# Analytic solution for these two antennas

I am trying to solve the following two antenna.

Perhaps they have already solved in some textbooks. Could anyone advice me where can I find them?

Baluncore
Perhaps they have already solved in some textbooks.
https://en.wikipedia.org/wiki/Loop_antenna
They are both loop antennas, one has a feedline. It will depend on the frequency of operation ?
They are very small antennas so maybe they are smaller than a wavelength ? Terrahertz, infra red ?
I assume they are fed at either the gap or at the end of the transmission line section ?
Are they operated in free space or are they metal antennas on a dialectric substrate with a ground plane ?
The sectional size of the material will be important, as will the length and impedance of the parallel wire transmission line in wavelengths.
For long wavelengths they will have far field dipole patterns and a low input impedance.
What solutions do you require for what frequency ?

https://en.wikipedia.org/wiki/Loop_antenna
They are both loop antennas, one has a feedline. It will depend on the frequency of operation ?
They are very small antennas so maybe they are smaller than a wavelength ? Terrahertz, infra red ?
I assume they are fed at either the gap or at the end of the transmission line section ?
Are they operated in free space or are they metal antennas on a dialectric substrate with a ground plane ?
The sectional size of the material will be important, as will the length and impedance of the parallel wire transmission line in wavelengths.
For long wavelengths they will have far field dipole patterns and a low input impedance.
What solutions do you require for what frequency ?

I am a physicist with basic training from Jackson's book on "classical electrodynamics" (no further on antenna)
I only got this fantasy a fey days ago.
The wavelength of operation should be around 800 nm to 900nm (which corresponds to arround 300-400THz?)
Will the feedline of a loop-antenna change the characters of a loop-antenna?
It will function as a receiver (but normal antenna should be the same whether they are receiver or transmitter.)
Therefore, receiving at the gap or at the end of the feedline.
For the first step, I am only looking for whether can I solve it, therefore for simplicity only consider in vacuum, copper or some good conductor.
Maybe, later I can consider it in water etc.
I think an analytic solution should be possible since in Jackson's book there is a solution for a center-feed linear antenna.
I only changed it into polar-coordinate, for the first picture without feedline.
For the antenna with feedline, I am not sure whether it can be solved analytically or not?
Perhaps, with some superposition methods?

Baluncore
For the first step, I am only looking for whether can I solve it, therefore for simplicity only consider in vacuum, copper or some good conductor.
Solve it for what ? Impedance or pattern, electric or magnetic, near or far field ?
Both will be dependent on environment and construction.
There are simple analytic solutions for small isolated loops in most books on antenna theory.
Find a copy of "Antennas" by John D. Kraus. See chapter 6.

I am trying to get a copy of that book. But the internet version is very poor quality.
I want to solve Firstly, electric and magnetic field other quantities should follow.
I think far field is more interesting for me, since I am considering a receiver.
I saw in the poor version I got there is indeed solution for loop antenna.
For my wave length and antenna diameter it should be the "small-loop" case.

The wavelength of operation should be around 800 nm to 900nm (which corresponds to arround 300-400THz?)

How are you going to drive this antenna at 300THz? How are you going to physically construct it with dimensions in nm?"

How are you going to drive this antenna at 300THz? How are you going to physically construct it with dimensions in nm?"

That is not a problem. Nowadays, there are nano-fabrication....
afterall I am a physicist who made only fantasy instead of an engineer....

a question: is there anyway that I can made the antenna received more than emit?
(Normally the receiving power is the same as emitting power....)

That is not a problem. Nowadays, there are nano-fabrication....
Can you provide a reference for a method of driving an antenna at 300THz?
afterall I am a physicist who made only fantasy instead of an engineer....

a question: is there anyway that I can made the antenna received more than emit?
(Normally the receiving power is the same as emitting power....)

If you give us some idea what you are trying to do we can do a better job of helping.

Baluncore
The wavelength of operation should be around 800 nm to 900nm (which corresponds to arround 300-400THz?)
I cannot see how you can possibly use transmission line coupling at those wavelengths without suffering tremendous losses.
At those wavelengths I think you would do better using a near-infrared photodiode as a detector.
I also think you would need to use an optical system. We really have no idea what you are contemplating here.

a question: is there anyway that I can made the antenna received more than emit?
(Normally the receiving power is the same as emitting power....)
The Reciprocity Principle says the transmit and receive patterns are the same.
You should not be considering "power" so much as "gain" relative to a dipole or an isotropic radiator, dBi.

