[Bored chemist]

I didn't hear about any law of physics, according to which it is impossible to concentrate EM radiation with a lense or concave mirror - can you please tell me, what exactly is that law?

I never heard of such a law either.
It seem that you made it up.

Why did you introduce it?

[Bored chemist]

near-field effects and not electromagnetic waves.

Please explain how the near field  propagates without using EM waves.

[Bored chemist]

It's only a matter of scale - the bigger is the radius of a lense/mirror, the more EM waves will be concentrated in one point, resulting in higher intensity... What makes it theoretically impossible?

Actual science, rather than your straw man version.
You may find this educational.
https://what-if.xkcd.com/145/

[Bored chemist]

In shortcut

Do you mean "in short"?

[Bored chemist]

In shortcut, you will be able to see your bacteria in great details, if the background light will have blue color. However light with a green color will giive you much worse results and internal structures of that bacteria no longer will be visible as clarly as with the blue light. And with the red light, the entire bacteria will become barely visible (or even completely invisible if the wavelenght will get large enough in relation to the size of observed bacteria)... Shortly speaking, the shorter will be the wavelenght (higher frequency) of light used by your microscope, the better results you'll get...

In fact the resolution is less than the wavelength
"When optimally used, confocal microscopes may reach resolutions of 180 nm"
so, as seems to often be the case, you are flat out wrong.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4379090/

[Bored chemist]

Inside a 1D tube, which is 100cm long, you can succesfully trap as much as 1 photon of 100cm wavelenght and/or 2 photons at 100//2cm wavelenght + 3 photons at 100/3cm wavelenght + 4 photons at 100/4cm wavelenght and so on.

An interesting conjecture.
Consider my microwave oven.
It runs at 2.4GHz with a corresponding wavelength of about 12.5 cm

Each photon carries about 1.6E-24 Joules.
It is rated for 900 watts.
So it produces about 5.6 E 26 photons per second.
and it's about 15 inches wide
So the cavity is 3 wavelengths long.

According to you it can therefore contain 3 photons of microwave radiation at any given time.

But in reality, about 10^27 photons pass through it every second.
The transit time is about 1.25 nanoseconds for light to travel from one side to the other.

So, at any one time, there must be about 7E15 photons in it.
And yet, you say there can only be 3

Can you explain the disparity?

[Bored chemist]

Only this way we'll be able to get a standing wave, which can be amplified through constructive interference with itself

Why do you keep going on about amplification?

If you impose unwarranted additional conditions then you change what can be done.
But they aren't relevant or helpful.
I'm talking about a box, not a laser.

[Bored chemist]

Sadly, everything I see, is some guy, who claims to have authority in science, while making claims which are 100% false.

Look away from the mirror and tell me why your microwave oven doesn't take roughly the age of the universe to heat a baked potato.

[Bored chemist]

Because it just so happens that I'm a guy, who doesn't believe in your supreme authority

No, because you only believe in your own supreme authority- even when you have been shown to be foolishly wrong- for example, about diathermy and FM radio.

As a consequence you miss the fact that I'm not really claiming much authority at all.
I'm just pointing out what science actually say.

[CrazyScientist (OP)]

Inside a 1D tube, which is 100cm long, you can succesfully trap as much as 1 photon of 100cm wavelenght and/or 2 photons at 100//2cm wavelenght + 3 photons at 100/3cm wavelenght + 4 photons at 100/4cm wavelenght and so on.

An interesting conjecture.
Consider my microwave oven.
It runs at 2.4GHz with a corresponding wavelength of about 12.5 cm

Each photon carries about 1.6E-24 Joules.
It is rated for 900 watts.
So it produces about 5.6 E 26 photons per second.
and it's about 15 inches wide
So the cavity is 3 wavelengths long.

According to you it can therefore contain 3 photons of microwave radiation at any given time.

But in reality, about 10^27 photons pass through it every second.
The transit time is about 1.25 nanoseconds for light to travel from one side to the other.

So, at any one time, there must be about 7E15 photons in it.
And yet, you say there can only be 3

Can you explain the disparity?

It's because the photon number is a function of probability and not the amplitude of electric/magnetic componentds. In a resonance cavity of a microwave oven you can in one time fit 6 photons in the n-3 mode of microwave frequency - but only if the standing wave criteria is met (proper volume of cavity). Thing is, that those 6 photons merge into 3 photns of the same wavelenght, but with twice as big electric/magnetic amplitude due to constructive interference of EM waves.

