Electromagnetic field theory. Q and A

[davefoc]

Vitnir,
The questions that you've raised have both simple and complex answers and involve a number of issues some of which involve disputed conclusions.

The simple answer as I understand it:

Most limits on RF exposure today are based on the idea that the radiation is non-ionizing and the only biological effect is heating. There is controversy as to whether this is a valid assumption. The bottom line is that despite many tests, no test has ever definitively proved that there is a biological risk associated with non-ionizing radiation. This site provides more discussion of this topic :
http://www.fda.gov/cellphones/qa.html#25

The FCC sets electric field strength, magnetic field strength, power density and absorpition limits on the radiation from an RF device. The FCC limits are similar to but not identical to European llimits.

The limits are given in this site:
http://www.fcc.gov/Bureaus/Engineering_Technology/Documents/bulletins/oet56/oet56e4.pdf

The power density limit for a cell phone that operatates at 900mHz (about the frequency of most cell phones) is a little less than 1 mw/CM^2 based on the way I read the table from the site referenced above.

The absoprtion limit is based on the SAR (specific absorption rate). The US limit for SAR is 1.6 watts per Kg. I don't understand what a SAR is. Perhaps somebody could talk about what it is and how it's measured.

The power density of the sun is about 1.4Kwatss/m^2 or .14watts/cm^2 according to this site:
http://hypertextbook.com/facts/1998/ManicaPiputbundit.shtml

However solar radiation is obviously at a much higher frequency than cell phone radiation and there are differences in the effects of the two kinds of radiation. For instance, I think a much higer percentage of the cell phone radiation is absorbed than the solar radiation. Clearly a lot of the solar radiation is reflected or we wouldn't be able to see.

You also asked about base stations in your question. Base stations vary from cell phones in several ways as to the radiation that a person is likely to absorb from them.

1. The operate at much higher power than the cell phones.
2. If one is exposed to base station radiaition it is likely to be over a longer period of time as the base station operates more or less continuously.
3. The exposure to base station radiation is likely to occur at a much greater distance from the antenna than exposure to the cell phone radiation.

Some of the sites listed above deal with these issues a bit but the bottom line seems to be that the risks associated with base station radiation are very small even if you are living fairly close to one.

 

[Rolfe]

I see Kumar has started his thread.

I suppose some idiot will be unable to resist replying....

Rolfe.

 

[davefoc]

My apologies to MRC for not waiting for his answer before I posted, I didn't realize he was writing a response at the same time I was,. I was hoping that MRC might be able to expand a little bit on areas that I don't understand.

One of the issues I was hoping that MRC could expand on was the idea of near and far field radiation. I am afraid I don't know enough here to ask intelligent questions but I will try.

As I understand it far field radiation is the term used to describe radiation where the ratio of the electric and magnetic field amplitudes have reached the characteristic ratio for the transmitting medicum. The ratio is measured in ohms and is about 300 for a vacuum (and about that for air).

A number of questions:
Are antennas designed so their impedance matches the air impedance?

What's going on in the near field as the ratio between the magnetic and electric fields transitions to that of the transmitting medicum?

Is it right that in the near field energy can be intercepted in such a way as to effect the transmitter like the coils of a transformer but once the wave as transitioned into a far field wave the transmitting device is unaffected by the receiving device (unless the receiving device reflects some part of the energy back at the transmitting antenna)?

 

[MRC_Hans]

davefoc:
My apologies to MRC for not waiting for his answer before I posted, I didn't realize he was writing a response at the same time I was,. I was hoping that MRC might be able to expand a little bit on areas that I don't understand.

You are welcome, this is a joint effort, and I think your post was a good expansion.

One of the issues I was hoping that MRC could expand on was the idea of near and far field radiation. I am afraid I don't know enough here to ask intelligent questions but I will try.

Q: As I understand it far field radiation is the term used to describe radiation where the ratio of the electric and magnetic field amplitudes have reached the characteristic ratio for the transmitting medicum. The ratio is measured in ohms and is about 300 for a vacuum (and about that for air).