Impedance matching is essential if energy is to be absorbed, rather than be reflected by the antenna.
You need to read up on anti-reflection coatings and quarter-wave matching transformers.

tech99
Gold Member
I am trying to solve the following two antenna.View attachment 101721 View attachment 101722
Perhaps they have already solved in some textbooks. Could anyone advice me where can I find them?View attachment 101721 View attachment 101722
Sorry I cannot provide the solutions you ask for but I can offer practical knowledge.The first antenna is the same as used by Heinrich Hertz when he first demonstrated radio waves. So it has been around a while. In both cases, the resonant wavelength is approximately twice the lengthy of conductor (actually a little longer, especially in case 2). In some cases for antenna 2, the end stubs are placed closely together, and may then have a loading effect, lowering the frequency, more than would be expected from their length.
The effect of the feeder depends on how you wish to couple it. This is a problem because the impedance across the open end is very high, much more than any transmission line. Hertz was not concerned about this because he was looking for a high voltage across the open ends.
Methods of effecting a match to a typical line include breaking the antenna conductor in the middle and making a connection there, or using a small coupling loop. The radiation pattern for all these antennas when mounted in a vertical plane is figure eight shaped in the horizontal plane and roughly circular in the vertical plane. The polarisation is essentially vertical.
It is commonly found that the pattern is distorted due to feeder radiation, and may be asymmetrical.
The gain of the antenna is basically that of a dipole, but due to the small size, we must expect a few decibels of ohmic loss.

Can you provide a reference for a method of driving an antenna at 300THz?

If you give us some idea what you are trying to do we can do a better job of helping.

Yes, I indeed hope some expert in antenna can joint me for this project.
However, there seems to have no way to send a private message to you?
Could you contact me at qnachhilfe at gmail

I cannot see how you can possibly use transmission line coupling at those wavelengths without suffering tremendous losses.
At those wavelengths I think you would do better using a near-infrared photodiode as a detector.
I also think you would need to use an optical system. We really have no idea what you are contemplating here.

The Reciprocity Principle says the transmit and receive patterns are the same.
You should not be considering "power" so much as "gain" relative to a dipole or an isotropic radiator, dBi.

Impedance matching is essential if energy is to be absorbed, rather than be reflected by the antenna.
You need to read up on anti-reflection coatings and quarter-wave matching transformers.

I am not sure about loss at this stage. Yes, you are right, it is optical system.
EM wave at wave lenght of 800nm is called light.

I am not sure about impedance matching and anti-reflection coating....but recent there is a paper to make it
asymmetry......http://www.pnas.org/content/113/13/3471

Sorry I cannot provide the solutions you ask for but I can offer practical knowledge.The first antenna is the same as used by Heinrich Hertz when he first demonstrated radio waves. So it has been around a while. In both cases, the resonant wavelength is approximately twice the lengthy of conductor (actually a little longer, especially in case 2). In some cases for antenna 2, the end stubs are placed closely together, and may then have a loading effect, lowering the frequency, more than would be expected from their length.
The effect of the feeder depends on how you wish to couple it. This is a problem because the impedance across the open end is very high, much more than any transmission line. Hertz was not concerned about this because he was looking for a high voltage across the open ends.
Methods of effecting a match to a typical line include breaking the antenna conductor in the middle and making a connection there, or using a small coupling loop. The radiation pattern for all these antennas when mounted in a vertical plane is figure eight shaped in the horizontal plane and roughly circular in the vertical plane. The polarisation is essentially vertical.
It is commonly found that the pattern is distorted due to feeder radiation, and may be asymmetrical.
The gain of the antenna is basically that of a dipole, but due to the small size, we must expect a few decibels of ohmic loss.

1. I indeed check the book of Kraus and Wiki. In my case it is the small-loop antenna. What you mentioned "the wave length is approximately twice the length of conductor" is the resonance-loop antenna.
2 The idea of "breaking the antenna" seems particular interesting for me........I am indeed considering breaking it....But it should come at later stage....
3. I checked Hertz's experiments. However, he did not seems to use a ring-shape. Although it is equivalent to a ring and many later people draw it as a ring.

