What fraction of long wavelength EM gets through a small hole?

[Buzz Bloom]

Assume a source of EM radiation at wave length λ hits a barrier with a small circular hole of diameter d << λ. What fraction of the radiated power (watts) that hits the hole passes through it? Does it depend on the thickness of the barrier?

I understand that after passing through the hole, the radiation diffracts almost uniformly over the entire
2 π rad² solid angle. For example, if d/λ = 1/30, the power at 90^o is 99.3% of the power at 0^o.

I have made an effort to find a source for this information on the Internet, but I have not had any success. If someone can cite a useful reference, I would much appreciate it.

 

[davenn]

Assume a source of EM radiation at wave length λ hits a barrier with a small circular hole of diameter d << λ. What fraction of the radiated power (watts) that hits the hole passes through it? Does it depend on the thickness of the barrier?

you need to do some reading up on faraday shields

 

[vsv86]

Theory of Diffraction by Small Holes
H. A. Bethe
Phys. Rev. 66, 163 – Published 1 October 1944

Also have a look at extraordinary optical transmission

 

[Buzz Bloom]

you need to do some reading up on faraday shields

Hi Dave:

I did a search on "Faraday shields" and found many links (including Wikipedia) for that phrase as well as for Faraday cages. I did a quick look at about a dozen of them, and none of these links dealt with the question I asked in my post.

These shields/cages are intended for an entirely different purpose (protecting electronics from EM pulses) than the one I am exploring. I am also thinking of a solid flat barrier (rather than a space bounded by some form of chain linked fence material) with a single circular hole. What I have read about diffraction says some of the long wave radiation gets through the small hole, but I found nothing that discussed quantitatively how much. I am trying to understand the math for this basic physics question. So far I have not found any related math.

Regards,
Buzz

 

[slow]

Assume a source of EM radiation at wave length λ hits a barrier with a small circular hole of diameter d << λ. What fraction of the radiated power ...

Would it be useful to change your initial question for another one, for example the following one?

Let us suppose that initially there are no photons, neither on one side of the pierced barrier or on the other. Can you calculate the probability of finding photons on the other side of the pierced barrier, when photons appear on the first side?

 

[Buzz Bloom]

Let us suppose that initially there are no photons, neither on one side of the pierced barrier or on the other. Can you calculate the probability of finding photons on the other side of the pierced barrier, when photons appear on the first side?

Hi Slow:

I confess that I am confused by your alternative problem statement. I may be mistaken, but it does not seem to me that this restatement clarifies the problem. Would you please explain why you think it makes the problem more understandable?

Regards,
Buzz

 

[Buzz Bloom]

Also have a look at extraordinary optical transmission

Hi vsv:

Thank you very much for citing the Bethe reference. I do not have any convenient access to a technical library. However, the research librarian at our town library does a very good job in tracking down copies of technical articles for me, although it can take several weeks to do so.

I did a search on "extraordinary optical transmission", and I found several articles that seemed not too difficult for me to understand. From these discussions I was unable to find anything directly related to the problem I asked about.

Regards,
Buzz

 

[davenn]

i Dave:

I did a search on "Faraday shields" and found many links (including Wikipedia) for that phrase as well as for Faraday cages. I did a quick look at about a dozen of them, and none of these links dealt with the question I asked in my post.

You don't understand faraday shields then, as your first statement in the OP describes such a shield ...

Assume a source of EM radiation at wave length λ hits a barrier with a small circular hole of diameter d << λ. What fraction of the radiated power (watts) that hits the hole passes through it?

actually, it does, and is very relevant in day to day technology, eg a microwave oven
I'm sure you have seen and used one of those ?
It has a Faraday shield on the door, full of holes that you can see through but the RF energy cannot escape from.

These shields/cages are intended for an entirely different purpose (protecting electronics from EM pulses) than the one I am exploring. I am also thinking of a solid flat barrier (rather than a space bounded by some form of chain linked fence material) with a single circular hole.

these shields DONT have a singular hole ... again, refer to the shield on a uWave oven

have a read of this page ...

https://forum.allaboutcircuits.com/threads/holes-in-a-faraday-cage.69512/

and this page ...

https://physics.stackexchange.com/q...araday-cage-mesh-size-and-attenuation-of-celland if neither of those 2 pages define what you are wanting. Then it is time you much more clearly stated what you are wantingDave

 

[vsv86]

Hi vsv:

Thank you very much for citing the Bethe reference. I do not have any convenient access to a technical library. However, the research librarian at our town library does a very good job in tracking down copies of technical articles for me, although it can take several weeks to do so.