A: Correct. [/blue]

A number of questions:

Q:Are antennas designed so their impedance matches the air impedance?

A: Not necessarily. Impedance matching is a question of efficiency of energy transfer. It is preferable if the antenna is matched to the air (~300 ohms), but it is essential that it is matched to the transmitter. Thus various practical considerations lead to the use of antennas with other impedances. Also, for long wavelengths, it may not be practical to build a half-wave antenna, so lower fractions are used. Likewise, directional antenna designs often give other impedances.

Q: What's going on in the near field as the ratio between the magnetic and electric fields transitions to that of the transmitting medicum?

A: Within the near-field, the electrical field and magnetical field are still separate (or separatable). This is because there is still capacitive and inductive coupling to the antenna.

Q: Is it right that in the near field energy can be intercepted in such a way as to effect the transmitter like the coils of a transformer but once the wave as transitioned into a far field wave the transmitting device is unaffected by the receiving device (unless the receiving device reflects some part of the energy back at the transmitting antenna)?

A: Yes, except that it is not only a transformer (inductive coupling) but also a capacitor (capacitive coupling), thus energy is coupled directly between the transmitter and receiver, and as this is essentially a bidirectional coupling path, the receiver will load the transmitter directly.

Once totally out of the near field (the boundary is by no means a sharp one), the waveform has "left" the transmitter, and the transmission path is now one-way. Thus, the receiver is no longer influencing the transmitter (except as you note, in the case of reflecting a significant signal back, but that should really be seen as a different signal).

Edited to add: As already mentioned, the transition to far field is not a sharp boundary. As you increase the distance, the direct coupling becomes less and less significant, untill you deem it unimportant. Depending on type of antenna, this happens at a distance of a half wavelenght to several wavelengths.

Hans

 

[Vitnir]

I asked two doctors in my department and they didn't feel the analogy between the sun and microwaves were so out of order. But I understand and agree with your counterarguments, however it wasn't exactly a scientific paper I wrote and given the space constraints in a letter to the editor I felt it was adequate. The analogy was based on that sunexposure gives heating effects to the brain causing a sunstroke.

And I didn't mean a mobile phone mast, I meant that the base unit you have in your home when you have a wireless phone can emit the same power as a mobile phone, about 250mW.

 

[Kumar]

I see Kumar has started his thread.

I suppose some idiot will be unable to resist replying....

Rolfe.

As one is unable to resist seeing my posts...

Just to expand this post to a materiastic level:-

Any possibility of physiological adaptation in this respect?

Adaptation

(1) Evolutionary adaptation - a genetically based characteristic expressed by a living organism. Particular adaptations found in populations become frequent and dominant if they enhance an individual's ability to survive in the environment.

(2) Physiological adaptation - change in an organism's physiology as a result of exposure to some environmental condition.

Adaptive Radiation

The evolution of a number of new species from one or a few ancestor species over many thousands or millions of years. Normally occurs after a mass extinction creates a number of vacant ecological niches or when a radical change in the environment produces new ecological niches.

 

[MRC_Hans]

I asked two doctors in my department and they didn't feel the analogy between the sun and microwaves were so out of order. But I understand and agree with your counterarguments, however it wasn't exactly a scientific paper I wrote and given the space constraints in a letter to the editor I felt it was adequate. The analogy was based on that sunexposure gives heating effects to the brain causing a sunstroke.

And I didn't mean a mobile phone mast, I meant that the base unit you have in your home when you have a wireless phone can emit the same power as a mobile phone, about 250mW.

Well, I guess I'm getting too scientific about it, then. OK a wirelss phone. Since you are almost per definition much farther away from the base station than the phone (why else have it?), it is unimportant. To speculate about possible adverse effects of such cmall power levels only makes sense if you have it close to your body.

