In microwave applications of coax cables and other class of waveguides, there are lots of components whose length is a fraction of wavelength at the operation frequency and still the electromagnetic field inside those components can be written as the superposition of forward and backward modes. These modes are the solutions of a two dimensional eigenvalue problem derived from Maxwell equations. The length of the cable has nothing to do with that. In a particular situation a finite length of cable (or waveguide) is terminated with a specific load. This load acts as a boundary condition for the waves propagating along the direction of the cable (or waveguide). A particular case of microwave cavity is a finite length section of cable (or waveguide) with, for instance, a short circuit at both ends. This structure has onviously a discrete spectrum of solutions. However, if the cavity has to be excited by means of , say, an aperture or a wire loop, for instance, the electromagnetic field inside the cavity is non-vanishing at any frequency and can be expressed as a linear combination of the modes of the structure. For real structures having material losses it is true that wave equations (in the case of a coaxial cable the current intensity and voltage along the line - TEM mode operation - obey one dimensional wave equations that may include a dissipation contribution) might be approximated by diffusion equation. This happens at frequencies low enough to make the inductive contribution in telegrapher's equations negligible in comparison with the resistive contribution. But this situation arises even if the length of the cable is infinite. The general solution of a problem involving a generator, a transmission line and a load can be written in terms of forward and backward TEM waves. If the length of the transmission line is very short the expressions obtained making use of wave description can be simplified and a lumped circuit model (quasi-static limit) can be always obtained. BUT this quasi-static limit depends on the nature of the load and its value when compared with the characteristic impedance of the transmission line (thus, for instance, a short section of coaxial cable terminated with a short-circuit can be replaced by the series connection of a resistor and a coil; the same cable section terminated as an open-circuit is better described using its capacitance; finally, the same section of cable terminated with a resistor having the same value that the characteristic impedance of the cable does not support reflected waves and the system cable+resistor is seen as the resistor alone). By the way, all these concepts are used in a lab work by my students. They use 200 m of TV coax cable and work at frequencies from 1 KHz to 1 MHz (thus, cheap instruments are required). The behavior in the quasi-static limit and the transition to the distributed-circuit limit is clearly seen in the oscilloscope traces. In particular, standing wave patterns can be easily visualized, as well as finite value of the electromagnetic waves speed.

Thank you for the interesting discussion.

Assuming you are analyzing a coaxial cable that is uniform (i.e. no bends or discontinuities), then a rigorous analysis shows this to be true. In a uniform cable, a mode can only accumulate phase in the direction of the cable. This has implications on Maxwell's equations, which can then be cast into an eigen-value problem from which the modes are calculated. There are no approximations to this and it shows discrete modes exist and length of the cable does not enter into it.

Let me add one thing, when a mode is cutoff, it can still "propagate" in the waveguide. It just decays at travels.

If there are any discontinuities along the waveguide, then additional physics kicks in and weirder things can happen that become a function of the distance between the discontinuities.

Here is another interesting thing. I claim that TEM, TM and TE waves do not exist in channel waveguides. In any text I've seen, they just set some field components to zero as a definition and proceed with the analysis. I've never seen any text justify why these can be set to zero. I don't think they can, rigorously. However, it is a very good approximation, but I have yet to see a text identify that as an approximation.

It is pretty well accepted that the modes are independent of length. I think the burden of proof is on your friends to show otherwise.

My understanding for your reference:

We we talk about modes in a coaxial cable, there is an implicit condition: the cable is infinitely long or perfectly matched with impedances at its two sides for any frequency. The best way, I think, is to start from the classical Maxwell's equations applying to a well defined model. The model can be: 1) an infinitely long coaxial cable; 2) or a finite long cable. It is straightforward to see that for the case of 1), there is no low-frequency cutoff. But for the case of 2), there are also boundary conditions at the two sides. It is obvious that the concept of (transverse) modes cannot apply if the wavelength of them are longer than the length of the cable.

@Demin. That's very interesting. Can you expand on reasons why you say transverse modes cannot apply if the wavelength is longer than the length of the cable? Is there a reference you can point me to about that?

@Derek. I have no good reference for this topic under discussion. But I always prefer Robert E. Collin's "Field theory of guided waves" as a starting point. To expand my arguments, I try to call your attention on the analogy of the difference between waveguide (usually assume long or even infinite length in z) and cavity (finite length in z). Adding one cable to a waveguide or cavity just leads to a coaxial cable.