Of course all of this doesn't involve photons at much shorter wavelenghts, like the visibe light - in the microwave owen cavity there can be a LOT of them...

[Bored chemist]

It's because the photon number is a function of probability and not the amplitude of electric/magnetic componentds.

You seem to be trying to say that having more photons does not correspond to a higher amplitude of the EM radiation.

That's not plausible.

You say that you can't have more than n photons in a box if the length of the box is n times the wavelength.
But When I point out that, for a microwave oven cavity n is 3 but you have about 10^16 photons at any time, you post a reply that simply makes no sense.

Are you able to clarify it?

[Bored chemist]

Thing is, that those 6 photons merge into 3 photns of the same wavelenght, but with twice as big electric/magnetic amplitude due to constructive interference of EM waves.

That's just not possible,
The energy of a photon is given by e=hf.
So, if you combined 2 photons into one, you have twice the energy and you would have half the wavelength.

This is the way in which most green "lasers" work.
They frequency double the IR emission at 1064 nm to produce 532 nm green light.

[CrazyScientist (OP)]

It's because the photon number is a function of probability and not the amplitude of electric/magnetic componentds.

You seem to be trying to say that having more photons does not correspond to a higher amplitude of the EM radiation.

That's not plausible.

What I'm trying to say, is that increase/decrease of the amplitude doesn't affect the number of photons traaped in a cavity - and yes: it's very much possible

[
You say that you can't have more than n photons in a box if the length of the box is n times the wavelength.
But When I point out that, for a microwave oven cavity n is 3 but you have about 10^16 photons at any time, you post a reply that simply makes no sense.

Are you able to clarify it?

It's because the owen is a 3D object - I'm speaking about 1 dimension only (momentun/propagation)

Thing is, that those 6 photons merge into 3 photns of the same wavelenght, but with twice as big electric/magnetic amplitude due to constructive interference of EM waves.

That's just not possible,
The energy of a photon is given by e=hf.
So, if you combined 2 photons into one, you have twice the energy and you would have half the wavelength.

https://asktowolrd.com/physics/how-is-it-that-increase-in-amplitude-of-electromagnetic-radiation-results-in-increase-in-number-of-photons/

"Strictly speaking, the amplitude of the field (meaning the operators of the electric and magnetic fields, see here) and the photon number do not commute. Thus, the claims that increasing the amplitude increases the number of photons or vice versa are technically not correct."

Are you saying that your authority is superior, compared to those people?

This is the way in which most green "lasers" work.
They frequency double the IR emission at 1064 nm to produce 532 nm green light.

Ahh - so it workis in the n2 mode.

Now tell me, if that laser emits as well twice as many photons at 1064nm? No? Hmm, I wonder, what happened with them...? Didn't they turn into photons at 532nm, and increae the power output for that wavelenght?

[Bored chemist]

It's because the owen is a 3D object - I'm speaking about 1 dimension only (momentun/propagation)

OK, 3 dimensions raises the total of 6 photons, compared to the real value which is about 10^16
Feel free to "solve" this problem with your view on how the world works.
Just remember that I will apply whatever process you need, to the case of the mirrored sphere.
If you can explain an arbitrarily large number of microwave photons in my oven, then , by the same process, I can get an arbitrarily large number of photons into the mirror sphere.

And even if you can't explain it, I will simply point out that I can get a lot more than 1 or 2 photons in a cavity and you are wrong.

Are you saying that your authority is superior, compared to those people?

I can't access that page, so I can't comment on them.
But I say that the conservation of energy has more authority than they do, and what you propose, breaks it.

Ahh - so it workis in the n2 mode.

That's meaningless.

Now tell me, if that laser emits as well twice as many photons at 1064nm? No?

I think it's probably more like 200 or 2000.
The process is rather inefficient.

I wonder, what happened with them...?

This
https://en.wikipedia.org/wiki/Second-harmonic_generation

increae the power output for that wavelenght?

No. The power out at 532 nm is something like 100 times less than the power in at 1064nm.
Your silly idea would break the conservation laws.

Incidentally, if you were somehow right about 2 photons magically  combining to make a "superphoton" of some sort, then it wouldn't matter.
The combination would- by the mass and energy conservation laws- have twice the mass of an ordinary photon.
And if I continued to add photons to it it would get more and more massive until it became a black hole.