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Baluncore
I am not sure about impedance matching and anti-reflection coating....but recent there is a paper to make it asymmetry....
You are entering the world of “phase conjugate mirrors” which theoretically leads to “invisibility”.
https://en.wikipedia.org/wiki/Nonlinear_optics#Optical_phase_conjugation
Unfortunately the invisibility is only possible over the narrow bandwidth of the wavelength-selective surface-structure.

In the real macro world phase coherency is lost rapidly so invisibility comes down to matching the albedo and surface temperature of the hopefully invisible item with it's environment.

A plane array of the loop antenna dipoles such as you are considering has no axial radiation perpendicular with the plane of the loops. The loops must be “edge on” to the line of sight which requires fabricating loops on edge. Then comes the problem of polarisation. You will need crossed loops for circular polarisation.

I think rather than analysing the receive and transmit antenna modes you should be considering scattering from wavelength selective surfaces. I doubt that fabrication of those surfaces from arrays of macro antenna elements will achieve as good a result as adjustable surface films.

tech99
Gold Member
Thank you for that insight.

Let's come back to my fantasy idea:
What I am considering is photosynthesis light-harvesting system. I am trying to understand it from antenna theory.

Thank you for that insight.

Baluncore
Methods of effecting a match to a typical line include breaking the antenna conductor in the middle and making a connection there, or using a small coupling loop.
The radiation from an antenna is due to the magnetic field produced by the currents flowing in the antenna. So, how can you get current into a loop or a dipole? You must break the antenna element and insert an oscillator, transformer or feedline connection that can deliver the signal current into the element.

The radiation from an antenna is due to the magnetic field produced by the currents flowing in the antenna. So, how can you get current into a loop or a dipole? You must break the antenna element and insert an oscillator, transformer or feedline connection that can deliver the signal current into the element.

Yes, my picture showing that I had a notch. I thought you were saying to break into more pieces, i.e. 8 segments or so.

However, it mentioned laser is a kind of optical antenna, which I do not agree
since laser is only a source of light but an antenna, I would say, is more than simply a source.
It can has various shape of radiation pattern.
I am not sure whether does other people agree with me or not?

tech99
Gold Member
The radiation from an antenna is due to the magnetic field produced by the currents flowing in the antenna.
Unsure about the statement. I think the underlying cause is the acceleration of charges. This causes ripples in their static electric field, and as the ripples pass an observer, the fluctuating electric field will, according to Maxwell, cause a magnetic field to be observed.
Of course, to accelerate the charges in the first place requires a powerful electric field, and this might be regarded as the electric induction field, coming from the energy supplied by the generator. Any comments very much requested please.

tech99
Gold Member
The radiation from an antenna is due to the magnetic field produced by the currents flowing in the antenna.
Apologies, messed up my quotation, think this is correct.
I think the underlying cause is the acceleration of charges. This causes ripples in their static electric field, and as the ripples pass an observer, the fluctuating electric field will, according to Maxwell, cause a magnetic field to be observed.
Of course, to accelerate the charges in the first place requires a powerful electric field, and this might be regarded as the electric induction field, coming from the energy supplied by the generator. Any comments very much requested please.

Baluncore
The complete radiated field pattern can be established if the current in the small loop is known.
The voltage that drives the current is irrelevant. There is no need to make it more complex or to look any deeper.

tech99
Gold Member
The complete radiated field pattern can be established if the current in the small loop is known.
The voltage that drives the current is irrelevant. There is no need to make it more complex or to look any deeper.
I agree with the statement as a means of calculating radiation, but I am wanting to look more deeply into the phenomenon. My feeling is that current is a symptom of radiation, not a cause. When the charges are accelerated, the velocity they acquire is, of course, related to the acceleration and time, but I cannot see a mechanism for the initial radiation of a wave to come from the magnetic field. It seems to have to originate with the acceleration of charges and their electric field, as proposed by J J Thompson. I have not seen a diagram showing how a magnetic field might radiate.
Further than this, if we look at a receiving antenna and consider reciprocity, I cannot see that an incoming magnetic wave will cause the charges in the antenna to move. They will only move in response to the electric wave.

Baluncore