And note that the eigenmodes of a waveguide and cavity have differences in z-direction. The key-point in physics is exactly the boundary conditions in z-direction when we apply the Maxwell's equations to them. Finally, replacing "cavity" by "finite-length cable" and "waveguide" by "infinite-length cable", the above discussions remains unchanged.

In microwave applications of coax cables and other class of waveguides, there are lots of components whose length is a fraction of wavelength at the operation frequency and still the electromagnetic field inside those components can be written as the superposition of forward and backward modes. These modes are the solutions of a two dimensional eigenvalue problem derived from Maxwell equations. The length of the cable has nothing to do with that. In a particular situation a finite length of cable (or waveguide) is terminated with a specific load. This load acts as a boundary condition for the waves propagating along the direction of the cable (or waveguide). A particular case of microwave cavity is a finite length section of cable (or waveguide) with, for instance, a short circuit at both ends. This structure has onviously a discrete spectrum of solutions. However, if the cavity has to be excited by means of , say, an aperture or a wire loop, for instance, the electromagnetic field inside the cavity is non-vanishing at any frequency and can be expressed as a linear combination of the modes of the structure. For real structures having material losses it is true that wave equations (in the case of a coaxial cable the current intensity and voltage along the line - TEM mode operation - obey one dimensional wave equations that may include a dissipation contribution) might be approximated by diffusion equation. This happens at frequencies low enough to make the inductive contribution in telegrapher's equations negligible in comparison with the resistive contribution. But this situation arises even if the length of the cable is infinite. The general solution of a problem involving a generator, a transmission line and a load can be written in terms of forward and backward TEM waves. If the length of the transmission line is very short the expressions obtained making use of wave description can be simplified and a lumped circuit model (quasi-static limit) can be always obtained. BUT this quasi-static limit depends on the nature of the load and its value when compared with the characteristic impedance of the transmission line (thus, for instance, a short section of coaxial cable terminated with a short-circuit can be replaced by the series connection of a resistor and a coil; the same cable section terminated as an open-circuit is better described using its capacitance; finally, the same section of cable terminated with a resistor having the same value that the characteristic impedance of the cable does not support reflected waves and the system cable+resistor is seen as the resistor alone). By the way, all these concepts are used in a lab work by my students. They use 200 m of TV coax cable and work at frequencies from 1 KHz to 1 MHz (thus, cheap instruments are required). The behavior in the quasi-static limit and the transition to the distributed-circuit limit is clearly seen in the oscilloscope traces. In particular, standing wave patterns can be easily visualized, as well as finite value of the electromagnetic waves speed.

Thank you for the interesting discussion.

@Francisco. A very nice discussion, thanks a lot!

The answer of Fransico Medina is very good. The solution for modes in TEM transmission line is a 2D problem and then is independent of the length of the line. I am very surprise to see that I have a quiet same lab for my students!

F.

Thanks to Francisco for very comprehensive answer. I would also like to add that one has to remember that the Maxwell equations themselves depend on coordinate and time and there is no modes unless you move to a frequency domain( or assume monochromatic excitation) and then for some classical geometries obtain the solution represented as a series of modes. Those are very useful for many applications but one always has to remember the modes is orthogonal basis for representing the solution. They will exist, either propagating or evanescent, the question is what contribution gives each of them into the overall solution. The closer those to the scatterer the higher contribution is there.

In the context of the paper itself I would agree that the telegraper's equations themselves within the problem posed contain the constant phase velocity and TEM solution. I would suggest you demonstrate the simulation of a length of transmission line shorter than 2lambda and show the standing wave pattern and the change of the field distribution depending on the boundary condition.

Dear Dmitry, thank you for your clarification. Yes, I completely agree with you. The only exception is the TEM mode for ideal transmission lines (perfect conductors and homogeneous dielectric). In that case the TEM solution can be directly used in time domain problems. This is related to the fact that TEM mode is not dispersive (the speed of the wave does not depend on frequency). You can start from time domain Maxwell equations and find the correct transverse 2D equations for the TEM solution.

Other modes are generally dispersive and are defined in the frequency domain. The 2D eigenvalue equation defining the mode spectrum has to be obtained from the frequency domain version of Maxwell equations (i.e., the Maxwell equations for the Fourier transforms of the electromagnetic quantities). Obtaining information in the time domain requires the use of Fourier transform techniques and the problem is not trivial. Thanks!.