Your idea- if it wasn't nonsense- would make the "kugelblitz".easier to make- no massive mirror ball needed. You seem to think the photons will somehow "stick" together.

[CrazyScientist (OP)]

I didn't hear about any law of physics, according to which it is impossible to concentrate EM radiation with a lense or concave mirror - can you please tell me, what exactly is that law?

I never heard of such a law either.
It seem that you made it up.

Why did you introduce it?

But in this case It was you who said, that it's theoretically impossible, to create a black hole by concentrating EM waves in one point of space with a lense or concave mirror - but it's  not that I disagree. In fact from the very beginning of this thread, I completely dismissed the idea of BH creation due to a high mean photon number in a given volume of space..It was you, who from the very beginning insisted some highly doubtful ideas about making a kugelblitz by trapping EM radiation...

near-field effects and not electromagnetic waves.

Please explain how the near field  propagates without using EM waves.

Like this:

Personally I believe that electric, magnetic and gravitational fields emerge from a single mechanism - maybe it's space-time curvature or/and differentials of energy states...(?)

In shortcut, you will be able to see your bacteria in great details, if the background light will have blue color. However light with a green color will giive you much worse results and internal structures of that bacteria no longer will be visible as clarly as with the blue light. And with the red light, the entire bacteria will become barely visible (or even completely invisible if the wavelenght will get large enough in relation to the size of observed bacteria)... Shortly speaking, the shorter will be the wavelenght (higher frequency) of light used by your microscope, the better results you'll get...

In fact the resolution is less than the wavelength
"When optimally used, confocal microscopes may reach resolutions of 180 nm"
so, as seems to often be the case, you are flat out wrong.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4379090/

This is exactly, what you said: "So, if I have an object the size of a small bacterium for example- about 0.5 micron then you can get just 1 photon of visible light into it"

0.5 micron is 500nm - green & blue have shorter wavelenghts while reds have them longer - and since "In fact the resolution is less than the wavelength" is actually a true statement, I was once again absolutely right

Thing is, that those 6 photons merge into 3 photns of the same wavelenght, but with twice as big electric/magnetic amplitude due to constructive interference of EM waves.

That's just not possible,
The energy of a photon is given by e=hf.
So, if you combined 2 photons into one, you have twice the energy and you would have half the wavelength.

Hello - didn't you hear about such thing, like constructive interference?

In the n-3 mode of resonant cavity (microwave owen) due to constructive interference you get a standing wave with the same wavelenght and with twice as high amplitude of the EM oscillation - but yet in a standing wave you ALWAYS have a definitive number of given wavelnghts (photons) in the resonant cavity volume. In shortcut: in the n-3 cavity mode 6 "injected" photons merge into 3 photons with 2x higher amplitude

It's only a matter of scale - the bigger is the radius of a lense/mirror, the more EM waves will be concentrated in one point, resulting in higher intensity... What makes it theoretically impossible?

Actual science, rather than your straw man version.
You may find this educational.
https://what-if.xkcd.com/145/

It's funny, how I many times I said all of this in this thread - you can't get a BH by increasing the intensity/amplitude of a EM wave... Maybe you didn't notice, but my proposition of making a BH by using a giant lense, was rather sarcastic - it's impossible to keep increasing the energy level of a system, without using some external force, to increase the frequency of trapped radiation - AMEN.

Are you saying that your authority is superior, compared to those people?

I can't access that page, so I can't comment on them.
But I say that the conservation of energy has more authority than they do, and what you propose, breaks it.

Weird - I don't have any problems with the access... But if not, then what about this one:
https://physics.stackexchange.com/questions/47105/amplitude-of-an-electromagnetic-wave-containing-a-single-photon?noredirect=1&lq=1

Equivalently, as @user1504 put it
The electric and magnetic field operators do not commute with the number operator which counts photons."

Still no access? Opening your mind a bit might help...

Incidentally, if you were somehow right about 2 photons magically  combining to make a "superphoton" of some sort, then it wouldn't matter.
The combination would- by the mass and energy conservation laws- have twice the mass of an ordinary photon.
And if I continued to add photons to it it would get more and more massive until it became a black hole.

No it wouldn't - just just like yu wouldn't get a BH by using a giant satellite dish or a lense. It's exactly the same principle, based on increasing the intensity of radiation of a specified wavelenght due to constructive interference of EM waves

Your idea- if it wasn't nonsense- would make the "kugelblitz".easier to make- no massive mirror ball needed. You seem to think the photons will somehow "stick" together.

