beam into a sum of infinite modes.
However, I...
I have been working with equations throughout the semester and using them to find cutoff frequencies and such, but when you say something like TE10, TE20, TE21, etc., I am realizing that I am having trouble getting a physical idea of what exactly these things are. Of course if you transmit at a...
Hello experts!
I am looking for the proof of the following equation:
\frac{∂^{2}E}{∂r^{2}}+\frac{1}{r}\frac{∂Ez}{∂r}+\frac{1}{r^{2}}\frac{∂^{2}Ez}{∂ø^{2}}+q²Ez=0
I think this equation is somehow related to the cylindrical waveguides. Right?
I am looking for it and I am unable to find...
Hi,
I am looking into some simulations of rib waveguide structures using Finite Element Method. I particularly solving modes for a 2D cross section of the optical waveguide, looking at TE and TM modes.
My questions is about modes called "degenerate" and "hybrid" modes. I haven't found...
Homework Statement
I have a rectangular, hollow, conductor. Something like this:
The length in z direction should be infinite. The propagation of electromagnetic waves in the conductor are given via the equations:
Homework Equations
\Delta \vec{E} = \frac{1}{c^2}...
Hi,
I'm rather confused as to how this diagram in my book. I know that in order for a mode to propagate, a standing wave must be formed in the waveguide, and this happens above some cutoff frequency that one designs for. What I don't understand is, below cutoff, what happens? I don't...
Hi,
The attenuation resulting from puting a signal into a parallel plate waveguide is dependent on the excited mode. Why does the TM mode have greater attenuation than the TE mode? I can see in the maths it 'works out' to be that, but what would be a more conceptual/physical reason?
Is the...
Hi,
I know that to receive or inject a signal into a rectangular waveguide (I'll just call it a waveguide from now on with the assumption that I mean rectangular waveguide), you can get a dipole of some sort, and poke it into the waveguide.
What I'm wondering about is, if I got a dipole...
Hi,
I think I'm missing something with how a parallel plate waveguide works. In the picture I've shown below, there intensity of the E-field change depending on how far across the waveguide it is. While I know that this has to happen in order for anything to propagate, I don't quite...
Homework Statement
Having trouble understanding why it is that inside a waveguide sides x=a,y=b propagating in z, subject to b.c. E parallel= 0 and Bperp=0... that for TE Bz=Bcos(pinx/a)cos(pimy/b) but for TM Ez=Esin(pinx/a)sin(pimy/a)?
Homework Equations
E parallel= 0 and Bperp=0
For...
Homework Statement
A parallel plate waveguide has perfectly conducting plates at y = 0 and y = b for 0 ≤ x < ∞ and -∞ < z < ∞. Inside that bound, the waveguide is filled with a dielectric with k as a propagation constant.
The Green's function to be satisfied is
\nabla^2G + k^2G =...
Hello everyone,
I'm trying to solve a problem but I want to find a simpler way if possible. The basic idea is that I would have one waveguide, for simplicity I will just take a slab waveguide. However instead of being constant there is a point at which the distance between the slab suddenly...