@Francisco. So the original question is: how do we explain it to the skeptic? There are a surprising number of physicists who will say things to the effect that it is unphysical to have a wavelength from here to the moon, in length, and yet which exists on a short transmission line.

What is the best physical picture we can give them to satisfy the paradox they are experiencing?

Supposing physical waves in the quasi-static limit violates at least 5 basic laws of physics including implying infinitely strong black body radiation, see here:

http://arxiv.org/abs/1404.4664

Often it is possible to expand/synthesize states mathematically as the superposition of non-physical states as often done in engineering to simplify calculations. However that does not make those non-physical components physical. One of the well-known examples is weighting function description in linear system theory, where the signal is supposed to consist of infinitely short pulses and the weighting function responses are added up at the output, see for example at http://en.wikipedia.org/wiki/LTI_system_theory#Impulse_response_and_convolution

Physically, these short pulses do not exist because that would for example imply hard gamma photon radiation and the like.

We have to be very careful about the physical validity/meaning mathematical treatments. The ultimate judge is always the laws of physics. When the laws of physics are violated, the game is over (at least, for me).

Dear Derek and Laszlo. Maybe I do not completely understand the basic physics behind the discussion. However, it is not a problem for me to accept the existence of REAL electromagnetic waves at extremely low frequencies (thus associated to extremely large wavelengths). For instance, Schumann resonances excited by lightning in the lossy cavity Earth/Ionosphere are known to exist at frequencies of just a few Hertz (100000 Km wavelength). Nevertheless, this is not a quasi-static problem at all since the involved cavity is also huge.

On the other hand, I agree with Laszlo that one must be careful when applying models that might be not suitable for the specific problem under consideration . Coming back to the case of the coax cable, in the low frequency limit the inductive term of telegrapher's equations is negligible in comparison with the resistive term (metal ohmic losses) and telegrapher's equations would lead to a diffusion equation rather than to a wave equation. The cable has to be described as a distributed system (instead as a lumped circuit), but use the concept of traveling waves is not the best model, probably (think about the problem posed by the first transoceanic telegraph cable, where long distances BUT extremely low frequencies were involved). Something similar can be said about electromagnetic field distribution inside good metallic conductors. Classical skin effect can be explained ignoring wave propagation since displacement current inside the metallic conductor is very small in comparison with ohmic current. However, one can start from the full-wave equations (inluding all the terms) and simplify the model without significant lost of information.

A different situation arises when we work with extremely high frequencies, when individual photon energy is relatively large and interaction with matter must be described using quantum electrodynamics, for instance. In those cases we are out of the classical theory and there is no classical way of explaining the physics.

Hi again. I have just started to have a look to the paper mentioned (and co-authored) by Laszlo and I have found this statement:

(i) In cables, wave modes with wavelengths greater than twice their length are forbidden states, meaning that such modes do not exist; consequently there are no waves in cables in the frequency range pertinent to the KLJN scheme.

Could you please clarify this?. In microwave systems there are lots of components having lambda / 4 (at the central frequency of operation), for instance. The behavior of such components is perfectly described by using waves going back and forth (even at frequencies much lower than the one for which the size of the cable section is lambda / 4. I do not understand claim (i).

Thanks.

Francisco

The fact that unphysical mathematical terms can be used for calculations of correct or approximate result does not make them physical. These methods are wide spread and important tools however one has to be careful with the unphysical aspects because one can end with perpetual motion machines and the like.

Note: for example, lambda/4 new medium within or at the end of a large wave space of another medium is totally different from a lambda/4 confined space. (In the first cases above it is a scattering volume or potential barrier depending on the physical model).

The assumption of any wave mode in a confined space of lambda/4 space is violation of all those laws, see the rest of the paper. According to an expert colleague, who is happy with the proofs in our paper, the wave/no-wave issue had been a historical open problem and even Nyquist has missed this one when he tried to explain the Johnson formula or thermal noise (I did not check these but happy to hear it).

Laszlo

Dear Laszlo. I am afraid that I am missing something. Of course, in a lambda/4 closed transmission line section terminated with two short-circuits at both ends we do not have a solution. However, this transmission line section, when shunt-connected to a perpendicular transmission line (in such a way that one of the ends is a short-circuit and the other is directly attached to the other line) is a "transmission line stub" providing a transmission peak for the wave propagating along the perpendicular line at that frequency at which the stub length is lambda/4. The fields inside that stub are essentially the superposition of two propagating TEM waves. (Only in the region close to the junction with the principal line we have many high-order modes operating below cutoff).

