Waveguide high frequency (past rating) behavior

[CopperCone]

So its difficult to google this and i dont have my book, i only renember a kind of vauge explaination from it

Waveguides have been described as high pass filters by most literature.

But if you look at waveguide designs they are specified with a pass band.

Wikipedia says the high cutoff is to prevent evanescent coupling. This links to stuff about optics. I dont really know what it means.

Does anyone have s parameter type plots that extend way above the high bound of manufactured waveguide so i can practically understand what it means?
I assume that the injector from coax to waveguide does not do a good job coupling out of band frequencies for possivbly different reasons,... Can you even have a good way to hook up a 15ghz signal to a 2ghz waveguide? Im kinda imagining putting a little horn in there with a coaxial feed would work better then the purpose designed coupler since the impedance taper would not match? But thats chicken or the egg not sure

Am i right in thinking you get some kind of farfield or opticallike coupling (this is the meaning of evanvescent?) so that stuff bounces around like a laser beam in a mirrored room and you end up getting constructive and destructive interference and hot spots so high energy loss before it gets to a exit?

Does this happen in the heating cavity of a microwave oven(its big compared to the feeder)?

[CopperCone]

a pleasing explanation I found is that "as the operating frequency is increased far above the cutoff frequency, the phase and group velocities approach the free-space velocity" but I would like to know more.

and some indian dude talking about KY too much (seriously) confused the shit out of me with the evanwhatever, is it like quantum tunneling or something??? wtf

[T3sl4co1l]

Higher frequency = more modes = multiple group delays / phase shifts.

Tim

[TheUnnamedNewbie]

So, you have to start by being clear what waveguide you are talking about - there are many types (some authors, such as Orfanidis, even consider transmission lines a subset of waveguides). For example, optical fiber is also a waveguide.

I'm going to assume that you are reffering to a metal, rectangular or circular waveguide.

First we need to understand what a propagation mode is. A very poor description is that a mode is a kind of ''stable'' configuration of the fields in a propagating wave. Think of it as if the wave were resonating between the top and bottom walls of the waveguide while it moves forwards. For example, the electric field of a TE₁₀ mode (where the names come from is not really important right now) looks like this, where you can see how it is ''resonating'' between the sides and resulting in a peak at the center:



What I think people are referring to when they describe a metal waveguide as a high-pass filter is the fact that for a certain size of waveguide, you need a minimum frequency before this "resonance" can occur - in other words, they only allow propagation above a certain frequency - below this they don't work¹.

But then why are waveguides given with a band of operation instead of just a minimum frequency? Because there can be multiple modes (if the wavelength is so small that it fits more than once within the tube, it can form a more complex resonance patter). The second TE mode, the TE₂₀ mode, for example, is shown below:



Because the resonance requires the wavelength to be at least half as short as the previous mode, this mode can only start propagating at a higher frequency.

Okay, but why is this an issue? As long as the wave is propagating we are good, no?
Not really! The problem is that different modes will travel at different speeds. This can give what we call modal dispersion. This is problematic because it will change our waveform - imagine that at a certain frequency, at our detector the two modes are exactly 180 degrees out of phase - as a result, they will cancel out (don't get me started on pulse smearing and ISI). Hence we don't want to use our waveguide at this frequency because it will not perform very well (there is also the fact that we get higher losses but that is secondary to multi-mode issues).

The band that a waveguide is specified for is also called the "single-mode region"  or single-mode band. The propagation constants for different modes vs frequency are often plotted in a dispersion diagram, which looks like this where we can see that the single-mode region extends from just under 7 GHz to just over 13 GHz for this waveguide:
 

If the difference in propagation speed is small enough for our applications, we can tolerate them and use a wider band. This is what happens in a multi-mode optical fiber: it is much bigger (= many more resonance modes possible) than the single mode fiber. But, for short ranges (few hundred meters) the modal dispersion due to the different possible modes is acceptable.
The bigger size of the multi-mode optical fiber results in it being much easier to couple light into, and hence the connectors and lasers need to be less precisely aligned, which makes things cheaper.

Notes:
¹In strict theory you can say that they do work but the propagation constant will be complex even for ideal, lossless conductors and dielectrics, which means that the fields will decay very quickly

[CopperCone]

Ok, that clears it up some.

But, if you have a piece of waveguide connected to a VNA, what would the plots realistically look like on the 2 port S parameters? I have a basic idea of what is happening but I don't know how the curves would look like.