Just like that?

Because it's exactly how I think photons "stick" together in a standing wave...  Is it really for you such an unimaginable idea?

It's because the owen is a 3D object - I'm speaking about 1 dimension only (momentun/propagation)

OK, 3 dimensions raises the total of 6 photons, compared to the real value which is about 10^16
Feel free to "solve" this problem with your view on how the world works.
Just remember that I will apply whatever process you need, to the case of the mirrored sphere.
If you can explain an arbitrarily large number of microwave photons in my oven, then , by the same process, I can get an arbitrarily large number of photons into the mirror sphere.

And even if you can't explain it, I will simply point out that I can get a lot more than 1 or 2 photons in a cavity and you are wrong.

I really appreciate all your efforts to appear as someone with actual authority in the discussed field of science - I find them very adorable... But still, before you convince me as for your superior knowledge and understanding of cavity QED, maybe let us hear, what some other people have to say about the discussed subject - I really recommend you such doing sometimes such activity, instead arbitrarily trusting in your own superiority...

Imaginge, that I don't have to "solve" this problem with my view on how the world works - some people did it already for me. Here's the basic knowledge regarding EM radiation trapped in the microwave owen
https://www.academia.edu/4621788/physics_of_microwave_ovens

But I recommend this one:
https://www.kth.se/social/files/5cb029dd56be5b49476c1e27/Lecture%202%20Photon%20Statistics.pdf
This part is most important for this subject:

Fock state
The Fock or photon number state |𝑛̂𝑖
⟩ results directly from the quantization of the
electromagnetic field, since the Fock state is the eigenstate of the photon number operator
𝑛̂𝑖
:
The eigenvalue ni of the photon number operator describes the number of photons in a
specific mode i. The probability PFock(n) to find ni photons in one mode is either 1 for n = ni or
0 for n ≠ ni. This is a special characteristic of the Fock state: The photon number is fully
determined. Thus. the probability distribution of the photon number follows a δ-distribution.
The expected value of the photon number in a Fock state is equal to the number of photons
in the state:
For the Fock state the variance is therefore:
The Fock state fulfills the inequality ∆𝑛 < √𝑛, showing a variance smaller than the Glauber
state. Such sub-Poisson statistics cannot be described by classical electromagnetic theory;
thus such light is classified as non-classical light. The figure below shows the photon number
distribution for two Fock states. Light emitters with a Fock state n = 1 are called single photon
sources, since they can only emit one single photon at a time

But I REALLY recommend you to read it whole - it's actually quite short and even I am capable to comprehend it and see, how niecely it confirms most of my claims from this thread...

TBC

[Bored chemist]

But in this case It was you who said, that it's theoretically impossible, to create a black hole by concentrating EM waves in one point of space with a lense or concave mirror

That is impossible.
But I asked why you made up this nonsense.

I didn't hear about any law of physics, according to which it is impossible to concentrate EM radiation with a lense or concave mirror - can you please tell me, what exactly is that law?

Nobody had said you can't concentrate light with a lens or mirror, had they?.
Please explain where you got that silly idea from.

[Bored chemist]

TBC

It's probably better if you don't continue until we fix the problems with your current understanding.

[Bored chemist]

This part is most important for this subject:

No it isn't.
This is.
"The Fock state fulfills the inequality ∆𝑛 < √𝑛, showing a variance smaller than the Glauber
state. Such sub-Poisson statistics cannot be described by classical electromagnetic theory;
thus such light is classified as non-classical light. The figure below shows the photon number
distribution for two Fock states. Light emitters with a Fock state n = 1 are called single photon
sources, since they can only emit one single photon at a time."

because it makes it clear that Fock states are "special".
There's no reason to say that that model applies to the photons in a box.

[Bored chemist]

Like this:

So... with a wavelength and frequency.
But I asked you to show "how the near field  propagates without using EM waves.".

So, I'm asking you again - though, perhaps you would like to simply accept that near and far field optics still use waves.

[CrazyScientist (OP)]

But in this case It was you who said, that it's theoretically impossible, to create a black hole by concentrating EM waves in one point of space with a lense or concave mirror

That is impossible.

Cool - Then we both agree, that it's impossible to create a BH by concentrating a huge number of photons in the frequency range of visible light in a small volume of space

But I asked why you made up this nonsense.