In other words, the sentence that I extracted before would be completely right if written, for instance, in the following way:

(i) In cables, SHORT-CIRCUITED AT BOTH ENDS, wave modes with wavelengths greater than twice their length are forbidden states, meaning that such modes do not exist.

Maybe this is enough for the discussion in your paper. But a cable section excited by a generator and terminated with a resistive load, for instance, supports forward and backward waves yielding a standing wave pattern that can be easily verified even if the cable is not lambda/2 long.

Best regards,

Francisco

@Laszlo. Can you also explain what you really mean by "waves." I also do not feel I have completely understood you.

Wave in physics is a phenomenon where the propagation takes place via the wave energy oscillating between two dual forms of energy types with 100% conversion ratio. Examples: elastic potential vs kinetic energy; magnetic field energy vs electrical field energy; etc.

In the short cable at long wavelengths (non-wave limit), the energy-crosstalk between the magnetic field and electrical field is negligible, and each transformed component decays exponentially in time. The magnetic energy and the electrical energy oscillates between the field and the generator, not between each other.

The physical law violation is obvious from the fact that, in thermal equilibrium, each physical wave mode has kT thermal energy (magnetic+electric forms). However, in the short cable at long wavelengths (the low-frequency limit, or quasi static limit), the whole thermal energy in the cable is less than kT. Thus the total energy in the cable is insufficient to supply even a single wave mode. Thus assuming waves leads to law violation; see the details in the paper.

Francisco,

For a simple visual answer, pls see pages 13-15, 17, and 20-22 of this informal seminar's extract:

http://www.ece.tamu.edu/~noise/research_files/No_wave_seminar_web_.pdf

If you have any further doubt please read the thermodynamics in the paper; that is the ultimate proof for no wave modesin the wire in that regime. Thanks/good luck,

Laszlo

@Laszlo. Ok, imagine a bucket of water. I throw a brick into it. There is a big splash and a rich set of waves are formed. I take the Fourier transform and find some wavelengths are larger than the size of the bucket!

A wave component that is much larger than the bucket will look like the surface of the water rocking back and forward, to an observer. When the water level on one side tilts up we have max potential energy. When it tilts down we have max kinetic energy. So it is still a wave by your definition. (In your definition, your requirement for 100% conversion is a bit restrictive as that means any attenuating wave is not a wave by your definition. There's always energy loss to the environment and thus attenuation with, say, acoustic waves.)

The motivation of your paper is to refute that in an electronic security system that these long wave phenomena can be detected. Whether you chose to call the rocking level of the water a wave or not, the fact is an observer can detect that moving level and extract information about it just like for a short wave.

The fact that the motion we see has a wavelength longer than the bucket does not stop us detecting the energy in that motion.

(As for your thermodynamic argument, I would suggest you look at it more closely and list out all the assumptions. You haven't done that yet. If any one of the assumptions is shown not to apply, then the argument is invalid. You have not demonstrated the range of validity of the argument in a rigorous way. At the end of the day such arguments always have to be backed up with experimental verification, to demonstrate there were no unaccounted assumptions in the theory. I do not see that your point is supported by experiment. Francisco has pointed you to many experimental facts that contradict your position. Therefore this points to the need to check your thermodynamics for all the hidden assumptions. Whilst I agree the 2nd Law is never wrong, you have to agree that all theories that rely on it have to also use correct assumptions. If those connecting assumptions themselves are wrong, the 2nd Law itself is not violated. It just means the connecting assumptions need rechecking. Experimental counter evidence, which we have given you in many examples, is a strong reason why rechecking is needed in this case).

Dear Laszlo. Your arguments are quite disturbing and strongly attract my curiosity. Do you mean that we can not solve the generator-transmission line-load problem using propagating waves and applying the boundary conditions at the ends of the transmission line if the frequency of operation is low enough? (imagine the transmission line section is a perfecty lossless transmission line: otherwise I admit that wave equation controling voltage and current along the line should be replaced by a diffusion equation). Thanks.