Hans

 

[MRC_Hans]

Kumar, I have asked you twice nicely to take your debate posts elsewhere. Now: Get the heII out of here!

... Did you understand that better?

(yes, it seems I have to read you posts here to try to keep you from hijacking the thread)

Hans

 

[Kumar]

I see Kumar has started his thread.

I suppose some idiot will be unable to resist replying....

Rolfe.

Mr.Hans,

I think Rolfe is not on your ignore list as either you have not seen the above post or just ignored. If you want nicely, I should Get the heII out of here!, Pls resist & oppose this type of posting in future.

I have lot more better works to do.

Bye.

 

[Pragmatist]

The absoprtion limit is based on the SAR (specific absorption rate). The US limit for SAR is 1.6 watts per Kg. I don't understand what a SAR is. Perhaps somebody could talk about what it is and how it's measured.

The SAR is simply a measure of power absorption in a standard quantity of tissue (usually 1cc). The formula is: SAR = (E² * conductivity)/density where E is the electric field strength. Because a standard sample size is used, the length over which the force of the E field acts is fixed and therefore it can be simply equated to a voltage. So you would measure it by measuring the voltage developed across a given standard sample (between two opposite faces of a cube 1cm apart) in response to a given radiation stimulus. The tissue conductivity can be calculated (from empirically developed formulae) as can the tissue density.

The SAR basically assumes that the E field will generate a current in the tissue (depending on the E field strength and the impedance of the tissue - which is reflected in the conductivity) and that current may generate power in the tissue. In reality the quantities (such as the tissue conductivity) are complex (as in complex numbers) and so the current may actually be reactive not real and hence no actual power may be generated. So quoted SAR's are usually just the real part of the complex result.

It is called a "rate" because it is effectively the ratio of power to tissue density, no "time" is involved, so the word "rate" seems a little inappropriate here.

As I pointed out in the Bioelectromagnetics thread, the E field is simply the most convenient parameter to measure. It does not imply that a given absorption is solely due to E field exposure, all that matters is the overall power developed in the tissue (you could just as easily work that out via the current induced by a magnetic field).

Hope that helps.

 

[Vitnir]

Precisely, my second point in my letter was that not many have their base units taped to their heads so in normal use radiation from them would rediculously low.

Incase anyone can read swedish check it out here

 

[Vitnir]

Interesting about the SAR-calculation. I always assumed that it was measured by using a doll with temperature sensors.

 

[Pragmatist]

My apologies to MRC for not waiting for his answer before I posted, I didn't realize he was writing a response at the same time I was,. I was hoping that MRC might be able to expand a little bit on areas that I don't understand.

One of the issues I was hoping that MRC could expand on was the idea of near and far field radiation. I am afraid I don't know enough here to ask intelligent questions but I will try.

As I understand it far field radiation is the term used to describe radiation where the ratio of the electric and magnetic field amplitudes have reached the characteristic ratio for the transmitting medicum. The ratio is measured in ohms and is about 300 for a vacuum (and about that for air).

A number of questions:
Are antennas designed so their impedance matches the air impedance?

What's going on in the near field as the ratio between the magnetic and electric fields transitions to that of the transmitting medicum?

Is it right that in the near field energy can be intercepted in such a way as to effect the transmitter like the coils of a transformer but once the wave as transitioned into a far field wave the transmitting device is unaffected by the receiving device (unless the receiving device reflects some part of the energy back at the transmitting antenna)?

Here is an idea I have about near/far field radiation which may help, it's not rigorous but I believe it's basically correct.

The impedance of free space is 376.73 ohms. That is the fixed ratio of the E to H fields in a classical electromagnetic wave in free space. In QM EM fields are described as superposed states of photons (which are quantum entities and hence their exact structure is unknown).