I did a search on "extraordinary optical transmission", and I found several articles that seemed not too difficult for me to understand. From these discussions I was unable to find anything directly related to the problem I asked about.

Regards,
Buzz

I am slightly new to contributing on this forum, so I may have misunderstood the situation. The article I gave you is available from Phys. Rev. website, but is only available you have the subscription. I get mine via the university.

If you do not have a subscription, you may find the paper in the library, but it becomes a long process which is the opposite of what I aimed to help you with. Another place where diffraction by a small hole is discussed is in "Classical Electrodynamics" by J.D. Jackson (Sec. 10.9 in the 3rd ed). This book may seem difficult, but this is only because it contains a lot and does a proper job of explaining it. I can suggest some other books on electrodynamics, but if you do not have access to a technical library it may be best to stick to the most popular ones, and Jackson is certainly that (at the university level).

Now regarding the extraordinary transmission. This is new-ish development in the problem of transmission through a small hole. Bethe established the first rigorous treatment of passing electromagnetic plane waves through a small aperture (other weaker treatments existed before), and for a while this remained the orthodoxy. Then Ebbesen noted that the amount of light transmitted by small holes in metallic screens was much larger then predicted by Bethe. Hence the "extraordinary". The reason for the discrepancy was that Bethe treated holes in a perfectly conducting sheet, whilst Ebbesen worked with noble metals at optical frequencies, where metals show plasmonic response. I thought it may be a good idea to get this on your radar, but basically Bethe's treatment (also done in Jackson) should be the first port of call.

Would it be useful to change your initial question for another one, for example the following one?

Let us suppose that initially there are no photons, neither on one side of the pierced barrier or on the other. Can you calculate the probability of finding photons on the other side of the pierced barrier, when photons appear on the first side?

I would argue that this is a very bad idea. Photons are not "balls of light". They are excitations of the quantum electromagnetic field. In essence, photons are Maxwell's Equations + a lot of other tricky effects which are hard to derive on paper, and hard to observe in experiment. My advice is to stick to Maxwell's Equations, it will give you the correct result. Only go to quantum picture if you have nonclassical light, or single quantum emitters etc., and if you are not talking about quantum fields then forget photons.

 

[davenn]

I would argue that this is a very bad idea. Photons are not "balls of light". They are excitations of the quantum electromagnetic field. In essence, photons are Maxwell's Equations + a lot of other tricky effects which are hard to derive on paper, and hard to observe in experiment. My advice is to stick to Maxwell's Equations, it will give you the correct result. Only go to quantum picture if you have nonclassical light, or single quantum emitters etc., and if you are not talking about quantum fields then forget photons.

totally agree and stick to a standard ( classical) EM wave theory

and BTW, welcome to PF

Dave

 

[anorlunda]

This thread was moved to Electrical Engineering. But I'm not sure that you will get betters answers here. I think the answers you alread got are as good as we can do with the information you gave.

Is the context of your question engineering design? or theoretical physics? or something else?

 

[slow]

Hi Slow:
Would you please explain why you think it makes the problem more understandable?

Regarding the proposal to modify the question, vsv86 explains, in the #9 post, the following.

I would argue that this is a very bad idea.

Reading that full post we learn something useful. Best regards.

 

[Tom.G]

What fraction of the radiated power (watts) that hits the hole passes through it?

These are for RF.
For a quick & easy explanation: https://www.electronic.nu/en/2015/10/13/the-ten-commandments-for-emc-part-4-2/
A more detailed explanation: https://evaluationengineering.com/features/0101emc.htm

Above found with: https://www.google.com/search?&q=rf+leakage+through+hole
Which has over 1 800 000 hits.

 

[Buzz Bloom]

Is the context of your question engineering design? or theoretical physics? or something else?

Hi anorlunda:

Thanks for your post. I am not sure if my explaining the motivation behind my question will be helpful to responders or just adding confusion. That is why I tried to phrase the question to be independent of my motivation.