Dear Laszlo. I had forgotten to say that I agree with you in the fact that, in the quasi-static limit, there is a "separation" of electric and magnetic fields, that is completely true. But there are different quasi-static limits (we must compare the "electromagnetic time" or delay of a wave along the cable with the electrical relaxation time and the magnetic diffussion time in order to predict what kind of limit - magnetoquasistatic or electroquasistatic - is reached at low frequencies). But I can propose you a mental experiment: Imagine that the load is identical to the characteristic impedance of the transmission line. In that case the "time delay" would be proportional to the frequency and the associated speed of the waves would be frequency-independent and equal to c / \sqrt(epsilon_r). Do you agree with this?. This might be wrong in the deep quasi-static limit, but you can measure something like that for a section of cable having an electrical length above, say, lambda / 10. Is this quasi-static enough or you are talking about much lower frequencies?. Thanks again. This is a very stimulating discussion.

@Laszlo. Thanks for very interesting presentation. You are right that working in engineering sometimes one gets used to certain assumptions which leads to omitting important underlying physics. Now I can recall that in near field of antenna we also observe dominance of one energy over the other and then it eventually levels. a similar phenomenon to the one you discussing.

Here's an experimental counterexample in the diagram below. You can reduce the width of a waveguide to get cut-off and so you get an evanescent wave. Moreover, it is experimentally well-known that the evanescent wave transforms into a normal propagating wave when it re-enters the waveguide of the correct width. This is the principle behind an attenuator. So what this means is that even when a wave is cut-off, the evanescence has all the properties of a real wave; the fact that it exponentially decays doesn't remove the essential wave nature. The passive structure, in the diagram below, experimentally proves that.

Laszlo is absolutely correct that one has to distinguish between a mathematical idealization and physical reality: the example he gave was that of the use of a delta function in analyzing an optical system would result in hard gamma ray photons if taken literally. Usually these type of idealizations are taken care of by the actual frequency response of a real system. In the case of Laszlo's gamma ray example, this is taken care of by the upper frequency cut-off of any real system.

In the case of coax, it is already experimentally known there is no low-frequency cut-off. So these two cases are quite different: (a) In the gamma case, no such photons are experimentally detected in an optical system, and (b) in the coax case, frequencies down to dc are experimentally detected by any laboratory network analyzer.

Thus there is a real detectable effect. This then reduces Laslzo's argument to one about terminology, whether this detectable effect should be called a "wave" or not, as far I as can see. Thus it loses its significance in my opinion.

If it is detectable then this means that for the physical layer of some cryptographic system, which operates at these long wavelengths, the eavesdropper can indeed detect them (and this is independent of what Laszlo chooses to name them).

Please correct me if I am missing something.

Dear Dmitry / Laszlo / Derek.

It could be a question of terminology in different branches (or, better, in different contexts). Yo might describe the electromagnetic field around the emitter in terms of an expansion of spherical "waves". An infinite number of those waves would be evanescent and they do not imply phase progression. Thus probably they would not be called "waves" in the context of Laszlo (?). Something similar happens with the example given by Derek. However, in principle, in a coax cable one could excite a single TEM mode. This mode could be reflected by a short circuit located at a distance shorter than lambda / 2 and no hig-order evanescent modes would be implied in the process. However, if the length of the transmission line section is below lambda / 4, magnetic energy stored in the transmission line section would dominate, in such a way that the short-circuited cable section is an inductive-like load. Indeed, if losses are neglected and the length of the short-circuited cable is sgnifcantly smaller (say, below than lambda / 8), the short-circuited cable section could safely be replaced in calculations by a lumped inductor whose inductance is just the p.u.l. inductance of the cable multiplied by the length of the cable. In this description the electrical engineer can see a portion of a pure standing wave pattern close to one of the zeros of such pattern (the point where the short-circuit is located). There are no evanescent waves there. However, I suspect that Laszlo suggests that there is something essentially wrong in this description that I can not see. In my experience any of the quasi-static limits can be derived from the "general full-wave" equations. It is the quasi-static limit what is a simplified model. If instead of having a closed transmission line we work with an open version of it, the quasi-static limit completely excludes the existence of radiation (which might be minimal, of course, if the transmission line length is very short, but existing if classical Maxwell equations prevail). I feel confused but excited about this interesting discussion. The final output would affect to a couple of my lab work for undergraduate students!. Thanks to everybody.

@Derek. I think the evanescent waveguide is inductive and thus is not a good example here as there would be no significant energy conversion from magnetic to electrical. in the context of @Laszlo statement there is no wave.