I am kind of assuming here that for the segment of waveguide that you linked a graph about, you would have 3 'curve behaviors' or 'regimes'

One between 6.5 - 13 GHz where its only the TE10, one between 13 and 14 GHz where its TE10 being superimposed on TE20, and a even more chaotic one 14-21 (upper bound) GHz where all three modes are interacting with each other.

In those interference bands I listed, would you get some kind of S-parameters that could be generalized based on the interference pattern formed? I traditionally heard the word "moding", and the plots I saw were kind of spikey.

I associate this with ripples in a small pond, where a single mode is a single rock being thrown into it, then the region between 13 and 14 ghz as 2 rocks, and the region between 14-21 as three rocks. If you find a program, you can visualize the end ripples and the kaledoscopic like pattern is kind of unique to each of them, so you look at it after some time has passed, you can kind of guess how many rocks were thrown into it. Can you do the same by looking at S parameter plots to kind of get an idea how a dispersion diagram would look like?

Also, what is the Y axis unit on that mean?

[TheUnnamedNewbie]

It is very hard to predict what you will see because it depends on what you are doing, how long the waveguide is, how the mode is launcherd, etc. I suspect you would get nulls in your S₂₁ at frequencies where the difference is half a wavelength. Likely for short sections you will not notice this that much, but citation needed. In fact, if you can have mode-selective coupleing structures this could not be a big issue at all, as is the case in dielectric ribbon waveguides, where we get many modes that can propagate, but because our coupler is 15-20 dB more sensitive to the fundamental mode, we don't worry that much.

The y-axis is the propagation constant beta relative to the free-space propagation constant k₀. If beta/k₀ = 1, the mode propagates at the same speed as in free space. If beta/k₀ = 0, the mode does not propagate.

[CopperCone]

Ok. Does that fully cover the evanescent propagation/coupling that people talk about? I watched an optical explanation and I have NO FUCKIN IDEA how it relates to any of this honestly.

And when you are propagating a mixture of modes, I get the feeling from what you write that the design suddenly becomes more sensitive to length? And the length effect can't be calculated by some kind of simple linear formula like insertion loss per foot or VSWR change per foot, it becomes some kind of high order equation (maybe quadratic, cubic sinusoidal or worse?) when the distance is long from the generator?

What do you consider short in the length axis?

I am also guessing that things would get funny around bends, particularly non-ideal ones, with much more sensitivity then the regular wave guide bending rules of thumb. Do typical coaxial to launcher section adapters tolerate it, or would you need a special launcher even if you decided to misuse the waveguide (assuming the coaxial cable and coaxial connector is capable of supporting the frequency).

I am starting to think that this is basically also true for coaxial cable that is wrong (i.e. passing 10GHz on thick coaxial meant for 1GHz)?

[T3sl4co1l]

Ok. Does that fully cover the evanescent propagation/coupling that people talk about? I watched an optical explanation and I have NO FUCKIN IDEA how it relates to any of this honestly.

Optics don't have too much direct relevance here, because the permittivity and permeability of most metals is bonkers up there.  Dielectric optics are mostly okay, as far as I know (e.g., fiber optic == dielectric waveguide).

Evanescent waves are modes that are confined to a surface or boundary, i.e., do not have a far field (radiating) component.  They may not necessarily be "near field" effects -- the field can extend for many wavelengths away from a point source -- but near fields around antennas are a special case of them.

And when you are propagating a mixture of modes, I get the feeling from what you write that the design suddenly becomes more sensitive to length? And the length effect can't be calculated by some kind of simple linear formula like insertion loss per foot or VSWR change per foot, it becomes some kind of high order equation (maybe quadratic, cubic sinusoidal or worse?) when the distance is long from the generator?

What do you consider short in the length axis?

Probably less than 1/4 wave in terms of the difference of velocity factors.  That is, the "electrically short" criterion, applied to a difference in velocities rather than one absolute velocity.

Note that the impedance, and coupling (to a given I/O structure), of higher modes need not be as good as the intended mode.  Ideally, TE2 (pictured above) has zero field in the middle, so a coax-to-waveguide adapter, perfectly centered, will not couple into that mode.  However, some energy inevitably ends up coupled, due to imbalance in the system: mechanical errors, resistance, etc.