So we have two different descriptions of radiation. We have the classical electromagnetic wave theory a la Maxwell, and then we have the QM photon theory. I believe the easiest way of understanding it is to consider the classical (EM wave) case as being the macroscopic manifestation of the QM effects. For example, in general dynamics, Newton's laws are generally true in a macroscopic sense, but at the quantum level we start to run into problems. However, to all intents and purposes what we observe in the "normal" world is in accordance with Newton's laws and we can use them as an excellent approximation for all practical purposes in everyday situations. In the same way the classical EM field theory is an excellent approximation in the everyday world to the GROUP macroscopic behavior of a collection of quantum entities called photons.

Now if we have an emitter (such as an antenna), that emitter, strictly speaking is emitting photons. But close to the antenna, the actual spacial density of photons is very high and as such the quantum peculiarities tend to be masked by the greater macroscopic effect of having many entities packed into a small volume of space. As you move away from the antenna, the photon density falls off with distance (inverse square), and therefore you eventually reach a point where the photons are "rarefied" sufficiently for their individual quantum nature to become more apparent (i.e. the "field" no longer behaves as a single macroscopic entity, but more like a group of individual photons).

So an individual photon behaves like a wave with impedance of 376 ohms, but the "near field" of the antenna behaves more like separate electric and magnetic fields in varying ratios depending on the method of generation. For example a dipole antenna will typically have an impedance greater than that of free space in the near field (i.e. the E field to H field ratio will be higher than 376). But a "magnetic" loop antenna will do the opposite and will typically have an impedance LESS than that of free space in the near field (the E field to H field ratio will be less than 376).

So in a very rough sense, you can consider a true (far field) EM wave as being analogous to a photon, but a near field is a macroscopic entity composed of a grouping of photons that tends to behave more "classically" than "quantumly". Therefore a near field is more like a classical "continuous" field, and the far field is more like a stream of individual quantum photons.

To make it clearer still, you can consider an "electric" or "magnetic" field to be artifical entities that are specific manifestations of particular photon combinations. The photon is the basic unit, but when there are many of them packed together, then macroscopically, the group as a whole can behave in a manner we call an "electric" or "magnetic" field.

I don't know if that makes things any clearer!

 

[Pragmatist]

Interesting about the SAR-calculation. I always assumed that it was measured by using a doll with temperature sensors.

You could do it that way. All that matters is that you somehow measure the actual power generated in the tissue. So if you have some material that is a good approximation to the electrical characteristics of tissue then you could measure the temperature rise and that would give you an idea of the power being generated in that material. However, that is a very crude method and would not be used for precision measurements, just rough estimates.

I believe in practice its is more usual to use a dummy head to generate a map of (projected) field or current intensities and patterns that you would expect in a real head, and then to use the figures from that in conjunction with real tissue data to calculate it. However, as always, techniques can vary from lab to lab. I don't know if there is some generally accepted standardized procedure.

 

[davefoc]

MRC,
Thanks for the response, that helped me understand it the near and far field concepts better.

Pragmatist,
Thanks for your posts. Your post about the near and far field went to one of the things I was trying to understand a bit.

OK from a quantum mechanical standpoint we have a mass of photons being emitted that somehow sum to the particular ratio of E to H fields that are observed.

So what's going on here as the E to H field ratio gradually changes to the ratio in free space? Are individual photons changing?

It's intriquing that when the photons are intercepted in the near field the emitter is affected and when the photons are intercepted in the far field the emitter isn't effected.

The idea of how the photons sum together is a little confusing. Somehow there must be a lot of synchronization in the way they are generated or you would think that they might just cancel themselves out. But they aren't completely except in the case of coherent emissions. Any thoughts about this. I have never quite gotten the concept of coherent light and how it is more in sync than normal light.

 

[69dodge]

I'm pretty sure the whole near field / far field thing is a classical phenomenon (i.e., a consequence of Maxwell's equations). The photons of quantum mechanics are their own can of worms.

 

[Zombified]

Well, classical Maxwell's equations are an approximation. In some cases, the approximation is imperfect, such as when the density of photons is low. It's analogous to saying the kinetic theory of gases is an approximation that's imperfect for extremely rarified gases, where individual collisions become interesting.