The origin of the topic is the thread

https://www.physicsforums.com/threads/is-there-a-plan-for-a-search-for-nearby-black-holes.940652/​

which led me to a discussion about Hawking radiation.

https://www.physicsforums.com/threads/questions-regarding-hawking-radiation.898762/
https://www.physicsforums.com/threads/qs-re-hawking-radiation-part-ii.873353/​

I have been trying to fills some holes in my knowledge so I can complete a rough conceptual design for a probe to orbit a black hole and detect Hawking radiation (HR) in spite of the CMB noise. The present probe idea I am investigating (as a hobby - not as a professional) involves a ellipsoidal cavity with one end truncated with a circular disk passing through a focus point of the ellipsoid. A hole in the disk at the center would let some of the HR would pass through the hole into the cavity, and it would be reflected by the ellipsoidal walls to the other focus where a monopole antenna would detect the HR. The design depends on a reasonable fraction of the HR hitting the disk from the outside will pass through the hole into the cavity. The assumption is that practicality requires that the semi-major axis of the ellipsoid (and the smaller hole in the disk) be much smaller than the peak HR wavelength.

Regards,
Buzz

 

[The Electrician]

Assume a source of EM radiation at wave length λ hits a barrier with a small circular hole of diameter d << λ. What fraction of the radiated power (watts) that hits the hole passes through it? Does it depend on the thickness of the barrier?

I understand that after passing through the hole, the radiation diffracts almost uniformly over the entire
2 π rad² solid angle. For example, if d/λ = 1/30, the power at 90^o is 99.3% of the power at 0^o.

I have made an effort to find a source for this information on the Internet, but I have not had any success. If someone can cite a useful reference, I would much appreciate it.

See: https://en.wikipedia.org/wiki/Evanescent_field

There is a short discussion of propagation of EM fields in a waveguide. If the guide is much smaller than the wavelength there is no propagation as a wave, but the fields as you move along the guide decrease exponentially.

If your hole was in a very thick conductor, the hole would be like a waveguide under cutoff frequency. The thicker the barrier the more the fields would have attenuated before they reach the other end of the hole. The fact that the hole comes to an end (the other side of the barrier) changes the boundary conditions and there would be some radiation of what's left of the (otherwise evanescent) exponentially attenuated fields. Somebody has probably worked out the actual numbers, but I don't have a ready reference.

 

[anorlunda]

The origin of the topic is the thread
https://www.physicsforums.com/threads/is-there-a-plan-for-a-search-for-nearby-black-holes.940652/which led me to a discussion about Hawking radiation.

That clarifies. I'm moving it again from Electrical Engineering to General Physics.

 

[Buzz Bloom]

With respect to the ellipsoidal cavity I described in post #14, further reading of the cited references (except for the ones I have not been able to obtain yet: Bethe and Jackson) tells me that these references are mostly about advising engineers how to create shields to protect electronic devices. For example:

https://www.electronic.nu/en/2015/10/13/the-ten-commandments-for-emc-part-4-2/
Openings should not exceed 1/200 of the wavelength of actual frequency, which gives theoretically 40 dB attenuation.​

The problem I am trying to study involves a hole large enough to let a substantial fraction of the outside radiation hitting the hole to get inside. The particular peak wave length I am dealing with (for Hawking radiation from a 5 solar mass black hole) is 235 km. 1/200 of that would be a hole of about 1.2 km. I understand that 40 dB means that only about 1/10,000 of the outside power gets inside. This is not enough to be useful. However, if the area of the hole is relevant to how much power gets through the hole, then a 12 km hole would admit about 1% of the power and a 36 km hole would admit about 10%. However, I as of yet I have no way of confirming that this calculation (or any other) would give me a correct value for the fraction of power admitted through a hole of a given size.

Also, the reference is talking about multiple holes, but does not say how many. Another reference

https://evaluationengineering.com/features/0101emc.htm​

gives a formula related to number of holes.

A(dB) = -10 log₁₀ n​

As you can see, this is not useful for n=1. (I assume A(dB) is the attenuation in dBs. If it means attenuation with respect to a baseline for n=1, it might be useful if I had a formula for n=1, or a formula for a specified value for n.)