I am also guessing that things would get funny around bends, particularly non-ideal ones, with much more sensitivity then the regular wave guide bending rules of thumb. Do typical coaxial to launcher section adapters tolerate it, or would you need a special launcher even if you decided to misuse the waveguide (assuming the coaxial cable and coaxial connector is capable of supporting the frequency).

Yes, bends are always a modest source of s12.

I am starting to think that this is basically also true for coaxial cable that is wrong (i.e. passing 10GHz on thick coaxial meant for 1GHz)?

Yes, coax has higher TE and TM modes, as well as a TEM00 mode (i.e., DC-light, no lower cutoff).

Tim

[CopperCone]

This is interesting, not sure if it relates I need to think about it. That is dielectric optics.

The only kind of dielectric I have seen other then in coaxial is the lens on a horn antenna. Not sure if they put em in waveguides for whatever reason, other then RF transparent ones to act as a lid (I used saran wrap)

I find it fairly bizarre. It makes me think of quantum tunneling. Like there is coupling between the two paraffin blocks at close distance.

What happens if you put a RF probe between the blocks? It gets detected right? You don't have some kind of bizarre teleportation happening do you?

does the sideway plane wave thing described in classical evanescene occur because atoms and their various forces/fields are round in space so you get some non dead on hits?

[ejeffrey]

Evanescent coupling and quantum tunneling are basically the same thing.  They are both consequences of fields (either EM fields or a quantum wavefunction) that can't go to zero sharply at a barrier.

[radar_macgyver]

@TheUnnamedNewbie gave a nice summary of the standard modes in a rectangular waveguide. For a given frequency and size of waveguide, evanescent fields will be set up when the input frequency is less than the cutoff of a given mode. Since evanescent waves do not propagate, they don't transmit energy through the transmission line and will appear as a high insertion loss. Referring to @TheUnnamedNewbie's figure (which looks like it's for WR90 waveguide), at ~13 GHz, one would expect TE10 to propagate, while TE20 would create an evanescent field which decays rapidly with distance. At 15 GHz, some energy would propagate through TE20, although most would still be at TE10. The propagation velocity difference between the TE10 and TE20 component would cause constructive/destructive interference along the guide, so that's why the exact frequency response becomes a function of guide length and shows ripples.

Another factor is that the coax to waveguide adapters are designed to launch TE10 since it's the dominant mode. They won't couple TE20 as efficiently, so that's another source of ripple in the insertion loss.

Given all of the above, nobody uses waveguides above their specified cutoff (the region between where TE10 propagates, and where TE20 propagates, with some margin added on both sides).

Here's a reference for the same thing happening in coax when TE11 starts propagating in addition to TEM. TE11 is the dominant mode for circular waveguide. For most cables, the frequency at which this happens is high enough that dielectric losses make the cable useless at those frequencies anyway.

I'll try to get a VNA plot from a length of waveguide when I get to work.

[TheUnnamedNewbie]

Regarding the coaxial higher order modes, I actually made this figure showing an example recently:



The desired mode has no lower cut-off frequency and is what we get when we think in classical two-wire models. But once the size of the coaxial cable is on the order of the wavelength, the outer conductor can start acting as a kind of circular waveguide and we get oddball modes.

As @radar_macgyver said this is generally not too much of an issue for lower-power or lower-frequency systems since losses become so high anyways, however they are the limiting factors for high power or high-frequency applications.

For high power, we are limited by the breakdown of the dielectric. We want a minimum distance for a certain voltage, but making the distance larger makes the outer conductor larger and lowers the lower cut-off of the TE₁₁ mode.

For high frequencies the problem is that the size of the cable has to be so small that they become stupendously difficult to manufacture. This is one of the reasons why 1 mm coaxial connectors costs hundreds if not thousands of euros/dollars/GBP a piece (and why we need a 1 mm connector for those frequencies in the first place, and cannot use something that doesn't break when looking at it the wrong way). 1 mm connectors were originally rated to go to about 110 GHz though I believe Keysight is pushing them to 120 GHz in their latest extenders (cost of one of those: 90-110 k USD). Anritsu recenetly released the first system witch uses a 0.8 mm connector, and that can go to 145 GHz if I remember correctly. I've seen them, and those things are so ridiculously tiny it is amazing they can be made in the first place (and they are working on even smaller connectors to push coaxial past 200 GHz).