For low energy photons, the waves simply add, whether you're talking about classical Maxwell's equations where you're talking about E/H fields or the probability densities in the case of quantum mechanics. In a quantum field the probability no longer means a single particle, rather, you have a probability of finding some number of particles in a given region.

But in both cases, the principle of superposition generally holds, so that photons don't interact with each other. Now, in non-coherent light, each photon/wave has a slightly different frequency and phase, so the waves add up more or less to noise. Picture the ripply surface of a sea; you could express it mathematically as a sum of many, many perfectly sinusoidal waves of different frequencies (in different directions) and phases, but put together it's just noise. By comparison, coherent light is like a single massive wave: all the components have the same frequency and phase, so they all add up. In classical terms, the E and H fields are strong at the peaks; in quantum terms, the probability distribution of number density has a high expectation value (that is, you're likely to detect many photons in a given region near a peak).

At sufficiently high energies, or for sufficiently precise measurements, the principle of superposition breaks down slightly. Photons can interact with each other if they have enough energy - if you bang two together with at least 511MeV each, you can produce an electron-positron pair. At lower energies, that pair is only a virtual pair that's reabsorbed by re-emitting photons again, and has a low probability, but its there. As a result, there is a slight amount of photon-photon scattering. But for normal optical photons, this scattering is pretty much undetectable.

 

[Pragmatist]

MRC,
Thanks for the response, that helped me understand it the near and far field concepts better.

Pragmatist,
Thanks for your posts. Your post about the near and far field went to one of the things I was trying to understand a bit.

OK from a quantum mechanical standpoint we have a mass of photons being emitted that somehow sum to the particular ratio of E to H fields that are observed.

So what's going on here as the E to H field ratio gradually changes to the ratio in free space? Are individual photons changing?

It's intriquing that when the photons are intercepted in the near field the emitter is affected and when the photons are intercepted in the far field the emitter isn't effected.

The idea of how the photons sum together is a little confusing. Somehow there must be a lot of synchronization in the way they are generated or you would think that they might just cancel themselves out. But they aren't completely except in the case of coherent emissions. Any thoughts about this. I have never quite gotten the concept of coherent light and how it is more in sync than normal light.

You're welcome!

The photons don't exactly SUM, it's a superposition of quantum states which is much more complicated than a simple sum. And there is a bit of a chicken and egg situation here. We're accustomed to thinking of photons as consisting of E and H fields, but in QM as I understand it, the E and H fields are actually the result of photon interactions or more fundamental QED fields. In that sense it doesn't make sense to speak of the E and H fields of a photon - however, it's the only representation I personally know that describes the impedance of the photon....confusing! You have to remember that what most people are taught about photons etc., traditionally has been classical field theory. It's rather like Newtonian mechanics. You can model an atom using mainly classical Newtonian type mechanics (Bohr did it), but the classical model, although it gives accurate answers in some respects is always inadequate overall, which is why new quantum descriptions were developed. In the same way, models of the photon based solely on classical ideas of E and H fields are somewhat inadequate.