It's because concetrating a large number of EM waves at a specific wavelenght in a small volume of space with a lense or concave mirror doesn't differ that much from trapping a large number of EM waves at a specific wavelenght inside an optical cavity. Both actions lead to the increase of radiation intensity (power/m3) - with optical cavities producing EM radiation, which is coherent and with lenses/concave mirrors producing one that is non-coherent. However this difference shouldn't matter, as it's possible to reach the same level of energy dnsity in coherent and non-coherent radiation fields

Since the beginning of our discussion, you're trying to imply, that inside a perfectly reflective optical cavity, uniform EM field can collapse gravitationally and become a BH if the intensity (photon density) in a given volume of space becomes high enough - energy density can reach the same level for coherent and non-coherent radiation, so theoretically you should be able to achieve the same result by concentrating a large number of photons in small volume using lenses and concave mirror. Keep also in mind that efficiency of optical lenses and concave mirrors increases with it's spatial volume. If you still have (use?) an old school lamp TV, then break it apart and use the thick 21'' slab of glass from it's screen to concentrate sunlight into a point on a sunny day - I can bet, that the "power output" in the dot of concentrated light, will be just as high (or even higher) as for most of modern high-powered lasers. Tell me please, why can't it be possible, to create a Kugelblitz by concentrating the light of a spiral galaxy with a lense of similar radius? Imagine, that light emitted by 250 billions of stars is being concentrated in a 1mm dot of sunlight. I'm sure that you can calculate the radiative power of that dot - and Im sure, that it will be A LOT. Enlighten me, why can't that dot of concentrated sunlight turn into a Kugelblitz at some level of photon density?

Nobody had said you can't concentrate light with a lens or mirror, had they?.
Please explain where you got that silly idea from.

Sure - just after you explain me, why can't we use a lense or concave mirror to increase the density of photons to a point, when a BH is created, while being able to achieve such result using an optical cavity.

Like this:

So... with a wavelength and frequency.

Ooof!

By making this deifinitive-looking statement, you did actually a pretty bad "oopsie!", which once again disqualifies you as someone, who suppose to have some/any authoity in the discussion about EM fields&waves.

Near fields doesn't affect the wavelenght nor frequency of EM waves. Where did you got such suprising and revolutional idea? I know - it came probably from the self-imposed knoledge about always being right in everything what incudes actual knowledge of modern science. Don't tell me  that it can actually work for actual scientists...?
I mean you don't need a Phd in physics, to paste "near field" in google search and check out first couple results, like this one.

https://en.wikipedia.org/wiki/Near_and_far_field#Near-field_characteristics

And now I have a small challenge for you: find anything about the near field propagating with wavelength and frequency of EM waves...Or even propagating at all...

Sure, you might find there such words like: "wavelength" and "frequency", but I want you to show me the part, in which it's being stated that near fields propagate using wavelengths and frequencies of EM waves as a carrier. This is your chance - let me feel your absolute authority by giving me one practical example that might finally give some evidence to the "(1)-Law of You Being Always Right ", which you're seem to constantly invoke, when it comes to showing me any "scientific evidence" to support your baseless claims.

No luck? I wonder why... Maybe it's because (1) is for you an arbitrary law, that is always valid in each possible case of scientific discussion - so you don't see any logical sense in fact-checking your own claims. What for? There's no need to confirm, that you are as always completely right or to verify once again, that all who disagree with you, are as always completely wrong about everything what might contradict the (1) Law.

Sure, it's a free world - you can freely believe in whatever BS you can possibly make up and be happy about it, but for someone, who doesn't apply the Law (1) in his everyday life, it doesn't look perfectly normal, when some guy from internet forum claims to have the authority, to disprove articles from Wikipedia with his own, completely made-up claims, that mostly don't make any scientific sense to people other than himself.

But I asked you to show "how the near field  propagates without using EM waves.".

It does such magic by being constantly "suspended" around a source of EM radiation (antenna) and not propagating at all...

For some reason, you seem to propose here a model of near field and EM waves, where the cause-effect relation is directly opposite to the currently accepted model... Near field doesn't use the EM waves to propagate - It's the EM waves that CAN (but doesn't have to) propagate in the near field, which surrounds a source of EM radiation. EM fields around antennas don't propagate - they are always "hanging around" a source of radiation making a EM field, characteristic only to that source. You can't use EM waves to move a near field from point A to point B, but you need to move the antenna...