[CopperCone]

I never understood why they are so difficult to manufacture, they have CNC mills, lathes, grinders and lappers that can do microns I am pretty sure (call them finishing tools), I think its the lack of demand honestly because someone had to buy a grinder or lathe and the ROI on it is mad long since the volume of sales is so low and they want to match the ROI on their other business models and add a premium to it since someone in sales decided to add a 'this shit is high tech as fuck we are awesome' fee (usually someone gets a dopamine rush patting themselves on the back before this happens).

Someone will just bottom line the numbers and say if the margin is not at some percentage, we are not doing it, despite the fact that its a secure investment, there is no industry competition likely, there is no expected end time at which the investment stops being profitable, there is no excessive management demands, it improves the company portfolio, improves company/employee pride (ok maybe not too much of this one or you get chronic under-payers like LM or supposedly NASA), improves the environment/allows for green advertising/publicity/public statements, improves quality and reliability, decreases maintenance demand, decreases sensitive to other market performance, improves company R&D capabilities in a nonlinear manner.. they just look at some number and say no despite there being like 20 hard to calculate upsides to doing it that don't look good in some quarterly review

I have some friends that work as technicians in certain expensive industries (nuclear manufacturing related) and I am not particularly impressed at where the cost comes from.. i.e. using highly inferior heat treating equipment to save 20% on something that costs 3-5 million and runs for 10 years while delivering 1/2 the quality and tons of process issues that lead to stock being thrown away, paying manufacturing employees low (keeps truly skilled workers out).. I get told things like some of the cost choices that are made lead to seriously expensive bottlenecks and chokes, then they just decide to overcharge to cover the 'unexpected' losses, ship low quality product that fits on their quality curve just barely if you look at it using old gauge equipment from a sharp angle slightly drunk without parallax correction, etc.

But if someone wants to link me a super cool and complicated manufacturing video of a APC connector or 1.1MM connector to prove me wrong and make me feel better about the microwave industry......

[TheUnnamedNewbie]

So let me get this straight, just a day ago you were having difficulty understanding the concept of higher order modes, and now you are claiming the people designing connectors have no idea what they are doing and are charging too much?

There are companies that do nothing except manufacturing connectors. They know exactly how to get their costs down, because if, say, Rosenberger can suddenly give me the same performance connector H+S can get me for 20% less cost, guess who I'm gonna order my connectors from...

I would suggest reading over this, it might clear some reasons up: http://www.mwrf.com/passive-components/reaching-beyond-100-ghz-coaxial-connectors

[CopperCone]

what does mechanical manufacturing have to do with understanding high order modes? The end product needs to conform to dimensions and surface finish. That's it. You don't need the RF engineer to do anything other then to design dimensions and determine acceptable tolerances for manufacturing to use for quality purposes. I would be shocked if they are asking someone with a PHD in RF physics to figure out what kind of saw to use and to estimate cost of running some kind of precision machine shop!

In fact most places I know of, you don't really do much more then that. The EE gives a schematic to some guy that does his own thing with a pick and place, then its done and you do something else.

I guess you also need a mechanical engineer to look at how things flex and if something is too thin. But I don't see why the overall designer would have anything to do with manufacturing.

[CopperCone]

Also I did not mean to offend people working for the RF industry, maybe I am a bit bitter because I bought these seemingly simple connectors like APC-7 for fairly ridiculous prices, especially considering that I got a whole fucking 30 pound spectrum analyzer made by HP for the price of a handful of connectors that weigh a few grams. It's hard not to feel that someone made a (advanced) burglary machine.

I mean I feel the same way about stuff like Swagelok. There is a reason they have 500 competitors like Hylok, Hoke, etc. If you look at a swagelok valve manufacturing video you kind of wonder what you are paying for.

https://www.bestvaluevacs.com/swagelok-1-4-fnpt-316ss-ball-valve.html?gclid=EAIaIQobChMI8KWb1N7a2wIVimSGCh0Fww2rEAYYAiABEgIVtvD_BwE

40$ max come the fuck on.  Especially after you have been making them for god long how long... its not like the machinists are getting exponential raises or the lighting in the factory is 1 billion lumens (watch their manufacturing video lol, 'we are not a dank ass shit hole like other places, we have lighting,you saw that other guy? that guy runs his business by torch light out of a cave, and we have electricity too, they power the mill with malnourished child slave labor'). I think they hired those employees from a different hell dimension given the kind of perks they are talking about.