Still I also do not understand why if the gradient and time derivative are detectable you method should not work.

The discussion is indeed very engaging. I would very much appreciated if @Laszlo could explain this.

I would like to thank everyone I have definitely benefited from taking part.

@Francisco. I think this chain of thought provides quite interesting angle on some of the metamaterial structures, effective medium and small antennas.

@Derek. I have given a thought to your statement that according to Laszlo wave definition the lossy structure cannot carry a wave. I think that by full conversion Laszlo did not mean 100% but that one form of energy goes to 0 and the rest of it with loss subtracted goes to the other form of energy. I think this is the way a loss mechanism is accommodated in the model.

Francisco: No, I did not mean that you cannot calculate correct solutions with wave solutions for infinite cables. You can; this is why I cited the weighting function method above, as a well-known example. What I meant, that those wave solutions are unphysical for short cables even if you can calculate the correct result. Simple example: using the weighting function method of linear response theory, you are allowed to calculate the low-frequency response in a short cable by dividing the input signal into infinitely short pulses, calculate the pulse response against these pulses, and finally summing up all these pulse responses at the output. It is obvious that infinitely short pulses have infinite bandwidth and most of their energy will be in the very high frequency domain; in the quasi static frequency regime only negligible fraction of energy will remain. Thus mathematically these pulses will propagate through the short cable as waves: you can solve the problem by using the wave formalism for each of these pulses and their responses. However, the assumption that these pulses and the related waves are physically there is absolutely wrong: the simplest way to see is the lack of gamma radiation coming from these pulses :-) There are many similar situations in engineering. Mathematics is too rich; many models can be created but a much smaller number of elements is physical; physics will select which elements of meth are physical and which are not.

Dmitry: a) Yes, you are right, of course: the proof that no waves can exist in the cable does not mean that there is no propagation and delay. There is, and it is even measured in our response paper linked above. The fundamental part of the wave debate has nothing to do with the security debate. However, using incorrect equations for the situation (like D'alambert's one) does. Concerning security; our response is here:

http://arxiv.org/abs/1405.2034

b) In the two-dual-energy-definition of waves I assumed lossless situation. In a lossless wave, 100% of the magnetic energy will be converted into electrical energy and vice versa. This does not happen in the quasi-static regime (including the lossless situation) because there are no waves there.

@Laszlo. I see your point with the example of the short pulses. A low-frequency excitation is decomposed into extremely short pulses, each of which gives place to a "dynamic" problem (going even beyond the limits of classical electromagnetism!) while the original problem was strictly quasi-static. This resembles the paradox of why an individual point charge in uniform circular movement radiates but a steady-state dc current in a circular loop only generates a static magnetic field.

However, in the specific problem we are talking about, we are not decomposing the source as the sum of point sources (in time or space domains). We are just solving Maxwell equations. For electrically short lines, depending on the nature of the load, a magnetoquasistatic or an electroquasistatic model can be used neglecting one of the time derivatives in Maxwell equations. I need to think a little bit more on the question. In particular, I wonder what happens in the transition from quasi-static to full dynamic situations. Are there waves or not?. Half and half?. Thanks.

@Laszlo. Do you have a reference for your 100% conversion requirement? If it is a new requirement that you have introduced can you explain the rationale? And in lossy cases how do you modify your definition of a wave?

Also, Laszlo, can you comment on whether you believe your point about waves vs. no-waves has experimental consequences or not within a coax. If no, then is this just terminology? If yes, then please propose an experiment that can be checked.

For example, we all know that holes in a semiconductor are imaginary. They obey equations just like for an electron (but with a different sign and effective mass) and these equations can be experimentally verified.

In the end it doesn't really matter that the holes aren't real. We use the equations as if they are real and we can engineer working devices.

However, there is one thought experiment that shows electrons are real and holes are not: the electron can be removed from the semiconductor, but holes cannot. They do not 'exist' outside, but electrons do.

Can you devise a thought experiment that similarly shows a difference in reality between the short waves and the long 'waves' in the case of coax?