Anyway, to put it simplistically, near the antenna, the (many) photons are tightly superposed and the resultant "fields" don't have to have exactly the same impedance as an individual photon. But the antenna is transmitting a spherical wavefront (ignoring complexities of polar response), and as the photon flux heads outwards the same number of photons emitted in a certain limited range of time are distributed over the surface of an ever expanding sphere, so the individual photons are further apart and so their superposition is less obvious. There comes a point where the individual photons are not tightly superposed and their individual impedance (that of free space) becomes more obvious. So the reason the E/H ratio or impedance appears to change as you head outward from the antenna is because the further out you go, the more individual "photon like" the whole thing appears, whereas at close range the composite "mass" of photons appears to behave more like a classical "field". They are one and the same, there is no actual change of impedance at the individual photon level, all that changes is whether the photons appear more as photons or more like a field (a composite mass of superposed photons). To use an analogy, you can imagine a large ball of sticky rice compressed together at some point in space. It doesn't appear to be "ricelike", it's just a white sticky amorphous mass. But if you could make it expand outward indefinitely, eventually you would find it breaking into recognisable individual grains of rice. And the behavior of a single grain may seem to be somewhat different in isolation than the original mass of compressed sticky rice. So the further you travel away from the origin the more obvious it is that the original mass was simply a load of individual grains of rice. In the same way, the further you travel outward from the antenna, the more obvious it is that the "fields" near the antenna are composed of individual photons. In the same way that individual grains of rice don't change when a rice ball is expanded, so individual photons don't change as they head out from an antenna. All that changes is the level of interaction between them as they get further apart. So in effect, when we measure the E and H fields all we are really measuring is a composite property of a "mass" of photons in close proximity.

The interaction between the "fields" and the emitter are not that mysterious either if you get the above idea. Near to the emitter, the superposed group of photons is more tightly coupled to the emitter than the photons further out. So there is more chance of a "backlash" that affects the emitter, NEAR the emitter, than further out. Think of it like a water tap. Water is running out of a tap. If you stick your finger in the flow of water after it has left the tap and when it is 100 yards from the tap, there is no apparent effect on the flow AT the tap - the water just flows around your finger. But if you stick your finger directly underneath the spout of the tap, then you will get a spray, and the change in pressure due to the obstruction will cause some pressure to "back up" inside the tap. So a disturbance in the flow NEAR the output of the tap will have more of an effect on the tap, than a disturbance in the flow at a significant distance away.

What you have to remember is that photons in (relative) isolation behave like photons...but a large number of photons in close proximity behave like a classical field or a classical wave. That is overly simplistic, but it is a difficult area to describe in simple terms.

Now, as I said before, the superposition of photons near an antenna in the near field is not a simple sum. It's not easily predictable in simple terms, although (in theory) one could presumably solve the composite wavefunctions of a mass of superposed photon states. In practice it is much easier to simply change the model and start thinking of "fields". Think of it this way - if someone throws a snowball at you, it's much easier to calculate its trajectory using classical approximations that it is just a single generic ball of "stuff" rather than trying to solve the individual trajectories of every single particle it's composed of. How the photons are "synchronized" near an antenna is rather like asking how the water molecules are "synchronized" in a snowball! Yes, there is probably a unique answer, but in general it's practically impossible to work out. What is important to remember is that the group behavior is more than just a sum of the parts. A snowball is just water, but it doesn't ACT like water...until it melts (i.e. the molecules become more unpacked).

As for coherent light, the simplest explanation is the classical one that you can consider it as a mass of waves. The more in phase each wave (that comprises the whole) is, the more coherent the light. Normal light can be considered as a collection of waves with a large variation in the individual phases, so the sum of the amplitudes of the whole (adding the waves) is much less than the sum of the individual peak amplitudes. In a laser, you excite a series of molecules or atoms into similar high energy states and then cause an "avalanche" of them to drop nearly simultaneously into the normal state, releasing a large number of similar or identical waves ALMOST simultaneously. Since there is much less time variation in the individual emissions, there is a much lower overall phase difference between the individual waves and so their sum is much closer to the theoretical maximum (which would be the absolute sum of all the peak ampltitudes simultaneously). So "coherence" refers to "coherence in time (or phase)". The intensity of the light is of course a function of the composite amplitude of all the waves, so the more coherent the individual waves, the more intense the light. It is impossible of course to achieve 100% coherence, but very high levels of coherence can be achieved and this is what we call a "laser beam".

I mentioned waves not photons, but of course the waves are simply trains of photons...as above, when many photons are in close proximity they behave more like a composite group (a classical wave) than as individual particles. But it would be a mistake to think of a photon as simply a kind of "wave", the quantum object referred to as a photon is really much more complex than just a simple wave - in theory at least.