[TheUnnamedNewbie]

CopperCone, I would like to appologise for my tone, I overreacted because I was frustrated at something unrelated to this forum. I will preface this by saying that I am not a connector designer, so take what I say with a grain of salt and citation needed.

The tolerances on these connectors are very tight (especially on the APC-7, which is the best of the best in it's frequency range). This is why you need to use a torque wrench to tie most RF connectors down, for example.

To give you an idea of the tolerances: There is a standard from the IEEE, 287-2007 - IEEE Standard for Precision Coaxial Connectors (DC to 110 GHz), that lists the dimensions for precision connectors. the 3.5 mm connector, which is the ''high performance'' version of the trusty SMA connector, has a center pin tolerance of 2 um, and a center bore diameter of 3.5 mm +- 2.5 um. The APC-7 even has a center bore diameter tolerance of 0.5 um! Just touching it with your fingers will heat it up enough to bring it out of spec, as will the dust or oil from your fingers on the front surface. I'm no ME, but I think it should be clear that that is not a level of quality you can achieve without some special tools and techniques.

Surface roughness is another often underestimated problem - Due to skin effect, the currents, especially those at a few gigahertz, flow almost exclusively through the top few tenths of a micrometer, and as a result, surface imperfections behave like slots and inductors. This will introduce reflections (more and more significant ones as we go up in frequency) and ruin the performance of the connector, meaning you can't just take a connector as it comes from a lathe and go with that.

If you see the microwavesRF link I posted earlier, you can see how much effort has to be put into these tiny connectors, with holes a few tens of micrometers in diameter.

And connectors are really only rated to a number of matings (SMA, to my knowledge, is only rated up to a couple dozen due to how the enter pin mating works), and thus they lose value.

[CopperCone]

Hmm those specifications are impressive but again i am not sure how difficult they are to achieve. A micrometer will measure to something like 0.1um for a good one.

A good lathe can do something like 0.0001 inches accuracy without requiring anything special then facilities temp control, good tool maintence and cleaning. This machine would be used for a rough cut probobly. Its about 2.5 microns.

You would need something like system c input on a finishing machine maybe to do the final accuracy cut. Not sure, this is where itgets trickysince you want that nice finish, so its plausible they use a system b capable lathe to 0.0001inches to do a rough cut then put it on some sort of grinder to hone it in and get the surface finish you want.

I think a facility that does just rf connectors would probobly not havy heavy wear from hogging giant billets so you dont have that old shit about people yelling that cost goes astronomical because of difficulty, you can do precision on worn equipment if you do frequent measueing to adjust for ware etc.

Im not impressed by the prices down to0.0001 inches. I have not explored the sub micon domain yet but i have seen videos of finishing tools that can pull that off.. And machines dont typically ware much if they are just doing a grind of say 0.00005 inches, so the connector ware should be low unless someone there decides to machine 50cal gun parts during lunch on the machine that typically does something super dedicated.

I am just in general less impressed by rf connectors and valves then something like high end tturbine design or semiconductor manufacturing equipment

I cant prove it yet but i suspect that unscrupulus vendors can hide behind a decimal point while it would take worn machines to justify.

Something i notice about human nature. People hate paying for

1) sandpaper (you get super worn shit being used)
2) capacitors (reforming  )
3) drillbits
4) laser diodes. I heard some stories about a fab having some serious process issues because for some reason someone refused to replace a certain diode that was due.
5) bearings
6) rags
7) table covers (hello there cardboard)
cleaning supplies (wipe it down you dont need soap)
9)plating bathes/cleaning bathes
10) automotive fluids. Your either religious or just dont do it.
11) air or water filters

I see people rich and poor doing this. Most of the time you get away with it but it makes me suspicious of certain industries efficencies.. I noticed when the above points are cheaped out on things and people enter... Bizzare.. Modes of operation.

Another big one is scotch brite pads.. Even when they completely lose their texture some people will scrub away 3 times longer rather then cutting a new piece then make a thing out of doing the dishes inefficently/demand dicksucking

Precision manufacturing is on my adgenda and i will one day make an air bearing lathe to enter this void so i have an idea of whats going on..

I did not think the specs were single digit micron though.
But what i mean in my rant is that human nature seems particularly unsuited for the type of work that kind of micron level finish requires and we might be paying for inefficency

Typically you have a time tradeoff for surface finish but the right tool is important. I suspect that certain tools that deliver better finishes have more heating and ware and the choice is materials dependant but so long you control your tool shape and stock material composition and temper the results should be very repeatable.