Francisco: Good questions. I was only concerned about the quasi-static limit, where the original debate was (short cable, near-to-zero frequency), where our proof and the answer is solid. But, I think, the answer in general is very clear, even in the wave-situation. In a confined physical system, stationary/steady state waves exist only at discrete frequencies. This includes waves in systems with lossy reflecting boundaries. At high frequency external driving between two discrete wave modes, the observed propagating oscillation, at the first order, belongs to the neighboring discrete wave modes because of the non-zero line width of these modes due to the loss (and the related decay's amplitude modulation). This is a standard physics stuff, see for example, the foundation basic CW laser theories. In the quasi-static limit this argument does not work because the total thermal energy in the cable in thermal equilibrium is less than the energy needed for the existence of a single wave mode.

Derek: this is not a church, thus it is unnecessary to show proper citations in scriptures to support a claim:-)

I agree, in engineering, which does not research the foundations of physics, you may need to seek to show sources. For us, physicists, it is enough to understand the matter and the 100% energy transfer in lossless waves is 2+2=4 :-)

(Think it over: if you analyze the properties of EM waves, you will see it there, too).

Now, I must terminate my further contributions here on RG; I lost already too much time for this; our paper with the proof is published; if there is further objections, please publish them…

All: Thanks for the discussion, it was educational with some really interesting comments.

Laszlo

BTW: I forgot to give the link to the published paper:

http://www.ece.tamu.edu/~noise/research_files/FNL_chen_nowave.pdf

@Laszlo: if you do not have time to follow on the discussion do not worry about, this comment can be useful for the others.

The transmission line section loaded with resistors is not a confined physical system at all. When Laszlo talks about "standing waves" it seems that is thinking exclusively on PURE standing waves (the electric field and the magnetic field minima are zero - or almost zero if there are some losses at the ends -). This is not the general situation, of course. For an arbitrary load having a resistive component there are maxima and minima, but the minima are not zero. This wave (also called standing wave in electrical engineering) transports energy from the generator to the load. This picture is valid even if the cable section is small in comparison with wavelength. However, for extremely low frequencies (20 KHz for a copper cable 2 m long, for instance) the inductance per unit length is not relevant because the associated per unit length impedance is negligible in comparison with the per unit length resistance. In such cases, one could better explain the transference of power from the generator to the load as a diffusion process, such as the conduction heat transfer thorugh a thick wall. In these circumstances, depending on the length of the line, the level of losses and the frequency of interest, it would be possible to use a lumped circuit model to describe the situation. BUT NOT ALWAYS. If the diffusion length is comparable or smaller than the cable length, a distributed model based on a RC transmission line (diffusion equation) must be used. In brief, the loaded transmission line problem with losses can give place to a variety of situations, but the physics is very clear too. From the whole dynamic solution of Maxwell's equations we can obtain all the particular limit cases as well as the transition from the quasi-static regime to the ondulatory (wave) regime. And, for the case of the coax cable, if small perturbations due to higher order modes excited close to the points where the cable is connected to the load and to the generator, Maxwell's equations are the telegrapher's equations because only the TEM mode is present (we are always working well below the cutoff frequency of the first higher-order mode). This is my (provisional) conclusion. :-)).

If by modes, you mean the "modes" that we all know in introductory text books, the answer is a short "No". Modes depend on the cross section and not the length.

@Tayfun. I agree. However, if you go back to the original question, I was asking for the clearest physical picture or demonstration we can use to convince a skeptic (such as Laszlo). Any ideas?

I am unclear as to the argument because "wave" isn't a rigorous term. Are we talking about resonant modes? Here are the truths that I know:

1) energy propagates from source to load along the cable and it propagates at a finite speed--there is a delay.

2) at any impedance discontinuity, there will be reflection of some of the energy.

3) Assuming the source is at frequency f, the physical quantities will all vary sinusoidally in time at this frequency f--this to me is a wave.

4) all physical quantities will vary sinusoidally in x, albeit you will only observe a small fraction (D/lambda) of a sinusoid along the cable at any given time

Thank Francisco for the professional explanation. I think coaxial cable do not have a low-frequency cut-off. Because in my earlier project DC to GHz signals are measured in a coaxial cable system. I am not a physicist but a researcher in electrical engineering. So I can say it can be proved by experiment. Modes depend on the frequency of the incident signals and crosssection but not the length. I used the different transmission line modelling like FDTD, lumped and distributed model with frequency dependend parameters under TEM Modes and Fullwave mode. The simulated results are compared with the measured data. They have the good matching. Wave exists always in the coaxial cable even in the power transmission line with 60 Hz. If the line enough long. Then, we can also measure the phase delay.

