You can do the inverse Fourier transform of the far-field to get the near-field, and there are other methods too - (perhaps maximum likelihood or minimum entropy?).  If you have enough signal-to-noise ratio and dynamic range then you can measure the evanescent waves too - they don't vanish at long range but get very small quickly, then at sufficient range result in propagating waves.  However, usually far-field to near-field reconstructions don't include evanescent modes so lack fine detail.  This is because the signal-to-noise ratios and dynamic ranges required are totally unrealistic in most cases, and the reconstruction mathematics is ill-posed - like finding the difference between two very large signals with noise on them!

SAR and ISAR are microwave (and  mm and RF) technologies that use far-field to near-field transform to generate images using measured far-field phase and amplitude - the maths is the same in optics.  You can also transform between intermediate ranges, it doesn't need to be complete near-field to far-field.

The summary of your comment is that Evanescent waves are there in a range but in a very weak value. If we can measure their quantum photon status then we can retrieve the near field information?? It depends on how fine reconstruction we have done right??

I think so.

Waves (as described by spherical harmonics) that are evanescent at a small radius can propagate at a larger radius, so are not evanescent in the far-field, just small.  The higher the order of harmonic, the further out they have to travel before they can propagate, and the more they fall off with radius while evanescent.

Simulations of double-negative lenses that are probably available on the net show that evanescent waves can be back-calculated to give high-resolution images, because this is what the simulation code does when it simulates the lens.

Thanks, Malcolm, Can you provide references where people imaged this near field signal in the far field region by inverse scattering calculation using the far field microscopy?

I thought I would just to add some other related points to your conversation.

Yes, all the information of the near fields is in the far field. One can think of it like this: If I have all the field values in a big sphere enclosing the radiating object, I can reverse propagate them using the Green's tensor and get as close as I want to the object, as long as no other sources are in the way. A related reference that I like is this one: http://aip.scitation.org/doi/abs/10.1063/1.1666629, which also contains the related idea that the outgoing multipolar fields always have evanescent plane wave components.

A different question is what is the accuracy with which you need to know the far field so that the error that you make in the calculation of the near fields is acceptable, which connects with the discussion that you guys have had.

Cheers

Ivan

Thank you very much dear Ivan Fernandez-Corbaton for your answer. Actually, the situation is that I have a system which employs an inverse scattering fitting method. I performed some measurement with that system using a nanoparticle of size 950 nm of a dielectric material/semiconductor material. (n=3.11,k=.24). The distributions which I get is amazing and I verified them via FDTD. So which proved that our system can detect the near field signals. Now I want to describe its Physics. and someone makes a question that the near field signal only can be measured by Scanning near field microscopy and your microscopy is just a far field. I want to explore it physically.

Some stuff here I found on the net in 5 minutes and can't vouch for, but I am afraid you will have to search for more and evaluate it yourself.

https://workspace.imperial.ac.uk/nde/Public/M_Fleming%20THESIS-Final-copy.pdf

http://www.math.hkbu.edu.hk/~yuliang/publication/prism_positive.pdf

Dear Kaleem,

I think the case you can make is not that you can detect the near field signal, but rather that you can detect the far field signal with enough signal to noise ratio and resolution so that the near field can be reconstructed with good accuracy by your fitting algoritm.

Besides the back-propagating Green's tensor argument, the article from Devaney and Wolf that I pointed you to has relevant arguments to build your case on physical grounds. In the abstract  you can read

"It is shown further that the electromagnetic field at all points outside a sphere that contains the charge-current distribution is completely specified by the radiation pattern (i.e., by the field in the far zone). Explicit formulas are obtained for all the multipole moments in terms of the radiation pattern."

which clearly addresses your needs, I believe.

Cheers

Ivan

Kaleem,

I am making a photoacoustic device that theoretically, should be able to measure the evanescent field distribution interacting with an optically absorbing material. This might be easier than trying to reconstruct it using the far field information. (Or alternatively you could use the system to verify your reconstruction, etc.)

Thank you very much dear Ivan Fernandez-Corbaton, Benjamin Samuel Goldschmidt, and Malcolm White.

So, Dear Ivan, You mean that my near field simulation results match with my experimental results because of the detection of the far field signal with a good signal to noise ratio and reconstruction algorithm give me the near field result with good accuracy? The reason can be stated like this because while detecting far field signal with a great signal to noise ratio, there are near field information in a weak value in those far field signals which retrieve in our reconstruction algorithm that is why our system gives us near field signal with a good accuracy? Also can you please tell me the title of that article so that I can cite that article in my reply ??

Dear Kaleem,

I cannot comment on the particular results that you are getting. But, if your fitting algorithm has the knowledge of the size and material of the particle, I see no problem in recovering the fields inside it as well.

Cheers

Ivan

That looks like a standard single resonant mode pattern, if you are just displaying positive and negative.

@Ivan Fernandez-Corbaton, It is inner side of the particle or on the surface of the particle or both are same. Our fitting algorithm uses the experimental data which means both info is there. 

https://www.osapublishing.org/oe/abstract.cfm?uri=oe-22-17-20446 

@Malcom,  I verified it through FDTD simulation get the same result. 

Hello Kaleem

Recently we have published article seems closely related to this subject:

https://doi.org/10.1364/OL.42.002263

Regards

It seems to me there is no evidence of evanescent modes in the picture.  The field pattern inside the circle is for one mode, which I don't think is evanescent. It does not show any detail of structure within the circle.  If there were evanescent modes outside the circle then I would have expected to see some ripple somewhere.  What does the picture display?  Is is just red = positive signal, blue = negative signal, white = small signal?  Do you have a contour plot showing amplitude with more than three colours?

It is drawn by me, it is not the actual result. The field distribution is given by the conventional field microscopy just represents the isotropic distribution and this distribution has been verified by FDTD near field simulation. Similar field distribution has been displayed by ASNOM in the following paper:

http://pubs.acs.org/doi/abs/10.1021/ph500232u

Thanks, Malcolm, I also measured the ripples around the nanoparticle. My point is that if the near field information in there in the far field, as because these values are so small so should we apply here quantum approach to retrieve the near field signals?

I did not find any experimental work which experimentally claim that they detected the near field signals with a far field optical microscopy or with inverse scattering method. If you have in your mind can you please share here??