The phase of any individual photon starts at zero, the instant it is emitted, so the general phase coherence of a series of photons depends on when they are emitted in relation to each other. It's also important to realise that photons in opposite phase don't actually "cancel" each other out, but what specifically happens in any individual case depends entirely on the specific circumstances and so it's difficult to make any generic prediction. It makes sense when you think about it, because any photon has energy, and if you have two photons with equal energy (say each with an energy of "E" units) and they are in antiphase, then if they cancel, you would have the sudden disappearance of 2E units of energy! Which is of course absurd, the energy has to go somewhere. You might want to look up the interaction of soliton waves in water on Google, there are similarities with photon behavior - you can set up two separate soliton waves in water and crash them into each other head on - they simply pass through each other and carry on, on their individual paths without apparently affecting each other (except at the instant they meet). That's not to say that photons ARE soliton waves but the analogous behavior can be instructive in forming some sort of conceptual vision of how photons behave.

I hope that's clearer, this is very difficult to describe in simple terms!

 

[Zombified]

Actually, superposition is just a simple sum, whether you're talking about classical E fields or quantum mechanical states. While the interpretation and a few mathematical details (like how phase gets handled by complex numbers in quantum mechanics) are different, for large numbers of particles, it works out the same.

 

[Pragmatist]

Well, classical Maxwell's equations are an approximation. In some cases, the approximation is imperfect, such as when the density of photons is low. It's analogous to saying the kinetic theory of gases is an approximation that's imperfect for extremely rarified gases, where individual collisions become interesting.

For low energy photons, the waves simply add, whether you're talking about classical Maxwell's equations where you're talking about E/H fields or the probability densities in the case of quantum mechanics. In a quantum field the probability no longer means a single particle, rather, you have a probability of finding some number of particles in a given region.

But in both cases, the principle of superposition generally holds, so that photons don't interact with each other. Now, in non-coherent light, each photon/wave has a slightly different frequency and phase, so the waves add up more or less to noise. Picture the ripply surface of a sea; you could express it mathematically as a sum of many, many perfectly sinusoidal waves of different frequencies (in different directions) and phases, but put together it's just noise. By comparison, coherent light is like a single massive wave: all the components have the same frequency and phase, so they all add up. In classical terms, the E and H fields are strong at the peaks; in quantum terms, the probability distribution of number density has a high expectation value (that is, you're likely to detect many photons in a given region near a peak).

At sufficiently high energies, or for sufficiently precise measurements, the principle of superposition breaks down slightly. Photons can interact with each other if they have enough energy - if you bang two together with at least 511MeV each, you can produce an electron-positron pair. At lower energies, that pair is only a virtual pair that's reabsorbed by re-emitting photons again, and has a low probability, but its there. As a result, there is a slight amount of photon-photon scattering. But for normal optical photons, this scattering is pretty much undetectable.

Ah, you posted as I was composing my last reply, so I didn't see it until after I posted - your version is more concise!

Actually, superposition is just a simple sum, whether you're talking about classical E fields or quantum mechanical states. While the interpretation and a few mathematical details (like how phase gets handled by complex numbers in quantum mechanics) are different, for large numbers of particles, it works out the same.

Agreed, but I was trying to convey (probably badly) the idea that it's not just a simple sum of a single amplitude and single phase. What I mean is that although it IS a simple sum in a more rigorous mathematical sense, it's a composite of simple sums of many different parts that are different in "kind" so to speak, i.e. a sum of amplitudes, phases, polarizations etc., and that the result is not necessarily obvious from simply imagining one or two individual (and identical) waves. What I was trying to do was convey the idea for lay readers that very simplistic pictures don't necessarily help.

For example if I add two waves each with total amplitudes of "1", then the result is not necessarily a single wave of amplitude "2", the actual result depends on the relative phases/frequencies/polarizations etc. In that sense it's more a "simple sum of complex parts", rather than a "simple sum", period, if you see what I mean.