A coaxial cable is nothing but a two-conductor transmission line. In such lines the lowest mode is the TEM ( transverse electromagnetic)mode, which propagates as a dominant pure mode at frequencies below roughly f_c= C/2(b-a), where b and a are the outer and inner radii of the cable. Higher TE and TM modes are possible above f_c. Now when length L of the cable becomes small so that L

Yes, but do you have any ideas how to counter the skepticism here for example:

http://vixra.org/abs/1403.0964 ?

I'm looking for a clear demonstration for the skeptic.

Perhaps turning the problem around in a rather simple way for the sake of argument helps:

If we assume a linear transmission line operating in a single mode with a defined Zo and generator and load impedances Z1 and Z2 well defined, then its behavior is perfectly well described by continuous functions from length L=0 to infinity, that is down to L=0 when Z1 and Z2 are simply connected together. This is true also for lossy and dispersive lines of normal physical dimensions.

If the purported wave cutoff would exists when L gets small compared to the wavelength, then there must exist both a mathematical discontinuity in the equations describing the properties of the transmission line as well as experimental evidence for this at the cutoff. As far as I know no such discontinuity or physical cut off mechanism for very small L can be shown to exists.

Therefore it can be clearly argued that shortening L to 0 gives a continuous transition from a bound EM waves in the line into energy bound in the components making up Z1 and Z2. When they are connected all the energy is bound. (Assuming Z2 is not an antenna of course...) Thus the wave is cutoff at exactly L=0. The mode therefore gradually disappears as L approaches 0.

The burden of proof in this case rests solely on who claims such a cutoff effect to exist. The previously mentioned papers claiming the effect do not show any of this to be the case as far as I can tell.

No such cutoff effect can as far as I know be seen empirically or by current advanced numerical modelling used in the field. Perhaps all this stems from misinterpreted coarse mesh models of transmission lines, thereby seeing artifacts resembling a wave cutoff in simulations. Just making the mesh finer should make this disappear into normal continuous behavior.

More complicated situations such as near field problems between coupled antennas in lossy nonlinear media etc can get arbitrarily complex. Then there is no clear cut distinction between transmission lines, components, antennas and the surrounding environment anymore. Many additional physical mechanism become important compared to well behaved transmission lines. This may perhaps also be misinterpreted in this context.

Going back to the original statement: "wave modes do have a cut-off versus the length of the cable."

I am having trouble as to what is exactly being claimed. I agree that no resonant TEM modes exist for wavelengths greater than 2L (or 4L, depending on boundary conditions). But driven TEM modes exist at any frequency, and wave behavior will be exhibited when the transmission line is driven by a wave of any frequency.

@Ronald I think that is the problem with the article. Resonant modes, quantum phenomena and thermodynamic arguments are put forward to make a case for the claim that waves do not exist in transmission lines short compared to the wavelength.

In far as I know this goes against experiments and established theory. A transmission line will conduct the signal the same way regardless of its length, and I find the definition of a wave only being allowed as a resonant system unphysical for the situation in macroscopic transmission lines. By similar reasoning there would be no waves in longer transmission lines that do not match multiple wavelengths, which is obviously absurd. As previously mentioned, it then becomes a question of semantics what You chose to define as a wave.

Also toroid directional couplers work on very short pieces of transmission lines the same as on longer lines. Perhaps this is relevant for the security part of the article which is a bit hard to understand from the article, at least for me. I guess it has something to do with total noise temperature of the cable being constant in the hope that a directional coupler would be unable to distinguish levels of information travelling in different directions.

See THE INFLUENCE OF NON-HOMOGENOUS DIELECTRIC MATERIAL IN

THE WAVEGUIDE PROPAGATION MODES

The propagation constant k for which the existing solutions constitute it’s own values of the way of propagation supported by the waveguide. For any of it’s own value there is an undetermined number of combinations for ω,µ,ε,γ which rouses this way

Ok, we have now written a paper replying to Laszlo's points:

https://www.researchgate.net/publication/260166605

In a nutshell, we believe Laszlo has essentially conflated  standing waves with propagating waves.  This is the only way we can see to understand some of his statements.

Article A directional coupler attack against the Kish key distribution system

Hi Everyone,

Could you please recommend me the basic and best book or Article to understand Coaxial cable?? You could also send me some good materials on [email protected]

Thanks in advance!!