And if anything, it's the intensity/amplitude, that is being affected by the near-field in EM waves which propagate near the source of EM radiation:

So, I'm asking you again - though, perhaps you would like to simply accept that near and far field optics still use waves.

Sorry to dissapoint you, but you're not a Jedi master and you're not capable of forcing me to accept statements which I consider to be incorrect, just by telling me to do so.

Near field is a local phenomenon and it doesn't use EM waves to propagate through space - however near field can affect the amplitude of electric/magnetic oscillations in EM waves which are propagating near a source of radiation.

Next time, instead of The Force, you should maybe try using some more dramatic measures, like magical incantantations or a voodoo doll. Try reciting: "By my will, I command you to respect my authoritaaa...!" at least 13 times, while jumping on one leg inside a burning pentagram - just don't forget to inform me, that you put a spell on me (or just send me a recording of the ritual)...

This part is most important for this subject:

No it isn't.
This is.
"The Fock state fulfills the inequality < , showing a variance smaller than the Glauber
state. Such sub-Poisson statistics cannot be described by classical electromagnetic theory;
thus such light is classified as non-classical light. The figure below shows the photon number
distribution for two Fock states. Light emitters with a Fock state n = 1 are called single photon
sources, since they can only emit one single photon at a time."

because it makes it clear that Fock states are "special".
There's no reason to say that that model applies to the photons in a box.

Of course, that Fock state IS special - because photons trapped in a reflective cavity IS a special case of EM radiation. Most of actual physicists would say, that there's no such thing as "stationary photon" or a rest frame for EM wave - unless they're not up-to-date with the recent trends in modern physics or they're not speciallized in the field of cavity QED...

To get the Fock state, you need to satisfy couple special conditons - you need to have a source of radiation emitting EM waves at one specific wavelenght and a cavity with size compatible with that wavelenght. But exactly because of this, Fock state is the most "pure" state of trapped radiation and is being introduced in the first order in most of publications regarding quantum optics and cavity QED - like this one:

Quantum Optics in Cavities and the Classical Limit of Quantum Mechanics
https://www.iimas.unam.mx/barberis/davidovich_elaf_1998.pdf

Generally, one can't discuss the theory of optical microcavities without speaking about the Fock states and you will find this term in most of sources, when it comes to cavity QED.

TBC

It's probably better if you don't continue until we fix the problems with your current understanding.

I bet you would love me to stop exposing the fact, that your self-imposed authority isn't necessarily based on your knowledge of the discussed subject. Problem is, that I try to base my understanding on actual sources and not on someone's self-imposed authority - so maybe it's not my understanding, which in this case should be fixed.

Let's  begin for example from your statement regarding number of photon photons in a cavity and the intensity of trapped radiation - as you seem to think that you can't change the field intensity without changing the photon number in the cavity. Let me show you, that this is not true and that those values are independent from each other - i.e. you can change the amplitude of electric/magnetic oscillations in a standing EM wave without changing the number of photons inside the cavity.

Here's a nice article: Filling a cavity with photons, and watching them leave https://physics.aps.org/articles/v1/39

And here's the important fragment:

Moreover, similarly to the cavity used by the CNRS group, excitations of the resonator are microwave photons. These essentially one-dimensional cavities have a small mode volume, resulting in a large electric field per photon.

So by adding more and more photons at a resonant frequency into the cavity, you don't change the number of photons in the standing EM wave, while increasing the amplitude of it's electric/magnetic oscillations, what results in the increase of radiation intensity.

And as for your claims regarding creation of BHs due to perfect reflectivity:
https://www.tcd.ie/Physics/people/Paul.Eastham/nanophotonics.pdf

...In fact, for lossless mirrors the reflectivity vanishes at the resonance condition δ = 2nπ. This is a surprising result: no matter how good the mirrors, they are effectively transparent at the resonance condition...

So, even if we trap a EM wave between perfect mirrors, there will be a certain "as much" for the increase of it's amplitude, at which the system will reach a thermal equilibrium.

You can't use a beam of photons at the wavelenght of 1024nm, to heat something to 10000°C, no matter how big is the photon density. Since 1024nm is the wavelenght characteristic to blacbody radiation at around 2500°C, to heat something beyond this temperature, you will need to use photons at shorter wavelenghts. By increasing the number of photons (intensity of radiation) at 1024nm in the beam, you will only decrease the time at which this beam will heat something to the temperature of 2500°C.- but not beyond that level