 

[davenn]

Openings should not exceed 1/200 of the wavelength of actual frequency, which gives theoretically 40 dB attenuation.The problem I am trying to study involves a hole large enough to let a substantial fraction of the outside radiation hitting the hole to get inside. The particular peak wave length I am dealing with (for Hawking radiation from a 5 solar mass black hole) is 235 km. 1/200 of that would be a hole of about 1.2 km. I understand that 40 dB means that only about 1/10,000 of the outside power gets inside. This is not enough to be useful. However, if the area of the hole is relevant to how much power gets through the hole, then a 12 km hole would admit about 1% of the power and a 36 km hole would admit about 10%. However, I as of yet I have no way of confirming that this calculation (or any other) would give me a correct value for the fraction of power admitted through a hole of a given size.

so why are you even trying to stop HR radiation from entering the detector ?
let in as much as possible ... your only physical constraint is trying to build something of the needed size

 

[Buzz Bloom]

so why are you even trying to stop HR radiation from entering the detector ?

Hi Dave:

In the PF discussions I have had about HR, it has been argued that the CMB would have so much more power than the HR that it would be impossible to detect the HR. In a PF discussion about the Holmdel telescope which made the first discovery of the CMB, I learned about how the horn blocked most noise sources, and how a sufficiently small portion of the the ambient 290 K temperature which heated the horn would reach the focus of the parabolic reflector where a monopole antenna picked us almost all of the CMB radiation that entered the horn's cavity. I have adapted that idea to the geometry of the ellipsoidal device. The HR problem is made more complicated because of the extremely long wavelength of the radiation. In this case, there needs to be an opening for the HR to enter the cavity while preventing most of the CMB from doing so. The intent it to stop almost all of the CMB from entering the cavity, but to allow enough HR to enter so that the electronics of tuned filter attached to the monopole antenna will output an acceptable signal to noise ratio.

I have not yet done the math, but my guess is that it will also be necessary to cool the entire ellipsoidal shell to a much lower temperature than the CMB 2.7 K. The needs of the Holmdel had to deal only with a temperature ratio of 290 K to 2.7 K, that is about a 100 ratio. The HR temperature is about 10^-8 K. The temperature ratio to manage is therefore about 30,000,000.

Regards,
Buzz

 

[davenn]

In the PF discussions I have had about HR, it has been argued that the CMB would have so much more power than the HR that it would be impossible to detect the HR.

irrelevant ... they are totally different frequencies/wavelengths and because the CMB is really REALLY high freq
any aperture you have to stop the CMB is NOT going to let any HR come through at all

The HR problem is made more complicated because of the extremely long wavelength of the radiation. In this case, there needs to be an opening for the HR to enter the cavity while preventing most of the CMB from doing so. The intent it to stop almost all of the CMB from entering the cavity, but to allow enough HR to enter so that the electronics of tuned filter attached to the monopole antenna will output an acceptable signal to noise ratio.

as I just stated above, that isn't going to happen ... ANY aperture to let a significant ( useful ) amount of HR through is going to let EVERY other frequency through
so you are not going to achieve your objectives that way

by design (physics) apertures/iris's are high pass filters

Unfortunately, as with your other threads (several of which have been closed), you don't understand the physics of what you are wanting to achieve

Dave

 

[davenn]

That clarifies. I'm moving it again from Electrical Engineering to General Physics.

This is still a radio/RF subject

 

[Buzz Bloom]

Unfortunately, as with your other threads (several of which have been closed), you don't understand the physics of what you are wanting to achieve

HI Dave:

I am sorry you feel that way. I have not, nor do I intend to in this thread describe in full detail all aspects of my idea for this HR detection device. That was not, and is not the purpose of this thread. I get a unpleasant feeling that you want me to tell you as much as I can about the idea just so you can tell me I am too ignorant to think about it properly. Even if that is the case, it is completely irrelevant to my OP.

By the way, I do understand that the design needs an additional barrier to prevent the CMB from having access to the hole, but I intentionally did not want this thread to become a discussion about the details of the design. The necessary size of the hole to achieve an acceptable signal to noise ratio will influence the design of this additional barrier, as well as other aspects of the design.

Regards,
Buzz

 

[anorlunda]

I think this thread has gone as far as possible to answer the OP's question. Now it is becoming heated.

Thread closed.