I know i sound super cynical but factories are super easy to fuck up with bottlenecks and tool maintence, and it creates hard to sort out chaos so people can hide in it and customers are no longer in the best interest. Granted obviously you can feel that my allegiance with the industry and goverment is not completely anarchistic like some buisnessmen, i like to see science move folward and i dont like technological bottlenecks forming because researxh efforts are pulled in different directions due to cost or see researchers developing their own equipment in parallel with major developmental efforts to save money. This causes data problems and such since they often lack experts for calibration, standardization etc

[T3sl4co1l]

I must say, I'm impressed how, no matter how many times you've been corrected by factual information, you still return to your primary refrain of loose speculation, without deference to those who actually have to practice their craft.

Tim

[CopperCone]

Ok bro, you must live in la la land if you think all the sales people and managers wanna bring you the lowest price and further science

Trades people are mad anarchistic. Wont say shit if you can possibly cut into their cash flow. Look at the patent office. Then realize thats no where near the end of it.

All that shit needs oversight and evaluation. Just like anything else they might not be holy.

[TheUnnamedNewbie]

A good way to show you that there must be more to it is that when you go to Chinese manufacturers of those connectors (and I'm talking proper connectors like 3.5 mm, 2.92 mm, etc.., not the attempt-at-SMA you find for a dollar on aliexpress and that will pretty much ruin any test port you connect them to - lets not even get started about their actual performance).
Even they, who usually manage to do everything for 1/10th the cost in the standard european/US markets, don't manage to produce 2.92 mm cables that I can buy for under a few hundred dollars, or 3.5 mm adapters that cost less than 35 dollars.

[CopperCone]

I read somewhere in this RF forum that the Chinese actually buy European cable and do the assembly themselves or sell it for more then whole sale prices, they don't exclusively produce things, they can buy bulk and resale just the same, but I never read if they make the connector or not, just that they resell/crimp cables

I figure maybe they can machine their own crimp tools and use cheap labour to bring the prices down a tad

The cable to me is more technologically impressive then the connector honestly, since the dielectrics are complicated and its a fusion of a few different materials not just a precise shape. I think plastics generally are more of a bitch to work with since their gummy and soft... metal is really repeatable. The connector has a bit of plastic though

I wonder how much an effect alloy composition and temper has on precision connector manufacturing. I wonder if it becomes kind of like wood where you have grain knots or some thing that makes it difficult to automate well.

[CopperCone]

Is a microwave oven cavity designed around specific transmission modes? Its essentially an oversized waveguide compared to the feed.

Would a 5ghz feed require a smaller cavity to cook food for any reasons?

It seems to me that above a certain point you get basically chaos and it does not really matter so long you disperse it with thefan.

How many transmission modes does the cavity need to support before you can use a fan to bounce the signal around inside to make for even heating? Can a rule of thumb be made like something along the lines of it needs 6 times specified waveguide dimensions?

Are there tendancies for things like dead spots in certain dimensional regions where you need some kind of threshold size? Do you eventually reach a multimode region where its chaotic or do you have bands forming in certain dimensions (i.e. there is some kind of coefficent or even sequence) that is notable?

[T3sl4co1l]

How many transmission modes does the cavity need to support before you can use a fan to bounce the signal around inside to make for even heating? Can a rule of thumb be made like something along the lines of it needs 6 times specified waveguide dimensions?

1 / (how even you need it)

Note that the load is a key part of absorbing standing waves.  Without a load, it's all standing waves, no matter the geometry or fan, and the poor magnetron sweats away.

Tim

[CopperCone]

What do you mean by 1/how even you need to heat it?

I don't get the direction and magnitude of the proportion from this statement. I assume larger is more even from my conceptual understanding.

I don't really understand what would happen if I placed a hot dog in a wave guide thats capped for instance. I assume it would get spot heated according to the standing wave pattern? I think I am getting hung up on if there is some kind of convergence (like with a sequence) between the dimension of the heating cavity and the wavelength/launcher dimensions. Like oscillation or divergence or convergence pattern? Are there ratios that will end up doing weird shit periodically, at the right dimensional ratio, so you can say it has a kind of relationship like some kind of oscillating series with a scaling factor?

by weird shit I mean something like total internal reflection in optical design, where the right angle makes for interesting results. Something to caution during design.